WATER POWER ENGINEERING 
 
 THE THEORY, INVESTIGATION AND DEVELOPMENT 
 OF WATER POWERS. 
 
 BY 
 
 DANIEL W. MEAD. 
 
 Member American Society Civil Enginet 
 
 Consulting Engineer 
 
 Professor of Hydraulic and Sanitary Engineering 
 University of Wisconsin 
 
 NEW YORK 
 
 McGRAw PUBLISHING Co. 
 1908 
 

 GENERAL 
 
 Copyrighted 1907-1908 
 
 BY 
 
 DANIEL W. MEAD 
 
 STATE JOURNAL PRINTING COMPANY 
 MADISON, WISCONSIN 
 
 A 
 
PREFACE 
 
 In the development of a water power project the engineer is fre- 
 qently called upon to do more than design and construct the power 
 plant. He may be required to report on the adequacy of the supply, 
 the head and power available and the probable variations in the 
 same, the plan for development, the cost of construction and opera- 
 tion, and the advisability of the investment. A study of the entire 
 project, therefore, becomes essential, and each factor must be care- 
 fully considered in detail to assure ultimate success. Each of the 
 features of the development is of equal importance to the commer- 
 cial success of the project. The majority of the failures in water 
 power development have occurred from causes other than structural 
 defects, and a knowledge of these other important and controlling- 
 factors is therefore quite as essential as a knowledge of design and 
 construction. It must be said, however, that in respect to some of 
 these controlling factors current practice has not been what it should 
 be. This has resulted in many over-developments and illy advised 
 installations, from which the power generated has not been equal 
 to tfiat anticipated, and in many poor financial investments amount- 
 ing frequently to practical failures. The engineer has given much 
 attention to design and construction but too little attention to the 
 other fundamental considerations mentioned above on which the 
 success of the project depends to an equal extent. 
 
 In the preparation of this book the author has endeavored to con- 
 sider, briefly at least, all fundamental principles and to point out the 
 basis on which successful water power development depends. The 
 method of study and investigation outlined herein was developed by 
 the author during twenty-five years of professional practice and in 
 his efforts to illustrate the principles underlying the subject in his 
 lectures to the senior class in water power engineering at the Uni- 
 versity of Wisconsin. A somewhat extended acquaintance with the 
 literature relating to water power engineering leads the author to 
 believe that in a number of features the principles and methods de- 
 scribed in this book are somewhat in advance of present practice. 
 
vi Preface. 
 
 In current practice, the hydraulic engineer, to determine the ex- 
 tent of a proposed hydraulic development, commonly depends on a 
 study of the monthly averages of stream flow and of observed maxi- 
 mum and minimum flows. He usually assumes from his previous 
 knowledge and study that the development should be based on a 
 certain minimum or average stream discharge per square mile of 
 drainage area. The value of this method depends on the breadth of 
 the engineer's local knowledge of rainfall and run-off relations. 
 With a sufficient knowledge of these conditions, this method may 
 form a safe basis for water power development but it fails to give 
 the complete information which is essential for a full comprehension 
 of the subject. In other cases the development is predicted on a 
 single, or on a very few, measurements of what is believed, or as- 
 sumed to be, the low water flow of the stream. This method, even 
 when accompanied by careful study of rainfall records, is a danger- 
 ous one to employ as many over-developed water power projects 
 demonstrate. Neither of these 'methods compares favorably with 
 the more exact method of studying flow by actual or comparative 
 hydrographs as is described in Chaps. IV, V, VIII and IX. 
 
 In current practice the head available is usually determined for 
 average conditions, or, perhaps, occasionally for low, average and 
 high water conditions, and no detailed study of the daily effect on 
 power is attempted. In Chaps. IV and V this subject is presented 
 in detail and a method of the investigation of this important subject, 
 under all conditions of flow and all conditions of use, is outlined. 
 
 On the basis of the knowledge gained from the study of flow and 
 head, the study of the power that can be developed for each day in 
 the year and during each year for which actual or comparative hy- 
 drographs are available, is outlined. An outline of a method for 
 the consideration of possible variations in flow during periods for 
 which no measurements are available based on the available rain- 
 fall records, is also given in Chaps. VI, VII and VIII. A study of 
 the effect of pondage on power, a most important matter, though 
 not always carefully considered, or appreciated, is also discussed in 
 considerable detail in Chaps. IV, V and XXVI. 
 
 In the selection of turbines for a water power project, the current 
 practice has been for the engineer, while drawing certain conclu- 
 sions from the tables of manufacturers' catalogues, to present to the 
 manufacturer the conditions under which the power is to be devel- 
 oped and to rely largely or entirely on the manufacturer for advice 
 
Preface. vii 
 
 as to machinery to be used. In such cases he is dependent for re- 
 sults on guarantees which are usually quite indefinite in character 
 and seldom verified by actual tests, under working conditions, be- 
 fore the wheels are accepted and paid for. This has resulted in 
 many cases in the installation of wheels which are entirely unsuited 
 to the particular conditions under which they are installed. 
 
 Practical turbine analysis has not been treated except in the most 
 general way in any publications except the various German treatises 
 on the turbine in which the subject is discussed from the basis of 
 turbine design. The author has developed the method of turbine 
 analysis and selection, outlined in Chapters XIV and XVI, 
 which applies to all wheels when tests of wheels of the series or 
 class considered are available. These methods are based on the 
 practical operating conditions of actual tests and are both theoreti- 
 cally and practically correct. The engineer should be able to intel- 
 ligently select the turbines needed for the particular conditions of his 
 installation and to determine, with a considerable degree of accuracy, 
 the results on which he can depend during all conditions of head 
 and flow. 
 
 It is believed that this treatment of the subject is sufficiently 
 complete to place the selection of turbines on a better footing and 
 that, when adopted, it will lead to the selection of better and more 
 improved designs and assure more satisfactory results. 
 
 The subject of turbine governing has, for electrical reasons, be- 
 come an important one. While a number of important papers have 
 appeared on this subject, there is, so far as the author knows, no 
 discussion in English which offers the engineer a basis for a com- 
 plete consideration of this subject. Chap. XVIII, on the principles 
 of turbine governing together with appendixes A, B and C, offer, 
 it is believed, suggestions for the consideration of this subject which 
 may prove of value to water power engineers. 
 
 The report on a water power project should involve a careful 
 and complete investigation of the entire subject, and should be 
 based on the broadest considerations of the project in all its rela- 
 tions. Many reports which have come to the author's attention 
 have been too limited in scope and have included only general opin- 
 ions which have not, to his mind, been sufficiently specific or based 
 on sufficient information to warrant approval without extended in- 
 vestigations. In Chap. XXVIII the author has outlined his idea 
 
viii Preface. 
 
 of the extent and scope of such investigation and report, which he 
 believes is essential for an intelligent investigation and a reliable 
 opinion on this subject. 
 
 ACKNOWLEDGMENTS. 
 
 There can be little which is strictly new or original in any technical 
 work, and in offering this book to the profession, the author wishes to 
 acknowledge his indebtedness to the large number of technical ar- 
 ticles that have already appeared on various phases of the subject. 
 Many references to such literature have been given at the end of the 
 various chapters. 
 
 Many illustrations have been taken, with more or less change 
 from Engineering News, Engineering Record, Cassier's Magazine 
 and Electrical World and Engineer. Various manufacturers have 
 furnished photographs and, in some cases, cuts of their wheels, gov- 
 ernors and apparatus, in connection with which their names appear. 
 
 The author has been greatly aided by his assistants, both of his 
 own private office and of the University staff. He wishes especially 
 to acknowledge the assistance of Mr. L. F. Harza to whom 
 Chap. XVIII on The Speed Regulation of Turbine Water Wheels 
 and appendixes A, B and C are largely due. Mr. Harza has also 
 been of much assistance in the editorial work of publication. Es- 
 pecial acknowledgment is also due to Professor G. J. Davis, Jr., 
 for the preparation of the diagrams of friction of water in pipes and 
 of Bazin's and Kutter's coefficients, etc. Mr. Robert Ewald assisted 
 in the selection of material for illustrations, in the investigation of 
 German literature, and the preparation of various graphical diagrams, 
 including the first development of the characteristic curve. 
 
 The author also desires to acknowledge his indebtedness to his 
 principal assistant, Mr. C. V. Seastone, for advice and assistance in 
 the arrangement of many of the chapters in this work and assist- 
 ance in the editorial work of publication. 
 
 The sources of various other tables, illustrations, etc., are ac- 
 knowledged in their proper places. D. W. M. 
 
 Madison, Oct. i, 1908. 
 
CONTENTS 
 
 CHAPTER I. 
 INTRODUCTION. 
 
 The History of Water Power Development Every Development of 
 Water Power The Earliest Type of Water Wheel The Undershot 
 Wheel The Overshot and Breast Water Wheel The Development 
 of the Turbine Fundamental Ideas of the Turbine The Modern 
 Turbine. The American or Francis Turbine Modern Changes in 
 Turbine Practice Historical Notes on Water Power Development 
 Development of Water Power in the United States Literature 1 
 
 CHAPTER II. 
 
 POWEB. 
 
 The Development of Potential Energy Definition of Energy Solar 
 Energy the Ultimate Source No Waste of Energy in Nature Laws 
 of Energy Conservation Efficiency Natural Limit to Efficiency < 
 Practical Limits to Efficiency Efficiency of a Combined Plant 
 Capacity of Each Part of a System not Identical The Analysis of 
 Losses The Losses in a Hydro-Electric Plant Units of Energy- 
 Conversion of Energy Units Kinetic Energy Uniform Motion 
 Uniform Varied Motion Compound Motion, Graphical Representa- 
 tion of the Laws of Motion Transformation Literature 19 
 
 CHAPTER III. 
 HYDRAULICS. 
 
 IBasis of Hydraulics Mathematical Expression for Energy Velocity 
 Head. Entrance Head Submerged Orifices Friction Head Kut- 
 ter's Formula Bazin's Formula Efficiency of Section Determina- 
 tion of Canal Cross-Section The Back Water Curve Flow of 
 Water in Pipes The Flow of Water Through Orifices Flow over 
 Weirs Literature 40 
 
 CHAPTER IV. 
 WATER POWEK. 
 
 The Study of the Power of a Stream as Affected by FlowSource of 
 Water Power Factors of Stream Flow Broad Knowledge of 
 
Contents. 
 
 Stream Flow Necessary The Hydrograph The Use of Local 
 Hydrographs Use of Comparative Hydrographs Reliability of 
 Comparative Hydrographs When no Hydrographs are Available 
 The Hydrograph as a Power Curve 79 
 
 CHAPTER V. 
 WATER POWER (Continued) 
 
 The Study of the Power of a Stream as Affected by Head Variations 
 in Head The Rating or Discharge Curve The Tail Water Curve 
 The Head Water Curve Graphic Representation of Head Effects 
 of Design of Dam on Head Effect of Head on the Power of the 
 Plant Graphical Representation of the Relations of Power, Head 
 and Flow Graphical Study of Power at Kilbourn Power of the 
 Kilbourn Wheels Under Variations in Flow Effects of Low Water 
 Flow Effects of Number of Wheels on Head and Power. . . 93 
 
 CHAPTER VI. 
 RAINFALL. 
 
 Importance of Rainfall Study Distribution of Rainfall The Rainfall 
 Must be Studied in Detail Local Variation in Annual Rainfall. 
 Local Variations in Periodical Distribution of Annual Rainfall 
 Accuracy of Rainfall Maps and Records Rainfall and Altitude 
 Value of Extended Rainfall Records Accuracy in Rainfall, Obser- 
 vation, District Rainfall Study of Rainfall as Affecting Run-off 
 Literature.. Ill 
 
 CHAPTER VII. 
 THE DISPOSAL OF THE RAINFALL. 
 
 Factors of Disposal The Rate or Intensity of Rainfall Condition of 
 Receiving Surfaces and Geological Strata Effects of Wind Effects 
 of Vegetation Percolation Evaporation Evaporation Relations 
 Practical Consideration of Losses Literature 133: 
 
 CHAPTER VIII. 
 RUN-OFF. 
 
 Run-off Influence of Various Factors Relations of Annual Rainfall 
 and Run-off of W r ater Year Relation of Periodic Rainfall to Run- 
 off Monthly Relation of Rainfall and Run-off Maximum Stream 
 Flow Estimate of Stream Flow 146 
 
Contents. 
 
 A.1 
 
 CHAPTER IX. 
 RUN-OFF (Continued) 
 
 Relation of Run-off to Topographical Conditions Effects of Geological 
 Condition on the Run-off The Influence of Storage on the Distri- 
 bution of Run-offEffects of Area on the Run-off The Study of a 
 Stream from Its Hydrographs Comparative Runoff and Compara- 
 tive Hydrographs Comparative Hydrographs from Different 
 Hydrological Divisions of the United States, Literature. . 175 
 
 CHAPTER X. 
 STREAM FLOW. 
 
 Flow in Open Channels Changes in Value of Factors with Changes 
 in Flow Effects of Variable Flow on the Hydraulic Gradient- 
 Effects of a Rising or a Falling Stream on Gradient Effects of 
 Channel Condition on Gradient Effect of Change in Grade and of 
 Obstructions Relation of Gauge Heights to Flow Variations in 
 Velocity in the Cross-Section of a Stream Effects of Ice-Covering 
 on the Distribution of Velocities 
 
 CHAPTER XI. 
 THE MEASUREMENT OF STREAM FLOW. 
 
 Necessity for Stream Flow Measurements Methods for the Estimate 
 or Determination of Flow in Open Channels Estimates from 
 Cross-Section and Slope Weir Measurement Measurement of 
 Flow by the Determination of Velocity The Use of the Current 
 Meter Current Meter Observatons and Computation- Float 
 Measurements The Application of Stream Gaugings Literature. 218 
 
 CHAPTER XII. 
 WATER WHEELS. 
 
 Classification of Water Wheels Gravity Wheels Reaction Wheels 
 Impulse Wheels Use of Water Wheels Classification of Tur- 
 bines Conditions of Operation Relative Advantage of Reaction 
 and Impulse Turbines Relative Turbine Efficiencies Turbine De- 
 velopment in the United States The American Fourneyron Tur- 
 bine The American Jonval Turbine The American Type of Re- 
 action Turbine The Double Leffel Turbine Other American 
 Wheels Early Development of Impulse Wheels American Im- 
 pulse Wheels Turbine Development in Europe 237 
 
xii Contents. 
 
 CHAPTER XIII. 
 TURBINE DETAILS AND APPURTENANCES. 
 
 The Runner Its Material and Manufacture Diameter of the Run- 
 ner The Details of the Runner Vertical Turbine Bearings, Hori- 
 zontal Turbine Bearings Thrust Bearing in Snoqualmie Falls 
 Turbine The Chute Case Turbine Gates The Draft Tube 284 
 
 CHAPTER XIV. 
 HYDRAULICS OF THE TURBINE, 
 
 Practical Hydraulics of the Turbine Nomenclature Used in Chapter 
 First Principles impulse and Reaction The impulse Wheel 
 Effect of Angle of Discharge on Efficiency Reaction Wheel 
 Graphical Relation of Energy and Velocity in Reaction Turbine- 
 Turbine Relations Relation of Turbine Speed to Diameter and 
 Head Graphical Expression of Speed Relations Relations of q> 
 and Efficiency Discharge of Turbine at Fixed Gate Opening, 
 Power of a Turbine The Relation of Discharge to the Diameter of 
 a Turbine The Relation of Power to the Diameter of a Turbine 
 Relation of Speed to Discharge of Turbines, Relations of Speed to 
 Power of Turbines Value of Turbine Constants Literature.... 309 
 
 CHAPTER XV. 
 TURBINE TESTING. 
 
 The Importance of Testing Machinery The Testing of Water Wheels 
 Smeaton's Experiments The Early Testing of Turbine Water 
 Wheels The Testing of Turbines by James Emerson The Holyoke 
 Testing Flume The Value of Tests Purpose of Turbine Testing 
 Factors that Influence the Results of a Test Measurement of Dis- 
 charge Measurement of Head Measurement of Speed of Rota- 
 tion Measurement of Power Efficiency Illustration of Methods 
 and Apparatus for Testing Water Wheels Tests of Wheels in 
 Place Literature 355 
 
 CHAPTER XVI. 
 THE SELECTION OF THE TURBINE. 
 
 Effect of Condtions of Operation Basis for the Selection of the Tur- 
 bine Selection of the Turbine for Uniform Head and Power The 
 Selection of a Turbine for a Given Speed and Power to Work under 
 a Given Fixed Head To Estimate the Operating Results of a Tur- 
 bine under one Head from Test Results Secured at Another Head 
 To Estimate the Operating Results of a Turbine of one Diameter 
 from Test Results of Another Diameter of the Same Series To 
 Estimate the Operating Results of a Turbine under Variable 
 
Contents. xiii 
 
 Heads from a Test Made under a Fixed Head A More Exact 
 Graphical Method for Calculation- The Construction of the Char- 
 acteristic Curves of a Turbine The Consideration of the Turbine 
 from its Characteristic Curve Other Characteristic Curves 
 Graphical Analysis as Proposed by Mr. W A. Waters 384 
 
 CHAPTER XVII. 
 
 THE LOAD CURVE AND LOAD FACTORS, AND THEIR INFLUENCE ON THE DESIGN OF 
 
 THE POWER PLANT. 
 
 Variation in Load Load Curves of Light and Power Plants. Factory 
 Load Curves Load Curve of London Hydraulic Supply Company 
 Railway Load Curves Load Conditions for Maximum Returns. The 
 Load Curve in Relation to Machine Selection Influence of Manage- 
 ment on Load Curve Relation of Load Curve to Stream Flow and 
 Auxiliary Power Literature 420 
 
 CHAPTER XVIII. 
 THE SPEED REGULATION OF TURBINE WATER WHEELS. 
 
 The Relation of Resistance and Speed Self-Regulation in a Plant with 
 Variable Speed and Resistance The Relations Necessary for Con- 
 stant Speed The Ideal Governor Present Status Value of Uni- 
 form Speed The Problem Energy Required to Change the Pen- 
 stock Velocity Hunting or Racing Nomenclature Shock of 
 Water Hammer Due to Sudden Changes in Velocity Permissible 
 Rates of Gate Movement Regulation of Impulse Wheels Influences 
 Opposing Speed Regulation, Change of Penstock Velocity Effect 
 of Slow Acceleration on Water Supplied to Wheel Value of Racing 
 or Gate Over-Run Energy Required to Change the Penstock Velo- 
 city Effect of Sensitiveness and Rapidity of Governor The Fly- 
 Wheel The Stand-Pipe The Air Chamber Predetermination of 
 Speed Regulation for Wheel set in open Penstocks Predetermina- 
 tion of Speed Regulation, Plant with Closed Penstock, Predeter- 
 mination of Speed Regulation, Plant with Standpipe Application 
 of Method, Closed Penstock Application of Method, Open Penstock 
 Application of Method, Plant with Standpipe Literature 440 
 
 CHAPTER XIX. 
 THE WATER WHEEL GOVERNOR. 
 
 Types of Water Wheel Governors Simple Mechanical Governors Anti- 
 racing Mechanical Governors Details and Applications of Wood- 
 ward Governors The Lombard-Replogle Mechanical Governors 
 Essential Features of an Hydraulic Governor Details of Lombard 
 Hydraulic Governor Operating Results with Lombard Governor 
 The Sturgess Hydraulic Governor Test Results with Sturgess Gov- 
 
xiv Contents. 
 
 ernor Control from Switchboard Connection of Governors to 
 Gates Relief Valves Lombard Hydraulic Relief Valves Sturgess 
 Relief Valves 470 
 
 CHAPTER XX. 
 ARRANGEMENT OF THE REACTION WIIKKL. 
 
 General Conditions Necessary Submergence of Reaction Wheels Ar- 
 rangement of Vertical Shaft Turbine Arrangement of Horizontal 
 Turbine?, Classification of Wheels Vertical Wheels and Their Con- 
 nection Some Installations of Vertical Water Wheels Some In- 
 stallations of Vertical Wheels in Series Some Installations of 
 Horizontal Water Wheels Some Installations of Multiple Tandem 
 Horizontal Wheels Unbalanced Wheels . 500 
 
 CHAPTER XXL 
 THE SELECTION OF MACHINERY AND DESIGN OF PLANT. 
 
 Plant Capacity Influence of Choice of Machinery on Total Capacity 
 Effect of Size of Units on Cost Overload Economy in Operation 
 Possibilities in Prime Movers Capacity of Prime Movers The In- 
 stallation of Tandem Water Wheels Power Connection Various 
 Methods of Connection in Use Use of Shafting The Wheel Pit 
 Turbine Support Trash Racks 525 
 
 CHAPTER XXII. 
 EXAMPLES OF WATER POWER PLANTS. 
 
 Sterling Plant, Plant of York-Haven Water Power Company Plant of 
 South Bend Electric Company Spier Falls Plant of the Hudson 
 River Power Transmission Company Plant of Columbus Power 
 Company Plant of the Dolgeville Electric Light and Power Co. 
 Plant of the Shawinigan Water and Power Company Plant of the 
 Concord Electric Company Plant of Winnipeg Electric Railway 
 Co. Plant of Nevada Power, Mining, and Milling Co. Literature. . 537 
 
 CHAPTER XXIII. 
 THE RELATION OF DAM AND POWER STATION. 
 
 General Consideration Classification of Types of Development Con- 
 Centrated Fall Examples of the Distribution of Water at Various 
 Plants Head Races only Plants Located in Dam High Head De- 
 velopments 561 
 
Contents. xv 
 
 CHAPTER XXIV. 
 PRINCIPLES OF CONSTRUCTION OF DAMS. 
 
 Object of Construction Dams for Water Power Purposes Height of 
 Dam Available Head The Principles of Construction of Dams 
 The Foundations of Dams Strength of Dams Flood Flows. Im- 
 pervious Construction, The Stability of Masonry Dams Calcula- 
 tions for Stability Further Considerations Types and Details of 
 Dams Literature 579 
 
 CHAPTER XXV. 
 APPENDAGES TO DAMS. 
 
 Movable Dams Flood Gates Flash Boards Head Gates and Gate 
 
 Hoists Fish ways Logways Literature 603 
 
 CHAPTER XXVI. 
 PONDAGE AND STORAGE. 
 
 Effect of Pondage on Power Effect of Limited Pondage on the Power 
 Curve Power Hydrograph at Sterling, Illinois Effect of Pondage 
 on other Powers Effect of Limited Storage Effect of Large Stor- 
 age Effect of Auxiliary Power Effect of Maximum Storage Cal- 
 culation for Storage Method of Storage Calculation Analytical 
 Method Literature 624 
 
 CHAPTER XXVI T. 
 COST, VALUE AND SALE OF POWER. 
 
 Financial Consideration Purpose of Development Cost of Water Pow- 
 er Depreciation Annual Cost of Developed Power Cost of Distri- 
 bution Effect of Partial Loads on Cost of Power Cost of Auxil- 
 iary Power or Power Generated from other than Water Power 
 Sources Market Price of Water Power Sale of Power An Equi- 
 table Basis for the Sale of Power Value of Improvements Intended 
 to Effect Economy Value of a Water Power Property Literature. G46 
 
 CHAPTER XXVIII. 
 THE INVESTIGATION OF WATER POWER PROJECTS. 
 
 The Extent of the Investigation Preliminary Investigation and Re- 
 portStudy of Run-off Study of Rainfall Study of Topographi- 
 cal and Geological Conditions Study of Flood-flow Study of 
 Back Water Curve Study of Head Study of Storage and Pond- 
 ageStudy of Probable Load Curve Study of Power Development 
 Study of Auxiliary Power Study of Site of Dam and Power Sta- 
 tion Study of Plant Desigrv The Estimate of Cost The Report. . 675 
 
xvi Contents. 
 
 APPENDICES. 
 
 A. Water Hammer B. Speed Regulation, a more Detailed Analysis 
 than in Chapter XVIII C. The Stand-Pipe D. Test Data of Turbine 
 Water Wheels E. Effect of an Umbrella upon Formation of Vor- 
 tices F. Evaporation Tables G. Two New Water Wheel Governors 
 H. Miscellaneous Tables Including: Equivalent Measures and 
 Weights of Water Equivalent Units of Energy Velocities in Feet 
 per Second Due to Heads from to 50 Feet Three Halves Powers 
 of Numbers, to 100 Five Halves Powers of Numbers, to 50 Re- 
 lation of mean Rainfall to Maximum and Minimum Discharge 
 of Various Rivers Rainfall, Run-off and Evaporation for Storage, 
 Growing and Replenishing Periods or 12 Streams of the United 
 States.. ..685-75T 
 
WATER POWER ENGINEERING. 
 
 CHAPTER I. 
 
 INTRODUCTION. 
 
 THE HISTORY OF WATER POWER DEVELOPMENT. 
 
 1. Early Development of Water Power. Most methods of 
 power generation can be traced to an origin at no very remote 
 period. Their development has been within historic times. The 
 first development of water power, however, antedates history. 
 Its origin is lost in remote antiquity. 
 
 Air and water, both physical agents most essential to life, have 
 ever been the most obvious sources of potential energy and have 
 each been utilized for power purposes since the earliest times. 
 Beside the Nile, the Euphrates, and the Yellow Rivers, thou- 
 sands of years ago the primitive hydraulic engineer planned and 
 constructed his simple forms of current wheels and utilized the 
 energy of the river current to raise its waters and irrigate the 
 otherwise arid wastes into fertility. Such primitive wheels were 
 also utilized for the grinding of corn and other simple power 
 purposes. From these simple forms and primitive applications 
 have gradually been developed the modern water power installa- 
 tions of to-day. 
 
 2. The Earliest Type of Water Wheel. The crude float wheel 
 driven directly by the river current developed but a small por- 
 tion of the energy of the passing stream. The Chinese Nora, 
 built of bamboo with woven paddles, is still in use in the east 
 (see Fig. i), and was probably the early form of development of 
 this type of wheel. The type is by no means obsolete for it is 
 yet used for minor irrigation purposes in all countries. These 
 wheels, while inefficient, served their purpose and were exten- 
 sively developed and widely utilized. One of the greatest de- 
 velopments of which there is record was the float wheel installa- 
 
Introduction. 
 
 Fig. 1. Chinese Nora or Float Wheel Used From Earliest Times to 
 
 Present. 
 
 tion used to operate the pumps at London Bridge for the first 
 water supply system of the city of London, and constructed 
 about 1581 (see Fig. 2). In all such wheels the paddles dip into 
 the unconfined current which, when impeded by the wheel, heads 
 up and passes around the sides of the wheel and thus allows 
 only a small part of the current energy to be utilized. 
 
 3. The Undershot Wheel. The introduction of a channel con- 
 fining the water and conducting it to a point where it could be 
 applied directly to the undershot wheel, was an improvement that 
 permitted the utilization of about thirty per cent, of the theo- 
 
 Fig. 2. Float Wheel Operating Pumps for Water Supply of London 1581. 
 (From Matthews' Hydraulia Lond. 1835.) 
 
The Overshot and Breast Water Wheel. 3 
 
 retical power of the water. This form of water wheel was most 
 widely used for power development until the latter half of the 
 eighteenth century. 
 
 In the float and undershot wheels the energy of water is ex- 
 erted through the impact due to its velocity. The heading up 
 of the water, caused by the interference of the wheel, results 
 also in the exertion of pressure due to the weight of the water, 
 but this action has only a minor effect. The conditions of the 
 application of the energy of water through its momentum is not 
 favorable to the high efficiency of this type of wheels and the 
 determination of this fact by Smeaton's experiments undoubt- 
 edly was an important factor in the introduction and adoption of 
 the overshot water wheel. 
 
 Fig. 3. Breast Wheel Used From About 1780 to About 1870. 
 
 4. The Overshot and Breast Water Wheel. In the overshot 
 water wheel the energy of water is applied directly through its 
 weight by the action of gravity, to which application the design 
 of the wheel is readily adapted. Such wheels when well con- 
 structed have given efficiencies practically equal to the best 
 modern turbine, but on account of their large size and the serious 
 effects of back-water and ice conditions, they are unsatisfactory 
 for modern power plants (see Fig. u). 
 
 Following the work of Smeaton, the breast wheel (see Fig. 3) 
 was developed in England largely through the work of Fairbairn 
 and Rennie. The latter in 1784 erected a large wheel of this 
 type to which he applied the sliding gate from which the water 
 flowed upon the wheel instead of issuing through a sluice as 
 formerly. About this time the fly-ball governor, which had been 
 designed and adapted as a governor for steam engines by Watt, 
 was applied to the governing of these wheels and by means of 
 these governors the speed of the wheel under varying loads was 
 
Introduction. 
 
 Fig. 4. Breast Wheel About 1790 Showing Early Application of Governor. 
 
 (After Glynn.) 
 
 kept sufficiently constant for the purpose to which they were 
 then applied. (See Fig. 4.) 
 
 Another mode of applying water to wheels under low falls was 
 introduced by M. Poncelet. (See Fig. 5.) Various changes and 
 improvements in the form of buckets, in their ventilation so as 
 to permit of complete filling and prompt emptying, and in their 
 structure, took place from time to time, and until far into the 
 middle of the nineteenth century these forms of wheels were 
 widely used for water power purposes. 
 
 Fig. 5. Poncelet's Wheel. 
 
 5. The Development of the Turbine. The invention of any 
 important machine or device is rarely the work of a single mind. 
 In general such inventions are the result of years of experience 
 of many men which may be simply correlated by some designer,. 
 
Fundamental Idea of the Turbine. 5 
 
 to whom often undue credit is given. To the man who has 
 gathered together past experiences and embodied them in a new 
 and useful invention and perhaps through whose energy practical 
 applications are made of such inventions, the credit is frequently 
 assigned for ideas which have been lying dormant, perhaps 
 through centuries of time. Every inventor or promotor of val- 
 uable improvements in old methods and old construction is en- 
 titled to due credit, but the fact should nevertheless be recalled 
 that even in the greatest inventions very few radical changes are 
 embodied, but old ideas are utilized and rearranged and a new 
 and frequently much more satisfactory combination results. Im- 
 provements in old ideas are the improvements which are the 
 most substantial. Inventions which are radically new and strictly 
 original are apt to be faulty and of little practical value. 
 
 Fig. 6. Ancient Indian Water Wheel. (After Glynn.) Containing Fun- 
 damental Suggestion of Both Turbine and Impulse Wheels. 
 
 6. Fundamental Ideas of the Turbine. The embryo turbine 
 may be distinguished in the ancient Indian water mill (see Fig. 6). 
 A similar early type of vertical wheel used in Europe in the six- 
 teenth century, the illustration of which was taken from aft an- 
 cient print (see Sci. Am. Sup. Feb. 17, '06) is shown m Fig. 7. 
 Barker's mill in its original form or in the form improved by 
 M. Mathon de Cour, embodied the principal idea of the pressure 
 
6 Introduction. 
 
 turbine, and was used to a considerable extent for mill purposes, 
 In 1845 James Whitlaw suggested an improved form which was 
 used in both England and Germany early in the nineteenth cen- 
 tury. (See Fig. 8.) Many elements of the modern turbine were 
 conceived by Benjamin Tyler, who received letters patent for 
 what he termed the "Wry Fly" wheel in 1804. The description of 
 this wheel as contained in the patent specifications is as follows : 
 
 Fig. 7. Early Vertical Wheel. Containing fundamental suggestion of the 
 
 Turbine. 
 
 'The Wry Fly is a wheel which, built upon the lower end of a 
 perpendicular shaft in a circular form, resembles that of a tub. 
 It is made fast by the insertion of two or more short cones, 
 which, passing through the shaft, extend to the outer side of the 
 wheel. The outside of the wheel is made of plank, jointed and 
 fitted to each other, dow r eled at top and bottom, and hooped by 
 three bands of iron, so as to make it water-tight; the top must 
 be about one-fifth part larger than the bottom in order to drive 
 
Barker's Mill. 
 
 the hoops, but this proportion may be varied, or even reversed, 
 according to the situation of place, proportion of the wheel, and 
 quantity of water. The buckets are made of winding timber, and 
 placed inside of the wheel, made fast by strong wooden pins 
 drove in an oblique direction ; they are fitted to the inside of the 
 tub or wheel, in such a manner as to form an acute angle from 
 the wheel, the inner edge of the bucket inclining towards the 
 water, which is poured upon the top, or upper end of it about 
 twelve and a half degrees ; instead of their standing perpendicular 
 with the shaft of the wheel they are placed in the form of a 
 screw, the lower ends inclining towards the water, and against 
 the course of the stream, after the rate of forty-five degrees ; this, 
 however, may be likewise varied, according to the circumstances 
 of the place, quantity of water, and size of the wheel." 
 
 Elevation. 
 
 Plan and Partial Section. 
 
 Pig. 7. Early Vertical Wheel. Containing Fundamental Suggestion of the' T 
 
 (After Glynn.) 
 
Introduction, 
 
 Fig. 9. Roue A' Curves (After Glynn). 
 
 From the description it will be noted that, with the exception 
 of the chutes, the principal features of the modern turbine were 
 here anticipated. The "Wry Fly" wheel was an improvement on 
 the "tub" wheel which was then in use to a considerable extent 
 in the country. 
 
 These various early efforts received their first practical con- 
 summation and modern solution through various French in- 
 ventors early in the nineteenth century. The "Roue a dives'* 
 (Fig. 9) and the "Roue Volant" (Fig. 10) had long been used 
 in France, and were the subject of extensive tests by MM. Pio- 
 bert and Tardy at Toulouse. Those various wheels received the 
 water tangentially through an opening or spout, being practically 
 an improvement on the old Indian mill by the addition of a rim 
 and the modification of the form of buckets. 
 
 7. The Modern Turbine. The next improvement in the United 
 States consisted in the addition of a spiral or scroll case to the 
 wheel, by means of which the water was applied equally to all 
 parts of the circumference passing inward and downward through 
 the wheel. To the. French inventors, Koechlin, Fourneyron and 
 Jonval, is largely due the design of the turbine in a more modern 
 and practical form. By the middle of the nineteenth century 
 these wheels had met with wide application in France and been 
 
The Modern Turbine, 
 
 Fig. 10. Roue Volant (After Glynn). 
 
 adopted and considerably improved by American and German 
 engineers, but were scarcely known in England. (See "Power 
 of Water," by Jos. Glynn, 1852.) The turbine was introduced 
 into the United States about 1843 by El wood Morris, of Penn- 
 sylvania, but was developed and brought to public attention more 
 largely through the inventions of Uriah A. Boyden, who in 1844 
 designed a seventy-five horse-power turbine for use at Lowell, 
 Mass. (See Fig. , page .) The great advantage of the tur- 
 bine over the old style water wheel may be summarized as fol- 
 lowvS: (See Figs, n and 12.) 
 
 I^irst : Turbines occupy a much smaller space. 
 
 Second: On account of their comparatively high speed they 
 can frequently be used for power purposes without gearing and 
 with a consequent saving in power. 
 
 Third : They will work submerged. 
 
 Fourth : They may be utilized under any head or fall of water. 
 (Turbines are in use under heads as low as sixteen inches and 
 as high a? several hundred feet.) 
 
 Fifth : Their efficiency, when the wheel is properly constructed, 
 is comparatively high. 
 
 Sixth : They permit a greater variation in velocity without ma- 
 terial change in efficiency. 
 
IO 
 
 Introduction. 
 
 ,0 
 5_ 
 
 & 
 
 o ? 
 
 I 
 ? a 
 5 
 
 
 I 
 
 g 
 
 r-4 O 
 
 II 
 
 * I 
 8 
 
 S s 
 
 a 
 
 1 6 
 
 73 
 
 
 S 
 
 tn 
 
 a 
 
The Francis Turbine. 
 
 ir 
 
 Seventh : They are more readily protected from ice interfer- 
 ence. 
 
 8. The American or Francis Turbine. Through the efforts of 
 Uriah A. Boyden and James B. Francis (1849), the Fourneyron 
 turbine became the leading wheel in New England for many 
 years. 
 
 In 1838 Samuel B. Howd of Geneva, New York, patented the 
 '''inward flow" wheel, in, which the action of the Fourneyron tur- 
 bine was reversed. This seems to have been the origin of the 
 American type of turbine, and the Howd wheel was followed by 
 a large number of variations of the same general design on 
 which American practice has been based for many years. About 
 ^849, James B. Francis designed an inward flow turbine of the 
 same general type as the Howd wheel. Two of these wheels 
 
 / c 
 
 Fig. 13. Inward Flow Wheel by S. B. Howd (After Francis). 
 
 were constructed by the Lowell Machine Shop for the Boott 
 Cotton Mills. In the Lowell hydraulic experiments (page 61) 
 Mr. Francis refers to the previous patent of Howd and says: 
 "Under this patent a large number of wheels have been con- 
 structed and a great many of them are now running in different 
 
;i2 Introduction. 
 
 parts of the country. They are known in some places as the 
 Howd wheel, in others as the United States wheel. They have 
 uniformly been constructed in a very simple and cheap manner 
 in order to meet the demands of the numerous classes of millers 
 and manufacturers who must have cheap wheels if they have 
 any." 
 
 Fig. 13 shows a plan and vertical section of the Howd wheels 
 as constructed by the owners of the patent rights for a portion 
 of the New England states. In this cut g indicates the wooden 
 
 Fig. 14. Original Francis Turbine. 
 
 guides by which the water is directed on to the buckets ; W in- 
 dicates the wheel which is composed of buckets of cast iron 
 fastened to the upper and lower crowns of the wheel by bolts. 
 The upright crown is connected with the vertical shaft S by arms. 
 The regulating gate is placed outside of the guides and is made 
 -of wood. The upright shaft S runs on a step at the bottom (not 
 shown in the cut). The projections on one side of the buckets, 
 it was claimed, increased the efficiency of the wheel by diminish- 
 ing the waste of the water. 
 
 The wheel designed by Francis was on more scientific lines, of 
 better mechanical construction (see Fig. 14) and is regarded by 
 
Modern Changes in Turbine Practice. 13 
 
 many as the origin of the American turbine. The credit of this 
 design is freely awarded to Francis by German engineers, this 
 type of wheel being known in Germany as the Francis Turbine. 
 The Francis wheel was followed by other inward flow wheels of 
 a more or less similar type. The Swain wheel was designed by 
 A. M. Swain in 1855. The American turbine of Stout, Mills and 
 Temple (1859), the Leffel wheel, designed by James Leffel in 
 1860, and the Hercules wheel, designed by John B. McCormick 
 in 1876, are among the best known and earliest of the wheels of 
 this class. 
 
 g. Modern Changes in Turbine Practice. A radical change has 
 taken place in later years in the design of turbines by the adop- 
 tion of deeper, wider and fewer buckets which has resulted in a 
 great increase of power as shown by the following table from a 
 paper by Samuel Webber (Transactions of Am. Soc. M. E. 
 Vol. XVII) : 
 
 TABLE I. Showing Size, Capacity and Power of Various Turbines Under 
 
 a 26-foot Head. 
 
 
 Inches 
 Diameter. 
 
 Cubic Feet 
 ' Water per 
 Second. 
 
 Horse 
 Power. 
 
 Boyden-Fourneyron 
 
 36 
 
 22.95 
 
 55 
 
 Ripdon 
 
 36 
 
 35.45 
 
 89 
 
 Risdon "L C." 
 
 36 
 
 48.27 
 
 121 
 
 Risdon "L 1) " 
 
 36 
 
 80. 
 
 199 
 
 Leffel, Standard 
 
 36 
 
 40.45 
 
 96 
 
 Leffel, Special 
 
 35 
 
 60. 
 
 148 
 
 Tyler 
 
 36 
 
 40.7 
 
 95.8 
 
 Swain 
 
 36 
 
 58.2 
 
 140 
 
 Hunt "Swain bucket" 
 
 36 
 
 48.8 
 
 121 
 
 Hunt New Style 
 
 36 
 
 98. 
 
 239.74 
 
 Leffel "Samson" 
 
 3,5 
 
 109.1 
 
 264 
 
 "Hercules" 
 
 36 
 
 107.6 
 
 253.5 
 
 "Victor" 
 
 25 
 
 108.8 
 
 266 
 
 New Swain 
 
 36 
 
 89.5 
 
 215 
 
 
 
 
 
 By 1870 the turbine had largely superseded the water wheel 
 for manufacturing purposes at the principal water power plants 
 in this country. The old time water wheel has since become of 
 comparatively small importance, but it is still used in many iso- 
 lated places where it is constructed by local talent, and adapted 
 to local conditions and necessities. 
 
14 Introduction. 
 
 The current wheel is still widely used for irrigation purposes 
 and in many instances is a useful and valuable machine. 
 
 10. Historical Notes on Water Power Development. Water 
 mills were introduced at Rome about seventy years B. C. (see 
 Strabo Lib. XII), and were first erected on the Tiber. Vitruvius 
 describes their construction as similar in principle to the Egyp- 
 tian Tympanum. To their circumference were fixed floats or 
 paddles which when acted upon by the current of the stream 
 drove the wheel around. Attached to this axis was another ver- 
 tical wheel provided with cogs or teeth. A large horizontal wheel 
 toothed to correspond with it worked on an axis, the upper head 
 of which was attached to the mill stone. The use of such water 
 wheels became very common in Italy and in other countries sub- 
 ject to Roman rule. 
 
 Some of the early applications of water power are of interest. 
 In 1581 a pump operated by a float wheel was established at 
 London Bridge to supply the city of London with water. In 
 1675 an elaborate pumping plant driven by water wheels was 
 established on the Seine river near Saint Germain. For this 
 plant a dam was constructed across the river and chutes were 
 arranged to conduct the water to the undershot water wheels. 
 These were twelve or more in number, each operating a pump 
 that raised the waters of the Seine into certain reservoirs and 
 aqueducts for distribution. 
 
 The pumping of water for agricultural irrigation and drainage, 
 domestic supplies and mine drainage, was undoubtedly the first 
 application of water power, and still constitutes an important 
 application of water. Fig. 15, from an article by W. F. Dupfee, 
 published in Cassier's Magazine of March, 1899, illustrates a 
 primitive application of the water wheel to the pumping of water 
 from mines. The frontispiece also shows the great Laxy over- 
 shot water wheel in the Isle of Man which is still used for mine 
 drainage. The wheel is about seventy feet in diameter and the 
 water is brought from the hills a considerable distance for power 
 purposes. 
 
 11. Development of Water Power in the United States. In 
 this country one of the first applications of water power was the 
 old tidal mill on Mill Creek near Boston, constructed in 1631, 
 which was followed by the extensive developments of small 
 powers wherever settlements were made and water power was 
 
Development of Water Power. 
 
 available. Often availability of water power determined the 
 location of the early settlement. 
 
 About 1725 the first power plant was established along the 
 Niagara River. This was a water-driven saw-mill constructed 
 
 Chronological Development of Water Power of the United States to 1898. 
 
 
 Year. 
 
 Fall 
 Ft. 
 
 Minimum 
 Horse 
 Power. 
 
 Drainage 
 Area Sq. 
 Miles. 
 
 Lowell Mass 
 
 1822 
 
 35 
 
 1 1 , 845 
 
 4 083 
 
 Nashua, N H 
 
 1823 
 
 36 
 
 1,200 
 
 516 
 
 Oohoes, N. Y 
 
 1826 
 
 104 
 
 9,450 
 
 3,490 
 
 Norwich, Conn 
 
 1828 
 
 16 
 
 700 
 
 1,240 
 
 Augusta. Me 
 
 1834 
 
 17 
 
 3,5(JO 
 
 5 907 
 
 Manchester N H 
 
 1835 
 
 52 
 
 12,000 
 
 2, 839 
 
 Hooksett N H 
 
 184L 
 
 14 
 
 1,8(0 
 
 2,791 
 
 Lawrence Mass 
 
 1845 
 
 30 
 
 11,000 
 
 4,625 
 
 A uo'usta Ga 
 
 1847 
 
 50 
 
 8,500 
 
 8,830 
 
 Holyoke, Mass .... 
 
 1848 
 
 50 
 
 14,000 
 
 8,000 
 
 Lewiston, Me 
 
 1849 
 
 50 
 
 11,900 
 
 3,200 
 
 Columbus, Ga 
 
 1850 
 
 25 
 
 10,000 
 
 14,900 
 
 Rochester, N. Y . 
 
 1856 
 
 236 
 
 8,000 
 
 2,474 
 
 St. Anthony Falls, Minn 
 
 1857 
 
 50 
 
 15,500 
 
 19,736 
 
 Niagara, N. Y. (Hy. canal) 
 Turner's Falls Conn 
 
 1861 
 1866 
 
 90 
 35 
 
 15,000 
 10,000 
 
 271,000 
 6,000 
 
 Fox River Wis 
 
 1866 
 
 185 
 
 
 6,449 
 
 Birmingham Conn 
 
 1870 
 
 22 
 
 1,000 
 
 2,000 
 
 Bangor, Me ... 
 
 1876 
 
 9 
 
 1,767 
 
 7,200 
 
 Augusta, Ga. . . . 
 
 1876 
 
 50 
 
 8,500 
 
 6,830 
 
 Palmer's Falls, N Y 
 
 1882 
 
 30 
 
 1,125 
 
 2,650 
 
 Mechanicsville, N Y 
 
 1882 
 
 20 
 
 3, 636 
 
 4,476 
 
 St. Cloud, Minn 
 
 1885 
 
 14 
 
 4,500 
 
 13,250 
 
 Little Falls, Minn 
 
 1887 
 
 14 
 
 4,000 
 
 11,084 
 
 Spokane \Vash 
 
 1888 
 
 70 
 
 18,000 
 
 4,180 
 
 Howland Me 
 
 1888 
 
 22 
 
 6,000 
 
 
 Great Falls, Mont 
 
 1890 
 
 42 
 
 16,000 
 
 22,000 
 
 Austin Texas 
 
 1891 
 
 ne 
 
 10,000 
 
 40, 000 
 
 Sault Ste Marie Out . 
 
 1891 
 
 18 
 
 10, 000 
 
 51,600 
 
 In'olsom Cal 
 
 1891 
 
 55 
 
 6,200 
 
 
 Concord, N H 
 
 1894 
 
 13 
 
 5,000 
 
 2,350 
 
 Niagara, N. Y. (tunnel) 
 O^den Utah 
 
 1894 
 1896 
 
 170 
 446 
 
 50, 000 
 2, U40 
 
 271,000 
 30 
 
 Helena Mont 
 
 ' 1897 
 
 32 
 
 10,000 
 
 14,900 
 
 Minneapolis Minn ... 
 
 1897 
 
 18 
 
 6,000 
 
 19,737 
 
 Mechanicsville NY 
 
 1898 
 
 18 
 
 3,270 
 
 4,478 
 
 
 
 
 
 
 by the French to furnish lumber for Fort Niagara. Mr. J. T. 
 Fanning gives the following list of the dates of establishing some 
 of the principal water powers of the United States : 
 
 The last few years have witnessed a still more rapid develop- 
 ment. The increase in manufacturing industries and other de- 
 
i6 
 
 Introduction 
 
 mands for power and energy, the increased cost of coal, and the 
 improvement in electrical methods of generation and transmis- 
 sion have all united to accelerate the development of water power 
 plants. Water powers once valueless on account of their dis- 
 tance from centers of manufacturing and population are now 
 accessible and such powers are rapidly being developed and their 
 energy brought into the market. 
 
 Fig. 15. Early Application of Undershot Water Wheel to Mine Drainage, 
 Date Unknown (from Cassiers Mag. March, 1899). 
 
 LITERATURE. 
 
 1. Appleton's Cyclopedia of Applied Mechanics. Modern Mechanis'm, Vol. 
 
 3, pp. 891-901. Description of the development of the turbine. 
 
 2. Spon's Dictionary of Engineering. Barker's Mill, pp. 230-235. 
 
 do. Float Water Wheels (including undershot wheels), pp. 1511-1524. 
 
 do. Overshot Water Wheels, p. 2557. 
 
 do. Poncelet's Water Wheels, p. 26GO. 
 
 do. Turbine Water Wheels, pp. 3014-3022. 
 
 3. Knight's Mechanical Dictionary, Vol. 3, Water Wheels, p. 2746; Tur 
 
 bines, pp. 2G5G-2G58. 
 
Literature. 17 
 
 4. Emerson, James. Hydrodynamics. Published by author. Willimansett, 
 
 Mass. 1892. Describes several types of American turbines. 
 
 5. Matthews, William. Hydraulia. London, 1835. (Description of London 
 
 Bridge Water Wheels, p. 28.) 
 
 6. Fairbairn, William. Machinery and Millwork. Description of undershot 
 
 water wheel, pp. 145-150; description of earlier types of tur- 
 bines, pp. 151-173. 
 
 7. Francis, James B. Lowell Hydraulic Experiments, pp. 1-70. Descrip- 
 
 tion and tests of Boyden-Fourneyron Tremond Turbines; also 
 the Boyden-Francis "Center-Vent" Turbine, in which the Flow 
 was Radially Inward. New York, D. Van Nostrand, 1883. 
 
 8. Weisbach, P. J. Mechanics of Engineering, vol. II. Hydraulics and 
 
 Hydraulic Motors 1 . Translated by A. J. DuBois. New York, 
 J. Wiley & Sons. 
 
 9. Morin, Arthur. Experiments on Water Wheels having a Vertical Axis, 
 
 Called Turbines, 1838. Translated by Ellwood Morris in Jour. 
 Franklin Inst, 3d ser., vol. 6, 1843, pp. 234-246, 289-302, 370-377. 
 370-377. 
 
 10. Morris, Ellwood. Remarks on Reaction Water Wheels Used in the 
 
 United States and on the Turbine of M. Fourneyron. Jour. 
 Franklin Inst, 3d ser., Vol. 4, 1842, pp. 219-227, 289-304. 
 
 11. Morris, Ellwood. Experiments on the Useful Effect of Turbines in the 
 
 United States. Jour. Franklin Inst, 3d ser., Vol. 6, 1843, 
 pp. 377-384. 
 
 12. Whitelaw, James. Observations of Mr. Ellwood Morris's Remarks on 
 
 Water Wheels. Jour. Franklin Inst, 3d ser., Vol. 8, 1844, 
 pp. 73-80. 
 
 13. Franklin Institute. The Koechlin Turbine. Jour. Franklin Inst, 3d 
 
 ser., Vol. 20, 1850, pp. 189-191. (Report of experiments made 
 by members of the institute at the request of Emile Geyelin, 
 who introduced the Koechlin turbine at Dupont's powder mill.) 
 
 14. Ewbank, Thos 1 . Hydraulic and Other Machines for Raising Water. New 
 
 York, 1847. 
 
 15. Geyelin, Emile. Experiments on Two Hydraulic Motors, Showing the 
 
 Comparative Power Between an Overshot Wheel and a Jonval 
 Turbine made for Troy, N. Y. Jour. Franklin Inst., 3d ser., 
 Vol. 22, 1851, pp. 418, 419. 
 
 16. Glynn, Joseph. Power of Water. London, 1850. pp. 39-97. Weales 
 
 Scientific Series. 
 
 17. Webber, Samuel. Ancient and Modern Water Wheels. Eng. Mag., Vol. 1, 
 
 1891, pp. 324-331. 
 
 18. Frizell, J. P. The Old-Time Water Wheels of America. Trans. Am. Soc. 
 
 C. E., Vol. 28, 1893, pp. 237-249. 
 
 19. Aldrich, H. L. Water Wheels. Description of Various Types of Ameri- 
 
 can Wheels. Power, Vol. 19, No. 11, 1894. 
 
 20. Francis, James. Water Power in New England. Eng. Rec., Vol. 33, 
 
 1896, pp. 418, 419. 
 2 
 
iS Introduction. 
 
 21. Geyelin, Emile. First Pair of Horizontal Turbines ever Built Working 
 
 on a Common Axis. Proc. Eng. Club, Philadelphia, Vol. 12, 
 
 1895, pp. 213, 214. 
 
 22. Francis, James. Water Power in New England. Eng. Rec. Vol. 33, 
 
 1896, pp. 418, 419. 
 
 23. Webber, Samuel. Water Power, its Generation and Transmission. Trans. 
 
 Am. Soc. Mech. Eng., Vol. 17, 189G, pp. 41-57. 
 
 24. Tyler, W. W. The Evolution of the American Type of Water Wheel. 
 
 Jour. West. Soc. Eng., Chicago, Vol. 3, 1898, pp. 879-901. 
 
 25. Johnson, W. C. Power Development at Niagara. Jour. Asso. Eng. Soc., 
 
 July, 1899, pp. 78-90. Hist, of early development of power at 
 Niagara. 
 
 26. Christie W. W. Some Old-Time Water Wheels. Description of Various 
 
 old wheels in Eastern U. S. Eng. News, Vol. 42, 1899, pp. 
 394-395. 
 
 27. Ruchel, E. Turbines at the World's Fair, Paris, 1900. Review of Tur- 
 
 bine development in various countries. Zeitschr. d ver Deutsch, 
 Ing. p. 657, 1900. 
 
 28. Foster, H. A. The Water Power at Holyoke. Jour. Asso. Eng. Soc., Vol. 
 
 25, 1900, pp. 67-84. 
 
 29. Thomas, R. Development of Turbine Construction. Zeitschr. d ver 
 
 Deutsch. Ing. p. 409, 1901. 
 
 30. Rice, A. C. Notes on the History of Turbine Development in America. 
 
 Eng. News, Vol. 48, 1902, pp. 208-209. 
 
 31. Fanning, J. T. History of the Development of American Water Powers. 
 
 Rept. 22d Ann. Meeting, Am. Paper and Pulp Asso., 1898, pp. 
 16-24. Progress 1 in Hydraulic Power Development. Eng. Rec- 
 ord, Vol. 47, 1903, pp. 24-25. 
 
 32. Fanning, J. T. Progress in Hydraulic Power Development. Eng. Rec- 
 
 ord, Jan. 3d, 1903. 
 
 33. Sickman, A. F. The Water Power at Holyoke. Jour. N. E. W. W. Asso., 
 
 Vol. 18, 1904, pp. 337-351. Historical. 
 
CHAPTER II. 
 
 POWER. 
 
 12. The Development of Potential Energy. The development 
 of natural sources of potential energy, the transformation of such 
 energy into forms which can be utilized for power, and its trans- 
 mission to points where it can be utilized for commercial pur- 
 poses, constitutes a large portion of the work of the engineer. 
 The water power engineer primarily deals with energy in the 
 form of flowing or falling water, but his knowledge must extend 
 much further for he encounters other forms of energy at every 
 turn. Much of the energy available from the potential source 
 will be lost by friction in bringing the water to and taking it 
 from the wheel. Much is lost in hydraulic and mechanical fric- 
 tion in the wheel ; additional losses are sustained in every trans- 
 formation, and, if electric or other forms -of transmission are 
 used or auxiliary power is necessary for maintaining continuous 
 operation, the engineer will be brought in contact with energy 
 in many other forms. 
 
 13. Definition of Energy. Energy is the active principle of 
 nature. It is the basis of all life, all action, and all physical 
 phenomena. It is the ability to exert force, to overcome resist- 
 ance, to do work. All physical and chemical phenomena are but 
 manifestations of energy transformations, and all nature would 
 be rendered inactive and inanimate without these changes. 
 
 14. Solar Energy the Ultimate Source. A brief consideration 
 of the various sources of potential energy makes the fact mani- 
 fest that solar energy is the ultimate source from which all other 
 forms are directly or indirectly derived. The variations in solar 
 heat on the earth's surface produces atmospheric currents often 
 of tremendous power. This form of energy may be utilized, in 
 its more moderate form, to drive the sailing vessel and the wind- 
 mill, and in other ways to be of service to man. The energy of 
 fuel is directly traceable to solar action. Through present and 
 past ages it has been the active cause of chemical and organic 
 
2O Power 
 
 change and growth. From this has resulted fuel supplies avail- 
 able in the original form of wood, or in the altered forms, from 
 ancient vegetation to the forms of coal, oil and gas, and from 
 which a large portion of the energy utilized commercially is 
 derived. 
 
 A brief study of meteorological conditions shows that through 
 the agency of solar heat, and the resulting atmospheric move- 
 ment, a constant circulation of water is produced on and near 
 the earth's surface. Hundreds of tons of water are daily evapor- 
 ated from the seas, lakes, rivers and moist land surface, rise as 
 vapor into the atmosphere, circulate with the winds, and, under 
 favorable conditions, are dropped again upon the earth's surface 
 in the rainfall. Those portions of the rain that fall upon the 
 land tend to flow toward the lower places in the earth's crust, 
 where lie the seas and oceans, and such portions of these waters 
 as are not absorbed by the strata, evaporated from the surface 
 or utilized in plant growth, ultimately find their way to these 
 bodies of water to again pass through this cycle of changes which 
 is' constantly in progress. Thus we find water always in motion, 
 and always an active agent in nature's processes. Due to its 
 peculiar physical properties and chemical relations, it is one of 
 the essential requisites of life, and is also of great importance in 
 nature's processes through the energy of which it is the vehicle. 
 
 15. No Waste of Energy in Nature. Active continuous en- 
 ergy transformation is a most important natural phenomenon. 
 Changes from one form to another are constantly in progress. 
 In nature's transformations energy is always fully utilized. As 
 the running stream plunges over the fall, the potential energy, 
 due to its superior elevation, is transformed into the kinetic en- 
 ergy of matter in motion, and through the shock or impact the 
 kinetic energy is transformed into thermal energy due to a higher 
 temperature, which again may be partially changed in form by 
 radiation or vaporization. Thus the quantity of energy is con- 
 tinually maintained, while its quality or conditions constantly 
 vary. There is, and can be, no waste or loss of energy as far as 
 nature itself is concerned. Wasted or lost energy are terms that 
 apply only to energy as utilized in the service of man. Nature 
 itself never seems to utilize the entire quantity of energy from 
 one source for the development of energy of a single form, but 
 always differentiates from one form into a number of other forms. 
 When the engineer therefore attempts to utilize any source of 
 
Laws of Energy Conservation. 21 
 
 potential energy for a single purpose, he at once encounters this 
 natural law of differentiation and finds it impossible to utilize 
 more than a portion of the energy used in the manner in which 
 he desires to utilize it. Much of this loss may be due to the form 
 of energy available, much to the medium of transformation and 
 transmission, and much to physical difficulties which it is im- 
 possible to overcome. 
 
 1 6. Laws of Energy Conservation. Primarily it should be 
 fully understood and clearly appreciated that matter and energy 
 can neither be created nor destroyed. Both may be changed in 
 form or they may be dissipated or lost so far as their utilization 
 for commercial needs is concerned. But in one form or another 
 they exist, and their total amount in universal existence is al- 
 ways the same. In any development for the utilization, trans- 
 formation or transmission of energy, the following fundamental 
 axioms must be thoroughly understood and appreciated: 
 
 First : That the amount of energy which can be actually utilized 
 in any machine or system can never be greater than the amount 
 available from the potential source. 
 
 Second: That the amount of energy which can be utilized in 
 any such system can never be greater than the difference be- 
 tween the amount entering the system and the amount passing 
 from the system as waste in the working medium. 
 
 17. Efficiency. Efficiency is the ratio or percentage of energy 
 utilized to energy applied in any system, part of a system, ma- 
 chine or in any combination of machines. 
 
 The efficiency of a given machine or mechanism, or the per- 
 centage of available energy which can be obtained from a given 
 system of generation and transmission therefore can never be 
 greater than represented by the equation : 
 
 pi -pi i 
 
 Efficiency or amount of available energy = = in which 
 
 jii 
 
 E equals the energy in the working medium entering the machine 
 
 E' equals the energy in the working medium passing from the machine. 
 
 1 8. Natural limit to efficiency. The total energy in a working 
 medium such as water, steam, air, etc., is the energy measured 
 from the basis of the absolute zero for the medium which is 
 being considered. For example, the average surface of Lake 
 Michigan is 580 feet above sea level ; each pound of water, there- 
 fore, at lake level contains 580 foot pounds of potential energy. 
 This amount of energy must therefore be expended in some man- 
 
22 . Power. 
 
 ner by each pound of water passing from the lake level to the 
 ocean level, which may be regarded as the absolute zero refer- 
 ence plane for water power. This energy cannot be utilized at 
 Chicago for there no fall is available. A small portion of this 
 energy is now utilized in the power plants at the falls of Niagara. 
 Some energy will be ultimately utilized on the Chicago Drainage 
 Canal, where a fall of some thirty-four feet is available from the 
 controlling works to Joliet. Perhaps ultimately in its entire 
 course one hundred and seventy feet of fall may be utilized by 
 the waters of the drainage canal, in which case the absolute avail- 
 able energy of each pound of water cannot be greater than shown 
 by the following equation : 
 
 Available energy = ^^ = = .2931, or 29.31 per cent. 
 
 OoU OoU 
 
 With any other form of energy the same conditions also pre- 
 vail. Consider a pound of air at 760 degrees absolute tempera- 
 ture Fahr., and at 75 pounds absolute pressure. The number of 
 heat units contained will be given by the equation : 
 
 Heat units temperature X weight X specific heat. 
 B. T. U. = 760 degrees X 1 X .169 = 128. 
 
 To utilize all of the energy in this air, it would be necessary 
 to expand it down to a temperature of absolute zero and exhaust 
 it against zero pressure. In any machine for utilizing com- 
 pressed air, it will be necessary to exhaust it against atmospheric 
 pressure. This will expand the air 3.10 times, and if expanded 
 adiabatically it will have a final temperature of 474 degrees. The 
 heat units in the exhaust will therefore be as follows : 
 
 B. T. U. = 474 degrees X 1 X .169 = 80, 
 and the available energy will be as follows : 
 
 1 OO QA AQ 
 
 Available energy = ^ - = -^- = .375, or 37.5 per cent. 
 
 IZo iZo 
 
 In this case also the temperatures vary directly as the heat 
 units, and are therefore a measure of available energy: 
 
 ygQ 474 
 
 Available energy = = .375 or 37.5 per cent. 
 
 In the ideally perfect furnace the efficiency is somewhat higher. 
 The fuel may be consumed at a temperature of about 4,000 Fahr. 
 absolute, and the gas may be cooled before escaping to about 600 
 Fahr. In this case the possible efficiency or available energy is : 
 
Practical Limits to Efficiency. 23 
 
 4QOO _ QQQ 
 
 Available energy = -- -- - = .832 or 83.2 per cent. 
 
 The above examples show, therefore, the limits which nature 
 itself places on the proportion of energy which it is theoretically 
 possible to utilize. For such losses the engineer is not account- 
 able except for the selection of the best methods for utilizing 
 such energy. The problem for his solution is, what amount of 
 this available energy can be utilized by efficient machines and 
 scientific methods. 
 
 19. Practical Limits to Efficiency. The preceding equations 
 are the equations of ideally perfect machines. Of this available 
 energy only a portion can be made actually available. In practice 
 we are met with losses at every turn. Some energy will be lost 
 in friction, as radiated heat, some in the slip by pistons, or as 
 leakage from defective joints. In many other ways the energy 
 applied may be dissipated and lost. From this it follows : 
 
 The amount of energy 'which can be utilized can never be 
 greater than the difference between the amount supplied to any 
 given machine or mechanism, and the amount lost or consumed 
 in such machines by friction, radiation or in other ways. Hence 
 it follows that the efficiency of a given machine, or the percent- 
 age of energy available, or which can be obtained from the ma- 
 chine, can never be greater than the following: 
 
 E CE ; +E" + E"' +E""etc.) . 
 Efficiency - - - ^ -- ! - - in which 
 
 E = total energy available 
 
 E' E" E"' etc. the energy lost in friction and in various other ways, in 
 the machine or system, and rejected in the exhaust from the same. 
 
 Every transmission or transformation of energy entails a loss, 
 hence, starting with a given quantity of energy, it gradually dis- 
 appears by the various losses involved in the mechanism or ma- 
 chines used. Other things being equal, the simpler the trans- 
 mission or transformation, the greater the quantity of the orig- 
 inal amount of energy that can be utilized. 
 
 The term efficiency as here applied represents always the ratio 
 between the energy obtainable from the mechanism or machine 
 and the actual energy applied to it. 
 
 Therefore the efficiency of a pumping engine is the ratio be- 
 tween the energy of the water leaving the pump and the energy 
 of the steam applied to the engine. 
 
2 4 
 
 Power. 
 
 The efficiency of a hydro-electric plant is the ratio between the 
 energy in the electric current delivered at the switch board and 
 the energy in the water entering the water wheel. 
 
 The efficiency of the dynamo in the same plant is the ratio be- 
 tween the energy furnished by the dynamo and the energy ap- 
 plied to it. 
 
 If a shaft receives from an engine 100 horse power and de- 
 livers 90, ten horse power being lost in friction, etc., the efficiency 
 of the shaft transmission is 90 per cent. 
 
 If a steam engine receives 1,000,000 heat units from the steam 
 it uses, and is able to deliver only the equivalent of 10,000 heat 
 units ; i. e., 7,780,000 foot pounds of work, the efficiency of the 
 engine is only one per cent. 
 
 20. Efficiency of a Combined Plant. In any plant or connected 
 arrangement of mechanisms and machines for the transforma- 
 tion or transmission of energy the efficiency of the plant is the' 
 product of the efficiency of each of its. parts. 
 
 Hence, to estimate total efficiencies, the efficiency of each part 
 may be estimated, and the combined efficiency then obtained. 
 From the. same calculation, the necessary relations between the 
 input and the output of energy can be obtained. Thus, if a 
 boiler has an efficiency of 50 per cent., and an engine has an 
 efficiency of 10 per cent, the combined efficiency will be .5oX.io 
 =.05 or five per cent. 
 
 In the following examples the loss and efficiency of the unit 
 and the combined efficiency of the various units in the system 
 are shown. 
 
 FIRST EXAMPLE. 
 Example of Energy Loss in Well-Designed Steam Power Plant. 
 
 
 Per Cent 
 
 Lost. 
 
 Per Cent 
 Efficiency 
 
 Net Effi- 
 ciency from 
 Potential 
 Source. 
 
 
 20 
 
 80 
 
 80 
 
 Boiler . . 
 
 15 
 
 85 
 
 68 
 
 Steam Pipe 
 
 5 
 
 ,95 
 
 64.5 
 
 Engine 
 
 94 
 
 6 
 
 3.87 
 
 Belt 
 
 5 
 
 95 
 
 3 . 67 
 
 Shafting, Belts and Counter Shafts 
 
 40 
 
 60 
 
 2.2 
 
 Lathes or other Machine Tools 
 
 50 
 
 50 
 
 1.1 
 
 Percentage of original energy utilized in 
 useful work 
 
 
 
 1 1 
 
 
 
 
 
Efficiency of a Combined Plant. 25 
 
 SECOND EXAMPLE. 
 Example of Energy Loss in Hydraulic Plant for Electric Lighting. 
 
 
 Per Cent 
 Lost. 
 
 Per Cent 
 Efficiency 
 
 .Net Effi- 
 ciency from 
 Potential 
 Source. 
 
 Head and Tail Races 
 
 5 
 
 95 
 
 95 
 
 Turbine 
 
 20 
 
 80 
 
 76 
 
 Gearing 
 
 15 
 
 85 
 
 64 6 
 
 Shaft 
 
 5 
 
 95 
 
 60 37 
 
 Belt 
 
 5 
 
 95 
 
 57 35 
 
 
 8 
 
 92 
 
 52 76 
 
 
 10 
 
 90 
 
 47 48 
 
 Transformer 
 
 20 
 
 80 
 
 37 98 
 
 Lamp 
 
 80 
 
 20 
 
 7 60 
 
 Percentage of original energy utilized in 
 useful work 
 
 
 
 7 60 
 
 
 
 
 
 THIRD EXAMPLE. 
 Example of Energy Lost in Steam and Electric Pumping Plant. 
 
 
 Per Cent 
 Lost. 
 
 Per Cent 
 Efficiency 
 
 Net Effi- 
 ciency from 
 Potential 
 Source. 
 
 
 30 
 
 70 
 
 70 
 
 Steam Pipe 
 
 5 
 
 95 
 
 66.6 
 
 
 90 
 
 10 
 
 6.65 
 
 Belt 
 
 5 
 
 95 
 
 6.32 
 
 Generator 
 
 20 
 
 80 
 
 5.05 
 
 Line 
 
 10 
 
 90 
 
 4.55 
 
 Motor 
 
 10 
 
 90 
 
 4'. 09 
 
 
 25 
 
 75 
 
 3.06 
 
 Suction and Discharge Pipe 
 
 20 
 
 80 
 
 2.45 
 
 Percentage of original energy utilized in 
 
 
 
 2.45 
 
 
 
 
 
 21. Capacity of Each Part of a System Not Identical. In each 
 of . the transmission systems outlined above a much larger 
 amount of energy enters the first unit of the system than is de- 
 livered by the last. Each unit in the system receives a decreas- 
 ing amount of energy. 
 
 In consequence, the first units in the system must be of greater 
 proportional capacity, and in practice each unit must be selected 
 of a size or capacity suited for its position in the system. Thus 
 in the first example, for each 100 units of energy received by the 
 furnace, the engine receives but 64.5, and the shafting but 4. 
 
26 Power. 
 
 22. The Analysis of Losses. In estimating power losses the 
 loss in each step from the generation to the utilization of the 
 power should be carefully examined. Four steps may ordinarily 
 be considered in any system : 
 
 1. Generation of power from potential source. 
 
 2. Conversion of power into form for transmission. 
 
 3. Transmission of power. 
 
 4. Utilization of power. 
 
 An analysis of the first three items is shown in Table II. In 
 Table III is shown the ordinary maximum and minimum ef- 
 ficiencies obtained from various motors and machines in prac- 
 tical work. Higher efficiencies are sometimes obtained under 
 test conditions where great attention is given to secure favorable 
 conditions, and, in many places where careless work is permitted, 
 neglect and unsatisfactory conditions will result in much lower 
 efficiencies than the minimum shown. 
 
 23. The Losses in a Hydro-electric Plant. To emphasize and 
 point out in greater detail the various losses encountered in the 
 generation and transmission of energy, especially as applied to 
 hydro-electric plants, attention is called to Fig. 16. In this 
 diagram is traced the losses from the potential energy of the 
 water in the head race of the power plant to the power avail- 
 able at the point where it is used. In each case considered it is 
 assumed that 1,000 horse-power of energy is applied to the par- 
 ticular work considered. 
 
 First, consider the transmission of power for traction pur- 
 poses. If a certain head is available when no water is flowing 
 in the raceways, that head becomes reduced at once when the 
 wheels begin to operate. A certain amount of head is also lost 
 in order to overcome the friction of flow through raceways, racks 
 and gateways. In the problem here considered it is assumed 
 that the above losses are five per cent, of the total energy avail- 
 able in the head-race, and that this loss occurs before the water 
 reaches the turbines: hence, 95 per cent, of the potential energy 
 is available at the turbine. The turbine loss is here assumed to 
 be about 20 per cent. First-class turbines under three-quarter 
 to full load conditions, will commonly give 80 per cent, efficiency, 
 or a little better. 
 
 Professor Unwin, in his "Development and Transmission of 
 Power," page 104, gives the following percentage of loss in tur- 
 bines: 
 
The Losses in a Hydro-Electric Plant. 
 
 27 
 
 Shafting, friction and leakage 3 to 5 per cent. 
 
 Unutilized energy 3 to 7 per cent. 
 
 Friction in shaft, guides and passages ' 10 to 15 per cent. 
 
 Total loss of energy 16 to 27 per cent. 
 
 TABLE II. 
 
 Method of Generation. Losses. 
 
 ( r Internal Combustion Engine 
 ^ Gas Oil Engine losses. 
 
 Fuel (Direct (Vacuum Pump) ( Furnace. 
 
 Steam j \ Boiler. 
 
 Fn ( Indirect ( Piping. 
 
 f Direct (Ram) Ram losses. 
 
 S g j Water ! 
 
 g<2 Power.. 1 indirect (Wheels) 
 
 a f Electric (Primary Batteries) . . . [ Various mechani- 
 
 Minor j Wind (Mills) I cal and other 
 
 O Sources . j Waves (Motors) ] losses due to 
 
 [ Sun Heat (Solar Engines) [ method used. 
 
 g f Internal Combustion Engine Included in engine 
 
 losses. 
 
 rv, * 
 
 rM Q 
 
 g| Steam Engine' and con- 
 
 g g nection losses. 
 
 Electrical Dynamos and wire 
 
 i H losses. 
 
 ^ rv* 
 
 x g Hydraulic Pump losses. 
 
 I Pneumatic Compressor losses . 
 
 , f Di rect connected, Shaft f 
 
 Mechan- j Cables, Ropes, Chains ) Various losses due 
 
 ical Electric ] to method used. 
 
 ^ [Combination I 
 
 o 
 
 I f Entrance head. 
 
 j Pipe friction. 
 
 g Hydraulic *j Motor losses. 
 
 ^ L Connections. 
 
 H . 
 
 fTranformer losses, 
 
 j Wire losses. 
 g Electrical 1 Motor losses. 
 
 [Connections. 
 
 [Pipe friction. 
 J Air cooling. 
 
 Pneumatic "j Motor losses. 
 
 I 1 Connections. 
 
Power. 
 
The Losses in a Hydro-electric Plant. 29. 
 
 The next loss shown on the diagram is the loss in transmitting 
 the energy through the bevel gear and the shafting to the gen- 
 erator. The loss in gearing, shafting, etc., is shown as 10 per 
 cent., which is probably much less than actually takes place in- 
 most plants of this kind, but may be considered as representing 
 the results of good practice. 
 
 The loss in the transformation of power in the generator is- 
 given as 8 per cent. The generator is an alternator, and the cur- 
 rent generated would be at about 2,300 volts. This current must 
 be raised to a higher voltage, by means of transformers, for 
 long distance transmission. These transformers would give an 
 efficiency of about 96 per cent. The line loss is dependent on the 
 size of the copper used, but would probably not exceed 10 per 
 cent. At the distributing point, where the energy is to be used,, 
 the high voltage current must be transformed again into suit- 
 able voltage for distribution. The same energy loss is estimated 
 for these transformers. If the current is to be used for traction 
 purposes, it will be necessary to convert it into direct current 
 by means of a rotary converter, the efficiency of which is esti- 
 mated at 92 per cent. The voltage from the general distribution 
 system would probably be too high for direct use in the rotary 
 converter, and would have to be transformed to a lower voltage 
 before passing into the converter. A loss of about 6 per cent., 
 therefore, should be allowed for this transformation. 
 
 The current from the rotary converter is subject to a line loss- 
 which may be again assumed at 10 per cent. The loss in the car 
 motor may be estimated at 7 per cent. The percentage of loss 
 and the percentage of efficiency for each unit in this generation 
 and transmission system is based, of course, on the actual energy 
 supplied and the unit next previous to it in the system, so that 
 the percentages mentioned are not based on the total potential 
 power available in the head-race but on the power actually reach- 
 ing the machine. 
 
 In the solution of any actual problems of this character it is 
 necessary to determine the efficiencies of the various units of 
 the plant under the condition of actual service. The efficiency 
 will be found to vary under various conditions of load. It may 
 therefore be desirable to determine the probable losses under 
 various working conditions. 
 
 In the selection of the various machines which are to form a. 
 part -of such a system of transmission, the choice should be 
 
Power. 
 
 based on an effort to establish a plant which will give the maxi- 
 mum economy when all conditions of loading are considered. 
 The losses in the transmission of power for traction purposes, 
 as shown on the diagram, may be traced through in tabular 
 form as follows : 
 
 
 TOTAL ENERGY 
 AVAILABLE. 
 
 1,000 HORSE 
 POWER. 
 
 Per Cent 
 Loss. 
 
 Per Cent 
 Efficiency. 
 
 Loss in 
 horsepower 
 
 
 5 
 
 20 
 10 
 8 
 4 
 10 
 4 
 6 
 8 
 10 
 7 . 
 
 95 
 80 
 90 
 92 
 96 
 90 
 96 
 94 
 92 
 90 
 93 
 
 50 
 190 
 76 
 54.7 
 25.2 
 60.4 
 21. 7 
 31.3 
 39.3. 
 45.1 
 28.4 
 
 
 Shaft and 2T69.ri.nsr . 
 
 Generator 
 
 Transformers 
 
 Transmission line 
 
 Step-down Transformers 
 
 Secondary Transformers 
 
 -Rotary Converters 
 
 Line .... . . . 
 
 Traction Motor - 
 
 
 Power utilized for operating the cars, or 37 per cent of the 
 original energy 374.5 Horse Power. 
 
 In the generation and transmission of power for lighting pur- 
 poses, the losses will be similar to those above mentioned, up 
 to and including the step-down transformers at the point of dis- 
 tribution. In this case, however, no secondary transformers or 
 rotary converters would be necessary. The only loss between 
 the step-down transformers and the light will be the line loss 
 assumed at 5 per cent. The loss in the individual transformer 
 for the light will be about 8 per cent., leaving the available en- 
 ergy for actual use in the lamp at about 456.2 horse power, or a 
 little less than 46 per cent., of the total energy in the head-race. 
 
 In the case of the utilization of this energy for manufacturing 
 purposes, the loss would be the same up to and including the 
 step-down transformers at the point of distribution. The line 
 loss in the distribution from the transformer house to the manu- 
 facturing establishment may be assumed at 5 per cent. The 
 motor, if properly selected, may be run at the line voltage, and 
 no transformer losses need be considered. The motor efficiency 
 is here shown at 92 per cent., although in most cases the per- 
 centage of efficiency would be considerably less. 
 
 The belt loss in transmitting the power from the motor to the 
 line shafting is estimated at 5 per cent. 
 
Efficiency of Generators and Motors. 
 TABLE III. Ordinary Efficiency of Generators and Motors. 
 
 
 CLASS OF MACHINERY. 
 
 EFFICIENCY PER 
 CENT AT FULL 
 LOAD. 
 
 Maxi- 
 mum. 
 
 Mini- 
 mum. 
 
 Water Wheels 
 
 f Overshot Wheels 
 
 75 
 05 
 
 40 
 85 
 85 
 
 75 
 95 
 
 18 
 15 
 12 
 12 
 
 12 
 
 9 
 9 
 
 7 
 
 7 
 
 ' 20 
 30 
 
 12 
 9 
 6 
 4.5 
 3 
 
 50 
 70 
 
 92 
 90 
 85 
 95 
 
 95 
 97 
 95 
 99 
 95 
 85 
 75 
 
 97 
 98 
 95 
 
 65 
 60 
 25 
 60 
 75 
 
 50 
 75 
 
 15 
 12 
 
 10 
 10 
 
 10 
 7 
 7 
 6 
 5 
 
 16 
 25 
 
 10 
 7 
 5 
 3 
 2 
 
 30 
 60 
 
 80 
 80 
 75 
 50 
 
 85 
 90 
 75 
 95 
 70 
 50 
 50 
 
 92 
 90 
 
 85 
 
 Breast Wheels 
 
 ^ Undershot Wheels 
 
 
 Turbines 
 
 (. Impulse Wheels 
 
 Boilers 
 
 Steam Generators. , 
 
 Condensing ) 
 Steam Engines . \ " 
 
 Non-Condensing ) 
 Steam Engines. . ) 
 
 
 f Triple Expansion Corliss 
 
 i Compound Corliss 
 
 Simple Corliss ... 
 
 i. Compound High Speed 
 
 f Compound Corliss 
 
 Simple Corliss 
 
 \ Compound High Speed 
 
 Simple Hi^h Speed 
 
 [.Simple Slide Valve . . 
 
 ( Gas or Oil Engines 
 
 Steam Air Compression . . 
 
 / Diesel Motor 
 
 f Compound Con Corliss 
 
 Simple Con Corliss 
 
 { Simple Corliss 
 
 High Pressure 
 
 [^ Small Straight Line 
 
 j Air, cold 
 
 Electrical Machinery 
 
 Transmitting Mechan- 
 isms 
 
 Air reheated 
 
 f Dymimos 
 
 ' Motor large 
 
 1 Motor small 
 
 I Transformer 
 
 CBelt 
 
 Rope 
 
 Cable 
 
 j Direct connection 
 
 Transmission Methods.. 
 
 Shafting 
 
 Gearing 
 
 1 Bevel Gearing 
 
 ( Pneumatic per mile 
 
 ] Hydraulic per mile 
 
 ( Electric usual 
 
 
32 Power. 
 
 The shafting necessary for the general distribution of power 
 through the factory is estimated at 75 per cent, efficiency. 
 
 The belt loss from the shaft to the individual machine is esti- 
 mated at an additional 5 per cent., leaving the total energy avail- 
 able for use in the machine at 308.8 horse power, or about 31 per 
 cent, of the original energy in the head-race. 
 
 It should be noted that in each of the three transmission sys- 
 tems mentioned above, the actual power utilized at the point of 
 application is less than half of the energy available in the head- 
 race. It is the function of the engineer to see that these losses 
 are reduced to the greatest practicable extent. These losses 
 must be limited in both directions. They must not be too great, 
 nor too small. They must be adjusted at the point where true 
 economy would dictate. This limit is the point where the cap- 
 italized value of the annual power lost is equal to the capitalized 
 cost of effecting further saving. In other words, true economy 
 means the construction of a plant that will save all the power 
 or energy which it is financially desirable to save, and will per- 
 mit such waste of energy as true economy directs. 
 
 24. Units of Energy. Energy is known by many names and 
 exists in many forms which seem more or less independent. The 
 principal forms of energy are measured by various units. Those 
 most commonly considered in power development and trans- 
 mission are as follows: 
 
 Work is energy applied to particular purposes. In general it 
 is energy overcoming resistance, mechanically it is the exertion 
 of force through space. 
 
 Power is the rate of work, or the relative amount of work done 
 in a given space of time. 
 
 The unit of work is the foot pound, or the amount of worx: 
 .required to raise one pound one foot. One pound raised one 
 foot, one-tenth pound raised ten feet, ten pounds raised one- 
 tenth of a foot, or any other sub-division of pounds and feet 
 whose product will equal one requires one foot-pound of work 
 to perform it. 
 
 The unit of power is based on the unit of work, and is called 
 "horse power." It is work performed at the rate of 550 foot 
 pounds per second, or 33,000 foot pounds per minute. 
 
 Units of Heat. The unit of heat is the amount of heat which 
 will raise one pound of water from 39 degrees Fahr. to 40 degrees 
 Fahr. at atmospheric pressure. It is called the British Thermal 
 Unit, and is indicated by the initials B. T. U. 
 
Conversion of Energy Units. 33 
 
 Electric Unit. The unit of quantity of electricity is the coulomb. 
 One coulomb per second is called an ampere, and one ampere un- 
 der a volt pressure is equal to a watt, the unit of electric power. 
 
 Water Power. Water power is the power obtained from a 
 weight of water moving through a certain space. In water power 
 the unit of quantity may be the gallon or the cubic foot ; the unit of 
 head may be the foot ; and the unit of time may be the second or 
 minute. The weight of water, unless highly mineralized, at ordi- 
 nary temperature, varies from 62.3 to 62.5 pounds per cubic foot. 
 As these weights vary from each other less than one-third of one 
 per cent., the difference is insignificant in practical problems where 
 the errors and uncertainties are often large. In the further discus- 
 sion of this subject, therefore, the weight of 62.5 pounds is used as 
 the most convenient in calculation. 
 
 Steam Pozver. The unit of steam power in ordinary use is the 
 pound of steam, its pressure, and rate of use. It is, however, based 
 on the heat unit, and must be so considered for detailed examina- 
 tion. 
 
 Definite quantities of work are also designated by the "horse 
 power hour," equivalent to 1,980,000 foot pounds, and the "kilowatt 
 hour," equivalent to 2,654,150 foot pounds. 
 
 The pound of steam may be considered as containing an aver- 
 age of 1,000 British thermal units, which may be utilized for power. 
 This is equivalent to 778,000 foot pounds. 
 
 25. Conversion of Energy Units, The various forms of energy 
 as expressed by the units named are convertible one into another in 
 certain definite ratios which have been determined by the most 
 careful laboratory methods. In considering these ratios, however, 
 it must be remembered that, as shown in the preceding examples, 
 in the transformation from one form of energy into another the 
 ratios given cannot be attained in practice on account of losses 
 which can not be practically obviated. Such losses must be, in 
 good practice, reduced to a minimum, and the ratios given are, 
 therefore, the end or aim toward which good practice strives to at- 
 tain as nearly as practicable when all conditions and facts are duly 
 considered. 
 
 Energy must be considered in two conditions as well as in the 
 above named forms, viz. : passive and active or potential and 
 kinetic. 
 
 Potential energy is energy stored and does not necessarily in- 
 volve the idea of work. Kinetic energy is energy in action and 
 8 
 
34 .Power. 
 
 involves the idea of work done or power exerted and for its meas- 
 urement must be considered in relation to time. 
 
 The most common units of potential energy and their equiva- 
 lents are as follows : 
 
 The footpound (one pound raised one foot). 
 
 =1/62.5 or .016 foot cubic foot (of water). 
 =1/8.34 or .12 foot gallon (of water). 
 =1/2655.4 or .0003766 volt coulombs. 
 =1/778 or .001285 British thermal units. 
 
 The foot cubic foot (one cubic foot of water raised one foot) . 
 =62.5 foot pounds. 
 =7.48 foot gallons. 
 =.08 British thermal units. 
 =.02353 volt coulombs. 
 
 The foot gallon (one gallon of water raised one foot) 
 =8.34 foot pounds. 
 =.01072 British thermal units 
 =.00314 volt coulombs. 
 =.1334 foot cubic feet. 
 The volt coulomb 
 
 =2655.4 foot pounds. 
 =42.486 foot cubic feet. 
 =318.39 foot gallons. 
 =3.414 British thermal units. 
 The British thermal unit 
 =778 foot pounds. 
 =12.448 foot cubic feet. 
 =93.28 foot gallons. 
 =.2929 volt coulombs. 
 
 Quantities of energy available, used or to be used, and either 
 potential or kinetic may be measured in the above units. 
 
 When the rate of expenditure is also stated these units express 
 units of power. Some of the equivalent values of power are as fol- 
 lows, those most commonly used being printed in black-face type: 
 The horse power 
 
 =1980000 foot pounds per hour. 
 =33000 foot pounds per minute. 
 =550 foot pounds per second. 
 =31680 foot cubic feet per hour. 
 =528 foot cubic feet per minute. 
 
Conversion of Energy Units. 35 
 
 =8.8 foot cubic feet per second. 
 
 =237600 foot gallons per hour. 
 
 =3960 foot gallons per minute. 
 
 =66 foot gallons per second. 
 
 =746 watts. 
 
 =2545 British thermal units per hour. 
 
 =42.41 British thermal units per minute. 
 
 ^=.707 British thermal units per second. 
 
 The foot pound per minute 
 
 =1/33000 or .0000303 horse power. 
 
 =1/778 or .00129 British thermal units per minute. 
 
 =.0226 watts. 
 
 =i/8.34=.i2 foot gallons per minute. 
 
 =i/62.5=.oi6 foot cubic feet per second. 
 
 The foot cubic foot per minute 
 =62.5 foot Ibs. per minute. 
 =i/528=.ooi89 horse power. 
 =1.412 watts. 
 
 =7.48 foot gallons per minute. 
 =.0803 British thermal units per minute. 
 
 The foot cubic foot per second 
 
 =375 f ot ft> s - P er minute. 
 =62.5 foot Ibs. per second. 
 =i/8.8=. 1 1 36 horse power. 
 =448.8 foot gallons per minute. 
 =7.48 foot gallons per second. 
 =4.820 British thermal units per minute. 
 =.0803 British thermal units per second. 
 The watt 
 
 =44.24 ft. Ibs. per minute/ 
 
 =.00134 horse power. 
 
 =.0568 British thermal units per minute. 
 
 =5.308 gallons feet per minute. 
 
 =.7089 ft. cu. ft. per minute. 
 
 The British thermal units~pef" rrrrirute 
 =778 ft. Ibs. per minute. 
 =.02357 horse power. 
 =17.58 watts. 
 =93.28 ft. gal. per minute. 
 =12.48 ft. cu. ft. per minute. 
 
36 Power. 
 
 26. Motion in General. In moving a body against a given force or 
 resistance the work done in foot pounds is the product of the space 
 passed through (in feet) and the resistance (in pounds). Thus in 
 raising a ten-pound weight 100 feet high, 1,000 foot-pounds of work 
 is performed. But this is not the only work performed. To pro- 
 duce motion in a body or to bring a body to a state of rest neces- 
 sitates a transfer of energy. For all moving bodies are endowed 
 with kinetic energy the energy of motion and this energy must 
 be given to them to produce motion, and must be taken from them 
 to produce a state of rest. 
 
 Hence, Newton's laws of motion: 
 
 1. "Every body continues in a state of rest, or of uniform mo- 
 
 tion in a straight line except in so far as it may be com- 
 pelled by impressed forces to change that state." 
 
 2. "Change of motion is proportional to the impressed" force 
 
 and takes place in the direction of the straight line in 
 which the force acts." 
 
 3. "To every action there is always an equal and contrary reac- 
 
 tion." 
 
 The acceleration of gravity is the acceleration due to the weight 
 of a body acting on its mass. 
 
 The weight of a body W (on account of centrifugal effect of the 
 earth's revolution) varies, being least at the equator and greatest 
 at the poles. From Newton's second law it follows that the accel- 
 eration in motion designated by g and caused by the weight of any 
 body acting on its mass will be proportional to its weight, i. e., g^= 
 constant X W, and hence the weight of a body divided by the ac- 
 celeration will always be constant. This constant quotent desig- 
 nated by the letter M is termed the mass of the body. 
 
 (:)M=|- 
 
 LetW=The weight of a body. 
 
 g=Acceleration due to gravity=velocity of a falling body at 
 end of first second, and is ordinarily taken as 32.2 ft. 
 per sec. per sec. 
 
 A=Acceleration of moving body=velocity of body at end 
 of first second. 
 
 W'=Weight acting. 
 
 W"=Weight acted on. 
 
Kinetic Energy. 37 
 
 V= Velocity at end of time t. 
 
 V a Average velocity. 
 
 t=Time force has acted. 
 
 S=Space passed through. 
 
 h=Height passed through by falling body. 
 
 V'=Initial velocity. 
 
 S'=Initial space passed through. 
 
 27. Uniform Motion. In uniform motion the moving body 
 passes through equal spaces in any equal divisions of time. 
 
 Hence by definition : 
 
 The space passed through (S) equals the product of the velocity 
 (V) and the time (t). 
 
 (2) S=Vt. 
 
 (3) VA 
 
 28. Uniformly Varied Motion. If the velocity of a body is in- 
 
 creased or diminished uniformly, the motion is termed uniformly 
 varied motion and is termed uniformly accelerated motion in the 
 first case and uniformly retarded motion in the latter case. 
 In all such cases the following relations hold: 
 
 ' 
 
 (5) V=At=g t. 
 
 (6) V a =Al 
 
 (8) V=VTA~S. 
 
 ith falling bodies : 
 
 S=h, 
 A=g. 
 From which equation (8) becomes 
 
 (9) V=V 2 gh, tne we ^ known basis of hydraulic calcu- 
 
 lations. 
 (10) Worfc=W h=W VV2ff=M V/2. 
 
 29. Compound Motion. When bodies are already in motion and 
 additional force is applied, the following relations hold : 
 
 (i i) V=V'+At. 
 (12) S= 
 
Power. 
 
 30. Graphical Representation of the Laws of Motion. In each 
 case 
 
 The vertical ordinates represent velocity 
 
 Abscissas represent time. 
 
 Areas represent space passed through. 
 
 TIME 
 UNIFORM MOTION 
 
 UNIFORM ACCELERATED MOTION 
 
 V = constant 
 
 S = Vt 
 
 V = At = gt 
 
 v f At 2 V 
 sV t:= T : 2A 
 
 V = T/2AS" 
 
 V = V + At 
 
 S- S' + V t 
 
 COMPOUND MOTION - 
 
 WITH INITIAL. 
 
 ACCELERATED. 
 VELOCITY 
 
 Fig. 17. Graphical Representation of the Laws of Motive. 
 
 31. Transformation. The transformation of potential to kinetic 
 energy is well illustrated by water acting upon a water wheel. The 
 energy in a body is always constant whatever its form, except' as 
 said energy be given up to other bodies or lost and wasted in vari- 
 ous ways. Consequently the sum of the potential and kinetic en- 
 ergies in any body is a constant quantity unless the difference be 
 accounted for by energy loss or transfer as above noted. 
 
 Water that has fallen to sea level has lost all the energy it may 
 have once possessed, its energy having been expended in perform- 
 ing some kind of work. 
 
 If, in a hydraulic plant, we have an available fall of 8.8 ft. every 
 cubic foot of water passing through this distance each second pro- 
 duced 33,000 ft. Ibs. of work, or one horse power. After the water 
 has passed through a well-designed turbine it flows sluggishly 
 away, having used up nearly all its energy in the turbine to which 
 
Literature. 39 
 
 it has transferred its energy. If, however, on account of bad de- 
 sign the water flows away at a rapid rate, say at 10 feet per second, 
 the head lost, h=v 2 /2g i. e. h=io 2 /6"44=i.55 ft. of vertical fall. 
 Under these conditions the energy due to this fall still remains in 
 the water, after it has left the wheel, and is lost, the loss being 
 17.8 per cent, of the original energy. 
 
 LITERATURE. 
 
 1. Thurston, Robert H. Conversion Tables of Weights and Measures. New 
 
 York. J. Wiley & Sons. 1883. 
 
 2. Oldberg, Oscar. A Manual of Weights and Measures. Chicago. C. J. 
 
 Johnson. 1887. 
 
 3. Everett, J. D. Illustrations of the C. G. S. System of Units. New York. 
 
 MacMillan & Co. 1891. 
 
 4. Anderson, William. On the Conversion of Heat into Work. Discussion 
 
 of energy conversion. London. Whittaker & Co. 1893. 
 
 5. Unwin, W. C. On the Development and Transmission of Power. Long- 
 
 man & Co. London. 1894. 
 
 G. Oswald, Wilhelm. Manual of Physics, Chemical Measurements. New 
 York. The MacMillan Co. 1894. 
 
 7. Peabody, Cecil H. Tables of the Properties of Saturated Steam. New 
 
 York. J. Wiley & Sons. 1895. 
 
 8. Richards, Frank. Compressed Air. New York. J. Wiley & Sons. 1895. 
 
 9. Bolton, Reginald. Motive Powers and Their Practical Selection. New 
 
 York. Longmans, Green & Co. 1895. 
 
 LO. Holman, Silas W. Matter, Energy, Force and Work. New York. The 
 MacMillan Co. 1898. 
 
 11. Kent, Wm. Notes of the Definition of Some Mechanical Units. Am. 
 
 Asso. Adv. of Sci. 1898. See also Eng. News, Vol. 40, p. 348. 
 
 12. Mead, Daniel W. Commercial Transformation of Energy. Trans. 111. 
 
 Soc. Eng. 14th report, 1899. 
 
 13. Reeve, Sidney A. The Steam Table. New York. The MacMillan Co. 
 
 1903. 
 
 14. Kohlrausch, F. An Introduction to Physical Measurements. New York. 
 
 D. Appleton & Co. 1903. 
 
 15. Carpenter, R. C. Experimental Engineering. New York. John Wiley 
 
 & Sons. 1903. 
 
 16. Herwig, Carl. Conversion Factors. New York. J. Wiley & Sons. 19u4. 
 
 17. Smithsonian Institution. Physical Tables. 3d Edition. 1904. 
 
 18. American Institute of Electrical Engineering. Report of Committee en 
 
 Standardization. 1907. Proc. Am. Inst. E. E. Vol. 26, pp. 1076- 
 HOG. 
 
CHAPTER III. 
 
 HYDRAULICS. 
 
 32. Basis of Hydraulics. The science of hydraulics is an empir- 
 ical, not an exact science, but is based on the exact sciences of 
 hydrostatics and dynamics. Its principal laws are therefore founded 
 on theory, but on account of the multitude of modifying influences 
 and of our necessarily imperfect theoretical knowledge of their 
 varying characters and extent, the formulas used must' be derived 
 from or at least modified by observation and experience and can- 
 not be founded solely on theoretical considerations. The condi- 
 tions under which hydraulic laws must be applied are so varied in 
 both number and kind that the application of the laws must be 
 modified to suit those various conditions and for this reason their 
 successful application depends largely on the practical experience 
 of the engineer. 
 
 In the following discussion the letters used will have the signifi- 
 cance shown below : 
 
 E=Energy (abstract). 
 
 P=Horse power. 
 
 W=Total weight of water. 
 
 h=The total available head in feet. 
 
 h x =The velocity head. 
 
 h 2 =The entrance head or influx head. 
 
 h 3 =The friction head. 
 
 q=The quantity of water (in cubic feet per second). 
 
 w The weight of each unit of water (cu. ft.=62.5 Ibs.). 
 
 a=Area (in square inches) against which pressure is ex- 
 erted. 
 
 s=The space (in lineal feet) through which the area moves 
 under pressure. 
 
 v=The velocity of flow (in feet per second). 
 
 ^^Acceleration due to gravity (32.2 feet per second per sec- 
 ond.) 
 
 t=The time in seconds. 
 
 33. Mathematical Expression for Energy. Mechanically, energy 
 is the exertion of force through space. The amount of available 
 
Mathematical Expression for Energy. 41 
 
 energy of water that may be theoretically utilized is measured by 
 its weight (the force available) multiplied by the available head 
 (the space through which the force is to be exerted), i. e., (i) E= 
 Wh. From this it will be noted that the energy of water is in 
 direct proportion to both the head and quantity. This energy may 
 be. exerted in three ways which may be regarded as more or less 
 distinct but which are usually exercised, to some extent at least. 
 in common. The exertion of this energy in the three ways men- 
 tioned, expressed in terms of horse power, are as follows : 
 
 First: By its weight which is exerted when a definite quantity 
 of water passes from a higher to a lower position essentially with- 
 out velocity. This method of utilization is represented by the 
 equation 
 
 Second: By the pressure of the water column on a given area 
 exerted through a definite space. This method of utilization is rep- 
 resented by the equation 
 
 434h as 
 
 Third : By the momentum of the water exerted under the full 
 velocity due to the head. The energy of a moving body is repre- 
 sented by the formula : 
 
 Wv 2 
 
 (4) E = -^~ 
 
 *g 
 
 The equation for the horse power of water under motion is there- 
 fore represented by the equation : 
 
 ~ 550 x 2g 
 
 An analysis of these formulas will show that under any given 
 conditions the theoretical power exerted will be the same in each 
 case. 
 
 34. Velocity Head (hj). It has already been pointed out (chap- 
 ter IT) that energy must be expended in order to produce motion 
 in any body and that the head (h x ) necessary to produce a ve- 
 locity (v) is 
 
 This proportion (h x /h) of the available head h has to be ex- 
 pended to produce and keep in motion the flow of water. This 
 head (h x ) is not necessarily lost (it has simply been converted into 
 
42 Hydraulics. 
 
 kinetic energy, and it may be re-converted into potential energy by 
 correct design or it may be utilized in some other way, as, for 
 example, by pressure or impact in hydraulic motors). 
 
 Whatever head (h x ) is necessary to maintain the velocity (v), 
 with which the water leaves the plant, will be lost to the plant. 
 It is, therefore, desirable to keep v at this point as low as may be 
 found practicable when other conditions are considered. 
 
 Sudden enlargements or contractions in pipes or passages may 
 wholly or partially destroy the velocity and cause the permanent 
 loss of the corresponding head (h ). 
 
 In this case an additional amount of the available head (r^) must 
 be used to again generate the velocity (v) required to convey the 
 water through the remainder of its course. Gradual change in the 
 cross-section of all channel conduits or passages is, therefore, de- 
 sirable in order that the transformation from kinetic to potential 
 energy, and the reverse, shall be made without material loss. 
 
 Not only the head (hj) but still other portions of the total avail- 
 able head (h) may be lost in the channels and passages of a ma- 
 chine or plant by improper design. 
 
 35. Entrance Head. The loss of head (h 2 ) which occurs at en- 
 trance into 1 a raceway, pipe or passage may be called the "influx 
 head." The amount of this loss differs considerably with the shape 
 and arrangement of the end of the pipe or passage. In general, the 
 influx head may be determined by the formula: 
 
 (7) h a = (r -(Merriman's Hydraulics, Art. 53) 
 
 In this formula the coefficient can be obtained from table VI, in 
 which the variations of the constant under various conditions, with 
 reference to a pipe inlet, are shown, and from which it will be noted 
 that its magnitude depends on the shape and arrangement of the 
 inlet. 
 
 TABLE IV. 
 Arrangements of a pipe inlet with corresponding coefficients. 
 
 Arrangement of Pipe. 
 
 c 
 
 c 8 l 
 
 A. Projecting into reservoir 
 
 ,715 
 
 956 
 
 B. Mouth flush with side of reservoir 
 
 .825 
 
 .469 
 
 (from 
 
 950 
 
 108 
 
 C. Bell shaped mouth (to 
 
 990 
 
 020 
 
 
 
 
Submerged Orifices. 
 
 To find the value of h 2 , the value of -\- 1 corresponding to the 
 
 c 
 
 given conditions, is to be selected from Table IV and substituted 
 in formula (7). The ordinary arrangement of suction pipes is for 
 
 a square ended pipe to project di- 
 rectly into the suction pit. In res- 
 ervoirs the pipe may be flush with 
 the masonry or project as in the 
 flcase of suction pipes. With condi- 
 tion (A) formula (7) becomes 
 
 (8) 
 
 h a = .956-^ 
 
 2g 
 
 The value of h 2 can be readily 
 obtained from equation (8), as it 
 will be 95.6 per cent, of the veloc- 
 ity head. 
 
 With the mouth of the pipe flush 
 with the side of the reservoir the 
 loss would be 46.9 per cent, of the 
 velpcity head, and with a bell 
 mouth pipe the loss would be de- 
 creased to from two per cent, to 
 10.8 per cent, according to the de- 
 sign of the bell mouth entrance. 
 
 The arrangements of inlet pipes 
 as referred to in Table IV are 
 Fi z- 18. shown in Fig> Ig> 
 
 36. Submerged Orifices. A similar loss is sustained in the flow- 
 through gates or submerged openings or in the flow past any form 
 of obstruction which may be encountered by the water in its flow 
 through channels, pipes or other forms of passages. Openings or 
 obstructions with square edges may cause a serious loss of head 
 which may, however, be reduced. 
 
 First: By increasing the opening, thus causing a reduction ini 
 velocity and consequently a saving in head, or 
 
 Second : By rounding the corners of the opening or obstruction, 
 thus causing a gradual change in velocity and a partial recovery 
 of any head necessarily used for creating greater velocity through- 
 such passage or past such obstruction. 
 
 But few experiments have been made on submerged orifices and" 
 tubes. These indicate a coefficient of about .62 for complete con- 
 traction which increases to .98 or even .99 with the contraction* 
 
44 Hydraulics. 
 
 completely suppressed. Certain experiments have recently been 
 made at the hydraulic laboratory of the University of Wisconsin, 
 on the discharge through orifices and tubes four feet square and of 
 various thicknesses or lengths and with various conditions of con- 
 traction. The values of the coefficients as determined in these ex- 
 periments with various losses of head and various conditions of 
 entrance, are shown in Table V.* 
 
 The Forms of Entrance and Outlet Used for the Tubes in the experiment 
 
 were as follows: 7 
 
 A. Entrance; all corners 90. 
 
 Outlet; tube projecting into water on down stream side of bulkhead. 
 a Entrance; contraction suppressed on bottom. 
 
 Outlet; tube projecting into water on down stream side of bulkhead. 
 b Entrance; contraction suppressed on botton and one side. 
 
 Outlet; tube projecting into water on down stream side of bulkhead. 
 c Entrance; contraction suppressed on bottom and two sides. 
 
 Outlet; tube projecting into water on down stream side of bulkhead. 
 c' Entrance; contraction suppressed on bottom and two sides. 
 
 Outlet: square corners with bulkhead to sides of channel preventing 
 
 the return current along the sides of the tube. 
 d Entrance; contraction suppressed on bottom, two sides and top. 
 
 Outlet; tube projecting into water on down stream side of bulkhead. 
 
 From this table it will be noted that a partial suppression of con- 
 traction does not always improve results, and that by complete sup- 
 pression, the coefficient is greatly increased with a corresponding 
 decrease in head lost. 
 
 37. Friction Head (h 3 ) In raceways and short pipes the velocity 
 head (hi) and the influx head (h 2 ) are frequently the sources of the 
 greatest losses of head. In canals and pipes of considerable length 
 the friction of flow may become the most serious sources of energy 
 loss. 
 
 The principles of flow in such channels may be considered as 
 follows : 
 
 First Principle : In any frictionless pipe, conduit, channel or pas- 
 sage of unit length the flow may be expressed by the formula : 
 
 (9) h = Y~ or v = i/2gh~ 
 
 In practice, however, we find friction is always present and a 
 friction factor must be introduced in the above formula in order to 
 
 *From experiments by Mr. C. B. Stewart at the Hydraulic Laboratory of 
 the University of Wisconsin. 
 
Friction Head. 45 
 
 represent the actual conditions of practice. (9) therefore becomes : 
 
 (10) 
 
 TABLE V. 
 
 Value of the Coefficient of Discharge for flow through horizontal submerged 
 tube, 4 feet square, for various lengths, losses of head and forms of entrance 
 and outlet. 
 
 Loss of 
 head, h 2 
 in feet. 
 
 Forms 
 of En- 
 trance 
 and 
 Outlet 
 
 Length of tube, in feet. 
 
 i 
 0.31 
 
 0.62 
 
 1.25 
 
 2.50 
 
 5.00 
 
 10.0 
 
 14.0 
 
 Value of the coefficient, c. 
 
 05 
 
 A 
 
 .631 
 
 .650 
 
 .672 
 
 .769 
 
 .807 
 
 .824 
 
 .838 
 
 
 a 
 
 .762 
 
 
 
 .742 
 
 .810 
 
 
 .848 
 
 
 b 
 
 .740 
 
 
 
 .769 
 
 .832 
 
 
 .862 
 
 
 c 
 
 .834 
 
 
 
 .769 
 
 .875 
 
 
 .890 
 
 
 c' 
 
 
 
 
 
 
 
 .875 
 
 
 d 
 
 .948 
 
 
 
 .943 
 
 .940 
 
 .927 
 
 .931 
 
 10 
 
 A 
 
 .611 
 
 .631 
 
 .647 
 
 .718 
 
 .763 
 
 .780 
 
 .795 
 
 
 a 
 
 .636 
 
 
 
 .698 
 
 .771 
 
 
 .801 
 
 
 b 
 
 .685 
 
 
 
 .718 
 
 .791 
 
 
 .813 
 
 
 c 
 
 .772 
 
 
 
 .718 
 
 .828 
 
 
 .841 
 
 
 c' 
 
 
 
 
 
 
 
 .830 
 
 
 d 
 
 .932 
 
 
 
 .911 
 
 .899 
 
 .892 
 
 .893 
 
 15 
 
 A 
 
 .609 
 
 .628 
 
 .644 
 
 .708 
 
 .758 
 
 .779 
 
 .794 
 
 
 a 
 
 .630 
 
 
 
 .689 
 
 .767 
 
 
 .803 
 
 
 b 
 
 .677 
 
 
 
 .708 
 
 .787 
 
 
 ,814 
 
 
 c 
 
 .765 
 
 
 
 .708 
 
 .828 
 
 
 .839 
 
 
 c' 
 
 
 
 
 
 
 
 .829 
 
 
 d 
 
 .936 
 
 
 
 .910 
 
 .899 
 
 .893 
 
 .894 
 
 20 
 
 A 
 
 .609 
 
 .630 
 
 .647 
 
 .711 
 
 .768 
 
 .794 
 
 .809 
 
 
 a 
 
 .63;! 
 
 
 
 .694 
 
 .777 
 
 
 .819 
 
 
 b 
 
 .678 
 
 
 
 .711 
 
 .796 
 
 
 .833 
 
 
 c 
 
 .771 
 
 
 
 .711 
 
 .838 
 
 
 .856 
 
 
 c' 
 
 
 
 
 
 
 
 .846 
 
 
 d 
 
 .948 
 
 
 
 .923 
 
 .911 
 
 .906 
 
 .905 
 
 .25 
 
 A 
 
 .610 
 
 .634 
 
 .652 
 
 .720 
 
 .782 
 
 .812 
 
 .828 
 
 
 a 
 
 .634 
 
 
 
 .705 
 
 .790 
 
 
 
 
 b 
 
 .683 
 
 
 
 .720 
 
 .809 
 
 
 
 
 c 
 
 .779 
 
 
 
 .720 
 
 .854 
 
 
 
 
 c' 
 
 
 
 
 
 
 
 
 
 d 
 
 .965 
 
 
 
 .938 
 
 .928 
 
 
 
 30 
 
 A 
 
 .614 
 
 .639 
 
 .660 
 
 .731 
 
 .796 
 
 .832 
 
 .850 
 
 
 -fi. 
 
 a 
 
 .639 
 
 
 
 
 
 
 
 
 b 
 
 .689 
 
 
 
 
 
 
 
 
 c 
 
 .788 
 
 
 
 
 
 
 
 
 c' 
 
 
 
 
 
 
 
 
 
 d 
 
 .984 
 
 
 
 
 
 
 
4 6 
 
 Hydraulics. 
 
 The formulas (9) and (10) represent one of the important funda- 
 mental principles from which many hydraulic formulas are de- 
 veloped. 
 
 Second Principle: In any pipe, conduit, channel or passage we 
 may fairly assume: 
 
 Frst: From axiomatic considerations the resistance to the flow 
 of water may be regarded as directly proportional to the area of 
 the surface in contact with the water. 
 
 Second: From observed conditions the resistance is found to be 
 directly proportional to the square of the velocity of flow. 
 
 Third : Experience leads to the conclusion that the resistance to 
 flow is inversely proportional to the cross-section of the stream. 
 
 These conclusions may be expressed by the following equation: 
 
 (Velocity) 2 X area of contact 
 
 Resistance = y ' , : 
 
 area ot section 
 
 Fig. 19. 
 
 The area of the surface of a channel is the product of the wetted 
 -section or wetted perimeter (p) tirnes the length of the section, or, 
 to p x 1. (See Fig. 19.) The velocity is represented by v and the 
 cross-section by a. Hence, from the above considerations, we may 
 write for the friction head: 
 
 (11) 
 
 h s = and by ; transposition v a = p 
 
 That is to say, the square of the velocity is in direct proportion 
 to the area of the section and to the friction head and inversely 
 proportional to the wetted perimeter and to the length of the sec- 
 tion. 
 
 In practice it is found that there are numerous factors which 
 
Kutter's Formula. 47 
 
 affect the theoretical conditions, as above set forth, which must 
 therefore be modified in accordance with the conditions which ob- 
 tain. In formula (n) therefore it is necessary to apply a coeffi- 
 cient (c') which represents the summation of such other influences. 
 The form in which this last equation is ordinarily written is 
 
 /ON , v 2 pl /ah, 
 
 h "= C a 0rV = C Afe- 
 
 Ordinarily this form is somewhat abbreviated by substituting- for 
 a/p the hydraulic radius which represents this ratio. That is to say, 
 
 area of cross section _ a 
 wetted perimeter " ^p~ " 
 
 I The "hydraulic radius" is also sometimes termed the "mean 
 dfepth" or the "mean radius." For the ratio of the resistance head 
 to the length of section the equivalent slope s is substituted. 
 
 That is to say: 
 
 Resistance head h 3 _ 
 Length of section ~ 1 
 
 With these substitutions the formula (12) assumes the final 
 fprm of: 
 
 (13) v = 
 
 In the use of this formula three factors must be determined by 
 measurement or estimate in order to derive the fourth, v, r and s 
 can be determined experimentally or measured directly. The 
 factor c is the most difficult to ascertain as it depends upon a very 
 great variety of conditions which can only be known and apprie- 
 ciated by a thorough knowledge of the conditions under considera- 
 tion, and by comparison of such conditions with similar observed 
 conditions. Various attempts have been made to derive a formula 
 which would give the value of c in accordance with the varying 
 conditions. The principal formulas for the values of c are those of 
 Ganguillet and Kutter and of Bazin. Ganguillet and Kutter's form- 
 ula for the value of c is as follows : 
 | 38. Kutter's Formula. 
 
 41 fl i 1 ' 811 _, 0-00281 
 
 >'...,.".. ..... 4-L.p -| -- -- 1- ;" . , , . , , 
 
 (14) c = 
 
 From this formula it will be seen that Ganguillet and Kutter as- 
 sume c to vary with the slope, with the square root of the hydraulic 
 radius and with a new factor "n" which is termed the coefficient 
 
Hydraulics. 
 
 HYPRAUL'IC RADIUS "r"- 
 
 rf. ,k 
 
 1.0 2.0 
 
 VELOCITY V- IN FEET PER SECOND 
 
 Fig. 20. 
 
Kutter's Formula. 
 
 49 
 
 Fig. 21. 
 
50 Hydraulics. 
 
 of roughness. The value of this coefficient as determined by these 
 
 experiments is as follows: 
 
 For large pipe with the following characteristics: 
 
 Exceptionally smooth cast iron pipe n = .on 
 
 Ordinary new cast iron or wooden pipe .0125 
 
 New riveted pipes and pipes in use .014 
 
 Pipes in long use .019 
 
 For open channels of uniform sections : 
 
 For planed timber sides and bottom 11= .009 
 
 For neat cement or glazed pipe .01 
 
 For unplaned timber '. .012 
 
 For brick work .013 
 
 For rubble masonry .017 
 
 For irregular channels of fine gravel .02 
 
 For canals and rivers of good section .025 
 
 For canals and rivers with stones and weeds . . . .030 
 
 For canals and rivers in bad order 0.35 
 
 The relation of the above factors may be determined by the dia- 
 grams, Figs. 20 and 21. If with a known slope and a known value 
 of n (for example, let n=o.i5 and s=.ooo2, as at A, Fig. 20), a 
 straight line be drawn on this diagram to the scales of the hydraulic 
 radius (at B) it will show at the intersection with the scale for the 
 coefficient (c) the relative value of this coefficient for these condi- 
 tions, or with a known c and the known hydraulic radius and the 
 given slope the value of n of a channel may be likewise determined. 
 After a line has once been drawn connecting these four known 
 values the velocity can be determined by drawing a line from the 
 hydraulic radius scale (B) to the proper point on the scale of slope 
 or hydraulic gradient at x, and then from the point of intersection 
 of the line A B with the coefficient scale at x' drawing a line par-, 
 allel with xB which will intersect the velocity scale at the point B', 
 giving the velocity (in this case equal to 1.34 ft. per second). These 
 formulas only apply with accuracy where the channels or passages 
 are uniform and if applied to channels or passages which are not 
 uniform the sections selected must be fairly representative. If the 
 sections selected are not fairly representative the value of c or n 
 determined from observations and experiments may vary consid- 
 erably from the values which would otherwise be anticipated. That 
 is to say, the* calculations based on c and n will take into account 
 irregularities in channels and other unknown or unrecognized con- 
 ditions, including curves, bends and obstructions which may not 
 
Bazin's Formula. 
 
 Bazin's Form 
 value of c in th 
 
 ula fc 
 e for 
 i En 
 
 7 
 
 >r the 
 niuk 
 glisl 
 
 J 
 
 L 
 L 
 
 I 
 
 I 
 
 I 
 
 
 i / i /i / 
 
 
 / / 1 
 
 
 / / fl 
 
 
 / / / 
 
 V 
 
 n 
 
 n 
 n 
 
 n 
 n 
 
 n 
 n 
 
 cv rs is, n 
 leasure, 
 
 s 
 
 
 / / / 
 
 
 / / / 
 
 
 M/ / 
 
 c 
 
 i-O 
 
 552 + 
 
 OGforsni( 
 matchec 
 10 for p 
 "ick. 
 40 for ma 
 85 for reg 
 ?ds. 
 30 for ( 
 >od order. 
 75 in \ 
 der. 
 
 m 
 
 
 3tjL m nt 
 
 l/r 
 )oth plant 
 boards, 
 anks anc 
 
 sonry. 
 ular eartt 
 
 canals in 
 ery bad 
 
 
 n I / 1 
 
 
 /N / 
 
 01 
 
 1=0. 
 bi 
 
 
 / / / 
 
 
 / / r i 
 
 
 / / 1 
 
 i O. 
 i=0 
 
 
 / / H \ \ \ 
 
 b< 
 1=1, 
 
 gc 
 i I . 
 
 j 
 
 ir / / 
 
 / 
 
 JLLLA IE it 
 
 / 
 
 / / / 
 
 or 
 
 / 
 
 / I / 
 
 / 
 
 / 
 
 L ji j n 
 
 
 i 
 
 /i i/i 1 1 1 
 
 
 
 / 
 
 1 
 
 i 
 
 / on 
 
 </ 
 
 i 
 7 
 
 f 
 
 T 
 
 it HTij 
 
 
 
 
 
 j 
 
 7 
 
 3 1 "/Ir 
 
 
 / 
 
 / 
 
 
 / 
 
 / 
 
 y / 
 
 , 
 
 / / 
 
 / 
 
 / 
 
 
 z 
 
 / / 
 
 
 / 
 
 / 
 
 ^ 
 
 v 
 
 
 
 / E 
 
 
 (_ / 
 
 ' 
 
 / 
 
 
 / 
 
 
 h 
 
 
 7 
 
 / 
 
 / 
 
 
 / 
 
 
 
 xl /I 
 
 
 / 
 
 
 / 
 
 
 X 
 
 
 
 4^ 
 
 [Z 
 
 A 
 
 ^ 
 
 X 
 
 ^^ 
 ^ 
 
 ~~ 
 
 _^ 
 
 
 
 
 ^ 
 
 
 
 ^^ 
 
 
 
 ,--- 
 
 ^ 
 
 i 
 
 if N 
 
 COEFFICIENT V IN FORMULA V = C/PT 
 Fig. 22. Diagram" for; Solution of Bazin's Formula. 
 
 
GRAPHICAL SDLUTII 
 
 v - c \/~ 
 
 V = VELDCITY IN FEET PER EECDND. 
 
 C "COEFFICIENT. 
 
 R- HYDRAULIC RADIUS IN FEET = -p- 
 
 T" 
 
 B = BINE OF SLDPE 
 
 a= AF 
 p = w 
 h= F; 
 
 I = LE 
 
 VALU E 
 
 .4 .5 .8 .7 .B .3 IB 
 
 VELOCITIES I 
 
 Figu 
 
I DF CHEZYS FORMULA 
 
 s = I 
 
 .IN BQ. FEET OF CHANNEL SECTION 
 FED PERIMETER DF CHANNEL SECTION IN LINEAL FEET. 
 
 IN FEET BETWEEN POINTS CONSIDERED. 
 ;TH OR DISTANCE, BETWEEN POINTS CONSIDERED, IN LINEAL FEET. 
 
 OF R . 5 
 
 5 2.0 ES 3.Q 4,0 SQ BD 7 BQ g , Q jg , , j 2 
 
 FEET PER SECOND 
 
54 Hydraulics. 
 
 have been considered at the time the original observations were 
 made. 
 
 39. Bazin's Formula. It has been questioned by many observers 
 whether the slope of the channel has any material influence on the 
 value of the coefficient c. Bazin has derived a formula based on 
 his examination of this subject in which he assumes that c does not 
 vary with the slope. His formula, which is intended for the calcula- 
 tion of flow in open channels is shown, together with a graphical 
 table based thereon, in Fig. 22. This figure illustrates the law of 
 variation of c and is applicable in principle in a general way to all 
 channels and passages. 
 
 The graphical diagram, Fig. 23, which was prepared by the writer 
 in connection with Mr. J. W. Alvord, affords a ready method of 
 solving Chezy's formula (13). 
 
 40. Efficiency of Section. From equations (12) and (13) 
 
 v = c T/^- = c ^/^p 
 
 (15) q = velocity X area = va 
 
 or q = ca^/rs = ca,. J -? 
 
 ' jo 3 
 
 "With c and s constant q varies as a-/r or as A | 
 
 \p 
 
 From this the conclusion may be drawn that other things being 
 equal the maximum quantity of water will pass through any sec- 
 tion of any river or other channel in which the hydraulic radius is 
 a maximum or the wetted perimeter a minimum. Where a choice 
 exists as to the class of material with which the channel is to be 
 lined c becomes a variable and q will vary as 
 
 ca i/r or as c *fi 
 
 That is to say, under circumstances where different characters of 
 lining may be used the maximum quantity will pass a given sec- 
 tion with c and r maximum or with c a maximum and p a minimum 
 for given a. 
 
 41. Determination of Canal Cross-section. The velocity of the 
 water in any artificial channel must be limited by the class of ma- 
 terial used in its construction and the head which it is found prac- 
 ticable to use. As noted above the efficiency of a section is greatest 
 with the value of p minimum. Therefore, the semi-circular sec- 
 tion is the most advantageous cross-section that can be used in a 
 channel where resistance alone is considered and when the canal 
 
Determination of Canal Cross-section. 
 
 55 
 
 is to be lined with material which can be readily shaped into this 
 form. If the canal is to be lined with stone masonry it is fre- 
 quently more advantageous to make the face perpendicular and 
 to place the batter of the wall at the back. Where the canal is cut 
 from stone or shales which will not readily disintegrate in contact 
 with the water, a slope of 90 to 40 may be sometimes used. 
 Quite steep slopes can also be used with dry masonry walls. In 
 material which can be handled with pick and shovel, slopes may be 
 used from I to 1.25 to I to 1.50. With artificial banks of dirt and 
 gravel a less slope angle is necessary and the slope must frequently 
 be made as low as one to two. 
 
 Table VI, which is taken partially from "Uber Wasserkraft und 
 Wasser Versorgungsanlagen," by Ferdinand Schlotthauer, is of 
 considerable value in determining the most advantageous cross- 
 section in various sections which may be adopted in the construc- 
 tion of a canal. As seen in the discussion above, the most advan- 
 tageous cross-section, other things being equal, is that in which the 
 
 r \ . 
 
 
 
 A 
 
 Fig. 24. 
 
 wetted perimeter is a minimum or the hydraulic radius is a maxi- 
 mum. The following general discussion of the relations is based 
 on Fig. 24. From this figure it will be seen that 
 
 (16) a = bd + d 2 cotor 
 
 (17) p = b -f 2d cosec a 
 The transposition of (i/) gives 
 
 ^18) b == p 2d cosec a 
 
 Substituting (18) in (16) 
 
 (19) a = dp 2d 2 coseca -f- d 2 cotor 
 
 The above equation now contains the area, depth, wetted peri- 
 meter and functions of the slope angle, in this case a constant. 
 The conditions of maximum efficiency of a canal section require 
 
56 Hydraulics. 
 
 that the wetted perimeter be a minimum or what amounts to the 
 same thing with a given wetted perimeter the area a must become 
 a maximum. The value of d which makes a the maximum is de- 
 
 termined by putting - = o 
 
 (20) = p _ 4d cosec a + 2d cota 
 
 (21) . = p 4d cosec a + 2d cota 
 
 ~" 4 coseca 2 cota 
 Substituting for p its value in (17) 
 
 b 4- 2d cosec a 
 
 (23) d = 
 
 4 cosec a 2 cota 
 Equation (16) transposed reads 
 
 (24) b = a - d d 2c0ta 
 
 Substituting this value in (23) we have 
 
 - -- d coto: -f- 2d cosec a 
 
 
 4 cosec a 2 cot a: 
 Clearing: 
 
 (26) 4d 2 cosec a 2d 2 cota = a d~cota -f 2d 2 coseca 
 Transposing: 
 
 (27) d 2 = - - - - - 
 
 2coseca cota 
 
 Transforming trigonometric functions 
 
 (28) d 2 = 2 
 
 -: cos a cosec a. 
 
 gin a 
 
 (29) = 2 sin a cos a cosec a 
 
 sin a 
 
 (30) 
 
 2 cos a: 
 Finally: 
 
 (31) d = 
 
 a sm a 
 
 2 cos a 
 Equation (24) may be written 
 
 (32) b = -| dcoto- 
 
 Table VI is calculated from the formulas 
 
 (31) d = J a Sln a 
 
 \2 cos a 
 
Determination of Canal Cross-section, 
 
 W 2 
 
 
 o 
 
 1 S 
 
 *1 
 
 -C s-l 0) 
 
 II 
 
 ^s 
 
 ft 
 Q 
 
 T*J ft 
 
 a 
 
 
 I* i U I 
 
 ^ ^ ^ i 
 
 GO GO CO 
 
 CO CO CO *O 
 
 i* l U I 
 
 cS oS I 03 
 
 CO CO 1C 
 O3 CO O 
 00 CO i> 
 
 U Ice L 
 
 CO CO (M 
 
 
 los ios | 
 
 311 
 
 IcS - I 
 
 <M 
 
 los L,U U I 03 IcS 
 
 ^ ^' ^ >. V ^ 
 
 ^ C^ C^ 1 CO GO CO 
 
 i I CC r-5 O < i O 
 
 Tf GO CD 1C Tf CO 
 
 U los 
 
 S 8 
 
 lea Ics loj I 
 
 5r <^> 
 1C O 
 
 C5 O r-i 
 
 I I 1 
 
 Ij, 2 
 
 So 
 9) 
 
 CO 
 
 57 
 
58 Hydraulics. 
 
 (32) b = -| d cot a 
 
 (33) B = b + 2dcoto: 
 
 (34) p = b+-^ 
 
 sin a 
 
 In the above, a=cross-section area; d=depth of water in channel; 
 b bottom width ; B=width at water level ; p=wetted perimeter ; 
 
 c=the length of slope which is equal to 
 
 sin a: 
 
 In Table VI the relation of these functions, for the slopes ordi- 
 narily used in practice have been calculated as well as for the semi- 
 circular section. The use of the table may be illustrated as fol- 
 lows : The quantity of water which it is desired to deliver is de- 
 termined by the conditions of the problem or by measurement. The 
 velocity to be maintained in the channel is determined by the ex- 
 isting slope, the nature of material encountered, or the friction 
 head which it is found desirable to maintain. The area of the 
 cross-section required to carry the quantity q with velocity v is 
 a=-^- After the slope angle has been selected, for the material in 
 which the channel is to be constructed, the corresponding values 
 may be taken out of the table from their respective columns and 
 multiplied by the square root of a. The result thus obtained gives 
 the desired dimensions. If, for example, we desire to carry 100 
 cu. ft. of water per second in a canal at a velocity of 2~ 1/2 ft. per 
 second at which velocity small pebbles are unaffected, and with a 
 side slope of 1.5 to I, which is suitable for loose earth, has been 
 decided upon, the required area of cross-section will be 100/2.5 
 =40 sq. ft. The square root of 40 is 6.33. The required dimensions 
 of canal as taken from the table are 
 
 Depth d= 689 x 6.33=4.36 ft. 
 
 Bottom width b 418 x 6.33=2.65 ft. 
 
 Top width 6=2.485 x 6.33=15.73 ft. and 
 
 The wetted perimeter p=2.9O4 x 6.33=18.38 ft. 
 Computation of the area from the above dimensions gives 40 sq. ft. 
 Hence the work has been checked. 
 
 42. The Back Water Curve. One of the problems which be- 
 comes very important in many water power installations is the 
 effect on the elevations of the stream produced by the erection of 
 a dam or other obstruction therein. The back water curve can best 
 be determined by the use of the simple formula of flow, equa- 
 tion (13). 
 
Flow of Water in Pipes. 50 
 
 (13) v = Cv/riT 
 
 From this, as shown in equation (15) 
 
 (15) q* = v'a* = 2f5j!l 
 
 From this equation can be derived 
 
 *> ". = = X i 
 
 With L constant, h 3 : h' 3 ::-- : --, therefore 
 
 3 3 
 
 That is to say, with the quantity of water and length of section 
 constant, if the coefficient remains constant the head due to any 
 obstruction will vary in accordance with equation (36). 
 
 Where the water is greatly deepened in proportion to its orig- 
 inal depth the value of c will not remain constant but will vary. 
 Where such is the case and where q 2 ! is constant, under which 
 condition 
 
 h 3 n'a 3 p 2 ha 2 rp z 
 
 /Q7\ -L.t v/ *^ 
 
 W'J n 3 ^/ 3 ^ A -7T , , , o 
 
 The difficulties in the determination of the value of c are, of 
 course, obvious, but it is believed that the back water curve can 
 be closely calculated by this simple formula in which the new 
 value of c is the only factor to be estimated, and where the other 
 elements of the problem can be determined by actual measure- 
 ments. In using this formula the original value of c under exist- 
 ing condition of flow can be determined by calculation based on 
 actual observation of flow under different conditions of water and 
 the conditions of the channel under the new regimen can be 
 closely estimated. New values of c can be very closely estimated 
 on the basis of the values known to exist under other similar cir- 
 cumstances. This method will permit of a more practical solution 
 of the problem than by the use of formulas based on entirely the- 
 oretical consideration of conditions which can never be approxi- 
 mated in practice. 
 
 43. Flow of Water in Pipes. Mathematical expressions for the 
 flow of water in pipes may be derived from either of the funda- 
 mental hydraulic formulas 
 
 v = CI/TS~ or v = c-/2gh, 
 Starting with the former equation, in the case of a pipe flowing 
 
60 Hydraulics. 
 
 full the hydraulic radius r - -where d is the diameter of the pipe 
 and for s we may substitute -^ We then have 
 (38) '= 
 
 In a pipe of unit length and unit diameter without friction the 
 flow would be expressed by the formula 
 
 v 3 
 v = i/2gh or h = -JT 
 
 To modify this for friction a friction factor f is introduced and the' 
 equation then reads : 
 
 The friction varies . directly as the length and is assumed to vary 
 inversely as the diameter. Hence, for any pipe of length 1 and 
 diameter d the complete equation is : 
 
 (39) h 3 = f JL -Xl or v : 
 
 Placing (38) and (39) equal it will be found that 
 
 16.04 
 
 iso that the equations can be made equivalent by the proper modi- 
 fications of friction factors. An extensively used formula for the 
 determination of c in equation (38) is that of Darcy. It reads : 
 
 (40) C = 7^ = ^ = 
 
 For new pipe a = .00007726 and ft .00009647. 
 For old pipe a = .0001543 and ft = .00001291. 
 
 These coefficients were determined from experiments on small 
 pipes and therefore in the case of large pipes with high velocities 
 the velocities computed by this formula are too small. 
 
 Various modifications of the Chezy formula, having the general 
 form 
 
 (41) v = cr n s m 
 
 have been proposed or derived from experiments. Lampes and 
 Flamant's are the best known of this type. Lampes reads 
 
 (42) V = 77.68dO.694 S 0.555 
 
 and Flamant's 
 
 (43) v = cd* s* 
 
 in which c 76.28 for old cast iron pipe and 86.3 for new pipe. 
 
Flow of Water in Pipes. 
 
 LOSS OF HEAD IN FEET PER 100 FEET 
 
 61 
 
62 
 
 Hydraulics. 
 
 The value of c in the formula v=c\/rs may vary from 75 to 150- 
 for large cast iron pipe. For riveted steel pipe the coefficient varies 
 but little with velocity and diameter and at ordinary velocities 
 ranges from 100 to 115. A. L. Adams gives values of c for wood 
 stave pipe ranging from 100 to 170. Experiments on the Ogden 
 pipe line showed average values of about 120. 
 
 An examination of the various formulas proposed for calculating 
 the flow of water in pipes will show a very wide range of results 
 For example, for calculating the head lost in a four-foot new cast 
 iron pipe, some of the principal formulas offered and the graphical 
 solution of the same are shown by Fig. 25. From these results it 
 will be seen that the data from which the formulas were derived 
 are evidently obtained under widely varying conditions and that 
 in the relation of such formulas for use on important work, they 
 must be chosen after a careful consideration of all the elements of 
 the problem, and that it is usually much better, when possible, to 
 utilize the original data and observation along similar lines when 
 such can be obtained, and derive the formula to be used instead of 
 accepting one whose basis may be obscure or unknown. 
 
 In construction where pipes are short and comparatively unim- 
 portant, a formula may be selected' which seems to agree with the 
 
 ASPHALT COATED 
 CAST IRON PIPE 
 BY TUTTON'S FORMULA 
 s 
 
 0.00" 
 
 6.0 
 
 Fig. 26. 
 
Flow of Water in Pipes. 
 
 LAP-RIVETED i 
 
 BY TUTTON'S FORMULA * 
 
 Fig. 27. 
 
 0.15 
 0.14 
 0.13 
 0.12 
 0.11 
 0.10 
 0.09 
 O.OB 
 0.07 
 006 
 O.OS 
 0.04 
 0.03 
 0.02 
 0.01 
 0.00 
 
 
 WOOD-STAVE PIPE 
 BY TUTTONS FORMULA 
 V =IS5R 6B S b ' 
 
 4 
 
 
 
 
 
 
 / 
 
 
 
 
 
 / 
 
 
 
 1.4 
 1.3 
 1.2 
 I.I 
 1.0 
 0.9 
 0.8 
 0.7 
 0.6 
 0.5 
 0.4 
 0.3 
 0.2 
 O.I 
 
 o.o. 
 
 
 ? 
 
 
 
 
 / / 
 
 
 
 
 
 / 
 
 
 
 
 / 
 
 
 
 
 v 
 
 / 
 
 
 
 
 / 
 
 
 
 
 x 
 
 
 / 
 
 
 
 
 / 
 
 
 
 / 
 
 X 
 
 
 
 fr 
 
 
 
 ^ 
 
 X 
 
 
 
 ^ 
 
 
 
 ^ 
 
 - 
 
 y 
 
 
 
 / 
 
 f 
 
 
 
 X 
 
 
 
 X 
 
 
 
 
 _ 
 
 / 
 
 
 
 x' 
 
 
 
 x 
 
 
 
 
 
 & 
 
 ':> 
 
 ^ 
 
 X 
 
 
 ^ 
 
 ^ 
 
 
 
 
 x 
 
 X s 
 
 
 S 
 
 f 
 
 -X* 
 
 <"** 
 
 
 
 . 
 
 X 
 
 ^ 
 
 
 
 
 
 
 
 Ix 
 
 '. 
 
 ^ 
 
 
 
 
 ,.x 
 
 ^' 
 
 
 
 
 
 
 
 x 
 
 /I x 
 
 / 
 
 r.. 
 
 i 
 
 ^ < 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 
 r 
 
 i 
 
 -^ r " 
 
 
 
 
 
 
 
 
 
 
 
 
 Lx 
 
 ^ 
 
 ^ 
 
 ^ 
 
 ;:; 
 
 ^ 
 
 
 
 ^ 
 
 5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^Z- 
 
 . 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2.0 
 
 
 3.0 
 
 4.0 SO 6.C 
 
 VELOCITY IN FEET PER SECOND 
 
 Fig. 28. 
 
64 Hydraulics. 
 
 elements of the problem. The formulas offered by Tutton seem 
 to agree well with the actual results of experiments and several 
 diagrams based thereon are shown in the following pages. In two 
 of these diagrams (Figs. 26 and 27) the limiting values are shown 
 and the results obtained from any pipe of the character represented 
 therein should lie between these limits depending on its condition. 
 44. The Flow of Water Through Orifices. It is found that 
 water flowing through an orifice in the side of a vessel acquires 
 a velocity practically equal to that which would be acquired by a 
 falling body in passing through a space equal to the head above 
 the center of the opening, i. e., 
 
 (44) v= i/2gh = 8.025/E 
 
 in which 
 
 v=velocity of spouting jet. 
 g=acceleration of gravity=32.2. 
 h=head on opening. 
 
 The discharge through the opening would therefore be (45) q= 
 va=aV 2 gh or practically (46) q=ca\/2gh where c is a coefficient 
 varying with the size and shape of the orifice and with various 
 other factors. 
 
 A more accurate determination of the theory of flow through a 
 given orifice is derived as follows: 
 
 If a thin opening is considered at a depth y be- 
 low the surface the discharge through the ele- 
 mentary section Idy would be 
 
 I 1 
 
 (47) dq = Idy 1 /2gy 
 
 Integrating this equation between the limits 
 2 and h i we obtain the following: 
 Fig. 29. 
 
 (48) q = |l(h a * h,^)v/2g~ or practically 
 
 (49) q = mfl l /2^(hj-h 1 f ) 
 
 m being the coefficient of practical modification due to condition 
 of the orifice. 
 
 45. Flow Over Weirs. In a weir h 1 =o. Hence equation (49) 
 becomes 
 
 (50) q = m (Dl/gg h* 
 
 in which h is the head on the crest of the weir. That is, the ver- 
 tical distance from the water level above to the crest of the weir. 
 
Flow Over Weirs. 
 
 For practical use the coefficient m together with the constants 
 
 ~ and 2g are combined as follows: 
 
 o 
 
 c = m i/2g = M !/2g and equation (50) becomes 
 
 (51) 
 
 = c 
 
 The value of m and consequently of c varies with the shape of 
 the weir and with other factors and must be determined experi- 
 mentally. This has been done with weirs of many forms, both by 
 Bazin in France and by Rafter and Williams at the Cornell hydrau- 
 lic laboratory. The results of these experimental determinations 
 are given by Figs. 30 to 34, .inclusive. These figures are reduced 
 directly from the diagrams of Mr. Rafter in the Report of the 
 Board of Engineers of Deep Waterways, 1900. 
 
 In practice many weir formulas are in use, based on various ex- 
 periments and observations. The formula of Francis', equation 
 (52), is probably the best known in this country. It is best adapted 
 to long, sharp crested weirs without end contractions. 
 
 (52) 
 
 q = 3.32 111* 
 
 oo 
 
 Head on Crest of Weir in 
 
 Fig. 30. Weir Coefficients for Weirs of Various Shapes. 
 
66 
 
 Hydraulics. 
 
 ad on Crest of Weir in Peer 
 
 ZO 3.O 4.0 
 
 Head on Crest of Weir in Feet 
 
 Fig. 31. Weir Coefficients for Weirs of Various shapes. 
 
Flow Over Weirs. 
 
 Head on Crest of Weir in feet 
 
 9n 10 4 
 
 Head on Crest of Weir in Feet 
 
 Fig. 32. Weir Coefficients for Weirs of Various Shapes. 
 
Bazin, Series 
 
 Flat crested V 
 
 3M. (e.56 Feet) wic 
 
 Ftefey and Stearns' Experiments E 
 not crested 
 
 MuHln's Formuk 
 Fiat crested w 
 Width of Crest, 
 
 3.O 40 50 60 7.O SO 9O IO.O HO 120 !3O 
 
 Discharge in Cubic Feet per second 
 
 Figu 
 
Francis' Formula for 
 Merrimack Dam. 
 
 rancfs' Formula. 
 Sharp crested Weir. 
 
 Muttirva Formula, 
 "Sharp crested Wefr 
 
 Bazin's Formula fbr a 
 High sharp c res-ted Weir 
 
 Feet 
 
 U.S.BOARD OF ENGINEERS ON DEEP WATERWAYS 
 WATER SUPPLY DIVISION. 
 
 Dmparative Discharqe over Weirs, by different Formulae, 
 For a Single Foot of Crest. 
 
 Barirrs Formula, Q-mLHVSqR 
 
 Crest, measured from trie 
 of sf fi Water, in feet. 
 
 of Discharge, derived by 
 t fbr ach Form of Weir ' 
 Francis' Formula fbr a Sharp Cnesfea Weir. 
 
 Formufq fbr Oam on tfie Mern'mac 
 f?iver, at Lawrence, Mass 
 Q 3.01206 LH' 
 
 FrizeilS Formula fora Flat Crested weir 
 
 Q-309LH* 
 Muiiin's Formula, used by Cast Indian Engineers 
 
 Q-S.SSLCH^ 
 
 For a Sharp Crest-eo Weir 
 
 >Q654-O.OIH 
 For a riot crested 
 
 To accompany Report on Special 
 Water Supply Investigation 
 
 'o TTO 155 lao" 5o5 5rS 555 eio 84-o 55 2&o ?r 
 
 one linear Foot of Crest. 
 
 .^-P-AK 
 
7o 
 
 Hydraulics. 
 
 Head on Crest of Weir in Feet 
 
 00 
 
 Head on Crest of Weir in Feet. 
 
 Fig. 33. Weir Coefficients for Weirs of Various Shapes. 
 
Flow Over Weirs. 
 
 
 
 Head on Crest 
 
 19 20 
 
 of 
 
 f- 
 
 Weir in Feet . 
 
 45 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 ^ 
 
 ^f 
 
 :f 
 
 a 
 
 si 
 
 ;t4 
 
 I 
 
 s 
 
 EE:: 
 
 
 
 
 
 
 
 
 44 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Sf 
 
 
 5 
 
 
 ^ 
 
 i 
 
 =1 
 
 t 
 
 N 
 
 
 5 G ~J - 
 
 
 
 
 
 J 
 
 t: 
 
 
 
 4* 
 
 
 
 -T~ 
 
 i 
 
 
 - 
 
 
 -ir* 
 
 I 
 
 f> 
 
 
 
 
 
 
 
 
 T 
 
 
 
 
 
 
 
 1 
 
 M 
 
 Mii 
 
 ii 
 
 e 
 
 K 
 
 TH- 
 
 i: 
 
 
 
 s 
 
 $z 
 
 u 
 
 10 
 
 i. 
 
 4- 
 
 '^ 
 
 z: 
 
 - 
 
 ]f 
 
 i 
 
 n 
 
 
 H ~ 
 
 i 
 i 
 
 \ 
 
 ? 
 T 
 
 -- 
 
 -1 
 
 i 
 
 -i 
 r? 
 
 fe 
 
 r 
 
 -r 
 
 pitt 
 
 fnie 
 
 n 
 
 IT 
 
 P 
 
 e 
 
 
 ^ 
 
 -r 
 
 
 
 
 ~r~|" 
 
 
 
 
 
 
 
 ^~ 
 
 4.5 
 f 4,1 
 
 t 
 
 ~: 
 
 h- 
 - : 
 
 ^ 
 
 i_J 
 
 :i 
 
 +- 
 
 if 
 ii 
 
 fc 
 
 n 
 p 
 
 Ota 
 
 i 
 
 3 C k 
 
 ! q 
 
 II 
 
 Efc 
 
 * 
 
 I! 
 
 a 
 
 P 
 5 
 
 U 
 
 r<a 
 n 
 
 V J 
 I 
 
 e 
 
 
 a 
 
 *~-"^ 
 
 44 
 
 ^, 
 ^ 
 
 i- 
 
 * 
 
 . 
 
 *^ 
 
 ^ 
 
 
 
 T 
 
 *^ 
 
 
 
 i. 
 
 i 
 
 i 
 
 *i-. 
 
 C 
 rT"i~" 
 
 =4 . 
 
 P- j . 
 
 =3 
 
 ^ 
 
 = 
 
 K 
 
 =r a 
 
 1 i_ 
 
 - 1 
 
 " ^ 
 
 34 
 
 
 
 
 
 
 
 
 
 
 * 
 
 
 - 
 
 
 - 
 
 JE 
 
 
 tf 
 
 n 
 
 1 
 
 * 
 
 H5 
 
 - f 
 
 s 
 
 ^ 
 
 1 
 
 b 
 
 H 
 
 i 
 
 li 
 
 -r-- 
 f 
 
 Ifr 
 
 ii 
 
 
 i 
 
 ^nJ 
 
 Illl 
 
 E: 
 
 ] S 11 i 
 
 ' 
 
 
 
 
 
 
 L. 
 
 MM 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r. 
 
 
 = & 
 
 1 
 
 
 
 
 i 
 
 i 
 
 
 j * 
 
 ^-^ 
 
 iEE: 
 
 *K 
 
 "m. 
 
 =j 
 
 v - 
 
 . M * 
 
 ~~ 
 
 M > 
 
 C3f 
 
 2^ 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 2.-0 
 
 
 -i 
 
 r 
 
 r * 
 
 i* 
 
 
 m 
 
 III 
 
 c 
 
 X 
 
 S f1 
 
 ^ 
 I 
 
 3! 
 
 id 
 
 ^ 
 
 3 
 
 ==i 
 T ' 
 
 i 
 
 F 5 
 
 , 1 - 
 
 = 
 
 
 
 
 
 
 aa 
 
 BM 
 
 
 
 v 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - -Q 
 
 K 
 
 
 
 w 
 
 19 
 
 
 fll 
 
 1 
 
 t 
 
 3^ 
 
 -=i 
 
 k. 
 +* 
 
 FT 
 
 ^ 
 
 a 
 
 rr 
 
 rfl 
 
 (t 
 
 "VI- 
 
 ^^ 
 
 - 
 
 ii 
 
 sj 3^. 
 
 f>^ 
 
 izz: 
 
 
 
 
 
 
 
 --4 
 
 1 
 
 ^ 
 
 
 
 
 
 
 I.O 
 
 
 
 
 I 
 
 i 
 
 
 Heo 
 
 d o 
 
 n 
 
 c 
 
 > 
 
 e 
 
 ST 
 
 4 
 
 v\ 
 
 1 
 reiri 
 
 n Fe< 
 
 tf 
 
 
 
 
 
 
 B 
 
 Fig. 34. Weir Coefficients for Weirs of Various Shapes. 
 
To accompany Report on Specjai 
 Water Supply Ir.v/esJiqation 
 
 1899 
 
 - MS BOARD OF ENGINEERS ON DEEP WATERWAYS 
 
 WATER SUPPLY DIVISION 
 Diaaram showing over Weirs with 
 
 Ser 
 
 :t- x 
 
 a sharp cresied we,r 
 
 me- 
 
 Discharge 
 
 in Cubic Feet per 
 
Sections cf experimental Weirs. 
 
 Direction of now 
 
 M 656 
 
 Series No. 1 17 
 
 162 
 
 173. 
 
 130. 
 
 170 
 
 Header 
 
 Crest of 
 Vetr in 
 
 nisrhartge over Weir, for a lenqrth of one Foot, in Cubic Feet per Second.(Approx.mate, 
 
 Series No 117 
 
 168 
 
 173 
 
 135 
 
 130. 
 
 170 
 
 Sharp gWMte- 
 
 Off' 
 0.5 
 
 10 
 
 IS 
 2.0 
 25 
 30 
 3.5 
 
 098 
 295 
 555 
 856 
 
 teas 
 
 1583 
 MOO 
 SA45 
 
 6.0 
 148 
 
 420 
 750 
 II 35 
 
 1568 
 2040 
 3545 
 
 0.0 ' 
 1.16 
 958 
 686 
 1085 
 15.40 
 2038 
 25.80 
 31 53 
 
 1.20 
 370 
 7.ZO 
 11.45 
 16.50 
 82.04- 
 28.15 
 34.75 
 
 i.se 
 
 396 
 7.6O 
 I2.0O 
 I7.OO 
 SB. 56 
 2660 
 35.15 
 
 1.20 
 3.90 
 7.6* 
 
 IE05 
 17 l 
 22.S5 
 29.10 
 3568 
 
 1 10 
 333 
 
 eie 
 
 942 
 13.16 
 17.30 
 2I9O 
 86.64 
 
 1 1 1 I 
 
 
 J 1 1 , 
 
 
 I 
 
 L 1 
 
 
 1 
 
 iss 196 ao.o ?rb sso g3 
 br one linear Foot of Crest. 
 
 o afar SB'O gfio 870 auo iiao AO.O *io -NIU ^^ ^* u JWU .,-- 
 
 ire 36. 
 
74 
 
 Hydraulics. 
 
 A number of different tormtilas for the flow over weirs are given 
 on Fig. 35 and the flow as calculated by these formulas is shown 
 on the diagram. L in these formulas represents the length of the 
 weir crest which. in the dimension above is represented by 1. 
 
 Figure 26 shows graphically the results of the application of the 
 value of c as given on Figs. 30 to 34 as compared with Francis* 
 formula. 
 
 In small weirs the effect of end contraction and of the velocity 
 of approach becomes important and corrections to the formulas 
 must be applied in order to allow for those influences. 
 
 If n =the number of end contractions and the effect of each is to 
 reduce the effective length of the weir by one-tenth the head on the 
 weir, equation (51) will become 
 
 (53) 
 
 q = c (1 - n 
 
 * 
 
 
 The effect of the velocity of approach is to reduce the head on 
 the weir by the velocity head. This reduction is given by the 
 formula : 
 
 (54) ht== lJF 
 
 in which v'=velocity of approach and h'=velocity head. 
 
 TABLE VII. 
 
 Coefficient of discharge C for use with Hamilton Smith, Jr.' 's formula (56} for 
 flow of water over sharp crested weirs having full contraction. 
 1 = length of weir. 
 
 Effective 
 head =h 
 
 .66 
 
 1(?) 
 
 
 
 2.6 
 
 3 
 
 4 
 
 5 
 
 7 
 
 10 
 
 15 
 
 19 
 
 .1 
 .15 
 .2 
 .25 
 .3 
 .4 
 .5 
 .6 
 .7 
 g 
 
 .632 
 .619 
 .611 
 .605 
 .601 
 .595 
 .590 
 .587 
 .585 
 
 .639 
 .625 
 .618 
 .612 
 .608 
 .601 
 .596 
 .593 
 .590 
 
 .646 
 .634 
 .626 
 .621 
 .616 
 .609 
 .605 
 .601 
 .598 
 595 
 
 .650 
 .637 
 .629 
 .623 
 .618 
 .612 
 .607 
 .604 
 .601 
 598 
 
 .052 
 .638 
 .630 
 .624 
 .619 
 .613 
 .608 
 .605 
 .603 
 600 
 
 .053 
 .639 
 .631 
 .625 
 .621 
 .614 
 .610 
 .607 
 .604 
 602 
 
 .653 
 .640 
 .631 
 .626 
 .621 
 .615 
 .611 
 .608 
 .606 
 604 
 
 .654 
 .640 
 .632 
 .627 
 .623 
 .617 
 .613 
 .611 
 .609 
 .607 
 
 .655 
 .641 
 .633 
 .628 
 .624 
 .618 
 .615 
 .613 
 .612 
 .611 
 
 .655 
 .642 
 .634 
 .628 
 .624 
 .619 
 .616 
 .614 
 .613 
 61? 
 
 .656 
 .642 
 .634 
 .629 
 .625 
 .620 
 .617 
 .615 
 .614 
 618 
 
 9 
 
 
 
 592 
 
 596 
 
 598 
 
 600 
 
 .603 
 
 .606 
 
 .609 
 
 611 
 
 61? 
 
 1 
 
 
 
 590 
 
 593 
 
 595 
 
 .598 
 
 .601 
 
 .604 
 
 .608 
 
 610 
 
 11 
 
 1 i 
 
 
 
 .587 
 
 .591 
 
 .593 
 
 .596 
 
 .599 
 
 .603 
 
 .606 
 
 609 
 
 610 
 
 1 2 
 
 
 
 .585 
 
 .589 
 
 .591 
 
 .594 
 
 .597 
 
 .601 
 
 .605 
 
 .608 
 
 .610 
 
 1 3 
 
 
 
 .582 
 
 .586 
 
 .589 
 
 .592 
 
 .596 
 
 .599 
 
 .604 
 
 .607 
 
 .609 
 
 1 4 
 
 
 
 .580 
 
 584 
 
 587 
 
 .590 
 
 .594 
 
 .598 
 
 .602 
 
 fiOfi 
 
 609 
 
 1 5 
 
 
 
 
 582 
 
 585 
 
 .589 
 
 .592 
 
 .596 
 
 .601 
 
 605 
 
 .608 
 
 1 6 
 
 
 
 
 .580 
 
 .582 
 
 .587 
 
 .591 
 
 .595 
 
 .600 
 
 .604 
 
 .607 
 
 1.7 
 
 
 
 
 
 
 
 
 .594 
 
 .599 
 
 .603 
 
 .607 
 
 2.0 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
Literature. 
 
 75 
 
 To allow for the influence of velocity of approach h' must be 
 added to h and equation (53) becomes 
 
 (55) q = c(l-ni)(h + hi)* 
 
 Experimental results at the hydraulic laboratory of the Uni- 
 versity of AVisconsin show that for small sharp crested weirs, with 
 end contraction, the formula (56) of Hamilton Smith, Jr., is prac- 
 tically correct: 
 
 (56) q = c /2 IbJ 
 In this formula 
 
 c=coefficient of discharge (to be taken from Table VII). 
 h=observed head on crest (H) plus correction due to velocity 
 of approach. 
 
 Variations in the forms of the crest of weirs and in the arrange- 
 
 o 
 
 ment of sides and bottom of the channel of approach cause con- 
 siderable variation in their discharging capacity. It is therefore 
 apparent that unless the conditions closely agree with those on 
 which experimental data is available that the error of calculation 
 may be considerable. 
 
 LITERATURE. 
 
 REFERENCES ON GENERAL HYDRAULICS. 
 
 1. Francis, Jas. B. Lowell Hydraulic Experiments. New York. D. Van- 
 
 Nostrand. 1883. 
 
 2. Fanning, J. T. Hydraulic and Water Supply Engineering. New York. 
 
 D. Van Nostrand & Co. 1886. 
 :3. Smith, Hamilton, Jr. The Flow of Water Through Orifices, over Weirs, 
 
 and through Open Conduits and Pipes. New York. Wiley & 
 
 Sons. 1886. 
 3a. Church, Irving P. A treatise on Hydraulics. New York, Wiley & Sons, 
 
 4. Weisbach, P. J. Hydraulics and Hydraulic Motors. Translated by A. 
 
 Jay Dubois. New York, Wiley & Sons. 1891. 
 
 5. Carpenter, L. G. Measurement and Division of Water. Bulletin No. 27, 
 
 Colo. Agri'c. Expt. Sta., Ft. Collins, Colo. 1894. 
 
 6. Bovey, Henry T. A Treatise on Hydraulics. New York. Wiley & Sons. 
 
 1895. 
 
 7. Merriman, Mansfield. Treatise on Hydraulics. New York. Wiley & 
 
 Sons. 1903. 
 
 8. Hydrographic Manual, Water Supply and Irrigation Paper No. 94. U. S. 
 
 G. S. 1904. 
 9. Hoskins, L. M. Hydraulics. New York, Henry Holt & Co. 1907. 
 
 REFERENCES ON FLOW OF WATER IN CANALS. 
 
 10. Hill, A. Flow o^ Water in Rivers and Canals. Van. Nost. Eng. Mag. 
 Vol. 3, p. 118. 1870. 
 
76 Hydraulics. 
 
 11. Gangtiillet, E. Uniform Motion in Canals and Rivers. Van. Nost. Eng. 
 
 Mag. Vol. 2, p. 211. 1870. 
 
 12. Searles, W. H. Slope of Water Surface in the Erie Canal. Trans. Am. 
 
 Soc. C. E., Vol. G, pp. 290-296. 1877. 
 
 13. Ellis, Theo. G. Flow of Water. Eng. News, Nov. 26, 1881, Vol. 8, pp. 
 
 478-9. 
 
 14. Cunningham, Allan. General Discussion of Flow in Canals. Proc. Inst. 
 
 Civ. Eng. 1882-83, pp. 1-95. 
 
 15. Fteley, A. and Stearns, F. P. Flow of Water in Conduits. Trans. Am. 
 
 Soc. C. E., Vol. 12 (1883), p. 114. 
 
 16. Flynn, P. J. Irrigation Canals and Other Irrigation Works and Flow of 
 
 Water in Irrigation Canals. Denver, Colo. 1892. 
 
 17. Adams, A. L. Diagram for Calculating Velocities, Grades and Mean 
 
 Radii for Flumes and Ditche3. Eng. News, Feb. 13, 1892, p. 157. 
 
 18. Ganguillet, E. and Kutter, W. R. A General Formula for the Uniform 
 
 Flow of Water in Rivers and Other Channels. Trans, by Ru- 
 dolph Herring and John Trautwine. New York, Wiley & Sons. 
 1893. 
 
 19. Boussinesq, H. The Gradual Variations in the Flow of Water in Chan- 
 
 nels of Large Section. Comptes Rendus^ May 31, 1897. 
 
 20. Boussinesq, J. Experimental Verification of the Theory of Gradually 
 
 Varied Flow in Open Channels. Comptes Rendus. June 14,. 
 1897. 
 
 21. The New Formula of Bazin. Genie Civil, March 5, 1898. 
 
 22. A New Formula by Bazin for Computing Flow of Water in Open Chan- 
 
 nels. Eng. News, July 14, 1898. 
 
 23. Bazin's New Formula for Flow in Open Channels. Eng. News, 1898, Vol. 
 
 2, p. 26. 
 
 24. A Study of a New Formula for Calculating the Discharge of Open Chan- 
 
 nels. Annales des Fonts et Chaussees. 2 Trimestre, 1898. 
 
 25. Determination of Flow in Rivers and Canals. Zeitschr. d Oesterr. Ing. u> 
 
 Arch. Ver., Vol. 50, pp. 533-534. 1898. 
 
 26. Swan, Chas. H. and Horton, Theo. M. Hydraulic Diagrams for the Dis- 
 
 charge of Conduits 1 and Canals. New York, Eng. News Pub. 
 Co. 1899. 
 
 27. Crosthwaite, Ponsby Moore. Two Graphic Methods Applied to Hydraulic 
 
 Calculations. Engineering. London. July 15, 1898. 
 
 28. Concerning the Conception of a Hydraulic Moment of Conduit Cross Sec- 
 
 tion. Zeitschr. fur Arch, u Ing. Vol. 46, 1900. Heft-Ausgabe. 
 Col. 402-417. 
 
 29. Siedek, Richard. Studies of a New Formula for Estimating the Velocity 
 
 of Water in Brooks and Small Channels. Zeitschr. d Oesterr. 
 Ing. und Arch. Ver. Vol. 55, pp. 98-106. 1903. 
 
 REFERENCES ON FLOW OF WATER THROUGH PIPES. 
 
 30. Francis, Jas. B. Flow Through Pipes. Trans. Am. Soc. C. E. Vol. 2, 
 
 ff p. 45. 1872. 
 
 31. Daaach, C. G. Flow of Water in Pipes under Pressure. Trans. Am. Soc. 
 
 C. E. Vol. 7, p. 114. 1878. 
 
 32. Wehage, H. Friction Resistance in Pipes. Dingler's Polytechnisches 
 
 Journal, 1884, p. 89. 
 
Literature. 77 
 
 33. Stearns, P. P. Flow of Water Through a 48" Pipe. Trans. Am. Soc. C. 
 
 E., Vol. 14, p. 1. 1885. 
 
 34. Mair, J. G. Flow Through Pipes at Different Temperatures. Proc. Inst. 
 
 C. E. Vol. 84, p. 424. 1886. 
 
 35. Duane, James. Effect of Tuberculation on Delivery of a 48" Water Main. 
 
 Trana Am. Soc. C. E. 1893, p. 26. 
 
 36. Tuttle, Geo. W. Economic Velocity of Transmission of Water Through 
 
 Pipes. E'ng. Rec. Sept. 7, 1895. 
 
 37. Coffin, Freeman C. The Friction in Several Pumping Mains. Eng. News, 
 
 Feb. 20, 1896. 
 
 38. Hawks, A. McL. Flowage Test of 14" Riveted Steel Main at New West- 
 
 minster, B. C. Eng. News, July 30, 1896. 
 
 39. Flow of Water in Wrought and Cast Iron Pipe. Am. Soc. Mech. Eng. 
 
 Dec. 1897. 
 
 40. Herschel, Clemens. 115 Experiments on the Carrying Capacity of Large 
 
 Riveted Metal Conduits. New York. John Wiley & Sons. 1897. 
 
 41. Gould, E. Sherman. The Flow of Water in Pipes. Am. Mach. Mar. 3, 
 
 1898. 
 
 42. Hawks, A. McL. Friction Coefficient for Riveted Steel Pipes. Proc. Am. 
 
 Soc. C. E. Aug. 1899. 
 
 43. Fulton, C. H. Flow of Water in Pipes. Jour. Ass'n Eng. Soc. Oct. 1899. 
 
 44. Marx, C. D., Wing, Chas. B., and Hoskins, L. M. Experiments on the 
 
 Flow of Water in the Six Foot Steel and Wood Pipe Line of 
 the Pioneer Electric Power Company. Proc. Am. Soc. C. E. 
 Feb., 1900; April, 1900; May, 1900. 
 
 45. Gregory, John H. Diagram Giving Discharge of Pipes by Kutter's For- 
 
 mula. E'ng. Rec. Nov. 3, 1900. 
 
 46. Formulas for Flow in Pipe. Eng. News, 1901. Vol. II, pp. 98, 118, 332, 
 
 476. 
 
 47. Noble, T. A. Flow of Water in Wood Pipes. Trans. Am. Soc. C. E. Vol. 
 
 49, 1902. 
 
 48. Saph, A. V. and Schoder, E. W. Experimental Study of the Resistance of 
 
 the Flow of Water in Pipes. Proc. Am. Soc. C. E. May, 1903; 
 Oct., 1903. 
 
 BEFEEENCES ON FLOW OF WATER OVER WEIRS. 
 
 49. Fteley, A. and Stearns, F. P. Flow of Water over Weirs. Trans. Am. 
 
 Soc. C. E. Vol. 12, p. 1. 1883. 
 
 50. Francis, J. B. Experiments on Submerged Weirs. Trans. Am. Soc. C. 
 
 E. Vol. 13, p. 303. 1884. 
 
 51. Herschel, Clemens. Problem of the Submerged Weir. Trans. Am. Soc. 
 
 C. E. Vol. 14, p. 189. 1885. 
 
 52. Investigations on the Flow over Submerged Weirs. Zeitschr. des Ver. 
 
 Deutsch. Ing. 1886, p. 47. 
 
 53. Hind, R. H. Flow over Submerged Dams. Proc. Inst. C. E. Vol. 85, p. 
 
 307. 1886. 
 
 54. Kaberstroh, Chas. E. Epxeriments on the Flow of Water Through Large 
 
 Gates and over a Wide Crest. Jour. Ass'n Eng. Soc. Jan., 1890, 
 p. 1. 
 
78 Hydraulics. 
 
 55. The Flow of Water over Dams and Spillways. Eng. Rec. June 2, 1900. 
 
 56. Flow of Water over Sharp Crested Weirs. Annales des Fonts et Chaus- 
 
 sees. Jan. 1, 1890; Nov., 1891; Feb., 1894. Also Proc. Eng. Club 
 of Philadelphia, Jan., 1890; July, 1892; Oct., 1892; Apr., 1893. 
 
 57. Flow over a Weir of Curved Profile. Zeitschr. d Oesterr. Ing. u Arch. 
 
 Ver. June 2, 1905. 
 
 58. Flynn, A. D. and Dyer, C. W. D. The Cippoletti Trapezoidal Weir. 
 
 Trans. Am. Soc. C. E. July, 1894. 
 
 59. Werenskiold, N. Flow of Water over Rounded Crest. Eng. News, Jan. 
 
 31, 1895. Yj^^, p. 75. 
 
 60. Frizzel, J. P. and HJ^^el, Clemens. Flow over Wide Horizontal Top 
 
 Weirs. Eng. News, 1892, Vol. II, pp. 290, 440, 446; 1895, Vol. I, 
 p. 75. 
 
 61. Johnson, T. T. and Cooley, E. S. New Experimental Data for Flow over a 
 
 Broad Crest Dam. Jour. W. Soc. Engrs. Jan., 1896. 
 
 62. Wide Crest Weirs. Bazin's Formula. Eng. News, 1890. Vol. I, p. 162. 
 
 Vol. II, p. 577; 1896, Vol. I, p. 26. 
 
 63. Experiments on Flow over Dams. Eng. News, 1900, p. 207. 
 
 64. Rafter, Geo. W. The Flow of Water over Dams. Proc. Am. Soc. C. E. 
 
 Mar., 1900. 
 
 65. Heyne H. Study of Hydraulic Coefficients. Zeitschr. d Oesterr Ing. u 
 
 Arch. Ver. Dec. 5 1900. 
 
 66. Dery, Victor A. E. D. Experiments on the Measurement of Water over 
 
 Weirs. Proc. Inst. C. E. Vol. 114, p. 333. 1893. 
 
 REFERENCES ON BACK WATER AND INTERFERENCE. 
 
 67. Wood, De Volson. Back Water in Streams as Produced by Dams. Trans. 
 
 Am. Soc. C. E. Vol. 2, pp. 255-261. 1873. 
 
 68. Hutton, W. R. Back Water Caused by Contractions. Trans. Am. Soc. C. 
 
 E. Vol. 11, pp. 212-240. 1882. 
 
 69. Gillmore, Q. A. Obstruction to River Discharge by Bridge Piers. Van. 
 
 Nost. Eng. Mag. Vol. 26, p. 441. 1882. 
 
 70. Back Water from Dams. Eng. Rec. July 9, 1892. 
 
 71. Ferriday, Robert. Measurements of Back Water. Eng. News, 1895, Vol. 
 
 II, p. 28. 
 
 72. Frescolm. S. W. Back Water Caused by Bridge Piers and other Obstruc- 
 
 tions. Jour. Eng. Soc., Lehigh Univ. Feb., 1899. 
 
 73. The Estimation of Damages to Power Plants from Back Water. Eng. 
 
 Rec. April 26, 1902. 
 
 74. Harris, E. G., Taylor, W. D., Ladshaw, Y. E. Back Water from Dams. 
 
 The Effect on Meadow Lands. Eng. News, 1902, Vol. II, pp. 
 142 and 316. 
 
 75. Tables for Computation of Swell on Open Water Courses. Zeitschr. fur 
 
 Arch, und Ing. Vol. 49, Cols. 258-274. 1903. 
 
 76. Fliegner, A. A New Method of Computing the Back Water Curve. 
 
 Schweizerische Bauzeitung. Aug. 22, 1903. 
 
 77. Tolman, Breitslav. The Computation of Back Water Curves. Oesterr. 
 
 Wochenschr. f d Oeffent Baudienst. July 1, 8, 1905. 
 
CHAPTER IV. 
 
 WATER POWER. 
 
 THE STUDY OF THE POWER OF A STREAMlJ^FFECTED BY FLOW. 
 
 46. Source of Water Power. Water power depends primarily 
 on the flow of the stream that is being considered for power pur- 
 poses, and on the head that can be developed and utilized at the 
 site proposed for the power plant. Both head and flow are essen- 
 tial for the development of water power, but both are variable 
 quantities which are seldom constant for two consecutive days at 
 any point in any stream. The variations in head and flow radically 
 affect the power that can be generated by a plant installed folr 
 power purposes. These variations also greatly affect the power 
 that can be economically developed from a stream at any locality. 
 The accurate determination of both head and flow therefore be- 
 comes very important in considering water power installations and 
 hence should receive the careful consideration of the engineer. The 
 neglect of a proper consideration of either or both of these factors 
 has frequently been fatal to the most complete success of water 
 power projects. 
 
 47. Factors of Stream Flow. The quantity of water flowing in a 
 stream at any time, which is more briefly termed "stream flow" 
 or "run-off," depends primarily upon the rainfall. It is, however, 
 influenced by many other elements and conditions. It depends not 
 only upon the total quantity of the yearly rainfall on the drainage 
 area, but also on the intensity and distribution of the rainfall 
 throughout the year. In addition to these factors the geological 
 structure of the drainage area, the topographical features, the sur- 
 face area of the catchment basin, the temperature, the barometric 
 condition, all influence and modify the run-off. Sufficient data is 
 not available for a full understanding of this subject, but enough 
 is available so that the general principles involved can be intelli- 
 gently discussed and the problems considered in such a way as to 
 give a fairly satisfactory basis for practical work. A. knowledge 
 of the importance of the factors above mentioned and the extent to 
 which they modify, influence or control stream flow, is essential 
 
8o Water Power. 
 
 to a broad knowledge of water power engineering. These factors 
 are discussed in more detail in chapters VI, VII and VIII. 
 
 48. Broad Knowledge of Stream Flow Necessary. The flow of 
 a stream is constantly changing and any single measurement of 
 that flow will not furnish sufficient data on which to base an in- 
 telligent estimate of the extent of its possible or even probable 
 economical power development. A knowledge of the economical 
 possibilities of such development must be based upon a much 
 broader knowledge of the variations that take place in the flow of 
 the stream. In order to fully appreciate the power value of a 
 stream, the character and extent of its daily fluctuations must be 
 known or estimated. Averages for the year, monthly averages, and 
 estimates of average power have been ordinarily taken as a basis 
 for water power estimates, but they are more or less misleading, 
 unsatisfactory and uncertain for the reason that such averages in- 
 clude extremes, the maximum of which are often unavailable for 
 water power purposes without more extensive pondage than is 
 usually practicable. These maximum and minimum flows which 
 affect the power of a stream not only through the quantity flowing 
 but also through the head as well, as will be hereafter discussed, 
 are of the utmost importance for a broad consideration of water 
 power. So also is a knowledge of the various stages of flow and 
 the length of time that each will prevail. Such knowledge demands 
 daily observations or estimates of daily flow which can be repre- 
 sented in graphical form by the hydrograph. 
 
 49. The Hydrograph. The hydrograph, constructed for the study 
 of stream flow and its influence on water power, may be drawn by 
 representing the daily flow in cubic feet per second at the point 
 of observation by the ordinates of the diagram and the element of 
 time by the abscissas. (See Fig. 37.) The result is a graphical 
 diagram which shows the character and extent of the daily fluctua- 
 tions in the flow of a stream at the point of observation during the 
 period for which the hydrograph has been prepared. 
 
 A single observation of the flow of a stream represents a totally 
 inadequate and unsatisfactory criterion for water power consid- 
 eration. By reference to Fig. 37 it will be seen that, if the dis- 
 charge of the Wisconsin River at Necedah had been measured only 
 on August 5, 1904, the conclusion would have been reached that 
 the discharge of the river was about 2,100 cubic feet per second. 
 If the measurement had been taken only on August 15, 1904, the 
 flow would have been determined at about 5,850 cubic feet per 
 second, or almost three times as great as on the first date. The 
 
The Hydrograph. 
 
 81 
 
 ON033S H3d 133J 3IBf)3 
 a a a a a 
 cu 
 
 Nl 39HVH08IQ 
 
 ONDa3S_U3d 133J_ 31803 Nl 39UVH3SIO 
 
82 Water Power. 
 
 difference between the dates might be even greater, and no single 
 measurement nor any series of rneasurements for a single week or 
 month would give a fair criterion from which the normal flow of 
 the river could be judged. 
 
 The hydrograph of the daily flow of a river for a single year 
 gives a knowledge of the variation in flow for that year only, 
 under the peculiar conditions of the rainfall, the evaporation, and 
 the other physical factors that modify the same and that obtain 
 for that particular year. Such information, while important, is not 
 altogether sufficient for the purpose of a thorough understanding 
 of the availability of the stream flow for power purposes. Observa- 
 tions show that stream flow varies greatly from year to year, and, 
 while, with a careful study of the influences of the various factors 
 on stream flow, together with a knowledge of the past variations 
 in such factors, the hydrograph for a single year may give a fairly 
 clear knowledge of the variations to be expected in other years 
 where conditions differ considerably, still it is desirable that the 
 observations be extended for as long a period as possible. Such 
 long time observations may remove the estimates of flow entirely 
 irom the domains of speculation and place them on the solid ground 
 of observed facts. Hydrographs of a river that cover the full range 
 of conditions of rainfall, temperature, etc., which are liable to pre- 
 vail on its drainage area,. give a very complete knowledge of the 
 flow of the stream for the purpose of the consideration of water 
 power. 
 
 It is rare, however, that observations of stream flow for a long 
 term of years are available at the immediate site of a proposed 
 power plant. Such observations are ordinarily made only at loca- 
 tions where power has been developed and where water power or 
 similar interests have been centered for a long period of time. Oc- 
 casionally, however, the future value of potential powers is recog- 
 nized and appreciated, and local observations are maintained for a 
 series of years by interested parties, having a sufficient knowledge 
 of the subject to recognize the value and importance of such in- 
 formation. The variation of flow for some considerable time pre- 
 vious to construction is thus available upon which to base the design. 
 
 In .considering new installations, one of four conditions obtains : 
 
 First : Hydrographs are available at the immediate site proposed. 
 
 Second: Hydrographs are available at some other point on the 
 river above or below the proposed installation. 
 
The Use of Local Hydrographs. 83 
 
 Third : Hydrographs are not available on the river in question 
 but are available on other rivers where essentially similar condi- 
 tions of rainfall and stream flow prevail. 
 
 Fourth : No hydrographs, either on the river in question or on 
 other rivers of a similar character and in the immediate vicinity, 
 are available. 
 
 50. The Use of Local Hydrographs. When hydrographs, con- 
 structed from observations taken at the immediate site of the pro- 
 posed water power installation, are obtainable, for a considerable 
 number of years, the most satisfactory -character of information is 
 available for the consideration of a water power project. Under 
 such conditions the engineer is not obliged to consider the rela- 
 tion of rainfall to run-off or to speculate as to the relative value of 
 the stream in question compared with other adjacent streams, or 
 as to the effects of the physical conditions of drainage area, evap- 
 oration, temperature and other factors on stream flow. The actual 
 daily flow of the stream from day to day, perhaps through all 
 ranges of rainfall, temperature, evaporation and other physical con- 
 ditions, is known and the principal points which must be consid- 
 ered are : First, the head available ; Second, the effects of the varia- 
 tions of flow on the variations in head ; and Third, the extent to 
 which the flow can be economically develo'ped or utilized. Gen- 
 erally, however, even where local hydrographs are available, they 
 are not sufficiently extended to cover all the variations in river flow 
 which must be anticipated, and it is ordinarily desirable to com- 
 pare the available data with the flow at other points on the stream 
 in question or with other streams in the immediate vicinity. 
 
 51. Use of Comparative Hydrographs. Hydrographs taken at 
 other points on the same river, or on other adjacent rivers where 
 conditions are reasonably similar, are of great value in considering 
 the local stream flow, provided all modifying conditions are under- 
 stood and carefully considered. Hydrographs are ordinarily pre- 
 pared to show the cubic feet per second of actual flow at the 
 point at which observations are made. If the observations (and 
 the hydrographs based thereon) made at some other point on a 
 stream, of on some other streams, are to be used for jthe considera- 
 tion of the flow at a point where a water power plant is to be 
 installed or considered, the relation of the flows at the several 
 points must be determined. 
 
 As a basis for such comparison of stream flow, it may be as- 
 sumed that the flow per unit of area at different points on the same 
 
Water Power. 
 
 Fig. 38. Drainage Area of Wisconsin River Above Kilbourn, Wis. 
 
Use of Comparative Hydrographs. 85 
 
 % 
 
 stream, or at points on different streams under similar circum- 
 stances, is essentially the same. This is not strictly true, or per- 
 haps it may be more truly said that the apparent similarity of condi- 
 tions is only approximate and hence differences in results must 
 necessarily follow. For a satisfactory consideration of the subject 
 of comparative hydrographs, the variations from this assumption, 
 as discussed in another chapter, must be understood and appre- 
 ciated. For practical purposes, however, the assumption is often 
 essentially correct and forms a basis for an intelligent considera- 
 tion of stream flow where local hydrographs are not available. Fig. 
 37 is a hydrograph constructed from observations made on the 
 Wisconsin River at Necedah, Wisconsin, by the U. S. Geological 
 Survey for the water year, 1904, and shows the daily rate of dis- 
 charge of the Wisconsin River at that point for the year named. 
 The area of the Wisconsin River (see Fig. 38) above Necedah is 
 5,800 square miles. If, therefore, we draw a horizontal line from 
 the point representing 5,800 cubic feet per second on the discharge 
 scale (see Fig. 37), the line so drawn will represent a discharge at 
 Necedah of one cubic foot per second per square mile of drainage 
 area, and a similar line drawn from the 11,600 cubic foot point on 
 the vertical scale will represent a discharge of two cubic feet 
 per second per square mile, and so on. These lines may be fairly 
 regarded not only as indicating the flow per unit of area of the - 
 river at Necedah, but also the relative flow per unit of area of the 
 Wisconsin River at points not greatly distant therefrom. At Kil- 
 bourn, (see Fig. 38) located on the same river about forty miles 
 below Necedah, the flow may be assumed to be similar and pro- 
 portionate to the flow at Necedah. Above Kilbourn the drainage 
 area is 7,900 square miles, and with similar flow the discharge 
 would be proportionately greater. The fact must be recognized, 
 and acknowledged, that the hydrograph is strictly applicable only 
 to the point at which it is taken, and that certain errors will arise 
 in considering its application to other points, yet observations and 
 comparisons show that, while such errors exist, they are not nearly 
 so important as the errors which arise from the consideration of 
 averages, either annually or monthly. 
 
 Consider, therefore, on this basis the Necedah hydrograph as 
 shown in Fig. 37. On this diagram a flow of one cubic foot per 
 second per square mile at Necedah, representing an actual flow of 
 5,800 cubic feet per second at that point, would, by proportion, 
 represent a flow of 7,900 cubic feet per second at Kilbourn and, 
 
86 
 
 Water Power. 
 
 ' ON003S 3d I33J DIBflD 
 
 31UN 
 
 Nl 39UVH3SIQ 
 
 QN033S Ud 133J 318(13 Nl 33UVH3SIO 
 
Reliability of Comparative Hydrographs. 87 
 
 with a suitable change in scale, the diagram may be redrawn to rep- 
 resent the flow at Kilbourn as shown in Fig. 39. This same method 
 can be applied to any point on the same river or to comparative 
 points on different rivers. 
 
 52. Reliability of Comparative Hydrographs. It must be clearly 
 understood that comparisons as above described hold good only 
 as the conditions are essentially similar at the various points com- 
 pared. 
 
 Stream flow at the best is very irregular and varies greatly from 
 year to year. The actual departure from the truth can best be 
 understood and appreciated from an actual comparison of flows 
 on adjacent drainage areas where observations have actually been 
 made for a term of years. From such an investigation, which can 
 be made as extended as desirable, the true weight to be given to the 
 comparative hydrograph can best be judged. It is not believed 
 that the actual variations from the truth, as shown by carefully 
 selected comparative hydrographs, will be any greater than the flow 
 variations which actually take place from a drainage area from year 
 to year under the varying conditions of rainfall and climate. This 
 method, therefore, is believed to be a scientific and systematic one 
 for the consideration and discussion of probable variations in stream 
 flow at any given point, if its limitations and the modifying in- 
 fluences known to exist on different drainage areas and under 
 different geographical, geological and meteorological conditions are 
 know r n and appreciated. 
 
 53. When no Hydrographs are Available. In a new country 
 where no observations are available either on the drainage area 
 under consideration or on other areas adjacent thereto, the study 
 of comparative hydrographs is impossible and a different method 
 of consideration must be used. If no data are available, time must 
 be taken to acquire a reasonable amount of local information which 
 should include not less than one year's observation. In addition 
 to such observation a study as thorough as practicable should be 
 made of the geology, topography, and other physical conditions 
 that prevail on the water shed. Rainfall data is commonly avail- 
 able for a much greater range of time than the observations of 
 stream flow. The relations of rainfall to run-off are hereafter dis- 
 cussed and approximate fixed relations are shown to exist between 
 them. From such relations, and from a single year's observations,, 
 conclusions may be drawn as to the probable variations from the 
 observed flow which will occur during the years where the rainfall 
 
Water Power. 
 
 B3A\Qd 3SUOH lVGI13dQ3Hl 
 
 
 o 
 en 
 
 f 
 
 c 
 
 j 
 
 in 
 
 ' 31IJN 
 
 ^ n <u 
 
 H3d QNQ33S H3d 133J 
 
 Nl 33UVH3SIO 
 
OF 
 
 Hydrograph as a Power Curve, 89. 
 
 varies greatly from that of the year during which observations are 
 available. Such conclusions are necessarily unsatisfactory, or at 
 least much less satisfactory than conclusions based on actual 
 stream flow. The consideration of the best information available 
 on any project is the basis on which the engineer should always 
 rest his conclusions, and all relations which will throw light "on the 
 actual conditions should be given careful attention. If a water 
 power plant must be immediately constructed upon a stream con- 
 cerning which little or no information is available, then the risk is- 
 proportionately greater, and safety is obtained only by building 
 in such a conservative manner that success will be assured for the 
 plant installed and on plans that will permit of future extensions 
 should the conditions that afterward develop warrant an extension 
 of the same. 
 
 54. The Hydrograph as a Power Curve. The hydrography by a 
 simple change in the vertical scale similar to that already consid- 
 ered, may also be made to show graphically the variations in the 
 power of the stream. If, for example, at Kilbourn, a constant fall of 
 seventeen feet be assumed, then a flow of one cubic foot per second 
 per square mile represents a total flow of 7,900 cubic feet per second, 
 and this flow, under 17 foot head, will give a theoretical hydraulic 
 horse power as follows: 
 
 7900X17 1t . 9A1 
 
 i..F. = J-TJ = 15251 
 
 o.o 
 
 Now if a hydrograph be constructed on such a scale that the line of 
 flow of one cubic foot per second per square mile will also repre- 
 sent 15,261 horse power, the result will be a power hydrograph 
 (see Fig. 40), which represents the continuous (24 hours per day) 
 theoretical power of the river under the conditions named. 
 
 On account of losses in the development of power the full theoret- 
 ical power of a stream cannot be developed, and hence the actual 
 power that can be realized is always less than the theoretical power 
 of the stream. If it is desired to consider the actual power of the 
 stream on the basis of developing the same with turbines of 80 
 per cent efficiency, the line representing the flow of one cubic foot 
 per second per square mile will represent the actual horse power 
 to an amount determined as follows: 
 
 _ 7900 X 17 X .80 _ 7900 X 17 _ 
 8.8 TT~ 
 
 A hydrograph platted so that the line of one cubic foot per 
 square mile will represent this amount, will represent the actual 
 
9 o 
 
 Water Power 
 
 ( 3 3*>V3S ] SbdQH 17 a 
 a CD 
 
 ID K 
 
 OJ SbflOH b3MOd 3SUQH 
 
 if in a 
 
 fi 
 
 a en 
 
 in aj 
 
 [ e 31VGS ] AVO b3d SHHQH 21 UQJ SnonNllNOD b3/V\Od 3SUQH 
 
 5J CO U CO O 
 
 IB ^ n 
 
 U3 CU < TJ- 
 
 tv n eo ^ 
 
 m r^ ^ nj 
 
 ^ 
 
 | 
 
 s 
 % 
 
 & 
 
 g 
 
 U 
 
 
 
 'O 
 
 M 
 
 3UVOBS U3d ON033S U3d 133J 
 
 Nl 33bVH3SIO 
 
 V 31V3S ] b3MOd 3SbOH SnOnNllN03 1VH13V 
 
The Hydrograph as a Power Curve. 91 
 
 AVO U3d SUnOH Qi UOJ SnOflNUNQO U3MOd 3SUOH 
 
 3 5 
 
 in ^ n 
 
 3TUN 3HVnDS H3d ON033S 3d 133J 3I8RD Nl 33UVHOSIO 
 
92 Water Power. 
 
 horse power of the river at Kilbourn with the wheels working with 
 the efficiency and under the head named. Such a hydrograph is 
 shown by Fig. 41, referred to by the left-hand scale (A). Power, 
 however, is not always used continuously for twenty-four hours. 
 If pondage is available the night flow may be stored and utilized 
 during the day. If the flow of twelve hours at night is impounded 
 and used during the day under the seventeen foot head, the power 
 will be double that shown on scale A, and can be represented by 
 another change in scale as shown by Fig. 41, referred to scale B. 
 If the flow for the fourteen hours of night is stored and utilized in 
 the ten hours of day, then the hydrograph can be made by another 
 change in scale to represent the ten hours power as shown by 
 Fig. 42. 
 
 The total horse power hours which are available from a stream 
 for each day may be represented (either theoretically or actually) 
 by multiplying the scale of continuous power by 24. The actual 
 horse power available at Kilbourn under the conditions named is 
 represented by scale C in Fig. 41. It will be noted that by pointing 
 off one place in the figures of scale C, Fig. 41, the hydrograph will 
 represent the same condition as shown in Fig. 42. 
 
CHAPTER V. 
 
 WATER POWER (Continued.) 
 THE STUDY OF THE POWER OF A STREAM AS AFFECTED BY HEAD. 
 
 55. Variations in Head. In the previous chapter the graphical 
 representation of stream flow has been considered. A method for 
 the expression of the power resulting from the fluctuations of 
 stream flow and under a constant head has also been shown. Ex- 
 perience shows, however, that such a condition seldom if ever 
 occurs. In some cases where the available head is a very large 
 element of the possible power, the fluctuations may be so small 
 as to be of little or no importance. In many other cases where the 
 available heads are considerable, the importance of the fluctuation 
 in head is comparatively small, under which condition the diagrams 
 already discussed are essentially correct and are satisfactory for 
 the consideration of the varying power of the stream. In power 
 developments under the low heads available in many rivers, the 
 fluctuation in head is almost or quite as influential on the con- 
 tinuous power that may be economically developed from a stream 
 as the minimum flow of the stream itself. 
 
 The hydraulic gradient of a stream varies with the quantity of 
 water flowing. At times of low water the fall available in almost 
 every portion of its course is greater than is necessary to assure 
 the flow between given points and frequent rapids result (see R. 
 R. Fig. 43) which are commonly the basis for water power develop- 
 
 Flood flow. 
 
 Medium Water 
 Low Water 
 Stream Bed- 
 
 Fi g . 43. Hydraulic Gradients of a Stream Under Various Conditions 
 
 of Flow. 
 
94 
 
 Water Power. 
 
 ments. As the flow increases, however, a higher gradient and 
 greater stream section is necessary in order to pass the greater 
 quantity of water, and the rapids and small falls gradually become 
 obscured (as shown by the medium water lines, Fig. 43) or dis- 
 appear entirely under the larger flows (as shown by the higher 
 water line, Fig. 43). Water power dams concentrate the fall of the 
 
 Hood Mow 
 Medium Wafer 
 Low Water. 
 Stream Bed. 
 
 Fig. 44. Hydraulic Gradients of the Same Stream After the Construction of 
 Dam and Under Various Conditions of Flow. 
 
 river that is unnecessary to produce flow during conditions of low 
 and moderate water (as shown in Fig. 44), and when the gradient 
 of the water surface and the cross section of the stream are in- 
 creased to accommodate the larger flow, the fall at such dams is 
 frequently greatly reduced (as shown by the medium water line in 
 Fig. 44) or, during high water, the fall is largely or completely de- 
 stroyed (as shown by the high water lines in the Figure), or at 
 least is so reduced as to be of little or no avail under practical water 
 power conditions. 
 
 The cross section of the river bed, its physical character and 
 longitudinal slope, are the factors which determine the hydraulic 
 gradient of a stream under different flows. They are so variable 
 in character and their detail condition is so difficult of determina- 
 tion that sufficient knowledge is seldom available, except possibly 
 in the case of some artificial channels, to determine, with reason- 
 able accuracy, the change of the surface gradient and cross section 
 of the water under various conditions of flow. Where a power plant 
 is to be installed, it is important to ascertain the relation of flow 
 to head in order that the available power may be accurately deter- 
 mined. Where a river is in such condition as to make the de- 
 termination of a discharge rating curve possible, either by direct 
 river measurement at the point in question or by a comparison with 
 the flow over weirs at some other point, such determination should 
 be carefully made, as such knowledge is of the utmost importance 
 in considering the problem of continuous power. 
 
The Rating Curve. 
 
 95 
 
 56. The Rating or Discharge Curve. The rating curve, which 
 will be discussed in some detail in a later chapter, is a hydrograph 
 that represents the relation of the elevation of the water surface in a 
 channel to the quantity of water passing a given cross section. The 
 form of this curve varies with the various conditions of the cross 
 section both at the immediate point and for a considerable distance 
 above and below the location considered and can usually be de- 
 termined only by detail observations. The rating curve is a uni- 
 form curve only for channels in which no radical change in form of 
 cross section occurs with the increase of flow. (See A Fig. 45.) If, 
 on account of overflow conditions, or sudden enlargements of the 
 cross section, that cross section varies radically in form at a given 
 height, then at this elevation a radical change in the slope of the 
 rating curve is likely to occur. (See B and C Fig. 45.) 
 
 B 
 
 Fig. 45. The Influence of the Stream Cross Section on the Rating Curve. 
 
 Any change in the bed of the stream may, and frequently does, 
 modify to a considerable extent the rating curve, which must be 
 expected to vary under such conditions to an extent that depends 
 on the variations that take place in the cross section and elevation 
 of the stream bed. Such variations, however, are not, as a rule, of 
 great magnitude and consequently will not usually affect the head 
 materially at a given point. 
 
9 6 
 
 Water Power. 
 
 In Fig. 46, which shows the rating curve of the Wisconsin River 
 at Necedah, Wis., as determined at different times during the years 
 1903 and 1904, an extreme change of head of about six inches will 
 be noted for ordinary flows. When the change in head is of suf- 
 
 fcJC 
 
 
 
 Sfcrf 
 
 * 
 
 '<- 
 
 EC 
 
 3 , 130* 
 
 Discharge in Cu. Ft. Per Second. 
 
 Fig. 46. Rating Curves, Wisconsin River at Necedah, Wis., Showing Changes 
 in Head Due to Changes in Cross Section, 
 
 ficient importance to warrant the expense, the river channel may be 
 so dredged out as to restore the original head when the reduction 
 in head is occasioned by the filling of the section. 
 
 57. The Tail Water Curve. It will be readily seen that while the 
 rating curve shows the relation between stream flow and river 
 height prior to the construction of a dam, it will still represent the 
 condition of flow below the dam after construction is completed. 
 The water flowing over the dam will create a disturbed condition 
 immediately below. If the velocity of the flow is partially checked 
 or entirely destroyed, a heading-up of the water may result below 
 the dam sufficient to give the velocity required to produce the flow 
 in the river below, but it will soon reach a normal condition similar 
 to that which existed previous to the construction of the dam. 
 
 58. The Head Water Curve. In Chapter III is shown (see Figs. 
 35 and 36) the discharge curves over weirs of various forms and the 
 formulas representing them are also quite fully discussed. From 
 
The Graphic Representation of Head. 
 
 97 
 
 these formulas or diagrams a discharge curve can be readily cal- 
 culated, with reasonable exactness, for a dam with a certain form 
 and length of crest. Such a curve will show the height of the head 
 waters above the dam and under any assumed conditions of flow. 
 From the rating curve of the river at the point considered, and the 
 discharge curve of the weir proposed, the relative positions of head 
 and tail waters under varying conditions of discharge can be readily 
 and accurately determined, and if a weir is to be built to a certain 
 fixed height, it will be seen that the head under any given conditions 
 of flow may be thus determined. 
 
 59. Graphic Representation of Head. Fig. 47 shows the rating 
 curve of the Wisconsin River (see lower curve marked "Tail Water 
 
 DISCHARGE IN CUBIC FEET PCQ SECOND 
 
 Fi g> 47. Showing Head at the Kilbourn Dam Under Various Conditions of 
 
 Flow. 
 
98 Water Power. 
 
 Curve") at Kilbourn. On this diagram has also been platted sev- 
 eral discharge curves, two being for a weir of 300 feet in length 
 and two for a weir of 350 feet in length. Both weir curves in the 
 upper set are based on the assumption that the entire flow of water 
 is passing over the weir. The crest of the dam is shown as raised 
 to gauge 19, and the distance between the rating curve, which now 
 represents the height of the tail water, and the weir discharge 
 curves, which represent the height of the head water (with two dif- 
 ferent lengths of weir) under different conditions of flow, will show 
 the heads that obtain at all times under these assumptions. 
 
 The entire discharge of the stream, however, will not pass over 
 the dam except when the plant is entirely shut down, which would 
 seldom be the case. The essential information which is desired 
 therefore is the available head when the plant is in active operation. 
 At the Kilbourn plant the discharge of the turbines to be installed 
 under full head will be 7,000 cubic feet per second, hence, with the 
 plant in full operation, this quantity of water will be passing 
 through the wheels. Therefore in determining the relation between 
 head water and tail water it must be considered that with a flow of 
 7,000 cubic feet per second, the water surface above the dam will 
 be at the elevation of its crest, no flow occurring over the spillway, 
 and that only the flows greater than this amount will pass over 
 the dam. Another curve for each weir has therefore been added 
 to the diagram in which the zero of the weir curves is platted 
 from the point where the line representing the height of the dam 
 (elevation 19) intersects the line representing a discharge of 7,000 
 cubic feet per second. From this diagram (Fig. 47) it will be seen 
 that other heads, shown in Table VIII, will obtain under various 
 conditions of flow. 
 
 It will readily be seen that the line representing the height of 
 the dam is not essential and that the curves may be platted relative 
 to each other, leaving the height of the dam out of the question 
 entirely and indeterminate. A curve constructed on this basis but 
 otherwise drawn in the same manner as in Fig. 47, is shown in Fig. 
 48. In Fig. 48, wherever the weir or head water curves pass above 
 the tail water curve, it shows that an increase in the head will re- 
 sult under the corresponding condition of flow and wherever they 
 pass below such curve, it shows that a decrease in the head will 
 result under the corresponding condition of flow, the amount of 
 which is clearly shown by the scale of the diagram. Consequently, 
 having given the height of the dam above tail water at the point 
 
The Graphic Representation of Head. 99 
 
 of no discharge, the head available under any other condition can 
 be immediately determined from the diagram. 
 
 From this diagram the changes in head (as shown in table IX) 
 can be determined and these, with a 17 foot dam, will give the total 
 
 TABLE VIII. 
 
 Gauge heights and heads available at Kilboum Dam under various conditions 
 of flow, with a length of spillway of 300 and 350 feet. 
 
 
 HEAD^ 
 
 WATER 
 
 
 HEAE 
 
 WITH 
 
 Flow in cubic feet 
 per second. 
 
 300 
 ft. dam. 
 
 350 
 ft. dam. 
 
 Tail 
 Water. 
 
 300 
 ft. dam. 
 
 350. 
 ft. dam. 
 
 7000.... 
 
 19 
 
 19 
 
 
 
 
 1 7 
 
 14000 
 
 22 9 
 
 2 9 > 
 
 *> 1 
 
 170 
 
 Ll 
 1 7 9 
 
 21000 
 
 25 2 
 
 24 6 
 
 Q 
 
 179 
 
 I/ ./ 
 1 K A 
 
 28000 
 
 27 
 
 26 9 
 
 mQ 
 
 1R 7 
 
 ID.O 
 
 -ICQ 
 
 0*5000 
 
 28 5 
 
 27 7 
 
 I 9 2 
 
 ifi *i 
 
 I C ft 
 
 42000 
 
 30.2 
 
 29 3 
 
 13 6 
 
 ifi fi 
 
 i c 7 
 
 49000 
 
 31.5 
 
 30 4 
 
 14 7 
 
 Ifi 8 
 
 ic 7 
 
 56000 
 
 32 7 
 
 31 6 
 
 1 ^ fi 
 
 17 1 
 
 -ICQ 
 
 
 
 
 
 
 10. o 
 
 heads available under various conditions of flow as shown in the 
 last two columns. These heads will be seen to correspond with the 
 heads given in table VIII. 
 
 DISCHARGE OF WISCONSIN RIVER AT KILBOURN IN CUBIC FT. PER SEC. 
 
 Fig. 48. Showing Change in Head at Kilbourn Dam Under Various Condi- 
 tions of Flow. 
 
100 
 
 Water Power. 
 
 TABLE IX. 
 
 Changes in head at Kilbourn Dam with lengths of crest of SOO and 350 feet and 
 under various conditions of floiv with resulting total available head ivith 17 ft. 
 dam. 
 
 Flow in cubic feet 
 . per second. 
 
 CHANGES IN HEAD WITH 
 
 TOTAL HEAD WITH 
 
 300 
 ft. dam. 
 
 350 
 ft. dam. 
 
 300 
 ft. dam. 
 
 350 
 ft. dam. 
 
 7000 ...... 
 
 
 + .8 
 + .2 
 .3 
 .5 
 .4 
 .2 
 + .1 
 
 
 + .2 
 .4 
 1.1 
 1.5 
 1.3 
 1.3 
 1.2 
 
 17 
 17.8 
 17.2 
 16.7 
 16.5 
 16.6 
 16.8 
 17.1 
 
 17 
 17.2 
 16.6 
 15.9 
 15.5 
 15.7 
 15.7 
 15.8 
 
 14000 
 
 21000 
 
 28000 
 
 35000 
 
 42000 . . . 
 
 49000 
 
 56000 
 
 
 60. Effects of Design of Dam on Head. It should be noted in 
 both of the last diagrams that the height of the water above the 
 dam is readily controlled by a change in the form and length of 
 the weir; that a contraction in the weir length produces a corre- 
 sponding rise in the head waters as the flow increases, while the 
 lengthening of the weir will reduce the height of the head water 
 under all conditions of flow. The physical conditions relative to 
 overflow above the dam will control the point to which the head 
 waters may be permitted to rise and will modify the length and the 
 construction of the dam. Where the overflow must be limited, the 
 waters, during flood times, must be controlled either by a suffi- 
 cient length of spillway or by a temporary or permanent reduction 
 in the height of the dam such as the removal of flash boards, the 
 opening of gates, or by some form of movable dam. 
 
 Having determined the head available at all conditions of river 
 flow, the hydrograph, as previously shown, may be modified to show 
 the actual power of the river under the varying conditions of flow. 
 The vertical scale, in this case, instead of being uniform must be 
 variable as the head varies. Fig. 49 shows graphically the variation 
 in the continuous theoretical power of the river taking into con- 
 sideration the variation in head which will actually occur. Com- 
 pare this hydrograph with Fig. 40 in which no variation in head 
 is considered. 
 
 6 1. Effect of Head on the Power of the Plant. It is important 
 at this point to take into consideration the effect of head and flow 
 on the actual power of the plant. In most rivers, under flood condi- 
 
Effects of Design of Dam 'on Ke'ad. 
 
 101 
 
 m ^ n cu 
 
 31IW 3UVntlS U3d QND33S H3d 133J 318(13 Nl 
 
 39UVH3SIO 
 
IO2 Water Power. 
 
 tions, 'the power theoretically * available is largely increased, for, 
 while the head may diminish, the flow becomes so much greater 
 that the effect of head on the theoretical power is more than off- 
 set thereby. Practically, however, the conditions of head under 
 which a given water wheel will operate satisfactorily (i. e. at a 
 fixed speed) are limited, and, while the theoretical power of the 
 river may radically increase, the power of the plant installed under 
 such conditions will often seriously decrease, and under extreme 
 conditions may cease entirely. The discharging capacity of any 
 opening is directly proportional to the square root of the head, and 
 the water wheel, or water wheels, simply offers a particular form 
 of opening, or openings, and operates essentially under this general 
 law. With a fixed efficiency, therefore, the power which may be 
 developed by a water wheel is in direct proportion to its discharging 
 capacity and to the available head. Hence, the power of the wheel 
 decreases as the product of these two factors, and therefore the 
 power available under conditions of high flow and small head are 
 much less than where the head is large and the total flow of the 
 river is less. The only way, therefore, to take advantage of the 
 large increase in theoretical power during the high water condi- 
 tions is to install a surplus of power for the condition of average 
 water. This may sometimes be done to advantage, but its extent 
 soon reaches a practical limitation on account of the expense. It 
 often becomes desirable to take care of such extraordinary condition 
 by the use of supplemental or auxiliary power. Such power can 
 usually also be applied during conditions of low water flow when 
 the power is limited by the other extreme of insufficient water under 
 maximum head. 
 
 In considering the effect of head on the power of a plant, it is 
 necessary to understand that water wheels are almost invariably 
 selected to run at a certain definite speed for a given power plant 
 and cannot be used satisfactorily unless this speed can be main- 
 tained. Also that any wheel will give its best efficiency at a fixed 
 speed only under limited changes in head. If the head changes 
 radically, the efficiency changes as well and this fact becomes 
 more serious under a reduction in head. As the head is reduced, 
 the discharging capacity of the wheel and its efficiency is also 
 rapidly reduced so that the power of the wheel decreases more 
 rapidly than the reduction in the discharging capacity would 
 mdicate. When the reduction of head reaches a certain point the 
 wheel is able to simply maintain its speed without developing 
 
Relations of Power, Head and Flow. 103 
 
 power, and when the head falls below that point, the speed can no 
 longer be maintained. It is therefore plain that when the head of 
 a stream varies greatly, it becomes an important and difficult matter 
 to select wheels which will operate satisfactorily under such varia- 
 tions, and, when the variations become too great, it may be prac- 
 tically or -financially impossible to do so. This subject is discussed 
 at length in a later chapter, but is called to the attention of the 
 engineer as an important matter in connection with the study of 
 head. 
 
 62. Graphical Investigation of the Relations of Power, Head and 
 Flow. The relation of head and flow to the horse power of any 
 stream on which a dam has been constructed, may be graphically 
 investigated and determined by a diagram similar to Fig. 50. On 
 this diagram are platted hyperbolic lines marked "horse power 
 curves" which show the relation of horse power to head and flow 
 within the probable limits of the conditions at Three Rivers, Mich. 
 These lines are drawn to represent the actual horse power of a 
 stream under limited variations in head and flow and on the basis 
 of a plant efficiency of 75 per cent. These heads, which actually 
 obtain at the Three Rivers dam, were observed under three condi- 
 tions of flow, and these observations were platted on the diagram 
 at e e e and a .curve was drawn through them. From the intersec- 
 tion of this curve with the horse power curves, the actual power 
 of the river available under the actual variations of head and flow, 
 is determined. These measurements were taken with all of the 
 water passing over the dam. 
 
 Let- us assume that it is desired to investigate the effect of an 
 installation of wheels, using 600 cubic feet per second, under a 
 nine foot head. Under these conditions part of the water will pass 
 through the turbines instead of over the crest of the dam, the 
 available head will therefore be somewhat reduced, and the power 
 curve of the river, under these new conditions, is shown on the 
 diagram by the curve f f f . This curve was platted from the curve 
 e e e by computing the amount the head on the crest of the 
 dam would be lowered at different stages of the river by diverting 
 through the wheels the quantity of water which they will pass under 
 the reduced head. The actual power of the river at different heads 
 and under these conditions is shown by the intersection of the line 
 f f f with the horse power curve, and the actual power of the pro- 
 posed plant under various conditions of flow is obtained by pro- 
 
104 
 
 Water Power. 
 
 2200 - * 
 
 I I I 
 
 CURVE: SHOWING RELATIONS or 
 POWER . DISCHARGE. MMD 
 
 u 
 
 B.5 9.0 9.5 ID.Q IQ.5 
 
 TOTAL FALL FROM ABOVE DAM TO MOUTH OF TAIL RACE 
 
 Fig. 50. Graphical Study of Head. 
 
 jecting the point of intersection of the discharge line with the 
 line f f f on the turbine discharge line d d. 
 
 Thus, with a flow of 600 cubic feet per second, the power of the 
 plant would be about 470 horse power, while, with a flow of 
 2,100 feet per second, the power of the plant would decrease to about 
 420 horse power. At discharges below 600 cubic feet per second, 
 the head would drop rapidly unless a portion of the installation was 
 shut down. 
 
 63. Graphical Study of Power at Kilbourn. A more detailed 
 
Relations of Power, Head and Flow. 
 
 105 
 
 S3NiaH.ni ,,/:S-- 
 
 INVld JO H3MOd 1VOI13a03Hl 
 
 OJ 
 
 7 
 
 C*5 
 
 I 
 
 CO 
 
 I 
 
 O 00 O 
 
 o oo o 
 
 CD f-*0 O 
 
 co eocu ao 
 
 038010 S31V3 T1V AV/VmidS ,036 - B3AIU JO 'd'H 
 
 ^fenmcucueu ^, 
 
 cu 
 
 00 
 
 00 
 
 to 
 
 cu 
 
 z o> 
 
 - a 
 
 I 
 
 * QN033S U3d 132J QIBRQ Nl 3SdVH3SIQ 
 
 O 
 
 T-H- 
 IO 
 
 60. 
 
 5- 
 
r o6 Water Power. 
 
 study of head in connection with the conditions at Kilbourn, Wis- 
 consin, is illustrated by Figures 51 and 52. In Figure 51 the theo- 
 retical horse power of any stream resulting from any variation be- 
 tween the head and flow is shown by the hyperbolic curves drawn 
 from the upper to the right hand side of the diagram. Figure 47, 
 already considered, shows the relation of the head and tail water at 
 Kilbourn, where a dam with a crest 350 feet in length is projected. 
 
 The curve on Figure 51 marked "Height of crest of dam above 
 tail water" was obtained by subtracting the height of tail water 
 at the various river stages, as given by the rating curve of the 
 river, from the height to w r hich the dam is to be constructed and 
 platting the same in their correct position on the diagram. The 
 dam here considered is 17 feet in height above average water or 
 with its crest at elevation 19 on the gauge. The curve on the right 
 marked "Fall over dam, all gates closed", is constructed in the 
 same manner by laying off as abscissas the actual head as deter- 
 mined from Fig. 47 under various conditions of flow when the 
 whole discharge of the river is passing over the dam. The ab- 
 scissas, therefore, between these two curves show the head on 
 the crest of the dam when the whole discharge of the river is 
 passing over the dam. For any given river discharge (as for in- 
 stance 16,000 cubic feet per second) the total fall can be obtained 
 (in this case 18.8) and the theoretical horse power of the river (in 
 this case 34,000 horse power) can be determined by finding the 
 intersection of the line for 16,000 cubic feet per second with the 
 curve marked "Fall over dam, all gates closed", and determining 
 the relation of this point to the power curves. This relation is 
 more clearly indicated by the first scale to the right. 
 
 64. Power of the Kilbourn Wheels Under Variations in Flow. 
 When the gates to the turbines are open a less quantity of water 
 will flow over the dam and the head on the crest will therefore be 
 diminished. The amount of water which will pass through the pro- 
 posed installation under various heads, is shown by the curve 
 marked "Discharge 24-57" turbines." The intersection of this curve, 
 with the discharge lines, at all points to the left of the curve marked 
 "Height of crest of dam above tail water" indicates that such flows 
 will pass through the wheels at the head indicated by the point of 
 intersection. The practical limit of the turbine capacity is the 
 discharge indicated by the point of intersection of the turbine 
 discharge curve with the "Height of crest of dam above tail water". 
 It will be noted that this intersection shows a maximum discharge 
 
Effects of Low Water Flow, icy 
 
 of 7,000 cubic feet per second under a head of 17 feet. A further 
 increase in the discharge of the river up to 8,700 cubic feet per sec- 
 ond, causes an increase in the head, which is found by following 
 upward the curve marked "Head 24 turbines" to the point m where 
 a maximum head is indicated. The discharge from the turbines 
 under this condition increases but slightly and is indicated by the 
 vertical projection of the point of greatest head (m) on the turbine 
 discharge line (at n) which is so slightly above the 7,000 cubic feet 
 line as to be hardly distinguishable on the diagram. 
 
 The power of the plant depends upon the head and the discharge 
 through the wheels, hence the theoretical power which might be 
 developed by the 24 turbines with a flow of 8,700 cubic feet per 
 second would be about 13,800 horse power, which can be deter- 
 mined by calculation or is shown by the relation of the point n to 
 the power curves. The actual value of these various points is more 
 clearly shown on the second scale to the right, marked "Theoretical 
 power of plant 24-57" turbines". A further increase in the dis- 
 charge decreases the head until for the 24 turbines a minimum is 
 reached at a discharge of 42,500 cubic feet per second. Under this 
 condition of head the discharge through the wheels has also been 
 somewhat reduced, and the corresponding rmrse power is reduced 
 to 11,300 as shown by the intersection of the discharge curve and 
 the line indicating the head existing under these conditions. 
 
 65. Effects of Low Water Flow. In the case of low water when 
 the flow is not sufficient to maintain the flow over the dam, if the 
 turbines are run at full capacity, the water level behind the dam 
 will drop until a point of equilibrium is attained where the head is 
 just sufficient to force the entire discharge through the turbines. 
 As the water level is lowered below the crest, the power of the plant 
 rapidly' diminishes owing to the great decrease in the head for a 
 small decrease in the flow. When the head decreases beyond a 
 certain point the power of the plant may be increased by closing 
 some of the gates of the turbines until the discharge through the 
 turbines is less than the discharge of the river, when the head will 
 increase by the backing up of the water behind the dam. 
 
 Thus it will be seen by the diagram that, with only 6,000 cubic feet 
 per second flowing in the river, if all of the turbines are operated 
 the head will drop to about 12.7 feet, and the power of the plant 
 under this head and flow would be about 8,660 horse power. If, 
 under these conditions, one unit of six turbines, amounting to one- 
 fourth of the plant, is shut down, the water will rise until the head 
 
io8 Water Power. 
 
 is increased to about 18 feet. Under these conditions about 800 
 cubic feet per second of this water will waste over the dam, and the 
 power developed by the remaining portion of the plant will be 10,630 
 horse power, or, about 2,000 horse power more with one unit shut 
 down and with the resulting head than with all units in operation 
 and the consequent lower head. The above discussion simply illus- 
 trates the point that it is rarely desirable to draw down the head 
 of an operating plant, at least to any great extent, for the sake of 
 operating a greater number of wheels, unless this is done for the 
 purpose of impounding the night flow for use during the day or at 
 times of maximum load. Even in this case too great a reduction 
 in the head is undesirable and uneconomical. 
 
 66. Effects of Number of Wheels on Head and Power. Fig. 52 
 is an enlarged section of that part of Fig. 51 shown by the dotted 
 lines. This diagram shows how the head on the wheels may be 
 maintained by shutting off some of the wheels in case the flow be- 
 comes so small as to entirely pass the wheels and thus reduce the 
 head, as described above. It will be noted that with a total instal- 
 lation of 48 wheels, by closing the gates of two wheels at a time, 
 the variation in the head would be only a fraction of a foot until as 
 ma^y as 24 wheels ahe closed. Hence it will be seen that when the 
 power has been decreased by a rduction of head, the wheels should 
 be closed off until the same power can be secured by the less num- 
 ber of wheels operating with the highest head that is available with 
 the given discharge of the river. As the lower flows of the river 
 are reached great fluctuation in the head will occur with the opera- 
 tion of the turbine gates. This diagram shows the actual delivered 
 power of the plant and is based on a plant efficiency of 75 per cent. 
 The power obtained for a given discharge is therefore less than 
 shown by Fig. 51. 
 
 In order to secure more accurate results a small correction for 
 the variations in efficiency under the variations in head may some- 
 times be desirable. ' In the problem under consideration this is 
 unnecessary on account of the small variation which takes place. 
 However, when the variations in head are considerable, this correc- 
 tion is essential if a close estimate of power at different heads is 
 desired. Figure 53 is a power hydrograph similar to those already 
 discussed but with such changes in the scale as to show the con- 
 tinuous power that could have been developed by these four groups 
 of turbines at Kilbourn, Wisconsin, during the year 1904, under 
 
Effects of Number of Wheels on Head and Power 109 
 
 10000 
 
 14000 
 
 12000 ^^ 
 
 10000 
 
 8000 
 
 6COO 
 
 4000 
 
 2000 
 
 14 
 
 15 
 
 .16 
 
 19 
 
 17 18 
 
 Head in Feet 
 
 Note H. P. Curves are based on 75$ efficiency 
 
 Fig. 52. Relation of Number of Wheels to Power and Head. 
 
 the variations in head which would actually have occurred with the 
 dam it is proposed to construct. 
 
 From the previous discussion of the conditions at Kilbourn it 
 is seen that with a dam with fixed crest the variations in head, 
 due to variations in flow, are comparatively small. Consequently 
 the power of the wheel to be installed will not decrease with an in- 
 crease in flow to as great an extent as usually occurs in water 
 power plants. If a system of flash boards or an adjustable crest is 
 found desirable in order to prevent overflow at times of flood, the 
 power of the plant when these are lowered will be still further 
 reduced. 
 
 The hydrograph may be utilized for more detailed analysis of 
 water power questions and will be further discussed in a future 
 chapter. 
 
no 
 
 Water Power. 
 
 93Miaani 
 
 o 
 
 ivDii3U03H 
 
 n 
 
CHAPTER VI. 
 
 RAINFALL. 
 
 67. Importance of Rainfall Study. The influence of rainfall on 
 the flow of streams is so direct that those unfamiliar with the sub- 
 ject are apt to assume that the relation may be represented by 
 some simple expression and that, therefore, if the rainfall for a 
 period of years be known, the corresponding stream flow may be 
 directly and readily calculated therefrom. With only a brief famil- 
 iarity with the subject it is evident that no such simple relation ex- 
 ists. The relationship is, in fact, complicated by a multiplicity of 
 other physical conditions which have an important if not an equal 
 influence. 
 
 Observations of stream flow are quite limited both in time and 
 geographical extent while the observations of rainfall have extended 
 over a long period of time and the points of observation are geo- 
 graphically widely distributed. If, therefore, it is possible to trace 
 such relationship between the flow of streams and the rainfall 
 and other physical conditions on the drainage areas as will enable 
 the engineer to calculate the flow even approximately, such relation- 
 ships become of great value to the water-power engineer, on ac- 
 count of the lack of other more definite information. It^is there- 
 fore important that the engineer inform himself as fully as pos- 
 sible on the relations that exist between rainfall and stream flow 
 and the modifications of those relations by other physical factors. 
 By such means the information regarding rainfall, already recorded 
 for long terms of years, may be applied to the problem of stream 
 flow in which the engineer is more directly concerned. For this 
 reason the subject of rainfall is here discussed in as much detail 
 as the space will permit. 
 
 68. Distribution of Rainfall. A continuous circulation of water 
 is in progress on the earth's surface. The evaporation from the 
 water and moist earth surfaces rises into the atmosphere in the 
 
129- 127' 125" 123' 121 119 117 115 113 111 109 7 105 103 101' 90' 95 
 
 119 117 US' H3- lir 109 107 
 
Jtf 03 91 89 87 85 83" 
 
 OP THE 
 
 UNITED^STATES 
 
ix 4 
 
 Rainfall. 
 
 1895 
 
 1896 
 
 1897 
 
 1898 
 
 IQ99 
 
 1900 
 
 E3 25 TO 30M 30 TO 35^33 TO 40^0VrB 40 
 llNCHES I! HI INCHES Y//A INCHES . E 3 INCHES . gra.NCHES . CINCHES . ^ INCHES . 
 
 Fig. 55. Distribution of Total Annual Rainfall in Wisconsin. 
 
Distribution of Annual Rainfall in Wisconsin. 115 
 
 1901 
 
 1902 
 
 1903 
 
 1904 
 
 1905 
 
 UNDERI5 Ijij ISTOaok%//320T025 
 INCHES. I |j INCHES. Y///A INCHES 
 
 23 TO 30 
 INCHES 
 
 30 TO 35 
 INCHES 
 
 AVERAGE 
 
 J35 TO 40 | 
 ilNCHES 
 
 | OVER 40 
 llNCHES 
 
 Fig. 56. Distribution of Total Annual Rainfall in Wisconsin. 
 
1. 1 6 Rainfall. 
 
 form of vapor, partially visible as clouds, mist and fog, and is 
 afterwards precipitated as rain and dew. The distribution of rain- 
 fall on the earth's surface is by no means uniform. An examina- 
 tion of Fig. 54, which is a map showing the average distribution of 
 the annual rainfall in the United States, will show how greatly the 
 average annual rainfall differs in various parts of the United States. 
 The local variation in the average annual rainfall in the United 
 States is from a minimum of no rainfall, during some years in the 
 desert regions, to an occasional maximum of more than one hun- 
 dred inches in the extreme northwest. From this map it will be 
 noted that from the Mississippi westward the lines of equal rain- 
 fall are approximately north and south and parallel with the moun- 
 tain ranges. In the Southern states, east of Texas, they are ap- 
 proximately parallel with the Gulf of Mexico, and on both the At- 
 lantic and Pacific coasts they are approximately parallel with the 
 coast lines. At various points in the United States other influences 
 come into play and greatly modify the general distribution as above 
 outlined. In a general way the rainfall may be said to be in- 
 fluenced by the topography of the continent and, to a considerable 
 extent, by its altitude. In general, the rainfall decreases as the 
 elevation above sea level increases, although in some cases the op- 
 posite effect holds. This general law seems to be substantiated by 
 reference to the annual rainfall map. In passing along the parallel 
 of 40 as we ascend from the Mississippi River to the western 
 mountains the annual rainfall decreases from about 35 inches an- 
 nually to 10 inches or less. On the other hand, a reference to our 
 Western coast will show that some of the heaviest rainfalls that 
 occur are due to precipitation caused by the moist winds from the 
 Pacific striking the higher mountain ranges. This is a local condi- 
 tion, however, and is quite different in its character from the gen- 
 eral law above stated. The mountain ranges along the Pacific 
 coast which intercept the moisture from the Pacific and cause the 
 heavy rainfalls in the higher mountain areas are also the direct 
 cause of the small rainfall in the arid regions lying east of these 
 mountains. 
 
 69. The Rainfall Must be Studied in Detail. The map of average 
 annual rainfall is of value only for a general view of the subject. 
 For special purposes a detail study of the local variations from the 
 average conditions is necessary. Great variations take place in the 
 annual rainfall of every locality. Sometimes the annual rainfall 
 will be for a series of years considerably below the average, and 
 
Distribution of Weekly Rainfall in Wisconsin. 117 
 
 MAY 13 TO MAY 20 
 
 MAY 20 TO MAY 27 
 
 MAY 27 TO JUNE 3 
 
 JUNE 3 TO JUNE 10 
 
 JUNE 10 TO JUNE 17 
 
 JUNE 17 TO JUNE 24 
 
 INCHES IN DEPTH 
 
 OT0.25" .25T0.50 .SO"TO.7S" .75"TO \". 
 
 Fig. 57. Distribution of Weekly Rainfall in Wisconsin 
 
u8 
 
 Rainfall. 
 
 Fig. 58. Rainfall Conditions in the United States at 8 A. M., July 10th, 1907. 
 
 Fig. 59. Rainfall Conditions in the United States at 8 A. M., July 17th, 1907. 
 
Local Variations in Annual Rainfall. 119 
 
 then for a number of years the average may be considerably ex- 
 ceeded. No general law seems to hold, however, in regard to this 
 distribution and the variation seems to occur either without law or 
 by reason of laws so complicated as to defy determination. The 
 variations in the distribution of the annual rainfall in the State of 
 Wisconsin for eleven years are shown by Figs. 55 and 56. From 
 these maps can be clearly seen how greatly the distribution of rain- 
 fall throughout the state differs in different years from the average 
 annual rainfall as shown on the last map of the series. It should 
 also be noted that in the same manner these annual rainfall maps 
 are the results of the summation of an irregular distribution of 
 numerous rainstorms, the irregularities of which can perhaps be 
 more clearly shown by the maps on Fig. 57 which show the weekly 
 distribution of rainfall in Wisconsin for six consecutive weeks in 
 May and June, 1907. All such maps are but the result or sum- 
 mation of individual rainstorms which occur during the period 
 considered. Individual rainstorms never occur twice over exactly 
 the same geographical extent of territory nor with equal intensity 
 at any points within the territory covered. They are not only 
 irregular in their distribution but progressive in both their dis- 
 tribution and intensity, changing from hour to hour during their 
 occurrence. The extent of a somewhat general rainstorm in pro- 
 gress at 8 : oo A. M. (Washington time) over the Northwest on July 
 i6th, 1907, is shown by Fig. 58. On the area over which this storm 
 extended, the actual precipitation varied widely and the extent of 
 the storm rapidly changed from hour to hour. At 8 : oo A. M. on 
 July I7th the general rainfall had ceased and the storm -had be- 
 come localized as shown by Fig. 59. The varying character and 
 extent of the rainfall as illustrated by those two maps show the 
 extremes of one storm which affected the Northwest, and illustrates, 
 in a general way, the irregularity and lack of uniformity in rainfall 
 occurrence and distribution. 
 
 70. Local Variation in Annual Rainfall. By reference to Fig. 60, 
 the variations which have occurred in the annual rainfall at various 
 localities in the United States will be seen, and from this data the 
 lack of uniformity in the annual rainfall will be more fully appre- 
 ciated. By an examination of the records of a sufficient number 
 of years the limiting conditions may be determined and an ap- 
 proximate determination of the relation between the extremely dry 
 and extremely wet periods made. 
 
120 
 
 Rainfall. 
 
 No. Atlantic, So Atlantic, St. Lawrence, Ohio River, 
 
 New Haven, Conn. Augusta, Ga. Detroit, Mich. Cincinnati, O. 
 
 
 
 
 
 
 
 
 
 
 
 
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 Eastern Gulf, Western Gulf. 
 Montgomery, Ala. San Antonio, Tex. 
 
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 Mi 
 Topeka, Kar 
 
 ssouri River, 
 is. Helena, Mont. 
 
 Red Riv 
 Moorehead, 
 
 er. 
 Minn. Tac 
 
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 :oma, Wash. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 t,y~0L$w)0$0W, 
 
 Columbia, Pacific, Colorado, Great Basin, 
 Spokane, Wash. Sacramento, Cal. Phoenix, Ariz. Winnemucca, Nev. 
 
 Fig. 60. Variation in Annual Rainfall at Various Points in the United States. 
 
Local Variations in Annual Rainfall. 
 
 121 
 
 Figure 61 i a diagram showing the fluctuations that have occurred 
 in the annual rainfall at Madison, Wisconsin, from 1869 to 1905. 
 The variation at Madison has been from a maximum of about 
 52 inches in 1881 to a minimum of about 13 inches in 1895 which 
 represents a greater range (4 to i) than ordinarily obtains. As a 
 general rule the maximum may be stated to be about double the 
 minimum annual rainfall. 
 
 FLUCTUATION OF ANNUAL RAINFALL AT MADISON, WIS. 
 
 Fig. 61 
 
 71. Local Variations in Periodical Distribution of Annual Rain- 
 fall. The amount of the annual rainfall is only one of the elements 
 that influence the run-off. The time of occurrence or the periodical 
 distribution of the rainfall is even of greater importance. The 
 general character of the periodic distribution of the annual rain- 
 fall is similar each year in each locality, for the maximum and 
 minimum monthly rainfalls occur in each locality at fairly definite 
 periods. As the cycle of the seasons changes, conditions favorable 
 or unfavorable to precipitation obtain, and, while these differ very 
 largely from year to year and are subject to such wide variations 
 as to render the character somewhat obscure, unless a number of 
 seasons are considered, yet the same general character ordinarily 
 prevails. 
 
 Figure 62 shows the extreme and the average variation of the 
 monthly rainfall at Madison. The monthly rainfall in the various 
 months differs widely in amount and is by no means proportional 
 to the total annual rainfall for the year. It is especially observable 
 that during the year of maximum rainfall, viz: for 1881, the rain- 
 fall for April was almost as low as for the April of the year 1895 
 when the total annual rainfall was at a minimum. It is also observ- 
 
INCHES OF RAINFALL. E 
 
 _ . - to 
 
 o rouJikCncnNicacaa - 
 
 i i ii 
 
 Rainfall. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
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 FLUCTUATION OF MONTHLY RAINFALL AT MADISON, WIS, 
 
 Fig. 62 
 
 able that the rainfall for August, 1881, was less than the rainfall for 
 August of 1895. Figure 63 shows the typical average monthly dis- 
 tribution of precipitation at various points within the United States, 
 and the general law to which even the variations mentioned par- 
 tially conform. The character of the monthly distribution varies 
 widely at different locations, but will be seen to have a similar 
 character wherever similar conditions prevail. Thus the New Eng- 
 land States present a similarity in the distribution of the monthly 
 rainfall. A similarity in the monthly distribution is also found, 
 throughout the lake region and the Ohio Valley. The monthly dis- 
 tribution throughout the Great Plains is also similar, and a marked 
 similarity exists at points along the Pacific coast. 
 
 72. Accuracy of Rainfall Maps and Records. It must be under- 
 stood that the rainfall maps, showing lines or belts of equal rain- 
 fall, are only approximately correct, and that it would be impossible 
 to show by such lines small differences in annual rainfall of less- 
 
Monthly Distribution of Rainfall. 
 "Types of Monthly Distribution of Precipitation in the United States. 
 
 Rainfall Distribution in the U. S. (Percentage of fall in each month represented by heavy lines.) 
 
 123 
 
 Fig. 63 
 
124 Rainfall. 
 
 than two or three inches. As a matter of fact, the rainfall actually 
 differs considerably within comparatively small limits, but within 
 such limits the average remains fairly constant for the year or sea- 
 son. Frequently, however, the rainfall variations even within 
 narrow limits differ widely. Many questions of importance in con- 
 nection with the consideration of rainfall are still open to debate 
 and are frequently answered in a diametrically opposite manner by 
 data secured from different localities. 
 
 73. Rainfall and Altitude. The relation of the rainfall to al- 
 titude has been a subject of frequent discussion and perhaps the 
 majority of data secured tends to show that there is a material 
 decrease in the fall of rain as the altitude increases, and this both 
 within a broad area and with great changes of altitude and within 
 a limited area and where the differences in altitude are compara- 
 tively small. Mr. Rafter, in the Hydrology of New York, points 
 out the fact that in the State of New York the rainfall records 
 show both increase and diminution of precipitation with increase of 
 altitude. The Hudson River catchment area shows a higher precipi- 
 tation at the mouth of the river than it does at its source in the 
 Adirondack mountains, while the Genesee River shows the op- 
 posite : that is, a higher precipitation at its source than at its mouth. 
 In this case the influence of altitude, if such influence can be said 
 to obtain on such limited areas, is overshadowed by other predomin- 
 ating influences. In this connection Fig. 64 is of interest. This 
 diagram shows the variation in the annual and monthly rainfall 
 at three stations within the City of Chicago. Curve No. I shows 
 the rainfall at the Auditorium Tower, at an elevation of 233 feet 
 above the level of the city. Curve No. 2 shows the rainfall at the 
 Chicago Opera House Building, at an elevation of 132 feet. Curve 
 No. 3 shows the rainfall at the Major Block, elevation 93 feet. The 
 relative monthly rainfall at these three stations varies greatly, and, 
 while the annual variations at these three points, all of which are 
 within a square mile in the business center of Chicago, differ- 
 considerably from each other, still the difference is insignificant in 
 comparison with the monthly variation. While the influence of alti- 
 tude may possibly be seen in the annual results and possibly in 
 the monthly results as shown at stations one and three, the monthly 
 results at station two show no such effect, or, at least, the effect is 
 greatly obscured by other influences. 
 
 74. Value of Extended Rainfall Records. One of the points that 
 becomes important in the consideration of rainfall records is the 
 
Value of Extended Rainfall Records. 
 
 125 
 
 ANNUAL 
 JAM. FEB. MAR. APR. MAY JUNE JULY AUG. SEPT. OCT. NOV. DEC. I B 3 
 
 30 
 
 
 
 
 
 
 
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 10 
 
 Fig. 4$. Monthly. and Annual Precipitation of Three Exposures in Chicago, 
 111. 1. Auditorium Tower, Elevation 238 feet. 2. Chicago Opera House 
 Building, Elevation 132 feet. 3. Major Block, Elevation 93 feet.* 
 
 length of time required to make such records safe as a basis for 
 future estimates. This subject is well considered in a paper by 
 Alexander A. Binnie, member of The Institute of Civil Engineers, 
 published in the Proceedings, Vol. 109, 'pages 89 to 172. Mr. 
 Binnie's conclusions are that: 
 
 "Dependence can be placed on any good record of 25 years' dura- 
 tion to give a mean rainfall correctly within 2 per cent of the truth." 
 
 Mr. Rafter, after reviewing this paper, concluded, that: 
 
 "For records from 20 to 35 years in length the error may be 
 expected to. vary from 3.25 per cent down to 2 per cent, and that 
 for shorter periods of 5 to 10 and 10 to 15 years the probable ex- 
 treme deviation from the mean would be 15 per cent to 4.75 per 
 cent respectively." 
 
 Mr. Henry from his examination of this question in reference to 
 various localities has drawn the following conclusion: 
 
 For a ten year period the following variations from normal have 
 occurred : 
 
 New Bedford + 16 per cent. 11 per cent. 
 
 Cincinnati +20 " 17 " 
 
 St. Louis +17 " 13 " 
 
 Fort Leavenworth +16 " 18 
 
 San Francisco.. + 9 10 " 
 
 Reproduced from original slide published by Geographical Society of Chicago. 
 
126 Rainfall. 
 
 For a 25-year period Mr. Henry found that the extreme variation 
 was 10 per cent both at St. Louis and New Bedford, and reached 
 the conclusion that at least 35 to 40 years' variations are required 
 to obtain a result that will not depart more than -j- or 5 per cent 
 from true normal. The average variation of the 35-year period Mr. 
 Henry found to be -f- or 5 per cent and for a total 4O-year period 
 + or 3 per cent. 
 
 75. Accuracy in Rainfall Observation. It must also be under- 
 stood that on account of the marked variations which actually occur 
 in rainfall within limited areas and by reason of limited difference 
 of elevation, the observation of actual rainfall is not without its 
 difficulties. In order to secure great accuracy great care must be 
 exercised in the placing of rain gauges so that they may receive 
 and record the rain received in an accurate manner. Subject, as 
 they are, to considerable variations, it would seem unwise to use 
 great refinement in the calculations of rainfall, and in recording 
 rainfall one decimal place is probably all that is warranted and 
 two places is the ultimate limit of possible accuracy. 
 
 76. District Rainfall. In determining the average rainfall on a 
 drainage area an extended series of observations over the entire 
 district considered become essential and conclusions drawn from 
 more limited observations are subject to considerable inaccuracies. 
 Rainfall stations, distributed as uniformly as possible over the 
 drainage area, should be selected, and the average result of the ob- 
 servations of these stations should be used as the basis of calcula- 
 tion. Possibly a still more accurate method of considering this 
 subject would be the selection of rainfall observations on each 
 particular branch of the stream considered. The value to be given 
 to each set of observations used should be in proportion to the ter- 
 ritory drained by the tributaries. 
 
 77. Study of Rainfall as Affecting Run-off. In considering the 
 rainfall on a district in relation to the run-off of streams, it is 
 desirable to study the rainfall records on the basis of what is 
 termed "water year". The water year for most of the area of the 
 United States, instead of coinciding with the calendar year may 
 be best divided into periods beginning, approximately, with De- 
 cember and ending, approximately, with the following November. 
 The first six months of this period, December to May inclusive, 
 is termed the "storage" period. June, July and August constitute 
 the "growing" period ; September, October and November, the "re- 
 plenishing" period. For the purpose of discussing rainfall in its 
 
Mean Monthly Rainfall 
 
 127 
 
 Northern Atlantic, 
 New Haven, Conn, 
 
 Southern Atlantic, 
 Augusta, Ga, 
 
 St. Lawrence, 
 Detroit, Mich. 
 
 Ohio River, 
 Cincinnati, O. 
 
 Eastern Gulf, 
 Montgomery, Ala. 
 
 Western Gnlf, 
 San Antonio, Tex. 
 
 Upper Mississippi, 
 Des Moines, Iowa. 
 
 Lower Mississippi, 
 Little Rack, Ark. 
 
 Fig. G5. Mean Monthly Rainfall at Various Points in the United States. 
 
128 
 
 Rainfall. 
 
 Topeka, Kas. 
 
 Missouri River 
 
 Helena, Mont. 
 
 40 
 
 30 
 
 Hudson Bay, 
 Moorehead, Minn. 
 
 Xo. Pacific, 
 Tacoma, Wash. 
 
 Columbia River, 
 Spokane, Wash. 
 
 Pacific, 
 Sacramento, Cal. 
 
 10 
 
 10 
 
 Colorado River, 
 Tucson, Ariz. 
 
 Great Basin. 
 Winnemucca, Nev. 
 
 Fig. 66. Mean Monthly Rainfall at Various Points in the United States. 
 
Rainfall on the Drainage Area of the Wisconsin River. 129 
 
 T3S.3 
 
 IAGE OF STORAGE^ GROWING^ AND 
 
 TOTAL 
 ANNUAL. 
 
 STORAGE 
 PERIOD 
 
 GROWING 
 PERIOD . 
 
 '(REPLENISHING 
 JJPERIOO. 
 
 Fig. G7. Rainfall on the Drainage Area of the Wisconsin River. 
 
130 Rainfall. 
 
 relation to run-off it is desirable to divide the annual rainfall in 
 accordance with these periods. Figures 65 and 66 show the average 
 monthly rainfall at various points in the United States, the average 
 rainfall for each of the periods above mentioned and an additional 
 diagram for each location showing the summation of the total rain- 
 fall for each period of the water year. 
 
 Here again attention is called to the fact that for most purposes 
 of the engineer the extreme conditions and the varying conditions 
 from year to year are of much greater importance than the average 
 conditions as shown on these diagrams. Figure 67 shows the annual 
 and periodic rainfall on the valley of the AVisconsin River at three 
 different points, the relative location of which will be seen by ref- 
 erence to the map on page 84. The upper diagram shows the rain- 
 fall on the drainage area above Merrill, the center diagram the rain- 
 fall above Necedah, and the lower diagram, the rainfall above Kil- 
 bourn. In these three diagrams it is important to note the variation 
 in the rainfall condition above the different points on the water- 
 shed. For example, considering the entire area above Kilbourn and 
 above Necedah, it will be noted that the annual rainfall for 1895 
 was the lowest within the period shown, while for the area above 
 Merrill the rainfall for 1892 was the lowest for the period dis- 
 cussed. This diagram will illustrate the fact, which is manifest on 
 the investigation of most large streams, namely, that frequently 
 the intensity of the rainfall upon part of the drainage area is radi- 
 cally different from that on other parts, and that, consequently, the 
 various quantities of rain falling on a large watershed tend to 
 balance each other and keep the total more constant than observa- 
 tion at any one point would seem to indicate, so that the minimum 
 rainfall at any one point on the area is not necessarily coincident 
 with the minimum rainfall that may occur at any other point or 
 on the stream as a whole. From this it is evident that in an area 
 of any magnitude it is necessary to consider the rainfall at a large 
 number of stations well distributed over the area. 
 
 LITERATURE. 
 
 GENERAL SUBJECT OF RAINFALL. 
 
 1. U. S. Weather Bureau. Annual Reports and Monthly Weather Reviews. 
 
 2. Meteorologische Zeitschrift. 
 
 3. Zeitschrift des Osterreichen Gesellschaft fur Meteorologle. 
 
 4. Symon's Meteorological Magazine. 
 
 5. Annucine d3 la Societe Meteorogique de France, Paris. 
 
Literature. 131 
 
 6. The Royal Meteorological Society of Great Britain. Quarterly Journal. 
 
 7. Hawksley, Thomas. Laws of Rainfall and Its Utilization. Proc. Inst. 
 
 C. E. Vol. 31, pp. 53-59. 1871. 
 
 8. Binnie, Alex. R. Tables of Mean Annual Rainfall in Various Parts of the 
 
 World, Proc. Inst. C. E. Vol. 39, pp. 27-31. 1874. 
 
 9. Schott, C. A. Tables and Results of the Precipitation of Rain and Snow 
 
 in the U. S. Smithsonian Contribution to Knowledge, No. 222, 
 1874. 
 
 10. Charts and Tables Showing Geological Distribution of Rainfall in the 
 
 U. S. U. S. Signal Service Professional Paper No. 9. 1883. 
 
 11. Rainfall Observations at Philadelphia. Reports Phila. Water Bureau, 
 
 1890-92. Eng. Record, 1891, p. 246. 1892, p. 360. 
 
 12. Binnie, Alex. R. Mean or Average Rainfall and the Fluctuations to 
 
 which It is Subject. Proc. Inst. C. E. Vol. 119 (1892), pp. 
 172-189. 
 
 13. Waldo, Frank. Modern Meteorology. New York, Scribner's Sons. 1893. 
 
 14. Davis, W. M. Elementary Meteorology. Boston, Ginn & Co., 1894. 
 
 15. Harrington, M. W. Rainfall and Snow of the United States. Bulletin 
 
 C., U. S. Weather Bureau, 1894. 
 
 16. Russell, Thomas. Meteorology. New York, MacMillan Co. 1895. 
 
 17. Henry, A. J. Rainfall of the United States. Bulletin D., U. S. Weather 
 
 Bureau. 1897. 
 
 18. Turneaure & Russell. Public Water Supplies. Chapter 4. New York, 
 
 Wiley & Sons. 1901. 
 
 19. Hann, Julius. Handbook of Climatology.' New York, MacMillan Co. 
 
 1903. 
 
 20. Handbook der Ingenieur Wissenschaften. Part 3, der Wasserbau; sec. 1, 
 
 Gewasserkunde. Leipzig, E. Engelmann, 1904. 
 
 21. Hann, Julius. Lehrbuch der Meteorologie. Leipzig. 1906. 
 
 EXCESSIVE RAINFALL. 
 
 22. Francis, Jas. B. Distribution of Rainfall during a Great Storm in New 
 
 England in 1869. Trans. Am. Soc. C. E. Vol. 77, p. 224. 
 
 23. The New England Rain Storm of Feb. 10-14, 1886. Eng. News, 1886, Vol. 
 
 15, p. 216. 
 
 24. Hoxie, R. L. Excessive Rainfalls Considered with Special Reference to 
 
 Their Appearance in Populous! Districts. Trans. Am. Soc. C. E., 
 p. 70. June, 1891. 
 
 25. Talbot, Arthur N. Rates of Maximum Rainfall. Technograph, Univ. of 
 
 Illinois. 1891-1892. 
 
 26. Duryea, Edwin, Jr. Table of Excessive Precipitation of Rain at Chi- 
 
 cago, Illinois, from 1889 to 1897, inclusive. Jour. W. Soc. of 
 Engrs. Feb., 1899. 
 
 CAUSES OF RAINFALL. 
 
 27. Henry, D. F. Rainfall with Different Winds. Rept. Chf. Engr. U. S. A. 
 
 1867, p. 598. 
 
 28. Blanford, H. F. How Rain is Formed. Smithsonian Report. 1889, pt. 
 
 1, p. 287. 
 
132 Rainfall. 
 
 29 Belschow, Frantz A. The Causes of Rain and the Structure of the At- 
 mosphere. Trans. Am. Soc. C. E. Vol. 23, p. 303. 1890. 
 
 30. Davis, W. M. The Causes of Rainfall. Journal of N. E. W. Wks. Ass'n. 
 
 1901. 
 
 31. Curtis, G-. E. The Effect of Wind Currents on the Rainfall. Signal Serv- 
 
 ice Notes No. 16. 
 
 THE EFFECT OF ALTITUDE ON RAINFALL. 
 
 32. Homersham, S. C. Variations of the Rainfall with the Elevation. Proc. 
 
 Inst. C. E., Vol. 7, pp. 276, 282 & 284. 1848. 
 
 MEASUREMENT OF RAINFALL. 
 
 33. Clutterbuck, J. C. Dalton's Rain-gage. Proc. Inst. C. E., Vol. 9, p. 157. 
 
 1850. 
 
 34. Fitzgerald, Desmond. Does the Wind Cause the Diminished Amount of 
 
 Rain Collected in Elevated Rain Gages? Jour. As so. of Eng. Soc. 
 1884. 
 
 35. Weston, E. B. The Practical Value of Self-recording Rain-gages. Eng. 
 
 News, 1889, Vol. 21, p. 399. 
 
 36. Self-Registering Rain-gages and Their Use for Recording Excessive Rain- 
 
 falls. Eng. Rec. 1891, Vol. 23, p. 74. 
 
 37. Duryea, Edwin, Jr. Effect of Wind Currents on Rainfall and on the 
 
 Gage Record. Signal Service Notes No. 16. 
 
CHAPTER VII. 
 
 THE DISPOSAL OF THE RAINFALL. 
 
 78. Factors of Disposal. The portion of the rainfall in which 
 the water power engineer is most directly interested is that which 
 runs off in the surface flow or flow of streams. In order to form 
 some idea of the amount of this run-off and the factors that control 
 it, it is necessary, however, to investigate and consider the various 
 ways in which the rainfall is distributed, for the ways in which the 
 distribution occurs are mutually inter-dependent and of necessity 
 modify and control each other. The rainfall disposal depends on a 
 large number of factors or conditions among the most important 
 of which may be named : 
 
 (1) The amount of the rainfall. 
 
 (2) The rate of rainfall. 
 
 (3) The condition of the surface on which the rainfall takes 
 place. 
 
 (4) The condition of the underlying geological strata. 
 
 (5) The atmospheric temperature. 
 
 (6) The direction and velocity of the wind. 
 
 (7) The nature and extent of vegetation. 
 
 (8) The surface topography. 
 
 (9) The evaporation. 
 
 It will be noted that some of the factors mentioned above tres- 
 pass more or less on others and are not clearly separable. 
 
 79. The Rate or Intensity of Rainfall. It will readily be recog- 
 nized that with very heavy or intense rainfall a larger percentage 
 of the water will run directly into the streams and a smaller per- 
 centage will be taken up by the strata than would be the case were 
 the rainfall very light. In very light rainfalls there is no run-off, 
 the water being either taken directly into the strata or re-evaporated 
 from the surface. 
 
134 Disposal of the Rainfall. 
 
 80. Condition of Receiving Surfaces and Geological Strata. 
 Next in importance in modifying the disposal of rainfall is the 
 condition of the surface on which the rain falls and of the under- 
 lying geological strata. If the geological strata are porus in na- 
 ture and comparatively free from water they will readily receive 
 and transmit the rainfall if the surface is in proper condition to re- 
 ceive it. The condition of the surface itself modifies the reception 
 of the rainfall in a very marked manner. With high surface slopes 
 the rainfall may be large, even with somewhat porous strata, and 
 yet very little water will be taken up by the strata. With low 
 slopes and porus strata a large amount of water will be received 
 directly by the surface and passed into the ground water and deep 
 waters of underlying geological strata. 
 
 The temperature has an important influence on the condition of 
 the strata, and consequently the disposal of the rainfall. Strata 
 otherwise porous but with saturated and frozen surface will re- 
 ceive and retain practically no water and the consequence is that 
 under these conditions even a low rainfall may produce a consider- 
 able run-off that under other temperature conditions would not 
 occur. 
 
 81. Effects of Wind. The wind has a marked effect on evapora- 
 tion and consequently on the quantity of rainfall that passes away 
 in the atmosphere. The average velocity of the wind will vary in 
 different parts of the United States from three to seventeen miles 
 per hour and, other things being equal, will increase evaporation as 
 such average velocity increases. 
 
 82. Effects of Vegetation. The nature and extent of the vege- 
 tation on a surface has a marked effect on the disposal of the rain- 
 fall. Experiments at the Wisconsin Agricultural Experimental 
 Station show that barley, oats and corn require 15.2, 19.6 and 26.4 
 inches of rainfall, respectively, to produce a crop. This includes 
 the transpiration and evaporation from the cultivated surface as 
 well as the actual quantity used by vegetation. The amount act- 
 ually retained as a part of the vegetable growth is, of course, very 
 small. The water simply serves to convey the soluble. foods of the 
 soil to the various fibres of the plant. The actual amount of 
 water used in irrigation is not a fair criterion of the amount 
 needed for the development of plant life as in most cases crops 
 are over-irrigated. The actual depth and the rainfall and irri- 
 gation water used on crops vary from as low as 12 inches to 
 sometimes as high as 16 feet, frequently running into quantities 
 
Effects of Vegetation. 
 
 135 
 
 much in excess of any ordinary rainfall in moist climates where 
 irrigation is found to be unnecessary. 
 
 In the Report of the Kansas State Board of Agriculture for De- 
 cember 31, 1889, Mr. W. Tweeddale, C. E., gives the following ta- 
 ble containing the results of investigations by M. E. Risler, a Swiss 
 observer, upon the daily consumption of water by different kinds 
 of crops: 
 
 TABLE. X 
 Daily Consumption of Water by Crops. 
 
 
 INCHES 01 
 
 p WATER. 
 
 
 Minimum. 
 
 Maximum. 
 
 Lucern grass 
 
 134 
 
 267 
 
 IVIeadovv 2rras c 
 
 1" 
 
 ''87 
 
 Oats 
 
 0.140 
 
 193 
 
 Indian Corn 
 
 110 
 
 1 570 
 
 Clover 
 
 140 
 
 
 Vinevard. ... 
 
 035 
 
 031 
 
 Wheat 
 
 106 
 
 110 
 
 Rye . . . . . . 
 
 091 
 
 
 Potatoes 
 
 038 
 
 055 
 
 Oak trees . . 
 
 030 
 
 0.038 
 
 Fir Trees 
 
 0.020 
 
 0.043 
 
 
 
 
 Mr. Tweeddale finds that this table agrees with careful experi- 
 ments made in France and elsewhere, and calculates from it that 
 from seed time to harvest cereals will take up 15 inches of water 
 and grass may absorb as much as 37 inches. 
 
 This table shows also one of the important reasons why a de- 
 crease of stream flow follows the destruction of forests and their 
 replacement by meadows and cultivated fields. It is quite evident 
 also that if the watersheds were covered by grasses or cereals there 
 would be comparatively little water left for the flow of streams. 
 From this it will be seen that the character of the vegetation on a 
 watershed exerts a considerable influence on the ultimate distribu- 
 tion of the rainfall. 
 
 The presence or absence of forests has also, as shown by a series 
 of observations in Germany, a marked effect on evaporation. Prof. 
 M. W. Harrington (see Bulletin No. 7, U. S. Dept. of Agriculture, 
 p. 97) has compiled the accompanying diagram (Fig. 68), which 
 illustrates clearly the effect of forests upon the monthly evapora- 
 tion. The upper curve represents the evaporation from water sur- 
 
136 
 
 Disposal of the Rainfall. 
 
 faces in the open country, while the lower curve shows the evap- 
 oration from water surfaces in the woods. The shaded area thus 
 illustrates the saving due to the cover and protection of forests. 
 
 83. Percolation. On pervious and unsaturated strata a portion 
 of the rainfall sinks below the surface until it reaches a saturated 
 
 Fig. 68. Reduction in Evaporation Due to the Presence of Forests. 
 
 or a relatively impervious stratum. The water then follows the dip 
 of the stratum until it reaches an outlet along some stream or ap- 
 pears in the form of springs, frequently in an entirely different 
 drainage area or possibly below the level of the sea itself. It is 
 this ground water that gives rise to the dry weather flow of 
 streams, and frequently is the only source from which stream flow 
 is maintained during the dry seasons of the year. The same sources 
 irequently maintain the winter flow at times when the rainfall is 
 stored on the watershed in the form of snow and ice. 
 
 Percolation is an important factor in the storage- of water and 
 in the construction of raceways and canals and needs most careful 
 attention when such works are under contemplation. 
 
 A large amount of valuable data concerning the losses due both 
 to evaporation and seepage has been collected by Mr. E. Kuichling 
 in connection with the study of the water supply for the New 
 York Barge Canal and is reproduced in the Appendix. 
 
 A small portion of the ground water is taken up by the roots of 
 plants and frequently feeds vegetation during dry periods. Water 
 drawn from the soil for such purposes, after fulfilling its functions 
 in vegetation, is transpired from the vegetable surfaces into the 
 atmosphere. Streams fed from areas where large deposits of fine 
 grained but porous material are developed, are usually more 
 constant in flow and less subject to fluctuations either from 
 flood or drought. The flows of the deeper strata usually pass far 
 from the watershed on which the rainfall occurs and modify to a 
 limited extent the stream flow in other valleys frequently far from 
 the original rainfall source. 
 
Evaporation. 137 
 
 84. Evaporation. Evaporation takes place from moist surfaces 
 and from the water surfaces of swamps, lakes, streams and the 
 oceans, whenever such surfaces are in contact with unsaturated 
 atmosphere. The absorption of the rainfall by the strata effectively 
 limits the amount of evaporation from a given area by reducing 
 the area of contact of wet surface with the atmosphere, thus con- 
 fining the evaporation largely to free water surfaces. Fig. 69 
 shows a map of the approximate annual evaporation which takes 
 place from water surfaces at various points within the United 
 States. It will be noted that this map shows, in the greater por- 
 tion of the United States, evaporations equal to or greater than 
 the annual rainfall at such localities. The total annual evaporation, 
 as shown in the map, is based, however, on free water surfaces 
 only, and evaporation from ground surfaces only takes place from 
 occasional moist surfaces which occur after rains and when the 
 humidity is high. The total amount of water evaporated, there- 
 fore, is very much less than that which the map would seem to in- 
 dicate. This map and the table of monthly evaporation in the 
 appendix are taken from data given in the Monthly Weather 
 Review of September, 1888. The Weather Review observations 
 are not based on absolute evaporation tests but are deduced from 
 readings of dry and wet bulb thermometers as observed at various 
 Signal Service Stations in 1887 and 1888. These deductions are 
 supplemented by observations at several stations by means of the 
 Piche evaprometer. While evaporation, like rainfall, varies from 
 year to year in accordance with the variation in the controlling 
 factors, yet in lieu of more extended observations this map and 
 table indicate relative conditions at the various stations and ap- 
 proximately the evaporation from free water surfaces. The com- 
 parative monthly evaporation at sixteen stations distributed 
 throughout the United States is shown graphically by Fig. 70. At a 
 number of Eastern points, namely, Boston, Rochester and New 
 York, evaporation observations have been made for a number of 
 years and from the data thus collected a knowledge of the local 
 variations that occur in evaporation at these points can be obtained. 
 
 Evaporation is greatly promoted by atmospheric currents which 
 have perhaps the most marked effect of any single influence. The 
 temperature of the water and the humidity of the atmosphere also 
 have a marked effect. Mr. Desmond Fitzgerald in a paper on 
 evaporation (see Trans. Am. Soc. C. E., Vol. XV, page 581) offers 
 the following formula for evaporation : 
 
izr las* 123' icr no* nriM* nr nr 100* lor wy toy ior 99 
 
 ii9 c lit" 115 H3' nr 109 loT 5 ios 5 103 101 
 
ANNUAL 
 EVAPORATION' 
 
 IN THE 
 UNITED STATES 
 
140 
 
 Disposal of the Rainfall, 
 
 No. Atlantic, So. .Atlantic, Gt. Lawrence, Ohio River, 
 
 New Haven, Conn. Augusta, Ga. Detroit, Mich. Cincinnati, O. 
 
 -B 
 
 Eastern Gulf, Western Gulf, 
 
 Montgomerj*, Ala. Palestine, Tex. 
 
 Upper Mississippi, Lower Mississippi, 
 Des Moines, la. Little Rock, Ark. 
 
 Missouri River, 
 Topeka, Kans. Helena, Mont. 
 
 Red River, 
 Moorehead, Minn. 
 
 No. Pacific. 
 Olympia, Wash. 
 
 Columbia, 
 Spokane, Wash. 
 
 Pacific, 
 Sacramento, Cal. 
 
 Colorado, 
 Yuma, Ariz. 
 
 Great Basin, 
 Winnemucca, Nev, 
 
 Fig. 70. Monthly Evaporation From Free Water Surfaces at Various Points 
 
 in the United States. 
 
Evaporation. 141 
 
 E=(V-v)( 1 --r) 
 60 
 
 In this formula V equals the maximum force of vapor in inches 
 of mercury corresponding to the temperature of the water; v, the 
 force of the vapor present in the air; W, velocity of the wind in 
 miles per hour; and E the evaporation in inches of depth per hour. 
 The value of v depends on certain relations between the tempera- 
 ture of the air and the water. From a careful examination of the 
 formula it will be seen that evaporation as represented thereby does 
 not depend largely on temperature. 
 
 Table XI is taken from a paper on "Rainfall, Flow of Stream, and 
 Storage" by Mr. Desmond Fitzgerald (Trans. Am. Soc. C. E., Vol. 
 XXVII, No. 3), and shows the monthly evaporation from water 
 surface at Boston, Massachusetts, for sixteen years. The table is 
 partially made up from a diagram of mean monthly evaporation but 
 only when the observation practically agreed with the same. 
 
 85. Evaporation Relations. Professor Cleveland Abbe gives the 
 following relations of evaporation, as established' by Professor 
 Thomas Tate : 
 
 (a) Other things being the same, the. rate of evaporation is 
 nearly proportional to the difference of the temperature indicated 
 by the wet-bulb and dry-bulb thermometers. 
 
 (b) Other things being the same, the augmentation of evapora- 
 tion due to air in motion is nearly proportional to the velocity of 
 the wind. 
 
 (c) Other things being the same, the evaporation is nearly in- 
 versely proportional tt> the pressure of the atmosphere. 
 
 (d) The rate of evaporation of moisture from damp, porous sub- 
 stances of the same material is proportional to the extent of the 
 surface presented to the air, without regard to the relative thickness 
 of the substances. 
 
 (e) The rate of evaporation from different substances mainly 
 depends upon the roughness of, or inequalities on, their surfaces, 
 the evaporation going on most rapidly from the roughest or most 
 uneven surfaces ; in fact, the best radiators are the best evaporizers 
 of moisture. 
 
 (f) The evaporation from equal surfaces composed of the same 
 material is the same, or very nearly the same, in a quiescent at- 
 mosphere, whatever may be the inclination of the surfaces ; thus a 
 
1 4 2 
 
 Disposal of the Rainfall. 
 
 
 ".COO?"-C<lCiC^lOC 
 CO CC C^J 1C *! -, t>- C: 
 
 C GC CO GC i 
 
 O r- ( 
 
 * * * 
 
 c: O c- i^ co Ci c cc c: c^i t^ io 
 
 o I-H i :M co 10 xc ic co co :M r- 1 
 
 C! ^C O 1^ CC 1C "-C O t^ ^ O i 
 
 C^Ol^OCOOC^^liCCOOiO 
 
 :ClCOCCiOlCOOOOr-ICO^H 
 O -r-i ' ' 
 
 CC>COGC3<|--C 
 
 Or- l^-iCOOO 
 
 * * * * 
 
 >i< * * -X- 
 
 1C O CO Tt^ CC -* TC -t -M Ct 
 O l^ Ct i I (M O rt O ^C Cvl 
 
 o c3. 
 
 a 2 
 
Evaporative Relations. 143 
 
 horizontal plate with its damp face upward evaporates as much as 
 one with its damp face downward. 
 
 (g) The rate of evaporation from a damp surface (namely, a 
 horizontal surface facing upward) is very much affected by the 
 elevation at which the surface is placed above the ground. 
 
 (h) The rate of evaporation is affected by the radiation of sur- 
 rounding bodies. 
 
 (i) The diffusion of vapor from a damp surface through a 
 variable column of air varies (approximately) in the inverse ratio 
 of the depth of the column, the temperature being constant. 
 
 (j) The amount of vapor diffused varies directly as the tension 
 of the vapor at a given temperature, and inversely as the depth of 
 the column of air through which the vapor has to pass. 
 
 (k) The time in which a given volume of dry air becomes satu- 
 rated with vapor, or saturated within a given percentage, is nearly 
 independent of the temperature if the source of vapor is constant. 
 
 (i) The times in which different volumes of dry air becon e 
 saturated with watery vapor, or saturated within a given per cent, 
 are nearly proportional to the volumes. 
 
 (m) The vapor already formed diffuses itself in the atmosphere 
 much more rapidly than it is formed from .the surface of the water. 
 (This assumes, of course, that there are no convection currents of 
 air to affect the evaporation or the diffusion.) 
 
 86. Practical Consideration of Losses. From the previous dis- 
 cussion it will be readily realized that it would be impossible to dif- 
 ferentiate all of the methods of the disposal of rainfall upon a drain- 
 age area. Evaporation differs widely from different classes of vege- 
 tation and from different classes of land surfaces ; also on account 
 of the slope and exposure. No two square miles upon a drainage 
 area offer the same conditions as affecting evaporation which differs 
 very widely with such conditions. Evaporation and seepage from 
 any surface varies with the temperature, with the moisture in the 
 air, and with the velocity of the wind. It is therefore impossible 
 to compute, with any degree of accuracy, evaporation over an ex- 
 tended surface of a watershed or drainage area, or to ascertain 
 with any degree of accuracy the probable losses that will take place 
 in the same area. 
 
 For water power purposes, the rainfall can, therefore, be divided 
 into two quantities in which the water power engineer is interested : 
 First : The run-off on which the power developed directly depends, 
 
 OF THE 
 
144 Disposal of the Rainfall. 
 
 and, Second : The losses, by whatever means they occur, which are 
 not available for such purposes. Evaporation is usually but not 
 always the source of greatest loss on a drainage area and commonly 
 other sources of loss are insignificant when compared with it. It is 
 therefore a common practice to deduct the run-off from the rainfall 
 on a given drainage area and to classify the difference as evapora- 
 tion, including under this term all losses of this same general 
 character, whether through seepage, evaporation or otherwise. 
 
 LITERATURE. 
 
 1. Vermeule, C. C. Report on Water Supply. Geol. Survey of New Jersey. 
 
 Vol. III. 1894. 
 
 2. Vermeule, C. C. Report on Forests. Geol. Survey of New Jersey. 1899. 
 
 3. Turneaure and Russell. Public Water Supplies, Chap. V. New York,. 
 
 Wiley & Sons. 1901. 
 
 4. Rafter, George. Hydrology of the State of New York. pp. 4G-197. Al- 
 
 bany, N. Y. New York State Education Dept. Bui. 85, 1905. 
 
 PERCOLATION. 
 
 5. Lawes, J. B. The amount and Composition of the Rain and Drainage 
 
 Waters Collected at Rothamsted. Jour. Royal Agric. Soc. of 
 England, Vol. 17, p. 241, 1881; Vol. 18, p. 1, 1882. 
 
 . Fortier, Samuel. Preliminary Report on Seepage Wiater, and The Un- 
 derflow of Rivers. Bulletin No. 38, Agric. Expt. Station, Logan, 
 Utah. 1895. 
 
 7. Seepage or Return Waters from Irrigation, Bulletin No. 33. Colo. 
 
 Agric. Expt. Sta., Fort Collins, Colorado. 1896. 
 
 8. Fortier, Samuel. Seepage Water of Northern Utah. Water Supply and 
 
 Irrigation Paper No. 7. 1897. 
 
 9. The Loss of Water from Reservoirs by Seepage and. Evaporation. Bul- 
 
 letin No. 45. Colo. Agric. Expt. Sta., Fort Collins, Colorado. 
 May, 1898. 
 
 10. Loss from Canals from Filtration or Seepage. Bulletin No. 48. Colo. 
 
 Agric. Expt. Sta., Fort Collins, Colorado. 1898. 
 
 11. Kuichling, Emil. Loss of Water from Various Canals by Seepage. (See 
 
 paper on Water Supply for New York State Canals, Report of 
 State Engineer on Barge Canal, 1901). 
 
 12. Wilson, H. M. Irrigation Engineering. New York, Wiley & Sons. 1903. 
 
 13. Wilson, H. M. Irrigation in India. Water Supply and Irrigation Paper 
 
 No. 87. 1903. 
 
 14. Mead, D. W. Report on Water Power of the Rock River. Chicago. Pub. 
 
 by the author. 1904. 
 
 EVAPORATION. 
 
 15. Greaves, Charles. On Evaporation and on Percolation. Proc. Inst. C. E. 
 
 1875-76. Vol. 45, p. 19. 
 
Literature. 145 
 
 16. Fitzgerald. Desmond. Evaporation. Trans. Am. Soc. C. E., Vol. 15, p. 
 
 581. Sept., 188G. 
 
 17. Loss of Water from Reservoirs by Seepage and Evaporation, Bulletin 
 
 No. 45, Colo. Agric. Expt, Sta., Fort Collins, Colo. May, 1898. 
 
 18. Depth of Evaporation in the United States. Monthly Weather Review. 
 
 September, 1888. 
 
 19. Depth of Evaporation in the United States, Engineering News, Decem- 
 
 ber 30th, 1888; January 5th, 1889. 
 
 20. Harrison, J. T. On the Subterranean Water in the Chalk Formation of 
 
 the Upper Thames and its Relation to the Supply of London. 
 Proc. Inst. C. E. 1890-91. Vol. 105, p. 2. 
 
 21. Fernow, B. E. Relation of Evaporation to Forests. Bulletin No. 7, For- 
 
 estry Div., U. S. Dept. Asric. and Engineering News, 1893, Vol. 
 30, p. 239. 
 
 22. Kimball, H. H. Evaporation Observations in the United States. Read 
 
 before the Twelfth National Irrigation Congress, 1904; Engi- 
 neering News, April 6, 1905. 
 
 USE OF WATER IN AGRICULTURE. 
 
 The Publications of the United States Experiment Stations on Irriga- 
 tion and of the Experiment Stations of the various States contain much 
 information on this subject. The following are of especial importance: 
 
 23. Hill, W. H. Report of State Engineer to Legislature of California, 2 
 
 Vols. Sacramento, 1880. 
 
 24. Carpenter, L. G. Duty of Water. Bui. 22, 'Agric. Expt. Sta., Fort Col- 
 
 lins, Colorado. 1893. 
 
 25. Fortier, Samuel. Water for Irrigation. Bui. 26, Utah Agric. Expt. Sta., 
 
 Logan, Utah. 1893. 
 
 26. Report of Irrigation Investigations, U. S. Dept. Agriculture, Irrigation 
 
 Inquiry. Bui. 86 for the year 1899. 
 
 27. King, F. H. Irrigation and Drainage. New York. MacMillan Co., 1902. 
 
 The amount of Water Used by Plants, pp. 16-46. Duty of Water, 
 pp. 196-221. 
 
 28. Mead, Elwood, Irrigation Institutions, Chap. VII, The Duty of Water. 
 
 New York. MacMillan Co. 1903. 
 
 29. Wilson, H. M. Irrigation Engineering, Chap. V., Quantity of Water Re- 
 
 .quired. New York, Wiley & Sons. 1903. 
 
CHAPTER VIII. 
 
 RUN-OFF. 
 
 87. Run-Off. That portion of the rainfall that is not absorbed 
 by the strata, utilized by vegetation or lost by evaporation, finds 
 its way into streams as surface flow or run-off. The demands of 
 the first named factors are always first supplied and the run-off is 
 therefore the overflow or excess not needed to supply the other 
 demands on the rainfall. The run-off, therefore, while a direct func- 
 tion of the rainfall, is not found to increase in direct proportion 
 thereto, except perhaps in seasons such as early spring when from 
 seasonal conditions the demands of vegetation, percolation and 
 evaporation are not active and all or most all of the rainfall flows 
 away on the surface. The remainder of the year the run-off may 
 be said to increase with the rainfall but usually at a much less 
 rapid rate and in many cases the rainfall is entirely absorbed by 
 the strata or vegetation, and does not influence or affect the run-off. 
 In this case the run-off is supplied from the ground water, stored 
 from previous rainfalls, and is entirely or largely independent of 
 the immediate rainfall conditions. 
 
 An examination of the observed run-off of streams, and the rain- 
 fall on their respective drainage areas, for annual, monthly and sea- 
 sonal periods, will show that there is a relation more or less direct 
 between the rainfall and run-off (see Fig. 71, et seq.). The relations 
 are shown by various diagrams and mean curves from which many 
 departures will be noted. The departure of individual observations 
 from the mean curve expressing these relations shows the relative 
 importance and influence of other factors in affecting such relations. 
 The relations of the numerous factors which are known to influence 
 the results are quite complex and are not well established and much 
 more meteorological information in much greater detail and a care- 
 ful consideration and study of the same will be necessary before 
 such relations can be even approximately established. 
 
Run-Off. 
 
 147 
 
148 Run-Off. 
 
 88. Influence of Various Factors. The influence of various 
 factors of disposal was discussed in the last chapter. Evaporation 
 is known to vary with temperature, the direction and velocity of 
 the winds, barometric pressure, and various other meteorological 
 influences, and yet no clearly defined relation has yet been shown 
 to exist between these factors, by means of which their actual in- 
 fluence on the run-off can be approximately calculated. Mr. C. C. 
 Vermeule (see Vol. Ill, Geol. Survey of New Jersey) considers 
 that annual evaporation depends largely on the mean annual tem- 
 perature #nd offers a formula for the calculation of the same, which,, 
 in many cases, gives results which seem to agree closely with the 
 facts and data collected from a number of Eastern drainage areas. 
 Mr. Vermeule'' s formula for the relation between annual evaporation 
 and precipitation on the Passaic River, and some other Eastern 
 drainage areas where conditions are similar, is : 
 
 E= 15-50+0.16 R 
 in which 
 
 E=The annual evaporation (including all losses on drainage area: 
 except from run-off) 
 
 and R=the annual rainfall. 
 
 For general application to all streams he suggests the formula 
 
 =(15.50+0.16 R) (0.05 T 1.48) 
 in which T= mean annual temperature. 
 
 Mr. Vermeule also offers a formula for the evaporation for each 
 month and discusses at length the influence of ground storage on 
 the flow of streams. Mr. Geo. W. Rafter (see Water Supply and 
 Irrigation Paper No. 80) has made a careful analysis of available 
 data which indicates that no such intimate relation can be found to 
 exist. In general, the information available does not seem to show 
 that other factors have a sufficiently definite relation to run-off or 
 to each other to make such relation clearly manifest and yet such 
 factors are known to have an unmistakable and constant influence. 
 This fact is quite clearly demonstrated by a number of diagrams 
 prepared by Mr. Rafter, which are here reproduced. 
 
 Figure 72 shows graphically the relation between precipitation, 
 evaporation, run-off and temperature on the Lake Cochituate basin 
 for thirty-three years. In this diagram the years are arranged in 
 accordance with the precipitation. In a general way the evapora- 
 tion and run-off for these years may be said to vary with the pre- 
 
Influence of Various Factors. 
 
 149 
 
 co 
 
 O> 
 
 * 
 
 15 
 
 4J 50 
 
 *53 
 
 c 4P 
 
 
 
 450 
 
 ^7 
 
 Years 
 
 Years arranged in order of dryness. 
 
 Fig. 72. Relation Between Precipitation, Evaporation, Run-off and Tempera- 
 
 ture on Lake Cochituate Basin. 
 9 
 
Run-Off. 
 
 cipitation. Evaporation, which, it must be remembered, here in- 
 cludes all losses except that due to run-off, increases in general 
 as the rainfall on the area increases and decreases with the rainfall, 
 For limited periods, however, this general law does not hold. 
 Other factors affect the relations and cause material departures 
 from the general law. This is particularly marked in the years 1891 
 and 1872. For these two years the rainfall was almost identical in 
 amount. The evaporation for the same years, however, differed 
 materially, being about 16 inches greater in 1891 than in 1872. As 
 a consequence the run-off for the year 1891 was about 15% inches 
 greater than in 1872. 
 
 In order to demonstrate the mutual relation between evaporation 
 and temperature the data illustrated in the previous figure has been 
 
 60 
 49 
 48 
 47 
 46 
 
 44 
 
 50 
 
 40 
 
 30 
 
 1G 
 
 i/ 
 Years 
 
 Fig. 73. Relation Between Evaporation and Temperature on Lake Cochituate 
 
 Basin. 
 
 Years being arranged according to amount of evaporation. 
 
Influence of Various Factors. 
 
 . 74 -Relations between reen- 
 tat,on, Run . 0ff , Evaporation and 
 Temperatnre on Sudbllry 
 
 ^ss&sas*** 
 
 ration respectively. ' g eVap - 
 
 
129" lay 125" i23 r 119 nr us* 113 ur 109* lor 105 103* ior 99' 
 
 47 
 
05 93 91* 89 flr ' 85" 83 81 79' 11' IS* 
 
 cy er 65 
 
 OP THE 
 
 UNITfcDJSTATES 
 
154 
 
 Run-Off. 
 
 60 
 
 40 
 
 30 
 
 20 
 
 JO 
 
 44 
 
 - 
 
 40 
 
 20 
 
 10 
 
 Vo/irc 
 
 Years 
 
 30 
 
 20 
 
 10 
 
 44 
 439 
 42 
 41 
 40 
 
 YEAXS* 
 
 Fis 75Relations Between Precipitation, Run-Off, Evaporation and Tempera- 
 ture on Upper Hudson River. 
 Years arranged according to regular order and decreasing evaporation. 
 
 rearranged by Mr. Rafter, and in Figure 73 the relation for the 
 years has been arranged in the order of their evaporation, and com- 
 pared with the mean temperature for the year. This figure serves 
 to show that while temperature may, and unquestionably docs, 
 influence evaporation, yet the mean annual temperature has no 
 controlling effect on the annual evaporation. It will be noted that 
 for the year 1878, when the mean temperature was a maximum, the 
 evaporation was considerably below the average for this drainage 
 
Relations of Annual Rainfall and Run-Off. 
 
 155 
 
 area. Similar relations for the Sudbury River basin are shown in 
 Fig. 74 and for the Upper Hudson River basin in Fig. 75. 
 
 89. Relations of Annual Rainfall and Run-Off. Figure 76 is a 
 mean run-off map of the United States and should be compared 
 with the map of average rainfall. The run-off as shown by this map 
 is expressed in inches on the drainage area and similarly to the com- 
 mon expression for the amount of rainfall. The value of this map 
 is comparative only. In this case, as in the cases of rainfall and 
 evaporation, the mean conditions are subject to wide variations. 
 A detailed study of local conditions is always necessary in order 
 to fully understand and appreciate the influence of extreme condi- 
 tions and of local factors. 
 
 The relation between the annual rainfall and run-off on various 
 drainage areas is shown in Figures 71 to 75, inclusive, as previously 
 described. The mean relations between these two factors on four 
 selected drainage areas are, however, more clearly shown by the 
 graphical diagrams Figs. 77, 78 and 79. From these diagrams a 
 
 Pig. 77. 
 
 RUN-OFF DIAGRAM OF HUDSON MD GENESEE RIKRS 
 . HUDSON RIVER, teaa-iooi 
 
 INCHES ON CATCHMENT AREA 
 
 PERIOD HAXIMUM YEAR HINIHUM YEAR HEAR 
 
 I *..-<./. fMw tahfalt. -/. ttatef J 5j 
 
 2.45 li.7 11. SI 4.11 20.1 16.1 4.5 
 
 19.12 C.S7 12.2S 10.37 2.33 .> 12.7 3.S 
 
 S.iO 3.71 S.09 10 Jt 3.4} 7.0i 10.} 3.7 
 
 S3.S7 33.08 10.79 31.17 17.4* IHJ1 4tJ S3J 
 
 of Hudson River Indicate* ikut & 
 
 iii 
 
 INCHES ON CATCHIKNT AREA 
 
 YEAR H/fHMUH YEAR 0CM 
 
 27.71 75.73 71. m 13.20 S.S3 7.57 11.4 li.S J 
 
 cn*taf 7.95 ;. e.iiii.n b.seto.77 11.9 1.7 *J 
 
 *,i*.i,u.g. li.it lit .4 jtCT M ii ^1 * Id 
 
 Total. 47.7* I.U 1S.41 31.00 C.tf H.33 10.3 lit , MLI 
 
 Prvipltatlon In tatefti eateluntirt *na 
 
 \ \ 
 
 Fig 78. 
 
156 
 
 Run-Off. 
 
 mean relation can be traced for each area from which, however, 
 there are considerable departures in individual years. The study, 
 therefore, of this subject on this basis will demonstrate the mean 
 relation and the departure therefrom which must be expected on 
 the area considered and other areas where physical conditions are 
 similar. 
 
 KUK-OFf DIAGRAM OF MUSK/NGUM RIVER 
 
 1888-1895 
 INCHES OH CATCHMENT AREA 
 
 HAXIMUM YEAH 
 
 HIHIHUH YEAR HEAM 
 
 Of. CM**. /tatnfaJl. frn.of. 
 
 I3.S4 4.04 g.OO 
 
 S.14 0.4 f.SS 
 
 7.6t OJ7 7.tt 
 
 2S.4 4JO 
 
 i rr~-(r i 
 
 44 45 SO SS 60 SS 
 
 Fig. 79 
 
 Table 'X.ll.Muskingum River, 1888-1895, inclusive. 
 
 [Catchment area=5,828 square miles.] 
 
 
 
 1888. 
 
 
 
 1889. 
 
 
 - 
 
 1890. 
 
 
 Period. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo" 
 ration- 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Storage 
 
 17.16 
 
 5.17 
 
 11.99 
 
 13.52 
 
 6/02 
 
 7 50 
 
 27.77 
 
 ]8 07 
 
 9 70 
 
 Growing 
 Replenishing ........... 
 
 14.31 
 11.14 
 
 1.77 
 3.39 
 
 12.54 
 7.75 
 
 12.12 
 10.24 
 
 1.24 
 96 
 
 10.88 
 9 28 
 
 13.68 
 15 52 
 
 2.64 
 6 13 
 
 11.04 
 9 39 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 42 61 
 
 10 33 
 
 32 28 
 
 35 88 
 
 8 22 
 
 27 66 
 
 56 97 
 
 26 84 
 
 30 13 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1891. 
 
 
 
 1892. 
 
 
 
 1893. 
 
 
 Storage 
 
 16 72 
 
 12 42 
 
 4 30 
 
 20 39 
 
 9 06 
 
 11 33 
 
 25 04 
 
 14 13 
 
 10 91 
 
 Growing 
 
 13 56 
 
 1 77 
 
 11 79 
 
 16 54 
 
 3 65 
 
 12 89 
 
 8 31 
 
 1 22 
 
 7 00 
 
 Replenishing 1 
 
 7 08 
 
 1 37 
 
 5 71 
 
 4 81 
 
 67 
 
 4 14 
 
 9 01 
 
 85 
 
 8 16 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 37.36 
 
 15.56 
 
 21.80 
 
 41.74 
 
 13.38 
 
 28.36 
 
 42.36 
 
 16.20 
 
 26.16 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1894. 
 
 
 
 J895. 
 
 
 Storage 
 
 
 
 
 16 93 
 
 7 63 
 
 9 30 
 
 13 04 
 
 4 04 
 
 fi 00 
 
 Growing 
 
 
 
 
 4 56 
 
 OC 
 
 3 90 
 
 9 14 
 
 49 
 
 8 6 
 
 Replenish ing 
 
 
 
 
 9 02 
 
 .41 
 
 8 61 
 
 7 6<> 
 
 37 
 
 *729 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 
 
 
 30.51 
 
 8.70 
 
 21. el 
 
 29.84 
 
 4.90 
 
 24.94 
 
 
 
 
 
 
 
 
 
 
 . J 
 
The Water Year. 157 
 
 90. The Water Year. The relation of annual rainfall and annual 
 run-off is more or less obscured by variations in the periodic dis- 
 tribution of the annual rainfall. A study of the relation of the 
 periodic rainfall and the periodic run-off is therefore necessary. 
 
 For a comprehensive understanding of the relation of rainfall to 
 run-off it is more convenient to refer to the water year instead of 
 the calendar year. The water year is the annual division of time 
 that represents the full annual cycle of change in hydrological 
 conditions. It does not, as a rule, conform very closely to the calen- 
 dar year, neither is the water year constant for each annual period 
 in its beginning or end, but varies as meteorological conditions 
 vary. 
 
 As previously stated, in the greater portion of the United States, 
 the water year naturally divides itself into periods, beginning, ap- 
 proximately, with December, and ending, approximately, with the 
 following November. The period from December to and including 
 May is termed the "Storage" period ; June, July and August con- 
 stitute the "Growing" period, and September, October and Novem- 
 ber are termed the "Replenishing" period. Not only the year but 
 these periods as well vary each year, and are not necessarily 
 limited by our artificial division of calendar months and years. 
 
 During the storage period, the snows of winter and the rains of 
 spring saturate the ground, and a large amount of water is held in 
 storage in lakes, swamps, and forests, and in pervious soils, sands 
 and gravels. The portions of this stored water tributary to a drain- 
 age area but not necessarily within the boundaries thereof, and at 
 elevations above the level of the stream, are, when conditions de- 
 mand, available to supply the stream flow, and are also available 
 for the purpose of sustaining plant life. Such waters will feed a 
 stream to an extent depending on their character and magnitude, 
 regardless of the amount of the immediate rainfall, and will cause a 
 stream to flow for several months, even without rain, if the per- 
 vious deposits and other storage resources are well developed 
 upon the area. These relations vary widely with each individual 
 area, and in areas not well provided with such deposits the streams 
 often run dry through the warm days of summer. 
 
 Whenever the surface of the stream falls below the ground water 
 gradient the ground water is affected and begins to supply the 
 stream flow. This sometimes occurs early in May, and seldom 
 later than the beginning of June. During June, July and August 
 the rainfall is rarely sufficient to take care of the evaporation and 
 
Run-Off. 
 
 growth of vegetation without something of a draft on the ground 
 water, and the stream flow during this period is usually entirely 
 dependent on the ground water, except during exceptionally heavy 
 rainstorms. By the end of the growing period about August 3ist 
 the ground water is often so reduced as to be capable of storing 
 several inches of rainfall. During the replenishing and storage 
 periods of winter and spring the ground begins to receive its store 
 of water, and, with favorable rainfalls, the ground becomes fully 
 saturated by the end of April or May. 
 
 Ta,ble XIII. Hudson River, 1888-1901, inclusive. 
 [Catchment area=4,500 square miles.] 
 
 
 
 1888. 
 
 
 
 1889. 
 
 
 
 1890. 
 
 
 Period. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Storage .......... 
 
 20.40 
 
 17.06 
 
 3.34 
 
 17.10 
 
 14.04 
 
 3.06 
 
 24.75 
 
 19.28 
 
 6.47 
 
 GrAwipg - - . ... 
 
 10.25 
 
 2.05 
 
 8.20 
 
 15.05 
 
 4.28 
 
 10.79 
 
 13.50 
 
 2.85 
 
 10.65 
 
 Replenishing - 
 
 13.27 
 
 4.53 
 
 8.74 
 
 10.81 
 
 3.41 
 
 7.40 
 
 12.10 
 
 6.81 
 
 5.29 
 
 
 
 
 
 
 
 
 
 
 
 Year. 
 
 43; 92 
 
 a 23. 64 
 
 20.28 
 
 a42.96 
 
 21.71 
 
 21.25 
 
 50.35 
 
 28.94 
 
 21.41 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1891. 
 
 
 
 1892. 
 
 
 
 1893. 
 
 
 Storage 
 
 20 69 
 
 IS 59 
 
 4 10 
 
 24 95 
 
 22 50 
 
 2 45 
 
 19 83 
 
 15 20 
 
 4 63 
 
 
 13 49 
 
 2 07 
 
 11 42 
 
 19 12 
 
 6 87 
 
 12 25 
 
 13 37 
 
 3 12 
 
 10 25 
 
 Replenishing 
 
 8.78 
 
 1.90 
 
 - 6.88 
 
 9.80 
 
 3.71- 
 
 6.09 
 
 8.98 
 
 3.59 
 
 5.39 
 
 
 
 
 
 
 
 
 
 
 
 Year...., 
 
 42.96 
 
 20.56 
 
 22.40 
 
 '53.87 
 
 33.08 
 
 20.79 
 
 42.18 
 
 21.91 
 
 20.27 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1894. 
 
 
 
 1895. 
 
 
 
 1896. 
 
 
 Storage 
 
 21.37 
 
 13.18 
 
 8.19 
 
 15.79 
 
 11.68 
 
 4.11 
 
 22 17 
 
 18.52 
 
 5 65 
 
 Growing 
 
 8.73 
 
 3.20 
 
 6.53 
 
 10.37 
 
 2.36 
 
 8.01 
 
 10 25 
 
 2 53 
 
 7 72 
 
 Replenishing 
 
 11 87 
 
 2 99 
 
 8.88 
 
 10.51 
 
 3.42 
 
 7.09 
 
 12 79 
 
 4 58 
 
 8 21 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 41.97 
 
 19 37 
 
 22 60 
 
 36 67 
 
 17 46 
 
 19 21 
 
 45 21 
 
 23 62 
 
 21 58 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1897 
 
 
 
 1898. 
 
 
 
 1899. 
 
 
 Storage 
 
 19.77 
 
 14.60 
 
 5.17 
 
 22.80 
 
 18.61 
 
 4.19 
 
 19.48 
 
 15.15 
 
 4.3S 
 
 Growing...... 
 
 15.80 
 
 7.79 
 
 8.01 
 
 13.52 
 
 8.24 
 
 10.28 
 
 7.40 
 
 1.63 
 
 6.77 
 
 Replenishing 
 
 10 94 
 
 3.80 
 
 7.14 
 
 12.19 
 
 5.27 
 
 6.92 
 
 8.91 
 
 2.76 
 
 6.15 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 46 51 
 
 26 19 
 
 20.32 
 
 48.51 
 
 27.12 
 
 21.39 
 
 35.79 
 
 19 54 
 
 16.25 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1900. 
 
 
 
 1901. 
 
 
 Storage...... 
 
 
 
 
 21.13 
 
 16.12 
 
 5.01 
 
 18.47 
 
 14 84 
 
 3 63 
 
 Growing 
 
 
 
 
 12.11 
 
 2.30 
 
 9.81v 
 
 15.09 
 
 4.02 
 
 11 07 
 
 ReptentflhiTi g 
 
 
 
 
 12.17 
 
 2.25 
 
 9.92 
 
 9.02 
 
 3 
 
 6 02 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 
 
 
 45 41 
 
 20.67 
 
 24.74 
 
 42.58 
 
 21.86 
 
 20.72. 
 
 
 
 
 
 
 
 
 
 
 
 i Approximate. 
 
Relations of Periodic Rainfall to Run-Off. 
 Table XIV. Connecticut River, 1872-1885, inclusive. 
 
 [Catchment area =10,334 square miles, j 
 
 159 
 
 
 
 1872. 
 
 
 
 1873. a 
 
 
 
 1874. 
 
 
 Period. 
 
 Rain- 
 fall. 
 
 Run-- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 fall. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 
 14.92 
 
 13.30 
 
 1.62 
 
 18.18 
 
 21.80 
 
 3.64 
 
 23.08 
 
 23.04 
 
 0.04 
 
 
 18.96 
 
 6.29 
 
 12.67 
 
 10.11 
 
 2.71 
 
 7.40 
 
 14.37 
 
 6.62' 
 
 . 7 75 
 
 
 12.42 
 
 6.64 
 
 5.78 
 
 15.04 
 
 5.22 
 
 9.82 
 
 7.76 
 
 2.15 
 
 5 61 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 48.30 
 
 26.23 
 
 20.07 
 
 43.31 
 
 29.73 
 
 13.58 
 
 45.21 
 
 81 81 
 
 13 40 
 
 
 
 
 
 
 
 
 
 
 
 Period 
 
 
 1875. 
 
 
 
 1876. a 
 
 
 
 1877. 
 
 
 Storage 
 
 17.51 
 
 15.-47 
 
 2.04 
 
 22.50 
 
 24.74 
 
 - 2.24 
 
 18.09 
 
 12.68 
 
 5 41 
 
 
 14.55 
 
 3.80 
 
 10.75 
 
 12.51 
 
 3.35 
 
 9.16 
 
 14.00 
 
 2 91 
 
 11 09 
 
 Replenishing 
 
 11 38 
 
 3.60 
 
 7.76 
 
 10.57 
 
 2.28 
 
 8.29 
 
 13 08 
 
 5 27 
 
 ' 7 81 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 43 42 
 
 22.87 
 
 20.55 
 
 45.58 
 
 30.37 
 
 15.21 
 
 45 17 
 
 20 86 
 
 24 81 
 
 
 
 
 
 
 
 
 
 
 
 Period. 1878. 1879. 
 
 1880; 
 
 Storage 
 
 21.88 
 13.59 
 10.58 
 
 18.02 
 3.45 
 3.06 
 
 3.86 
 10.14 
 
 7.50 
 
 23.19 
 18.07 
 
 9.48 
 
 21.49 
 2.92 
 2.93 
 
 1.70 
 13.15 
 6.55 
 
 18.29 
 11.82 
 11.58 
 
 14.78 
 2.45 
 2.62 
 
 3.51 
 9. S7 
 8.96 
 
 
 Replenishing 
 
 Year 
 
 46.03 
 
 24.53 
 
 21.50 
 
 ' 48.74 
 
 27.34 
 
 21.40 
 
 41.69 
 
 19.85 
 
 21.84 
 
 
 Period. 
 
 1881. 
 
 1882. 
 
 1883. 
 
 Storage 
 
 20.83 
 11.30 
 11.38 
 
 16.02 
 2.93 
 3.39 
 
 4.81 
 8.37 
 7.99 
 
 &20.50 
 611.45 
 b6. 50 
 
 12.14 
 3.35 
 
 2.17 
 
 8.38 
 8.10 
 4.33 
 
 ft 12. 65 
 &13.50 
 &6.20 
 
 8.73 
 2.51 
 1.37 
 
 4.12 
 10.99 
 4.88 
 
 Growing 
 
 Replenishing 
 
 Year 
 
 43.51 
 
 22.34 
 
 21.17 
 
 38.45 
 
 17.66 
 
 20.79 
 
 32.55 
 
 12.61 
 
 19.94 
 
 
 Period. 
 
 1884. 
 
 1885. 
 
 Storage 
 
 21.42 
 12.14- 
 8.51 
 
 20.20 
 2.79 
 2.61 
 
 1.22 
 9.35 
 5.90 
 
 18.58 
 14.82 
 11.76 
 
 13.63 
 3.20 
 5.61 
 
 4.85 
 11.62 
 6.15 
 
 Growing 
 
 Replenishing 
 
 Year 
 
 42.07 
 
 25.60 
 
 16.47 
 
 45.16 
 
 22.44 
 
 22.72 
 
 
 "Not included in mean. 
 
 b Rainfall computed, approximate. 
 
 91. Relation of Periodic Rainfall to Run-Off. For streams where 
 the observations of flow have been made for a number of years, 
 comparisons can readily be made of the relation of annual and 
 periodic rainfall and run-off. Such investigations should be made 
 by the water power engineer when considering a river relative to 
 its availability for water power purposes. An analysis of such 
 data for the Muskingum, Hudson, and Connecticut Rivers as made 
 by Mr. Rafter, is shown in Tables XII, XIII and XIV (for ad- 
 
i6o 
 
 Run-Off. 
 
 ditional tabular data see Appendix). Graphical representations of 
 the periodic relations of the rainfall and run-off on the Upper 
 Hudson River basin are shown in Fig. 80, and the same relations 
 for the Sudbury River basin are shown in Fig. 81. 
 
 9 , 
 '0 
 tf ^ 
 
 Storage period 
 
 25, 
 
 SO, 
 
 40 
 
 80 
 
 15 20 
 
 Precipitation in inches 
 
 25 
 
 JO 15 20 
 
 Precipitation in inches 
 
 25 
 
 30 
 
 25 
 
 30 
 
 5 10 15 ?0 
 
 Precioitatfon in Inches 
 
 Fig. 80. Rainfall and Run-Off of Upper Hudson River for Each Period of the 
 
 Water Year. 
 
 [From W. S. and I. Paper No. 80 "Relation of Rainfall to Run-Off.' ] 
 
Relations of Periodic Rainfall and Run-Off. 
 
 161 
 
 40 
 
 20-= 
 
 Qc 
 10 10 
 
 Storage period 
 
 30 
 
 25 
 
 JO 15 20 25 
 
 Precipitation in inches 
 10 15 20 25 
 
 40 
 
 30 
 
 35 
 
 30 S5 
 
 10 
 
 Crowing period 
 
 10 15 
 
 Precipitation in Incites 
 10 15 20 
 
 25 
 
 30 
 
 20 20 
 
 Replenishing period 
 
 10 $ 70 
 
 w 
 
 15 
 
 20 
 
 Precipitation in inches 
 10 15 20 
 
 30 
 30 
 
 Fig. 81. Rainfall and Run-Off of Sudbury River for Each Period of the 
 
 Water Year. 
 
 [From W. S. and I. Papar No. 80 "Relation of Rainfall to Run-Off. "J 
 
1 62 Run-Off, 
 
 92. Monthly Relation of Rainfall and Run-Off. The relations of 
 rainfall to run-off from month to month on a given drainage area 
 are not usually as direct and definite as the annual and periodic re- 
 lations. The mean and extreme relations can, however, often be 
 established within somewhat wider limits, and such relations will 
 permit of the formation of at least a general idea of the probable 
 limits of the monthly run-off, under other rainfall conditions. The 
 wide range of the possible error of such estimates will be shown 
 by the divergence of independent observations from the normal. 
 To establish accurately the maximum and minimum limits, it is 
 probable that observations, at least as extended as those needed 
 for accurate rainfall estimates, will be needed. 
 
 The observed relations between the monthly rainfall and the 
 monthly run-off in various drainage areas are shown by Figs. 82, 83, 
 84 and 85. 
 
 On Fig. 82 are shown the relations of monthly rainfall and run-off 
 for several Northern river basins, and on Fig. 83 are shown the 
 same relations for several Southern river basins. An examination 
 of these diagrams will show the marked effect of seasonal tempera- 
 tures and conditions upon the quantity of run-off. The high per- 
 centage of run-off in the spring should be noted ; also how the per- 
 centages of run-off in these rivers drop with the advance of the 
 season and rise again in the fall. 
 
 On Fig. 84 are given the monthly relations of rainfall and run-off 
 for thirty years on three small river basins in the immediate 
 vicinity of Philadelphia. These drainage areas, being small, are 
 more readily and directly affected by rainfall, hence the relations 
 are much more marked and uniform than those that exist on larger 
 rivers. The marked variation from normal due to the influence of 
 other varying conditions on the drainage area, especially during the 
 summer months, should be noted. 
 
 Figure 85 shows a set of monthly diagrams prepared by Emil 
 Kuichling, C. E., for his discussion of the relation of rainfall to 
 run-off in certain rivers in the Eastern part of the United States. 
 
 On these diagrams the figures not enclosed are numbers of ob- 
 servations from drainage basins Nos. I to 8 inclusive, of the fol- 
 lowing list. The figures enclosed in circles are the numbers of 
 observations from drainage basins Nos. I to 28, inclusive. 
 
Relations of Monthly Rainfall and Run-Off. 
 
 163. 
 
 
 
 
 I 
 
 A 
 
 4 
 
 
 JANUARY 
 
 ' * 
 
 
 ^ 
 
 
 
 
 
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 ^x 
 
 ^ 
 
 
 
 
 
 
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 JULY 
 
 
 
 
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 123456789 10 0123456789 10 
 
 Horizontal Ordinates Rainfall in Inches. 
 
 Wisconsin River at Necedah. 
 D Chippewa River at Eau Claire. 
 A Grand River at Grand Rapids. 
 
 V Grand River at Lansing. 
 X Thunder Bay River. 
 Rock River at Rocktoiu 
 
 Fig. 82. Monthly Rainfall and Run- Off Northern Rivers. 
 
164 
 
 Run-Off. 
 
 
 
 
 & 
 
 1 
 
 u 
 
 '___ 
 
 ^ 
 
 x 
 
 JANUARY 
 
 
 
 
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 1 2 3 4 5 6 7 9 10 11 12 13 1 2 3 4 5 6 
 
 Horizontal Ordinates Rainfall in Inches. 
 
 Talladega Creek, Watershed Area 156 Square Miles. 
 
 V Upadachee River, " "440 " 
 
 Alcovy River " " 228 " " 
 
 Fig. 83. Monthly Rainfall and Run-OffSouthern Rivers. 
 
Relations of Monthly Rainfall and Run-Off. 
 
 165 
 
 / 
 
 D 
 5 
 4 
 3 
 
 2 
 1 
 
 
 7 
 
 e 
 
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 I 2 3 4 5 B 7 B 3 ID II 121314 
 RAINFALL IN INCHES 
 
 I 2 3 4 5 B 7 B 3 ID II 121314 
 
 RAINFALL IN INCHES 
 WATERSHED AREA 
 102.2 SQUARE MILES 
 
 O B S E RVAT IONS 
 XTOHICKON CREEK 
 ANESHAMINY " 139.3 
 
 OPERKIOMEN " 152. 
 
 Ffg. 84. Relation between Kainfall and Run-Off on Tohickon, Neshaminy, and 
 Perkiomen Creeks near Philadelphia, Pennsylvania. 
 
1 66 
 
 Run-Off. 
 
 ui 
 
 -I 
 
 
 ,\ 
 
 \- 
 
 V 
 
 \ 
 
 
 *. 
 
 a 
 
 a; 
 
 9 I 
 
 fc 
 
 
 ni 
 
Relation of Monthly Rainfall and Run-Off. 167 
 
 Watersheds from which Observations were platted on Diagram 85. 
 
 No. 
 
 Name of Basin. 
 
 Area in Sq. 
 Miles. 
 
 No. of 
 Years 
 Record. 
 
 1 
 
 Crotoii River, N. Y 
 
 338 
 
 Qrt 
 
 2 
 
 Perkiomen Creek Pa 
 
 152 
 
 i q 
 
 g 
 
 Neshaminy Creek Pa . 
 
 139 3 
 
 1 '\ 
 
 4 
 
 Tohickon Creek Pa ... 
 
 10'' 2 
 
 14 
 
 5 
 
 Sudbury River Mass 
 
 75 2 
 
 25 
 
 5 
 
 Hemlock Lake NY . . 
 
 43 i 
 
 12 
 
 
 Mystic Lake Mass . . 
 
 27 7 
 
 18 
 
 8 
 
 Cochituate Lake Mass 
 
 19 
 
 QQ 
 
 9 
 
 Cayadutta Creek N Y , 
 
 40 
 
 2 
 
 10 
 
 Saquoit Creek N. Y 
 
 51 5 
 
 2 
 
 11 
 
 Oneida Creek, N Y 
 
 59 
 
 2 
 
 12 
 
 Nine-Mile Creek, N. Y 
 
 63 
 
 1 
 
 13 
 
 
 80 8 
 
 1 
 
 14 
 
 E. Branch Fish Creek, N. Y 
 
 104 
 
 1 
 
 la 
 
 Oriskany Creek, N. Y 
 
 144.0 
 
 2 
 
 ](> 
 
 Mohawk River N Y at Ridge Mills 
 
 153 
 
 2 
 
 17 
 
 W Branch Fish Creek N Y 
 
 187 
 
 3 
 
 18 
 
 Salmon River N Y 
 
 191 
 
 1 
 
 19 
 
 East Canada Creek N. Y 
 
 256 n 
 
 2 
 
 20 
 
 West Canada Creek N Y . 
 
 518 
 
 2 
 
 21 
 
 Schroon River N Y. . 
 
 563 
 
 4 
 
 22 
 
 Passaic River, N J 
 
 822 
 
 17 
 
 23 
 
 Raritan River, N. J 
 
 879 
 
 3 
 
 24 
 
 Genesee River, N. Y 
 
 1070 
 
 
 25 
 
 Mohawk River, N. Y., at Little Falls . . 
 
 1306 
 
 2 
 
 26 
 
 Black River, N. Y 
 
 1889 
 
 4 
 
 27 
 28 
 
 Hudson River N. Y., at Mechanic vi lie, N. Y . . . . 
 Muskingum River, Ohio 
 
 4500.0 
 5828 
 
 12 
 8 
 
 
 
 
 
 A continuous graphical record for ten years, showing the rela- 
 tions of rainfall to run-off on the Illinois River basin, based on ob- 
 servations of stream flow made at Peoria, 111., is shown by Fig. 71. 
 
 93. Maximum Stream Flow. In the construction of spillways, 
 dams, and reservoirs, and the study of their effect on the overflow 
 -of embankments, levees, and lands, the question of maximum run- 
 off becomes important. 
 
 Many formulas have been suggested by engineers for determin- 
 ing flood flows, each of which is based on more or less extended 
 observations, and are applicable only when used under conditions 
 similar to those on which they are founded. Very few of these 
 formulas take into account the great number of conditions that 
 modify the results. For this reason most of such formulas are of 
 little use except for the purpose of rough approximation. None of 
 these should be used without a knowledge of the conditions under 
 
i68 
 
 Run-Off. 
 
 Max. rate of Discharge in Cu. Ft. per Sec. per Sq. Mile, (q) 
 
Maximum Stream Flow. 169 
 
 which they are applicable. Such calculations should, wherever pos- 
 sible, be based on the known ratio of actual maximum and mini- 
 mum flows on the drainage areas, or on drainage areas adjacent and 
 similar thereto, and the use of a factor of safety as great as the 
 importance of the local condition will warrant. Such data serves 
 as the best and most conservative guide for all calculations of this 
 class. 
 
 A record of the maximum and minimum flows of various Ameri- 
 can and foreign streams from the report of Mr. Kuichling, to which 
 reference has already been made, is contained in the Appendix. 
 
 Figure 86 shows a graphical representation of the actual rate of 
 maximum flood discharge of these rivers and on this diagram is 
 given the formulas, both graphically and analytically, for ordinary 
 %nd occasional maximum floods as proposed by Mr. Kuichling. It 
 is evident that Mr. Kuichling has endeavored to represent the 
 maximum flood conditions that may occur on any river. In many 
 localities, the results given are much larger than the actual condi- 
 tions of flow will warrant. 
 
 In some cases the overflow of lands and property by floods, 
 caused by back water or otherwise, may be prevented by the con- 
 struction of levees and the installation of .pumping plants for drain- 
 age purposes. Under such conditions both the extreme height pf 
 the flood and the length of its occurrence become important and 
 can be determined only by gauge observation. A graphical study 
 of such data affords the best means for its consideration. Figure 87 
 shows hydrographs of the high water conditions on the Fraser 
 River at Mission Bridge, British Columbia. This stream is fed by 
 the melting snows of the foot-hills, and the floods occur at essen- 
 tially the same time each year within certain limits, as a rule reach- 
 ing a maximum during May, June or July. The differences that 
 occur from year to year are shown by the different hydrographs 
 which represent, however, gauge heights in feet and not discharges. 
 The highest record is that of the flood of June 5, 1894, of which, 
 however, no hydrograph was obtained. 
 
 94. Estimate of Stream Flow. For the purpose of estimating 
 water power no safe deduction can be made from average run-off 
 conditions, although a knowledge of such conditions is desirable. 
 The information that is needed for the consideration of water power 
 ic a clear knowledge of the maximum and minimum conditions, 
 the variations which occur between these limits and a knowledge 
 of the length of time during which each stage is likely to occur 
 10 
 
i7o 
 
 Run Off. 
 
 -{- 
 
 &i 
 
 i* 
 
 O 00 
 
 Gauge Height in Feet. 
 
Estimate of Stream Flow. 71 
 
 throughout the year or throughout a period of years. As pointed 
 out in the previous section, the extreme conditions are important in 
 considering the height of flood as influenced by spillways and 
 other obstructions in the river. The extrejn^jmd^average low water 
 conditions commonly control or limit theexTelirr^i^tlie~pTant which 
 should be installed. 
 
 [y~~tne illustrations already shown it is fully demonstrated 
 that the run-off of any stream, either for the year, period or month, 
 cannot be approximately expressed either as an average amount or 
 as a fixed percentage of the rainfall. An expression showing the 
 relation between rainfall and run-off necessarily assumes quite a 
 complex form, from which large variations must be expected. 
 Where average amounts of run-off are considered, care must be 
 used to base the deduction on correct principles. In considering the 
 variation in the monthly flow of a stream, the flows of such stream 
 should be considered in the order of their monthly discharge 
 rather than, in their chronological order. For example : in Table 
 XV, the mean monthly flows, of various streams, in cubic feet per 
 second per square mile of drainage area are given. These flows 
 are arranged in the chronological order of the months. The aver- 
 age monthly discharges of the streams' are calculated therefrom, 
 and are shown in the last column. An examination of this table will 
 show that the minimum monthly flow of a stream does not always 
 occur during the same month for each year. For the consideration 
 of these streams for water power purposes, the better arrangement 
 of the recorded flow is not in the sequence of the months, but by the 
 monthly periods arranged in the relative order of the quantities of 
 flow. 
 
 In Table XVI this data has been rearranged. In this arrange- 
 ment the least flow for any month in a given year is placed in the 
 first line and the flows for other months are arranged progres- 
 sively from minimum to maximum. The average for each month 
 will, by this arrangement, give a much better criterion of the 
 average water power to be expected from each drainage area dur- 
 ing each year than the average monthly flow as determined in 
 Table XV. 
 
172 
 
 Run-Off. 
 
 TABLE XV. 
 
 Mean Monthly Flows of Various Eastern Streams Arranged in Chronological 
 Order. (In Cubic Feel per Second per Square Mile. ) 
 
 Kennebec Kiver at Waterville, Me. 
 Drainage Area 4380 sq miles. 
 
 Year. 
 
 '9:) 
 
 '94 
 
 '95 
 
 '96 
 
 '97 
 
 '98 
 
 '99 
 
 '00 
 
 '01 
 
 '02 
 
 '03 
 
 '04 
 
 '05 
 
 Ave. 
 
 January . . 
 
 .60 
 .53 
 .95 
 2.64 
 6.92 
 3 47 
 
 .37 
 
 .40 
 .91 
 3.33 
 2.17 
 
 .46 
 .41 
 .45 
 5.43 
 2.17 
 1.46 
 .80 
 .61 
 .40 
 .28 
 1.27 
 1.37 
 1.27 
 
 .98 
 .64 
 2.98 
 6.21 
 3.87 
 1.25 
 1.21 
 .71 
 .77 
 .83 
 2.07 
 .62 
 1.84 
 
 .81 
 .84 
 .86 
 5.75 
 6.10 
 2.94 
 2.96 
 1.65 
 1.04 
 .60 
 1.29 
 1.21 
 2.17 
 
 .',3 
 
 2!56 
 6.76 
 5.70 
 2.26 
 .89 
 .71 
 .59 
 .92 
 1.77 
 .59 
 1.97 
 
 .53 
 .54 
 .73 
 5.31 
 1.81 
 2.00 
 1.14 
 .73 
 .43 
 .28 
 .40 
 .51 
 1.46 
 
 .54 
 
 2.05 
 2.07 
 6.45 
 6.41 
 2.28 
 1.31 
 .95 
 .63 
 
 .<;9 
 
 1.44 
 .93 
 
 2.14 
 
 .73 
 .57 
 1.10 
 9.39 
 3.46 
 1.8S 
 1.17 
 .95 
 .64 
 .67 
 .55 
 1 72 
 1.9U 
 
 .88 
 .87 
 6.57 
 5.07 
 3.85 
 i.4H 
 1.79 
 1.15 
 .96 
 1.20 
 1.03 
 .99 
 2.32 
 
 .9i 
 .88 
 4.42 
 3.74 
 1.66 
 1.52 
 1.19 
 .88 
 .57 
 .44 
 .33 
 .32 
 1.41 
 
 2.22 
 .20 
 .86 
 3.41 
 4.71 
 1.89 
 1.22 
 1.07 
 .98 
 1.07 
 .77 
 .60 
 1.58 
 
 .70 
 
 .60 
 1.20 
 3.08 
 2.40 
 1.53 
 1.07 
 .73 
 .68 
 .40 
 .52 
 .47 
 1.12 
 
 .FC 
 .72 
 1.97 
 5.13 
 4.17 
 2.14 
 1.34 
 .87 
 ,68 
 
 >J9 
 
 .78 
 
 February 
 
 March 
 
 April . . , 
 
 May 
 
 
 July 
 
 1.81 
 .51 
 .46 
 .53 
 .51 
 .36 
 1.65 
 
 1.30 
 .67 
 .62 
 .85 
 .85 
 .44 
 1.12 
 
 August .... 
 
 September 
 
 October 
 
 November .... . . 
 
 
 Average . . . .. 
 
 
 
 Merrimac River at Lawrence, Mass. 
 Drainage Area 4553 sq. mi. 
 
 Tsar. 
 
 '90 
 
 '91 
 
 '92 
 
 '93 
 
 '94 
 
 '95 
 
 '96 
 
 '97 
 
 '98? 
 
 '99 
 
 '00 
 
 '01 
 
 '02 
 
 '03 
 
 '04 
 
 'o:> 
 
 Ave. 
 
 January 
 
 1.53 
 1 70 
 
 2.92 
 2.96 
 5.19 
 4.73 
 1.61 
 1.00 
 .64 
 .54 
 .56 
 .47 
 .54 
 90 
 1.84 
 
 1.87 
 .94 
 1.61 
 1.79 
 2.25 
 1.28 
 1.05 
 1.06 
 .87 
 .47 
 1.43 
 .86 
 1.29 
 
 .65 
 1.10 
 2.36 
 3.42 
 4.28 
 .97 
 .52 
 .57 
 .61 
 .79 
 .74 
 1.17 
 1.43 
 
 .66 
 .94 
 3.16 
 2.43 
 1.54 
 1.33 
 .50 
 .37 
 .40 
 .50 
 .78 
 .67 
 1.11 
 
 .63 
 .51 
 1.28 
 4.35 
 1.37 
 .67 
 .57 
 .48 
 .37 
 .88 
 2.10 
 2.06 
 1.27 
 
 1.44 
 2.00 
 4.62 
 4.00 
 .98 
 .77 
 .45 
 .44 
 .67 
 1 14 
 1.46 
 .96 
 1.58 
 
 .75 
 1.01 
 2.32 
 
 3.87 
 2.22 
 2.79 
 2.37 
 1.12 
 .61 
 .48 
 1.2$ 
 2.2K 
 1.76 
 
 1.62 
 1.71 
 4.09 
 3.34 
 2.42 
 1.42 
 .58 
 .83 
 .64 
 1.41 
 2.17 
 1.93 
 1.85 
 
 1.73 
 1.07 
 2. 6-> 
 5.81 
 2.09 
 .65 
 .54 
 .46 
 .44 
 .39 
 .61 
 .61 
 1 42 
 
 .74 
 3.62 
 3.56 
 4.06 
 2.21 
 .87 
 .40 
 .41 
 .33 
 .55 
 1.28 
 1.4.) 
 1.63 
 
 72 
 
 .53 
 2.04 
 3.94 
 4.04 
 1.61 
 .62 
 .6 
 .57 
 .86 
 .65 
 2.09 
 1.53 
 
 2.24 
 
 1.20 
 6.06 
 3.72 
 2.18 
 1.13 
 ".93 
 .81 
 .74 
 1.54 
 1.23 
 1.74 
 1.96 
 
 .86 
 1.99 
 5.66 
 3.34 
 0.94 
 2.21 
 1.00 
 .72 
 .51 
 .79 
 .64 
 .80 
 1.62 
 
 ,57 
 .63 
 2.64 
 4.45 
 3.74 
 1.00 
 .60 
 .55 
 .6^ 
 .78 
 .58 
 .39 
 
 138 
 
 .83 
 .49 
 2.2(i 
 3.47 
 1.12 
 .89 
 .57 
 .58 
 1.64 
 .70 
 .73 
 1.82 
 
 ,. 
 
 1.24 
 1.40 
 3 30 
 3.7S 
 2 26 
 1.27 
 .75 
 .67 
 1 38 
 .90 
 1.14 
 1.29 
 
 
 March 
 
 3.44 
 3.79 
 3.14 
 1.73 
 
 .69 
 .75 
 1.84 
 2.70 
 1.95 
 1.44 
 2.06 
 
 April 
 
 May .. 
 
 June 
 
 July 
 
 August 
 
 September 
 October 
 
 November 
 
 December 
 
 Average 
 
 
 Hudson River at Mechanicville, N. Y. 
 Drainage Area 4500 sq. mi. 
 
 Year. 
 
 '88 
 
 '89 
 
 '90 
 
 '91 
 
 '92 
 
 '93 
 
 '94 
 
 ,'95 
 
 '96 
 
 '97 
 
 '98 
 
 '99 
 
 '00 
 
 '01 
 
 '02 
 
 '03 
 
 '04 
 
 '05 
 
 Ave. 
 
 January .... 
 February... 
 March 
 April 
 May 
 June . . 
 
 1.41 
 
 .82 
 1.52 
 4.73 
 4.76 
 1.09 
 .34 
 .38 
 .63 
 1.02 
 2 36 
 2.22 
 1.77 
 
 2.44 
 .84 
 1.84 
 3.04 
 1.97 
 1.52 
 1.28 
 .95 
 .41 
 .83 
 1.77 
 2.93 
 1.65 
 
 2.50 
 1.74 
 2.47 
 3.35 
 3.98 
 1.64 
 .43 
 .45 
 1 97 
 2.05 
 2.03 
 .72 
 1.94 
 
 1.84 
 2.59 
 3.94 
 4.45 
 1.23 
 .71 
 .52 
 .59 
 .45 
 .33 
 .91 
 1.91 
 1.62 
 
 4.19 
 2.06 
 2.41 
 4.79 
 4.37 
 2.80 
 2.06 
 1.22 
 .99 
 .63 
 1.69 
 .93 
 2.34 
 
 .71 
 1.02 
 1.97 
 3.98 
 4.95 
 1.07 
 .56 
 1.11 
 1.53 
 .86 
 .81 
 1.60 
 1.68 
 
 1.50 
 1.07 
 3.28 
 2.47 
 1.68 
 1.58 
 .70 
 .55 
 .42 
 .81 
 1.42 
 .97 
 1.37 
 
 .86 
 .79 
 .93 
 5.29 
 1.52 
 .63 
 .57 
 .87 
 .58 
 .58 
 1.87 
 2.42 
 1.41 
 
 1.51 
 1.04 
 3.02 
 5.55 
 1.02 
 1.05 
 .62 
 .54 
 .64 
 .91 
 2.52 
 1.54 
 1.66 
 
 .89 
 .87 
 2.71 
 4.24 
 2.70 
 2.63 
 2.47 
 1.83 
 .61 
 .56 
 2.22 
 3.20 
 2.08 
 
 1.72 
 1.50 
 4.49 
 3.05 
 2.46 
 1.17 
 .57 
 1.14 
 .86 
 1.75 
 2.05 
 1.25 
 1.83 
 
 1.49 
 1.17 
 2.14 
 
 5.25 
 2.17 
 .58 
 .54 
 .31 
 .46 
 .58 
 1 49 
 
 1.30 
 2.77 
 1.72 
 5 02 
 2.00 
 .91 
 .52 
 .60 
 .42 
 .47 
 1 11 
 
 .69 
 .54 
 1 80 
 6.28 
 2.60 
 1.73 
 .79 
 1.03 
 .89 
 .94 
 83 
 
 l"53 
 5.53 
 
 2.38 
 1.76 
 1.40 
 1.98 
 1.40 
 .81 
 1.53 
 1 41 
 
 1.56 
 2.19 
 6.87 
 3.11 
 .78 
 1.8S 
 l.OF 
 1.31 
 .91 
 2.25 
 1 ^ 
 
 1.2J* 
 1.52 
 2.46 
 4.61 
 2.96 
 1.50 
 .58 
 1.39 
 1.4H 
 2.62 
 1.03 
 .87 
 1.86 
 
 1.35 
 .79 
 2.09 
 5.06 
 1.82 
 2.12 
 1.54 
 1.25 
 2.67 
 1.35 
 
 1.60 
 1.38 
 2.84 
 4.15 
 2.48 
 1.45 
 .96 
 .94 
 .93 
 1.12 
 1.57 
 1.6.' 
 
 July 
 August 
 September . 
 October 
 November. . 
 December. . 
 Average 
 
 1.02 
 1 43 
 
 1.13 
 1 50 
 
 1.88 
 1.67 
 
 1.83 
 .... 
 
 1.18 
 2.03 
 
Estimate of Stream Flow. 
 
 173 
 
 TABLE XV. Continued. 
 
 Potomac River at Point of Rocks, Md. 
 9654 sq. mi. 
 
 Year. 
 
 '98 
 
 '99 
 
 '00 
 
 '01 
 
 '0^ 
 
 '03 
 
 '01 
 
 '05 
 
 Ave. 
 
 January 
 
 2.40 
 
 1.95 
 
 .&3 
 
 . 57 
 
 1.81 
 
 1.78 
 
 .76 
 
 .89 
 
 1.38 
 
 February 
 
 85 
 
 3 00 
 
 1.38 
 
 .37 
 
 3.37 
 
 2 .10 
 
 1.81 
 
 ' .58 
 
 1.71 
 
 March 
 
 1 59 
 
 3 72 
 
 1.93 
 
 1 45 
 
 5.64 
 
 2.77 
 
 1 16 
 
 2 43 
 
 2 58 
 
 Vpril 
 
 1 b7 
 
 1 22 
 
 96 
 
 4 07 
 
 2 99 
 
 2 99 
 
 77 
 
 68 
 
 1 92 
 
 .May 
 
 1 89 
 
 1 20 
 
 45 
 
 2 85 
 
 .02 
 
 .64 
 
 97 
 
 .46 
 
 1 13 
 
 June 
 
 42 
 
 54 
 
 .86 
 
 2 01 
 
 .33 
 
 1 86 
 
 1 05 
 
 .68 
 
 97 
 
 July 
 
 26 
 
 27 
 
 31 
 
 1 11 
 
 32 
 
 1 32 
 
 47 
 
 1 06 
 
 64 
 
 Vugust 
 
 2 34 
 
 25 
 
 20 
 
 .87 
 
 .26 
 
 .50 
 
 .25 
 
 .60 
 
 .66 
 
 September 
 
 <!6 
 
 25 
 
 14 
 
 77 
 
 15 
 
 48 
 
 .17 
 
 ,3i 
 
 32 
 
 October 
 
 1 45 
 
 .18 
 
 .14 
 
 .40 
 
 .29 
 
 .33 
 
 .12 
 
 .30 
 
 .40 
 
 November 
 
 87 
 
 33 
 
 48 
 
 48 
 
 29 
 
 M 
 
 .14 
 
 24 
 
 38 
 
 December 
 
 1.60 
 
 42 
 
 .64 
 
 2.6-3 
 
 1.96 
 
 .30 
 
 .23 
 
 1.10 
 
 1.11 
 
 Average 
 
 1 30 
 
 1 11 
 
 69 
 
 " 1 46 
 
 1 50 
 
 1 29 
 
 .66 
 
 .78 
 
 
 
 
 
 
 
 
 
 
 
 
 From Table XVI it will be seen that the average minimum 
 monthly flow of the Hudson River at Mechanicville, N. Y., is .52 
 cubic foot per second per square mile, the smallest monthly mini- 
 mum for any year during the period of the observations being .31 
 and the largest monthly minimum for any year being .81. On the 
 Potomac River, with a somewhat greater, total annual rainfall, the 
 average minimum monthly flow is .21, the smallest monthly mini- 
 mum for the year being .12, and the largest monthly minimum for 
 any year being .37. These figures, it must be remembered, are aver- 
 ages for each month, and the actual minimum flow during the period 
 is a much less quantity. These records show that the minimum flow 
 GI a stream cannot be based on the mean annual rainfall. This same 
 
 TABLE XVI. 
 
 Mean Monthly Flow of Various Eastern Streams Arranged in Order of their 
 . Magnitude. (In Cubic Feet per Second per Square Mile.) 
 
 Kennebec River at Waterville, Me. 
 441 Osq. mi. 4380 sq mi. 
 
 Year. 
 
 '93 
 
 '94 
 
 '95 
 
 '96 
 
 '97 
 
 '98 
 
 '99 
 
 '00 
 
 '01 
 
 '02 
 
 '03 
 
 '04 
 
 '05 
 
 Ave. 
 
 Minimum. 
 
 36 
 
 .37 
 
 28 
 
 .62 
 
 .60 
 
 .28 
 
 .59 
 
 .54 
 
 .55 
 
 .87 
 
 .32 
 
 .20 
 
 .40 
 
 46 
 
 
 .46 
 
 .40 
 
 .40 
 
 .64 
 
 .81 
 
 .43 
 
 59 
 
 .63 
 
 .57 
 
 .88 
 
 .33 
 
 .60 
 
 .47 
 
 .56 
 
 
 .51 
 
 .42 
 
 .41 
 
 .71 
 
 .84 
 
 .46 
 
 .71 
 
 .69 
 
 .64 
 
 .96 
 
 .44 
 
 .77 
 
 .52 
 
 .62 
 
 
 .51 
 
 .62 
 
 .45 
 
 .77 
 
 .85 
 
 .51 
 
 .73 
 
 .93 
 
 .67 
 
 .99 
 
 .57 
 
 .86 
 
 .60 
 
 .70 
 
 
 .53 
 
 .67 
 
 .46 
 
 .as 
 
 1.04 
 
 .53 
 
 .77 
 
 .95 
 
 .73 
 
 1.03 
 
 .88 
 
 .98 
 
 .68 
 
 .78 
 
 
 .53 
 
 .85 
 
 .61 
 
 .98 
 
 1.21 
 
 .54 
 
 .89 
 
 1 31 
 
 .95 
 
 1.15 
 
 .88 
 
 1.07 
 
 .70 
 
 .90 
 
 
 .60 
 
 .85 
 
 .80 
 
 1.21 
 
 1.29 
 
 .73 
 
 .92 
 
 1.44 
 
 1.10 
 
 1.20 
 
 .92 
 
 1.07 
 
 .73 
 
 .99 
 
 
 .95 
 
 .91 
 
 t.27 
 
 1.25 
 
 1.65 
 
 .73 
 
 1.1? 
 
 2.05 
 
 1.17 
 
 1.79 
 
 1.19 
 
 1.22 
 
 1.07 
 
 1.26 
 
 
 1.31 
 
 1.30 
 
 1.37 
 
 2.07 
 
 2.94 
 
 1.14 
 
 2.26 
 
 3.07 
 
 1.72 
 
 3.48 
 
 1.52 
 
 1.89 
 
 1.20 
 
 1.87 
 
 
 1.64 
 
 1.77 
 
 1.46 
 
 2.98 
 
 2.96 
 
 2.00 
 
 2.50 
 
 2.28 
 
 1.88 
 
 3.85 
 
 1.66 
 
 2.22 
 
 1.53 
 
 2.23 
 
 
 3.47 
 
 2.17 
 
 2.17 
 
 3.87 
 
 5.75 
 
 4.81 
 
 5.70 
 
 6.41 
 
 3.46 
 
 5.07 
 
 3.74 
 
 3.41 
 
 2.40 
 
 4.05 
 
 
 6.9:2 
 
 3.33 
 
 5.43 
 
 6.21 
 
 6.10 
 
 5.31 
 
 6.76 
 
 6.45 
 
 9.39 
 
 6.57 
 
 4.42 
 
 4.71 
 
 3.08 
 
 5.73 
 
 
Run-Off. 
 
 TABLE XVI. Continued. 
 
 Hudson River at Mechanicville, N. Y. 
 Drainage Area 4500 sq. mi. 
 
 Year. 
 
 '88 
 
 '89 
 
 '90 
 
 '91 
 
 '92 
 
 '93 
 
 '94 
 
 '95 
 
 '96 
 
 '97 
 
 '93 
 
 '99 
 
 '00 
 
 'OL 
 
 '02 
 
 '03 
 
 '04 
 
 '05 
 
 Ave. 
 
 Minimum .. 
 
 .34 
 
 .44 
 
 .43 
 
 .33 
 
 .63 
 
 .56 
 
 .42 
 
 .57 
 
 .54 
 
 .56 
 
 .57 
 
 .31 
 
 .42 
 
 .54 
 
 .81 
 
 .78 
 
 .58 
 
 
 .52 
 
 
 H8 
 
 88 
 
 .45 
 
 45 
 
 93 
 
 71 
 
 55 
 
 58 
 
 (W 
 
 61 
 
 86 
 
 46 
 
 47 
 
 6<1 
 
 
 91 
 
 87 
 
 79 
 
 66 
 
 
 .68 
 
 .84 
 
 .72 
 
 .52 
 
 .99 
 
 ,81 
 
 .70 
 
 .58 
 
 .64 
 
 .87 
 
 1.14 
 
 .54 
 
 .52 
 
 .79 
 
 1.40 
 
 1.08 
 
 1.08 
 
 
 .81 
 
 
 82 
 
 95 
 
 1 64 
 
 .59 
 
 1 22 
 
 86 
 
 ,81 
 
 .79 
 
 .91 
 
 ,89 
 
 1.17 
 
 .58 
 
 .60 
 
 .83 
 
 1.4(1 
 
 1.18 
 
 1 29 
 
 1 25 
 
 99 
 
 
 1.02 
 
 1.88 
 
 1.74 
 
 .71 
 
 1.69 
 
 .02 
 
 .97 
 
 .86 
 
 1.02 
 
 1.83 
 
 1.25 
 
 .58 
 
 .91 
 
 .89 
 
 1.41 
 
 1.28 
 
 1.39 
 
 1.35 
 
 1.18 
 
 
 1 09 
 
 1,52 
 
 1.97 
 
 .91 
 
 2.0fi 
 
 .07 
 
 1.07 
 
 .87 
 
 1.04 
 
 2 22 
 
 1.50 
 
 1.02 
 
 1.11 
 
 .94 
 
 1 .59 
 
 1.31 
 
 1.48 
 
 1,35 
 
 1.34 
 
 
 1.41 
 
 1.77 
 
 2.03 
 
 1.23 
 
 2.06 
 
 .11 
 
 1.42 
 
 .93 
 
 1.05 
 
 2.47 
 
 1.72 
 
 1.17 
 
 1.13 
 
 1.03 
 
 1.53 
 
 1.56 
 
 1.50 
 
 1.54 
 
 1.48 
 
 
 1 52 
 
 1.84 
 
 2.05 
 
 1.84 
 
 2.41 
 
 .53 
 
 1.50 
 
 1.52 
 
 1.51 
 
 2.63 
 
 1.75 
 
 1.42 
 
 1.30 
 
 1.73 
 
 1 76 
 
 1.88 
 
 1,52 
 
 1.82 
 
 1.75 
 
 
 2 22 
 
 1.97 
 
 2.47 
 
 1 91 
 
 2.80 
 
 .60 
 
 1.58 
 
 1.54 
 
 1.54 
 
 2.70 
 
 2.05 
 
 1.49 
 
 1.72 
 
 1,80 
 
 1.8:- 
 
 2,19 
 
 2.46 
 
 2 09 
 
 2.00 
 
 
 2 3t> 
 
 2 44 
 
 2 50 
 
 2 59 
 
 4.19 
 
 1 97 
 
 1.68 
 
 1,87 
 
 2.52 
 
 2.71 
 
 246 
 
 2 14 
 
 200 
 
 1 88 
 
 1 t.8 
 
 2.:>5 
 
 2 6;' 
 
 2 12 
 
 2.35 
 
 
 4.73 
 
 2.93 
 
 3.35 
 
 3.94 
 
 4.87 
 
 3.98 
 
 2.47 
 
 2.42 
 
 3.02 
 
 3.20 
 
 3.05 
 
 2.17 
 
 2.77 
 
 J.60 
 
 >.3f- 
 
 3.11 
 
 2.96 
 
 2.67 
 
 3.12 
 
 Maximum.. 
 
 4.76 
 
 3.04 
 
 3.98 
 
 4.45 
 
 4.79 
 
 4.95 
 
 3.28 
 
 5.29 
 
 5.55 
 
 4.24 
 
 4.49 
 
 5.25 
 
 5.02 
 
 6.28 
 
 5.5t 
 
 6.87 
 
 4.61 
 
 5.06 
 
 4.85 
 
 Merrimac River at Lawrence, Mass. 
 4553 sq. mi. 
 
 Year. 
 
 '90 
 
 '91 
 
 '92 
 
 '93| 
 
 '94 
 
 '95 
 
 '96 
 
 '97 
 
 '98 
 
 '99 
 
 '00 
 
 '01 
 
 '02 
 
 '03 
 
 '04 
 
 '05 
 
 Ave. 
 
 "Mini mil in 
 
 .69 
 
 47 
 
 47 
 
 .52 
 
 37 
 
 37 
 
 .44 
 
 .48 
 
 .58 
 
 .39 
 
 .33 
 
 .53 
 
 74 
 
 .51 
 
 .39 
 
 .49 
 
 48 
 
 
 .75 
 
 .54 
 
 .86 
 
 .57 
 
 .40 
 
 .48 
 
 .45 
 
 .61 
 
 .64 
 
 .44 
 
 .40 
 
 .57 
 
 '.81 
 
 .64 
 
 .55 
 
 .57 
 
 .59 
 
 
 .44 
 
 .54 
 
 .87 
 
 .61 
 
 .44 
 
 .57 
 
 .67 
 
 .75 
 
 .83 
 
 .46 
 
 .41 
 
 .62 
 
 .93 
 
 .72 
 
 .57 
 
 .58 
 
 .60 
 
 
 .53 
 
 .59 
 
 .94 
 
 .65 
 
 .50 
 
 .57 
 
 .77 
 
 1.01 
 
 1.41 
 
 .54 
 
 .55 
 
 .65 
 
 1.13 
 
 .79 
 
 .58 
 
 .70 
 
 .88 
 
 
 .70 
 
 .64 
 
 1.05 
 
 .74 
 
 .50 
 
 .63 
 
 ^96 
 
 1.12 
 
 1.42 
 
 .61 
 
 .74 
 
 .72 
 
 1.20 
 
 .fO 
 
 .60 
 
 73 
 
 .87 
 
 
 .73 
 
 .90 
 
 1.06 
 
 .79 
 
 .66 
 
 .67 
 
 .98 
 
 1.S8 
 
 1.62 
 
 .61 
 
 .87 
 
 .86 
 
 1.23 
 
 .86 
 
 .62 
 
 .83 
 
 .96 
 
 
 .84 
 
 1.00 
 
 1.28 
 
 .97 
 
 .67 
 
 .88 
 
 1.14 
 
 2 22 
 
 1.71 
 
 .65 
 
 1.28 
 
 .96 
 
 1.54 
 
 .94 
 
 .63 
 
 .89 
 
 1.12 
 
 
 .95 
 
 1.61 
 
 1.43 
 
 1.10 
 
 .78 
 
 1.28 
 
 1.44 
 
 2.28 
 
 1.93 
 
 1.07 
 
 1.49 
 
 1.61 
 
 1.74 
 
 1.00 
 
 .78 
 
 1.12 
 
 1.42 
 
 
 .7.) 
 
 2.92 
 
 1 61 
 
 1.17 
 
 .94 
 
 1.37 
 
 1.46 
 
 2 32 
 
 2.17 
 
 1.73 
 
 2.21 
 
 2.04 
 
 2.18 
 
 1.99 
 
 1.00 
 
 1.22 
 
 1.88 
 
 
 .14 
 
 2.96 
 
 1.79 
 
 2.36 
 
 1.33 
 
 2.06 
 
 2.00 
 
 2.37 
 
 2.42 
 
 2.09 
 
 3.56 
 
 2.09 
 
 2.24 
 
 2.21 
 
 2.64 
 
 1.64 
 
 2.30 
 
 
 .44 
 
 4.73 
 
 1.87 
 
 3.42 
 
 2.43 
 
 2.10 
 
 4.00 
 
 2.79 
 
 3.34 
 
 2.62 
 
 3.62 
 
 3.94 
 
 3.72 
 
 3.34 
 
 3.74 
 
 2.26 
 
 3.20 
 
 Maximum 
 
 .79 
 
 5.19 
 
 2.25 
 
 4.28 
 
 3.16 
 
 4.35 
 
 4.62 
 
 3.87 
 
 4.09 
 
 5.81 
 
 4.06 
 
 4.04 
 
 6.06 
 
 5.66 
 
 4.45 
 
 3.47 
 
 4.32 
 
 
 Potomac River at Point of Rocks, Md. 
 9654 sq. mi. 
 
 Year. 
 
 '98 
 
 '99 
 
 '00 
 
 '01 
 
 '0> 
 
 '03 
 
 "04 
 
 '05 
 
 Ave. 
 
 
 26 
 
 18 
 
 14 
 
 37 
 
 15 
 
 .22 
 
 .12 
 
 .24 
 
 .21 
 
 
 .26 
 
 .25 
 
 .14 
 
 .40 
 
 .26 
 
 .30 
 
 .14 
 
 .80 
 
 .26 
 
 
 .42 
 
 .25 
 
 .20 
 
 .48 
 
 .29 
 
 .33 
 
 .17 
 
 .33 
 
 .31 
 
 
 .85 
 
 .*7 
 
 .31 
 
 .57 
 
 .29 
 
 .48 
 
 .23 
 
 .46 
 
 .43 
 
 
 .87 
 
 .33 
 
 .45 
 
 .77 
 
 .32 
 
 .50 
 
 .25 
 
 .58 
 
 .51 
 
 
 1 45 
 
 .42 
 
 .48 
 
 .87 
 
 .33 
 
 .64 
 
 .47 
 
 .60 
 
 .66 
 
 
 1.59 
 
 .54 
 
 .64 
 
 1.11 
 
 .62 
 
 1.32 
 
 .76 
 
 .68 
 
 .91 
 
 
 1.60 
 
 1.20 
 
 .83 
 
 1.49 
 
 1.81 
 
 1.78 
 
 .77 
 
 .68 
 
 1.27 
 
 
 1.67 
 
 1.22 
 
 .86 
 
 2.01 
 
 1.96 
 
 1.86 
 
 .97 
 
 .89 
 
 1.43 
 
 
 1.89 
 
 1.95 
 
 .9ti 
 
 2.62 
 
 2.99 
 
 2.30 
 
 1.05 
 
 1.06 
 
 1.85 
 
 
 2.34 
 
 3. CO 
 
 1.38 
 
 2.85 
 
 3.37 
 
 2.77 
 
 1.16 
 
 1.10 
 
 225 
 
 Maximum 
 
 2 40 
 
 3 72 
 
 1 93 
 
 4 07 
 
 5 64 
 
 2.79 
 
 1.81 
 
 2.43 
 
 3.01 
 
 
 
 
 
 
 
 
 
 
 
 fact is more fully demonstrated by the tables on maximum and min- 
 imum run-off given in the Appendix. From the data in the Appen- 
 dix it will be noted that the recorded minimum of some of the 
 Southern streams is between .5 and .6 cubic feet per second per 
 square mile, while numerous other streams will vary from .2 to .4; 
 nevertheless a large oortion of the streams shown have minimum 
 flows of .1 and less. 
 
CHAPTER IX. 
 
 RUN-OFF (Continued). 
 
 95. Relation of Run-Off to Topographical Conditions. The rel- 
 ative run-off from a drainage area depends largely on its topo- 
 graphical condition. This is due to the fact that climatic condition 
 depends on the elevation and slope of the drainage area, and also 
 to the fact that the rapid removal of the water from steep slopes 
 assures less activity in the other factors of rainfall disposal and 
 consequently a greater run-off. Mr. F. H. Newell in a paper before 
 the Engineering Club of Philadelphia (see Proceedings Engineer- 
 ing Club of Philadelphia, vol. 12, page 144, 1895) presents a dia- 
 gram (see Fig. 88) which shows in a broad way, the influence of 
 such conditions. In describing this diagram Mr. Newell says : 
 
 "The diagonal line represents the limit or the condition when 
 all of the rain falling upon the surface, as upon a steep roof, runs 
 off; the horizontal base, the conditions when none of the water 
 
 DEPTH OF MEAN 'ANNUAL RUN-OFF IN INCHES 
 _ M ro a 
 _ in a cn^a m c 
 
 
 
 
 
 7 
 
 z 
 
 / 
 
 / 
 
 
 i 
 
 7 
 
 * 
 
 / 
 
 
 
 
 
 // 
 
 ^S 
 
 
 / 
 
 / 
 
 
 / 
 
 
 
 
 / 
 
 
 -^ 
 
 / 
 
 
 / 
 
 
 
 /- 
 
 / 
 
 / 
 
 
 / 
 
 
 / 
 
 / 
 
 / 
 
 / 
 
 
 
 
 
 2 
 
 ] j 
 
 
 _S 
 
 *S 
 
 2 
 i ANNU/ 
 
 5 2 
 
 <L RAIN 
 
 3 
 FALL Ih 
 
 5 4 
 1 INCHE 
 
 5 4: 
 
 s 
 
 5 50 
 
 ^ 
 
 ^ 
 
 5 2 
 
 r ME At 
 
 
 > i 
 
 D 
 
 A 
 D 1. 
 EPTH C 
 
 Fig. 88 
 
176 Run-Off. 
 
 flows away. Between these are the two curved lines, the lower rep- 
 resenting the assumed condition prevailing in a catchment basin of 
 broad valleys and gentle slopes, from which as a consequence there 
 is relatively little flow, and the upper curve, an average condition 
 of mountain topography, from which large quantities of water are 
 discharged. For example, with a rainfall of 40 inches on an un- 
 dulating catcl ment basin, about 15 inches is discharged by the 
 stream, while from steep slopes 30 inches runs off. With less 
 mean annual rainfall the relative run-off is far less, as for example, 
 with 20 inches, about 7 inches of run-off is found in steep catchment 
 basins, and about 3 inches on the rolling plains and broad valleys 
 of less rugged topography. Following these curves down, it would 
 appear that as the average yearly rainfall decreases the run-off 
 diminishes rapidly, so that with from 10 to 15 inches no run-off 
 may be expected on many areas, and from 2 to 4 inches from the 
 mountains. There is an apparent exception to this, in that with 
 very small annual rainfall the precipitation often occurs in what is 
 known as cloudbursts, large quantities of water falling at a sur- 
 prisingly great rate. Under these conditions the proportion of run- 
 off to rainfall increases, as the water does not have time to sat- 
 urate the ground." 
 
 "These curves should not be regarded as exact expressions, but 
 as indicating general relationships and as showing graphically de- 
 ductions based upon long series of observations of quantities not 
 determined with exactness. Computations of this relation made 
 in various parts of the country have, when platted graphically, 
 fallen near or between these curves, according to the character of 
 the country from which the water was discharged. On the figure 
 are shown three average determinations, numbered i, 2 and 3, rep- 
 resenting respectively the relation of run-off to rainfall, for the 
 Connecticut, Potomac and Savannah Rivers. The horizontal lines 
 indicate determinations made for western streams coming from 
 areas of small precipitation. The exact amount of rainfall is not 
 known, as the observations are not representative of the conditions 
 prevailing upon the mountains, and therefore the horizontal line has 
 been used instead of a dot, as indicating the probable range of 
 rainfall, as, for example, being from 10 to 15, or from 15 to 20 
 inches. The height of these short lines above the base indicates 
 the average annual run-off of the basin, a quantity which has been 
 determined with considerable accuracy according to the method 
 just described." 
 
Effects of Geological Conditions on the Run-Off. 177 
 
 Figure 88 is presented on account of the .general principles 
 illustrated thereby and should be used for such purpose only. 
 While the limits given by Mr. Newell are sufficiently broad to 
 include many of the conditions in the United States, they are too 
 broad to give a sufficiently definite relation for most local conditions 
 and too narrow to include all conditions which may occur in the 
 United States. The latter fact is perhaps best illustrated by Fig, 
 89, reproduced from a paper by Messrs. J. B. Lippincott and S. G. 
 Bennett on "The Relation of Rainfall to Run-Off in California", 
 published in the Engineering News, vol. 47, page 467. This figure 
 shows the annual and mean run-off from various California drain- 
 age areas based on several years' observations. The diagram shows 
 both the Newell curves, illustrated in Fig. 88, and three mean curves 
 for California conditions, also several mean and numerous annual 
 run-off observations which can be studied in detail in the article 
 above referred to. The general curve for large drainage areas is 
 for areas of 100 square miles or over. 
 
 S 10 IS 20 25 
 
 ANNUAL RAINFALL IN INCHES 
 
 Fig. 89 
 
 96. Effects of Geological Condition on the Run-Off. The geo- 
 logical condition of a drainage area has a marked effect on the 
 run-off. The determination of the exact geological conditions of 
 any drainage area, which control or modify the resulting run-off, 
 is difficult or even impossible and can seldom be done with suf- 
 ficient accuracy so that the results may be even approximated with- 
 out actual observations on the drainage areas. The effects of these 
 conditions, however, are important and they are here pointed out 
 
Run-Off. 
 
 so that such effects may be realized and the fact appreciated that 
 the run-off of streams otherwise similarly located may be materially 
 different on account of difference in these conditions. A good ex- 
 ample of the geological influence on run-off may be seen by compar- 
 ing the stream flow of any of the Northern Wisconsin streams with 
 that of the Rock River in the Southern portion of the state. Most 
 of the Northern Wisconsin streams flow, in part, over pervious 
 beds of sand-stone and a considerable amount of the water falling 
 on their drainage areas is undoubtedly lost through absorption by 
 the underlying strata. These losses undoubtedly affect the flow of 
 the stream to a considerable extent. These streams, however, have 
 no large under-flow through loose material which can absorb and 
 transmit any considerable portion of the rainfall that would other- 
 wise appear as surface run-off. The Rock River, on the other hand, 
 follows for a considerable portion of its course through Wisconsin, 
 its pre-glacial drainage valley which is filled to a depth of 300 feet 
 or more with drift material consisting largely of sands and gravels 
 through which a large amount of water doubtlessly escapes. The 
 
 TABLE XVII. 
 
 Comparative Mean Monthly Run-Off of ihe Wisconsin River at Necedah, Wis- 
 consin, and the Rock River at Rock! on, Illinois, in Cubic Feet 
 Per Second Per Square Mile. 
 
 19O3. 
 
 
 g 
 
 H-5 
 
 & 
 
 r 
 EH 
 
 jj 
 
 1 
 
 h 
 
 Cu 
 
 << 
 
 >, 
 
 c3 
 
 g 
 
 s 
 
 3 
 
 1-5 
 
 j>> 
 
 3 
 
 H-5 
 
 M 
 
 % 
 
 a 
 
 CD 
 
 OQ 
 
 +3 
 
 o 
 
 o 
 
 > 
 
 
 
 ft 
 
 6 
 a> 
 P 
 
 Wisconsin river 
 
 45 
 
 44 
 
 04 
 
 1 48 
 
 9 50 
 
 1 IP 
 
 1 56 
 
 1 15 
 
 9 73 
 
 1 83 
 
 86 
 
 1 34 
 
 Rock river 
 
 
 
 
 
 
 
 91 
 
 6i 
 
 91 
 
 78 
 
 44 
 
 45 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1904. 
 
 Wisconsin river 
 Rock river 
 
 45 
 
 77 
 
 2 80 
 
 2.21 
 1 76 
 
 2.63 
 
 88 
 
 1.96 
 39 
 
 1.02 
 ?6 
 
 .66 
 ?4 
 
 .90 
 38 
 
 2.34 
 50 
 
 .98 
 
 30 
 
 41 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1905. 
 
 Wisconsin river 
 
 
 
 1.56 
 2.10 
 
 2.72 
 1.63 
 
 1.91 
 1.10 
 
 4.02 
 1.06 
 
 1.50 
 .64 
 
 1.05 
 .4] 
 
 1.28 
 .41 
 
 .99 
 
 .39 
 
 .81 
 
 .40 
 
 1.53 
 .44 
 
 Rock river 
 
 .60 
 
 .53 
 
 
 19O6. 
 
 ^Wisconsin river 
 
 
 
 
 3 90 
 
 1 81 
 
 1 86 
 
 1 13 
 
 90 
 
 89 
 
 83 
 
 1.17 
 
 1 41 
 
 Rock river 
 
 1 56 
 
 1 59 
 
 1 9? 
 
 1.49 
 
 58 
 
 37 
 
 38 
 
 
 
 10 
 
 ?1 
 
 ?8 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
Effects of Area on the Run-Off. 179 
 
 deposits of this old river bed have been quite extensively explored 
 for water supply purposes and yield very large quantities of water 
 for domestic and manufacturing supplies. Most of the under-flow, 
 however, undoubtedly passes away to an unknown outlet as the 
 modern river leaves the old valley near Rockford, 111. 
 
 A comparison between mean monthly flows of the Wisconsin and 
 Rock Rivers, as shown in Table XVII, will give an idea of the effect 
 of these different conditions as shown by the run-off of these two- 
 rivers. 
 
 97. The Influence of Storage on the Distribution of Run-Off. 
 Favorable pondage conditions on a watershed have an important* 
 effect on the distribution of the run-off, and this effect is readily 
 discernible in the records of flow from such areas. 
 
 Figure 90 is a hydrograph of the discharge of the various rivers 
 draining the Great Lakes for the years .1882 to 1902. A general 
 similarity is seen in the annual variations in these hydrographs and 
 yet there is a considerable variation from the maximum to the 
 minimum discharge in accordance with the rainfall and other condi- 
 tions prevalent on the watershed. In every case, however, the 
 minimum of the year is found to occur at about the same time, and 
 the time of maximum height is also fairly constant. The ratios 
 between maximum and minimum flow are very much less than those 
 that obtain on other watersheds where the pondage area is much 
 less. 
 
 In the St. Lawrence River the maximum mean monthly discharge 
 is about 320,000 second feet, and the minimum is about 185,000 
 second feet, the maximum being not quite double the minimum. In 
 the discharge of the Niagara River the maximum mean monthly 
 discharge is about 260,000 cubic feet, and the minimum about 
 175,000, the fluctuation being still more moderate. 
 
 The mean monthly discharge of the St. Marys River shows a 
 maximum of about 110,000 second feet, and a minimum of about 
 50,000. The ratio here is somewhat higher, because, in this case, 
 Lake Superior and its drainage area being the source of supply, 
 the relation of pondage to drainage area is less than in the com- 
 bined lakes, and the effect is seen in the variation in the discharge 
 of this river. 
 
 98. Effects of Area on the Run-Off. The size of the drainage 
 area of any stream has a marked effect on the distribution of the 
 run-off. The hydrographs of small areas show the effects of 
 heavy rains by an immediate and marked increase in the flow. 
 
i So 
 
 Run-Off. 
 
The Study of a Stream from its Hydrographs. 181 
 
 This is well shown by a comparison of the hydrographs of Per- 
 kiomen Creek and the Kennebec River (Fig. 96), and of the 
 Hood and Spokane Rivers (Fig. 99). On small streams where per- 
 vious deposits are largely developed, the rainfall is rapidly absorbed 
 and does not so radically affect the run-off. Large streams do not 
 feel the immediate effect of rainfall, on account of the time required 
 for the run-off to reach the main stream. The flow of large streams 
 is also modified by the fact that uniform conditions of rainfall 
 seldom obtain on the entire area. On large drainage areas, condi- 
 tions of rainfall may prevail on one or more of the tributaries only, 
 while on other portions of the drainage area the conditions may 
 be quite different. Such conditions may frequently be reversed, 
 with the result that the larger the stream the less becomes the 
 extremes of flow and the greater the uniformity of flow. 
 
 99. The Study of a Stream From Its Hydrographs. The influ- 
 ences of various factors on the run-off, as above discussed, can be 
 clearly seen from an analysis of the stream flow data, but they can 
 best be appreciated by noting their effect on the hydrograph. The 
 hydrograph of the actual flow of a stream is the best means of 
 studying its manifold variations, but to fully comprehend the wide 
 limit of such variations, hydrographs must be available for a 
 long term of years. When the hydrographs are sufficiently ex- 
 tended to cover all of the usual variations in rainfall and other 
 meteorological conditions, they afford a comprehensive view of 
 the entire subject of the run-off of the stream. 
 
 Figures 91 and 92 show hydrographs of the Passaic River for 
 seventeen years. From these hydrographs the actual variations in 
 flow as they have occurred on this drainage area during this period 
 can be seen. The average monthly rainfall on the drainage area has 
 also been shown on these diagrams and the effects of such rainfall 
 on the run-off should be noted. It is important to note especially 
 the marked effect of a limited rainfall during the months of the 
 storage period, when the ground has previously become saturated, 
 as compared with the effects of the same or greater rainfalls during 
 the growing period, when the ground water has been partially ex- 
 hausted by the demands of vegetation and the draft of the low 
 water flow. 
 
 In these diagrams, and those following, the flows are shown 
 in cubic feet per second per square mile, in order that their 
 value for comparative purposes may be increased. The absolute 
 discharge of a river in cubic feet per second gives no comparative 
 
182 
 
 Run-Off. 
 
 2.40 I 2^2 I 4.12 -89 I 0.61 U4 | 7.69 
 
 Figures near top of each diagram show total monthly rainfall. 
 Fig. 91. Daily flow of Passaic River, Little Falls, N. J. 
 
The Study of a Stream from its Hydrographs. 183 
 
 ^ 8 
 
 2 6 
 
 JT 
 
 I 
 
 ^ 12 
 
 10 
 
 I 
 
 3 i 
 
 G 
 O) 
 
 ? 12 
 
 I 10 
 
 tn 8 
 
 S 6 
 4 
 2 
 
 Figures near top of each diagram show total monthly rainfall. 
 F i g 92. Daily flow of Passaic River, Little Falls, N. J. 
 
184 Run-Off. 
 
 measure of discharge values, but when the corresponding area is 
 also shown, the diagram becomes more or less applicable for com- 
 parative purposes to other areas. Hence, for general or compara- 
 tive discussion, the discharge per unit of area should be the basis 
 of consideration. 
 
 100. Comparative Run-Off and Comparative Hydrographs. In 
 studying and comparing all run-off data and the hydrographs based 
 thereon it is important to note that a uniformity of conditions pro- 
 duces a uniformity of results. Such data is not only of value in 
 the study of the river from which it is obtained, but also furnishes 
 information regarding other streams that exist under the same or 
 similar conditions, both physical and meteorological. 
 
 Table XVIII, which shows the monthly run-off for a term of years 
 of certain Michigan streams, gives a comparison of the flow of 
 streams under such conditions, as expressed by their comparative 
 monthly run-off. The relative geographical locations of these 
 streams are shown in figure 93. The run-off from each drainage 
 area is given in cubic feet per second per square mile, so that the 
 results are strictly comparable, the question of size of area being 
 eliminated. A general resemblance can be traced between most of 
 these streams. The Manistee and Au Sable Rivers, in the Northern 
 portion of the state, have sand and othef pervious deposits largely 
 developed on their drainage areas, and show, in consequence, 
 greater uniformity of flow and a greater mean flow than that of 
 the other streams. 
 
 Comparative hydrographs of some of these streams for the year 
 1904 are shown in Fig. 94. The vertical scale for each of the 
 hydrographs shown on the diagram is the same, and represents the 
 discharge in cubic feet per second per square mile. The relative 
 flows of the different streams are thus easily compared. On these 
 diagrams has also been shown the average rainfall which occurred 
 on each drainage area for each month. A study of the rainfall 
 record in connection with the flow lines of the hydrograph, will 
 show that the difference in flow is not entirely attributable to the 
 prevailing rainfall conditions on the drainage area, but that other 
 physical influences have a material effect. These hydrographs 
 were originally prepared in order to form a basis for an estimate 
 of the probable horse power on the White River, on which no 
 gauge readings had been taken. On the right of the diagram is 
 shown a horse power scale from which the probable power of the 
 White River, with a given fall and drainage area, and on the basis 
 
Comparative Hydrographs. 
 
 185 
 
 Fig. 93. Map showing location of various Michigan drainage areas. 
 11 
 
i86 
 
 Run-Off. 
 
 3*6 
 
 BRAND RIVER AT NORTH 
 3.86 2.18 3.64 2.74 1.91 
 
 LANS 
 3.60 
 
 20000 a 
 
 a ' 
 
 GRAND RIVER AT CRAN 
 2.48 I 3.62 I IJ9 
 
 RAPID 
 2.89 
 
 
 80000 
 40000 
 
 299 
 
 AJ SABLE: RIVER 
 
 3.14 344 
 
 Fig. 94. Comparative Hydrographs of Various Michigan Rivers for the year 
 
 1904. 
 
Comparative Hydrographs. 
 
 33VONOd HUM SHOOK H3MDd 16UOK 
 
 I8 7 
 
 .1 
 2 
 o 
 
 s 
 
 
 311ft 3HVnl)S 3d ON033S U3d 133J 
 
 Nl 33dVH3Sia 
 
i88 
 
 Run-Off. 
 
 TABLE XVIII. 
 
 Discharge in cubic feet per second per square mile of drainage area of various 
 
 Michigan rivers. 
 
 
 Ihunder 
 Bay river 
 at Alpena 
 
 At Grand 
 Rapids. 
 
 f-b 
 
 river 
 
 &b 
 
 -u.3 
 <1 
 
 Kalamazoo 
 river at 
 Allegan. 
 
 St. Joseph 
 river at 
 Buchanan. 
 
 Muskegon 
 river at 
 Newayga. 
 
 Manistee 
 river at 
 Sherman. 
 
 Au Sable 
 river at 
 Bamfield. 
 
 White river 
 at Moran's 
 Bridge. 
 
 1901 
 March 
 
 
 3.25 
 
 2 73 
 
 
 
 
 
 
 
 April 
 
 1.49 
 
 1.39 
 
 1 06 
 
 64 
 
 1 29 
 
 
 
 
 
 May 
 
 1.18 
 
 .66 
 
 48 
 
 .53 
 
 76 
 
 
 
 
 
 June ... 
 
 .63 
 
 49 
 
 34 
 
 57 
 
 53 
 
 45 
 
 
 
 
 July 
 
 .74 
 
 .92 
 
 78 
 
 51 
 
 45 
 
 45 
 
 
 
 
 August 
 
 .51 
 
 .38 
 
 58 
 
 52 
 
 38 
 
 40 
 
 
 
 
 September 
 
 1.31 
 
 .39 
 
 .44 
 
 .50 
 
 54 
 
 37 
 
 
 
 
 October 
 
 .70 
 
 .47 
 
 .51 
 
 50 
 
 71 
 
 50 
 
 
 
 
 November . . .' 
 
 .41 
 
 .42 
 
 .35 
 
 57 
 
 .70 
 
 38 
 
 
 
 
 December 
 
 .32 
 
 .65 
 
 .66 
 
 .54 
 
 .82 
 
 .38 
 
 
 
 
 1902 
 January 
 
 40 
 
 .46 
 
 .55 
 
 .46 
 
 69 
 
 30 
 
 
 
 
 
 29 
 
 .40 
 
 43 
 
 .46 
 
 .62 
 
 .33 
 
 
 
 
 March 
 
 1.31 
 
 1.41 
 
 1 26 
 
 .58 
 
 1 32 
 
 57 
 
 
 
 
 April 
 
 .91 
 
 1.03 
 
 1.02 
 
 .55 
 
 90 
 
 1.03 
 
 
 
 
 Alay 
 
 78 
 
 1.15 
 
 1 09 
 
 55 
 
 98 
 
 1 34 
 
 
 
 
 June 
 
 .74 
 
 .70 
 
 .88 
 
 .56 
 
 .92 
 
 .77 
 
 
 
 
 July 
 
 40 
 
 1.57 
 
 1 78 
 
 .62 
 
 1 10 
 
 .64 
 
 
 
 
 August 
 
 46 
 
 .53 
 
 57 
 
 54 
 
 60 
 
 .47 
 
 
 71 
 
 
 September . . . 
 
 .21 
 
 .57 
 
 50 
 
 .52 
 
 .58 
 
 .46 
 
 
 71 
 
 
 October 
 
 48 
 
 .79 
 
 84 
 
 .61 
 
 .84 
 
 67 
 
 
 .75 
 
 
 November 
 
 77 
 
 .95 
 
 .66 
 
 .63 
 
 79 
 
 57 
 
 
 95 
 
 
 December 
 
 .34 
 
 .96 
 
 .62 
 
 .64 
 
 1.00 
 
 .54 
 
 
 .91 
 
 
 Yearly mean 
 
 .59 
 
 .88 
 
 .85 
 
 .56 
 
 .86 
 
 .68 
 
 
 
 
 1903 
 January 
 
 .44 
 
 1.53 
 
 83 
 
 93 
 
 1.13 
 
 
 
 1 48 
 
 
 February .... , 
 
 55 
 
 2.26 
 
 1.36 
 
 1 20 
 
 1.52 
 
 .67 
 
 
 1.18 
 
 
 March 
 
 1.67 
 
 2.13 
 
 2.69 
 
 1.84 
 
 2.05 
 
 1.58 
 
 
 1.43 
 
 
 April 
 
 1 16 
 
 2.04 
 
 2 45 
 
 1 63 
 
 1 76 
 
 1.38 
 
 
 1 38 
 
 
 May 
 
 62 
 
 .68 
 
 52 
 
 .76 
 
 
 .91 
 
 
 .97 
 
 
 June 
 
 44 
 
 .53 
 
 46 
 
 .69 
 
 
 
 
 .78 
 
 
 July. 
 
 48 
 
 .45 
 
 53 
 
 .62 
 
 
 
 22 
 
 .79 
 
 
 August 
 
 .83 
 
 52 
 
 .79 
 
 .69 
 
 
 
 40 
 
 1.03 
 
 
 September 
 
 .79 
 
 1 06 
 
 1,04 
 
 .92 
 
 
 
 40 
 
 1.01 
 
 
 October 
 
 .68 
 
 1 15 
 
 62 
 
 81 
 
 
 
 35 
 
 .86 
 
 
 November 
 
 43 
 
 54 
 
 43 
 
 68 
 
 41 
 
 
 28 
 
 78 
 
 
 December. . . 
 
 .38 
 
 62 
 
 33 
 
 .72 
 
 .66 
 
 
 41 
 
 1.13 
 
 
 Yearly mean 
 
 1904 
 January . 
 
 .71 
 
 .38 
 
 1.05 
 
 1.00 
 48 
 
 .93 
 
 .82 
 
 1 49 
 
 
 
 1 28 
 
 1.07 
 1.94 
 
 
 
 February 
 
 46 
 
 
 1 07 
 
 98 
 
 1 48 
 
 
 1 18 
 
 2 35 
 
 
 March 
 
 64 
 
 
 3 05 
 
 3.44 
 
 3 07 
 
 
 1 29 
 
 1.79 
 
 
 April 
 
 3.48 
 
 2.90 
 
 2.22 
 
 2.08 
 
 2.24 
 
 
 2.35 
 
 1.89 
 
 
 May 
 
 1 79 
 
 1.00 
 
 69 
 
 1.03 
 
 95 
 
 
 2 00 
 
 1.49 
 
 
 June . . 
 
 1.17 
 
 .52 
 
 .33 
 
 .73 
 
 .68 
 
 
 1.42 
 
 1,05 
 
 
Comparative Hydrographs. 
 
 189 
 
 TABLE XVIII. Continued. 
 
 
 ~ S3 
 
 y ? 
 I-| 
 
 2 ^ 
 
 H3 
 
 At Grand J 
 Rapids, g 
 
 0. 
 
 river 
 
 
 51 
 
 Kalamazoo 
 river at 
 Allegan. 
 
 St. Joseph 
 river at 
 Buchanan. 
 
 Muskegon 
 river at 
 Newayga. 
 
 Manistee 
 river at 
 Sherman. 
 
 3^2 
 
 -*i 
 
 5> 
 
 "J'CPQ 
 
 O> 02 
 "& 
 
 *H CS . 
 
 So 
 ^3 
 ^c5 
 
 July 
 
 36 
 
 35 
 
 25 
 
 66 
 
 67 
 
 
 1 22 
 
 90 
 
 46 
 
 August 
 
 36 
 
 29 
 
 24 
 
 .55 
 
 
 45 
 
 1 18 
 
 85 
 
 66 
 
 September 
 October 
 
 .34 
 
 38 
 
 .35 
 .59 
 
 .21 
 .32 
 
 .61 
 
 71 
 
 .33 
 
 .47 
 
 .33 
 .45 
 
 l.ll 
 1 19 
 
 .77 
 82 
 
 .68 
 93 
 
 November 
 December 
 
 .35 
 .35 
 
 .37 
 
 .24 
 .26 
 
 .55 
 
 .56 
 
 .47 
 
 .40 
 
 .42 
 .39 
 
 1.09 
 1 08 
 
 .76 
 1.37 
 
 .79 
 .94 
 
 Yearly mean 
 
 .84 
 
 
 .78 
 
 1.06 
 
 
 
 1.36 
 
 1.33 
 
 
 Mean for last 5 or 
 6 months 
 
 .35 
 
 41 
 
 25 
 
 61 
 
 47 
 
 41 
 
 1 14 
 
 91 
 
 74 
 
 1905 
 January 
 
 
 "fi3 
 
 
 
 
 
 1 20 
 
 1.31 
 
 1 34 
 
 February 
 
 
 67 
 
 
 
 
 
 1 31 
 
 1.97 
 
 1 51 
 
 March 
 
 
 1 94 
 
 
 
 
 
 1 52 
 
 1 19 
 
 1 55 
 
 April 
 
 
 1 47 
 
 
 
 
 
 1 81 
 
 1 07 
 
 1 55 
 
 Mav 
 
 
 1 40 
 
 
 
 
 
 1 51 
 
 1.14 
 
 1 47 
 
 June 
 
 
 2 76 
 
 
 
 
 
 1 29 
 
 .98 
 
 1.84 
 
 Mean for 6 mos. . . 
 
 
 1.49 
 
 
 
 
 
 1.61 
 
 1.11 
 
 1.54 
 
 
 
 
 
 
 
 
 
 
 
 of the comparative flows of various Michigan rivers, could be es- 
 timated. In Fig. 95 these hydrographs have been re-drawn, the 
 daily flows being platted in the order of their magnitude. This 
 form of diagram represents the best basis for the comparative 
 study of stream flow for power purposes where storage is not 
 considered, and where the continuous power of the passing stream 
 is to be investigated. 
 
 A careful study of Figs. 94 and 95 will show that the run-off is 
 similar in streams situated under similar geographical, topograph- 
 ical, and geological conditions, and having equal, or similar, rain- 
 falls on the drainage area. The departure of the various streams 
 here considered, from the average of all, gives a very clear idea of 
 the errors which may be expected in estimating the flow of any par- 
 ticular stream from the hydrographs of other adjacent streams, or 
 from the flow of streams more remote, and which are located under 
 different physical conditions. 
 
 10 1. Comparative Hydrographs From Different Hydrological 
 Divisions of the United States. The hydrographs oif streams differ 
 widely in character, both in accordance with their geographical 
 location and the diverse physical character of their drainage areas. 
 Their geographical location affects their climatic, geological and 
 
ipo 
 
 Run-Off. 
 
 Kennebec River, Waterville, Me.: Drainage Area, 4410 Sq. Mi. 
 
 Perkiomen Creek, Frederick, Pa.: Drainage Area, 152 Sq. Mi. 
 
 Yadkin River, Salisbury, N. C.: Drainage Area, 3399 Sq. Mi. 
 
 1903 
 
 1904 
 
 Alcovy River, Covington, Ga.: Drainage Area, 228 Sq. Mi. 
 
 Coosa River, Riverside, Ala.: Drainage Area, 70G5 Sq. Mi. 
 
 I 
 
 1903 
 
 Creek, Nottingham, Ala.: Drainage Area, 156 Sq. Mi. 
 Fig. 96. Hydrographs of Atlantic and Eastern Gulf Drainage. 
 
Comparative Hydrographs. 
 
 191 
 
 12 
 
 10 
 8 
 6 
 4 
 
 8 
 U 
 <D 4 
 
 ^ 2 
 
 f|sfli 
 
 1 
 
 -) 
 
 -3 
 
 U 
 
 0. 
 UJ 
 
 en 
 
 
 
 
 
 a 
 
 u 
 
 Ul 
 
 a 
 
 5 
 
 m 
 
 Ul 
 
 u. 
 
 ocl a: 
 
 m 
 
 | 
 
 z 
 
 =3 
 -3 
 
 L3 
 
 =3 
 
 ol 
 
 Ul 
 
 en 
 
 o 
 
 
 
 
 
 Z 
 
 u 
 
 Ul 
 
 a 
 
 bX) 
 
 <S 
 
 i i ^ 
 
 to 
 
 
 1903 
 
 
 
 
 
 
 
 
 
 
 1904 
 
 
 
 
 
 
 i i ~ 
 
 tjfo 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i i 
 
 in 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i i 
 
 nj 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i i 
 
 ra 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i i 
 
 ra 
 
 
 
 
 
 
 
 
 
 
 
 , 
 
 
 
 
 
 
 
 
 
 i i 
 
 m 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 it lit 
 
 \Y\ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 IA AHA 
 
 If^X 
 
 
 
 
 
 
 
 
 
 
 
 I] 
 
 
 
 
 
 
 
 
 
 K^HB^v 
 
 ^//fy 
 
 
 j 
 
 
 
 
 
 
 
 
 
 E9 
 
 
 
 
 
 
 
 
 
 ^y^/fflffiW/// 
 
 \ 
 
 \ 
 
 A 
 
 j 
 
 
 
 
 
 j 
 
 A$M2W 
 
 *A^ 
 
 
 
 
 
 
 
 -M 
 
 Tennessee River, Knoxville, Tenn., Drainage Area 8990 Sq. Mi. 
 
 S 
 
 fcn 
 
 a> 
 
 
 
 
 
 s 
 
 a 
 
 CJ 
 
 fl 
 a> 
 
 ^ 
 
 
 I 
 
 
 
 1903 
 
 
 
 
 
 
 
 
 
 
 
 1904 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 fli 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 m 
 
 j 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 m 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 $\ 
 
 H 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 i 
 
 
 
 
 
 
 3 
 
 frwxh 
 
 E2 
 
 
 
 
 
 
 
 
 1-4. 
 
 f 
 
 d 
 
 -rrTs 
 
 ^ 
 
 
 
 t 
 
 
 
 
 
 
 
 03 
 
 ^ 
 
 M 4 
 
 I* 
 Q) > ! 
 
 ft - 
 
 Licking River, Pleasant Valley, O., Drainage Area 690 Sq. Mi. 
 
 
 
 
 
 
 1903 
 
 
 
 
 
 
 
 
 
 ^^ 
 
 
 1904 
 
 
 
 
 
 
 
 
 >9^ 
 
 ^xN 
 
 
 
 
 
 
 
 
 
 r^' 
 
 ^fa 
 
 ^ J 
 
 
 
 
 
 
 &2 
 
 kW, 
 
 ^ 
 
 y ///, 
 
 ^ 
 
 'T^^C 
 
 
 
 /: 
 
 >?>/; 
 
 
 
 N^V 
 
 '///< 
 
 y//4. 
 
 ^/; 
 
 ^k^, 
 
 
 
 
 
 
 -0 
 
 a 
 
 S 10 
 
 - 
 
 8 
 
 - 6 
 4 
 .S 2 
 
 Seneca River, Baldwinsville, N. Y., Drainage Area, 3103 Sq. Mi. 
 
 
 
 
 
 1303 
 
 
 
 
 
 
 
 
 
 
 
 1904 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 BJ 
 
 
 
 
 
 
 
 
 
 
 
 
 8 
 
 
 
 
 
 
 
 
 
 ii yiA Ji 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 
 
 IffArtt 
 
 
 
 
 
 
 
 
 
 
 
 
 B 
 
 
 
 
 
 
 
 
 
 M W/ffl/M 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 . Y\ rv^33k 
 
 
 
 
 
 
 
 
 
 
 i 
 
 \ 
 
 ^A 
 
 
 
 
 
 
 
 
 
 TM/tyPx/^ 
 
 
 i 
 
 
 
 
 ^ 
 
 
 
 r, ^ 
 
 ^ 
 
 ft 
 
 ^ 
 
 ^ 
 
 
 
 =^A 
 
 
 
 
 
 08 
 
 1 s 
 
 Q 6 
 4 
 2 
 
 8 
 6 
 4 
 2 
 
 Chittenango Creek, Chittenango, N. Y., Drainage Area, 79 Sq. Mi. 
 
 
 
 
 
 
 1903 
 
 
 
 
 
 
 
 
 
 
 
 1904 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 S 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 \ A 
 
 ^\ 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 r /x 
 
 ML 
 
 
 
 
 
 
 
 
 
 *\i 
 
 ^^J 
 
 ^2 
 
 
 
 
 
 
 
 
 A. 
 
 
 
 
 ^_i 
 
 if^ 
 
 ^^ 
 
 / 
 
 
 
 
 
 
 
 
 
 ^^/ 
 
 Gr 
 
 an 
 
 d Riv< 
 
 ''rrrtkf? 
 
 3r, Gr 
 
 2^ 
 
 anc 
 
 i^J 
 
 1 R 
 
 ap 
 
 fazz 
 ids 
 
 L^ 
 
 M 
 
 Ld 
 
 ich 
 
 ^^ 
 
 <?^ 
 Dn 
 
 tins 
 
 Lge 
 
 k*Lrt 
 
 Area 
 
 Le^2 
 
 4< 
 
 L&d 
 )00 
 
 2^2 
 
 s< 
 
 zzzz 
 
 1. K 
 
 22^ 
 
 
 
 
 i 
 
 1903 
 
 
 
 
 
 
 
 
 
 
 
 1904 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 !i I 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 ft 
 
 
 
 
 
 
 
 
 
 
 
 InA 
 
 
 
 i 
 
 ft 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 
 
 r*\t 
 
 
 
 !\ 
 
 R 
 
 
 
 
 
 
 
 
 \\ 
 
 
 
 
 
 
 
 
 
 
 
 ^jy//. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f^ 
 
 
 
 Iron River, near Iron River Mich., Drainage Area 75 Sq. Mi. 
 g 97. Hydrographs of Ohio Valley and St. Lawrence Drainage. 
 
I 9 2 
 
 Run-Off. 
 
 i 
 
 1903 
 
 S 
 
 1904 
 
 Wisconsin River, Necedah, Wis., Drainage Area, 5800 Sq. Mi. 
 
 1903 
 
 1904 
 
 Meramec River, Eureka, Mo., Drainage Area, 3497 Sq. Mi. 
 
 1903 
 
 104 
 
 Otter Creek, Mountain Park, Okla., Drainage Area, 126 Sq. Mi. 
 
 Clear Creek. Buffalo. Wyo., Drainage Area, 116 Sq. Mi. 
 
 Yellowstone River, Livingston, Mont., Drainage Area, 3580 Sq. Mi. 
 
 Niobrara River, Valentine, Neb., Drainage Area, 6070 Sq. Mi. 
 
 1803 
 
 WWk 
 
 fa 
 
 Rio Grande River, Labatos, N. M., Drainage Area, 7695 Sq. Mi. 
 
 
 
 
 
 
 1903 
 
 
 
 
 
 
 
 
 
 
 
 191 
 
 3 A II 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A II 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 II B 
 
 1 
 
 
 
 
 
 ^r 
 
 7^7 
 
 
 
 2 
 
 
 ^ 
 
 ^~> 
 
 
 
 
 
 
 
 
 
 
 
 | 
 
 
 
 
 Salt River, McDowell, Ariz., Drainage Area, 6260 Sq. Mi. 
 Fig. 98. Hydrographs of Mississippi Valley and Gulf Drainage. 
 
Comparative Hydrographs. 
 
 193 
 
 Spokane River, Spokane, Wash., Drainage Area, 4005 Sq. Mi. 
 
 Hood River, Tucker, Ore., Drainage Area, 350 Sq. Mi. 
 
 Kalawa River, Forks, Wash., Drainage Area, 213 Sq. Mi. 
 
 
 
 
 
 
 1903 
 
 
 
 
 
 
 
 
 
 
 
 1904 
 
 
 
 
 
 
 
 
 
 ^Tr 
 
 y&r. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Kern River, Bakersfield, Cal., Drainage Area, 2345 Sq. Mi. 
 
 oS 
 
 i : 
 
 >Q 
 
 
 Pacific E 
 
 
 
 jjr^ 
 
 
 1903 
 
 
 
 
 
 
 
 
 
 
 
 1904 
 
 
 
 
 
 
 
 
 fYt 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^k 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 San Gabriel River, Azusa, Cal., Drainage Area, 222 Sq. Mi. 
 
 Bear River. Collinston, Utah, Drainage Area, 6000 Sq. Mi. 
 
 Walker River, Coleville, Cal., Drainage Area, 306 Sq. Mi. 
 Fig. 99. Hydrographs of Western Drainage. 
 
194 Run-Off. 
 
 topographical conditions, and results in a material difference in 
 the distribution and quantity of run-off. 
 
 Hydrographs from the various hydrological divisions of the 
 United States are shown by Figs. 96 to 99, inclusive. For each 
 drainage area hydrographs for two years are shown in order to 
 eliminate, partially at least, the effect of any peculiar conditions 
 which might have obtained during a single year, and to show that 
 the hydrographs are characteristic. 
 
 102. General Conclusions. A complete discussion of run-off is 
 impossible in the space available in this volume. Attention has 
 been called to the general laws upon which the amount of run-off 
 depends, and to the similarity in flow that obtains on watersheds 
 which are physically similar, also to the variations in run-off that 
 occur on different watersheds due to differences in physical condi- 
 tions. 
 
 Each stream presents peculiarities of its own, and in investigating 
 stream flow the data available is seldom the same and is always 
 found to be much too limited for a complete understanding. Only 
 general suggestions can be offered for the study and investigation 
 of these subjects. Attention has been directed, as clearly as pos- 
 sible, to the errors which are likely to arise in the investigation of 
 water power conditions by comparative study. From a knowledge 
 of such errors the engineer will realize the limiting values of his 
 conclusions, and hence 'should so shape his design as to effect as 
 safe a construction as the condition will permit, and also a construc- 
 tion which will bear out fairly well his conclusions at the time of its 
 inception. It is evident that no exact conclusions are possible in 
 these matters, and that an element of uncertainty is always pres- 
 ent. A knowledge of the extent of these uncertainties and the 
 probable limits of exact knowledge are as important to the engineer 
 as his ability to draw correct conclusions from data which is known 
 to be correct. 
 
 LITERATURE. 
 
 RESULTS OF STREAM FLOW MEASUREMENTS. 
 
 1. Annual Reports of the Water Bureau of Philadelphia. Contain com- 
 
 plete data relating to the Perkiomen, Tohickon and Neshaminy. 
 
 2. Monthly Data Relating to the Sudbury, Cochituate, and Mystic. Reports 
 
 of the Boston Water Board, and of the Metropolitan Water 
 Board, Boston. 
 
 Publications of the U. S. Geological Survey contain data for the years 
 indicated below : 
 
Literature. 
 
 3. 1888. Tenth Annual Report. Part I. 
 
 4. 1889. Eleventh Annual Report. Part II. 
 
 5. 1890. . Twelfth Annual Report. Part II. 
 
 6. 1891. Thirteenth Annual Report. Part III. 
 
 7. 1892. Fourteenth Annual Report. Part II. 
 
 8. 1893. Bulletin No. 131. 
 
 9. 1894. Sixteenth Annual Report. Part II. 
 
 10. 1894. Bulletin No. 131. 
 
 11. 1895. Seventeenth Annual Report. Part II. 
 
 12. 1895. Bulletin No. 140. 
 
 13. 1896. Eighteenth Annual Report. Part IV. 
 
 14. 1896. Water Supply and Irrigation Paper, No. 11. 
 
 15. 1897. Nineteenth Annual Report. Part IV. 
 
 16. 1897. Water Supply and Irrigation Papers, Nos. 15 and 16. 
 
 17. 1898. Twentieth Annual Report. Part IV. 
 
 18. 1898. Water Supply and Irrigation Papers, Nos. 27 and 28. 
 
 19. 1899. Twenty-first Annual Report. Part IV. 
 
 20. 1899. Water Supply and Irrigation Papers, Nos. 35 to 39, inclusive. 
 
 21. 1900. Twenty-second Annual Report. Part IV. 
 
 22. 1900. Water Supply and Irrigation Papers, Nos. 47 to 52, inclusive. 
 
 23. 1901. Water Supply and Irrigation Papers, Nos. 65, 66 and 75. 
 
 24. 1902. Water Supply and Irrigation Papers, Nos. 81 to 85, inclusive. 
 
 25. 1903. Water Supply and Irrigation Papers, Nos>. 97 to 100, inclusive. 
 
 26. 1904. Water Supply and Irrigation Papers, Nos. 124 to 135, inclusive. 
 
 27. 1905. Water Supply and Irrigation Papers, Nos. 165 to 178, inclusive. 
 
 RELATIONS OF RAINFALL AND STREAM FLOW. 
 
 28. Fteley, A. The Flow of the Sudbury River, Mass. Trans. Am. Soc. C. E. 
 
 Vol. 10, p. 225, 1881. 
 
 29. Lawe, J. B. On the Amount and Composition of Rain and Drainage 
 
 Waters, collected at Rothamsted. Jour. Royal Agric. Soc. Eng. 
 Vol. 17, p. 241, 1881, and Vol. 18, p. 1, 1882. 
 
 30. Coghlan, T. A. Discharge of Streams in Relation to Rainfall, New South 
 
 Wales. Proc. Inst. C. E., Vol. 75, p. 176, 1884. 
 
 31. Croes, J. J. R. Flow of the West Branch of the Croton River. Trans. 
 
 Am. Soc. C. E., Vol. 3, p. 76. May, 1884. 
 
 32. Brackett, Dexter. Rainfall Received and Collected on the Water-sheds 
 
 of Sudbury River and Cochituate and Mystic Lakes. Jour. Asso. 
 Eng. Soc., Vol. 5, p. 395, 1886. 
 
 33. McElroy, Samuel. The Croton Valley Storage. Jour. Asso. Eng. Soc. 
 
 1890. 
 
 34. Fitzgerald, Desmond. Rainfall, The Amount Available for Water Sup- 
 
 ply. Jour. New Eng. W. Wks. Assn. 1891 
 
 35. Fitzgerald, Desmond. Yield of the Sudbury River Watershed in the 
 
 Freshet of February 10-13, 1886. Trans. Am. Soc. C. E., Vol. 
 25, p. 253, 1891. 
 
 36. Talbot, A. N. The Determination of the Amount of Storm Water. Proc. 
 
 111. Soc. Eng. & Surveyors. 1892. 
 
196 Run-Off. 
 
 37. Fitzgerald, Desmond. Flow of Streams and Storage in Massachusetts. 
 
 Trans. Am. Soc. C. E., Vol. 27, p. 253. 1892. 
 
 38. Fitzgerald, Desmond. Rainfall, Flow of Streams, and Storage. Trans. 
 
 Am. Soc. C. E., Vol. 27, p. 304, 1892. 
 
 39. Babb, C. C. Hydrography of the Potomac Basin. Trans. Am. Soc. C. 
 
 E., Vol. 27, p. 21, 1892. 
 
 40. Babb, C. C. Rainfall and Flow of Streams. Trans. Am. Soc. C. E., Vol. 
 
 28, p. 323, 1893. 
 
 41. Mead, D. W. The Hydrogeology of the Upper Mississippi Valley, and of 
 
 Some of the Adjoining Territory. Jour. Ass'n Eng. Soc., Vol. 
 13, p. 329, 1894. 
 
 42. Report on Water Supply of New Jersey. Geol. Survey of N. J., Vol. 3. 
 
 1894. 
 
 43. Starling, Wm. Measurements of Stream Flow Discharge of the Missis- 
 
 sippi River. Trans. Am. Soc. C. E., Vol. 34, pp. 347-492, 1895. 
 
 44. McLeod, C. H. Stream Measurements. The Discharge of St. Lawrence 
 
 River. Trans. Can. Soc. C. E. June, 1896. 
 
 45. Data Relating to the Upper Mississippi. Report, Chief of Engineers, U. 
 
 S. A., 1896, p. 1843. 
 
 46. Wegmann, Edward. The Water Supply of the City of New York. Data 
 
 Relating to the Croton. Wiley & Sons. 1896. 
 
 47. Johnson, T. T. Data Pertaining to Rainfall and Stream Flow. Jour. 
 
 Wes. Soc. Eng., Vol. 1, p. 297, June, 1896. 
 
 48. Chamier, Geo. Capacities Required for Culverts and Flood Openings. 
 
 Proc. Inst. C. E., Vol. 134, p. 313. 1898. 
 
 49. Pannalee, W. C. The Rainfall and Run-off in Relation to Sewage Prob- 
 
 lems. Jour. Asso. Eng. Soc., Vol. 20, p. 204, Mch., 1898. 
 
 50. Seddon, J. A. A Mathematical Analysis of the Influence of Reservoirs 
 
 upon Stream Flow. Trans. Am. Soc. C. E., Vol. 40, p. 401. 1898. 
 
 51. Sherman, C. W. Run-off of the Sudbury River Drainage Area, 1875-1899, 
 
 inclusive. Eng. News, 1901. 
 
 52. Clark, E. W. Storm Flow from City Areas, and Their Calculation. Eng. 
 
 News, Vol. 48, p. 386, Nov. 6th, 1902. 
 
 53. Pence, W. D. Waterways! for Culverts. Proc. Purdue Soc. C. E., 1903. 
 
 54. Weber, W. O. Rainfall and Run-off of New England Atlantic Coast and 
 
 Southwestern Colorado Streams, with Discussion. Jour. Asso. 
 Eng. Soc. Nov., 1903. 
 
 55. Abbott, H. L. -Disposition of Rainfall in the Basjn of the Chagres. 
 
 Monthly Weather Review, Feb., 1904. 
 
 56. Mead, D. W. Report on the Water Power of the Rock River. Chicago, 
 
 1904. Published by the Author. 
 
 FLOODS. 
 
 57. The Flood in the Chemung River. Report State Engineer, N. Y., 1894, 
 
 p. 387. 
 
 58. The Floods of February 6th, 1896. Geol. Survey of N. J. 1896, p. 257. 
 
 59. Morrill, Park. Floods of the Mississippi River. Bui. E., U. S. Dept. of 
 
 Agric. 1897. 
 
Literature. 197 
 
 60. Starling, Wm. The Floods of the Mississippi River. Eng. News, Vol. 
 
 37, p. 242. Apr. 22nd, 1897. 
 
 61. Starling, Wm. The Mississippi Flood of 1897. Eng News, Vol. 38, p. 2, 
 
 July 1st, 1897. 
 
 62. McGee, W. J. The Lessons of Galveston. Nat. Geo. Mag. Oct., 1900. 
 
 63. Study of the Southern River Floods of May and June, 1901. Eng. News, 
 
 Vol. 48, p. 102. Aug. 7th, 1902. 
 
 64. Brown, L. W. The Increased Elevation of Floods in the Lower Missis- 
 
 sippi River. Jour. Asso. Eng. Soc., Vol. 26, p. 345, 1901. 
 
 65. Holister, G. B. and Leighton, M. O. The Passaic Flood of 1902. Water 
 
 Supply and Irrigation Paper No. 88, U. S. G. S, 
 
 66. Leighton, M. O. The Passaic Flood of 1903. Water Supply and Irriga- 
 
 tion Paper No. 92, U. S. G. S. 
 
 67. Murphy, E. C. Destructive Floods in the United States in 1903. Water 
 
 Supply and Irrigation Paper No. 96, U. S. G. S. 
 
 68. Frankenfield, H. C. The Floods of the Spring of 1903 in the Mississippi 
 
 Watershed. Bui. M., U. S. Dept. of Agric. 1903. 
 
 69. Flood Damages to Bridges at Paterson, N. J. Eng. News, Vol. 50, p. 377, 
 
 Oct. 29th, 1903. 
 
 70. Kansas City Flood of 1903. Eng. News, Vol. 50, p. 233, Sept. 17th, 1903. 
 
 71. Engineering Aspect of the Kansas City Floods. Eng. Rec., Vol. 48, p. 
 
 300, Sept. 12th, 1903. 
 
 72. Murphy, E. C. Destructive Floods in the United States in 1904. Water 
 
 Supply and Irrigation Paper No. 147, U. S. G. S, 
 
 FORESTS IN RELATION TO RAINFALL AND STREAM FLOW. 
 
 73. Swain, Geo. F. The Influence of Forests Upon Me Rainfall and Upon the 
 
 Flow of Streams. Jour. New Eng. W. Wks. Ass'n. 
 
 74. Rafter, Geo. W. Data of Stream Flow in Relation to Forests. Ass'n 
 
 C. E., Cornell Univ., Vol. 7, p. 22, 1899. 
 
 75. Thompson, D. D. Influence of Forests on Water Courses. Scientific 
 
 American Sup. No. 807. 
 
 76. Vermeule, C. C. New Jersey Forests and Their Relation to Water Sup- 
 
 ply. Abstract of Paper Before Meeting of The American For- 
 estry Ass'n. New Jersey, June 25th, 1900; Eng. News, July 26th, 
 1900; Eng. Record, Vol. 42, p. 8, July 7th, 1900. 
 
 77. Bremner. Water Ways for Culverts and Bridges. Jour. West. Soc. Engrs., 
 
 Vol. 11, p. 137. April, 1906. 
 
CHAPTER X. 
 
 STREAM FLOW. 
 
 103. Flow in Open Channels. The discussion of the flow of water 
 in open channels in Chapter III includes only such channels as 
 have uniform cross sections, alignment, and gradient and a bed of 
 uniform character throughout the length considered. Such condi- 
 tions are closely approximated in artificial channels in which the 
 quantity of water flowing is under control. In such channels, and 
 with a steady flow, that is with the same quantity of water passing 
 
 every cross section in the same time, it is shown that: 
 
 / 
 
 (1) v = c A /ah = c T/rs" and that 
 
 (2) q = av = ac A = ac l/rs" 
 
 v 
 
 In natural water courses no two cross sections are the same but 
 may differ in area, a, and wetted perimeter, p ; and the fall, h, in any 
 length, 1, usually differs considerably from reach to reach. The 
 quantity, q, of water flowing in any such stream is also constantly 
 changing. There every condition of uniform flow is lacking and 
 can only be approximated for selected reaches of such streams and 
 during periods when stream flow is fairly steady. 
 
 104. Changes in Value of Factors with Changes in Flow. From 
 an examination of equation (2) it is evident that in any channel as 
 the quantity of water flowing, q, changes, there must be a corre- 
 sponding change in some or all of the factors on the other side of the 
 equation. 
 
 For steady flow in a uniform channel, s remains constant and all 
 changes are confined to the values of a, c and r. The laws of 
 change in the values of c are given by Kutter's and Bazin's formu- 
 las, but are best illustrated and understood by reference to Fig. 22, 
 which is a graphic expression of the formula of Bazin. 
 
 In variable flow a change in all of the factors usually accompa- 
 nies a chang:e in the value of q, each factor changing in accordance 
 with the physical conditions of the channel. 
 
 The changes in the value of c, in an irregular channel, do not al- 
 ways seem to follow Bazin's law. In some cases c is even found to 
 
Flow in Open Channels. 
 
 199 
 
 decrease as r increases. The law of simultaneous increase in c and 
 r presupposes a channel of uniform character and condition. If an 
 increase in the hydraulic radius, r, in any channel is accompanied by 
 a radical change in the character of its bed the law will not hold. 
 It is evident that under such conditions the values of c for different 
 values of r are not fairly comparative. No more uniform law of 
 change can be expected under such conditions than would occur in 
 the comparison of the relation of c and r for entirely different chan- 
 nel sections. 
 
 In Fig. .TOO are shown the observed values of c and r for certain 
 reaches of the Wisconsin River above Kilbourn, Wis. It will be 
 
 10 20 30 40 SO 6O 70 80 90 100 110 120 
 
 Pig. 100. Relations of Coefficient to Hydraulic Radius in Certain Reaches 
 
 of the Wisconsin River. 
 
200 
 
 Stream Flow. 
 
 noted that the value for readies A, D and E follow in general the 
 law as established by Bazin. These are fairly uniform. On the 
 other hand the values of c and r for reaches b and c seem to follow 
 an entirely different law, a condition due to irregularities in the 
 cross section of the reach. 
 
 Where the values of a, p and r vary radically from section to sec- 
 tion and differ materially from the values in the sections considered 
 and on which calculations are based, the value of c will be found to 
 differ radically from that which the character of the bed and the en- 
 tire section would indicate. Absurd values of c are a clear indica- 
 tion that the sections selected are not representative. The calcu- 
 lated value of c is modified by all unknown or unconsidered factors 
 of the reach. The influences of irregularities in bed or section, the 
 presence of unconsidered bends or changes in the gradient, and all 
 other irregularities in the channels, modify the values of c. 
 
 105. Effects of Variable Flow on the Hydraulic Gradient. In 
 order to understand the effect of variable flow on the surface gradi- 
 ent of a stream, and in order to realize how conclusions drawn from 
 the laws of uniform flow must be modified to meet conditions found 
 in natural streams, it is necessary to consider the cause of variable 
 flow in a stream, the variation in channel conditions, and both the 
 effect of flow on such conditions and the effect of such conditions on 
 the flow of a stream. 
 
 Tnic^t by Time Fti 
 
 REPRODUCTION OF RECORD OF U. S.L.S. GAUGE. No. 5 FOR MAY 17, 1609. 
 
 He AD OF <ST:CLAin ft/vcn. 
 7 a e 10 u "i?* ia 14 
 
 7r*(eStr TTme ft/id fs. 
 
 Fig. 101. Variations in Gauge Height of the St. Clair River. 
 
Effects of a rising or a Falling Stream on Gradient. 201 
 
 The surface of a stream is constantly fluctuating, not oaily on ac- 
 count of the variation in flow, but also on account of wind, baro- 
 metric pressure and changes in the hydraulic gradient. Such 
 changes occur from hour to hour, and even from minute to min- 
 ute. Larger rivers, fed directly by great lakes, are more sus- 
 ceptible to these changes on account of the broad lake area, giving 
 wind and barometric pressure greater opportunity to act. Every 
 stream is, however, more or less susceptible to these changes, and 
 gauge readings taken daily, therefore, show only in an approximate 
 way the true height of the surface of the river at the point of ob- 
 servation. This is well shown by Fig. 101, which is reproduced 
 from the autographic record of a gauge at the head of the St. Claire 
 River. 
 
 106. Effects of a Rising or a Falling Stream on Gradient. In a 
 channel of uniform section, the bed of the channel AB (see diagram 
 A, Fig. 102) having a uniform slope, all cross sections, such as Aa 
 and Bb, will be alike and the wetted perimeters and the hydraulic 
 radii will be identical for all sections. The fall, bx, will be uniform 
 in all equal lengths, 1, of the channel, and such uniform conditions 
 will be maintained for all regular discharges after regular flow is 
 once established. 
 
 In such channels, during changes in the stages of flow, the hy- 
 draulic gradient or slope will change until uniform flotw is estab- 
 lished. In all cases illustrated in Figs. 102 and 103, the line ab rep- 
 resents the hydraulic gradient which will obtain if uniform flow is 
 maintained in the channel and if there be no change in the channel 
 section or other conditions^ The actual water surface, caused by 
 variable flow, is in each case shown by the line a'b. In each case, the 
 fall, bx, would be necessary to produce uniform flow from A to B 
 and to assure the flow of the normal quantity of water passing the 
 section Bb as in diagram A. In diagram B and C, Fig. 102, the con- 
 ditions of variable flow in a uniform channel are graphically repre- 
 sented. The actual flow is greater or less than the normal quantity, 
 according as the gradient is increased or diminished. 
 
 In diagram B, the conditions with a rising stream are shown. 
 Under these conditions the quantity of water passing the section 
 Aa is greater than the quantity passing the section Bb, by the quan- 
 tity of water necessary to fill up the channel of the stream to a new 
 and uniform surface gradient. The head needed to produce the flow 
 past the section, Aa, is represented by the height, xx'. The total 
 fall between A and B is therefore greater than that required for the 
 
 12 
 
202 
 
 Stream Flow. 
 
 H 
 
 Fig. 102. Effects of Variable Flow on the Hydraulic Gradient of a Stream. 
 
Effects of Channel Conditions on Gradient. 203 
 
 uniform flow as represented by the head bx'. This produces not 
 only a greater flow at Aa, but also a flow greater than would be nor- 
 mal at section Bb. 
 
 In diagram C, Fig. 102, the conditions of a falling stream are rep- 
 resented. In this case, the head at section Bb at the moment of 
 observation would, if the flow was uniform, produce a normal flow 
 which would require the fall, bx, to maintain it. With a falling 
 stream, the section AB is emptying and the quantity of water pass- 
 ing the sectian Aa is less than the quantity of water passing the 
 section Bb, which in turn is also less than the normal flow 'for the 
 existing head. A less fall is therefore required to produce the flow 
 passing Bb, which, with the lower slope and the same cross section, 
 is less in quantity than would be the case under conditions of uni- 
 form flow. This fall is represented by the height, bx', which is less 
 than the height bx, required for uniform flow by the height xx': 
 consequently the slope of the river is a'b. 
 
 From the above considerations it will be seen (see diagram D, 
 Fig. 102) that a given gauge height, Bb, may not always represent 
 the same flow, for the discharge, Q, is a function not only of the 
 cross section, a, but also of the slope, s. A single gauge height may 
 therefore represent a considerable range of flows depending on the 
 hydraulic gradient which may pass through the point with a uni- 
 form, a rising or a falling stream. It is obvio'us that the flows rep- 
 resented by the hydraulic gradient, a' be', abc and a"bc", while pro- 
 ducing the same gauge height at Bb, nevertheless represent three 
 different conditions of flow. 
 
 In the establishment of the relations between gauge heights and 
 flow, it is therefore important that the observed flow corresponding 
 to a given gauge reading be taken during a period of essentially uni- 
 form flow, for, from the above considerations, it will be seen that 
 any determination or observation made with a rising or a falling 
 stream must necessarily be more or less in error. It will also follow 
 that, .after a rating curve and rating table have been established, 
 the gauge height taken during changes in the conditions of flow will 
 be more or less in error, although such errors will equalize to a con- 
 siderable extent and will, in the main, prove unimportant. 
 
 107. Effects of Channel Condition on Gradient. The flow of 
 water in a natural channel is far from being uniform and it is im- 
 portant for the engineer to realize this lack of uniformity and the 
 effect of such conditions upon the flow of the stream. In any chan- 
 nel of uniform gradient, as AB in diagram E (Fig. 102), if at the 
 
204 
 
 Stream Flow. 
 
 B' 
 
 Fig. 103. Effects of Channel Grade and of Obstruction on the Hydraulic 
 
 Gradient of a Stream. 
 
 section Bb the coefficient c is decreased on account of increased 
 roughness in the bed of the stream, or if the area of the channel, a, 
 is contracted, a change in the hydraulic gradient will follow. The 
 normal gradient with uniform flow would take the position ab, but 
 on accoamt of the change in conditions at Bb, the depth must in- 
 crease to keep q a constant ; a must increase to offset the decrease in 
 c or c must increase to offset the decrease in a if q remains constant. 
 The surface must therefore rise to the point x and a new hydraulic 
 
Effect of Change in Grade. 2o5 
 
 gradient will be established and maintained until other changes in 
 the channel condition again modify the same. Between the new and 
 old gradients, a transition curve will be established extending both 
 above and below the point at which the change in condition takes 
 place to some point, y, frequently a long distance upstream. 
 
 The opposite condition is shown by diagram F, Fig. 102. In this 
 diagram the effect of an increase in the coefficient, c, of the bed or 
 in the area, a, of the stream is represented. If c increases, a less 
 section will be required below that point and again the surface is 
 lowered; or if the width of the stream increases, the depth will 
 diminish in order that ca may remain constant. 
 
 Variable flow is also caused by a sudden enlargement in the 
 river section or by a discharge of the stream into a larger stream or 
 into a lake or pond. Such conditions are shown by diagrams G 
 and H, Fig. 102. The character of the transition curve in such 
 cases will depend on the height of the surface of the water into 
 which the stream is discharged. If the water surface of the lake 
 is above b, the curve will be concave upward (see diagram G) and 
 if the surface is below b, the curvature will be doiwnward (see dia- 
 gram H). 
 
 108. Effect of Change in Grade and of Obstructions. Variable 
 flow may also be caused by changes in the slope of the stream bed 
 as shown by diagrams A and B, Fig. 103. The area of the stream 
 must increase as the bed slope is decreased, or must decrease as 
 the slope of the bed is increased in order to fulfill the conditions of 
 equation (2). 
 
 It is evident that uniform slope may be maintained even with 
 changed conditions if the changes that occur give rise to equal and 
 opposite effects. For example, uniform slope may be maintained 
 if the area of section a is reduced and the coefficient c is increased 
 to such an extent that the product ac remains constant at each sec- 
 tion of the channel. 
 
 Variable flow is also caused by the passage of the stream over 
 weirs or dams and the effect on the gradient will vary as shown by 
 diagram C and D, Fig. 103. Variations may also be caused by a 
 change in the bed (see diagram E, Fig. 103), or by local contrac- 
 tions, submerged weirs or other obstructions as shown by dia- 
 gram F, Fig. 103. 
 
 In all of the above described cases it is obvious that if the slope 
 of the stream is measured on any of these transition curves, a false 
 idea of slope will obtain and a false relation will be established for 
 
206 
 
 Stream Flow. 
 
 43 
 46 
 44 
 42 
 40 
 38 
 36 
 34 
 32 
 30 
 28 
 26 
 24 
 22 
 20 
 18 
 
 n 
 
 n 
 
 pig. 
 
 15 16 17 18 19 20 21 22 23 24 23 
 GAUGE HEIGHTS AT KILBOURN. 
 
 104. Relations of Guage Heights at Various Stations on the Wiscon- 
 sin River. 
 
Effect of Change in Grade. 207 
 
 the condition of stream flow. It is therefore essential in any meas- 
 urement of a stream or in the establishment of any gauging station 
 that the location for such observations be carefully selected on a 
 reach of the stream where conditions of essentially uniform flow 
 prevail and that all observations be taken during stages where the 
 flow of the stream is practically constant. If gauges are established 
 at various points along the course of a river and are read simultan- 
 eously, and if the flow is uniform and no falls, rapids or tributaries 
 intervene, the same differences in elevation should always obtain 
 with the same stage of water. 
 
 A system of gauges as described above was recently established 
 at Kilbourn on the Wisconsin River in order to determine the river 
 slopes near that place. A large number of practically simultaneous 
 readings were taken in order to determine the relations between the 
 gauge heights at the various points compared with the Kilbourn 
 gauge. 
 
 Fig. 104 shows the results of the gauge readings at the various 
 stations compared with the gauge readings at Kilbourn. It will 
 be noted from the diagram that the slope of the river was far from 
 uniform at different times during these readings, and, in a number 
 of cases, the same gauge reading at Kilbourn was accompanied by 
 readings at other gauges that differed from each other by more 
 than a foot. For example, compare the gauge readings at Kilbourn 
 with the readings at gauge No. 5. With a gauge reading of 17 ft. 
 at Kilbourn, the normal gauge reading at No. 5 should be 23 feet, 
 and with a normal flow, the fall between gauge No. 5 and the Kil- 
 bourn gauge would be 5 ft. From the diagram it will be seen that 
 during a certain stage of flow in the river the gauge reading at 
 gauge No. 5, with a 17 foot reading at Kilbourn, was about 22 J ft. 
 Under these conditions the fall between gauge No. 5 and the Kil- 
 bourn gauge was only 4^ ft. The slope being reduced, the quantity 
 of water actually passing the Kilbourn gauge under these condi- 
 tions was less than the normal flow for the 17 ft. gauge height. 
 On two other occasions where the gauge reading at Kilbourn was 
 approximately 17 feet, the actual gauge reading at gauge No. 5 was 
 about 24 feet. During these conditions the actual fall in the river 
 between gauge No. 5 and the Kilbourn gauge was 5 feet, or one 
 foot more than normal. Hence the quantity of water flowing by the 
 Kilbourn gauge at this time was more than the normal quantity 
 indicated by the Kilbourn gauge. 
 
 Readings of other gauges compared with the Kilbourn readings 
 
208 
 
 Stream Flow. 
 
 B 
 
 will show that at certain times the flow 
 was normal and at other times the river 
 must have been rising or falling and that 
 consequently the gauge at Kilbourn at the 
 time of such reading, was not accurately 
 representing the quantity of water flow- 
 ing by the Kilbourn section. The above 
 example taken of the variation in slope 
 between the Kilbourn gauge and gauge 
 No. 5 indicated practically the maximum 
 abnormal conditions. The actual varia- 
 tion in flow at Kilbourn during these con- 
 ditions was not determined and is not 
 definitely known. 
 
 109. Relation of Gauge Heights to 
 Flow. The area of any cross section 
 equals the product of the height of the 
 section into some function of its width : 
 
 (3) 
 
 = h X f 
 
 In a rectangular cross section f=i, (see A, Fig. 105). In a tri- 
 angular section, f=-5 (see B, Fig. 105). In all cases of regular sec- 
 tion f can be mathematically expressed, and for irregular sections 
 (see C, Fig. 105) the relation may be obtained by measurement. 
 If the height of the surface is referred to a gauge height, H, the 
 zero of the gauge may or may not correspond with the bottom of 
 the channel. If H=the gauge height, then h=-H-fe, in which e is 
 the distance from the bottom of the channel to the bottom of the 
 gauge. Substituting, therefore, the value of h in equation (3) it 
 becomes : 
 
 (4) a = (H + e) X f (w) - Hf(w) -f- ef(w), 
 And substituting this value in equation (2) it becomes : 
 
 (5) Q = Hf(w) c Vn + ef( w) c l/rs 
 
 With this equation, and with the flow in a fixed and uniform chan- 
 nel, if the relation can be established between r, s, c, e, w and f for 
 each gauge height, H, the corresponding value of Q can be deter- 
 mined. As these relations are mathematically expressed for uni- 
 form flow by the above equation, they can also be represented 
 graphically by a curve which will show the relation between Q and 
 H for all conditions of uniform flow that obtain in the given chan- 
 
Relation of Gauge Height to Flow. 
 
 209 
 
 nel. Such a curve is called a discharge or rating curve. This equa- 
 tion (5) can be readily solved when f is a regular variable and when 
 c, r and s can be determined. Where the function, f, is an irregular 
 variable, no mathematical solution is practicable but the relations 
 may be determined experimentally and can be expressed by a rating 
 table or graphically by a rating curve. Such a rating table and curve 
 can be constructed for every fixed channel or section of a stream 
 for condition of uniform flow, no matter how irregular the section 
 or how the values of the function of the section may vary for differ- 
 ent gauge heights. 
 
 Discharge in Cubic Feet per Second. 
 Fig. 10G. Rating Curve for Wisconsin River at Kilbourn, Wis. 
 
 Fig. 106 shows a rating curve established for the Wisconsin River 
 at Kilbourn, Wis. The small circles show the flow relative to gauge 
 'height at the time the observations were made. They were care- 
 fully made in a fairly satisfactory section and fall fairly well on a 
 smooth curve drawn from this data to represent the relation of 
 gauge height to flow at similar or intervening heights. 
 
 The character of the rating curve for regular and irregular sec- 
 tions is shown by Fig. 45, page 95. Whenever the section remains 
 
2IO 
 
 Stream Flow. 
 
 similar for different gauge heights, the rating curve will be a smooth 
 curve, but when irregularities occur in the section, the curve be- 
 comes broken more or less according to the extent of the irregu- 
 larity. 
 
 It has already been pointed out that any change in the cross sec- 
 tion of the stream after a rating curve has been established will 
 necessitate the establishment of a new curve. The variation in rat- 
 ing curves under variation in channel conditions is shown in Fig. 46, 
 page 96. 
 
 1234587 
 
 Fig. 107. Variations in the Cross-section of the Missouri River near 
 
 Omaha, Neb.* 
 
 The actual change in channel conditions that affects the relation 
 of head and flow is well illustrated by Fig. 107 which shows the 
 changes that actually took place in the cross section of the Missouri 
 River near Omaha, Nebraska. 
 
 no. Variations in Velocity in the Cross-section of a Stream. 
 The velocity of flow of a stream varies greatly at different points in 
 any cross section. In any channel the friction of the sides and bed 
 reduces the velocity of that portion of the stream in contact and 
 adjacent to them. If the bed at different points of the cross-section 
 is not uniform, as is always the case in the beds of natural streams, 
 the retarding effects on different portions of the stream varies, and 
 a consequent variation in velocity results. The distribution of the 
 velocities in the cross section of the St. Clair River is shown in Fig. 
 108, both by lines of equal velocity and by figures giving the ve- 
 locity as actually measured. In this figure the effect of the friction 
 
 *Todd. Bull. 158 U. S. Geol. Surv. 
 
Variation in Velocity in the Cross-Section of a Stream. 211 
 
 Curves of Equal Velocity 
 Section Dm Dock 
 
 Mean Wafer Stage - 
 Mean Velocity -3.33 t 
 
 STATIONS. I 1 3 
 
 Fig. 108. 
 
 S> K> nf g 13 
 
 
 Transverse Curve of Mean Velocities 
 'Section 'Dry Dock' 
 
 Mean Hbter'ttyi-5766 
 
 Fig. 109. 
 
 I 2 3 4 5 6 7 8 9 10 II 12 13 14 15 16 17 IB 19 20 2> 
 
 5FT 
 10- 
 15" 
 20- 
 25- 
 30- 
 35- 
 
 \/ 
 
 Fig. 110. Vertical Velocity Curves, Section Dry Dock. 
 
212 
 
 Stream Flow. 
 
 of the bed and banks is clearly shown. 
 The friction between the stream sur- 
 face and the atmosphere is also 
 shown by the fact that the maximum 
 velocity is not at the surface but is a 
 short distance below the surface. 
 The surface velocity may be modified 
 radically by the direction and velocity 
 of the wind. 
 
 Fig. 109 shows the transverse 
 curve of mean velocities in this sec- 
 tion. The distribution of velocities 
 in each vertical section is shown in 
 Fig. no. The velocities here shown 
 are relative only as compared with 
 each vertical. The velocity at the 
 bottom of each curve is that shown 
 by figures in Fig. 108. 
 
 The distribution of velocities in 
 any section is not the same under all 
 conditions of flow but differs mater- 
 ially with the stage of the river. This 
 is illustrated by Fig. in in which is 
 shown three sections of the same 
 stream illustrating conditions of low, 
 medium and high water. Above each 
 section is shown a corresponding 
 transverse curve of mean velocities 
 of flow. The change in the distribu- 
 tion of velocities as the stream in- 
 creases should be noted. 
 
 The distribution of velocity is also 
 affected by bends in the stream above 
 the point of observation which tends 
 to throw the current of the stream 
 toward the concave side, and to cause 
 a transverse slope in the section of 
 the stream at the curve. Such a condition (see Fig. 112) creates 
 cross currents and eddies and produces conditions of variable flow. 
 From Fig. 108 it will be seen that in any vertical line in a given 
 section, the velocities will vary with the condition of the bed, and 
 
Variation in Velocity in the Cross-Section of a Stream. 213 
 
 Fig. 112. 
 
 CALM WIND DOWN STREAM WIND, UP STREAM ICE COVERED 
 
 20 
 
 : 
 
 ^r 60 
 
 u 80 
 
 or 
 
 a 100 
 
 
 ) 
 
 1 
 
 \ 
 
 
 
 / 
 
 1 
 
 
 
 \ 
 
 
 / 
 
 / 
 
 J 
 
 
 ) 
 
 z 
 
 / 
 
 y 
 
 
 / 
 
 
 
 ^ 
 
 _^ 
 
 
 100 
 PER CENT OF MEAN VELOCITY 
 
 Fig. 113. Ideal Vertical Velocity Curves. 
 
 100 
 
 u 
 10 
 
 20 
 
 X. 
 
 30 
 
 o 
 
 jt*. 
 
 
 K 
 
 u 50 
 
 
 60 
 
 U 
 
 u 
 it 70 
 
 bl 
 
 a 
 do 
 
 90 
 100^ 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 MEAN OF 31 CURVES- VARIOUS STREAMS. 
 
 
 \ 
 
 
 
 
 MEAN OF 7 CURVES- WEST CANADA. 
 
 
 
 
 
 MEAN OF 4 CURVES- MOHAWK RIVER UTlCA, N.Y. 
 
 / 
 
 
 
 MEAN OF 12 CURVES- MOHAWK RIVER LITTLE FALLS. 
 
 1 / 
 
 
 
 MEAN OF 8 CURVES -MOHAWK RIVER SCHENECTADY. 1 
 
 / t 
 
 
 
 
 
 
 
 
 
 i 
 
 ' / 
 
 
 
 
 
 
 
 
 
 'I 
 
 1 I 
 
 
 
 
 
 
 
 
 
 i 
 
 / 
 
 
 
 
 
 
 
 
 
 J 
 
 
 
 
 
 
 
 
 
 
 y/ 
 
 
 
 
 
 
 
 
 
 
 il 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 /// 
 
 7 
 
 
 
 
 
 
 
 
 X 
 
 '/> 
 
 
 
 
 
 
 
 
 
 X/i 
 
 /// 
 
 
 
 
 
 
 
 
 ~2L 
 
 //,\ 
 
 s 
 
 
 
 
 
 
 
 ^ 
 
 ^/ 
 
 "/ 
 
 
 
 
 
 
 .,. 
 
 ^^^ + ~ 
 
 ^ 
 
 &*' 
 
 
 
 
 
 
 
 -- 
 10 5 
 
 6 
 
 ^Zf** 
 
 7 
 PER 
 
 5 a 
 
 CENT 
 
 9 
 OF 
 
 ~ M 
 XEAN 
 
 )0 1 
 VELOC 
 
 10 li 
 ITY 
 
 >o i: 
 
 30 14 
 
 Fig. 114. Mean Vertical Velocity Curves. 
 
Stream Flow. 
 
 the influence of air current or ice at the surface. These conditions 
 have an influence on the velocities in each section considered. Vari- 
 ations in the vertical velocities can be better studied by means of the 
 vertical velocity curve, which can be obtained by means of velocity 
 observations taken in a vertical line from the surface to the bed of 
 the stream. Ideal curves under various conditions are illustrated by 
 Fig. 113. Figs. 114, 115 and 116 are reproduced from the report of 
 the State Engineer of New York for the year 1902. These diagrams 
 show comparisons between the mean vertical velocities of streams 
 having different classes of beds. From these illustrations it will be 
 noted that there is a general similarity between the various velocity 
 curves which aids materially in the measurement of stream flow. It 
 will be noted, for example, that the mean velocity, in any vertical 
 velocity curve from an open channel, lies near the point of .6 total 
 depth but that with varying conditions this position may vary from 
 55 per cent, to about 75 per cent, of the depth. The velocity at .6 
 depth is found to average nearly 100 per cent of the mean velocity, 
 but may actually vary from 95 per cent, to 105 per cent, of the mean 
 
 
 
 
 \ 
 
 
 
 
 
 \ 
 
 
 
 in 
 
 MEAN OF 52 CURVES- GENERAL CONDITIONS. 
 
 
 
 
 - 
 
 
 20 
 
 I 
 1- 
 
 u 30 
 
 
 
 < 40 
 
 
 
 * so 
 
 o 
 
 l_ 
 
 z 
 
 bl 
 O 
 
 a 70 
 
 hi 
 
 a 
 80 
 
 90 
 100 
 
 -MEAN OF 31 CURVES-SMOOTH BED. 
 
 
 
 
 
 
 
 'MEAN OF 15 CURVES -ROUGH BED. 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 ft 
 
 / 
 
 
 
 
 
 
 
 
 
 1 
 
 I/ 
 
 
 
 
 
 
 
 
 
 ~J\ 
 
 
 
 
 
 
 
 
 
 
 //I 
 
 
 
 
 
 
 
 
 
 
 /'/ 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ' / 
 
 
 
 
 
 
 
 
 
 5 
 
 ' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x XX 
 
 / x 
 
 
 
 
 
 
 
 
 X X 
 
 x/ x 
 
 
 
 
 
 
 
 
 ^ 
 
 ^x^ 
 
 x" 
 
 
 
 
 
 
 
 ^ 
 
 ^J>-^ 
 
 ^^' 
 
 
 
 
 
 
 
 ^* 
 
 ^^' 
 
 """ 
 
 
 
 
 
 
 
 
 10 SO GO 70 80 90 100 110 120 130 \A 
 PER CENT OF MEAN VELOCITY 
 
 Fig. 115. Mean Vertical Velocity Curves. 
 
Effects of Ice-Covering on the Distribution of Velocites. 215 
 
 u 
 10 
 20 
 
 X 
 
 1- 
 30 
 
 
 
 <40 
 
 
 
 1- 
 
 t 50 
 
 o 
 
 Is 60 
 
 o 
 
 tt 70 
 u 
 a 
 
 80 
 90 
 
 100 
 
 4 
 
 
 1 
 
 
 
 
 
 
 
 
 
 </IEAN OF 15 CURVES -VARIOUS STREAMS. 
 
 
 n 
 
 
 
 MEAN OF 9 CURVES-BEAVER RIVER TISSE BRIDGE, N.Y. /'J| 
 
 
 MEAN OF 5 CURVES -SALMON RIVER PULASKI. N.Y. 
 
 
 
 
 
 
 
 
 
 
 / \\ 
 
 
 
 
 
 
 
 
 
 ' III 
 
 
 
 
 
 
 
 
 1 
 
 \ 
 
 
 
 
 
 
 
 
 
 /' 
 
 
 
 
 
 
 
 
 
 77 
 
 
 
 
 
 
 
 
 ; / 
 
 / 1 
 
 
 
 
 
 
 
 
 1 // 
 
 
 
 
 
 
 
 
 
 fj,' 
 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 
 
 
 jf 
 
 
 
 
 
 
 
 
 S/ 
 
 Y 
 
 
 
 
 
 
 
 s 
 
 '// 
 
 
 
 
 
 
 
 
 ^'S' 
 
 f 
 
 
 
 
 
 
 
 ^,^"^> 
 
 ^_ < 
 
 ,' . 
 
 
 
 
 
 
 ^*^> 
 
 S^ 
 
 
 
 
 
 
 
 ^-^^ 
 
 ^ 
 
 
 
 
 
 
 
 (_ G 
 
 50 60 7O 80 90 IOO 110 120 130 U 
 PER CENT OF MEAN VELOCITY 
 
 Fig. 116. Mean Vertical Velocity Curves. 
 
 velocity. The velocity at the surface is subject to the external influ- 
 ence of atmospheric currents and is not so constant in its relation to 
 the mean velocity. The surface velocity will average about no per 
 cent of the mean velocity of the vertical curve, but is found to vary 
 with the variations in conditions from 105 per cent, to 130 per cent. 
 of such velocity. 
 
 in. Effects of Ice-Covering on the Distribution of Velocities. 
 The effect of the formation of an ice sheet over a stream is to ma- 
 terially increase the surface friction and results in a rearrangement 
 of velocities in the cross section. As the ice sheets form in winter, 
 the conditions will vary from that of an open stream to that of a 
 closed channel. The velocities are gradually affected as the ice be- 
 gins to form, until the entire surface is affected where the stream 
 becomes entirely covered. As the ice sheet thickens more of the 
 cross section of the stream is occupied by the ice sheet, and greater 
 friction results. Fig. 117 shows two vertical velocity curves, one for 
 an open and one for an ice-covered channel. These may be regarded 
 
2l6 
 
 Stream Flow. 
 
 
 10 
 20 
 30 
 
 60 
 Id 
 O 
 
 a 70 
 u 
 
 a 
 
 80 
 90 
 
 MEAN OF 4 CURVES -OPEN SECTION. 
 
 --- MEAN OF 1 3 CURVES - UNDER ICE. 
 
 40 50 
 
 120 130 
 
 140- 
 
 60 70 80 90 100 NO 
 
 PER CENT OF MEAN VELOCITY 
 
 Fig. 117. Comparative Mean Vertical Velocity Curves for Open and Ice 
 
 Covered Section. 
 
 as typical of open and closed conditions between which the actual 
 velocities wall vary with the conditions of the ice. 
 
 The change in the distribution of velocities results in an entire 
 change in the relation between gauge height and flow so that the 
 rating curve for an open section will not apply to the river under 
 ice conditions. 
 
 If therefore the stream flow is to be accurately determined during 
 such condition, it becomes necessary to establish the new relation 
 between gauge height and flow. 
 
 As before noted, such relations vary somewhat with the condi- 
 tions of the ice sheet but may be regarded as fairly constant when! 
 the section is fairly clear and deep. The relations between the rat- 
 ing curves for this open channel and for ice conditions as deter- 
 mined by the United States Geological Survey for the Wallkill 
 River at Neupaltz, N. Y. is shown in Fig. 118. 
 
 Table XXI, from an article by F. A. Tillinghast (sec Engineer- 
 ing News, May nth, 1905), shows the relations of maximum and 
 
Effects of Ice-Covering on Velocities. 
 
 217 
 
 o> 14 
 
 1 
 
 iu 
 
 1 12 
 
 Ul 
 
 o 
 
 2 
 
 10 
 8 
 
 
 EOQO 
 
 4000 6000 8000 
 
 DISCKAB3E IN CUBIC FEET PER SECOND. 
 
 10000 
 
 Fig. 118. Rating Curve for Wallkill River at Newpaltz, N. Y. 
 
 mean velocities in the verticals. It should! be noted that there are 
 two points of mean velocity under ice conditions that average n 
 per cent, and 71 per cent, of the total depth below the Surface. The 
 point of maximum velocity is at an average depth of 36 per cent, of 
 the total depth of the stream and averages IIQ per cent, of the mean 
 velocity; 
 
 TABLE XXI. 
 Position o/ Mean and Maximum Velocities in a Vertical Plane Under Ice. 
 
 
 
 
 
 
 Coeffi- 
 
 
 
 
 
 Depth 
 
 
 Stream and Place 
 
 Depth from 
 Under Sur- 
 face of Ice 
 Feet 
 
 Num- 
 ber of 
 curves 
 
 Depth of 
 Mean 
 Velocity 
 
 of 
 Maxi- 
 mum 
 Veloc- 
 
 to re- 
 duce 
 Max. 
 
 tn 
 
 
 
 
 
 ity 
 
 Mean 
 
 Wallkill at Neupaltz, N. Y. . . . (a) 
 Wallkill at Neupaltz, N. Y. . . . (b) 
 Esopus at Kingston, N. Y (a) 
 Esopus at Kingston, N. Y (b) 
 Rondout at Rosendale, N. Y. . . (a) 
 Rondout at Rosendale, N. Y. . . (b) 
 Connecticut at Urford, N. H. . .(c) 
 
 4 to 12 
 4 to 19 
 2.3 to 7.4 
 5 to 8 
 4 to 8 
 5to7 
 2.5 to7.7 
 
 20 
 26 
 16 
 8 
 5 
 8 
 18 
 
 0.12 
 0.13 
 0.08 
 0.11 
 0.08 
 0.13 
 0.11 
 0.11 
 
 0.71 
 0.74 
 0.68 
 0.73 
 0.68 
 0.21 
 0.69 
 0.71 
 
 0.38 
 0.38 
 0.36 
 0.37 
 0.35 
 0.35 
 0.35 
 0.36 
 
 0.85 
 0.86 
 0.80 
 0.85 
 0.82 
 0.86 
 0.85 
 0.84 
 
 
 
 
 Notes: a. By F. H. Tillinghast. 
 
 b. By W. W. Schlecht. 
 
 c. By C. A. Holden. 
 
 13 
 
CHAPTER XI. 
 
 THE MEASUREMENT OF STREAM FLOW. 
 
 112. Necessity for Stream Flow Measurements. In order to 
 ascertain the value of a stream for water power purposes, it is neces- 
 sary to determine the amount and variations in its continuous flow 
 either by comparison with the flow of other streams or by the direct 
 observation of the flow of the stream itself. As has already been 
 shown, the latter method is by far the most satisfactory as the de- 
 termination of the actual flow of the stream eliminates all errors of 
 comparison, and the necessity for any allowances or modifications 
 on account of differences in geological, geographical, topographical 
 or meteorological conditions on the drainage area. 
 
 The Hydrographic Division of the United States Geological Sur- 
 vey has undertaken the gauging of a large number of streams in the 
 United States and has established numerous gauging stations at 
 which observations have been made for a number of years. This 
 data, references to which are given in the list of literature appended 
 to Chapter IX, is of great value for comparative purposes. It is 
 seldom, however, that, when a stream is to be investigated for water 
 power purposes, flow data, at the particular point under consider- 
 ation, is available. One of the first duties of the engineer, there- 
 fore, usually consists in making measurements of the stream flow 
 and establishing stations at which the daily flow can be observed 
 and recorded. 
 
 The methods in use by the United States Geological Survey are 
 the result of much study and investigation and probably represent 
 the most practical methods for making such observations with a fair 
 degree of accuracy. Many of the methods and suggestions in this 
 chapter are based on the methods and conclusions of the Survey as 
 modified by the experience and practice of the writer.* 
 
 * These methods are described in detail in Water Supply and Irrigation 
 Papers No 94, entitled, "Hydrographic Manual of the United States Geologi- 
 cal Survey," and No. 95, entitled "Accuracy of Stream Measurements." See 
 also "River Discharge" by J. C. Hoyt and N. C. Grover, John Wiley and 
 Sons, 1907. 
 
Methods for the Determination of Flow. 219 
 
 113. Methods for the Estimate or Determination of Flow in 
 Open Channels. There are three general methods of estimating or 
 determining the flow of water in streams with open channels. 
 
 First By the measurement of the cross section and slope and the 
 calculation of flow by Chezy's formula, together with Kutter's or 
 Bazin's formulas for estimating the values o<f the coefficient. 
 
 Second By means of weirs or dams of such form that the coeffi- 
 cient of discharge is known, and 
 
 Third By the measurement of the cross section area and the 
 velocity of current passing through the same. 
 
 The method which should be selected for any particular location 
 depends o<n the physical conditions of the problem, the degree of 
 accuracy required, the expense which may be permissible and the 
 length of time during which the record is to be continued. 
 
 114. Estimates from Cross-section and Slope. Chezy's formula, 
 
 together with the formulas of Kutter and Bazin, for the determin- 
 ation of the flow of streams, has already been discussed in Chapters 
 III and X. Much information is now available in regard to the 
 value of the coefficient c, but this value varies greatly in different 
 streams, in accordance with the conditions of the beds, and in the 
 same stream under various conditions of flow. The results obtained 
 from the application of these formulas are therefore necessarily very 
 approximate. The method, however, is of considerable value in es- 
 timating the flood discharge of streams and in obtaining an approxi- 
 mate knowledge of flow under other conditions where other methods 
 are not available or are difficult of application. 
 
 In using this method two or more cross sections of the stream 
 should be measured on reaches of the river where the cross section 
 and other conditions are fairly uniform and can be readily deter- 
 mined and at a time when the flow is steady. It is also important 
 that the stream in which the flow is to be estimated shall be compar- 
 able in cross-section, depth, and other conditions, on which the 
 value of the coefficient c depends, with other streams on which the 
 value of c has been determined. 
 
 115. Weir Measurement. Where dams are so located that they 
 can be utilized for weir measurements, and are so constructed that 
 such measurements are reasonably accurate, or where suitable weirs 
 can be constructed from which such measurements can be made, 
 such dams and weirs afford the best practicable method for measure- 
 
22O The Measurement of Stream Flow. 
 
 ments of the flow of a stream. In order to assure accurate results in 
 weir measurements, the following conditions must be fulfilled : 
 
 First The dam or weir must have sufficient height so that back 
 water will not interfere with the free fall over the same ; otherwise 
 the dam will be available for purposes of measurement only during 
 stages when no such interference exists. 
 
 Second The dam or weir body must be so constructed that no 
 leak of appreciable size will occur during the time when it is utilized 
 for measuring purposes. 
 
 Third The abutments of the dam or sides of the weir must be so 
 constructed as to confine the flow over the dam at all stages : other- 
 wise the weir will be useless for measurements during flood condi- 
 tions. 
 
 Fourth the crest of the weir must be level and must be kept free 
 from obstructions caused by floating logs or ice. 
 
 Fifth The crest of the dam or weir must be of a type for which 
 coefficients for use in the ordinary weir formula have been deter- 
 mined. (See Chapter III.) 
 
 Sixth If the dam has an adjustable crest, great care must be used 
 to prevent leakage along such crest and to keep a complete and 
 detailed record of the condition of the crest during the time of the 
 observations. 
 
 Seventh If water is diverted around the dam, which is usually 
 the case when a dam is built for power purposes or for navigation, 
 the diverted water must be measured or estimated and added to the 
 amount passing over the dam. Such diverted water can sometimes 
 be measured by a weir or current meter. When such water is used 
 in water wheels, an accurate record of the gate opening of the 
 wheels can be kept, from which the amount of water used in the 
 wheels can be estimated if the wheel's discharge has been calibrated 
 or if the wheel is of some well known type.* The conditions for the 
 accurate determination of weir discharge should be such as not to 
 involve the use of low heads of less than 6" over broad crested dams. 
 
 Measurements by means of a weir or dam have the general advan- 
 tage of continuity of record during the periods of ice and flood and 
 the disadvantage of uncertainty of the coefficient to be used in the 
 weir formula, of complication by the diversion of water around the 
 dam, and the interference of flow by the occasional lodgement of 
 material, or of injury to the crest. 
 
 * See Water Supply and Irrigation Paper No. 180, Turbine Water Wheel 
 Tests and Power Tables by R. E. Horton. 
 
The Use of the Current Meter. 
 
 221 
 
 116. Measurement of Flow by the Determination of Velocity. 
 
 The discharge of a stream, or the quantity of water flowing past a 
 certain section of the stream in a given time, is the product of two 
 factors : first, the area of the cross section ; and second, the mean 
 velocity of flow through said section. 
 
 If the flow in the cross-section of the stream were uniform the 
 measurement erf the flow would be a simple matter. A surface float, 
 timed between given stations, or a current meter placed at any 
 point in the cross-section, would then indicate the average velocity. 
 Such conditions, however, never obtain. It is therefore necessary 
 to ascertain the mean velocity of flow in the section which is a 
 much more difficult matter. 
 
 Two methods of measuring the velocity of a stream are in use: 
 first, by the use of a current meter, and second, by the use of 
 floats. Each of these methods has advantages peculiar to itself, 
 which must be knotwn and appreciated in order that intelligent 
 measurements may be made. 
 
 117. The Use of the Current Meter. The current meter (Fig. 
 119) is an instrument designed to revolve freely with the current so 
 that by determining the number of its revolutions the velocity of 
 
 Fig. 119. Price Electric Current Meter with Buzzer. 
 
222 
 
 The Measurement of Stream Flow, 
 
 Section A- A 
 
 Fig. 120. Cross Section of small Price Electric Current Meter, Showing 
 
 details.* 
 
 the current will be known. A well made current meter carefully 
 maintained and frequently rated is reasonably accurate when prop- 
 erly used under conditions to which it can be applied. As the fric- 
 tion of operation is rarely constant, the relation of current velocities 
 to number of revolutions is not always strictly proportional and it is 
 necessary to determine the relation between the revolutions of the 
 meter and the corresponding velocity of water. This is accomplished 
 by rating the meter, which is usually done by passing it through 
 still water at known velocities and noting the results. It is assumed 
 that the same relation will exist between the revolutions of the 
 meter and its longitudinal velocity through still water and between 
 its revolution and the velocity of flowing water' when this meter is 
 held in a similar position in a stream. The meter should be rated 
 under conditions as nearly similar as possible to those under which 
 it was, or is to be, used. The meter when being rated is usually at- 
 
 *Prom W. S. & I. Paper No. 94 Hydrographic Manual, by E. C. Murphy. 
 J. C. Hoyt and G. B. Hollister. 
 
Current Meter Observations. 
 
 223 
 
 1LLL 
 
 
 Fig. 121. Current Meter Rating Station at Denver, Col.* 
 
 tached to some movable device (see Fig. 121) such as a carriage or 
 boat which is propelled by hand or machinery at a known rate over 
 a fixed distance. Observations of the revolutions of the meter at 
 various rates of speed are noted and the relation is then established 
 between the velocity of the meter and the revolutions of the meter 
 wheel. This data may be platted upon cross-section paper or so 
 arranged in tabular form that the corresponding velocity may be 
 immediately ascertained when the revolutions of the meter are 
 known. (See Fig. 122.) Experiments have shown that with veloci- 
 ties less than one-half of a foot per second little or no dependence 
 can be placed upon the meter observations and that for velocities 
 below one foot per second, the meter usually under registers. Where 
 such low velocities obtain, float measurements are believed to be 
 more accurate. 
 
 118. Current Meter Observations and Computation. On account 
 of the great variation in velocity at different points in the cross-sec- 
 
 *From Hydrographic Manual. 
 
22 4 
 
 The Measurement of Stream Flow. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 7 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x 
 
 * 
 
 
 
 
 
 
 
 Q 2.8 
 
 Sac 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 
 
 
 
 
 
 
 o 
 
 UJ 9 A 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 <n 2 - 4 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 2 - 2 
 
 ^90 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x 
 
 
 
 
 
 
 
 
 
 
 
 
 Q.Z.O 
 
 
 
 
 
 
 
 
 
 
 
 
 X" 
 
 x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <n 
 
 Z 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 = ,.. 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 _i 
 
 1 9 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 > l.2 
 10 
 
 
 
 
 
 
 
 t 
 
 x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 1 
 
 x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 4.0 
 
 X 
 
 3 
 
 1 
 
 
 
 
 - 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 3 
 
 1 
 
 
 i, 
 
 ! 
 
 VELOCITY. IN FEET PER SECOND 
 Fig. 122. Current Meter Rating Curve. 
 
 tion, the flow through any unit of area may vary more or less from 
 the flow through other similar areas. On this account it is desir- 
 able, in order to systematically survey the velocities in a cross-sec- 
 tion, as well as for ease in calculation, to divide the cross-section area 
 into parts, both horizontally and vertically, and determine the actual 
 velocity of each of said parts. As a basis for the work, the cross- 
 section of the stream should first be obtained by sounding. The 
 vertical sections, chosen for the purpose of water observation, are 
 usually five feet or more apart but the horizontal divisions are 
 usually somewhat less as the variations in the vertical velocities are 
 usually much greater than in horizontal velocities. The size of both 
 horizontal and vertical division depends on the irregularity of the 
 distribution of velocity in the cross-section as well as on the ac- 
 curacy required in the determination af flow. The greater the care 
 used in the determination of the velocities in the unit areas and the 
 greater the number of such sub-divisions of the cross-section, the 
 more accurate will be the work. 
 
UNIVERSITY 
 
 CF 
 
 Current Meter Computations. 225 
 
 The meter readings may be made in one of four ways : 
 
 First By determining the velocity at frequent, definite intervals 
 of depth and then ascertaining the point and amount of average velo- 
 city in each vertical section. 
 
 Second By what is known as the integration method, which 
 consists in lowering and raising the meter with uniform motion 
 from the surface to the bottom of the vertical section and noting the 
 average velocity determined by this method. 
 
 Third By making a point measurement at the depth correspond- 
 ing to the thread of mean velocity as determined in the first method. 
 
 Fourth By determining the velocity at some other point of 
 observation and deducting the mean velocity from the known rela- 
 tion of the point measured to the point of mean velocity. The last 
 two methods can be safely used where the vertical velocity curve 
 lias been determined with sufficient accuracy, and are fairly approxi- 
 mate at other sections where the conditions are not of an unusual 
 nature. 
 
 Distance from inftial point 
 ,/\5|0 I 610 
 
 Fig. 123. Cross-section of Saline River at Guaging Station near Salina, 
 
 Kans. 
 
 "Fig. 123 shows the cross section of the Saline River near Salina, 
 Kan., on September 3<Dth, 1903, while the discharge measurements 
 recorded in Table XXII were being made. The soundings were 
 taken at each 5 feet of width from the initial point and the velocity 
 was observed at 0.6 depths below the surface in each of these verti- 
 cals. 
 
 The discharge through each 5-foot strip might be computed sep- 
 arately, but the computations are shortened by finding the discharge 
 through each double strip at a time." 
 
 * From Water Supply and Irrigation Paper No. 94, Hydrographic Manual 
 by E. C. Murphy, J. C. Hoyt and G. B. Hollister. See page 46 et seq. 
 
226 The Measurement of Stream Flow. 
 
 Let d' m = mean depth for double strip; 
 V' m = mean velocity for double strip; 
 a, b, c are three consecutive depths, L feet apart; 
 V a V b V c are observed velocities in the verticals a, b, c 
 L = the width of a single strip; 
 Q' = the discharge through double strip. 
 
 "The mean depth and the mean velocity for the double strip of 
 width 10 feet are found from the formula : 
 
 C) 
 
 The discharge through the double strip is . 
 (3) Q , =d . mV . m L 
 
 Formulas (i) and (2) are based on the assumption that the 
 stream bed is a series of parabolic arcs, also that the horizontal ve- 
 locity curves are parabolic arcs, both of which assumptions are 
 approximately true at good current-meter stations. 
 
 In computing the discharge and the mean depth through a 
 single strip near the stream bank or a pier the mean velocity is 
 found from the formulas : 
 
 (4) V m = ^ + 7 a 
 
 (5) d = 
 
 where either Vo or V a and a' or a may be "0". 
 
 Velocity is computed to two places of decimals, mean depth, 
 area, and discharge to one place of decimals for streams of ordinary 
 size ; for small streams with hard, smooth botton, where depth can 
 be measured to hundredths foot, the mean depth and area should be 
 computed to two places of decimals and the discharge to one place." 
 
 These observations can be taken in shallow streams by wading 
 or from a cable car (see Fig. 124), boat or bridge as the circum- 
 stances and conditions permit. A rope or cable, marked into suit- 
 able divisions and stretched across the stream, offers the best means 
 of locating the horizontal points at which observations in the verti- 
 cal planes are to be made. 
 
 119. Float Measurements. Where a single or only an occasional 
 measurement of the flow of a stream is to be made, the use of floats 
 
Current Meter Measurements. 
 
 227 
 
 Ka 
 
 con 
 
 Salina, State 
 
 2. Discharge, 1 
 
 R 
 
 !? 
 e 
 
 d 
 
 H i" 
 
 x ^ 
 
 X ^ 
 
 w -I 
 
 ^ I 
 $ 
 
 Ga 
 
 ging made September 30, 1003, by E. 
 
 e height: Beginning 7. 96 ft., ending 7. 96 feet. 
 
 Remarks. (On condition of chan- 
 nel, wind, equipment, gage, boat, 
 cable, methods, accuracy. Use 
 cross-section pages in back of 
 book for sketches.) 
 
 T5 
 
 i 
 
 d 
 
 0> !>. 
 
 |l| 
 
 &b 
 
 ^^ Q O 
 
 3 O 
 
 Computed by E. C. Murphy. Checked by E. C. Murphy. 
 
 if- 1| 
 
 
 
 ^ 
 
 % 
 
 t^ ri co o 
 
 tO CO 
 
 1 
 
 M 
 
 o o o 
 
 OrH 
 
 t^ 
 
 3 i 
 
 !M to OD C5 
 
 1 
 
 Computa- 
 tions of 
 
 qidap 
 
 o oq co 
 
 <M lO '-O M 
 
 
 
 O Tf ?O 
 
 10 H^ CO rH 
 
 
 
 W 
 
 T-H O O 
 rH T-H 
 
 <O ^^ i^o 1 s * 
 
 rH rH 
 
 
 
 Velocity computatoins. 
 
 puooas aad 
 X^pojaA 
 iiB9j\r 
 
 !>j r^- ci 
 
 rH CO J^O 
 
 
 
 O 00 
 
 rH O OO 
 
 
 puooas jad 
 
 o ,2~.88 
 
 
 
 O O O rH O O i I i I O O O O 
 
 
 puooas 
 jad suorj 
 
 
 
 
 
 
 -Aai jo iaq 
 -ranu [raioj, 
 
 ^M. : a-o 
 
 
 
 Obervations. 
 
 SUO1 1 ) 
 
 -n{OAa[ 
 
 CC 1>- 'N OO O ^ CO IO CC O O 
 rH OS rH <M (M <M r-l 
 
 rHJxJrHrHl^^rH^ 
 
 
 
 spuooas 
 ui aiuij, 
 
 LCiClO>OOiOiOCiOOO 
 
 
 
 jo qidaa 
 
 t-t-OCrHlCOOCOt-t-^ 
 
 
 
 O^CO^COCOCO^^r.0 
 
 
 ^a 
 
 Ci rH LO CO CO Ci O O ^ 1C CC CO O 
 
 
 rH^*iO00^^00 
 
 ."Sill 
 
 O O^COiOOiOOiOO>OOC<l 
 
 
228 
 
 The Measurement of Stream Flow. 
 
 is believed to be preferable, as under such conditions the calibration 
 of the current meter and the exercise of necessary skill in its use are 
 not apt to receive proper attention. Under such circumstances, 
 therefore, float measurements are believed to be more accurate. 
 
 In the use of floats the writer usually selects round soft wood one 
 to two inches in diameter and in various lengths, varying by about 
 6". These are weighted at the lower end, usually by attaching pieces 
 of lead pipe so that they will float with only about one to three 
 inches of the rod exposed. To the exposed end is usually attached 
 small red or white streamers so that they may be readily seen and 
 yet not be seriously affected by wind. 
 
 A point for the gauging is selected where the stream is fairly 
 straight and uniform in section, and ropes, wires, or cables are 
 
 Fig. 124. Cable Station, Car Guage, etc. 
 
 stretched tightly across the stream, parallel to each other and 25, 50 
 or 100 feet apart, as the location and velocity of the stream seem 
 to demand. The ropes or wires should be tagged at intervals of 5, 
 10 or 25 feet, as the conditions seem to warrant, beginning at zero on 
 the straight bank. 
 
 In starting the work a float is selected that will reach as near the 
 bottom as possible without touching and should be about .9 depth. 
 The float is started 5 to 10 feet above the upper line and so placed 
 that it will pass as nearly as possible under one of the tags. The 
 point at which it actually passes under the line is noted and re- 
 corded, also the point and time at which it passes the lower line. If 
 the float should touch the bottom or a snag in its passage, the next 
 shorter length should be used until the float passes both lines freely. 
 Floats should be run at frequent intervals across the stream usually 
 at each of the tagged stations. 
 
The Application of Stream Gaugings. 229 
 
 Extensive experiments were made by Francis at Lowell, Mass., 
 in 1852 to determine the accuracy of rod float measurements.* 
 
 He found that discharge measurements based on the determina- 
 tion of velocities by floats were nearly always large as compared 
 with measurements by a standard weir. This was due to the fact 
 that the rod, on account of not reaching the bottom, was not 
 affected by the low velocity near the stream bed and hence indi- 
 cated too great a velocity. He found that the effect could be cor- 
 rected by multiplying the discharge as obtained by the floats by a 
 coefficient as follows : 
 
 (6) Q = CQ A in which 
 
 Q = actual discharge 
 
 Q! = discharge as determined by floats. 
 
 C = coefficient = 10.116 (l/lT 0.1) and 
 
 .. distance of bottom of float from bottom of stream 
 
 D = ratio j : j 
 
 depth of stream. 
 
 It will be observed that this coefficient C is always less than 
 unity except where D is less than o.oi which condition could not 
 be possible in any natural stream. 
 
 The Francis experiments were made in a channel of rectangular 
 cross section and floats of uniform length were used. In a natural 
 stream the depth will vary at different points in the cross section 
 and floats of different lengths must be used. In such cases D will 
 vary widely for the various floats used and to apply the correction, 
 the velocity as determined by each float should be reduced by its 
 particular consatnt, C. 
 
 Experiments made at the Cornell Hydraulic Laboratory in 1900 
 by Kuichling, Williams, Murphy and Boright confirmed Francis' 
 conclusion that rod float measurements are too large, only two out 
 of thirty being smaller than measurements made by a standard 
 weir. No attempt was made, however, to verify Francis' formula 
 for the correction of such observations.* 
 
 In calculating the discharge from these measurements the ave- 
 rage cross-section, in cubic feet, of each division is calculated and 
 multiplied by the average velocity for the same in feet per second 
 and the product will represent the discharge in cubic feet per second 
 of the section represented by that float and the sum of the sections 
 of all the floats will give the total discharge of the stream. 
 
 * See "Lowell Hydraulic Experiments" by James B. Francis, pp. 146-208. 
 
 * See W. S. & I. Paper No. 95, Accuracy of Stream Measurements, p. 54. 
 
230 
 
 The Measurement of Stream Flow. 
 
 10 20 30 40 50 60 70 80 90 100 110 
 
 Fig. 125. Graphic Determination of Stream Flow From Measurements. 
 
The Application! of Stream Gaugings. 231 
 
 It is frequently desirable to calculate the discharge graphically, 
 which may be done as shown by Fig. 125. This is done by plotting 
 the two sections at the tag lines over each other and drawing in an 
 average section between them. It is frequently desirable to draw 
 in the floats in their true length and average position so that it may 
 be seen at once how well the section was covered by the floats. 
 
 Under each float is laid off the velocity as determined by the 
 same, to a selected scale, and a mean velocity curve is drawn 
 through these points. By multiplying the ordinate of the velocity 
 curve by the ordinates! of the mean section, a quantity is obtained 
 on the discharge curve which, when fully constructed, gives a dis- 
 charge polygon, the area of which represents at the correct scale 
 the discharge in cubic feet per second of the stream. 
 
 1 20. The Application of Stream Gaugings. A single measure- 
 ment of stream flow is of comparatively little value as a basis for es- 
 timating the continuous character of the flow of the stream, as will 
 be seen by examination of any of the hydrographs previously shown. 
 The flow of a stream, while it may appear to the casual observer uni- 
 form, is actually subject to many and violent fluctuations and the 
 flow may vary several hundred per cent, from minimum to maxi- 
 mum within a few days. 
 
 It has already been pointed out that in order to study the flow of a 
 stream intelligently it is necessary to know the variations in flow 
 that take place from day to day for a long term of years during 
 which the effect of the extreme of all of the factors controlling 
 stream flow may have made themselves manifest. 
 
 The actual measurement of the flow of a stream by current meter 
 or floats is usually accomplished with considerable difficulty, and it 
 would be practically impossible to repeat such measurements daily 
 for the length of time for which records are desired. It has 
 already been pointed out that under many conditions it is possible 
 to establish a discharge or rating curve which will show the relation 
 of the height of the water surface to the flow through orifices over 
 weirs or through channels of various forms. In the establishment of 
 such relation it is assumed that the raising of the water surface to a 
 given height is always accompanied by the same flow of water 
 through the section. In order to assure accuracy in the observa- 
 tions based on such a rating curve, sections must be selected where 
 the conditions assumed are correct. Such stations should be se- 
 lected, where possible, on a fairly long uniform reach of the stream 
 
2 3 2 
 
 The Measurement of Stream Flow. 
 
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 10.000 20,000 30,000 40,000 50.000 60.000 70,000 80.000 90.000 100.000 110 
 Discharge in second-feet 
 
 Fig, 126, Discharge, Velocity and Area Curved for the Potomac River at Poin 
 
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 MEASUREMENTS IN /9O^ NO. 1 
 - 1903 NO. 2 TO 7 
 
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Literature. 233 
 
 and beyond the influences of the back water from large rivers or 
 dams. 
 
 After gaugings of the stream have been made under a considerable 
 range of conditions and a rating curve is established therefrom, it is 
 not necessary thereafter to measure the daily flow but only to note 
 daily the gauge height. It has been determined by many observa- 
 tions that under constant conditions a fixed relationship exists be- 
 tween gauge height and the discharge of a stream, subj-ect to the 
 errors due to variable flow as described in Chapter X. If the section 
 and other conditions of the stream flow remain unchanged, the rat- 
 ing curve will remain constant and hence the daily gauge height 
 can be quickly read and recorded and will give at once, by reference 
 to the rating curve or table, the quantity of water flowing in the 
 stream at all times. 
 
 From the soundings and levels made to determine the cross sec- 
 tion, an area curve can be constructed showing the variation of 
 area with gauge height. The float or current meter observations 
 furnish the necessary data for the construction of a curve of mean 
 velocities. The product of the area and mean velocity, as shown 
 by these two curves, for any given gauge height, must equal the 
 discharge and must equal the reading of the discharge curve for 
 the same gauge height. The construction of these curves, and a 
 consideration of their properties, furnishes a check on the construc- 
 tion of the discharge curve and aids materially in correcting any 
 apparent irregularities therein.* 
 
 Fig. 126 shows the discharge, mean velocity and area curves for 
 the Potomac River at Point of Rocks, Aid. 
 
 LITERATURE. 
 
 STREAM GAUGING. 
 
 1. Baumgarten, M. Pulsations of Velocity in River Current. Annales des 
 
 Fonts et Chaussees. 1847. 
 
 2. A Study of the Law of Flows in Rivers, Oscillations of Velocity, Obser- 
 
 vations of Vertical and Transverse Velocity Curves. Annales 
 des Fonts et Chaussees. 1847. 
 
 3. Croes, Jas. R. Flow of the West Branch of the Croton River, N. Y. 
 
 Trans. Am. Soc. C. E. vol 3, pp. 76-90. 1874. 
 
 4. Ellis, Theo. G. Flow of Water in Open Channels. Trans. Am. Soc. C. E. 
 
 vol. 6, pp. 250-258. 1877. 
 
 *See "River Discharge," Hoyt and Grover. 
 14 
 
234 The Measurement of Stream Flow. 
 
 5. Wood, de Volsen. Flow of Water in Rivers. Trans. Am. Soc. C. E. vol. 
 
 8, p. 173. 1879. 
 
 6. McMath, R. E. River Hydraulics. Trans. Am. Soc. C. E. vol. 9, pp. 378- 
 
 390. 1880. 
 
 7. McMath, R. E. The Mean Velocity of Streams Flowing in Natural Chan- 
 
 nels. Trans. Am. Soc. C. E. vol. 11, pp. 186-211. 1882. 
 
 8. Current Meter Measurements on the Rhine. Allgemeine Bauzeitung, Vol. 
 
 47, pp. 53-80. 1882. 
 
 9. Unwin, W. C. Current Meter Observations in the Thames. Proc. Inst. 
 
 C. E. Vol. 71, p. 338. 1883. 
 
 10. Stearns, F. P. Why the Maximum Velocity is Below the Surface. Trans. 
 
 Am. Soc. C. E. Vol 12, p. 331. 1883. 
 
 11. Cunningham, Allan. Recent Hydraulic Experiments. Proc. Inst. C. E. 
 
 Vol. 71, p. 1. 1883. 
 
 12. Fteley, A. and Stearns, E. P. Description of Some Experiments on the 
 
 Flow of Water. Trans. Am. Soc. C. E. Vol. 12, pp. 1-118. 1883. 
 
 13. Measurement of Water. Bui. G, Montana Agric. Expt. Sta. 1885. 
 
 14. Isakoski, R. Discharge of Rivers from the Drainage Areas. Zeitschr. 
 
 d Oesterr. Ing. u Arch. Ver. 1886, pp. 69-98. 
 
 15. Seddon, J. A. Consideration of the Relation of Bed to the Variables. 
 
 Jour. Assn. Eng. Soc. Vol 5, p . 127. 1886. 
 
 16. The Determination of Normal Cross-Sections of the Elbe. Taubert. Zeit- 
 
 schrift fur Bauwesen, pp. 551-562. 1886. 
 
 17. Green, J. S. Fourth Biennial Report State Eng. of Colo. 1889. 
 
 18. Bazin, M. Recent Experiments on the Flow of Waters over Weirs. An- 
 
 nales des Fonts et Chaussees, Oct. 1888; see also Proc. Eng. Club 
 of Phila. Vol 7 p 260. 1890. 
 
 19. Flynn, P. J. Flow of Water in Irrigation Canals. San Francisco. Pub- 
 
 lished by the Author. 1892. 
 
 20. Ganguillet, E. and Kutter,' W. R. A General Formula for the Uniform 
 
 Flow of Water in Rivers and Other Channels. Trans, by Hering 
 and Trautwine. New York. Wiley & Sons. 1893. 
 
 21. Foss, W. E. New Formula for Calculating the Flow of Water in Pipes and 
 
 Channels. Jour. Asso. Eng. Soc. Vol. 13, p. 295. 1894. 
 
 22. Flynn and Dyer. The Cippoletti Trapezoidal Weir. Trans. Am. Soc. C. E. 
 
 Vol. 32, p. 9, 1894. 
 
 23. Carpenter, L. G. Measurement and Division of Water. Bui. 27, Colo. 
 
 Agric. Expt. Sta., Fort Collins, Colo. 1894. 
 
 24. Newell, F. H. Discharge Measurements of Streams. Proc. Eng. Club, 
 
 Phila. Vol. 12, No. 2, p. 125. 1895. 
 
 25. Humphreys, D. C. Discharge Measurements. Jour. Assn. Eng. Socs. Vol. 
 
 15, No. 5, p. 187. 1895. 
 
 26. Starling, Wm. The Discharge of the Mississippi. Trans. Am. Soc. C. E. 
 
 Nov. 1895. 
 
 27. Grunsky, C. E. Method for Approximate Gauging of Rivers. Eng. Rec. 
 
 March 7, 1896 
 
 28. Keating, W. J. Coefficients in Hydraulic Formulas. Jour. Wes. Soc. Eng. 
 
 Vol. 1, p. 190. 1896. 
 
 29. Johnson, F. T. and Cooley, E. L. Experimental Data for Flow over Broad 
 
 Crest Dam. Jour. Wes. Soc. Eng. Vol. 1, p. 30. 1896. 
 
Literature. 
 
 235 
 
 30. A Study of Gauging Statistics. Annales des Fonts et Chaussees. Part III. 
 
 1897. 
 
 31. Jasmund, R. Variation in Velocity in Cross- Section of a Stream, Es- 
 
 pecially with Obstructions on the Surface and Ice. Zeitschr. fur 
 Bauwesen. 1897, pp. 303, 465, 585. Centrallb. der Bauverwaltung 
 p. 101. 
 
 32. Johnson, Clarence T. Stream Gaugings. Proc. Purdue Soc. Civ. Eng. 
 
 1897. 
 
 33. Skinner, John W. Description of the Method of Gauging the Discharge 
 
 Through the Outlet of Hemlock Lake, N. Y. Trans. Assn. Civ. 
 Engs. of Cornell University. 1898. 
 
 34. Bindemann, H. Difference Between Average Flow and Flow at Center of 
 
 Stream. Centralblatt der Bauverwaltung, p. 638. 1898. 
 
 35. Lippincott, J. B. Low Water Measurements in the State of California dur- 
 
 ing the Summer of 1898. Eng. News. Jan. 12, 1899. 
 
 36. Average Velocity of Water in Natural Streams. Zeitschrift. fur Gewas- 
 
 ser, pp. 20-36. 1899. 
 
 37. Newell, F. H. Stream Measuring in the United States. Sci. Am. Sup. 
 
 Nov. 11, 1899. 
 
 38. Fuchs, Paul. The Measurement of the Velocity of Flow of Streams. Ge- 
 
 sundheits Ing. Nov. 30, 1899. 
 
 39. Stewart, Clinton B. Discharge Measurements of the Niagara River at 
 
 Buffalo, N. Y. Jour. W. Soc. Engs. Dec. 1899. 
 
 40. Investigation of Relationship of Average Flow of a Stream with the Flow 
 
 at the Center. Zeitschrift fur Gewasser, p. 212. 1900. 
 
 41. Manner of Movement of water in Streams. Zeitschr. fur Bauwesen. Nos. 
 
 VII to IX. Centralblatt der Bauverwaltung, p. 611. 1900. 
 
 42. Methods of Stream Measurement. Water Supply and Irrigation Paper 
 
 No. 56. 1901. 
 
 43. Murphy, E. C. Accuracy of Stream Measurement. Water Supply and Irri- 
 
 gation Paper, No. 64. 1901. 
 
 44. Turneaure and Russell. Public Water Supplies. Chap. 12. New York. 
 
 Wiley & Sons. 1901. 
 
 45. Tutton, C. H. The Laws of River Flow. Jour. Assn. Eng. Socs. Jan. 
 
 ary, 1902. 
 
 46. The Natural Normal Sections of Streams. Zeitschr. d Oesterr. Ing. u Arch 
 
 Ver. Feb. 21, 1902. 
 
 47. Relation of Surface to Mean Velocities of Flow. An Investigation Con- 
 
 ducted by J. B. Lippincott and others in the West. Eng. News. 
 Vol. 1, p. 424. 1902. 
 
 48. Annual Report Chief Eng. U. S. A. 1900. Appendix I. I. I. Survey of N. 
 
 and N. W. Lakes. Same 1902. Appendix E. E. E. and 1903 Ap- 
 pendix F. F. F. 
 
 49. Pressey, H. A. Methods of Measuring Velocity in River Channels. Sci. Am. 
 
 Sup. Sept. 5, 1903. 
 
 50. Merriman, Mansfield. Treatise on Hydraulics. New York. Wiley & Sons. 
 
 1903. 
 
 51. Bellasis, E. D. Hydraulics with Tables. New York. D. Van Nostrand 
 
 Company. 1903. 
 
236 The Measurement of Stream Flow. 
 
 52. Murphy, E. C., Hoyt, J. C. and Hollister, G. B. Hydrographic Manual of 
 
 the U. S. G. S. Water Supply & Irrigation Paper No. 94. 1904. 
 
 53. Hoyt, John C. Methods of Measuring the Flow of Streams. Eng. News. 
 
 Jan. 14, 1904. 
 
 54. Miller, C. H., Pratt, R. W., Robinson, H. F. Methods of Determining 
 
 the Mean Velocity of Cross-Sections. Eng. News. Vol. 1, pp. 
 258-307. 1904. 
 
 55. Anderson, R. H. Some Flood Discharges and Values of "n" in Kutter's 
 
 Formula. Eng. News. Aug. 4, 1904. 
 
 56. Hoyt, John C. Methods of Estimating Stream Flow. Eng. News. Aug. 4, 
 
 1904. 
 
 57. Recent Russian Studies of Flow in Rivers. Eng. News. Sept. 1, 1904. 
 
 58. Stout, O. V. P. Notes on Computation of Stream Measurements. Eng. 
 
 News. Vol. 2, pp. 521-547. 1904. 
 
 59. Mullins, J., and Span, F. N. Irrigation Manual. 1905. 
 
 60. Hermanek, Johann. The Mean Velocity in Natural and Artificial Chan- 
 
 nels. Zeitschr. d Oesterr. Ing. u Arch Ver. Apr. 21, 1905. 
 
 61. Murphy, E. C. A Method of Computing Flood Discharge and Cross-Section 
 
 Area of Streams. Eng. News. Apr. 6, 1905. 
 
 62. Barrows, H. K. Work of the Hydrographic Branch of the United States 
 
 Geol. Sur. in N. E. and a Discussion of the Methods used for Es- 
 timating Stream Flow. Jour. Assn. Eng. Socs. July, 1905. 
 
 63. Butcher, W. L. The Gaging of Streams by Chemical Means. Eng. News. 
 
 Dec. 14, 1905. 
 
 64. Hoyt, J. C. and Grover, N. C. River Discharge. New York. J. Wiley & 
 
 Sons. 1907. 
 
CHAPTER XII. 
 
 WATER WHEELS. 
 
 121. Classification of Water Wheels. Water wheels include 
 most of the important hydraulic motors that are adaptable to large 
 hydraulic developments. They may be divided into three classes, 
 viz: 
 
 First Gravity wheels. 
 
 Second Reaction wheels. 
 
 Third Impulse wheels. 
 
 In gravity wheels the energy of the water is exerted by its weight 
 acting through a distance equal to the head. 
 
 In both reaction and impulse wheels the potential energy 'due to 
 the weight of the water under the available head is first converted 
 into kinetic energy. This kinetic energy does work in the reaction 
 wheel through the reactive pressure of the issuing streams upon 
 the movable buckets from which they issue. 
 
 In the impulse wheel the nozzles or guides are stationary and 
 the energy of the issuing streams is utilized by the impulsive force 
 which they exert in impinging against movable surfaces or buckets. 
 
 Figs. 127, 128 and 129, which illustrate the various types of 
 wheels included in the above classes, are adapted, with many mod- 
 ifications from Reuleaux's "Constructor." : 
 
 122. Gravity Wheels. Fig. 127 shows the various types of grav- 
 ity water wheels or those wheels that are driven by the weight of 
 the water. At moderate velocity, these motors are practically 
 operated by gravity only, although under some conditions the im- 
 pulse due to the velocity of the entering water may have an appreci- 
 able effect. In Fig. 127, A is an undershot water wheel ; B is a 
 half-breast wheel (see also Figs. 3 and 4), and C is a high breast 
 wheel. D is an overshot wheel. In C and D the buckets should be 
 so designed as to retain the water until they reach the lowest point 
 in the revolution of the wheel. E in this Figure illustrates Dup- 
 
 * "The Constructor." F. Reuleaux trans, by H. H. Suplee, Philadelphia. 
 Pa., 1893. 
 
2 3 8 
 
 Water Wheels. 
 
 A 
 
 D 
 
 
 ii I J 
 
 Fig. 127. Diagram of Gravity Wheels. 
 
Reaction Wheels. 
 
 239 
 
 pinger's side-fed wheel. F illustrates an endless chain of buckets 
 which is essentially the same in principle as the overshot wheel. G 
 is a similar arrangement using discs running with as small a clear- 
 ance as possible in a vertical tube. When the water acts only by 
 gravity, the wheels represented by A to E, inclusive, are only prac- 
 ticable when the wheel can be made as large or larger in diameter 
 than the fall of the water. Where small diameters must be used, 
 the arrangements shown in F and G are available. Very small 
 wheels acting under high pressures may be employed by making 
 use of the so-called chamber wheels, illustrated in H, I and J. 
 
 123. Reaction Wheels. The wheels illustrated by the diagrams 
 in Fig. 128 are of the second class or reaction wheels. Diagram A 
 illustrates Barker's Mill of the form known as the Scotch turbine 
 illustrated also by Fig. 8. This form of turbine is known in Ger- 
 many as the Segner wheel. The water enters the vertical axis and 
 discharges through the curve arms. B represents a screw turbine 
 which is entirely rilled with water. C shows a Girard current tur- 
 bine which has a horizontal axis and is only partially submerged. 
 D is Cadiat's turbine with central delivery. It resembles the Four- 
 neyron turbine except that there are no guides to direct the flow 
 into the buckets. E is Thompson's turbine with circumferential 
 delivery and horizontal axis. The discharge from this turbine is 
 about the axis at both sides. 
 
 In diagrams A, B, C, D and E the column of water is received as a 
 whole and enters the wheel undivided. The remainder of the forms 
 illustrated in Fig. 128 show wheels in which the flow is divided into 
 a number of separate streams by guides interposed in the streams 
 before the water enters the wheel. Diagram F illustrates the Four- 
 neyron jturbine which acts with central delivery. The guide veins 
 arTfixed and the discharge of the water is at the circumference of 
 the wheel. The ordinary vertical form of the Fourneyron turbine is 
 illustrated in Fig. 128. Diagram G, also in Fig. 128, is a modification 
 of the Fourneyron turbine in which the water is being delivered 
 upward from below. This form is sometimes called the Nagel's tur- 
 bine. Diagram H is the Jonval or Henschel turbine. (See also 
 Fig- I35-) The- guide vanes in this turbine are above the wheel 
 which is entirely filled by the water column. Diagram J is the 
 Francis turbine in practically its original form. (See also Fig. 14.) 
 Diagram I illustrates the present American form or modification of 
 the original Francis turbine. K is the Schiele turbine, a double 
 wheel with circumferential delivery and axially directed discharge. 
 
240 
 
 Water Wheels. 
 
 I 
 
 Fig. 128. Diagrams of Reaction Wheels 
 
Impulse Wheels. 241 
 
 In forms H, I, J and K, a draft tube may be used below the wheel to 
 utilize any portion of the fall which occurs below the level of the 
 bottom of the wheel. 
 
 In all reaction turbines, the water acts simultaneously through a 
 number of passages around the entire cirpumference of the wheel. 
 In the impulse or action turbine, the water may be applied to all of 
 the buckets simultaneously or to only a portion of the circumference 
 at a time. 
 
 124. Impulse Wheels. The wheels illustrated in Fig. 129 are the 
 third class of wheels which are driven by the impulse due to the 
 weight of water acting through its velor.ity. Of these wheels, A is 
 the current wheel or common paddle wheel. The paddles are 
 straight and either radial or slightly inclined toward the current, 
 as in the illustration. (See also Figs. I and 2.) 
 
 Diagram B is Poncelet's wheel. (See also Fig. 5.) The buckets 
 run in a grooved channel and are so curved that the water drives 
 upward and then falls downward, thus giving a better contact. 
 
 Diagram C shows an externally driven tangent wheel. The buck- 
 ets are similar tx> the Poncelet wheel but with a sharper curve 
 inward. The discharge of the water is inward. D is an internally 
 driven tangent wheel similar to the preceding but with an outward 
 discharge. 
 
 E is the so-called hurdy-gurdy or tangential wheel. The water 
 is delivered through a nozzle and the wheel is practically an ex- 
 ternally driven tangent wheel of larger diameter and with a smaller 
 number of buckets. 
 
 Diagrams F, G and H illustrate three types of impulse wheels 
 with inclined delivery. (See also Figs. 6, 7, 9 and 10.) Diagram F 
 shows a crude form of vertical wheel similar in form to the Indian 
 wheel, Fig. 6. It is used on rapid mountain streams and is probably 
 the original conception from which the turbine has been developed. 
 Diagram G is the Borda turbine and consists of a series of spiral 
 buckets in a barrel-shaped vessel. Diagram H is a Danaide turbine 
 which has spiral buckets enclosed in a conical tube. This is an old 
 form of wheel formerly used in France. 
 
 125. Use of Water Wheels. Almost all water wheels in prac- 
 tical use are modifications of some of the above forms and by a 
 study of these forms a wheel may be classified and a clearer under- 
 standing obtained of the principles of its operation. Many of the 
 forms of wheels shown in Figs. 127, 128 and 129 are practically ob- 
 solete or are used onlv in minor plants or for special conditions 
 
2 4 2 
 
 Water Wheels. 
 
 B 
 
 H 
 
 
 Fig. 129. Diagrams of Impulse Wheels 
 
Use of Water Wheels. 243 
 
 that make them of only general interest in the study of water 
 power. 
 
 While gravity wheels are still occasionally used their application 
 is entirely to the smaller water power plants. In many cases the 
 turbines purchased for such installations are of cheaper make, 
 poorly designed, constructed and selected, and often improperly set 
 and, consequently, inefficient. In such cases, and where the ques- 
 tion of back water and the interference of ice is not important, the 
 
 Fig. 130. "Overshot" Water Wheel. Manufactured by Fitz Water Wheel Co. 
 
 gravity wheel may be more efficient and quite satisfactory. Well 
 designed and well constructed gravity wheels are said to give effi- 
 ciencies of 85 per cent, and above. (See Frontispiece and Fig. 
 130). With such plants the engineer has usually little to do and 
 consequently they will not be further considered here. The types 
 of wheels now most largely used for moderate and large water 
 power developments are the reaction and impulse turbines. 
 
 126. Classification of Turbines. All moder turbines consist of 
 a wheel to which buckets are attached and whicn is arranged to re- 
 volved in a fixed case having attached to it a nozzle, guide or 
 
244 Water Wheels. 
 
 series of guides. The guide passages or nozzles direct the water 
 at a suitable angle onto the buckets of the wheel. The revolving 
 wheel contains curved buckets or passages whose functions are to 
 receive the water, utilize its energy and discharge or waste it as 
 nearly devoid of energy as possible. 
 
 Turbines may be classified in various ways: 
 
 First. In accordance with the action of the water on the same. 
 
 (A) Reaction or pressure turbines, such as the Fourneyron, Jon- 
 val, Francis, etc. (See Fig. 128, G, H, I and J.) 
 
 (B) Action or impulse turbines, such as the Girard and tangen- 
 tial wheels. (See Fig. 129, diagrams D and E.) 
 
 (C) Limit turbines, which may act either by reaction or impulse. 
 Second. In accordance with the direction of flow in reference 
 
 to the wheel. 
 
 (A) Radial flow turbines. In these turbines the water flows 
 through the wheel in a radial direction. These may be subdivided 
 into 
 
 (a) Outward radial flozv turbines, such as the Fourneyron and 
 Cadiat. ,(See Fig. 128, diagrams F and D.) 
 
 (b) Inward radial flow turbines, or wheels in which the water 
 flows inward in a radial direction such as the Francis and Scheile 
 turbines. (See Fig. 128, J and K.) 
 
 (B) A. vial flow turbines in which the general direction of the 
 water is parallel to the axis of the wheel such as the Jonval and 
 Girard wheels of similar design. (See Fig. 128, H.) 
 
 (G) Mixed flow turbines, or turbines in which the flow is par- 
 tially radial and partially axial as in turbines of the American type. 
 (See Fig. 128, diagram I; also Figs. 143 to 158 inclusive). 
 
 Third. In accordance with the position of the wheel shaft. 
 
 (A) Vertical (See Figs. 132, 134, 135, 151, etc.). 
 
 (B) Horizontal (See Figs. 140, 152.) 
 
 Fourth. In accordance with the arrangement of nozzles or 
 guides. 
 
 (A) Complete turbines with guides surrounding the entire wheel. 
 
 (B) Partial turbines with guides partially surrounding the wheel 
 in one or more groups. 
 
 The re-action turbine is a turbine with restricted discharge which 
 acts through the reactive pressure of the water. Under some con- 
 ditions the energy of the water may be exerted, at least in part, 
 by its impact or momentum. The impulse turbine acts princip- 
 
Condition of Operation. 245 
 
 ally through the momentum of the moving mass of water although, 
 when the current reverses, some reactive pressure may be recog- 
 nized. The limit turbine may act entirely as a reaction or as an 
 impulse turbine according to the conditions under which it oper- 
 ates. 
 
 127. Condition of Operation. These wheels operate under the fol- 
 lowing conditions : 
 
 REACTION OE PRESSURE TURBINES. 
 
 Guides complete. 
 
 Buckets with restricted outlets. 
 
 Buckets or wheel passages completely filled. 
 
 Energy most largely developed through reactive pressure. 
 
 Discharge usually below tail water or into a draft tube. 
 
 ACTION OR IMPULSE TURBINES. 
 
 Guides partial or complete. 
 Buckets with outlets free and unrestricted. 
 Wheel passage never filled. 
 Energy entirely due to velocity. 
 Discharge must be above tail water. 
 
 No draft tube possible, except with special arrangement which 
 will prevent contact of tail water with wheels. 
 
 LIMIT TURBINES. 
 
 (A) Buckets so designed that the discharge is unrestricted when 
 above tail water. 
 
 Buckets in this case are just filled. Act without reactive effect. 
 Discharge above tail water. 
 
 (B) If tail water rises to buckets, the discharge is restricted and 
 reaction results. 
 
 In this case the full bucket admits reaction and discharge may be 
 below tail water. 
 
 128. Relative Advantage of Reaction and Impulse Turbines. 
 The reaction wheel is better adapted for low and moderate heads, 
 especially when the height of the tail water varies and where the 
 amplitude of such variation is a considerable percentage of the 
 total head. Such a wheel, which is designed to operate with the 
 buckets filled, can be set low enough to utilize the entire head at 
 
246 Water Wheels. 
 
 all times and will operate efficiently when fully submerged. The 
 reaction wheel can therefore be set to utilize the full head at time 
 of low tail water and when the quantity of flow is limited. For 
 low head developments this is an important factor. The impulse 
 turbine, on the other hand, must have a free discharge and must 
 therefore be set far enough above the tail water to be free from back 
 water if it is to be operated at such times. 
 
 Another difference between the reaction and the impulse turbine 
 is the higher speed with which the former operates. This is often 
 a distinct advantage, for direct connection with high speed ma- 
 chinery, and with low and moderate heads. On the other hand, 
 with high heads the slower speed of the impulse wheels is frequently 
 of great advantage, especially in the form of the tangential wheel 
 when the diameter can be greatly increased and very high heads 
 utilized with moderate revolutions. In such cases the height of 
 the back water is usually but a small percentage of the total head, 
 and the loss due to the higher position of the wheel is compara- 
 tively small. 
 
 The speed of a wheel for efficient service is a function of the ratio 
 of the peripheral velocity of the wheel to the spouting velocity of 
 water under the working head. This ratio will vary from .65 to .95 
 in reaction turbines, according to the design of 1 the wheel. In im- 
 pulse turbines this ratio varies from .40 to .50. 
 
 129. Relative Turbine Efficiencies. The impulse turbine has the 
 further advantage of greater efficiency under part gate, that is, 
 at less than its full capacity. When, as is usually the case, a wheel 
 must operate under a variable load it becomes necessary to reduce 
 the discharge of the wheel in order to maintain a constant speed 
 with the reduced power required. (See Fig. 131). This is ac- 
 complished by a reduction in the gate opening which commonly 
 greatly affects the economy of operation. 
 
 The comparative efficiencies of various types of the turbines are 
 shown in Fig. 131. The maximum efficiency of turbines when 
 operated at the most satisfactory speed and gate will be about the 
 same for every type, if the wheel is properly designed and con- 
 structed and the conditions of operation are suitable for the type 
 used. This maximum efficiency may vary from 75 to 85 per cent., 
 or even between wider limits, but, with suitable conditions, should 
 not be less than 80 per cent. In order to make the curves on the 
 diagram truly comparative, the percentage of maximum efficiency 
 
Relative Turbine Efficiencies. 
 
 247 
 
 20 
 
 30 40 50 60 70 
 
 PER CENT OF MAXIMUM DISCHARGE 
 
 80 
 
 90 
 
 100 
 
 Fig. 131 Comparative Efficiencies of Various Types of Turbines. 
 
 -and of maximum discharge are plotted instead of the actual effi- 
 ciencies and actual discharge. 
 
 The Fourneyron turbine usually shows very poor efficiencies at 
 part gate as shown in Fig. 131. The curve for this turbine is 
 drawn from Francis' test of the Tremont (Fourneyron) turbine 
 {see Fig. 132, also Table LXI) and is substantiated by efficiency 
 curves shown by various tests by James Emerson.* 
 
 The Janval turbines usually show better part gate efficiencies 
 than the Fourneyron but are not as efficient, under such conditions, 
 as turbines of the inward flow or Francis type. The Jonval curve, 
 shown in Fig. 131, is plotted from the test made in 1884 at the 
 
 See "Hydrodynamics" by James Emerson. 
 
248 Water Wheels. 
 
 Holyoke testing flume * of a 3O-inch regular Chase-Jonval turbine. 
 (See Table LXXVI). 
 
 The American-Francis turbine varies greatly in part gate effi- 
 ciency according to the details of design and the relation of speed 
 and head under which it operates. The curve shown in Fig. 131,. 
 representing this type, is from the test of a wheel manufactured by 
 J. & W. Jolly of Holyoke, Massachusetts, similar but not the same- 
 as that illustrated by the characteristic curve Fig. 249. 
 
 The impulse wheels when properly designed and operated show 
 a higher part gate efficiency than any other type of w r heel. The 
 curve shown in Fig. 131 is from a test o.f a 12" Doble tangential 
 wheel in the laboratory of the University of Wisconsin.! 
 
 As already indicated, the design of the wheel has a great in- 
 fluence on its efficiency at part gate. Individual wheels or series 
 of wheels of any type may therefore depart widely from the curves- 
 above shown, which are intended only to show as fairly as possible 
 the usual results obtained from well made w r heels of each type. 
 
 It should be noted also that efficiency is only one of the factors- 
 influencing the choice of a wheel and that many other factors, must 
 be weighed and carefully considered before a type of wheel is se- 
 lected as the best for any particular set of conditions. 
 
 130. Turbine Development in the United States. The develop- 
 ment of the turbine in the United States has been the outgrowth 
 of some seventy years of practical experience. In the early settle- 
 ment of the country the great hydraulic resources afforded facili- 
 ties for cheap power and numerous water powers were developed 
 under low and moderate heads. These developments created a 
 corresponding great demand for water wheels and stimulated in- 
 vention and manufacturing in this line. American inventors have 
 devised many different forms of wheels which were patented, con- 
 structed, tested and improved to meet the prevailing conditions. 
 When a successful wheel was designed, it was duplicated in its 
 original form and its proportions increased or diminished, to con- 
 form to the desired capacity. As wheels of greater capacity or of 
 higher speed have been required, modifications have been made 
 and improved systems have resulted. 
 
 * See page 44 of 1897 catalogue of Chase Turbine Manufacturing Co.. 
 Orange, Mass. 
 
 tFrom "Test of a 12" Doble Tangential Water Wheel," an unpublished) 
 thesis by H. J. Hunt and F. M. Johnson. 
 
Turbine Development in the United States. 249 
 
 The best American water wheel construction began with the 
 Boyden-Fourneyron and Geylin-Jonval turbines of improved 
 French design, but modern American practice began to assume its 
 characteristic development with the construction of the Howd-Fran- 
 cis turbines, already described. Moderate changes in the form and 
 arrangement of buckets and other details gave rise' to the earlier 
 forms' of ''Swain/' "Leffel" and "American" wheels each of which 
 consisted of an inward flow turbine modified from the earlieY de- 
 signs of Howd and of Francis as the experience of the inventor 
 seemed to warrant. In all of these cases the wheels discharged 
 inward and essentially in a radial direction and had to be built af 
 sufficient diameter to provide an ample space for receiving the dis- 
 charging waters. This necessitated slow speed wheels of com- 
 paratively low capacity (see Table I, page 13). In order to secure 
 higher speed, the diameters of the wheels were reduced thus re- 
 ducing the power. This reduction was, however, more than coun- 
 terbalanced, in the later wheels, by an increase in the width of 
 the bucket in an axial direction.' It was found also that the cap- 
 acity of the wheels could also be materially increased, with only 
 small losses in efficiency, by decreasing the number of buckets. 
 Wheels were gradually reduced in diameter and the buckets in- 
 creased in breadth until, in many cases, they reached very nearly 
 to the center of the wheel. This necessitated a downward dis- 
 charge in the turbine and resulted in the prolongation of the buck- 
 ets in an axial direction in many cases to almost double the width 
 of the gate. From this development has resulted the construction 
 of a series of wheels known as the "American turbines" having 
 higher speed and greater power than has been reached in Euro- 
 pean practice. 
 
 The entire line of development has, until within the last fifteen 
 years, been toward the increase of speed and power for low and 
 moderate head conditions. It is only within this period that a con- 
 siderable demand has been felt in this country for turbines having 
 other characteristics and adapted for higher heads. 
 
 The American type of turbine, in its modern form is not designed 
 or suitable for high heads its origin being the result of entirely 
 different conditions. About 1890 came a demand for turbine wheels 
 under comparatively high heads which manufacturers of wheels of 
 the American type were therefore poorly equipped to meet. The 
 first of such wheels supplied were therefore of European types, 
 
 15 
 
250 Water Wheels. 
 
 which apparently better suited such conditions. Recognizing, 
 however, the importance of meeting such demands, the American 
 manufacturer found that the wheels of essentially the original 
 Francis type were well suited for this purpose. The narrow wheel 
 and numerous buckets of the earlier types reduced the discharge of 
 water, and, increasing the diameter, reduced the number of revo- 
 lutions. Such types of wheels of high efficiency can now be 
 obtained from the leading manufacturers in the United States, and, 
 while many manufacturers still prefer to furnish simply their stock 
 designs, which are only suited for the particular conditions for which 
 they were designed, still, other manufacturers are prepared to 
 furnish special wheels which are designed and built for the particu- 
 lar conditions under which they are to be used. 
 
 The systems of wheels offered by American manufacturers, which 
 can be readily and quickly duplicated at a much less expense than 
 would result from the design of special wheels for each particular 
 customer, has resulted in the ability of American manufacturers to 
 furnish water wheels of a fairly satisfactory grade and at a cost 
 which would have been possible in no other way. In the United 
 States the cost of labor has been comparatively high and special 
 work is particularly expensive, much more so than in Europe where 
 skilled mechanics receive a compensation for labor which is but 
 a small fraction of that of their American competitors. Average 
 American practice, at the present time, leaves undoubtedly much 
 to be desired and considerable advance may be expected from the 
 correction of designs, resulting from practical experience and by the 
 application of scientific analysis. 
 
 131. The American Fourneyron Turbine. As noted in Chapter 
 I, one of the first reaction turbines developed in the United States 
 was the Bo)^den wheel of the Fourneyron type. 
 
 In these wheels (see Fig. 132) the water entered from the center, 
 guided by fixed curve guides, g, (Fig. 133) and discharged outward 
 through the buckets, B. The use of these wheels gradually spread 
 and they rapidly replaced many of the old overshot and breast 
 wheels used up to that time, and soon became the foremost wheel 
 in New England. 
 
 The manufacture of the Fourneyron turbine has, for common 
 use, been discontinued on account of the competition of other 
 cheaper wheels which were found to be more efficient at part gate 
 
The American Fourneyron Turbine. 
 
 251 
 
 Fig. 132. Tremont (Boyden-Fourneyron) Turbine (after Francis). 
 
 Fig. 133. Guides and Buckets of Tremont (Boyden-Fourneyron) Turbine. 
 
252 Water Wheels. 
 
 and more generally satisfactory under ordinary conditions of serv- 
 ice. 
 
 The Fourneyron turbine, when well designed and constructed, is 
 a turbine of high full gate efficiency. This wheel is adapted for 
 high heads where a comparatively slow speed is desired, and it 
 is now frequently used for high grade and special work where its 
 peculiarities seem best suited to such conditions. 
 
 One of the modern applications of the Fourneyron turbine is 
 that in the power plant of The Niagara Falls Water Power Com- 
 pany. Fig. 134 shows vertical and horzontal sections of one of the 
 double Fourneyron units used by this company in their first plant. 
 These wheels discharge 430 cubic feet per second and make 250 
 revolutions per minute ; at 75 per cent, efficiency each wheel will 
 develop 5,000 horse power. The buckets of these wheels are di- 
 vided vertically into three sections or stories in order to increase 
 their part gate efficiencies. These wheels are of Swiss design by 
 the firm of Faesch and Picard and were built by The I. P. Morris 
 Company of Philadelphia. [The wheels are vertical and connected 
 by vertical shafts, each with one of the dynamos in the station 
 above. The shaft is built of three-quarter inch steel, rolled into 
 tubes 38 inches in diameter. At intervals the shafts pass through 
 journal bearings, or guides, at which points the shafts are reduced 
 to ii inches in diameter and are solid. The speed gates of these 
 wheels are plain cylindrical rims which throttle the discharges 
 on the outside of the wheels and which, with the co-operation of 
 the governor, keeps the speed constant within two per cent under 
 ordinary conditions of operation. Another wheel of this type is 
 that manufactured and installed at Trenton, Falls, N. Y., by the 
 same firm. (See Fig. 311.) 
 
 132. The American Jonval Turbine. The Jonval turbine, orig- 
 inally of French design, was introduced into this country about 
 1850 and became one of the most important forms of turbine of 
 early American manufacture. In the tests of turbines at Phila- 
 delphia in 1859-60 (see page 360) a Jonval turbine developed the 
 highest efficiency and the type was adopted by the city for use in 
 the Fairmount Pumping Station. Like the Fourneyron turbine, 
 these wheels, while highly efficient at full gate, have largely been 
 superceded by other cheaper and more efficient part gate types, 
 except for special conditions. 
 
The American Jonval Turbine. 
 
 253 
 
 Pig. 134. Double Fourneyron Turbine of The Niagara Falls Water Power 
 Company. (Designed by Faesch & Picard; built by I. P. Morris & Co.) 
 
2 54 
 
 Water Wheels. 
 
 
 Fig. 135 shows the Geylin-Jonval turbine as manufactured by 
 the R. D. Wood Company of Philadelphia. W represents the run- 
 ner, B the buckets which receive the water through the guides, g. 
 The wheel shown has double inlets that are closed by the double 
 
 cylinder gates, GG. This 
 gate closes up against the 
 hood, C, by means of the 
 rod r, r, which connect 
 with the governor mech- 
 anism. The general de- 
 sign of the ordinary wheel 
 of this type is perhaps 
 best shown by Fig. 136.* 
 In this figure A is the 
 fixed or guide wheel and 
 B is the movable or tur- 
 bine runner. 
 
 In the later hydraulic 
 developments the use of 
 this -wheel has been con- 
 fined, largely at least, 
 to locations that require 
 special designs. One 
 of the later develop- 
 ments of the Jonval tur- 
 bine has been that for 
 The Niagara Falls Paper 
 Company. The first in- 
 stallation consisted of three upward discharge Jonval turbines of 
 1,100 horse power each, under a head of 140 feet. The installation 
 provided, however, for a total installation of six turbines. The ver- 
 tical shafts are 10 inches in diameter and 140 feet in length and 
 weigh about 19 tons each. These shafts, in addition to the weight 
 of the wheels, which are 4' 8" in diameter, are supported by marine 
 thrust bearings, under the beveled wheels, together with a step 
 bearing under the turbine. When the turbine is in use, however, 
 the weight of the wheel and the shaft is balanced by the upward 
 pressure of the water which at two-thirds gate is designed to ex- 
 actly balance this weight. At full gate there is an unbalanced up- 
 
 Fig. 135. Vertical Geylin-Jonval Turbine 
 (Manufactured by R. D. Wood & Co.). 
 
 * See page 7, 1877 catalogue, J. L. & S. B. Dix, Glen Falls, N. Y. 
 
The American Jonval Turbine. 
 
 255 
 
 ward pressure, and, at less than two-thirds gate, an unbalanced 
 downward pressure; these pressures are, however, only the differ- 
 ence between the weights and the water pressure and are easily 
 cared for by the bearings above described. 
 
 These wheels have thirty open- 
 ings and operate at 260 revolu- 
 tions per minute. The gates are 
 provided with sleeves (cylinder 
 gates) each weighing 2,800 pounds 
 and slide outside the guide wheels 
 to the hood. These sleeves are 
 guided by four rods which extend 
 above the turbine casing about 10 
 feet to a yoke which is counter- 
 balanced. A sectional view of 
 one of these turbines is shown in 
 Fig. 137 and the general arrange- 
 ment of the plant is shown in Fig. 
 138. 
 
 A still more recent type of the 
 Jonval turbine is the double, hor- 
 izontal wheel, built for The Niag- 
 ara Falls Hydraulic Power and 
 Manufacturing Company and in- 
 stalled in 1898. (See Figs. 139, 
 140). These wheels have a common, central intake and quarter- 
 turned draft tube which turns down to and is sealed in the tail 
 race below the floor. The speed control is effected by a register 
 gate through which the water passes before it reaches the guide 
 ring. This is said to give a somewhat lower efficiency at part gate 
 than does a gate interposed between the guide tubes and runner 
 bucket. Economy of water at part gate is said to be no particular 
 object in this plant and reduced efficiency is, in fact, an advantage 
 in that it reduces the gate movement and retains a velocity in the 
 penstock, with a given change of load, and consequently reduces 
 the inertia action and aids the speed regulation. This turbine is 
 rated at 2,500 H. P. at 250 revolutions per minute, under the normal 
 head of 210 feet.* 
 
 Fig. 13G. Jonval Turbine as Manu- 
 factured by J. L. & S. B. Dix. 
 
 * See "The Electrical World," January 14, 1899. 
 
256 
 
 Water Wheels. 
 
 Fig. 137. Geylin-Jonval Turbine of Niagara Falls Paper Mill Co. Manufac- 
 tured by R. D. Wood & Co. (From Eng. News, Apr. 5, 1894.) 
 
 133. The American Type of Reaction Turbine. The Howd 
 Wheel (Fig. 13) from which the idea of the Francis inward flow 
 wheel (Fig. 12) was derived, was invented in 1838 and acquired a 
 considerable market throughout New England. From these wheels 
 originated the American inward and downward or mixed flow tur- 
 bines. 
 
 The early wheels of American manufacture were designed very 
 much after the style of the Francis wheel with changes, more or 
 less radical, in the shape and details of the buckets. The demand 
 for wheels of greater power, and -higher speed, has resulted in a 
 gradual development of other and quite different forms. 
 
 The development of the turbine in the United States is well 
 illustrated by that of the "American" turbine of Stout, Mills & 
 Temple, now The Dayton Globe Iron Works Co. This wheel was 
 
The American Jonval Turbine. 
 
 257 
 
 Fig. 138. Plant of the Niagara Falls 
 Paper Co. Showing Installation of 
 Jonval Turbines. (From Gassier' s 
 Magazine, Nov., 1904. 
 
 designed in 1859 and was called '' 
 the American Turbine. The 
 general form of the original tur- 
 bine wheel is shown in Fig. 141. 
 
 This was followed (1884) by 
 the design of what is known as 
 the "New American" turbine, 
 illustrated by Fig. 142. In this 
 wheel the buckets are length- 
 ened downward and have a 
 partially downward as well as 
 inward discharge. 
 
 This wheel was followed in 
 1900 by the "Special New 
 American" illustrated in Fig. * 
 143, having a great increase in 
 capacity and power. 
 
 The fourth and most recent 
 type (1903) is the "Improved 
 New American" illustrated in 
 Fig. 144. The comparative 
 power and speed of these vari- 
 ous wheels is shown in the 
 tables on pages 258 and 259. 
 
 Table XXIII is misleading to 
 the extent that while the diam- 
 eter of each wheel is given as 
 48" such diameters are not 
 strictly comparative. Part of 
 the additional capacity and 
 power of the "Special New 
 American" and of the "Im- 
 proved New American" is due 
 to the cutting back of the buck- 
 ets (see Figs. 141 to 144) which, 
 while it reduces the diameter 
 at the point of measurement, 
 gives a discharge which would 
 be fairly comparative with 
 wheels of the older type of per- 
 haps three or four inches larger 
 diameters. (See Sec. 140.) 
 
258 
 
 Water Wheels. 
 
 TABLE XXIII 
 
 Development of "American" Turbines. Capacity, Speed and Power of a 
 Turbine under a 16-foot Head. 
 
 
 Year 
 brought out. 
 
 Discharge 
 in cu. ft. 
 
 Eev. per 
 min. 
 
 Horse 
 power. 
 
 
 1859 
 
 3271 
 
 102 
 
 79.1 
 
 Standard. New American 
 
 1884 
 
 5864 
 
 102 
 
 141.8 
 
 New American 
 
 1894 
 
 9679 
 
 107 
 
 234 
 
 Special New American 
 Improved. New American .... 
 
 1900 
 1903 
 
 11061 
 13234 
 
 107 
 139 
 
 267.0 
 3^5.0 
 
 
 
 
 
 
 Fig. 139. Horizontal Geylin-Jonval Turbine of Niagara Falls Hydraulic- 
 Power & Manufacturing Co. Showing Guide Chutes.* 
 
 * Cuts 139 and 140 reproduced from Electrical World, Jan. 14, 1899. Tur- 
 bines manufactured by R. D. Wood & Co. 
 
The American Type of Reaction Turbine. 
 
 259 
 
 The development of turbines may also be illustrated by a compar- 
 ison of the size and speed of turbines of various series required to 
 develop essentially the same power. (See Table XXIV.) 
 
 TABLE XXIV 
 Increase in Speed of "American" Turbines for Same Power (16-foot head). 
 
 
 Size of 
 wheel. 
 
 Horse 
 power. 
 
 R. P. M. 
 
 
 48 
 
 79.1 
 
 102 
 
 New American 
 
 36 
 
 81.5 
 
 136 
 
 
 27^ 
 
 87.3 
 
 186 
 
 Imprcw6(l New American .... 
 
 25 
 
 87.5 
 
 267 
 
 
 
 
 
 Fig. 140. -Horizontal Geylin-Jonval Turbine Showing Bucket Ring* 
 
 Figs. 145 and 146 show a vertical and a horizontal half plan, half 
 section of a vertical Improved New American turbine. W is the 
 crown and hub of the wheel; B, the buckets; G, G, are the wicket 
 
 *See foot note r a S e 258 
 
260 
 
 Water Wheels. 
 
 gates that control the admission of water to the wheels and which 
 are operated by means of the ring Gr, which is moved by an eccen- 
 tric and rod, r, connected with the governor through the shaft, P. 
 
 The inner edges of the bucket are spaced some distance from the 
 shaft and the main discharge is inward and downward, though a 
 portion of the bucket will admit of a slightly outward discharge. 
 
 134. The Double Leffel Turbine. Perhaps the greatest depar- 
 ture of American inventors from the lines of the original Francis 
 
 Fig. 142. New American 
 Turbine Runner. 
 
 Fig. 141. American Turbine Run- 
 ner.* 
 
 TABLE XXV. 
 
 Development of "Leffel" Wheel. Capacity, Power and Speed of 40-inch 
 Wheel Under 16-foot Head. 
 
 
 Year 
 brought out. 
 
 Discharge. 
 
 Kev. per 
 minute. 
 
 Horse 
 power. 
 
 Standard 
 
 1860 
 
 2547 
 
 138 
 
 
 Special 
 
 1870 
 
 3672 
 
 138 
 
 93 
 
 
 1890 
 
 6551 
 
 158 
 
 155 
 
 Improved Samson 
 
 1897 
 
 8446 
 
 163 
 
 207 
 
 
 
 
 
 
 * Manufactured by The Dayton Globe Iron Works Co. 
 
The American Type of Reaction Turbine. 261 
 
 Fig. 143. Special New American Turbine 
 Runner.* 
 
 Fig. 144. Improved New American Tur- 
 bine Runner.* 
 
 type of turbine was that 
 of James Leffel. In this 
 wheel was combined a 
 double runner, the upper 
 half being a radial inflow 
 runner of the Francis type 
 and the lower half con- 
 sisting of a runner with 
 inward radial admission 
 and axial discharge, es- 
 sentially on the line of the 
 later development of tne 
 American type of wheels. 
 The wheel, as originally 
 designed, had the narrow 
 bucket, slow speed and 
 low power of all early 
 American wheels. In its 
 later development the 
 buckets have been extend- 
 ed inward and downward 
 and these wheels have 
 found their best modern 
 development in the Sam- 
 son-Leffel wheel, illustrat- 
 ed in Figs. 147 to 151. 
 
 In Fig. 147, W repre- 
 sents the hub and crown 
 of the wheel which is se- 
 curely keyed to the shaft, 
 S. B' B' are the upper 
 buckets that discharge 
 inward and downward 
 through the passage aa. 
 The lower buckets, BB, 
 it will be noted, have the 
 same lines as other modern 
 wheels of the American 
 type. They receive the 
 
 * Manufactured by The Dayton Globe Iron Works Co. 
 
262 
 
 Water Wheels, 
 
 Pigs. 145 and 146. Section and Plan of ImprovedNew American Turbine.* 
 
 * Manufactured by The Dayton Globe Iron Works Co. 
 
The American Type of Reaction Wheels. 263 
 
 Figs. 147 and 148. Section and Plan of Samson Turbine.* 
 
 Manufactured by The James Leffel & Co. 
 
264 
 
 Water Wheels. 
 
 Figs. 149, 150 and 151. Top View, Runner and Outside View of Samson Tur- 
 bine.* 
 
 * Manufactured by The James Leffel & Co. 
 
The Double Leffel Turbine. 
 
 265 
 
 water inward and discharge it downward, outward and inward with 
 the general purpose of distributing it over the cross-section of the 
 turbine tube. The gates, G, are of the wicket type and are con- 
 nected by rods with an eccentric circle which is operated through 
 the arm, A, and the gearing, Gr, by the governor shaft, P. The 
 gate gearing is well shown by reference to the section-plan, Fig. 
 148, and the top view, Fig. 149. 
 
 The Samson turbine runner is illustrated in Fig. 150, and Fig. 
 151 shows an outside view of one of the vertical, turbine units. 
 
 Fig. 152. Double Horizontal Leffel Turbine of The Niagara Falls Hydraulic 
 Power & Manufacturing Co. Manufactured by The James Leffel & Co. 
 
 The development of this wheel is illustrated by Table XXV. This 
 table is fairly representative of the growth of this turbine as the 
 diameter is, in all cases, the maximum diameter of the wheel. (See 
 
 Sec. 140.) 
 
 The adaptability of the earlier turbine designs to the later mod- 
 erate head developments is well illustrated in the design of the 
 16 
 
266 
 
 Water Wheels. 
 
 wheels for The Niagara Falls Hydraulic Power and Manufacturing 
 Company, installed by The James Leffel Company about 1892. 
 These turbines have the single narrower buckets, smaller discharge 
 and relatively slower speed of the earlier designs. The runners are 
 double discharge, horizontal, seventy-four inches in diameter and 
 operate at a speed of 250 revolutions per minute under a head of 
 215 feet, and each wheel develops about 3,500 horse power. 
 
 Fig. 153. Leffel Double Runner of The Niagara Falls Hydraulic Power & 
 Manufacturing Co. Manufactured by The James Leffel & Co. 
 
 Fig. 152 shows one of these units complete. Fig. 153 is a view 
 of the runner. For a test of this wheel, made December 1903, see 
 page 381. 
 
 J 35- Other American Wheels. The development of modern 
 American wheels could, perhaps, have been equally well illustrated 
 by the growth of various other American turbines. The develop- 
 ment of all American wheels up to the present time has been on 
 the line of increasing both the speed and the power of the wheel 
 for low head, with a return to the earlier type for wheels to be used 
 under the moderate heads. 
 
 Fig. 154 illustrates a runner of the well-known McCormick pat- 
 tern. Mr. J. B. McCormick, who had previously become familiar 
 
Other American Wheels. 
 
 267 
 
 with certain wheels of large capacity designed and patented by 
 Matthew and John Obenchain, re-designed and improved these 
 wheels, about 1876, and secured high efficiencies together with 
 increased power far beyond any other wheels of that period. Mc- 
 
 Cormick wheels in their 
 original or modified form 
 are now made by a large 
 
 If j|r& number of American man- 
 
 | uTacturers and these 
 
 wheels have had a marked 
 effect on the design of 
 almost all modern Ameri- 
 can water wheels. The 
 runner in the illustration 
 is the Hunt-McCormick 
 runner as manufactured by 
 The Rodney Hunt Ma- 
 chine Company, but is 
 very similar to the Mc- 
 
 Fig. 154. Hunt-McCormick Runner of The 
 Rodney Hunt Machine Co. 
 
 Cormick wheels of various 
 other manufacturers. 
 
 The Smith-McCormick 
 runner is manufactured by 
 The S. Morgan Smith 
 Company. This company 
 has also recently brought 
 out a new wheel called 
 the "Smith Turbine/' 
 of greater power and 
 higher speed, the runner 
 of which is illustrated by 
 Fig. 155. Fig. 156 repre- 
 sents the Victor runner or 
 "type A" runner of The 
 Platt Iron Works Com- 
 pany, designed for low 
 heads. 
 
 Fig. 157 is the "typeB" 
 runner, of the same Corn- 
 Fig. 155.-Smith Runner of S. Morgan pany, designed for medi- 
 Smith Co. 
 
 um heads. This runner 
 
268 
 
 Water Wheels. 
 
 again illustrates the tendency to return to the earlier forms of 
 runner for medium head wheels. This latter type has also been 
 adopted by other manufacturers of turbines, as may be seen by ref- 
 erence to Fig. 158 which shows the Hunt runner manufactured for 
 moderate heads by The Rodney Hunt Machine Company. 
 
 Fig. 159 is from a shop 
 photograph of the Shawin- 
 igan Falls turbine manu- 
 factured by the I. P. Mor- 
 ris Company. This is one 
 of the largest turbines ever 
 constructed and develops 
 10,500 horse power under 
 a head of 140 feet. It is a 
 double mixed inflow type 
 with spiral casing and a 
 double draft tube through 
 which the water discharges 
 outward from the center. 
 The diameter of the cas- 
 ing at the intake is 10i 
 feet and the sectional 
 area gradually diminishes 
 around the wheel in pro- 
 portion to the amount of 
 water flowing at each 
 point. The wheel com- 
 plete is 30 feet in height 
 and weighs 182 tons. The 
 runner, which is of bronze, 
 is shown in Fig. 160. 
 
 Figs. 161 and 162 show 
 two sections of a single 
 turbine of the Francis in- 
 flow type built for the 
 Snoqualmie-Falls plant of 
 The Seattle & Tacoma 
 Power Company by The 
 Platt Iron Works Corn- 
 Fig. 157. High Head or "Type B" Runner pany. The turbine has 9 
 of The Platt Iron Works Co. capacity of about 9.000 
 
 Fig. 156. Victor or "Type A" Runner of 
 The Platt Iron Works Co. 
 
Other American Wheels. 
 
 269 
 
 H. P. under 270-foot head .at 300 R. P. M. The runner is 66 inches 
 in diameter and has a width of 9i inches through the buckets.* 
 This is believed to be the largest capacity single discharge wheel 
 yet constructed. 
 
 For further details see Figs. 183, 189 and 190. 
 136. Early Development of Impulse Wheels. As already pointed 
 out (see Chapter I, Figs. 6 and 7), water wheels of the impulse 
 type were among the earlier forms used. In the practical construc- 
 tion of water wheels for commercial purposes in this country, the 
 
 reaction turbine was, how- 
 ever, the earliest form of 
 development. This was 
 because the reaction tur- 
 bine was best suited for 
 the low heads first devel- 
 oped. As civilization ad- 
 vanced from the more level 
 country into the moun- 
 tainous regions the condi- 
 tions were found to radi- 
 cally differ. In the form- 
 er location large quanti- 
 ties of water under low 
 heads were available; in 
 the latter, the streams 
 diminished in quantity 
 but the heads were enorm- 
 ously increased. These 
 conditions demanded an entirely different type of wheels for power 
 purposes and the demand was met by the construction of the tan- 
 gential wheel now so widely and successfully used in the high head 
 plants of the West. 
 
 The earliest scientific consideration of impluse wheels in this 
 country was by Jearum Atkins who, apparently, anticipated the 
 design of the wheels of the Girard type in Europe by his design of 
 such a wheel in 1853. t (See Fig. 163.) 
 
 Fig. 
 
 158. Hunt Runner of The Rodney 
 Hunt Machine Co. 
 
 * See "Engineering News," March 29, 1906. 
 
 t See "Tangential Water Wheels" by John Richards, Cassier's Magazine, 
 vol. v, p. 117. 
 
270 
 
 Water Wheels. 
 
 Fig. 159. Shawinigan Falls Turbine, Manufactured by I. P. Morris Co. 
 
Other American Wheels. 271 
 
 In Atkins' first application for a patent (in 1853) he shows a 
 clear conception of the principles of the impulse wheel. 
 
 After describing the mechanical construction of his wheel, Mr. 
 Atkins says: "The important points to be observed in the con- 
 struction of this wheel and appendages, are : First, that the gear- 
 ing * * * should be so arranged as to allow the wheel's veloc- 
 ity at the axis of the buckets to be equal to one-half the velocity 
 of the water at the point of impact, * * * 
 
 "As the power of water, * * * is measured by its velocity, 
 * * * it is obvious that in order that the moving water may 
 communicate its whole power to another moving body, the velocity 
 of the former must be swallowed up in the latter. This object is 
 
 Fig. 1GO. Shawinigan Falls Turbine Runner. 
 
 effected by the before-described mode of applying water to a wheel 
 in the following manner, the velocity of the wheel, as before 
 stated, being one-half that of the water. 
 
 "Let us suppose the velocity of the water to be twenty-four feet 
 per second ; then the velocity of the wheel being twelve feet per 
 second, the relative velocity of the water with respect to the wheel, 
 or the velocity with which it overtakes the wheel, will be twelve 
 feet per second. Now it is proved theoretically, and also demon- 
 strated by experiment, that water will flow over the entire surface 
 of the semi-circular buckets of the wheel with the same velocity 
 with which it first impinged against them, or twelve feet per sec- 
 ond. Then, as the water in passing over the face of the buckets 
 
272 
 
 Water Wheels. 
 
 has described a semi-circle, and as its return motion on leaving 
 the wheel is in an opposite direction from that of the wheel, its 
 velocity with respect to the wheel being twelve feet per second, 
 and as the wheel has an absolute velocity of twelve feet per sec- 
 
 Fig. 161. Section Snoqualmie Falls Reaction Turbine. The Platt Iron Works 
 
 Company. 
 
 ond, it is obvious that the absolute velocity of the water with re- 
 spect to a fixed point is entirely suspended at the moment of leav- 
 ing the inner point of the buckets, its whole velocity, and conse- 
 quently its whole power, having been transmitted to the wheel." 
 
Early Development of Impulse WheeL 
 
 273 
 
 Pig. 162. Section-Elevation Snoqualmie Falls Reaction Turbine (The Platt 
 
 Iron Works Co.). 
 
 Fig. 163. Plan of Atkins Wheel and Wheel Case (1853). From Cassier's 
 Magazine, Vol. v, p. 119. 
 
274 
 
 Water Wheels. 
 
 a. Moore bucket, 1874. 
 
 6. Knight buckets, 1870. 
 
 c. Dodd bucket, 1889. 
 
 d. Hug bucket, 1897. 
 
 e. Doble Ellipsoidal bucket, 
 
 1889. /. Pelton bucket, 1880. 
 
 Fig. 1C4. Buckets of Tangential or Impulse Water Wheels. (Trans. Am. 
 Inst. Mining Eng. 1899. 
 
 Mr. Atkins' first application for a patent was rejected. After a 
 long illness, from which he finally recovered, he again applied for a 
 patent which was finally granted in 1875. The Atkins' patents are 
 simply of historical interest as his inventions have had little effect 
 on the practical development of the impulse wheel. 
 
American Impulse Wheels. 
 
 275 
 
 137. American Impulse Wheels. The impulse wheel found its- 
 earliest practical development in California where the conditions for 
 the development of power made such a wheel necessary. The 
 early tangential wheel, used on the Pacific Coast, was quite simple 
 in construction and the development of the buckets, which began 
 with the simpler flat and curved forms, was very largely based on 
 the experimental method used for the development of the reaction, 
 
 Fig. 1G5 . Telluride Double Tangential Wheels. 2000 H. P. 500 Foot Head. 
 (Pel ton Water Wheel Co.) 
 
 turbine in the East. Experiments were made at the University 
 of California, by Mr. Ralph T. Brown, as early as 1883, and the 
 bulletin, published by the department was the earliest literature on 
 tangential wheels published in this country. 
 
 With the early development of the tangential bucket are con- 
 nected the names of Knight, Moore, Hesse, Pelton, Hug, Dodd 
 and Doble, and many other inventors, whose wheels have become 
 well-known and widely used. The most extensive early develop- 
 
276 
 
 Water Wheels. 
 
 ment of this wheel was by The Pelton Water Wheel Company 
 whose work has been so widely known and used as to make the 
 name "Pelton Wheel" a common title for all wheels of the tangen- 
 tial type. 
 
 Some of the many forms of American buckets used are shown in 
 
 Fig. 164 with the approximate 
 date of their invention or de- 
 sign. 
 
 The general arrangement of 
 a double 2000 H. P. unit, run- 
 ning at 200 R. P. M. under 500 
 foot head is shown in Fig. 165. 
 This is one of three units in- 
 stalled by The Pelton Water 
 Wheel Company for The Tellu- 
 ride Transmission Plant of Col- 
 orado. 
 
 The wheels are of cast steel 
 fitted with steel buckets, held 
 in position by turned steel 
 bolts. They are connected by 
 a flexible coupling to a 1,200 
 H. P. generator. 
 
 Fig. 166 shows the runner of 
 an impulse wheel made by the 
 same company. This is 9' 10" 
 in diameter, and is designed to 
 develop 5,000 H. P. at 225 R. 
 P. M. under an effective head 
 of 865 feet. 
 
 Fig. 167 shows the runner of an impulse wheel manufactured by 
 the Abner Doble Company. This runner was from the Doble Wa- 
 ter Wheel Exhibit at the St. Louis Fair and developed 170 H. P. 
 at 170 R. P. M. under a head of 700 feet and generated direct cur- 
 rent for use on the intramural railway. 
 
 In addition to the tangential wheels already described, a few 
 manufacturers have developed wheels of the Girard type. One 
 such wheel, designed and built by The Platt Iron Works Company, 
 is illustrated in Figs. 168 to 171, inclusive. Fig. 168 is a section- 
 elevation showing the arrangement and design of the guides and 
 
 Fig. 166. Pelton Tangential Water 
 Wheel Runner. Designed for 5000 
 H. P. at 865 foot head and 225 E. 
 P. M. (Pelton Water Wheel Co.) 
 
American Impulse Wheels. 277 
 
 buckets of the wheel. Fig. 169 shows a section through the wheel 
 and on the line of the shaft. In these figures W represents the 
 runner; BB the buckets; g, the inlet guides, and G, the gate by 
 which all or a portion of the guide passages may be closed and the 
 power of the wheels reduced. The gate, G, is connected by the 
 gearings, Gr, with the rod, r, which is connected through the rocker 
 
 Fig. 167. Doble Runner. (Abner-Doble Co.) 
 
 arm with the governor mechanism. The wheel or runner of this 
 turbine is shown by Fig. 170, and a general view of the wheel is 
 shown by Fig. 171. 
 
 138. Turbine Development in Europe. Modern European tur- 
 bine practice has been the development of the last twenty years. 
 European manufacturers have approached the subject more on the 
 
Water Wheels. 
 
 t>asis of theoretical analysis than has been done in America. The 
 conditions of development have also been largely special and not 
 under such uniform conditions as in America. The result has been 
 the development of special designs for special locations and the 
 rapid accumulation of a considerable experience under a wide range 
 
 Fig. 168. End Section and Elevation, Girard Impulse Turbine with Draft 
 Tube. (Platt Iron Works Co.) 
 
 of conditions. While the radial flow turbines were the earlier type 
 developed, European practice has been largely centered on the axial 
 flow wheels of the Jonval type for complete turbines, and axial 
 flow and radial flow wheels of the Girard type for partial turbines 
 under high heads. * 
 
American Impulse Wheels. 
 
 279 
 
 The axial flow turbine while simple in construction and low in 
 cost is difficult to regulate and hence the demands of electrical de- 
 velopment for close regulation has given rise to a variety of mod- 
 ern designs which are summarized by Mr. J. W. Thurso essentially 
 as follows : * 
 
 Fig. 169. Longitudinal Section Girard Impulse Turbine. (Platt Iron Works 
 
 Company.) 
 
 ist. For low heads to 20 feet. Radial inward flow, reaction tur- 
 bines with vertical shafts and draft tubes. 
 
 2nd. For medium heads, 20 to 300 feet. Radial inward flow reac- 
 tion turbines with horizontal shafts and concentric or spiral cases 
 and draft tubes. 
 
 3rd. For high heads over 300 feet. Radial outward flow, full or 
 partial action turbines (of the Girard type) with horizontal shafts, 
 
 * See "Modern Turbine Practice" by J. W. Thurso. 
 
280 
 
 Water Wheels. 
 
 Fig. 170 Runner of Girard Turbine. Type 
 High-Pressure Runner. (Platt Iron Works Co.) 
 
 Fig. 171. General View of Girard Turbine with 
 Cover Raised. (Platt Iron Works Co.) 
 
 often with draft tubes; 
 also, modified impulse 
 wheels of a tangential 
 type. 
 
 The types of tur- 
 bines for low and mod- 
 erate heads are mod- 
 ifications of the Fran- 
 cis inward flow turbine. 
 Earlier European 
 practice is perhaps well; 
 represented by Fig. 
 172 which represents 
 one of eight turbines 
 installed by Messrs. 
 Escher, Wyss & Co. 
 c > for the City of Geneva, 
 Switzerland. These 
 wheels are of the Jon- 
 val type and operate 
 under heads some- 
 times as great as 12 
 feet but during high 
 water the heads de- 
 crease to about five 
 and one-half feet. 
 The turbines consist of 
 three annular rings or 
 buckets and are so de- 
 signed that the water 
 is admitted to as many 
 buckets as may be re- 
 quired for economical 
 operation under ' the 
 very great differences 
 in the condition of 
 supply. The width of 
 the inner and interme- 
 diate rings are each 
 seventeen and three- 
 
Turbine Development in Europe. 
 
 281 
 
 quarters inches, and the outer ring is eleven inches, all meas- 
 ured radially. The outside diameter of the wheel is thirteen feet, 
 eleven inches. The outer ring of guides is not provided with 
 means for excluding the water from the buckets but the intermedi- 
 ate or inner rings can be entirely and independently closed. The 
 
 Fig. 172. One of the seventeen 210 H. P. Jonval Turbines at the Geneva 
 Water Works. Built by Eecher, Wyss & Co. 
 
 gates for closing the intermediate and inner rings consist of a flat 
 plate in the form of a half ring, which lies on the top of the crown 
 and a vertical curtain which hangs from the end of the plate and 
 
 completes the closure of the other half of the bucket the openings 
 17 
 
282 
 
 Water Wheels. 
 
 of which are on the side of the same, the water entering the buckets 
 by a quarter-turn. 
 
 These turbines are used to operate the pump that furnishes the 
 water supply for the city of Geneva for domestic and manufactur- 
 ing purposes. 
 
 Fig. 173. The 1200 H. P. Double Turbine at Chivres near Geneva. 
 Escher, Wyss & Co. ( Gassier' s Magazine, October, 1897.) 
 
 Fig. 173 shows a pair of vertical turbines furnished by the same 
 company for Chivres near Geneva. Here the fall in summer is 15 
 feet and in winter 28 feet. The lower turbine will develop 1,200 
 
Turbine Development in Europe. 283 
 
 H. P. at 80 R. P. M. under the higher head, and under the lower 
 head the turbine above works w r ith the lower one. 
 
 Each turbine is cone shaped and divided into three compart- 
 ments in order to maintain the efficiency of the wheels at the same 
 revolutions under the wide range in heads. 
 
 Rapid advancement is now being made in turbine design both in 
 this country and in Europe and the progress can best be known and 
 appreciated by reference to the current technical press. 
 
CHAPTER XIII. 
 
 TURBINE DETAILS AND APPURTENANCES. 
 
 139. The Runner Its Material and Manufacture. The runners 
 of most reaction turbines (see Figs. 136, 142 to 149, 151, 154 to 159, 
 161) consist of hubs, crowns and rings, to which the buckets are at- 
 tached. The wheels are sometimes cast solid, and sometimes built 
 up. In built-up wheels the buckets are first cast, or otherwise 
 formed, after which they are placed in a form or moulded, and the 
 crowns, hubs and rings are cast to them. Turbine water wheels 
 for low heads are usually made of cast iron or of cast iron with 
 steel buckets. Wheels for high heads are frequently made of cast 
 bronze or of cast steel. (See Figs. 158 and 159.) 
 
 Probably the majority of cast wheels manufactured at the pres- 
 ent time are cast in one solid casting of buckets, rings, hubs, and 
 crowns. The buckets are formed by carefully prepared cores and 
 in such manner as to leave them uniform in spacing and thickness, 
 and smoothly finished so as to admit of the passage of water through 
 or between them without excessive friction. With wheels so cast, 
 no material finishing or smoothing of the surfaces of the bucket is 
 practicable, and the casting must come from the sand with a satis- 
 factory surface. In wheels cast solid, great care is necessary in 
 order to prevent serious shrinkage strains. This is partially over- 
 come by the use of soft iron, which results, however, in increased 
 wear of runners subject to the action of sand-bearing waters. 
 
 With buckets cast separately, a higher surface finish of the 
 bucket is possible ; but when separate buckets are made and after- 
 wards united, the runner must be strongly banded in order to give 
 it the necessary strength. Buckets of sheet steel, forged or bent 
 to the desired shape, present a uniform and satisfactory surface, 
 and when punched at the edges before casting, form a solid and 
 substantial wheel. 
 
 The runners of Girard impulse wheels (see Fig. 171) are made 
 in the same manner as reaction runners. 
 
 The runners of tangential wheels are usually made with separate 
 buckets and body. (See Figs. 167 and 168.) The bodies are made, 
 
Diameter of Runner. 285 
 
 according to the severity of the service, of cast iron, semi-steel, 
 forged steel, etc. The buckets, dependent on the conditions of 
 service, may be of cast iron, cast steel, gun metal, bronze, etc. The 
 buckets, in the best wheels, are cast, shaped and polished and care- 
 fully fitted to the wheel body. The bolt holes are then carefully 
 drilled and reamed and the buckets are bolted in position by care- 
 fully turned and fitted bolts. 
 
 140. Diameter of the Runner. The diameters of reaction runners 
 are measured at the inlet, and, when the buckets at the inlet are 
 parallel and of one size, the determination of the turbine diameter 
 is a simple matter. (See Fig. 174, diagram A.) In order to give 
 the runner greater speed and capacity, the buckets are sometimes 
 cut back at a point opposite the bottom of the gate opening (see 
 diagram B), and the diameter of the runner opposite to the gates is 
 reduced below that of the lower diameter. In such cases the edges 
 of the buckets are sometimes made parallel with the shaft but are 
 usually inclined upward. In the latter case, the diameter of the 
 wheel at its top may be considerably reduced over its diameter at 
 the offset. In such cases the cutting back of the runner may be one 
 or more inches at the bottom line of the gate with an inch or more 
 inclination to the top of the buckets, and the diameter of the wheel 
 at D and D'", diagram B, may differ from two to six inches or even 
 more. 
 
 With wheels so constructed, there is considerable difference in 
 the practice of different manufacturers in measuring and listing the 
 diameter of the wheels made by them. In some cases, the inside 
 diameter, from rjng to ring, D, diagram B, of the runner, is given 
 as the list diameter. In other cases, the diameter is taken at the 
 inner angle of the offset as D'. In a number of cases the diameter is 
 measured at about the center of the gateway, D", and in other cases, 
 the diameter is measured at the upper and smaller diameter of the 
 runner, D"'. This variable practice leads to a considerable differ- 
 ence in the nominal diameter of the various turbines as listed in 
 the catalogues, and frequently a runner listed as of a certain diame- 
 ter by one manufacturer may be two to six inches larger than the 
 runner of another manufacturer which is listed as of the same di- 
 ameter. This discrepancy in the method of measuring and listing 
 the diameter of turbine runners accounts, in some degree, for the 
 apparent greater capacity, higher speed or greater power of the 
 wheels of one manufacturer over those of another. 
 
286 
 
 Turbine Details and Appurtenances. 
 
 The practice of some of the American manufacturers of turbines, 
 in measuring and listing the diameters of their wheels, is shown 
 in Table XXV. In this table, all runners which are not cut back 
 and with edges parallel to the shaft, are classified as Style A, even 
 where they differ widely from the form shown in diagram A, Fig. 
 174. 
 
 All runners with buckets cut back are classified as Style B, even 
 where the bucket edges are parallel with the shaft. 
 
 The diameters of tangential runners are usually measured be- 
 tween the centers of buckets or on the diameter of the circle on 
 which the center of the jet impinges on the buckets. 
 
 TABLE XXV. 
 
 Practice of Various American Manufacturers i>i Measuring and Cataloging 
 the Diameter of Turbine Water Wheels. 
 
 Manufacturer. 
 
 Name of Kunner. 
 
 Style. 
 
 Point of 
 measure- 
 ment. 
 
 Dayton Globe Iron Works 
 
 American 
 
 A 
 
 j) 
 
 
 New American 
 
 A 
 
 D 
 
 Rodney Hunt Machine Co . . 
 
 Special New American 
 Improved New American 1 . . 
 McCormick 8 
 
 B 
 B 
 B 
 
 \y 
 
 D' 
 j) 
 
 
 Hunt 
 
 A 
 
 D 
 
 The James Leffel & Co 
 
 Standard Leffel 
 
 A 
 
 D 
 
 
 Special Leffel 
 
 A 
 
 p 
 
 
 Samson 
 
 B 
 
 D 
 
 Platt Iron Works Co 
 
 Improved Samson 
 Type A 
 
 B 
 B 
 
 D 
 D" 
 
 
 Tvpes B and C 
 
 A 
 
 D 
 
 S Morgan Smith Co 
 
 McCormick 3 
 
 B 
 
 D' 
 
 
 Smith 
 
 B 
 
 D' 
 
 The Trump Manufacturing Co. 
 
 Standard Trump 4 
 
 B 
 
 jy, 
 
 
 Hisrh Speed Trump 
 
 B 5 
 
 P 
 
 Wellman, Seaver, Morgan Co 
 
 Jolly-McCormick 
 
 B 
 
 D" 
 
 
 
 
 
 1 Fillet at angle. Diameter measured just above. 
 
 2 Diameter of Hunt-McCormick runners as measured at the crown which pro- 
 jects beyond the tips of the buckets and is essentially the same in diameter as at D' 
 
 3 Diameter of the Smith-McCormick runners is measured at the crown which 
 projects beyond the tips of the buckets and is essentially the same in diameter as 
 atD'. 
 
 4 Diameter at D is 20# greater than at D". 
 
 5 Bucket of of high speed runner has parallel edges but is cut back as shown in B. 
 
 141. The Details of the Runner. The reaction runner will vary 
 in design with the conditions under which it is to operate and the 
 experience and ideas of its designer. In American practice the 
 
Details of the Runner. 
 
 287 
 
 manufacturer usually constructs a series of runners of similar ho- 
 mogeneous design ; that is to say, each wheel of the series has all 
 of its dimensions proportional to that of every other wheel of the 
 series, and is of similar design in all of its parts. 
 
 On account of demands for considerable variations in speed or 
 power, or on account of improvements which have been found de- 
 sirable by reason of the demands of his trade, the manufacturer 
 often designs and constructs several series of wheels, each of which 
 is particularly adaptable to certain conditions which he has had to 
 meet. (See Tables XXII and XXIV.) In such cases each series 
 is best suited for the particular condition for which it was designed, 
 and is not necessarily obsolete or superseded by the later series. 
 
 Fig. 174. 
 
 The curves of the runner buckets (see Figs. 13, 14, 133, 134, 136, 
 146-148, 175) must be such as to receive the jet of water from the 
 nozzle or guides without shock, permit it to pass along the surface 
 of the buckets or through the passages in the runner with mini- 
 mum friction, and discharge it as nearly devoid of velocity as prac- 
 ticable. 
 
 To accomplish this, the relative position and relation of the 
 curves of guides and buckets must be carefully arranged. As the 
 jet of water, is always directed forward in the direction of the revo- 
 lution of the wheel, the jet has an original velocity in that direc- 
 tion, and, since the bucket must be so shaped as to give a continued 
 contact, as the jet progresses and the wheel revolves, the portion of 
 the bucket farthest away from the guides must be curved back- 
 ward, and terminate at such an angle as shall permit the jet to 
 pass away from the wheel with free discharge. (See Figs. 175 and 
 128.) 
 
283 Turbine Details and Appurtenances. 
 
 B 
 
 Fig. 175. Curves of Buckets and Guides in Turbine Wheels. 
 
Vertical Turbine Bearings. 
 
 289 
 
 RIGHT HAND 
 
 HAND 
 
 Reaction runners are made either right or left handed as de- 
 sired. When looking at the top of the runner, if the wheel is de- 
 signed to move in the direction of the hands of a watch, it is called 
 a right handed wheel, and if it moves in the other direction, it is 
 called a left handed wheel. (See Fig. 176.) 
 
 The buckets, hub, crown, and ring of the reaction runner must 
 be of sufficient strength to receive the impact or pressure of the 
 moving column of water under the working head, and to transmit 
 the energy to the shaft through which it is to be transmitted to the 
 machinery to be operated. 
 
 A heavy ring is usually desirable, both to give strength and 
 support to the outer edge of the buckets and also, under some cir- 
 cumstances, to give the effect of 
 a fly-wheel in order to materially 
 assist in maintaining uniform 
 speed. Floating blocks or other 
 material, in spite of the use of 
 trash racks, sometimes reach the 
 turbine, and when caught between 
 the buckets and the case are apt 
 Pig. 176. "Hand" of Water Wheels. to cause ser ious injury to the 
 
 buckets. 
 
 The runner is attached to a shaft passing through the hub, to 
 which it should be closely fitted and strongly keyed to prevent its 
 becoming loosened by vibration and the strain of operation. This 
 is^ especially necessary in vertical wheels, for if, under these con- 
 ditions, the wheel becomes loosened and drops from the shaft, it is 
 apt to be practically destroyed. Impulse runners acting under high 
 heads are subject to heavy shocks and must be especially sub- 
 stantial. 
 
 142. Vertical Turbine Bearings. In all turbines where the dis- 
 charge is axial and only in one direction, there is a reaction in the 
 other direction that tends to unbalance the wheel and to cause a 
 thrust in the direction opposite to the discharge. The leakage into 
 the space back of the runner frequently produces a thrust in the 
 opposite direction which may be wholly or partially relieved by 
 openings left in the runner, usually close to the axis. In large 
 units an attempt is made to balance these various pressures with 
 some form of thrust bearing to sustain the difference in pressure 
 which will occur under different conditions of operation. 
 
290 
 
 Turbine Details and Appurtenances. 
 
 In most single vertical turbines a simple step bearing is used. 
 The bearing itself in American turbines usually consists of a lig- 
 num vitae block, turned to shape, and centered in a bearing block 
 which is held firmly and centrally in place by the cross trees. The 
 bearing block is shown by T, and the cross trees by t, in Figs. 146, 
 147 and 185. The bearing on the shaft" itself is usually a spherical 
 sector, or some other symmetrical curve of similar form. In some 
 cases this bearing is cut directly in the shaft itself. (See Fig. 147.) 
 In others, a cast iron shoe is provided and attached to the shaft. 
 (See M, Figs. 145 and 184.) Above the turbine a second bearing 
 is also provided (see T', Figs. 145 and 147) to keep the shaft in 
 vertical alignment. This bearing in American wheels is usually 
 
 Fig. 177. Geylin (Patent) Glass Suspension Bearing (R. D. Wood & Co.). 
 
 of the type shown in Fig.. 182, except that it is adapted to its ver- 
 tical position. 
 
 In the Geylin-Jonval turbine, manufactured by R. D. Wood 
 Company, a patent glass suspension bearing is used. (Fig. 177.) 
 This bearing is attached above the wheel (see T, Fig. 135) and has 
 the advantage of being readily accessible. The turbine is here sus- 
 pended on a circular disc composed of segments of glass, B. B. 
 Fig. 177, arranged with depressed divisions which form a continu- 
 ous space around each segment of which the disc is composed, al- 
 lowing, while the turbine is in motion, a perfect, free circulation 
 of the lubricating matter with which the space is filled.* The bear- 
 ing is a true metallic ring, A, firmly secured to the turbine shaft 
 which revolves on these stationary glass segments. 
 
 In most European vertical turbines the step bearing is simply a 
 guide, the main bearing being above the turbine and more readily 
 accessible than in the American form. 
 
 * Catalogue of R. D. Wood & Co., 1901, p. 107. 
 
Vertical Turbine Bearings. 
 
 291 
 
 Figs. 178 and 179 represent vertical bearings of this kind. In 
 these bearings C is a spherical sector so arranged as to take up any 
 slight error in the vertical alignment of the shaft. Fig. 178 is a 
 
 ball bearing; the hardened 
 steel balls, AA, revolve 
 between the special bear- 
 ing plate, B and Bi. 
 
 In Fig. 179 oil is pumped 
 under pressure through the 
 inlet, pipe OE, into the 
 space A. By its pressure 
 the bearing plate, B, is 
 raised from its companion 
 plate, B, and the oil es- 
 caping between the plates 
 lubricates them and over- 
 flows through the overflow 
 pipe, OO. 
 
 In both Figs. 178 and 
 179 the height of the shaft 
 is adjusted by the nut,' N, 
 which, after adjustment, is 
 fastened securely in such 
 position. 
 
 At the power plant of 
 The Niagara Falls Power 
 Company a thrust or hang- 
 ing bearing of this disc 
 type, somewhat similar to 
 Fig. 179, is used (See Fig. 
 180). In this bearing the 
 shaft is suspended to a 
 revolving disc carried on 
 a stationary disc. The 
 
 Fig 178. Vertical Suspension Ball Bear- discs are of close-grained 
 
 i ng .* charcoal iron of 25,000 
 
 pounds tensile strength 
 
 and of 14" inside, 34" outside diameter. The lower or fixed disk is 
 dowelled to a third disk with a spherical (3' 4" radius) seat. This 
 
 *Wasserkraftmaschinen von L. Quantz. 
 
2 9 2 
 
 Turbine Details and Appurtenances. 
 
 is to provide for an automatic adjustment for slight deviations from 
 the vertical due to uneven wear of the discs and other causes. 
 
 The bearing surfaces between the discs are grooved to allow a 
 circulation and distribution of the oil over the surface. 
 
 Three methods of lubri- 
 cation, forced, self, and 
 a combination system, 
 were experimented with 
 and the combination sys- 
 tem finally adopted. In 
 the system of forced lub- 
 rication, the oil enters the 
 fixed disc at two diamet- 
 rically opposite points and 
 is forced between the discs 
 under 400 pounds pres- 
 sure. Self-lubrication is 
 accomplished by oil sup- 
 plied at the inner circum- 
 ference of the disc and 
 thrown outward by cen- 
 trifugal force. 
 
 The disc bearings are 
 
 enclosed in a case provided with sight holes through which the 
 condition of the bearing as well as the temperature of the oil can 
 be observed. A thermometer and an incandescent light are sus- 
 pended in the casing for this purpose. The oil is cooled by water 
 circulating pipes inside the casing. 
 
 The shaft is provided with a balancing piston (see Fig. 181) 
 supplied with water from a pipe entirely independent of the pen- 
 stock and under a head of 136 feet. This piston carries the greater 
 part of the load, less than 2 per cent, of the load being left to be 
 carried by the oil-lubricated disc bearing described above. 
 
 143. Horizontal Turbine Bearings. In horizontal wheels vari- 
 ous forms of bearing may be used according to the conditions and 
 circumstances of their operation. When practicable the bearings 
 should not be submerged and should otherwise be made as accessi- 
 ble as possible. In such cases the forms of bearings may be the 
 same as those used on other machines subject to similar strains. 
 
 Fig. 
 
 179. Vertical Suspension 
 sure Bearing.* 
 
 Pres- 
 
 * Wasserkraftmaschinen von L. Quantz. 
 
Horizontal Turbine Bearings. 
 
 293 
 
 In many horizontal American wheels, where submerged bearings 
 are necessary, lignum vitae bearings are used similar in type to the 
 upper vertical bearing before mentioned (see T', Figs. 145 and 147). 
 Such a bearing is shown in detail in Fig. 182. In this bearing the 
 shaft, S, is sustained in position by the blocks, TT, which fit the 
 
 For Elecfr*. 
 V/ires 
 
 Thrust Girder 
 Section through Ball Disk Oil Inlet 
 
 OH Catcher 
 Section through Oil Sight Hole. 
 
 Fig. 180. Vertical Thrust or Hanging Bearing of the Ni- 
 agara Falls Power Co. (See Eng. Record, Nov. 28, 1903.) 
 
 recesses of the cast iron bearing block, K, which in turn is attached 
 to a cross tie in the case or to a pedestal, P. The blocks, TT, are 
 adjusted by means of the screws, BB, which, after adjustment 
 are locked in position by the lock nuts, LL. Such submerged 
 bearings are sometimes lubricated by water only, in which case op- 
 
294 
 
 Turbine Details and Appurtenances. 
 
 portunity must be given for the free circulation of the water. In 
 other cases the boxes are made tight and flow into them along the 
 shaft is prevented by stuffing boxes at each end of the main box, 
 
 the boxes being lubricated 
 by forced , grease lubrica- 
 tion. 
 
 Bronze boxes of the types 
 used for other high grade 
 machines are sometimes 
 used for submerged bear- 
 ings. In such cases great 
 care is necessary to pre- 
 vent the entrance of grit- 
 bearing waters. Such 
 bearings are lubricated by 
 forced oil or. grease. 
 
 In forced lubrication it 
 is desirable that both a 
 force and return pipe be 
 used so as to give visible 
 evidence that- the lubri- 
 cant is actually reaching 
 the bearing. In some 
 
 Fig. 181. Section of Turbine used in new 
 Power House of The Niagara Falls Power 
 Company, showing Balancing Hydraulic 
 Position used to sustain Turbine and Shaft. 
 (Eng. Record, Nov. 28, 1903.) 
 
 cases bearings that would 
 be otherwise submerged 
 are made accessible at all 
 times by metallic tubes 
 (see Fig. 322) used as 
 manholes. 
 
 Where the turbine is placed horizontally, gravity can no longer 
 offset the thrust caused by the reaction of the turbine when the 
 discharge is in one direction, and the thrust must therefore be over- 
 come by the use of some form of thrust-bearing. Where other con- 
 ditions permit, it is quite common practice to install two turbines 
 on a single horizontal shaft, having their discharges in opposite di- 
 rections, in which case the thrust of each turbine is overcome by 
 the thrust of its companion (see Figs. 153, 160 and 316). In many 
 cases, however, the arrangement, size and capacity of the wheels 
 to be used are not such as will permit the use of twin turbines and 
 thrust-bearing, and other means of taking up the thrust must be 
 provided. 
 
Horizontal Turbine Bearings. 
 
 295 
 
 144. Thrust-Bearing in Snoqualmie Falls Turbine. In the Sno 
 qualmie Falls Turbine, manufactured by The Platt Iron Works 
 Company (see Figs. 161 and 162), the device for taking up the 
 thrust is thus described by the designing engineer, Mr. A. Giesler:* 
 
 "Single-wheel horizontal-shaft units are relatively infrequent in 
 turbine practice, especially in large sizes, where the thrust of a sin- 
 gle runner is large enough to require careful consideration. The 
 thrust is made of two parts : (I) that due to the static pressure or 
 effective head of water at the various points of the runner surface ; 
 .and (2) that due to the deflection of the water from a purely radial 
 
 B 
 
 Fig. 182. Horizontal- Lignum Vitae Bearing as Used in American Turbines. 
 
 path through the wheel. As concerns the first part, the front face 
 of the wheel is pressed upon by a pressure varying from the supply 
 head at the outer circumference to the discharge pressure (vacuum) 
 at the inner edge of the vanes, which latter extends over the whole 
 central area of the runner (and shaft extension). The rear face of 
 the runner is subjected to the pressure of water leaking through 
 the radial air-gap between casing and runner, substantially equal to 
 the supply head. This greatly overbalances the pressure on the 
 front face, and the resultant thrust is\to the right in Fig. 161 (to- 
 ward the draft tube). The. discharge ends of the vanes, being 
 :urved transversely, also havfe a pressure component directed to- 
 
 * See "Engineering News" of March 29, 1906. 
 
296 
 
 Turbine Details and Appurtenances. 
 
 ward the right. The velocity effect produces a thrust directed to- 
 ward the left, but this is very small and does not materially reduce 
 the pressure thrust. 
 
 "By far the larger part of the pressure thrust is eliminated by 
 venting the space back of the runner into the discharge space. Six 
 holes through the wheel near the shaft, indicated in Fig. 161, have 
 this function. The water leaking in through the air-gap is continu- 
 ously discharged through these vents into the draft-tube, and the 
 accumulation of any large static pressure back of the wheel is 
 thereby avoided. 
 
 "The average pressure on the front of the runner, however, is 
 always lower, and the resultant thrust is therefore toward the draft- 
 
 f *- * 
 
 Cross Section. Longitudinal Section* 
 
 Fig. 183. Thrust-Bearing Snoqualmie Wheels. 
 
 tube, though its amount varies considerably, being greatest for full 
 gate opening. This thrust is taken up by the balancing piston im- 
 mediately back of the rear head of the wheel case, and the ultimate 
 balance and adjustment of position is accomplished by the collar 
 thrust-bearing behind the balancing piston. 
 
 "The balancing piston is a forged enlargement of the shaft, fin- 
 ished to a diameter of 17 inches, which works in a brass sleeve set 
 in a hub-like projection on the back of the wheel-housing. The in- 
 side of the sleeve has six circumferential grooves, each one inch wide 
 and one-quarter inch deep, as water packing. The chamber in front 
 of the piston communicates by a pipe (containing a strainer) with 
 the supply casing of the water-wheel, and therefore receives the 
 full pressure of the supply head. The chamber back of the piston 
 
Thrust-Bearing in Snoqualmie Falls Turbine. 297 
 
 is drained to the draft-tube, so as to carry off any leakage past the 
 piston. The device thus produces a constant thrust on the piston, 
 directed toward the left. By throttling the pressure pipe this 
 thrust can be adjusted as desired. 
 
 "The thrust-bearing shown in Fig. 161 and in detail in Fig. 183 
 consists of a group of four collars on the shaft, working in a babbit- 
 ted thrust-block which is bolted to the back of the wheel-housing. 
 The collars are formed on a steel sleeve which fits over the shaft 
 and is bolted to the rear face of the balancing piston ; this makes 
 it possible, when the collars are worn out, to renew the bearing by 
 dismounting the thrust-block and placing a new sleeve. The 
 thrust-bearing is lubricated by oil immersion. An oil chamber is 
 cored in the block and communicates by numerous oil holes with 
 the bearing faces ; a constant flow of oil is maintained by means of 
 oil-supply and drain-pipes. Concentric with the oil chamber and 
 outside of it a water chamber is cored in the block. Cooling water 
 is supplied to this chamber by a pipe from the pressure side of the 
 turbine, and drains from the top of the bearing through a drain-pipe 
 to the draft-tube. A U-pipe attached at one side of the bearing forms 
 connection between the water chambers of the upper and lower 
 halves of the block. This detail avoids making the connection by a 
 hole through the joint face, which would allow leakage of water 
 into the oil-space and into the bearing. 
 
 "The balancing piston is so proportioned and the pressure supply 
 pipe is throttled to such a point as to give exact balance (i. e., with 
 zero thrust in the thrust-bearing) at about half to five-eighths the 
 full output of the wheel. At larger power there will be an unbal- 
 anced thrust to the right, and at smaller output to the left, which 
 are taken by the thrust-bearings. The maximum thrust on the 
 collars is about 25,000 Ibs. The collars are 2i/ 2 inches high (2% 
 .inches effective) by 131/2 inches mean diameter, giving a total effec- 
 tive bearing area on four collars of 418 sq. inches. The maximum 
 collar pressure is thus about 60 Ibs. per sq. in." 
 
 145. The Chute Case. The chute case (see Figs. 146, 147 and .184) 
 consists of the fixed portion of the turbine to which are attached 
 the step and bearings of the wheel (T), the guide passages (g) 
 which direct the passage of the water into the turbine bucket, and 
 the gates (G) which control the entrance of the water, and also 
 the case cover (C). The case cover keeps the wheel from contact 
 18 
 
298 
 
 Turbine Details and Appurtenances. 
 
 with the water except as it passes through the guide and gates. To 
 the chute case is usually attached the apparatus and mechanism for 
 manipulating or controlling the position and opening of the gate. 
 (A. P, Gr., etc.) In vertical turbines a tube, d, is usually attached 
 to the lower ring, forming a casing in which the lower portion of 
 the turbine revolves and on which the bridge tree, t, holding the 
 
 step bearing is attached. 
 When this tube is no long- 
 er than one diameter it is 
 usually called the turbine 
 tube; but when it is con- 
 siderably extended, it is 
 termed a draft tube. 
 
 The design of the tur- 
 bine tube depends largely 
 on the character of the 
 wheel. Some wheels dis- 
 charge downward and in- 
 ward, some almost entire- 
 ly downward, some down- 
 ward and outward, and in 
 some cases, the wheel dis- 
 charges in all three direc- 
 tions. For the best re- 
 sults the tube should be 
 so designed that the water 
 from the wheel shall be 
 received by it with no 
 radical change of velocity 
 and so that the remaining 
 velocity will be gradually 
 reduced and the water 
 discharged at the lowest 
 practicable velocity. 
 
 The chute case and its appurtenances should be so designed that 
 the water will enter the bucket with the least possible shock or re- 
 sistance at all stages of gate and with a gradual change in velocity, 
 and will discharge from the buckets into the turbine tube with as 
 little eddying as possible and be evenly distributed over the cross 
 section of the tube so as to utilize the suction action of an unbroken 
 column of water. The case must also be designed of sufficient 
 
 Fis. 184. 
 
The Chute Case. 
 
 299 
 
 Fig. 185. Section Swain Turbine. 
 
 strength to sustain the weight of the turbine wheel and so that the 
 step bearings are accessible and can be readily replaced or adjusted. 
 The arrangement of the case must also be such that the openings 
 between the wheel and the case are as small as practicable and the 
 
 line of possible leakage 
 will be as indirect as pos- 
 sible so as to avoid leak- 
 age loss. 
 
 Most chute cases are 
 either cast or wrought 
 iron. Cast iron usually 
 lends itself to a more sat- 
 isfactory design for receiv- 
 ing and passing* the water 
 without sudden enlarge- 
 ment and opportunities 
 for losses by sharp angles 
 and irregular passageways. 
 Wrought iron, while not 
 always lending itself read- 
 ily to designs which elim- 
 inate all such losses, possesses much greater strength for a given 
 weight which is a great advantage under some conditions. 
 
 146. Turbine Gates. Three forms of gates are in common use 
 for controlling the admission of water into reaction turbines. The 
 cylinder gate consists of a cylinder closely fitting the guide that 
 by its position admits or restricts the flow of water into the buck- 
 ets. Fig. 184 is a section of a turbine of the McCormick type, 
 manufactured by the Wellman-Seaver-Morgan Company, having 
 a gate of this type, GG, between the guides and runners, which is 
 shown closed in the cut. The gate is operated by the gearing, Gr., 
 which raises it into the dome, O, through connection with the gov- 
 ernor shaft, P. This same type of gate is used over the discharge 
 of the Niagara- Fourneyron turbine (see GG, Fig. 134), over the 
 inlet of the Geylin-Jonval turbine, GG, Figs. 135 and 137, and be- 
 tween the guides and buckets of the Niagara turbine, shown in 
 Fig. 101. 
 
 A modified form of the cylinder gate is that used by the Swain 
 'Turbine Company (see Fig. 185), which is lowered instead of being 
 raised into the dome as in Fig. 184. 
 
3 
 
 Turbine Details and Appurtenances. 
 
 A similar modification, called a sleeve gate by its designer, J. W. 
 Taylor, is shown in Fig. 186. 
 
 When partially closed the cylinder gate causes a sudden contrac- 
 tion in the vein of water which is again suddenly enlarged in enter- 
 ing the runner after opening the gate. (See Fig. 188.) These con- 
 ditions produce eddying which results in decreased efficiency at 
 part gate. (See Figs. 185 and 186.) 
 
 The wicket gate, when well 
 made, is perhaps the most satisfac- 
 tory gate, especially for moderate 
 or high heads. It can be readily 
 balanced and should be made with 
 perhaps a tendency to drift shut, 
 so that should the governor mech- 
 anism break or become disabled, 
 the gates will drift shut. These 
 gates are illustrated by GG, 
 Figs. 147 and 148, which illustrate 
 the wicket gate of the Samson 
 turbine of The James Leffel & 
 Company, and Fig. 187 which 
 shows the wicket gate of the Well- 
 man-Seaver-Morgan Company. 
 In both cases the wickets are con- 
 nected by rods with the eccentric 
 circle and through an arm and 
 section with the gearing Gr. 
 
 Figs. 145 and 146 show the wick- 
 et gate of the Improved New 
 American, and Figs. 161 and 162 
 show the wicket gates of the Sno- 
 qualmie Falls turbine, manufact- 
 ured by The Platt Iron Works. - 
 In both the New American and 
 Fig. 186. Section Taylor Sleeve Snoqualmie wheels, the gates are 
 Gate - moved by a gate ring (see Gr. 
 
 Fig. 145). Figs. 189 and 190 show 
 
 the details of the wicket gates and connection of the same to the 
 gate ring of the Snoqualmie Falls Turbine. 
 
 The tendency to produce eddying is much reduced in well de- 
 signed wicket gates, although the sudden enlargement of the re- 
 
Turbine Gates. 
 
 301 
 
 duced vein at part gate undoubtedly reduces the efficiency of the 
 wheel. (See Fig. 191, A and B.) 
 
 The register gate (see G, Fig. 192) consists of a cylinder case 
 with apertures to correspond with the apertures in the guides, g, 
 and is so arranged that, when in proper position, the apertures reg- 
 ister and freely admit the water to the wheel, and is also so con- 
 structed that when properly turned the gate cuts off the passage 
 completely or partially as desired. 
 
 Considerable eddying is produced by the partially closed reg- 
 ister gate, with a consequent decrease in part gate efficiency. (See 
 
 Fig. 193.) The cylinder 
 gate is usually the cheapest 
 and most simple form of 
 gate, but the wicket gate, 
 if properly designed and 
 constructed seems to ad- 
 mit of the entrance of 
 water into the bucket with 
 least possible resistance 
 and eddying, and in the 
 most efficient manner. 
 This form of gate is the 
 most widely used in high- 
 grade turbine construc- 
 tion at the present time, 
 although the cylinder gate 
 is 'largely in use and has 
 given satisfactory results. 
 In some cases the pas- 
 sage of water is restricted 
 or throttled by the use of 
 
 a butterfly valve, either in the inlet or in the turbine tube. This 
 throttles the inlet or discharge and regulates the head in a very 
 inefficient manner, but may be reasonably satisfactory where econ- 
 omy of water is unnecessary. 
 
 In impulse wheels the gates are usually so arranged that the 
 guide passages are opened one at a time instead of all opening par- 
 tially, as in part gate conditions with the reaction wheel. This re- 
 sults in less loss in the eddyings caused by part gate. Fig. 194 
 shows the type of gate used by The Platt Iron Works in their Gir- 
 
 Fig. 
 
 187. Wicket Gate of the Wellman- 
 Seaver Morgan Co. 
 
302 
 
 Turbine Details and Appurtenances. 
 
 ard turbines where the guide passages are arranged symmetrically 
 in three groups about the wheel. In the tangential wheel, where 
 a single nozzle is used, the most efficient method found for redu- 
 cing the opening is with the needle as illustrated in Fig. 195. This 
 figure shows a cross section of +he Doble needle nozzle, a form 
 which gives a high velocity coefficient under a very wide range of 
 opening. The character of the stream from a needle nozzle when 
 
 greatly reduced is shown by Fig. 
 196 where the clear and solid 
 stream gives evidence of high effi- 
 ciency. If the flow of water 
 through the nozzle is regulated by 
 throttling the water with a valve 
 before it reaches the nozzle, a 
 very low efficiency results. 
 
 147. The Draft Tube. The re- 
 action wheel is of particular ad- 
 vantage under low heads on ac- 
 count of the fact that it can run 
 efficiently under water, and there- 
 fore, under backwater conditions, 
 can be made to utilize the full head 
 available. It is not necessary, 
 however, to set the reaction wheel 
 low enough so that it will be below 
 water at all times for the principle 
 of the suction pipe can be utilized 
 and the wheel set at any reason- 
 able ^distance above the tail water 
 and connected thereto by a draft 
 tube which, if properly arranged, 
 
 will permit the utilization of the full head by action of the draft 
 or suction pull exerted on the* wheel by the water leaving the 
 turbine through the tube from which all air has been exhausted. 
 The water issuing from the turbine into a draft tube, which at the 
 starting is full of air, takes up the air in passing and soon estab- 
 lishes the vacuum necessary for the draft tube effects. The func- 
 tion of the draft tube is not only to enable the turbine to utilize 
 by suction that part of the fall from the wheel discharge to the tail 
 water level, but it should also gradually increase in diameter so as 
 
 Fig. 188. Showing Cylinder Gate 
 Partially Open and Eddies Caused 
 by Sudden Contraction and En- 
 largement of Entering Vein of 
 Water. 
 
Turbine Gates. 
 
 303 
 
 Section A-B. 
 
 ;-*^jf 
 
 it**? 3 -* 
 
 Fig. 189. Showing Relations of Gate Guides and Buckets in Snoqualmie 
 Falls Turbine (Platt Iron Works Co.). 
 
 Gate Arm 
 
 Cover Ring *_ 
 
 f/r^/%^ 
 
 '&zfe Operating 
 Ring 
 
 ^<&/%yy2r ' 
 
 w fro.m Governor Ar/n> 
 
 ''Operating Pin oj 2 Operating Pin Brackets 1 
 " ' Screwd to Gate Operating 
 ffing; I80apart, 
 
 Section A-B. 
 ^ 
 
 Fig. 190. Showing Rigging for the Operation of Wicket Gate in Snoqualmie 
 Falls Turbine (Platt Iron Works Co.). 
 
304 
 
 Turbine Details and Appurtenances. 
 
 A. Gate wide open. B. Partial gate. 
 
 Fig. 191. Showing Condition of Flow Through Open and Partially Closed 
 
 Wicket Gates. 
 
 to gradually decrease the 
 velocity of the water after 
 it is discharged from the 
 turbine wheel, thus enab- 
 ling the turbine to utilize 
 as much as possible of the 
 velocity head with which 
 the water leaves the tur- 
 bine. It should be noted 
 that a partial vacuum is 
 established in the draft 
 tube and, therefore, the 
 draft tube must be strong 
 enough to stand the exte 
 rior pressure due to the 
 vacuum so created. In or- 
 der to perform its functions 
 Iron .. ,. e 
 
 in a more satisfactory man- 
 ner, it must also be made 
 perfectly air tight. 
 
 One of the great advantages in the use of the draft tube is the 
 possibility, by its use, of setting the wheel at such an elevation 
 
 Fig. 
 
 192. Register Gate 
 Works Co.). 
 
 (Platt 
 
Turbine Gates. 
 
 305 
 
 above the tail water that the wheel and its parts can be properly 
 inspected, by draining the water from the wheel pit. Otherwise it 
 would be necessary to install gates in the tail race and pumps for 
 pumping out the pit in order to make the wheel accessible. The- 
 oretically, the draft tube can be used of as great length as the suc- 
 tion pipe of a pump, and this is probably true of draft tubes for 
 
 very small wheels. Practically, the 
 draft tube should seldom be as 
 long as 20 feet, especially for large 
 wheels, for its success in the util- 
 ization of the head depends on the 
 maintenance of an unbroken col- 
 umn of solid water, which is diffi- 
 cult to maintain in large tubes. As 
 the size of the wheel increases the 
 difficulties of maintaining a vac- 
 uum increase and the length of the 
 draft tube should correspondingly 
 decrease. It is practically impos- 
 sible to maintain a working head 
 with large turbines through long 
 draft tubes with the turbine set at 
 great distances above the water. 
 Long draft tubes should, as a rule, 
 be avoided and in all cases where 
 
 I ^jfij |H J^ draft tubes are used, they should be 
 
 as straight and direct and as nearly 
 vertical as possible. It is the prin- 
 ciple of the draft tube that per- 
 mits horizontal shaft wheels to be 
 utilized, as otherwise, with this 
 
 type of machinery, only a small portion of the head could be used 
 to advantage under normal conditions, for such wheels being often 
 direct connected to the machinery are, of necessity, placed above 
 the tail water. The draft tube is commonly of iron or steel, but in 
 plants where concrete construction is used the draft tube may be 
 formed directly in the concrete of the station or wheel foundations. 
 On the Fourneyron turbine Boyden used what he termed a diffu- 
 ser. (See Fig. 197.) The main purpose of the diffuser, and of the 
 conical tube as well, is to furnish a gradually enlarged passage 
 through which the velocity of the water as it leaves the wheel is 
 
 Fig. 193. Showing Eddying Caused 
 by Partial Closure of Register 
 Gate. 
 
306 
 
 Turbine Details and Appurtenances. 
 
 Fig. 194. Gates and Guides of Girard Impulse Turbine. (Turbine Design 
 as Modified for Close Speed Regulation, G. A. Buvinger, Proc. Am, Soc. 
 M. E., Vol. XXVII.) 
 
 Fig. 195. Cross-section of Doble Needle Nozzle.* 
 
 * From Bulletin No. 6, Abner Doble Co. 
 
The Draft Tube. 
 
 307 
 
 Fig. 196. Stream from Doble Needle Nozzle.* 
 
 so gradually reduced as to 
 enable the velocity head to 
 be utilized in the wheel, 
 thus saving head which 
 would otherwise be lost. 
 It has already been noted 
 that impulse wheels of the 
 Pelton and Girard types 
 cannot operate satisfactor- 
 ily submerged, and must 
 be set at such positions 
 that they will be above the 
 tail water at all times. In 
 many localities where the 
 
 Fig. 197.-Boyden Diffuser. variation in the surface of 
 
 tail waters is considerable, 
 
 this means a large relative loss in the head utilized and that this 
 type of wheel will therefore not be practicable except under high 
 
 ' * From Bulletin No 6, Abner Doble Co. 
 
308 Turbine Details and Appurtenances. 
 
 head conditions and where the loss entailed by the rise and fall of 
 the tail water will be inconsiderable. An attempt has been made, 
 however, to so design a draft tube that a vacuum will be established 
 and maintained below the wheel, in such a manner, however, that 
 the water will not come in contact with the wheel. The vacuum is 
 so maintained as to hold the water at an established point just below 
 the wheel, thus permitting the wheel to utilize the full head except 
 for the small clearance between the wheel and the water surface in 
 the draft tube. This arrangement is shown in Figs. 168 and 171, as 
 applied by The Platt Iron Works Company to a Girard turbine. 
 
CHAPTER XIV 
 
 HYDRAULICS OF THE TURBINE. 
 
 148. Practical Hydraulics of the Turbine. It is not the purpose 
 of this chapter to consider mathematically and at length the princi- 
 ples of hydraulic flow in relation to the curves of guides and buckets 
 and the effects of such curves on the power and efficiency of the tur- 
 bine. These relations are expressed by long and involved equations 
 of considerable interest to the engineer who is to design and con- 
 struct the turbine but of little practical value to the engineer who is 
 to select and install it in a water power plant. Few of the designers 
 of American wheels have given much attention to the involved 
 mathematics of hydraulic flow in the turbine and the designs of 
 most American wheels are based on the results of experiment and 
 broad practical experience. The designs of Swiss and German 
 wheels are, to a much greater extent, based on mathematical 
 analysis. It is an open question whether the best work of either 
 American or foreign manufacture shows any marked superiority 
 in comparison with the other. The results actually attained in the 
 manufacture of wheels in this country seem to show that the 
 American practice in wheel design will give equal and even more 
 uniformly satisfactory results than the European methods, at 
 least as carried out by foreign engineers under American condi- 
 tions. 
 
 Correct theory must be the basis of all successful work. The 
 theory of the experienced man may be unformulated and unex- 
 pressed, but correct design has always a correct theory as its basis 
 even if unrecognized as such, and such a theory properly applied will 
 lead to correct results. On the other hand, formulated theory will 
 lead to correct results only as far as the theory is correct and takes 
 into account all controlling or modifying factors and is properly ap- 
 plied. A correct theory, carefully formulated and properly applied, 
 cannot fail to be of great service to the engineer in extending his 
 experience to wider fields. Scientific study and mathematical an- 
 alysis of the turbine, based on wide experience and careful experi- 
 ments, can but lead to the accomplishment of better results than 
 have vet been attained. 
 
3io Hydraulics of the Turbine. 
 
 An understanding of certain laws of flow through turbines as con- 
 firmed by both theory and practice is essential to a proper compre- 
 hension of the principles which should govern the selection and 
 installation of such wheels and these laws are considered in this 
 chapter. 
 
 149. Nomenclature used in Chapter. In the discussion in this 
 chapter the letters and symbols used have the following signifi- 
 cance: 
 
 a Area of gate orifice or orifices. 
 
 a Angle of deflection of jet. 
 
 ft = Supplement to angle of deflection = 180 a.. 
 
 D = Diameter of wheel in inches. 
 
 E = Energy in foot pounds per second. 
 
 F = Force producing pressure or motion. 
 
 g = Acceleration of gravity. 
 
 h = Effective head at the wheel. 
 
 n = Number of revolutions per minute. 
 
 nj = Number of revolutions per minute for head h^. 
 
 it Ratio of circumference to diameter = 3.1416 
 
 P = Horse powers of turbine at any given head. 
 
 P! = Horse power of turbine at head hj. 
 
 q = Discharge in cubic feet per second at any given head. 
 
 q 1 = Discharge in cubic feet per second at head h x . 
 
 r x = Internal radius of wheel. 
 
 r 2 = External radius of wheel. 
 
 S = Space passed through by force acting. ; 
 
 iij Velocity of wheel at gate entrance. 
 
 u 2 Velocity of wheel at point of discharge. 
 
 v = Theoretical spouting velocity due to head = 
 
 v' = Velocity of the periphery of the impeller, in feet per second. 
 
 v, = Absolute velocity of water entering the wheel. 
 
 v 2 = Absolute velocity of water leaving the wheel. 
 
 v r = Relative velocity of water entering the wheel. 
 
 V R = Relative velocity of water leaving the wheel. 
 
 v a = Average velocity. 
 
 W Total weight per second. 
 
 w = Weight of unit of water = 62.5 Ibs. 
 
 cp = Ratio peripheral velocity of wheel to spouting velocity of water = 
 
 TURBINE CONSTANTS. 
 
 C = Coefficient of discharge of gate orifice or orifices. 
 
 A = Constant relation of turbine diameter and speed. 
 
 K = Constant relation of turbine diameter to discharge. 
 
 K 3 = Constant relation of turbine diameter to power. 
 
 K a = Constant relation of peripheral velocity. 
 
 K 4 = Coefficient of relation of turbine speed and discharge. 
 
 K 6 = Coefficient of relation of turbine power and speed. (Specific speed.) 
 
First Principles. 311 
 
 150. First Principles. In the utilization of water for power pur- 
 poses it is the first principle of design that the water should enter 
 the wheel without shock and leave it without velocity. This should 
 be interpreted to mean that the approaches of the water to the wheel 
 must be such as to cause no loss by undue friction or by sudden con- 
 tractions or enlargements (inducing eddies and other sources of lost 
 energy), and that all shocks should be confined as far as possible to 
 the action on the wheel buckets leaving the full amount of energy, 
 and consequently the velocity, to be entirely converted to power 
 therein. 
 
 In gravity wheels, illustrated by the various overshot wheels for- 
 merly so extensively used for water power purposes, the water 
 sho'tild enter the wheel at the lowest practicable velocity and should 
 be retained in the buckets until the buckets have made the greatest 
 possible descent from the nearest practicable approach to the eleva- 
 tion of head-water, to the nearest practicable approach to the eleva- 
 tion of the tail water. Part of the velocity of approach to the wheel 
 may be utilized by impact on the buckets but the entire energy re- 
 maining in the water as it falls or flows away from the wheel is lost, 
 and cannot be further utilized in the wheel. 
 
 The greater the reduction in velocity, the greater the proportion 
 of energy that can be utilized, but there comes a limit beyond which 
 it is not practicable to go. This limit varies with different condi-> 
 tions and may be the result of too great expense in the building of 
 raceways or in the construction of the machine itself. A point will 
 be reached where the friction expended in the large machine needed 
 to reduce the velocity will consume more energy than would be lost 
 in inducing a higher velocity. These losses must be equalized. In 
 practice it is found that about two or three feet per second are satis- 
 factory velocities at which to reject or discharge the water used by 
 motors. These velocities represent heads of from .062 to ,14 feet, 
 or from three-quarters to slightly less than two inches. The veloc- 
 ity of discharge must, however, be fixed for each individual case and 
 after all conditions are fully understood and considered. 
 
 151. Impulse and Reaction. A jet of water spouting freely from 
 any orifice will acquire a velocity (see Eq. 9, Chap. II). 
 
 (1) v = -/2JpT 
 
 and will possess energy in foot pounds per second (see Eq. 10, 
 Chap. II) as follows: 
 
 Wv 8 
 
3 I2 
 
 Hydraulics of the Turbine. 
 
 The energy of the- jet leaving the orifice is the product of a force, 
 F, which acting on the weight of water, qw, for one second gives it 
 the velocity v. 
 
 The space passed through by the force in one second, in raising 
 the velocity from to v is (see Eq. 6, Chap. II) 
 
 (3) 
 
 S = v a t 
 
 and the work done in foot pounds is therefore 
 (4) E = FS = - 
 
 From Equations 2 and 4 therefore 
 
 Fv _ gwv 2 
 ( 5 ) - 9^r- 
 
 (6) 
 
 and therefore 
 
 F _ qwv 
 g 
 
 The force, F, is exerted, by reaction on the vessel of which the 
 orifice is a part and may produce motion in that vessel if it be free 
 to move, or it may produce motion in another body by impulse 
 through the extinction of the momentum of the jet in impinging 
 against it. 
 
 These equal and opposite forces are well shown: 
 
 ist. By the force required to sustain a hose nozzle against the 
 reaction of a fire stream, and 
 
 2nd. By the force of the jet, from the nozzle so sustained when 
 exerted against any object in its course. 
 
 These conditions are illustrated by Figs. 198 and 199. 
 
 The force, F, which may be exerted by a jet impinging against 
 a surface depends on the momentum of the moving stream of wa- 
 ter and is directly proportional to its velocity. It is also a function 
 
 Fig. 198. 
 
 Fig. 199. 
 
The Impulse Wheel. 
 
 3i3 
 
 of the angle through which the jet is deflected. If friction be ig- 
 nored, the stream will be deflected without change in velocity, and 
 the force exerted against the surface in the original direction of the 
 jet will be equal to the momentum of the original stream less 
 
 Fig. 201. 
 
 Fig. 202. 
 
 Fig. 200. 
 
 the component, in the original direction, of the momentum of the 
 diverted jet. (See Fig. 200). 
 
 (7) 
 
 (1 cos a) 
 
 If the jet impinges against a flat surface (see Fig. 201) 
 a = 90, Cos a and 
 
 If the jet is deflected 180 by means of a semi-circular bucket 
 (see Fig. 202) 
 
 Cos 180 = 1, and therefore 
 
 >) - * = ^ 
 
 152. The Impulse Wheel. Impulse water wheels utilize the im- 
 pulsive force of a jet impinging against buckets attached to the 
 circumference of the wheel. The bucket must move under the 
 impulse in order to transform the energy of impact into work and 
 the ratio of v', the velocity of the periphery of wheel, to the velocity 
 v of the jet is indicated by # 4f 
 
 (10) 
 
 tp = and v ' = q> v 
 
 19 
 
314 
 
 Hydraulics of the Turbine. 
 
 In determining the force, F, exerted upon the moving bucket, the 
 relative instead of the actual velocity of the jet must be considered 
 
 and it is readily seen that the 
 value of the relative velocity v r 
 will be as follows: 
 
 (11) 
 
 v r = v <? v = (1 
 
 The relative weight of water 
 that strikes a single bucket per 
 second will also be less on ac- 
 count of the movement of the 
 buckets, but as. new buckets con- 
 stantly intercept the path of the 
 jet the total amount of water 
 
 effective is equal to the total discharge of the jet. Hence from 
 
 equations (7 and 11) 
 
 Fi 
 
 (12) 
 
 F = (1 cos a) 
 
 (1 <p) 
 
 The work done upon the buckets per second is equal to the force, 
 F, times the distance < v through which it acts, i. e. 
 
 (13) 
 
 E = 
 
 = (1 cos a) (1 
 
 is a maximum the solution 
 
 This is a maximum when (1 < 
 of which gives # = .5 
 
 Substituting 4> = .$ and a =180, in equation (13), there is ob- 
 tained 
 
 (14) 
 
 E = 
 
 q wv- 
 
 That is, E equals the entire energy of the jet (see equation 2), and 
 hence the theoretical efficiency when (=0.5 is 100 per cent. 
 
 Another criterion for maximum efficiency is that the absolute 
 velocity of the water in leaving the bucket must be zero. 
 
 When a =180, the absolute velocity with which the water 
 leaves the bucket is evidently the velocity relative to the bucket 
 minus the velocity of the bucket or 
 
 (15) v 
 
 This gives 
 
 = (1 <p) v (pv = v 2<p v = 
 
Effect of Angle of Discharge on Efficiency. 315 
 
 153. Effect of Angle of Discharge on Efficiency. In an impulse 
 wheel it is not practicable to change the direction of the water 
 through 180 as it would then interfere with the succeeding bucket. 
 a must hence be less than 180 and the absolute velocity of the 
 water in leaving the buckets cannot be zero. The loss from this 
 source is small as a may differ considerably from 180 without 
 much effect on the bucket pressure and hence on the efficiency. 
 For example, the ratio of actual pressure when a is less than 
 1 80 to maximum possible pressure with a =180 is (see Fig. 203). 
 
 (1 cos a) qw (I <p] (1 ~ *) V 
 , A ' ' g 1 cos a _ 1 + cos ft 
 
 If ft = 8, a = 172, and 1 ~ f, S a = .995 
 
 6 
 
 showing only 0.5 per cent, reduction. The effect on the efficiency 
 is in the same ratio. 
 
 Fig. 204 illustrates the flow o'f the water in entering and leaving 
 the bucket with all velocities given relative to that of the bucket. 
 The jet leaves the bucket as shown with a relative velocity of (i <) 
 v. If this velocity is combined graphically with the velocity of 
 the bucket, <v, the true absolute residual velocity V R of the water 
 will be obtained. The efficiency is evidently maximum when < has 
 a value which makes V R a minimum. This condition can readily 
 be shown to maintain when the triangle is isoceles or when 
 
 (17) <p v = (i-<f>) v 
 
 which gives 
 
 (p = 0.5 
 
 as obtained by two other methods and here shown to be indepen- 
 dent of the angle ft. 
 
 The absolute path of the water in space is shown by ABCD Fig. 
 204, and the magnitude of this velocity is shown below in curve EF 
 where ordinates are absolute velocities along the tangent lines to 
 curve ABCD at the point directly above. These curves are based 
 on the assumption that < 0.5 and the bucket is semi-circular in 
 cross s'ection as shown. 
 
 The theoretical considerations thus far discussed are modified by 
 the frictional resistance which the bucket offers to the flow of wa- 
 ter over its surface and by the spreading of the original jet from 
 its semi-circular section to a wide thin layer in leaving the bucket. 
 
Hydraulics of the Turbine. 
 
 Further loss no doubt takes place as a result of the fact that the 
 bucket is in its assumed position at right angles to the direction 
 of the jet only at one instant during its rotation. Upon entering 
 
 D 
 
 Fig. 204. 
 
 and leaving the jet it is inclined considerably to this direction and 
 doubtless operates less efficiently. These conditions result in a 
 much greater drop in efficiency than the above analysis would 
 seem to indicate. 
 
 154. Reaction Wheel The flow of water through the buckets of 
 a reaction wheel is less easily analyzed than in the case of the im- 
 pulse wheel. The chief difference in the two types of wheels arises 
 
Reaction Wheel. 
 
 from the fact that the reaction wheel is "filled" and hence the ve- 
 locity of the water relative to the buckets at any point does not 
 remain constant but varies inversely as the cross sectional area of 
 the passageway. 
 
 The path described by a particle of water in passing through the 
 
 Fig. 205. 
 
 wheel has been investigated by Francis,* by a method based upon 
 the assumption that "every particle of water contained in the 
 wheel, situated at the same distance from the axis, moves in the 
 same direction relative to the radius and with the same velocity." 
 This assumption becomes more accurate as the number of buckets 
 increases. 
 
 Fig. 205 shows the path, resulting from the application of this 
 assumption, of the water through the "Tremont" Fourneyron wheel 
 and Fig. 206, through the center vent wheel a.t the Boott Cotton 
 Mills. The former indicates, since the jet of water is carried for- 
 ward in the direction of rotation, that the water resists the rota- 
 
 Fig. 206. 
 
 * See "Lowell Hydraulic Experiments," p. 39. 
 
Hydraulics of the Turbine. 
 
 Fig. 207. 
 
 tion of the wheel until nearly to the circumference when it is sud- 
 denly deflected and leaves the wheel, as it should, in a direction 
 nearly normal to the wheel. 
 
 The jet of water in the Boott wheel (Fig. 206), on the other 
 hand, shows a continual backward deflection of its path from the 
 
 point where it leaves the guides, and 
 hence a continual delivery of its 
 energy to the wheel. This seems to 
 indicate a more logical condition and 
 . a better shaped bucket than that of 
 the Fourneyron. It will be noted 
 that the actual path of the water in 
 this case is very similar to that in the 
 impulse wheel shown in Fig. 204. 
 
 For the economical operation of 
 the reaction wheel the following 
 principles must be observed: 
 
 I St. In order that the jet of water may enter the wheel without 
 shock the resultant of the velocity of the water as it leaves the 
 guides and the velocity of the periphery of the runner must have 
 a direction parallel to the bucket blades at this point, and a mag 
 nitude equal to that which will produce the required discharge 
 through the cross sectional area of the passageway. 
 
 2nd. The relative velocity of the bucket and of the water relative 
 to the bucket at the point of discharge must be such that the water 
 leaves the buckets with the minimum practicable absolute velocity. 
 3rd. Such residual velocity as may remain in the discharging wa- 
 ter must be conserved and utilized as far as practicable by the 
 proper arrangement of the draft tube. 
 
 4th. In all wheels it is also essential by proper design to reduce 
 losses from friction, eddying, etc., as greatly as possible. 
 
 The first requirement is illustrated in Fig. 207 where AB is one 
 of the runner buckets of an outward flow wheel. The guides, AC, 
 direct the water into the buckets with an absolute velocity, v 2 . The 
 velocity of the runner at point A, where the water enters, is u 2 . 
 The two velocities combined graphically give a resultant, v r , which 
 must be tangent to the curve of the bucket and equal to 
 
 (18) v 9.2 where 
 
 * Q 
 
 
 q 3 = required discharge through the passageway, and 
 
 a 2 = area of cross section of the passageway at point of entrance, A. 
 
Reaction Wheel. 319 
 
 This requirement does not enter into the design of an impulse 
 wheel since the jet impinges against the edge of the wedge-shaped 
 partition in the bucket always in a direction tangent to the bucket 
 curve at that point regardless of the relative speeds of runner and 
 jet. Further, since the discharge is "free" and the buckets not 
 "rilled," no sudden change of velocity occurs. 
 
 The effect of part gate conditions upon the first requirement de- 
 pends upon the type of speed gate and may best be studied from 
 Figs. 188, 191, 193 and 207. A change in either direction or mag- 
 nitude of v l will change v r unless the two effects tend to neutralize 
 which may happen in some instances. In all reaction wheels the 
 velocity of inflow, v 15 through the guides is increased by partly 
 closing the gate, while the velocity, Ui, of the wheel remain un- 
 changed. v r will therefore change, and a change in either its direc- 
 tion or magnitude will produce an impact or sudden enlargement 
 respectively- as the water enters the runner, and therefore a loss, 
 unless the direction of the guides is changed to correspond. 
 
 The wicket gate, when carefully designed, has given rise to part 
 gate efficiencies more nearly approaching those of impulse wheels 
 than with gates of any other type (see Figs. 131 and 236). 
 
 The second requirement, that of minimum residual velocity of 
 the water in leaving the buckets, is shown graphically in Fig. 207. 
 VR is the velocity of discharge of the water relative to the bucket 
 and is, of course, tangent to the curve of the bucket. u 2 is the 
 peripheral velocity of the runner. The resultant of two velocities 
 is the absolute velocity with which the water is discharged from the 
 wheel, and is shown in magnitude and direction by line v 2 . Now, at 
 part gate the quantity of water discharged is less than that at full 
 gate and hence VR must also be less since the cross section of the 
 passage must be filled. u 2 remains unchanged and hence the resul- 
 tant v 2 will be increased with a corresponding waste of energy and 
 loss in efficiency. This is an unavoidable loss in a wheel operating 
 under part load and makes it impossible to maintain full efficiency of 
 operation by any design whatever of the regulating gates. This 
 loss does not appear in the impulse wheel since the velocity with 
 which the water leaves the bucket is theoretically at least not in- 
 fluenced by the quantity. 
 
 The third requirement is partially satisfied by gradually expand- 
 ing the draft tube from the wheel to the point of discharge. This 
 will recover only the component of the residual velocity in the axial 
 
320 
 
 Hydraulics of the Turbine. 
 
 direction. The larger component of the residual velocity however 
 tends to produce a rotation of the water column in. the draft tube, 
 and is not recovered by any present design. 
 The fourth requirement is evident. 
 
 L.3 
 
 Figs. 208-209. Reaction Wheel with Concrete Draft Tube.* 
 
 100 
 
 TOTAL AVAILABLE ENERGY 
 
 ENTRANCE .GATES 
 
 Fig. 210. Graphical Relation of Velocity and Energy in the Flow Through 
 
 a Reaction Turbine with Draft Tube. 
 * Turbinen and Turbinenanlagen, Viktor Gelpke-, page 61. 
 
Energy Transformation, Reaction Turbine. 321 
 
 155. Graphical Relation of Energy and Velocity in Reaction Tur- 
 bine. The relations of the changes in velocity and in energy in the 
 passage of water through a reaction turbine and its draft tube are 
 graphically shown in Fig. 210.. 
 
 Fig. 208 shows the cross section of a radial inward flow reaction 
 turbine with a concrete draft tube. The cross sections of the draft 
 tubes at various points are shown in Fig. 209 from which it will 
 be seen that the draft tube of this turbine gradually changes form 
 and increases in cross section in order that the velocity of flow may 
 be gradually decreased from the point of discharge of the turbine 
 to the end of the draft tube. 
 
 The changes in absolute velocity in the passage of water into and 
 through the turbine and draft tube are shown by line V, V x , V 2 , V 4 , 
 V 5 ; the height of the ordinates at these points shows the approxi- 
 mate absolute velocities at such points in the flow. The absolute 
 velocity is a maximum at or near the point where the water enters 
 the runner and is decreased as greatly as possible at the point of 
 its discharge into the draft tube. By gradually increasing the area 
 of the draft tube, an additional reduction in velocity is obtained, 
 the water finally issuing with a velocity V 5 . The maximum veloc- 
 ity, measured by the ordinate V 2 , is, in reaction wheels, consider- 
 ably below the spouting velocity (i/2gh) 
 
 In its flow through the wheel, the velocity of the water relative 
 to the bucket increases and becomes a maximum at the outlet of 
 the wheel. This increase in relative velocity is shown by the line 
 V,, V.. 
 
 The energy transformation which takes place during the change 
 in velocity is illustrated by the dotted line marked "Energy trans- 
 formation" which begins at a maximum of 100 per cent, at the en- 
 trance of the wheel ; is decreased by friction, leakage, shocks, etc., 
 by about 16 per cent, under full gate conditions. The energy is 
 transformed into useful work in the wheel by the reaction at the 
 point of discharge and utilizes about 80 per cent, of such energy, 
 the remaining 4 per cent, being rejected in the discharge from the 
 draft tube with a slight recovery of velocity energy as before de- 
 scribed. 
 
 156. Turbine Relations. In all water wheels the quantity of dis- 
 charge, the power, speed, efficiency and effective head on the wheel 
 are closely related and vary in accordance with certain definite laws 
 modified by the design of the turbine and the conditions under 
 
322 
 
 Hydraulics of the Turbine. 
 
 which it is operated. The conditions of operation must be adapted 
 to the type of machinery used, or the machinery must be selected in 
 accordance with the conditions under which it must operate, in or- 
 der that the best results may be attained. 
 
 If a jet or stream of water, with a velocity, v, acts on the moving 
 surface of a motor bucket, this bucket, if the friction of the wheel is 
 negligible, may acquire a velocity essentially equal to that of the 
 jet, i. e., to the theoretical velocity due to the head. In actual prac- 
 tice the velocity of the bucket will always be less by the amount of 
 velocity lost in overcoming the friction of the wheel. The velocity 
 of the wheel here considered must be measured at the center of ap- 
 plication of the forces, i. e., at the point of application of the result- 
 ant of all the forces of all the filaments of water that act on the 
 wheel. Under conditions where the resultant velocity of water and 
 bucket are the same, it is evident that the water will produce no 
 pressure o-n the bucket and the motor can deliver no power. As 
 soon as resistance occurs, the speed of the wheel is reduced. Under 
 reduced speed the momentum of the jet, or the reactive pressure of 
 the water, according to the circumstances of design, is converted 
 into power. This impact or pressure increases as the speed or ve- 
 locity of the bucket decreases until the maximum impact or pres- 
 sure results with the bucket at rest, in which case also no work is 
 done. At some speed, therefore, between these extremes the maxi- 
 
 90 
 
 BP 
 
 30 
 
 80 80 100 
 
 REVOLUTIONS PER MINUTE 
 
 140 
 
 Fig. 211. Efficiency Speed Curves of a 48" "Victor Turbine." 
 
Turbine Relations. 
 
 323 
 
 & 
 
 II 
 
 IS , 
 Ip 2 
 
 < , 
 
 
 
 \ 
 
 *-* 
 
 
 
 
 
 \\ 
 
 o or 
 
 hU 
 
 o $ 
 
 > ft 
 
 a: ^ 
 P 
 
 o 
 
 000000 
 ^ C4 O CD (O * 
 
 QV2H 100J fJ331ti!HJ. d3QNR b3A\Od 3SUOH 
 
324 Hydraulics of the Turbine. 
 
 mum amount of work, from a given motor, will be obtained. That 
 is to say, at a certain fixed speed the maximum work and the maxi- 
 mum efficiency of a given wheel will be obtained, and at any speed 
 below or above this speed, the power and efficiency of the wheel 
 will be reduced. These conditions vary considerably according to 
 the type and design of the wheel considered and also according to 
 the gate opening at which the wheel may be operated. 
 
 The efficiency curves of a 48" Victor turbine, under a thirteen 
 foot head and under various conditions of gate, are shown in Fig. 
 211. Fig. 212 shows the <-power cttrve of the same wheel under 
 the same conditions of head and gates. 
 
 157. Relation of Turbine Speed to Diameter and Head. The 
 velocity of the periphery of the impeller or buckets of a wheel is 
 not necessarily and in fact is not usually the same as the velocity of 
 the point of application of the resultant of the forces applied to the 
 wheel. This point may be at some considerable distance within the 
 wheel and at a point not easily determined. This point of applica- 
 tion of the resultant forces may vary in position with the gate open- 
 ing. The peripheral diameter is fixed and is therefore more conve- 
 nient for consideration than the point of application of the forces. 
 The peripheral diameter, or the catalogued diameter, is therefore 
 used in the discussion of the general subject. Many wheels vary in 
 diameter at various points on the periphery (see Fig. 174), and there 
 is no uniform practice among manufacturers in designating such di- 
 ameters so that the diameters used in the following discussion and 
 the functions based thereon are in accordance with the practice of 
 each maker and are therefore not strictly comparative. In this dis- 
 cussion the laws discussed are equally true if based on any actual 
 diameter or any simple function of the same. The diameter chosen 
 simply influences the magnitude of the derived function and not the 
 character. The discussion holds therefore in each case regardless of 
 the method of measurement except for the purpose of comparison 
 between wheels of various makers in which case similar diameters 
 must be used. 
 
 In reaction wheels, the buckets extend from the periphery of the 
 wheel to a point quite near the axis of revolution (see Fig. 128, 
 Diagram I). In such wheels the resultant of the forces applied falls 
 a considerable distance within the circumference of the wheel. In 
 such wheels the peripheral velocity may exceed the velocity of the 
 jet acting on the wheel. In impulse wheels (see Fig. 129, Diagram 
 E) the buckets are small in comparison to the wheel diameter and 
 
Relation of Speed to Diameter and Head. 325 
 
 are located at the periphery; hence, in this class of wheels, the re- 
 sultant of the forces applied lies at or near the periphery, and the 
 peripheral velocity will be less than that of the jet acting on the 
 wheel. 
 
 Taking the velocity of the periphery of the wheel as a function 
 of the velocity due to head, the relations may be expressed by the 
 formula : 
 
 (19) v' = <Pi/2gh~ from which 
 
 v' v' 
 
 (20) <p = 
 
 l/2gh 
 
 The velocity of the periphery of the impeller may be expressed 
 by the following formula : 
 
 _ D*n ._ 3.1416 D n 
 ' 12 x 60 ~ 720 
 
 Combining equations (20) and (21) it follows that: 
 
 3.1416 D n D n 
 
 (22) * = 720xb.025 v / F = - 000543 7^ 
 
 From this may also be written: 
 
 <P ^h" 1841. 6 <?/" 
 
 (23) 
 
 .000543 D D 
 
 As equation (22) is general, it follows that when V~q> is constant: 
 
 D n 
 
 (24) r=* 1841.6 cp = A is constant. 
 
 v n 
 
 If h I, this will reduce to: 
 
 (25) D nj = 1841.6 <p = A 
 
 The catalogue speed, power and discharge of each series of 
 wheels, as given in the catalogues of manufacturers, are usually 
 based on the conditions of maximum efficiency and constant <. 
 
 From the above considerations it follows that in any homogen- 
 eous series of wheels, that is in any series of wheels constructed on 
 uniform lines and with dimensions proportional, the wheels of the 
 series are designed to run at the same relative velocity, and there- 
 fore 
 
 D n D! n t 
 
 ( 26 ) Vb~ ~ I/IT 
 
3 26 
 
 Hydraulics of the Turbine. 
 
 That is to say : In any homogeneous series of turbines the pro- 
 duct of the diameter of any wheel D, and the number of revolutions 
 n } divided by VW will be a constant A provided < remains constant. 
 
 In investigating the values of A and <j> for various makes of 
 wheels, as expressed by the data in the manufacturers' catalogues, 
 it is found that these values vary somewhat for different wheels of 
 a series but are usually practically constant. It will be noted, 
 however, from the efficiency speed curve, shown in Fig. 211, and 
 the <j> power curve, shown in Fig. 212, that the speed, and conse- 
 quently the values of <f> and A, may vary somewhat without materi- 
 ally affecting the efficiency or power of the wheel. 
 
 It should also be noted from Figs. 211 and 212 that if it is de- 
 sired to secure the greatest efficiency and power at part gate, the 
 values of <f> and A for a given wheel must be reduced. Table 
 XXVI gives the values of A and <f> for various American wheels, 
 calculated from the catalogues of the manufacturers. 
 
 TABLE XXVI. 
 
 Showing Relation of Diameter and Speed of Various American Turbines working 
 under Catalogue Conditions. 
 
 _ D n _ v^ = D n 
 
 Vh v 
 
 
 "Worno rf Whool 
 
 L 
 
 ^ 
 
 c/ 
 
 3 
 
 
 
 Min. 
 
 Max. 
 
 Min. 
 
 Max. 
 
 Reaction Wheels. 
 T. C. Alcott & Son... 
 
 Alcott's Standard 
 High Duty 
 
 1210 
 
 1254 
 
 .658 
 
 .682 
 
 
 Alcott's Special High 
 Duty 
 
 1211 
 
 1253 
 
 .658 
 
 .682 
 
 Alexander, Bradley & 
 Dunning 
 
 Syracuse Turbine 
 
 1203 
 
 1226 
 
 .654 
 
 666 
 
 American Steel Dredge 
 Works 
 
 Little Giant 
 
 1235 
 
 1462 
 
 671 
 
 794 
 
 Camden Water Wheel 
 Works. 
 
 United States Turbine 
 
 1372 
 
 1588 
 
 745 
 
 864 
 
 Chase Turbine Mfg. Co. 
 
 Christiana Machine 
 Co 
 
 *Chase-Jonval Tur- 
 bine (regular) 
 *Chase-Jonval Tur- 
 bine (special) 
 
 Balanced Gate Tur- 
 
 1612 
 1840 
 
 1997 
 2237 
 
 .876 
 .999 
 
 1.084 
 1.2H 
 
 
 bine 
 
 1220 
 
 1298 
 
 .663 
 
 .706 
 
 *NOTE. Wide variation in constants due to the design being special for various sized wheels 
 (series not exactly homogeneous). 
 
Relation of Speed to Diameter and Head. 
 
 327 
 
 TABLE XXVI Continued 
 
 Showing Relation of Diameter and Speed of Various American Turbines working 
 under Catalogue Conditions. 
 
 D n v ' D n 
 
 A = -/== q>= = .000543 7= 
 
 V\\ v Vh 
 
 
 
 t 
 
 S 
 
 <7 
 
 3 
 
 Manufacturer. 
 
 
 Min. 
 
 Max. 
 
 Min. 
 
 Max. 
 
 Reaction Wheel Con. 
 
 Craig Ridgway & Son 
 Co 
 
 Double Perfection 
 
 1186 
 
 1250 
 
 .614 
 
 .679 
 
 Craig Ridgway & Son 
 Co 
 
 Standard 
 
 1200 
 
 1275 
 
 652 
 
 693 
 
 Dayton Globe Iron 
 Works Co 
 
 American Turbine... 
 
 1218 
 
 1295 
 
 .662 
 
 .704 
 
 
 fNew American Tur- 
 bine (high head 
 type) 
 
 1064 
 
 1077 
 
 .578 
 
 .585 
 
 
 Improved New Amer- 
 ican 
 
 1632 
 
 1738 
 
 .886 
 
 .944 
 
 J. L. &S. B. Dix 
 
 Special New American 
 Improved Jonval Tur- 
 bine 
 
 1284 
 1474 
 
 1340 
 1617 
 
 .697 
 800 
 
 .727 
 880 
 
 Dubuque Turbine & 
 Roller Mill Co 
 Dubuque Turbine & 
 Roller Mill Co 
 
 Flenniken Turbine... 
 McCormick'sHolyoke 
 
 1511 
 
 1533 
 
 .821 
 
 .833 
 
 
 Turbine 
 
 1196 
 
 1296 
 
 650 
 
 704 
 
 Humphrey Machine 
 Co 
 
 Hercules Turbine. . . . 
 JIXL Turbine 
 
 1160 
 1198 
 
 1170 
 1209 
 
 .630 
 .652 
 
 .636 
 .657 
 
 
 JXLCR Turbine 
 
 1196 
 
 1206 
 
 .652 
 
 .656 
 
 Rodney Hunt Ma- 
 chine Co 
 
 McCormick Holyoke 
 
 
 
 
 
 
 Turbine 
 
 1159 
 
 1278 
 
 .630 
 
 .694 
 
 
 Hunt McCormick Tur- 
 bine 
 
 1158 
 
 1272 
 
 .629 
 
 .691 
 
 
 New Pattern Hunt 
 Turbine 
 
 1163 
 
 1415 
 
 .632 
 
 .768 
 
 
 Standard Wheel, 1887 
 Pattern 
 
 1200 
 
 1291 
 
 .651 
 
 .701 
 
 E. D. Jones & Sons Co. 
 James Leffel & Co . . . 
 
 Crocker Wheel 
 Samson W r ater Wheel 
 Improved Samson 
 Standard 
 
 1208 
 1543 
 1578 
 1330 
 
 1292 
 1554 
 1H32 
 1339 
 
 .657 
 
 . 838 
 . 856 
 . 7'2>2 
 
 .702 
 .84* 
 .886 
 .727 
 
 
 Special 
 
 1380 
 
 1434 
 
 .750 
 
 . 779 
 
 Munson Bros. Co 
 
 Phoenix "Little 
 Giant".. 
 
 1001 
 
 1020 
 
 .544 
 
 .554 
 
 tCatalogue recommends a maximum and minimum 
 age speed. 
 
 ^Tables based on full theoretical power of the water, 
 to 90 per cent efficiency, depending on location. 
 
 speed. Constants given are for the aver- 
 Wheels are said to give from 75 per cent 
 
328 
 
 Hydraulics of the Turbine. 
 
 TABLE XXVI. Continued. 
 
 Showing Relation of Diameter and Speed of Various American Turbines 
 working under Catalogue Conditions. 
 
 A = 
 
 Dn 
 Vh 
 
 = .000543 JL 
 
 i/h 
 
 
 
 'I 
 
 i. 
 
 < 
 
 p 
 
 Manufacturer. 
 
 ^ame 01 wneei. 
 
 Min. 
 
 Max. 
 
 Min. 
 
 Max. 
 
 Reaction Wheel Con. 
 
 Norrish, Burnham & 
 Co 
 
 
 1213 
 
 1233 
 
 659 
 
 670 
 
 Platt Iron Works Co. . 
 
 Victor Register Gate. 
 Victor Standard Cyl- 
 
 1181 
 1380 
 
 1221 
 1410 
 
 .641 
 .749 
 
 .663 
 
 .765 
 
 Poole Engineering & 
 Machine Co 
 
 Poole-Leffel 
 
 1341 
 
 1380 " 
 
 728 
 
 749 
 
 T. H. Risdon & Co. ... 
 
 Risdon Standard 
 Risdon Turbine Type 
 T C 
 
 1213 
 1213 
 
 1420 
 1420 
 
 .659 
 659 
 
 .772 
 772 
 
 
 Ris.don Turbine Type 
 D. C 
 
 1213 
 
 1420 
 
 .659 
 
 .772 
 
 S. Morgan Smith Co . . 
 
 Smith-McCormick . . . 
 Smith 
 
 1180 
 1655 
 
 1344 
 1679 
 
 .641 
 
 898 
 
 .730 
 911 
 
 Trump Mfg. Co 
 
 Standard Trump 
 
 1320 
 
 1380 
 
 .716 
 
 749 
 
 Wellman, Seaver, 
 IMorgan Co 
 
 McCormick 
 
 1212 
 
 1260 
 
 658 
 
 684 
 
 Impulse Wheels. 
 
 DeRemer Water 
 Wheel Co 
 
 DeRemer Water 
 
 
 
 
 
 
 Wheel 
 
 962 
 
 1001 
 
 .522 
 
 .545 
 
 Abner Doble Co 
 
 Tangential \Vheel 
 
 841 
 
 848 
 
 456 
 
 460 
 
 Pelton Water Wheel 
 Co 
 
 Tangential Wheel 
 
 912 
 
 92] 
 
 495 
 
 500 
 
 Platt Iron Works Co.. 
 The Risdon Iron Wks. 
 
 Victor High Pressure 
 Tangential Wheel 
 
 915 
 
 917 
 
 919 
 920 
 
 .497 
 .498 
 
 .499 
 .499 
 
 From equation (26) may be derived 
 (27) = ^ff- 
 
 From this equation the economical speed or correct number of 
 revolutions n for any wheel of diameter D, at any head, i/F, can 
 be obtained if the revolutions n of any other wheel of the series 
 at head h, and of diameter D, is known. 
 
Relations of and Efficiency. 329 
 
 If in equation (27), D = D a , the equation reduces to 
 
 (28) n- ^Eor^ = -^ 
 
 T/hi Vh T/hi 
 
 That is to say : The economical speed of any wheel will be in direct 
 proportion to the square root of the head under which it acts. 
 If in the equation (28), n 1, the equation reduces to 
 (39) n n lV /K 
 
 From which it follows that tLe revolutions of a wheel (n) for any 
 head, h, is equal to the evolutions n x for one foot head multiplied 
 by Vh. 
 
 158. Graphical Expression of Speed Relations. The relation 
 expressed by equations 18 to 27, inclusive, between the values of v, 
 <, D, n, and h, are graphically shown by Fig. 213. The theoretical 
 relations between v' and h, and <j> as expressed by equation (19) 
 when 4>-i, are represented by the upper curved line in the diagram 
 referred to ordinates and abcissas. The relation between </>, v and h, 
 where <f> has a fractional value or is less than 100 per cent., as is the 
 case for all wheels working under practical conditions, is shown by 
 reference to the curved lines below ; the fractional value of <f> as rep- 
 resented by each line is given thereon. The relations between v, D 
 and n are shown by the relations of the straight lines originating 
 near the lower right-hand corner of the diagram referred ta ordi- 
 nates and abcissas, and the mutual relations of all lines on the dia- 
 grams show the mutual relations between the various factors that 
 are here considered. 
 
 159. Relations of < and Efficiency. In any turbine running 
 under different heads but otherwise under the same physical condi- 
 tions as to gate opening, setting, draft tubes, etc., the efficiency will 
 remain constant provided the ratio of the velocity of rotation to the 
 theoretical spouting velocity of the water under the given head 
 remains the same. This is to say, the efficiency of a wheel will 
 remain constant under various conditions of head as long as the 
 value of < remains constant. This law is well demonstrated by ex- 
 periments made on a 12" Morgan-Smith wheel at the Hydraulic 
 Laboratory of the University of Wisconsin.* These experiments 
 were made under seven different heads varying from about 7.10 feet 
 to about 4.25 feet. The results of all these experiments have been 
 
 * "Test of a Twelve-Inch McCormick Turbine," an unpublished thesis by 
 O. W. Middleton and J. C. Whelan. 
 20 
 
330 
 
 Hydraulics of the Turbine. 
 
 REVOLUTIONS PER MINUTE 
 
 Fig 213. Speed Relations of the Turbines. 
 
Relations of and Efficiency. 
 
 0.0 O.I 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1. 1 
 VALUES OF $ 
 
 Fig. 214. Efficiency^ Curve of a 12 "Smith-McCormick Turbine. 
 
332 Hydraulics of the Turbine. 
 
 platted in a single diagram (see Fig. 214) from which it will be 
 noted that all experiments are fairly close to the mean curve ; that 
 the variation therefrom is probably due to experimental errors 
 (principally, it is believed, in the determination of the relative 
 velocities) and that reduction in head shows no uniform decrease 
 in efficiency. The experiments referred to, which are soon to be 
 published in a University bulletin, show that this law is true under 
 all conditions of gate as well as for the full gate conditions, illus- 
 trated in Fig. 214. Hence the conclusion may be drawn that the 
 efficiency of a wheel will remain essentially constant if < remains 
 constant at least under moderate changes in head. 
 
 160. Discharge of a Turbine at Fixed Gate Opening. The dis- 
 charge of a turbine with fixed gate opening, but at various speeds, 
 is not always the same but varies within certain limits and as the 
 speed varies. In some cases the discharge of a wheel increases as 
 the speed increases. (See discharge of Tremont turbine, Fig. 215.) 
 Sometimes the discharge decreases as the speed increases (see dis- 
 charge of Victor and McCormick turbines, Fig. 215), and some- 
 times the discharge increases with the speed to a certain point and 
 then decreases with a further increase in the speed (see discharge of 
 Samson ; and New American wheels, Fig. 215.) 
 
 In reaction turbines the discharge takes place first through the 
 guide from which it passes into and through the buckets of the 
 wheel. The relations of these two sets of orifices change as the 
 speed of the wheel changes and affects the total discharge. If dur- 
 ing such changes of speed, the ratio, $- , remains constant, it 
 is found by experiment that the conditions remain similar to thost; 
 of any short tube or orifice. The discharge of a turbine may there- 
 fore be determined by the formula : 
 (30) q = Cat/2jh 
 
 And it may be stated : In a given turbine with fixed gate opening, 
 the discharge will be proportional to the square root of the head, 
 i. e., the discharge divided by Vh is constant. 
 
 The values of C and a vary with the opening of the gate or gates, 
 but for any one position are essentially constant. 
 
 Let the discharge of a wheel under fixed gate conditions and with 
 a given head, h a , be given by the formula: 
 
 C3i; q, = 
 
Discharge of a Turbine at Fixed Gate Opening. 333 
 
 The discharge of any other head will be proportional to i/h" and 
 therefore 
 
 T= hence 
 
 (32) 
 (33) 
 
 (34) q = 
 
 Therefore, it may be stated : In a given turbine with fixed gate 
 opening the discharge at any head h will be equal to the discharge at 
 one foot head multiplied by -\/h. 
 
 That this law is essentially correct may be demonstrated by ex- 
 periment. Fig. 216 shows the results from the series of tests on 
 the McCormick turbine, before mentioned, at full gate. Three sets 
 
 no 
 
 100 
 
 90 
 
 80 
 
 70 
 
 60 
 
 50 
 
 X 
 
 i 
 
 A- 48 ff VICTOR CYLINDRICAL GATE 
 B- 99j"TURBINE LOWELL MASS 
 C- 44"lMPROVED NEW AMERICAN 
 
 D- 45 "SAMSON 
 
 E- 5l"MCORMICK W-S-MORGAN 
 
 25 30 35 40 45 50 
 
 DISCHARGE IN CUBIC FEET PER SECOND UNDER ONE FOOT HEAD 
 
 Fig. 215. Full Gate <p- Discharge Curves of Various Turbines. 
 
 55. 
 
334 
 
 Hydraulics of the Turbine. 
 
 of experiments are platted with values of < equal to .35, .65 and .90 
 and for heads from about 4.25 feet to 7 I feet. Fig. 217 shows the 
 discharge of this turbine at various gate openings and under seven 
 different heads. For the purpose of this diagram the discharges 
 under each head have been reduced to the theoretical discharge at 
 one foot head by equation 16, It will be noted from both Fig. 216 
 and Fig. 217 that all experiments where <f> is the same lie close to 
 the average line, and that the departures from this line are prob- 
 ably due to experimental errors. The results are sufficiently close, 
 however, to demonstrate that the discharge under practical condi- 
 tions essentially follows the law above expressed. 
 
 // 
 
 la. 
 
 5 4 
 
 d 
 
 < 
 u 
 
 012345678 
 DISCHARGE IN CUBIC FEET PER SECOND 
 
 Fig. 216. The Relations of Head to Discharge of a 12 "SmithrMcCormick 
 
 Turbine. 
 
Discharge or a Turbine at Fixed Gate Opening. 335 
 
 161. Power of a Turbine. The power which may be generated 
 by any wheel depends on the head a/ailable, the quantity of water 
 which may be discharged through the wheel under the given head, 
 the relative speed at which it may be run, and the efficiency of 
 operation. Hence 
 
 (35) 
 
 q w h e _ q h e 
 
 550 8.8 
 
 Combining equations (30) and (35) there results 
 
 (36 
 
 550 
 
 8.8 
 
 From equation (36) it is apparent that if C, e and a are constant 
 for any given turbine and fixed gate opening, and if the value of <f> 
 remains constant, the power of the turbine will be in direct propor- 
 tion to h^. consequently 
 
 1 
 
 0.9 
 
 
 P0.7 
 o 0.6 
 
 i 
 
 0.4 
 
 k. 
 
 O 
 
 gO.3 
 0.2 
 O.I 
 
 0.0 
 
 
 
 07.10 FOOT HEAD 
 O6.80 
 6.40 
 ttS.70 
 
 AS. 20 
 4.70 . 
 U4.25 
 
 
 
 
 
 
 k 
 
 
 \ 
 
 ^H- 
 
 N 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 A 
 
 
 
 
 xj 
 
 
 
 
 
 
 
 
 
 
 
 
 
 t 
 
 
 ^ 
 
 V 
 
 u 
 
 \ 
 
 & 
 
 
 
 
 
 
 f 
 
 
 
 
 
 o jt* 
 
 
 
 
 \o. 
 
 
 V 
 
 w 
 
 
 
 
 
 
 
 
 
 
 | 
 
 
 
 
 
 
 5 
 
 
 
 
 \ 
 
 ^ 
 
 
 
 u 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 jdi 
 
 
 
 
 
 
 
 
 
 
 
 
 - 
 
 
 Ni 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 o 
 
 fe 
 
 
 
 
 ^ "i 
 
 L 
 
 
 ^ 
 
 .f 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 i 
 
 
 
 A 
 
 
 
 tit 
 
 s 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 < 
 
 
 
 
 
 l<> ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 u 
 
 
 
 
 5 
 
 
 o 
 
 ; 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 u ^ 
 
 J 
 
 1 
 
 
 
 
 
 
 . 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 VI 
 
 c 
 
 
 
 
 
 u 
 
 
 
 
 
 
 
 
 
 
 
 
 u 
 
 & 
 
 1 
 
 
 
 
 - 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 k 
 
 
 
 
 
 
 
 
 
 U 
 
 
 >. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ! 
 
 
 
 
 J 
 
 i 
 <. 
 
 ) 
 i 
 
 
 
 
 a 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 T 
 
 - t 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 J3 
 
 " 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 
 
 
 
 
 E 
 
 
 
 
 
 
 o 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 I 
 
 h 
 
 i. ". 
 
 
 
 
 
 ft 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 g 
 
 
 
 
 h- 
 
 8 
 
 
 
 
 
 t- 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 uu 
 
 
 
 
 -i 
 
 JL 
 
 
 
 
 
 
 
 
 
 
 Zi 
 
 
 
 
 
 .5 1.0 1.5 2.0 _ 2. 5 2.9 
 
 DISCHARGE IN t CUMC FEET PEK.tCCONO UNDER ONE FOOT HEAD 
 
 Fig, 217. Relations of Velocity to Discharge for a 12" "Smith-McCormick' 
 Turbine at Various Gate Openings. 
 
336 
 
 Hydraulics of the Turbine. 
 
 U-.l 
 
 Equation (37) may be reduced to 
 
 (38) 
 
 P = 
 
 From which can be determined the power of a wheel at any given 
 head, provided its power at any other head is known. 
 In equation (38) if h =i, there results 
 
 (39) P = P 1 h 2 ' 
 
 From which it may be stated: In a given turbine with a fixed gate 
 opening, the power that can be developed at any head will be equal- 
 to the power at one foot head multiplied by h*. 
 
 This law may also be demonstrated experimentally as will be 
 seen by reference to Fig. 218, in which is shown the theoretical 
 curve representing the relation between head and horse power of 
 the 12" McCormick turbine before mentioned. The turbine on 
 which these experiments were made was small and the heads were 
 
 & 
 
 
 1.0 2.0 3.0 4.0 
 
 ACTUAL HOPSE POWER OF WHEEL 
 
 Fig. 218. Relations of a Power to Head in a 12 "Smith-McCormick Turbine.' 
 
The Relation of Discharge to Diameter of a Turbine. 337 
 
 limited so that there is some variation from the theoretical curves 
 but the fact expressed by the general law is quite clearly shown. 
 
 162. The Relation of Discharge to the Diameter of a Turbine. 
 In any homogeneous system of water wheels, the diameter, height 
 and corresponding openings and passages are proportional and it 
 follows that in such similar wheels similar areas are proportional to 
 each other and to the squares of any lineal dimension. In such 
 wheels, therefore, the area a of the gate openings is proportional to 
 the square of the diameter of the wheel, and the equation may there- 
 fore be written : 
 
 (40) Cal/ 2g~ = K D 8 
 
 In this equation K is a constant to be determined by experiment. 
 Combining equations (40) and (30) there results 
 
 (41) q = KDVF 
 
 from which can be obtained, by transposition 
 
 (42) 
 
 Equation (41) is not only theoretically but is also practically cor- 
 rect, as is shown by the data in Table XXVII, which is also graphi- 
 cally represented in Fig. 219. These data are taken from a paper 
 
 TABLE XXVII. 
 
 Discharge of thirteen water wheels of the same manufacture but of different di- 
 ameters, as determined by actual tests, compared with value computed by the 
 formula: 
 
 q = K D 2 t/h in which h = 13, K = .0172 
 DISCHARGE. 
 
 No. 
 
 Diam- 
 eter in 
 inches. 
 
 Reduced 
 from actual 
 tests, Cu. ft. 
 per Sec. 
 
 Computed 
 ( Mean 
 Curve) Cu. 
 ft. per Sec. 
 
 Variation 
 from Com- 
 puted Dis- 
 charge Cu. 
 ft. per Sec. 
 
 Per cent. 
 Variation 
 from Com- 
 puted Dis- 
 charge. 
 
 1 . 
 
 9 
 
 5.17 
 
 5.02 
 
 + 0.15 
 
 + 2.99 
 
 2... 
 
 12 
 
 8.79 
 
 8.92 
 
 0.13 
 
 1.46 
 
 3 
 
 15 
 
 13.85 
 
 13.93 
 
 0.08 
 
 0.57 
 
 4 
 
 18 
 
 18.85 
 
 20.07 
 
 1.22 
 
 6.08 
 
 5 
 
 12 
 
 29.07 
 
 27.32 
 
 + 1.75 
 
 + 6.41 
 
 6 
 
 24 
 
 35.31 
 
 35.68 
 
 0.37 
 
 1.04 
 
 7 . 
 
 27 
 
 47.81 
 
 45.16 
 
 + 2.65 
 
 + 5.87 
 
 8. 
 
 30 
 
 54.15 
 
 55.75 
 
 1.60 
 
 2.87 
 
 9. , 
 
 36 
 
 77.33 
 
 80.28 
 
 2.95 
 
 -3.67 
 
 10 
 
 39 
 
 93.51 
 
 94.22 
 
 0.71 
 
 -0.75 
 
 11 
 
 42 
 
 107.73 
 
 109.27 
 
 1.54 
 
 1.41 
 
 12. 
 
 45 
 
 128.53 
 
 125.44 
 
 + 3-09 
 
 + 3.10 
 
 13. - 
 
 51 
 
 161.07 
 
 161 . 12 
 
 0.05 
 
 0.03 
 
 
 
 
 
 
 
338 
 
 Hydraulics of the Turbine. 
 
 by A. W. Hunking, entitled "Notes on Water Power Equipment," 
 in vol. 13, No. 4, of Jour. Asso. Eng. Soc., April, 1894. In this table 
 are given the discharges of thirteen water wheels of various diam- 
 eters, the discharges of which were determined from actual tests. 
 
 DISCHARGE IN CUBIC FEET PER SECOND 
 
 c 
 
 r 
 
 3 C 
 
 3 i 
 
 3- i 
 
 5 S 
 
 D ( 
 3 t 
 
 I \ 
 
 o . 
 
 3 ( 
 
 & 1 
 3 C 
 
 s i 
 
 s i 
 
 3 R 
 
 D C 
 
 2 - 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 n 
 
 3 " 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 * a 
 ^ u 
 
 
 Vx 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 5SJ 
 
 ^ 
 
 ^~ 
 
 
 
 
 
 
 
 2 a 
 
 i. 
 
 
 
 
 
 to 
 
 ^j 
 
 ^> 
 
 
 
 
 
 5" 
 
 en 
 
 
 
 
 
 
 
 
 ** 
 
 
 
 
 Fig. 219. Relations of Discharge to Diameter in Reaction Turbine of the 
 
 same manufacture. 
 
 These results have been reduced to the common basis of the dis- 
 charge at 13 foot head. The computed discharges at 13 foot head 
 on the basis of equation (41) are also given, as well as the percent- 
 age of variations of the actual from the theoretical discharges. The 
 wheels were of the same make with inward and downward dis- 
 charge. The departures or variations from the mean values, as de- 
 termined by calculation, are probably due both to imperfections in 
 the construction of the wheel and to errors in making the tests. 
 They may be seen, however, to practically conform to the theoreti- 
 cal deductions. The values of the coefficient K, as calculated from 
 the tables contained in the catalogues of various manufacturers of 
 American wheels, are given in Table XXVIII. 
 
 163. The Relation of Power to the Diameter of a Turbine. By 
 substituting the value of q from equation (41) in equation 
 
 (35) 
 
 there results 
 (43) 
 
 qhe 
 
 " 8.8 
 
The Relation of Power to the Diameter of a Turbine. 339 
 
 TABLE XXVIII. 
 
 Showing Relation of Diameter and Discharge of Various American Turbines- 
 working under Catalogue Conditions. 
 
 K= WL 
 
 Manufacturer. 
 
 Name of Wheel. 
 
 K 
 
 Min. 
 
 Max. 
 
 Reaction Wheels. 
 
 T. C. Alcott & Son , 
 
 Alexander, Bradley & Dunn- 
 ing 
 
 American Steel Dredge Wks.. 
 Camden Water Wheel Worki- 
 Chase Turbine Mfg. Co 
 
 Christiana Machine Co 
 
 Craig, Ridgway & Son Co 
 Craig, 'Ridgway & Son Co 
 Dayton Globe Iron Works Co. 
 
 J. L. &S. B. Dix 
 
 Dubuque Turbine & Rollei 
 Mill Co 
 
 Dubuque Turbine & Roller 
 Mill Co. . . 
 
 Holyoke Machine Co 
 
 Humphrey Machine Co 
 
 Rodney Hunt Machine Co.. 
 
 E. D. Jones & Sons Co . 
 James Leffel & Co 
 
 Munson Bros. Co 
 
 Norrish, Burn ham & Co. 
 Platt Iron Works Co 
 
 Alcott' s Standard High Duty 
 Alcott' s Special High Duty. 
 
 *Syracuse Turbine 
 
 * Little Giant 
 
 United States Turbine 
 
 *Chase-Jonval Turbine (reg- 
 ular) 
 
 *Chase-Jonval Turbine 
 (special) 
 
 Balanced Gate Turbine 
 
 Double Perfection 
 
 Standard 
 
 *American Turbine 
 
 New American (high head 
 type) 
 
 Improved New American.. 
 
 Special New American 
 
 Improved Jonval Turbine. . 
 
 Flenniken Turbine. 
 
 McCormick's Holyoke Tur 
 bine 
 
 Hercules Turbine 
 
 flXL Turbine 
 
 fXLCR Turbine 
 
 McCormick's Holyoke Tur- 
 bine 
 
 *Hunt-McCormick Turbine. 
 
 New Pattern Hunt Turbine. 
 
 Standard Wheel, 1887 pat- 
 tern 
 
 Crocker Wheel 
 
 Samson 
 
 Improved Samson 
 
 Standard 
 
 Special 
 
 J Phoenix "Little Giant" . . . 
 
 Victor Register Gate ....'. 
 
 Victor Standard Cylinder 
 
 Gate 
 
 .00654 
 .0157 
 
 .00538 
 
 .0205 
 
 .0214 
 
 .01086 
 
 .00902 
 
 .0116 
 
 .00586 
 
 .00543 
 
 .00509 
 .0233 
 .0175 
 .00454 
 
 .00652 
 
 .0184 
 .0162 
 .00351 
 .00645 
 
 .01877 
 .01913 
 .01297 
 
 .0123 
 
 .0175 
 
 .0170 
 
 .022 
 
 .00612 
 
 .00937 
 
 .00924 
 
 .00917 
 
 .0167 
 
 .0222 
 
 -00860 
 .0168 
 
 .00622 
 
 .0340 
 
 .0229 
 
 .00913, 
 
 .01346 
 
 .00952: 
 
 .0142 
 
 .00659- 
 
 .00801 
 
 .00644- 
 .0263 
 .0205 
 .00546- 
 
 .0088 
 
 .0191 
 .0175 
 .00536 
 .00953 
 
 .01929 
 .02867 
 .01543 
 
 .0141 
 
 .0179 
 
 .0171 
 
 .022 
 
 .00640* 
 
 .00965 
 
 .0172 
 
 .00955- 
 
 .0186 
 
 .0227 
 
340 
 
 Hydraulics of the Turbine. 
 
 TABLE XXVIII. Continued. 
 
 Showing Relation of Diameter and Discharge of Various American Turbines 
 working under Catalogue Conditions. 
 
 - q 
 
 
 
 
 K 
 
 Manufacturer. 
 
 Name of Wheel. 
 
 Min. 
 
 Max. 
 
 Reaction Wieels.CoTi. 
 
 Poole Engineering and Ma- 
 chine Co 
 
 Poole-Leffel .... 
 
 .00625 
 
 .00827 
 
 T. H Risdon & Co 
 
 *Risdon Standard Turbine . . 
 
 .00501 
 
 .00698 
 
 -'S. Morgan Smith Co 
 
 *Risdon Type T. C. Turbine 
 *Risdon Type D. C. Turbine 
 *Smith-McCormick 
 
 .00753 
 .0100 
 0187 
 
 .00948 
 .0132 
 0238 
 
 
 Smith . . ... 
 
 0247 
 
 .0256 
 
 Trump Mfg Co . . 
 
 Standard Trump 
 
 0210 
 
 0263 
 
 Wellman, Seaver, Morgan Co. 
 
 McCormick 
 
 .0185 
 
 .0199 
 
 Impulse Wheels. 
 DeRemer Water Wheel Co. . 
 Abner Doble Co 
 
 *DeRemer Water Wheel. . 
 *Tangential Wheel 
 
 .000135 
 000075 
 
 .000173 
 000119 
 
 Pelton Water Wheel Co. . 
 
 ^Tangential Wheel. 
 
 00010 
 
 000135 
 
 Platt Iron Works Co 
 
 Victor High Pressure ... . 
 
 0170 
 
 0''*47 
 
 Risdon Iron Works 
 
 *Tangential Wheel 
 
 000134 
 
 000173 
 
 
 
 
 
 *Wide variation in constants due to the design being special for various sized wheels (series 
 not exactly homogeneous). 
 
 tTables in catalogue based on full theoretical power of the water. Wheels are said to give from 
 75 per cent to 90 per cent efficiency, depending on location. 
 
 $Munson Bros. Co. make several types of "Litte Giant" turbines causing above wide variation in 
 -constants. 
 
 - is constant for a given wheel, as long as <f> is constant, 
 this expression may be represented by a constant K 2 which may 
 1^e derived independently for each make of wheel, or may be deter- 
 mined from the equation 
 
 (44) 
 
 K - Ke 
 
 K ~ 
 
 With this substitution (43) becomes 
 (45) p rr K 2 D 2 h* 
 
 That is to say: With wheels of homogeneous design, the power of 
 any wheel under the given head is in direct proportion to the square 
 -of its diameter. This law is both theoretically and practically cor- 
 rect, as demonstrated by Table XXIX, and Fig. 220, taken from the 
 paper by Mr. Hunking to which reference has previously been 
 
Relation of Speed to Discharge of Turbine. 
 
 34* 
 
 TABLE XXIX. 
 
 Horse Power of thirteen water wheels of the same manufacture but of different 
 diameters, as determined by actual tests, compared with values determined 
 by the formula: 
 
 P=K 2 D 2 h 1 
 
 K 2 =.00158 
 HORSE POWER 
 
 h = 13 
 
 No. 
 
 Diame- 
 ter in 
 inches. 
 
 From Tests. 
 
 Computed. 
 
 Variation 
 from Com- 
 puted H. P. 
 in H. P. 
 
 Variation 
 from Com- 
 puted H. P. 
 Percent. 
 
 1. 
 
 9 
 
 6 10 
 
 6 00 
 
 + 10 
 
 + 1.67 
 
 2 
 
 12 
 
 1041 
 
 1067 
 
 026 
 
 2.44 
 
 3 
 
 15 
 
 16 49 
 
 1667 
 
 018 
 
 1.08- 
 
 4 
 
 18 
 
 22 89 
 
 24 00 
 
 1.11 
 
 4.62- 
 
 5 
 
 21 
 
 33 71 
 
 32.67 
 
 + 1.04 
 
 + 3.18 
 
 6 
 
 24 
 
 41.53 
 
 42.67 
 
 1.14 
 
 2.67 
 
 7 
 
 27 
 
 56 67 
 
 54 07 
 
 + 2 60 
 
 + 4.81 
 
 8 
 
 30 
 
 63 69 
 
 66 68 
 
 299 
 
 -4.48 
 
 9 
 
 36 
 
 97 45 
 
 9600 
 
 + 1.45 
 
 + 1.50 
 
 10 
 
 39 
 
 10998 
 
 112 68 
 
 2.70 
 
 2.40 
 
 11 
 
 42 
 
 13309 
 
 13069 
 
 + 2.40 
 
 + 1.84 
 
 12 
 
 45 
 
 15382 
 
 150.02 
 
 + 3.80 
 
 + 2.53 
 
 13 
 
 51 
 
 196 28 
 
 192.69 
 
 + 3.59 
 
 + 1.86 
 
 
 
 
 
 
 
 Fig. 220. Relation of Power to Diameter in Reaction Turbines of the same 
 
 manufacture. 
 
34 2 
 
 Hydraulics of the Turbine. 
 
 made. This table and figure illustrate the relation between the the- 
 oretical power, as determined by equation (45), and the actual horse 
 power of thirteen wheels of the same manufacture but different 
 diameters, as determined by actual tests. 
 
 The values of the constant K 2 for the most efficient relation of 
 power to diameter in various American turbines, as calculated from 
 the tables contained in the catalogues of various American manu- 
 facturers of turbines, are given in Table XXX. The values of K 2 
 and other turbine constants will be found to vary widely in the 
 various types of turbines, not only of different manufacturers but 
 of the same manufacturer. The interpretation of this fact is not 
 that one turbine is, in the abstract and according to the relative 
 value of the constants, more valuable than another, but that each 
 turbine is best fitted for a particular range of conditions for which 
 it was presumably designed. 
 
 TABLE XXX. 
 
 Showing Halation of Power and Diameter of Various American Turbines Work 
 ing under Catalogue Conditions. 
 
 K = "~ 
 
 Manufacturer. 
 
 Name of Wheel. 
 
 K. 
 
 Min. 
 
 Max. 
 
 Reaction Wheels. 
 
 T. C. Alcott & Son, 
 
 Alexander, Bradley & Dunn- 
 ing 
 
 American Steel Dredge Wks. 
 Camden Water Wheel Works 
 Chase Turbine Mfg. Co 
 
 Christiana Machine Co 
 
 Craig, Ridgway & Son Co 
 
 Craig, Ridgway & Son Co 
 
 Dayton Globe Iron Works Co. 
 
 J. L. &S. B. Dix 
 
 Dubuque Turbine & Roller 
 Mill Co 
 
 Dubuque Turbine & Roller 
 Mill Co.. 
 
 Alcott' s Standard High Duty 
 Alcott's Special High Duty. 
 
 Syracuse Turbine 
 
 Little Giant 
 
 United States Turbine. . . . 
 
 *Chase-Jonval Turbine (reg- 
 ular) 
 
 *Chase-Jonval Turbine 
 (special) 
 
 Balanced Gate Turbine 
 
 Double Perfection 
 
 Standard 
 
 * American Turbine 
 
 *New American (high head 
 type) 
 
 Improved New American. . . 
 
 Special New American 
 
 Improved Jonval Turbine. . 
 
 Flenniken Turbine 
 
 McCormick's Hoi yoke Tur- 
 bine.. 
 
 .000589 
 .00141 
 
 .000483 
 
 .00190 
 
 .00190 
 
 .000590 
 
 .000932 
 
 .000800 
 
 .00113 
 
 .000538 
 
 .000434 
 
 .000422 
 .00212 
 .00158 
 .000447 
 
 .000596 
 
 .00167 
 
 .000999 
 .00155 
 
 .000565 
 
 .00332 
 
 .00207 
 
 .000780 
 
 .001150 
 
 .000854 
 
 .00120 
 
 .000629 
 
 .000726 
 
 .000588 
 .00244 
 .00187 
 .000532 
 
 .000802 
 
 .00173 
 
The Relation of Power to the Diameter of a Turbine. 343 
 
 TABLE XXX. Continued. 
 
 Showing Relation of Power and Diameter of Various American Turbines Work- 
 ing under Catalogue Conditions. 
 
 
 
 * 
 
 ^2 
 
 Manufacturer. 
 
 JSame of Wheel. 
 
 Min. 
 
 Max. 
 
 Reaction Wheel. Con. 
 Holyoke Machine Co 
 
 Hercules Turbine 
 
 00147 
 
 001 ^Q 
 
 Humphrey Machine Co 
 
 |IXL Turbine 
 
 0003Q7 
 
 OOfkrtOft 
 
 
 fXLCR Turbine 
 
 000730 
 
 001 31 
 
 Rodney Hunt Machine Co. . . 
 
 McCormick Holyoke Tur- 
 bine 
 
 00169 
 
 00173 
 
 
 *Hunt McCormick Turbine. 
 New Pattern Hunt Turbine 
 Standard Wheel, 1887 Pat- 
 tern . . : 
 
 .00173 
 .00120 
 
 00101 
 
 .00260 
 .00146 
 
 00122 
 
 E. D. Jones & Sons Co 
 
 Crocker Wheel 
 
 00159 
 
 00163 
 
 James Leffel & Co 
 
 Samson . 
 
 00158 
 
 00159 
 
 
 Improved Samson 
 
 00201 
 
 00202 
 
 
 Standard 
 
 00056 
 
 00058 
 
 
 Special 
 
 000897 
 
 000920 
 
 
 JPhoenix "Little Giant" 
 
 000842 
 
 001 560 
 
 
 
 000852 
 
 000885 
 
 Platt Iron Works Co 
 
 Victor Re^i^ter Gate 
 
 00158 
 
 00179 
 
 
 Victor Standard Cylinder 
 Gate 
 
 00205 
 
 00205 
 
 Poole Engineering and Ma- 
 chine Co. 
 
 Poole-Leffel 
 
 000625 
 
 000650 
 
 T. H. Risdon & Co 
 
 *Risdon Standard Turbine. 
 
 000485 
 
 000675 
 
 S. Morgan Smith Co. 
 
 *Risdon Type T. C. Turbine 
 *Risdon Type D. C. Turbine 
 Sinith-McCormick 
 
 .000672 
 .000781 
 00169 
 
 .000913 
 .00135 
 00217 
 
 
 Smith 
 
 00232 
 
 00236 
 
 The Trump Mfg. Co 
 
 Standard Trump 
 
 00191 
 
 00241 
 
 Wellman, Seaver, Morgan Co. 
 
 
 .00168 
 
 .00171 
 
 Impulse Wheels. 
 
 DeRemer Water Wheel Co.. 
 Abner Doble Co . . . 
 
 *DeRemer Water Wheel . . . 
 *Tan w ential Wheel 
 
 .000124 
 0000055 
 
 .000186 
 0000107 
 
 Pelton Water Wheel Co 
 Platt Iron Works Co 
 
 ^Tangential Wheel 
 
 .0000093 
 00154 
 
 .0000130 
 00^23 
 
 Risdon Iron Works Co 
 
 *Tangential Wheel 
 
 0000128 
 
 0000165 
 
 
 
 
 
 *Wide variation in constants due to the design being special for various sized wheels (series not 
 exactly homogeneous). 
 
 tTables based on full theoretical power of the water. Wheels are said to give from 75 per cent 
 to 90 per cent efficiency, depending on location. 
 
 fcMunson Bros. Co. make several types of "Little Giant" turbines, causing above wide variation 
 in constants. 
 
344 
 
 Hydraulics of the Turbine. 
 
 C"J 
 
 CM 
 
 c 
 
 LJ 
 
 H 
 O 
 
 
 01 
 
 \ 
 
 
 CD 
 
 V 
 
 
 VN 
 
 X 
 
 ^^ 
 
 \ 
 
 
 CO 
 
 CNJ 
 
 ^ 
 
 "*-.. 
 
 
 \ 
 
 \\ 
 
 
 
 
 CD 
 10 
 
 in 
 
 a 
 m 
 
 CM 
 
 S3HONI HI 133HM JO 
 
Relation of Speed to Discharge of Turbine. 345 
 
 As the power of a wheel varies directly with the value of K 2 , this 
 constant is a direct measure of comparative power and indicates 
 the relative power that can be developed by various types of wheels 
 of the diameter and under a given head. The range of values for 
 K 2 as found in American practice is shown graphically in Fig. 221 
 where the power of turbines of various diameter and types under 
 one foot head is given. The power of a wheel varies under differ- 
 ent heads as h^, and therefore the power at any head can be de- 
 termined directly by multiplying the readings of the graphical table 
 by h*. For example, from Fig. 221 it will be seen that various 
 types of 40" American wheels, under one foot head, will give from 
 .75 to 4 H. P. and at 16 foot head they will therefore develop 64 
 times the H. P. at one foot head or from 48 to 256 H. P. within 
 which range a choice must be made. 
 
 164. Relations of Speed to Discharge of Turbines. As the speed 
 of all wheels of the same series must be proportional to Vh> the 
 equation may be written : 
 
 (46) v' = K.T/F 
 
 from which and from equations (19) and (21) 
 
 (47) K 3 - _ - r ^ 12 x 
 From equations (42) and (47) may be derived 
 
 (48) n = H 
 
 As the first term of the last expression is constant, there may be 
 written : 
 
 (49) K 4 = 
 
 12X60 K 3 K 
 
 from which equation (48) may be re-written. 
 
 K^W 
 
 (50) n = - 
 
 A 
 
 'For a head of one foot, h=i, equation (50) becomes 
 
 (51) n -r-L 
 
 Equation (50) may be rearranged to read: 
 
 (52) K 4 = -lL|/^= = n 
 
 21 
 
346 
 
 Hydraulics of the Turbine. 
 
 TABLE XXXI. 
 
 Showing Relation of Speed and Discharge of Various American Turbines 
 Working under Catalogue Conditions. 
 
 
 
 I 
 
 ^4 
 
 Manufacturer. 
 
 Name of Wheel. 
 
 Min. 
 
 Max. 
 
 Reaction Wheels. 
 T. C. Alcott & Son 
 
 
 
 
 Alexander, Bradley & Dunn- 
 ing. . 
 
 Alcott's Standard High Duty 
 Alcott' s Special High Duty. 
 
 98.8 
 154.5 
 
 114.7 
 159.2 
 
 American Steel Dredge Wrks. 
 
 ^Syracuse Turbine 
 *Littie Giant 
 
 89.8 
 172 
 
 108 . 2 
 9 43 8 
 
 Camden Water Wheel Works 
 Chase Turbine Mfg. Co 
 
 United .States Turbine 
 
 205.2 
 
 239.2 
 
 
 * Chase Jon val Turbine (reg- 
 ular) . 
 
 140 
 
 174 
 
 
 *Chase-Jonval Turbine 
 (special) 
 
 9 01 
 
 255 
 
 Christiana Machine Co 
 
 
 
 
 
 Balanced Gate Turbine . . 
 
 115 8 
 
 126 2 
 
 Craig, Ridgway & Son Co 
 
 Double Perfection 
 
 90 5 
 
 97 2 
 
 Craig, Ridgway & Son Co 
 
 Standard 
 
 94 
 
 101 2 
 
 Dayton Globe Iron Works Co. 
 
 ^American Turbine. . . . . 
 
 83.0- 
 
 109 
 
 
 fNevv American (high head 
 type) . . 
 
 75 4 
 
 85 9 
 
 J. L. & S. B. Dix. . 
 
 Improved New American. . . 
 Special New American 
 
 265.0 
 170.5 
 
 ft_t A 
 
 268.0 
 190.0 
 i on n 
 
 Dubuque Turbine & Roller 
 Mill Co 
 
 
 mn 
 
 1 C> A 
 
 Dubuque Turbine & Roller 
 Mill Co 
 
 IVTnr^rkrmipb-'fi T^nlvrifca Tii r 
 
 
 
 
 bine 
 
 IP)'? 
 
 176 
 
 Holvoke Machine Co 
 
 
 148 
 
 154 
 
 Humphrey Macnine Co 
 
 1IXL Turbine 
 
 71 3 
 
 88 3 
 
 
 JXLCR Turbine. . 
 
 90 5 
 
 116 9 
 
 Rodney Hunt Machine Co. . . 
 
 McCormick's Holvoke Tur- 
 bine. 
 
 159 5 
 
 176.0 
 
 
 *Hunt McCormick Turbine. 
 *New Pattern Hunt Turbine 
 Standard Wheel, 1J87 Tat- 
 tern 
 
 161.4 
 132.4 
 
 19(3 o 
 
 207.5 
 174.8 
 
 145 
 
 E. D. Jones & Sons Co 
 
 Crocker Wheel 
 
 161 
 
 169 8 
 
 James Leffel & Co 
 
 
 9n i 7 
 
 9/VJ A 
 
 
 Improved Sampson 
 
 240 
 
 241.5 
 
 
 Standard 
 
 ]03 7 
 
 107 
 
 
 Special 
 
 134 7 
 
 139.8 
 
 Munson Bros. & Co 
 Norrish, Burnham & Co. ... 
 
 tJPhoenix -'Little Giant" 
 
 102.0 
 1 15 . 9 
 
 132.1 
 120.0 
 
 Platt Iron Works Co 
 
 V T? ' f C" f 
 
 1 Y3 
 
 Wo 
 
 
 Victor Standard Cylindei 
 Gate . . 
 
 205.0 
 
 2:2.0 
 
Relation of Speed to Power of Turbine. 
 
 347 
 
 TABLE XXXI. Continued 
 
 Showing Relation of Speed and Discharge of Various American Turbines 
 Working under Catalogue Conditions, 
 
 
 
 L 
 
 "-4 
 
 Manufacturer. 
 
 JName of Wheel. 
 
 Mm. 
 
 Max. 
 
 Reaction Wheels. Con. 
 
 Poole Engineering and Ma- 
 chine Co . . 
 
 Poole-Leffel 
 
 1104 
 
 me 
 
 T H Risdon & Co 
 
 *Risdon Standard Turbine 
 
 QQ 4 
 
 mo 
 
 S. Morgan Smith Co 
 
 *Risdon Type T. C. Turbine 
 *Risdon Type D. C. Turbine 
 Smith-McCormick 
 
 100.7 
 108.0 
 163 7 
 
 137.3 
 158.0 
 185 
 
 
 Smith 
 
 265 
 
 266 
 
 The Trump Mfg. Co 
 
 Standard Trump 
 
 194 
 
 in o 
 
 Well man, Seaver, Morgan Co. 
 
 McCormick 
 
 168.5 
 
 179 
 
 Impulse Wheels. 
 DeRemer Water Wheel Co. . 
 
 DeRemer Water Wheel. . . . 
 
 11 10 
 
 13 20 
 
 Abner Doble Co 
 
 ^Tangential Wheel 
 
 6 61 
 
 9 20 
 
 Pelton Water Wheel Co 
 
 Tangential Wheel 
 
 9 21 
 
 10 92 
 
 Platt Iron Works Co 
 
 Victor High Pressure 
 
 37 8 
 
 42 2 
 
 Risdon Iron Works 
 
 Tangential Wheel 
 
 10 67 
 
 12 10 
 
 
 
 
 
 *Wide variation in constants due to the design being special for various sized wheels (series not 
 exactly homogeneous). 
 
 tUatalogue recommends a maximum and minimum speed. Constants given are for the average 
 speed. 
 
 ^Tables in catalogue based on full theoretical power of the water. Wheels are said to give from 
 75 per cent to 90 per cent efficiency, depending on location. 
 
 $$Munson Bros. Co. make several types of "Little Giant" turbines causing above wide variation 
 in constants. 
 
 It is evident that K 4 is constant for all turbines with constant K 
 and K 3 ; also, for all turbines where q, the discharge, is equal at the 
 same speed, n, and under the same head, h, K 4 must be constant for 
 different heads since n and q are proportional to V n - The values of 
 the constant K 4 as calculated from the tables contained in the 
 catalogues of various American manufacturers are given in Table 
 XXXI. 
 
 i64a. Relation of Speed to Power of Turbines. From equation 
 (35) may be derived 
 
 8.8 P 
 
 (53) 
 
 eh 
 
348 Hydraulics of the Turbine. 
 
 From equation (48) may be derived 
 
 (*) K, !/K = 12 X u X Vh * 7? 
 
 Combining equations (53) and (54) 
 
 (55) 
 
 12 X 60l/e 
 By transposing 
 
 K.T/K 12X60 nr = 
 
 (56) 
 
 As the first member of the equation is constant for any given 
 wh el, there may be written 
 
 (57) 
 and hence 
 
 (58) K < n"^ 
 
 From equation (58) it will be noted that the value of K 5 under a 
 given head is in direct proportion to the square of the velocity of 
 the wheel and to its power. K 5 is termed the "specific speed" of the 
 wheel. A high value of K 5 is an indication of high speed, and a 
 low value, of low speed. 
 
 The values of the constant K 5 as calculated from the tables con- 
 tained in the catalogues of various manufacturers of American 
 wheels are given in Table XXXII. 
 
 Fig. 2-22 shows graphically the relation of power to speed under 
 one foot head, as expressed by the constant K 5 within the range of 
 practice of American turbine builders. 
 
 The use of the diagram may be illustrated as follows : 
 
 At 35 revolutions per minute various types of American wheels 
 will develop from I to 5.8 horse power. For the best efficiency, 
 that is for a constant value of <, the number of revolutions ot a 
 
 wheel will vary as i/h, and the power will vary as h*. Thus for 
 a 1 6 foot head these wheels will run four times as fast as for a one 
 foot head or at 140 R. P. M., and will develop 64 times the power 
 that will be developed at a one foot head, or from 64 to 371 H. P., 
 between which limits the wheel must be chosen. 
 
 Suppose a wheel is desired to develop 500 H. P. at 150 R. P. M. 
 under 25 foot head. These conditions correspond to 4 H. P. at 30 
 
Relation of Speed to Power of Turbine. 
 
 349 
 
 3 4 5 6~~ 8 8 10 II 
 
 HORSE POWER UMDEfl ONE FOOT HEAD. 
 
 Fig. 222. Speed Curves of Various Standard American Wheels. 
 
350 
 
 Hydraulics of the Turbine. 
 
 TABLE XXXII. 
 
 Showing Relation of Speed and Power of Various American Turbines working 
 under Catalogue Conditions. 
 
 
 
 1 
 
 ^5 
 
 Manufacturer. 
 
 Name of Wheel. 
 
 Min. 
 
 Max. 
 
 Reaction Wheels. 
 T. C. Alcott & Son 
 
 Alcott' s Standard High Duty 
 
 941 
 
 1216 
 
 Alexander, Bradley & Dunn- 
 iner. . 
 
 Alcott's Special High Duty. 
 
 2152 
 723 
 
 2300 
 830 
 
 American Steel Dredge \Vrks 
 
 ^Little Giant 
 
 2880 
 
 5420 
 
 Camden Water Wheel Works 
 Chase Turbine Mfg Co 
 
 United States Turbine 
 *Chase-Jonval Turbine ( reg- 
 
 3780 
 
 4570 
 
 
 ular ^ 
 
 1680 
 
 2580 
 
 
 *Chase-Jonval Turbine 
 (special ) 
 
 3460 
 
 5530 
 
 Christiana Machine Co 
 
 Balanced Gate Turbine 
 
 1220 
 
 1475 
 
 Craig, Ridgway & Son Co 
 
 Double Perfection . 
 
 840 
 
 895 
 
 Craig, Ridgwav & Son Co 
 
 Standard . ... 
 
 776 
 
 975 
 
 Dayton Globe Iron Works Co 
 
 *American Turbine. . . 
 
 623 
 
 1140 
 
 
 fNew American (high head 
 type) 
 
 520 " 
 
 674 
 
 J. L. &S. B. Dix . 
 
 Improved New American . . 
 Special New American 
 Improved Jonval Turbine 
 
 6100 
 2490 
 965 
 
 . 6477 
 3293 
 1363 
 
 Dubuque Turbine & Roller 
 Mill Co. . 
 
 Flenniken Turbine 
 
 1350 
 
 1880 
 
 Dubuque Turbine & Rollei 
 Mill Co 
 
 McCormick's Holyoke Tur- 
 
 
 
 
 bine . . 
 
 2380 
 
 2810 
 
 Holyoke Machine Co 
 
 Hercules Turbine 
 
 2030 
 
 2155 
 
 Humphrey Machine Co . 
 
 JIXL Turbine. 
 
 572 
 
 889 
 
 
 JXLCR Turbine 
 
 1052 
 
 1545 
 
 Rodney Hunt Machine Co. . 
 
 McCormick's Holyoke Tur- 
 bine 
 
 2310 
 
 2810 
 
 
 *Hunt McCormick Turbine. 
 *New Pattern Hunt Turbine 
 *>'tandaid Wheel, 1887 Pat- 
 tern 
 
 2360 
 1624 
 
 1665 
 
 3910 
 2900 
 
 2160 
 
 E. D. Jones & Sons Co 
 
 
 2360 
 
 2680 
 
 James Leffel & Co 
 
 Samson 
 
 3775 
 
 3833 
 
 
 Improved Samson 
 Standard 
 
 5013 
 948 
 
 5400 
 1063 
 
 
 Special 
 
 1730 
 
 1858 
 
 Munson Bros. & Co 
 
 JJPhoenix "Little Giant" 
 
 843 
 
 1600 
 
 Norrish, Burnharn & Co. . . 
 
 
 1130 
 
 1345 
 
 Platt Iron Works Co 
 
 Victor Register Gate 
 
 2254 
 
 2712 
 
 
 Victor Standard Cylinder 
 Gate 
 
 3733 
 
 4145 
 
 
 Victor High Pressure 
 
 129 10 
 
 169.50 
 
Relation of Speed to Power of Turbine. 
 
 TABLE XXXII. Continued. 
 
 Showing Relation of Speed oni Power of Various American Turbines working 
 under Catalogue Conditions. 
 
 
 
 ] 
 
 *. 
 
 Manufacturer. 
 
 Name of Wheel. 
 
 Min. 
 
 Max. 
 
 Reaction Wheels. Con. 
 
 TJ oole Engineering and Ma- 
 chine Co 
 
 Poole-Leffel 
 
 1170 
 
 1239 
 
 T H Risdon & Co 
 
 *Risdon Standard Turbine 
 
 2351 
 
 3680 
 
 8 Morgan Smith Co 
 
 *Ri.-don Type T. C. Turbine 
 * Risdon Tvpe D. C. Turb.ne 
 Smith McCormick 
 
 3520 
 46UO 
 2640 
 
 5070 
 7370 
 3013 
 
 
 Smith 
 
 6165 
 
 6640 
 
 The Trump Mfg Co 
 
 Standard Trump 
 
 ;# 07 
 
 4250 
 
 Wellman, Seaver, Morgan Co. 
 
 
 2380 
 
 2862 
 
 Impulse Wheels. 
 
 DeRemer Water Wheel Co. . 
 Abnei' Doble Co 
 
 *DeRemer Water Wheel. . . . 
 ^Tangential Wheel 
 
 12.34 
 4.00 
 
 18.01 
 
 7 62 
 
 Pelton Water Wheel Co 
 
 ^Tangential Wheel 
 
 7.84 
 
 11.42 
 
 Risdon Iron Works 
 
 *Tangential Wheel 
 
 8.24 
 
 11.22 
 
 
 
 
 
 *Wide variation in constants due to the design being special for various sized wheels (series not 
 exactly homogeneous). 
 
 tCatalogue recommends a maximum and minimum speed. Constants given are for the average 
 speed. 
 
 ^Tables in catalogue based on full theoretical power of the water. Wheels are said to give from 
 75 per cent to 90 per cent efficiency, depending on location. 
 
 ft.Munsoti Bros. Co. make several types of "Little Giant" turbines causing above wide variation 
 in constants. 
 
 R. P. M. under one foot head, and would require a wheel having a 
 constant K 5 = 36oo. 
 
 165. Value of Turbine Constants. The values of the constants 
 discussed in this chapter have been determined fro-m the cata- 
 logues of the manufacturers of American turbines and are the values 
 which may be used for determining the manufacturer's standard re- 
 lations of the wheel for particular and fixed conditions where < is 
 constant, as, for example, the development of a certain power under 
 a fixed head and with a given speed. When the head varies at dif- 
 ferent times, the value of <j> also varies and the value of the other co- 
 efficients of the turbine, A, K, K 2 , K 4 , and K 5 , will also vary. In 
 order to discuss such conditions the laws of the variations of these 
 constants, for any series of wheels, must be known. These laws 
 
352 Hydraulics of the Turbine. 
 
 can be ascertained from a complete test of any one wheel of the 
 series and the laws so determined will hold for the entire series if 
 the series is actually constructed on homogeneous lines. Owing to 
 imperfections in the processes of manufacture, there is actually 
 more or less variation between different wheels of a series. It is 
 therefore desirable, when the approximate size of the wheel needed 
 is known, to secure a test of a wheel of that particular size and 
 hand. 
 
 Of the constants discussed, < and A express the standard rela- 
 tion recommended by the manufacturer between diameter and speed 
 in the series of wheels he offers. See equations 
 
 (23) n 
 
 (24) 
 
 ii 
 
 The coefficient K is the constant of discharge and shows the 
 standard relation for various types of turbines between the quantity 
 of water discharged and the diameter of the wheel. See equations 
 
 (41) q = 
 
 (42) D = 
 
 K 2 is the constant of power and shows the standard relation be- 
 tween the diameter of the wheel and the power. See equation 
 
 (45) P = K 2 D 2 h* 
 
 K 4 is the constant of discharge and shows the standard relation 
 between speed and discharge. See equation 
 
 (30) n - I 
 
 q 
 
 K 5 is the constant expressing the standard relation of power and 
 speed for a particular series of wheels. See equation. 
 
 (58) P = K 5 1^1 
 
 The catalogue tables of turbines from which the standard values 
 of the constants in the preceding tables have been calculated are 
 presumably based on the actual tests of certain wheels of the series. 
 The actual results of a test of any individual wheel of the series is 
 likely to depart to an extent from the tabular value. Differences 
 
Literature. 
 
 353 
 
 will often be found between wheels of different diameters, between 
 wheels of the same diameter but of opposite hand, and even between 
 wheels of the same size and hand which are supposed to be con- 
 structed on identical lines. 
 
 These differences in results are due to carelessness in construc- 
 tion, or to unusually good construction in the effort to secure special 
 results, where the conditions warrant special effort. Any change in 
 the design of a wheel for the purpose of reducing or increasing the 
 discharge, and hence reducing or increasing its power, will give 
 rise to differences in these coefficients which must be taken into 
 account in any calculations made thereon. A careful study of these 
 coefficients as determined from the actual tests of any wheel, to- 
 gether with a study of the design of the wheel itself, will form the 
 basis of a complete and systematic knowledge of water wheel de- 
 sign. 
 
 LITERATURE. 
 
 1. Hermann, Gustav. Die graphische Theorie der Turbinen and Kreisel- 
 
 pumpen. Verhaldung des Vereines zur Beforderung des Gewerb- 
 feisses in Preussen. 1884, pp. 307-379; 521-580. 
 
 2. Arnot, C. Graphic Turbine Tables. Showing relation of head and dis- 
 
 charge for various sizes of turbines. Zeitschr. d ver Deutsch. 
 Ing. p. 980. 1890. 
 
 3. Ludewig, H. Allgemeine Theorie der Turbinen. Berlin. L. Simon, 
 
 1890. 
 
 4. Richards, John. Turbines Compared with Water Wheels. Eng. News. 
 
 Vol. 1, p. 530. 1892. 
 
 5. Hunking, A. W. Notes on Water Power Equipment. Jour. Asso. Eng. 
 
 Soc. Vol. 13, p. 197. 1894. 
 
 6. Moissner, G. Die Hydraulik und die hydraulischen Motoren. Jena. 1895. 
 
 7. Bodmer, G. R. Hydraulic Motors, Turbines and Pressure Engines. New 
 
 York. Van Nostrand. 1895. 
 
 8. Elaine, R. G. Hydraulic Machinery. New York. Spon & Chamberlain. 
 
 1897. 
 
 9. Heines, Charles N. Centrifugal Pumps, Turbines and Water Motors. 
 
 Manchester, Eng., Technical Pub. Co. 1898. 
 
 10. Fox, William. Graphics of Water Wheels. Stevens Indicator. Vol. 16, 
 
 p. 30. 1899. 
 
 11. Brauer, Ernst A. Grundriss der Turbinen Theorie. Leipsig, S. Hirzel. 
 
 1899. 
 
 12. Zeuner, Gustav. Vorlesungen iiber Theorie der Turbinen mit vorbereiten- 
 
 den untersuchungen aus der technischen hydraulik. Leipsig. 
 Arthur Felix. 1899. 
 
 13. Rateau, A. Traite des turo-machines. Paris. Ch. Dunod. 1900. 
 
354 Hydraulics of the Turbine. 
 
 14. Henrotte, J. Turbines-hydrauliques, pornpes et ventilateurs, centrifuges,. 
 
 princeps theoriques, dispositions pratiques et calcul des dimen- 
 sions. Liege, Imprimerie Liegeoise. 1900. 
 
 15. Marks, G. Croiden. Hydraulic Power and Engineering. New York. Van 
 
 Nostrand. 1900. 
 
 16. Wood, DeVolson. Turbines, Theoretical and Practical. New York. Wiley 
 
 & Sons. 1901. 
 
 17. Miiller, Wilhelm. Die Francis-Turbinen. Hanover, Janecke. 1901. 
 
 18. Kessler, Jos. Berechnung and Konstruktion der Turbinen. Leipsig. J. 
 
 M. Gebhardt. 1902. 
 
 19. Camerer, R. Diagrams of Theory of Turbines. Graphic Representa- 
 
 tion of Equation with Proof and Application. Dingler's Poly- 
 tech. Jour. p. 693. 1902. 
 
 20. Thurso, John Wolf. Modern Turbine Practice and the Development of 
 
 Water Power. Eng. News. Dec. 4, 1902. 
 
 21. Rea, Alex. Turbines and the Effective Utilization of Water-Power. 
 
 Mech. Engr. March 22, 1902. 
 
 22. Osterlin, Hermann. Untersuchungen iiber den Energieverlust des Was- 
 
 sers in Turbinenkanalen. Berlin. Julius Springer. 1903. 
 
 23. Thurso, John Wolf. Effect of Draft Tube. Eng. News. Vol. 1, p. 29. 
 
 1903. 
 
 24. de Graffigny, Henri. Les Turbo-moteurs et les Machines Rotatives. Paris 
 
 E. Bernard. 1904. 
 
 25. Dickl, Ignaz. Die Berechnung der achsialen Actionsturbinen auf zeich- 
 
 nerischem Wege. Vienna. Spielhagen & Schurich. 1904. 
 
 26. Danckwerts. Die Grundlagen der Turbinenberechung fur Pratiker and 
 
 Studierende des Bauingenieurfaches. Wiesbaden. C. W. Krei- 
 del. 1904. 
 
 27. Thurso, John Wolf. Modern Turbine Practice. New York. Van Nos- 
 
 trand. 1905. 
 
 28. Church, Irving P. Hydraulic Motors. New York. Wiley & Sons. 1905. 
 
 29. Basshnus, N. Klassifikation von Turbinen. Zeitschritt der Verenier 
 
 Deutschjer Ingenie for 1905, p. 922. 
 
 30. Graf, Otto. Theorie, Berechnung und Konstruktion der Turbinen und 
 
 deren Regulatoren; ein Lehrbuch fur schule und praxis. 
 Munich. August Lachner. 1904 and 1906. 
 
 31. Wagenbach, Wilhelm. Neuere Turbinenanlagen. Berlin. 1905. 
 
 32. Gelpke, Viktor. Turbinen und Turbinenanlagen. Berlin. Julius; 
 
 Springer. 1906. 
 
 33. Pfarr, A. Die Turbinen fur Wasserkraftbetrieb. Berlin. Julius 
 
 Springer. 1907. 
 
 34. Tangential Water Wheel Buckets. The Engr. May 1, 1904. 
 
 35. Kingsford, R. T. A Complete Theory of Impulse Water Wheels and Its- 
 
 Application to Their Design. Eng. News. July 21, 1898. 
 
CHAPTER XV. 
 
 TURBINE TESTING. 
 
 166. The Importance of Testing Machinery. A correct theory 
 based on mathematical analysis forms a valuable foundation for 
 machine design. In the construction of any machine, however, 
 theoretical lines can seldom be followed in all details, and, even if 
 this were possible, the truth of the theory must be demonstrated 
 by actual trial for there are usually many factors involved which 
 cannot be theoretically considered and yet affect practical results. 
 In any machine much depends upon the character of the workman- 
 ship, on the class of material used, and on all the details of manu- 
 facture, installation and operation as well as on design. All of 
 these matters can hardly be included in a theoretical consideration 
 of the subject, and it therefore becomes necessary to determine 
 the actual results attained by a trial of the machinery under work- 
 ing conditions. 
 
 General observations or even a detailed examination of any 
 machine and its operation can rarely be made sufficiently com- 
 plete to give any accurate knowledge of the quantity or quality of 
 the results which it can and does accomplish. It is only when the 
 actual effect of slight changes in design can be accurately deter- 
 mined by careful experiment that a machine can be improved and 
 practical or approximate perfection attained. 
 
 The ease with which such determination can be made is usually 
 a criterion of the rapidity with which the improvements in the de- 
 sign and construction of a particular machine take place. Where 
 such determinations are readily made, rapid advancement results, 
 but where they are costly and require a considerable expenditure 
 of time or money, the resulting delays and expenses usually so 
 limit such determinations that good results are attained but slowly. 
 
 The invention of the steam engine indicator and the Piony brake 
 placed in the hands of the engineer instruments by means of which 
 he could readily determine the action of steam within the engine 
 cylinder and the actual power developed therefrom. The knowl- 
 edge thus gained has been one of the most potent factors in the 
 rapid advancement of steam engineering. 
 
35^ Turbine Testing. 
 
 The physical results of radical modifications or changes in de- 
 sign are sometimes quite different from those anticipated by the 
 designer. Improvement in any machine means a departure from 
 the tried field of experience and the adoption of new and untried 
 devices or arrangements. Frequently a line of reasoning, while 
 apparently rational, is found to be in error on account of unfore- 
 seen conditions or contingencies and the results anticipated are 
 not borne out in the actual practical results. Unless, therefore, 
 such results are carefully and accurately determined by exact 
 methods the actual value of changes in design may never be known 
 or appreciated and designs may be adopted which, while apparently 
 giving a more desirable form of construction, actually accomplish 
 less than the form from w r hich the design has departed. 
 
 167. The Testing of Water Wheels. The value of the testing of 
 water wheels was recognized by Smeaton who- tested various 
 models of water wheels about the middle of the Eighteenth Century. 
 Methods of turbine testing were also devised with the first develop- 
 ment of the turbine, which have been potent factors in the improve- 
 ment of the turbine. While the methods of testing have been 
 greatly improved since that time, they have not as yet reached a 
 state that can be considered reasonably satisfactory, and turbine 
 testing has not become so general as to assure the high grade of 
 design and workmanship in their manufacture as in other machin- 
 ery where testing is more easily and regularly practiced. 
 
 The principal causes of the backward condition of turbine test- 
 ing lie in the difficulties and expense of making an accurate test 
 in place, and the expense and unsatisfactory results of testing tur- 
 bines in a testing flume where the head and capacity are so limited 
 as to confine satisfactory tests to heads of 17 feet or less and to 
 wheels of a capacity of about 250 cubic feet per second, or less if 
 the full head of 17 feet is to be maintained. There is an urgent 
 demand for accurate and economical methods for the measurement 
 of the water used and of the power developed by water wheels in 
 place, that can be readily and quickly applied without the almost 
 prohibitive expense of the construction of expensive weirs and 
 other apparatus now used for such purposes. Apparently slight 
 variations in turbine construction produce radical changes in prac- 
 tical results. The high results achieved under test by a well- 
 designed and well-constructed wheel is no assurance that wheels 
 of the same make and of the same design, even though they be ~>f 
 the same size and even from the same pattern, will give similar 
 
Smeaton's Experiments. 
 
 357 
 
 results. This is especially true when the contingencies of compe- 
 tition and the knowledge that a test of the wheel is impossible, or 
 at least highly improbable, offer a premium on careless construc- 
 tion and cheap work. 
 
 A brief examination of the work already done in this line, and 
 of the methods now in vogue, may afford suggestions for future 
 improvements and development in this important w r ork. 
 
 1 68. Smeaton's Experiments. John Smeaton, the most experi- 
 enced and eminent engineer of his time, made a series of experi- 
 ments on the power and effect of water used by means of various 
 forms of water wheels for mill purposes. Accounts of these experi- 
 ments were published in the Transactions of The Royal Society of 
 
 England in 1759. Until that 
 time the relative values of the 
 different types of water 
 wheels of that day were very 
 poorly understood and ap- 
 preciated. 
 
 Smeaton's apparatus for 
 measurement of the power 
 of overshot and undershot 
 wheels is shown by Figs. 223 
 and 224 taken from "The 
 Encyclopedia of Civil En- 
 gineering" by Edward 
 Cressy. Water was pumped 
 by means of the hand pumps 
 from the tail basin, X, to the 
 supply cistern, V, from which 
 it was admitted to the wheel 
 through an adjustable gate. 
 The power developed was 
 measured by the time re- 
 
 Fig. 223. Smeaton's Apparatus for Testing 
 Water Wheels. 
 
 quired to raise a known 
 weight through a known 
 height by means of a cord 
 
 passing through a system of pulleys and attached to a small wind- 
 ing drum or collar upon the wheel shaft. This drum revolved only 
 when, by slight longitudinal movement, it was made to engage a 
 
 pin on the shaft. 
 
 In these experiments Smeaton found a maximum efficiency of 
 
358 
 
 Turbine Testing. 
 
 32 per cent., and a minimum efficiency of 28 per cent, for undershot 
 wheels. He also observed that the most efficient relations between 
 the peripheral velocity of the wheel and velocity of the water were 
 attained when the former was from 50 per cent, to 60 per cent, of 
 the latter, and that the force that could be exerted by a wheel to 
 
 Fig 224. Section of Smeaton's Apparatus for Testing Water Wheels. 
 
 advantage was from 50 per cent, to 70 per cent, of tne force re- 
 quired to maintain it in stationary equilibrium. 
 
 For overshot wheels Smeaton found that the efficiency varied 
 between 52 and 76 per cent. From his experiments he concluded 
 that the overshot wheel should be as large as possible, allowing, 
 however, a sufficient fall to admit the water onto the wheel with a 
 velocity slightly greater than that of the circumference of the 
 wheel itself, and that the best velocity of the circumference of the 
 wheel was about three and one-half feet per second. This speed 
 he found applied both to the largest as well as to the smallest 
 water wheel. 
 
 From these experiments Smeaton concluded that the power of 
 water applied directly through the exertion of its weight by grav- 
 ity, as with the overshot wheel, was more effective than when its 
 power was applied through its acquired momentum, as in the 
 
The Early Testing of Turbine Water Wheels. 359 
 
 undershot wheel, although his line of reasoning indicated other- 
 wise. The later development of impulse wheels shows that his 
 reasoning was correct, and that the low efficiency of the impulse 
 wheel was due to the method of applying the momentum of the 
 water rather than to any inherent defect in the impulse principle. 
 
 The experiments or tests of Smeaton, while crude and imperfect 
 and performed upon wheels which were merely models, afforded 
 a comparative measurement of the efficiency of the undershot, over- 
 shot and breast wheels then in use and had a marked effect on the 
 further selection of such wheels. 
 
 169. The Early Testing of Turbine Water Wheels. The testing 
 of turbine wheels began many years ago in France before the turb- 
 ine became well known in the United States.* 
 
 Fourneyron began the study of the early forms of turbines as 
 early as 1823, and, in 1827, he introduced his well-known wheel 
 and also brought into notice a method of systematic testing of the 
 same by means of the Prony brake. 
 
 "La Societe d' Encouragement pour T Industrie Nationale" is 
 credited by Thurston with the introduction of a general system for 
 the comparison of wheels and correct methods of determining the 
 efficiency.** Other engineers immediately accepted this method of 
 comparison of wheels. Morin, in 1838, reported the results of a 
 trial of a Fourneyron wheel as giving an efficiency of 69 per cent, 
 with only slight changes in values for a wide range of speed. With 
 another wheel he obtained 75 per cent, efficiency.f 
 
 Combes tested his reaction wheel and found that an efficiency 
 of about 50 per cent, could be obtained.]! 
 
 The first systematic test of turbines in the United States was 
 made by Mr. Elwood Morris of Philadelphia in 1843 and reported 
 in the Journal of The Franklin Institute for December of that year. 
 
 The maximum efficiency reported was 75 per cent. This result 
 was reached when the value of < for the interior circumference of 
 the Fourneyron turbine was .45. In 1844 Mr. James B. Francis 
 determined the power and efficiency of a high breast water wheel 
 
 * See "The Systematic Testing of Water Wheels in the United States," by 
 ft. H. Thurston, Trans. Am. Soc. Mech. Eng. vol. 8. 
 
 * :: See "Memoire sur les Turbines Hydrauliques," by H. Fourneyron, Brus- 
 sels, 1840. 
 
 t See "Experiences sur les Power Hydrauliques," Paris, 1838. 
 
 t See "Mechanics of Engineering," Weisbach. Translated by A. J. DuBois. 
 Hydraulics and Hydraulic Motors, vol. II, part I, p. 470. 
 
360 
 
 Turbine Testing. 
 
 in the City of Lowell, using a Prony brake fitted with a dash-pot 
 to prevent irregular operation. 
 
 In 1845 M r - Uriah A. Boyden made a trial of a turbine designed 
 by himself, using the Prony brake, and obtained an efficiency of 78 
 per cent, as the maximum. In 1846 a similar test of one of the 
 Boyden turbines was made at the Appleton Mills in Lowell, and 
 an efficiency of 88 per cent, was reported. He continued the work 
 of the testing of water wheels for several years and tested many 
 wheels of various types.* Mr. Francis introduced the system of 
 testing wheels which were to be used by purchasers of water from 
 the water power company which he represented. The chief pur- 
 pose of the tests was that the wheels might be used as meters in 
 determining the amount of water used by the various purchasers. 
 
 In 1860 the City of Philadelphia undertook a comparative trial 
 of various turbines in order to determine their relative merits for 
 used in the Fairmount Pumping Plant. The results o'f these tests 
 given in Table XXXIII are somewhat questionable but have a 
 comparative value. 
 
 TABLE XXXIII. 
 
 Water Wheel Tests at Philadelphia in 1860. 
 
 Name of Wheel. 
 
 Kind of 
 Wheel. 
 
 Per 
 cent 
 of 
 Effect 
 
 3 per 
 cent 
 added 
 for 
 frict'n 
 
 Where built. 
 
 Stevenson's second wheel 
 
 Jonval . 
 
 .8777 
 
 9077 
 
 Paterson N J 
 
 Geyelin's second wheel 
 
 Jonval . 
 
 .8210 
 
 8510 
 
 Philadelphia P^ 
 
 Andrews & Kalbach's third wheel 
 Collin's second wheel 
 
 Spiral . . 
 Jonval 
 
 .8197 
 7672 
 
 .8497 
 7972 
 
 Bernville, Pa. 
 Trov N Y 
 
 Andrews & Kalbach's second 
 wheel 
 
 Spiral . . 
 
 .7591 
 
 .7891 
 
 Bernville Pa 
 
 Smith's, Parker's fourth trial 
 Smith's, Parker's third trial. .... 
 Steven's first wheel 
 
 Spiral . . 
 Spiral . . 
 Jonval . 
 
 .7569 
 . 7467 
 7335 
 
 .7869 
 .7767 
 7635 
 
 Reading, Pa. 
 Reading, Pa. 
 Paterson N J 
 
 Blake 
 
 Scroll . . 
 
 7169 
 
 7469 
 
 East Pepperell Mass 
 
 Tyler 
 
 Scroll . . 
 
 .7123 
 
 .7423 
 
 West Lebanon N. EL 
 
 (jlevelin's first, wheel 
 
 Jonval 
 
 6799 
 
 7099 
 
 Philadelphia Pa 
 
 Smith's, Parker's second wheel. . 
 Merchant's Goodwin 
 
 Spiral. . 
 Scroll . . 
 
 .6726 
 .6412 
 
 .7026 
 6712 
 
 Reading, Pa. 
 G nil ford, N Y 
 
 Mason's Smith 
 
 Scroll . . 
 
 . 6324 
 
 .6624 
 
 Buffalo N Y 
 
 Andrew's first whefl 
 
 Spiral 
 
 6205 
 
 6505 
 
 Bernville PH 
 
 Rich 
 
 Scroll . 
 
 6132 
 
 .6432 
 
 Salmon River N Y 
 
 Littlepa^e 
 
 Spiial. . 
 
 5415 
 
 .5715 
 
 Austin Texas 
 
 Monroe 
 
 Scroll . . 
 
 .5359 
 
 . 5659 
 
 Worcester Mass 
 
 Collin's first wheel . . 
 
 Jonval 
 
 4734 
 
 5034 
 
 Troy N Y 
 
 
 
 
 
 
 * See "Lowell Hydraulic Experiments. 
 
The Testing of Turbines by James Emerson. 361 
 
 170. The Testing of Turbines by James Emerson. One of the 
 
 men who did much valuable work of this character was Mr. James 
 Emerson who designed a new form of .dynamometer of the trans- 
 mitting kind. At the request of Mr. A. M. Swain, Mr. Emerson 
 designed a Prony brake, embodying this dynamometer for the pur- 
 pose of testing a Swain turbine in a flume built from designs by 
 Francis. The results obtained by Mr. Emerson from this test 
 were so satisfactory that The Swain Turbine Company decided to 
 open the flume for the purpose of a competitive test of all turbines 
 which might be offered for this purpose. Announcement of this 
 test was dated June i6th, 1869. The pit was fourteen feet wide, 
 thirty feet long, and three feet deep, measured from the crest of the 
 weir. The best results of this competitive test, the accuracy of 
 which has since been .questioned by Mr. Emerson, were attained 
 with the Swain and Leffel wheels. The former ranged from 66.8 
 up to 78.9 per cent, efficiency, and the latter from 61.9 to 79.9 per 
 cent, efficiency. This competitive test was the beginning of a series 
 of such tests as well as of a general system of the public testing of 
 turbines. The testing flume was opened to all builders and users 
 of turbine wheels and such tests have been continued in the United 
 States up to the present time. 
 
 The report of the results of this test attracted the attention of 
 Mr. Stewart Chase, then agent of The Holyoke Water Power Com- 
 pany, who, recognizing its very great importance, secured the 
 adoption of a systematic testing of water wheels at Holyoke for 
 the benefit of the Company and wrote to Mr. Emerson as follows: 
 
 'The testing of turbines is the only way to perfection, and that 
 is a matter of great importance. Move your work to Holyoke and 
 use all the water that is necessary for the purpose, and welcome, 
 free of charge." 
 
 Mr. Emerson, who had been conducting the testing of water 
 wheels as a matter of private business at Lowell, at which place 
 he was obliged to pay for the water used, at once accepted the 
 liberal offer thus tendered him and removed to Holyoke where he 
 continued the testing of water wheels until it was taken in hand 
 by The Holyoke Water Power Company. 
 
 The reports of Mr. Emerson's work were published and undoubt- 
 edly were the means of bringing a number of wheels up to a state 
 of high efficiency. The reports were found to be full of valuable 
 
362 
 
 Turbine Testing. 
 
 data, and, although not systematically arranged, formed an exten- 
 sive and valuable collection of figures.* 
 
 In 1879, The Holyoke Water Power Company, for the purpose of 
 determining the standing of wheels offered for use at that place, 
 
 80 
 
 70 
 
 60 
 
 so 
 
 40 
 
 30 
 GATE 
 
 | GATE 
 
 5 GATE 
 
 Fig. 225. 
 
 GATE 
 
 FULL 
 GATl : 
 
 arranged for a comparative or competitive turbine test at the flume 
 constructed by Mr. Emerson at Holyoke. The wheels were set 
 under the direction of Mr. Emerson and a part of the tests were 
 
 * See James Emerson's "Hydro-Dynamics." 
 
The Testing of Turbines by James Emerson. 
 
 made or witnessed by Mr. Samuel Weber and Mr. T. G. Ellis. 
 Their report was accompanied by a graphical diagram (Fig. 225 
 and Table XXXIV) on which they commented as follows : 
 
 "By examining the diagram and table, the peculiarities of the 
 several wheels will be readily seen. It will be observed that the 
 Houston turbine, which has the highest percentage of effect at full 
 gate, is really the least efficient at from half to three-quarters, and 
 from half to full gate, of all those shown on the diagram, and is 
 only superior to the Nonesuch at from three-quarters to full gate, 
 and that by a very trifling amount; so that the wheel which ap- 
 parently has the highest percentage is really the least desirable for 
 actual use. The Thompson turbine, which has the lowest percentage 
 of those shown at full gate, rises to the sixth place at from one-half 
 to full gate, and to the fourth place at from one-half to three-quart- 
 ers gate. The Tyler turbine, which has the second highest per- 
 centage at full gate, falls to the sixth place at from one-half to 
 three-quarters gate. The Hercules turbine, which stands third 
 only at full gate, takes the first rank at from half to full gate, or 
 any of its subdivisions. The New American turbine, which stands 
 only fifth in the percentage at full gate, is second only to the Her- 
 cules at from one-half to full gate or either of its subdivisions, and, 
 indeed, differs from the Hercules very slightly in its useful effect 
 through the whole range shown. 
 
 "Taking the average useful effect of the wheels shown from one- 
 half to full gate as a measure of their efficiency, their relative value 
 is in the order shown in the table." 
 
 TABLE XXXIV. 
 Showing Average Percentage at Part Gafe. 
 
 Name. 
 
 ^toM 
 Per cent. 
 
 % to Full 
 Per cent. 
 
 K to Full 
 Per cent. 
 
 
 .737 
 
 .805 
 
 .771 
 
 
 .732 
 
 .795 
 
 .763 
 
 
 .708 
 
 .786 
 
 .747 
 
 Tyler 
 
 .665 
 
 .766 
 
 .715 
 
 Tait 
 
 .680 
 
 .744 
 
 .712 
 
 
 .696 
 
 .721 
 
 .709 
 
 
 .619 
 
 .712 
 
 .666 
 
 
 .397 
 
 .717 
 
 .557 
 
 
 
 
 
364 
 
 Turbine Testing. 
 
 The report of Mr. Emerson covered a much larger number of 
 wheels. The diagram accompanying Mr. Emerson's report* is re- 
 produced in Fig. 226. 
 
 | GATE 
 
 FULL 
 GATE 
 
 Fig. 220. 
 
 171. The Holyoke Testing Flume. The later work of systematic 
 testing of American turbines has been carried on principally at the 
 Holyoke flume. 
 
 t "The object aimed at by the. Water-power Companies of Lowell 
 and Holyoke, in the establishment of testing flumes for turbines, 
 
 * Emerson's "Hydro-Dynamics," page 300. 
 
 f"The Systematic Testing of Water Wheels," by R. H. Thurston. 
 
The Holyoke Testing Flume. 365 
 
 is the determination of the power and efficiency, the best speed, 
 and the quantity of water flowing at from whole, to, say, half gate, 
 so exactly that the wheel may be used as a meter in the measure- 
 ment of the water used by it. The quantity of water passing 
 through the wheel, at any given gate-opening, will always be prac- 
 tically the same at the same head, and the wheel having been 
 tested in the pit of the testing flume, and its best speeds and highest 
 efficiency determined, and a record having been made of the quan- 
 tity of water discharged by it at these best speeds and at all gates, 
 the turbine is set in its place at the mill, speeded correctly for the 
 head there afforded, and a gauge affixed to its gate to indicate the 
 extent of gate opening. The volume of water passing the wheel 
 at various openings of gate having been determined at the testing 
 flume, and tabulated, the engineer of the Water-power Co. has 
 only to take a look at the gauge on the gate, at any time, or at regu- 
 lar times, and to compare its reading with the table of discharges, 
 to ascertain what amount of water the wheel is taking and to de- 
 termine what is due the company for the operation of that wheel, 
 at that time. The wheel is thus made the best possible meter for 
 the purposes of the vender of water." 
 
 The present Holyoke Testing Flume was completed in 1883. 
 The plan of this flume is shown in Figs. 227 and 228. 
 
 The testing flume consists of an iron penstock, A, about nine feet 
 in diameter, through which the water flows from the head race 
 into a chamber, B, from which it is admitted through two head 
 gates, G,G, into the chamber, C, and from thence through trash 
 racks into the wheel pit, D. Passing through the wheel to be 
 tested, it flows into the tail-race, E, where it is measured as it 
 flows over a weir, at O. The object of the chamber, B, is to afford 
 opportunity for the use of the two head gates, G,G, to control the 
 admission of water, and consequently the head acting on the wheel. 
 There is also a head gate at the point where the penstock, A, takes 
 in water from the first level canal. A small penstock, F, about 3 
 feet in diameter, takes water from the chamber, B, independently 
 of the gates and leads to a turbine wheel, H, set in an iron casing, 
 in the chamber, C, in order that this wheel can run when C and the 
 wheel pit, D, are empty. The wheel, H, discharges through the 
 floor at the bottom of C, and through the arch, I, and the supple- 
 mentary tail-race, K, into the second level canal. This wheel is 
 used to operate the repair shops ; also to operate the gates, G. The 
 chamber, C, is bounded on one side by a tier of stop-planks, L, and, 
 
3 66 
 
 Turbine Testing. 
 
The Holyoke Testing Flume. 
 
 367 
 
 on another side, by a tier of stop-planks, M. The object of the 
 stop-planks, L, is to afford a waste-way out of the chamber, C. 
 This is of especial use in regulating the height of the water when 
 testing under low heads. The water thus passed over the planks, 
 L, falls directly into the tail-race, K. and passes into the second 
 level. The stop-planks, M, are used when scroll or cased wheels 
 
 Fig. 228. -Testing Flume of Holyoke Water Power Co. Arranged for Testing 
 Horizontal Turbines. 
 
 are tested. In such cases D is empty of water and the wheefr case 
 in question is attached by a short pipe or penstock from an open- 
 ing cut in the planks, M. Flume wheels are set in the center of the 
 floor of D, and D is filled with water. They discharge through the 
 floor of D and out of the three culverts, N,N,N, into the tail-race, 
 E. Horizontal wheels are set in the pit, D, with their shafting 
 projecting through a stuffing-box in the side of the pit (See Fig. 
 228). At the down-stream end of the tail-race is the measuring 
 weir, O (Fig. 227). The crest of the weir is formed of a strip of 
 planed iron plate twenty feet in length. The depth of water on the 
 weir is measured in a cylinder, P, set in a recess, Q, fashioned in 
 the sides of the tail-race. These recesses are water-tight, and the 
 observer is thus enabled to stand with the water-level at convenient 
 
368 Turbine Testing. 
 
 height for accurate observation. The cylinder, P, is connected with 
 a pipe that crosses the tail-race or weir box about ten feet back of 
 the weir crest. The pipe is placed about one foot above the floor 
 and is perforated in the bottom with inch holes. A platform, R, 
 surrounds the tail-race, and is suspended from the iron beams that 
 carry the roof. Above the tail-race is the street, over which the 
 wheels to be tested arrive on wagons from which they are lifted 
 by a traveling crane that runs on a frame-work over the street, and 
 by means of which the wheels are carried into the building and are 
 lowered into the wheel pit, D. Spiral stairs lead into a passageway 
 that leads in turn to the platform, R. In the well-hole of these 
 stairs are set up the glass tubes which measure the head of water 
 upon the wheel. These gauge tubes are connected with the pit, D, 
 and the chamber, C, by means of pipes, one of which enters the 
 wheel pit through a cast iron pipe, T, built into the masonry dam 
 which forms the down stream end of the wheel pit, D. The other 
 pipe passes back under the wheel pit, D. and crosses the tail-race 
 at the extreme back line and close under the pit floor. This pipe 
 is perforated throughout its length across the race in a manner 
 similar to the pipe used for determining the head on the weir. To 
 enable the observers at the brake wheel, head gauge and measuring 
 weir to take simultaneous olbservations, an electric clock rings 
 three bells, simultaneously, at intervals of one minute. 
 
 The usual method of testing a wheel is as follows : After the 
 wheel is set in place (See Figs. 227 and 228) a brake pulley and 
 Prony brake are attached to the shaft, the gates are set at a fixed 
 opening and water is admitted. The runaway speed of the wheel 
 is first determined with the brake band loose, after which a weight 
 is applied and the brake tightened until the friction load balances 
 the weight. As soon as this balance is attained, which requires 
 only a few seconds, the revolution counter is read and the heads 
 in the head-race, tail-race and on the weir are observed. Observa- 
 tions are repeated simultaneously each minute at the stroke of the 
 bell and for a period of from three to five minutes. The weight 
 is then changed and the observations repeated for a different load 
 and speed. After observations are made over the range of speeds 
 desired, the gate opening is changed, and a similar series of obser- 
 vations are made for the new gate opening. This is repeated for 
 each desired gate opening, usually from full gate to about one-half 
 gate. 
 
 The results are calculated and reported in the form shown in 
 Table LX. It is usually stated in the report whether the test is 
 
The Value of Tests. 369 
 
 made with a plain or conical draft tube, whether plain or ball bear- 
 ings are used, and also the pull necessary, at a given leverage, to 
 start the turbines in the empty pit. No attempt is made in these 
 reports to describe the bearings or finish of the wheels in detail. 
 
 The maximum head available is about 17 feet under small dis- 
 charges and this decreases to about 9 feet under a discharge of 300 
 cubic feet per second. The capacity of the tail-race and weir is 
 hardly sufficient for the accurate measurement of the latter quan- 
 tity. 
 
 172. The Value of Tests. There can be no question as to the 
 very great value of carefully-made tests of any machine. It must 
 be borne in mind, however, that any test so made represents results 
 under the exact conditions of the test, and, in order to duplicate the 
 results, the conditions under which the test 'was made must be 
 duplicated. Any changes in the design or finish of the wheels, any 
 alterations in the method of setting, or in the gates, draft tube or 
 other appurtenances connected with the same are bound to affect 
 the power and efficiency to a greater or less extent. 
 
 It is unfortunate for the world's progress that the records and 
 conditions of failures are seldom made known. The record of a 
 failure, while of great value from an educational standpoint, may 
 considerably injure the reputation of an engineer or manufacturer, 
 and consequently results of tests and experiments, unless fully 
 satisfactory, are seldom published or known except by those closely 
 interested. For this reason, the published tests of water wheels 
 usually represent the most successful work of the maker and the 
 best practical results he has been able to secure. Tests, unless 
 fairly representative, do not assure that similar turbines of the 
 same make, or even similar turbines of the same make, size and 
 pattern, will give the same efficient results unless all details of their 
 design, construction, and installation are duplicated. There is no 
 doubt that in many cases the published tests of water wheels are 
 the final consummation of a long series of experiments, made in 
 order to secure high results, and do not give assurance that such 
 results can be easily duplicated. The manufacturers have acknow- 
 ledged this by calculating their standard tables on a basis of power 
 and efficiency below that of the best tests they are able to obtain, 
 and it is only a matter of reasonable precaution for the engineer, 
 who is utilizing the results of any such tests for the purposes of 
 his design, to discount the test values to such an extent as will 
 assure him that his estimates will be fulfilled. 
 
370 Turbine Testing. 
 
 In water wheels for high-grade work, it is important that the 
 specifications for their, construction be carefully drawn and that, 
 by inspection and tests, the results of the work be fully assured. 
 It is unfortunate that no easily applied method is available for the 
 testing of water wheels in place. Such tests as are now carried on 
 involve the shipment of one or more of the wheels from the place 
 of manufacture to Holyoke, their tests under the conditions there 
 obtainable and their reshipment to the point where they are to be 
 installed. Here they may be set to operate under conditions en- 
 tirely different from those of the Holyoke test and the actual 
 results obtained cannot usually be determined. The most satisfac- 
 tory test of any machine is a test made under the conditions of 
 actual service, and, when such tests can be made, the results are 
 much more definite and of greater value than the tests of the wheel 
 made under conditions entirely different from those under which it 
 is to operate. 
 
 The Holyoke Testing Flume is performing valuable service and 
 the results of its work have been of material assistance in the de- 
 velopment and improvement of a number of high grade wheels. 
 Much remains to be done, however, in the development of turbine 
 testing so as to make it possible to more readily determine results 
 under working conditions. More uniform work will undoubtedly 
 result as the mechanical methods of manufacture improve and man- 
 ufacturers are able to more nearly duplicate the satisfactory con- 
 ditions which they have found to obtain in special cases. 
 
 173. Purpose of Turbine Testing. Water turbines may be tested 
 for various purposes among which may be named: 
 
 1. To establish the general principles of the operation of such 
 wheels. 
 
 2. To ascertain the most favorable condition for the operation 
 of a particular type of wheel. 
 
 3. To ascertain the results of operating a particular wheel, or 
 size or type of wheel, under particular conditions. 
 
 4. To investigate the various losses in the turbine in order that 
 such losses may be reduced as low as possible. 
 
 The quantities to be measured in a water wheel test are revolu- 
 tions per minute or speed, discharge, and power output. 
 
 In the fourth case the determination of heads, velocities and 
 friction losses at various points in the wheel case and wheel may 
 be essential. 
 
 The extent to which a test should be carried will depend on its 
 
Factors that Influence the Results of a Test. 371 
 
 purpose. For the first purpose above mentioned the range of ex- 
 periments should be as complete as possible, the discharge, and 
 power of the wheel being determined from numerous speeds from 
 zero to the runaway value and at various heads within the limits 
 of the physical conditions. 
 
 For the second purpose mentioned, the test may be carried only 
 through the range of commercial conditions under which the wheel 
 would ordinarily operate, but should, however, be broad enough to 
 include the range of conditions which will obtain in practice due 
 to the variations in head which are anticipated at various seasons. 
 
 For the third purpose mentioned, the wheel need be tested only 
 under the particular condition for which information is desired. 
 The test may be to determine whether or not certain guarantees 
 of the manufacturer have been, or will be, fulfilled. 
 
 For the fourth purpose a special line of investigation and tests 
 are necessary, which, while of great importance, are of special in- 
 terest to the manufacturer only or to those interested in the detail 
 development of some wheel for 'special purposes. 
 
 For the purpose of any test a clear conception of the nature of 
 the information sought is essential and each determination must 
 be made with proper precaution in order to secure accurate results, 
 174. Factors that Influence the Results of a Test. It is appar- 
 ent from the principles discussed in Chapter II that the actual 
 power developed by a turbine will be somewhat less than the 
 theoretical power of the water passing into it, depending on the 
 character of the wheel and the various energy losses involved in its 
 operation. The efficiency of the wheel, representing the ratio of 
 power developed to power applied, depends on the same factors. 
 
 These losses, incidental to the operation of a turbine, include the 
 friction of the shaft on its bearings, the hydraulic resistance from 
 the friction and shock of the water in the guides and passages, the 
 slip or leakage between the fixed and revolving parts of the wheel, 
 and the unutilized energy due to the velocity remaining in the 
 water when discharged from the wheel. 
 These losses are estimated as follows :* 
 
 Shaft friction from 2 to 3 per cent. 
 
 Slip or leakage from 2 to 3 per cent. 
 
 Hydraulic friction and f^hock from 10 to 15 per cent. 
 
 Energy in water leaving wheel from 3 to 7 par cent. 
 
 Total loss of energy from 17 to 28 per cent 
 
 * See "Development of Transmission of Power," by Unwin, p. 104; also- 
 'Francis Turbinen," by Muller, p. 18. 
 
37 2 Turbine Testing. 
 
 The total lasses given above correspond well with current prac- 
 tice. Under the best conditions efficiencies greater than 83 per 
 cent, are often obtained, and, under unfavorable conditions with 
 poor design and poor construction, efficiencies much less than the 
 minimum of 72 per cent, are common. While these losses can never 
 be entirely obviated they should be reduced to the practical mini- 
 mum that good design and good workmanship will permit. 
 
 175. Measurement of Discharge. The discharge, q, of the wheel 
 is commonly measured in cubic feet per second and should repre- 
 sent only the actual discharge through the wheel itself. This dis- 
 charge is usually measured, after it has passed the wheel, by the 
 flow over a standard weir. Any leakage around the wheel into the 
 weir box or from the weir box around the weir must be determined 
 and deducted from or added to the amount passing the weir. The 
 actual weir discharge must be known either by a direct calibration 
 of the weir or by the construction of the weir on lines for which 
 the discharge coefficients are well established. Errors in weir 
 measurements often reach values of nearly 5 per cent, due to the 
 erroneous use of coefficients obtained from other weirs not strictly 
 comparative. 
 
 The head on the weir must be accurately determined by means 
 of a hook gauge which should usually read to .001 of a foot. An 
 error of .01 foot in reading the head on the weir represents about i 
 per cent., and an error of .001 about .1 per cent., in the computed 
 discharge with a 1.5 foot head on the weir and a much greater error 
 at a lower head. 
 
 The construction of weirs in the tail-race of power plants, es- 
 pecially where large quantities of water are used under low heads, 
 involves an expense which is often prohibitive. In addition to this, 
 the construction of such weirs in plants working under low heads 
 wooild often seriously reduce the head and alter the working 
 conditions. 
 
 Other methods of accurately determining the flow should be 
 developed. There are two methods which seem to give promise 
 of good results: 
 
 First: By the careful determination of the velocities of flow in 
 the cross-section of the head or tail-race at points far enough from 
 the wheel to guarantee steady flow. This may be done by means 
 of a carefully calibrated current meter, a pitot tube, or by floats 
 To secure good results these instruments must be in the hands of 
 
Measurement of Head. 373 
 
 one familiar with their use and with the sources of error to which 
 each is liable if carelessly used. (See Chapter XL) This method in- 
 volves no loss in head. 
 
 Second : By the construction in the head or tail race of sub- 
 merged orifices of known dimensions and of a character for which 
 the coefficient of discharge has been determined. Some work in 
 this line has been done at the University of Wisconsin (See pages 
 43 to 45) which will soon be made accessible in detail in a bulletin 
 now in press. This method will involve only small losses of head 
 and by a sufficient range of experiments can perhaps be made 
 nearly as accurate as weir measurements. 
 
 Fig. 229. Doble Tangential Wheel Arranged for Brake Test. 
 
 176. Measurement of Head. The power of water applied to the 
 wheel depends on both quantity and head. The head is more easily 
 measured than the quantity, but, nevertheless, requires consider- 
 able care for its accurate determination. 
 
 The head of the wheel must be measured immediately at the 
 wheel both for the head-water and tail-water. If measured some 
 distance away it is apt to include friction losses, which should not 
 be charged against the wheel in raceways, penstocks and gates. 
 The measurement of head should usually be to about .01 feet, al- 
 though this depends on the magnitude of the heads involved. 
 
 177. Measurement of Speed of Rotation. The speed of the 
 wheel is usually recorded in revolutions per minute and may be 
 
Turbine Testing. 
 
 230. Section and Plan of Apparatus for Testing Swain Turbine (by 
 James B. Francis). 
 
Measurement of Power. 375 
 
 determined by a revolution-counter which records the number of 
 revolutions made in a given interval of time ; or by a "tachometer" 
 which, by means of certain mechanism, indicates at once on a dial 
 the revolutions per minute. The latter method is more convenient 
 if the instrument is correct, but frequent calibration and adjustment 
 are necessary and a correction must usually be applied to values 
 thus observed. 
 
 The revolution-counter is more accurate, and, while not so con- 
 venient, is to be preferred. 
 
 178. Measurement of Power. The power of the wheel may be 
 determined by placing a special brake pulley on the turbine shaft 
 and applying a resistance by means of a Prony brake or some other 
 form of dynamometer. This resistance is then measured by some 
 form of scales (See Figs. 229 and 230). The power thus consumed 
 by the friction of the brake can be calculated by equation (i) 
 
 2/r 1 n w 
 
 W Pl 33000 ^ which 
 P = Horse power 
 
 1 = length of lever or brake arm from center of revolution, in ft. 
 n = revolution per minute. 
 
 it = ratio of the circumference to the diameter of a circle = 3.1416. 
 w = weight on the scale in pounds. 
 
 This is the method applied in all laboratory work (see Fig. 229) and 
 is that used at the Holyoke Testing Flume. If properly applied, 
 it is probably subject to minimum error. When wheels are tested 
 in place, it is sometimes more convenient, and often essential, to 
 determine the power output from the current generated by elec- 
 trical units, which, when measured by aid of the known efficiency 
 of the generator, will give the actual power of the wheel. If these 
 units be direct-connected so that little or no transmission loss is 
 involved, and if the generator is new and its efficiencies have been 
 accurately determined, the errors involved by this method are 
 comparatively small. The transmission of the power before mea- 
 surement through gearing, through long shafts and bearings or by 
 other means, involves losses, the uncertainties of which must be 
 avoided if accuracy is essential. 
 
 179. Efficiency. The efficiency of a machine is the ratio of 
 energy delivered by the machine to that which was supplied to it 
 and it may have various significations. 
 
 In an impulse wheel (See Section 152) the theoretical energy of 
 the water in the forebay in foot pounds per second is : 
 (2} E -- qwh 
 
376 
 
 Turbine Testing. 
 
 The energy just inside the outlet of the pipe is 
 
 (3). E x =qw(h' + h") 
 
 The energy of the jet is 
 
 (4) E * = ^ir ' 
 
 and the theoretical power delivered to the bucket is 
 
 qw (1 <?) v (1 cos a) cp v 
 
 E.= -5- 
 
 If e represents the actual ft. Ibs. of work delivered by the wheel 
 per sec. then 
 
 (6) g = the efficiency of the entire installation including pipe, jet, 
 
 wheel, etc. 
 
 (7) -fir- = efficiency of the water wheel, including nozzle and buckets, 
 
 (8) 
 
 = efficiency of the runner, and 
 
 (9) -jg = hydraulic efficiency of the bucket 
 
 In the testing of water wheels, the efficiency (7), -g-, is the ratio- 
 ordinarily to be determined since it involves the losses in the noz- 
 
 1 u_ 
 
 II 
 
 "Bolt 
 
 1 
 
 
 1 
 
 1 
 
 
 1 
 
 1 
 
 
 1 
 
 I 
 
 
 1 
 
 1 
 
 
 1 
 
 1 
 
 1 
 
 "\ 1" 
 
 1 
 
 1 
 
 1 
 
 1 
 
 I 
 
 1 
 
 Half End Elevation 
 W.O.Weber 
 
 Half Sectional 
 Side Elevation 
 
 Fig. 231. 
 
 zle, jet and buckets as well as from residual energy in the water 
 discharged by the buckets, all of which are properly chargeable to 
 the operation of the wheel. 
 
Measurement ot Power. 
 
 377 
 
 End Elevation of Rings 
 
 W.o. freber Part Side Elevation 
 
 End Elevation 
 
 ... W.O. Wetter 
 
 Fig. 232. 
 
 Flan 
 
 Fig. 233. 
 
 The efficiency represented by (9) involves only the effects of 
 losses of energy by the water in passing over the buckets and 
 its theoretical value is 100 per cent, for all values of 0. It elim- 
 inates the effect of uneconomical speed of rotation of the wheel 
 which leaves residual lost energy in the water discharged by the 
 buckets and not properly chargeable to bucket imperfections. It 
 23 
 
378 
 
 Turbine Testing. 
 
 would be determined only in a detailed study or test made for the 
 first purpose above mentioned. 
 
 1 80 Illustration of Methods and Apparatus for Testing Water 
 Wheels: Fig. 230 shows the apparatus used for testing turbines 
 on a vertical shaft, by Mr. J. B. Francis to test a Swain wheel at the 
 
 aoo 
 
 BO 70 
 
 PER CENT BATE OPENING 
 
 80 
 
 Fig. 234. 
 
 Boott Mills, Lowell, Massachusetts (See "Lowell Hydraulic Ex- 
 periments.") 
 
 The section represents a vertical turbine in the testing plant with 
 testing apparatus in place. 
 
 The plan of the plant shows the arrangement of the Prony brake. 
 
 In these drawings P is the friction pulley ; b is the brake ; c are 
 counter balances to remove the load of the brake from the wheel 
 shaft; L is the bent lever or steel beam for transferring horizontal 
 motion to a vertical lift; S is the scale pan for the weight; d is the 
 dash-pot; w is the weir for measuring the water, and r is the rack 
 for stilling the water after leaving the wheel. 
 
 Figs. 231, 232, 233, show the brake wheel and Prony brake de- 
 tails used by Mr. William O. Weber for determining the efficiency 
 
Tests of Wheels in Place. 
 
 379 
 
 of various turbine water wheels as described by him in a paper on 
 "The Efficiency Tests of Turbine Water Wheels," (See vol. 27, Xo. 
 4, American Society of Mechanical Engineers). (See also Section 
 171, Experiments at the Holyoke Testing Flume.) 
 
 181. Tests of Wheels in Place. In April, 1903, a Leffel turbine 
 was tested at Logan, Utah, at the station of The Telluride Power 
 Transmission Company, by P. N. Nunn, Chief Engineer. The 
 wheel was directly connected to a General Electric generator the 
 efficiency of which has been determined as follows : 
 
 125 per cent load 96.7 per cent, efficiency . 
 
 100 per cent load 96 . 2 per cent, efficiency 
 
 75 per cent load 95.3 per cent, efficiency 
 
 50 per cent load 93 . 5 per cent, efficiency 
 
 25 per cent load 88 . per cent, efficiency 
 
 The output of this generator was used as a basis for calculating 
 the work done by the water wheel. 
 
 The results of the tests and methods of calculation are shown in 
 Table XXXV and graphically illustrated in Fig. 234. 
 
 TABLE XXXV. 
 
 Test of High Head Leffel Horizontal Turbine at Logan Station of Telluride 
 Power Trans. Company, Logan, Utah. Efficiency of Test at Constant Speed, 
 April 28, 1908. 
 
 P. N. Nunn, Chief Engineer. 
 
 Gate opening 
 
 75 
 
 0.50 
 
 0.40 
 
 50 
 
 75 
 
 % 
 
 HeaM on 15 feet weir in feet 
 Discharge of weir in cubic feet 
 per second 
 
 1.394 
 81 85 
 
 1.132 
 59 76 
 
 0.969 
 
 47 27 
 
 1.129 
 59 66 
 
 1.368 
 79 55 
 
 1.475 
 88 )4 
 
 Leakage around weir in sec- 
 ond, feet 
 
 85 
 
 85 
 
 0.85 
 
 0.85 
 
 85 
 
 85 
 
 Exciter water in second feet 
 Water through turbine in 
 second feet 
 
 1.98 
 80.72 
 
 1.98 
 58.63 
 
 1.98 
 46.14 
 
 1.98 
 58.53 
 
 1.98 
 78.42 
 
 1.98 
 87 81 
 
 Pressure at shaft center in 
 pounds per square inch . . 
 Effective head above shaft 
 center in feet 
 
 86.5 
 199.3 
 
 87.3 
 201.2 
 
 87.5 
 201.6 
 
 87.2 
 200.9 
 
 86.5 
 199.3 
 
 86.2 
 IPS 6 
 
 Vacuum head measured in 
 feet 
 
 10.4 
 
 10.6 
 
 10.8 
 
 10.6 
 
 10.4 
 
 10.3 
 
 Total working head in feet 
 Theoretical horse power .... 
 K.W. output at Sw. Bd 
 Generator efficiencv 
 
 209.7 
 1921 
 1152 
 0.965 
 
 211.8 
 1409 
 739 
 0.952 
 
 212.4 
 1112 
 500 
 0.935 
 
 211.5 
 1405 
 737 
 0.952 
 
 209.7 
 1866 
 1123 
 0.965 
 
 208.9 
 2082 
 1210 
 0.967 
 
 Brake horse power of turbine 
 Efficiencv of turbine 
 
 1600 
 0.833 
 
 1041 
 0.738 
 
 717 
 0.644 
 
 1038 
 0.739 
 
 1560 
 0.836 
 
 1677 
 0.806 
 
 Gate opening 
 
 0.75 
 
 0.50 
 
 0.40 
 
 0.50 
 
 0.75 
 
 0.96 
 
 
 
 
 
 
 
 
 NOTE Speed, 400 K. P. M. (normal). 
 
 Generator efficiency taken from test of machine made by The General Electric 
 Company. (Record of test in office of chief engineer). 
 
380 
 
 Turbine Testing. 
 
 A similar test of one of a number of wheels installed by The 
 James Leffel Company in the plant of the Niagara Hydraulic 
 Power and Manufacturing Company was made in December, 1903, 
 by Mr. John L. Harper, engineer of that company. The following 
 table XXXVI is the condensed data of the test of wheel No. 8 
 which is also illustrated by Fig. 235. 
 
 
 89 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^rf- 
 
 1 7O 
 
 
 
 
 
 
 / 
 
 ^ 
 
 
 
 
 / 
 
 ^ ~~~ 
 
 ^^ 
 
 ^ 
 
 1 BO 
 
 
 
 
 
 / 
 
 
 
 
 x 
 
 / 
 
 
 ^-- ' 
 
 - 
 
 - '< 
 
 1 50 Q 
 
 
 
 
 */ 
 
 / 
 
 
 
 / 
 
 ' 
 
 / 
 
 ^ 
 
 
 
 
 Z 
 
 o 
 
 140 m 
 
 
 
 ,< 
 
 f 
 
 
 
 / 
 
 / 
 
 / 
 
 
 
 
 
 
 m 
 1 30 
 
 
 
 t 
 
 
 
 , 
 
 / 
 
 / 
 
 
 
 
 
 
 
 n. 
 
 | 
 
 IENCY 
 R 
 
 R C 
 
 / 
 
 
 i 
 
 
 
 / 
 
 
 
 
 
 
 
 
 ui 
 
 k. 
 
 1 1 
 
 
 o 
 
 U. 
 
 E 
 
 
 
 f 
 
 . f 
 
 7 
 
 
 
 
 
 
 
 
 tn 
 
 o> 
 
 Z 
 1800 
 
 4-S 
 
 
 / 
 
 i 
 
 / 
 
 
 
 
 
 
 
 . -r^. 
 
 
 Z 
 
 BO 
 
 
 
 2 
 
 7 
 
 /A 
 
 
 
 
 
 
 
 
 
 
 UI 
 
 u 
 or 
 
 
 
 / 
 
 
 i 
 
 
 
 
 
 
 
 
 
 
 * 2 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 IDDD 
 
 25 
 
 
 \J 
 
 
 
 
 
 
 
 
 
 
 
 5Q 
 
 
 
 
 f 
 
 
 
 
 
 
 
 
 
 
 
 
 BO 
 
 55 BO 85 70 75 80 
 PER CENT GATE OPENING 
 
 85 80 95 
 
 Fig. 235. 
 
 The water was measured by a standard contracted weir 16.23 
 feet long and discharge computed by Francis' formula: 
 
 q = 3.33(L 0.2h) h 
 
 The load was computed from the voltmeter and ammeter read- 
 ings of two generators Nos. 5 and 12 which were both driven by 
 this wheel and then corrected for the generator loss by a factor 
 estimated from the shop tests of the generators. 
 
Tests of Wheels in Place. 
 
 TABLE XXXVI. 
 
 Test of a Double Horizontal Leffel Turbine installed in the plant of the 
 Niagara Hydraulic Company, Niagara Falls, N. Y. 
 
 
 GATE OPENING. 
 
 .45 
 
 .7 
 
 1.0 
 
 Dec. 5th 
 
 Dec. 6th 
 
 Xiine 
 
 3:21 p. m. 
 1.365 
 84.76 
 213.0 
 2045 
 255 
 
 178 
 5065 
 .92 
 1314 
 
 Friction 
 Load 
 Only 
 17 
 1331 
 .651 
 
 5:01 p. m. 
 1.978 
 146.6 
 212.4 
 3528 
 259 
 
 178 
 5020 
 .92 
 1302 
 
 12200 
 57.7 
 .95 
 1720 
 3022 
 .856 
 
 4:59 p. m. 
 2.257 
 178.3 
 212.7 
 4320 
 250 
 
 184 
 5833 
 .92 
 1563 
 
 13000 
 60.5 
 .955 
 1912 
 3475 
 .805' 
 
 Hook gaujje readin * (corrected) . 
 
 Discharge of wheel by Francis' formula 
 
 Head on turbine 
 
 Hydraulic horse power 
 
 R. P. M 
 
 Generator No. 5* 
 V ]ts 
 
 Amperes 
 
 Efficiency 
 
 Horse power taken from wheel by generator .... 
 
 Generator No. 12** 
 Volts 
 
 
 Efficiency 
 
 Horse power taken from wheel by generator 
 Total horse power output of wheel 
 
 Efficiency of wheel 
 
 8000 
 
 4000 6000 8000 
 
 HORSE POWER 
 
 Fig. 236. 
 
 10000 
 
 9GO 
 
 800 a 
 
 700 
 
 600 
 
 500 
 
 400 5 
 
 3002 
 
 200 
 
 100 a 
 
 12000 
 
 * Generator No. 5 is a G. E. 5000 A. 175 V., D. C. machine. 
 
 ** Generator No. 12 is a Bullock 1000 W. W., 3 phase A. C. generator. 
 
332 
 
 Turbine Testing. 
 
 The 10,500 h.p. turbine manufactured by the. I. P. Morris Com- 
 pany for the Shawinigan Power Company was also tested in a 
 similar mariner. A brief outline of this test is given on page 416 
 The graphical result of the same is shown by Fig. 236. Fig. 237 
 illustrates the test of a 25" Victor High Pressure Turbine, manu- 
 factured by the Platt Iron Works Co., at the Houck Falls Power 
 Station at Ellensville, New York. 
 
 The results of various tests at the Holyoke Testing Flume, col- 
 lected from divers sources, are given in the appendix. Most of the 
 later tests have been furnished by manufacturers and represent the 
 best results of modern turbine manufacture. 
 
 70 
 
 8 
 
 tf> 
 
 
 609 
 
 SCO 
 
 300 
 
 "1.0 
 
 200 .8 
 
 .i <: 
 
 a 
 
 200 400 600 800 1000 1200 1400 1600 4800 2000 2200 8400 
 DISCHARGE IN CUBIC FEET PER MINUTE/ 
 
 .2 
 
 
 
 Fig. 237. 
 
Literature. 383 
 
 LITERATURE. 
 
 TURBINE TESTING. 
 
 1. Smeaton, James. "An Experimental Inquiry, read in the Philosophical 
 
 Society of London, May 3rd and 10th, 1759, concerning the 
 Natural Powers of Water to Turn Mills and Other Machines, 
 Depending on a Circular Motion." 
 
 2. Morin. "Experiences sur les Power Hydraulicques." Paris, 1838. 
 
 3. Fourneyron, H. "Memoire sur les Turbines Hydraulicques." Brussels, 
 
 1840. 
 
 4. Francis, J. B. Tests of Several Turbines Including the Tremont-Fourney- 
 
 ron and the Boott Center Vent Wheels. Lowell Hydraulic Ex- 
 periments, 1847-1851. 
 
 5. Francis, J. B. Test of Humphrey Turbine, 275 h. p. Trans. Am. Soc. 
 
 C. E., vol. 13, pp. 295-303. 1884. 
 
 6. Webber, Samuel. Turbine Testing. Elec. Rev. Oct. 18, 1895, p. 477. 
 
 7. Webber, Samuel. Instructions for Testing Turbines. Eng. News, 1895. 
 
 Vol. 2, p. 372. 
 
 8. Cazin, F. M. F. The Efficiency of Water Wheels. Elec. Wld. Jan. 9, 1897. 
 
 9. Report of Tests of a 28-inch and. 36-inch "Cascade" Water. Wheel. Jour. 
 
 Fr. Inst. May, 1897. 
 
 10. Hitchcock, E. A. Impulse Water Wheel Experiments. Elec. Wld. June 
 
 5, 1897. 
 
 11. Hatt, W. Kendrick. An Efficiency Surface for Pelton Motor. Jour. 
 
 Franklin Inst, June, 1897, vol. 143, p. 455. 
 
 12. Thurston, R. H. Systematic Testing of Turbine Watev Wheels in the 
 
 United. States. Am. Soc. Mech. Eng. 1897, p. 359. 
 
 13. Results of Tests of Cascade Wheel. Eng. News, 1897, vol. 2, p. 27 
 
 14. Results of Tests of Hug Wheel. Eng. News, 1898, vol. 2, p. 327. 
 
 15. Efficiency Curves. Eng. News, 1903, vol. 2, p. 312. 
 
 16. Houston, W. C. Tests with a Pelton Wheel. Mech. Engr., May 30, 1903. 
 
 17. Henry, Geo. J., Jr. Tangential Water Wheel Efficiencies. Am. Inst. Elec. 
 
 Eng., Sept. 25, 1903. 
 
 18. Crowell, H. C. and Lenth, G. C. D. An Investigation of the Doble Needle 
 
 Regulating Nozzle. Thesis, Mass. Inst. of Tech. 1903. 
 
 19. LeConte, Joseph N. Efficiency Test of an Impulse Wheel. Cal. Jour, of 
 
 Tech. May, 1904. 
 
 20. Groat, B. F. Experiments and Formula for the Efficiency of Tangential 
 
 Water Wheels. Eng. News, 1904, vol. 2, p. 430. 
 
 21. Webber, Wm. 0. Efficiency Tests of Turbine Water Wheels. Am. Soc. 
 
 of Mech. Engrs., May, 1906. 
 
 22. Horton, R. E. Turbine Water Wheel Tests. Water Supply and Irriga- 
 
 tion Paper 180, 1906. 
 
 23. Westcott, A. L. Tests of a 12-inch Doble Water Wheel. Power, Dec. 
 
 1907. 
 
CHAPTER XVI. 
 
 THE SELECTION OF THE TURBINE. 
 
 182. Effect of Conditions of Operation. For high and moder- 
 ate falls the variations in head under different conditions of flow 
 are of small importance and water wheels can commonly be 
 placed high enough above tail-water to be practically free from 
 its influences. In such cases variations in head are comparatively 
 so slight as to have little effect on the operation of the wheels 
 which can therefore be selected for a single head. Such condi- 
 tions are the most favorable for all types of wheels. 
 
 When low falls are developed the rise in the tail-water is often 
 comparatively great, and, as the head water cannot commonly 
 be permitted to rise to a similar extent on account of overflow 
 and damage from back water, the heads at such time are consider- 
 ably reduced. As is pointed out in Chapter V, under such con- 
 ditions and for continuous power purposes wheels must be se- 
 lected, if possible, that will operate satisfactorily under the entire 
 range of head variations that the conditions may demand, or at 
 least under as great a range of such variations as practicable. 
 
 In some cases the change in head is so great that no wheel can 
 be selected which will work satisfactorily under the entire range 
 of conditions. In other cases, the head becomes so small that 
 the power which can be developed is insufficient without a large 
 and unwarranted first cost. In many such cases the use of the 
 water power plant must be discontinued, and, if the delivery of 
 power must be continuous, it must be temporarily supplemented 
 or replaced by some form of auxiliary power. 
 
 In Chapter XVII it is shown that, almost without exception, 
 great variations take place in every power load and that a plant 
 must therefore be designed to work satisfactorily under consider- 
 able changes in load. Most plants are called upon to furnish 
 power for a considerable portion of the time under much less 
 than their maximum load, but must occasionally furnish a maxi- 
 mum load for a short period. 
 
Basis tor the Selection of the Turbine. 385 
 
 If power is valuable, and the quantity of water is limited, it is 
 desirable to select a wheel that will give the maximum efficiency 
 for the condition of load under which it must operate for the 
 .greater portion of the time and that will also give, if possible, 
 high efficiency under the head available at the lowest stages of 
 the water. High efficiency is not essential to economy during 
 high water, for there is plenty of water to spare at such times; 
 neither is high efficiency as important during unusual load con- 
 ditions, which obtain for only brief intervals, as it is during the 
 average conditions under which the plant operates. 
 
 183. Basis for the Selection of. the Turbine. In Chapter XV 
 the testing of water wheels has been discussed and a number of 
 tabulated results of such tests are given. (See appendix D). The 
 standard water wheel tables are calculated from the results of 
 these tests but the values of power and efficiency, as given therein, 
 are usually reduced somewhat for safety from the results deter- 
 mined experimentally. Such tests also give data for a much 
 broader consideration of the question, and for the determination 
 of the results that can be obtained under the actual conditions 
 of installation and operation, even when such conditions are sub- 
 ject to wide variations. 
 
 In Chapter XIV the hydraulics of the turbine are discussed, 
 various turbine constants are considered, and the constants are 
 calculated for a number of standard American turbines in accord- 
 ance with the conditions of operation as recommended in the -cata- 
 logues of their makers. It will be seen from a study of the tables 
 that the turbines designed and built by various manufacturers 
 sometimes have widely different constants, indicating that each is 
 best adapted to certain conditions of which the values of these 
 constants are an index. 
 
 It is also shown that the various constants for a homogeneous 
 series of wheels may be calculated from experimental data for 
 any desired condition of gate opening and fixed value of <j>, and 
 that from these constants the operating results, that is, the dis- 
 charge, power, speed, and efficiency for any wheel of the series, 
 with the given gate opening and value of (f> and for any desired 
 head, can be calculated. For most purposes, where the head is 
 constant or where the range in heads and other conditions to be 
 considered are not extreme, the necessary calculations can be 
 readily made from a satisfactory test, by applying some of the 
 
38 The Selection of the Turbine. 
 
 formulas developed and discussed in Chapter XIV. The formu- 
 las of greatest value for this purpose are as follows: 
 
 ^ ^ P n 
 
 
 1842 cp 
 
 2 Hi= jr , when h = 1 
 
 D n _ D, n t 
 
 3 A = / . / when cp is constant. 
 
 v h V h , 
 
 4 / : = " /- when q> and D are constant. 
 Vh 1/h, 
 
 5 n = n, Vh when (p and D are constant. 
 
 7 7= = -7= when cp and D are constant. 
 
 Vh Vh, ^ > 
 
 g q = q, Vh when (p and D are constant. 
 
 P PI 
 
 9 K 2 = ~ = TTn 7" when (p is constant. 
 
 D* h DI hjk 
 
 P PI 
 
 10 - 3 = 3 when (p is constant. 
 
 p _ p iva when <^ and D are constant and hi = 1. 
 12 
 
 In using these formulas it must be remembered that each is 
 essentially correct only when the condition specified after each 
 equation obtains ; also that as long as </> remains constant the 
 efficiency obtained by the test will remain practically constant 
 for the same wheel, under all conditions of head. It should also 
 be noted that, with a fixed diameter of wheel and a fixed head, <f> 
 and n are in direct proportion, and most calculations can be made 
 by a direct consideration of the values cf n without a determina- 
 tion of the value of <f>. 
 
 When the operating results are calculated for a wheel of a given 
 series but of a diameter differing from that on which the experi- 
 ments were made, the results are liable to differ from the true 
 results on account of variations in manufacture, and allowance 
 must be made for such differences, at least until the art of manu- 
 facturing turbines has further advanced. 
 
Selection of the Turbine for Uniform Head 387 
 
 184. Selection of the Turbine for Uniform Head and Power. 
 
 The conditions of operation, as catalogued, are usually based upon 
 tests of a few turbines of the series, and represent the best con- 
 ditions of operation for that series of wheels as determined by 
 such tests. Where the conditions of installation and operation 
 are fixed, and are not subject to radical changes in head or to great 
 variations in the demand for power, the selection of a wheel may 
 be made by inspection directly from the catalogues. This method 
 of selection is based on the assumption that the catalogue data is 
 correct, which assumption should be verified by the records of 
 an actual test of the series of wheels and, if possible, of the size 
 and hand which are actually to be used. 
 
 The examination of the many catalogues of turbine manufactur- 
 ers, in order to determine the wheel best suited to the conditions, 
 is a tedious method of procedure and can be greatly shortened by 
 brief calculations which are described in the following sections : 
 
 185. The Selection of a Turbine for a Given Speed and Power 
 to Work under a Given Fixed Head. It is frequently necessary 
 to select a turbine which must have a given speed and power in 
 order to successfully operate machinery for w 1 iich such require- 
 ments obtain. It is desirable to select a wheel which will furnish 
 essentially the amount of power required as all machinery will 
 work more efficiently and more satisfactorily at or near full load 
 conditions. It is also desirable to use a single turbine rather than 
 two turbines, and if more than one turbine is required, the least 
 number found practicable should usually be selected because the 
 multiplication of units involves an increase in the number of bear- 
 ings which must be maintained and kept in alignment. 
 
 To determine the best installation of turbines necessary to ful- 
 fill the given conditions, the value of K 5 as given by equation (12) 
 should be determined. Having determined the value of K 5 , a 
 turbine should be selected having a constant K 5 not less than the 
 amount determined, and if it is desired to operate the turbine at 
 its maximum efficiency, the value of K 5 for the turbine selected 
 should not greatly exceed the value found by computation. If 
 the value of K 5 as computed greatly exceeds the value of K 5 for 
 the various makes of turbines, then the power must be divided 
 between two or more units in order that the conditions may be 
 satisfied. As K 5 is in direct proportion to P, one-half, one-third or 
 any other fraction of K 3 will give the value of K 5 for a wheel 
 having a similar fractional value of the power, P, and will there- 
 
388 The Selection of the Turbine. 
 
 fore show the type of wheel which' must be selected in order that 
 two, three, or more will do the work in question. The great varia- 
 tions in the value of K 5 for different types of wheels and the in- 
 fluence of this variation on the relation of speed and power will 
 be seen by reference to Fig. 222 which shows the curves of re- 
 lation between revolution and power of various wheels for one 
 foot head. This may be used for any other head by considering the 
 revolutions in proportion to the square root of the head and the 
 power in proportion to the three-halves power of the head. A 
 brief study of this diagram will show its use more plainly. For 
 example : under a one foot head, and for 30 revolutions per minute, 
 turbines may be selected that will deliver from 1.3 to 6.6 horse 
 power. 
 
 Suppose we desire to determine the power that will be available 
 under a 16' head at 100 revolutions per minute. 100 revolutions 
 per minute at 16' head would correspond to 25 revolutions per 
 minute at i' head. 
 
 For since 
 
 n = -7=5=1 
 
 Vh> 
 
 vr 
 
 therefore n 1 = -j= 100 = .25 X 100 = 25. 
 V10 
 
 At 25 r. p. m. the diagram shows that turbines are obtainable 
 that will give 1.8 to 10 horse power at one foot head. 
 
 The power at 16 foot head will be to the power at one foot head 
 as the three-halves power of the head. The three-halves power of 
 16 is 64; hence the power at 16 feet will be 64 times the power at 
 ooie foot head, and, hence, wheels under a 16 foot head operated at 
 100 revolutions per minute, will furnish from 122 to 657 horse 
 power and the most satisfactory wheel within these limits for the 
 problem at hand can be selected. 
 
 The diagram, however, is a convenience, not a necessity, and a 
 problem can often be more readily solved by the direct applica- 
 tion of equation 12. If, for example, it is desired to operate a 
 turbine at 100 revolutions per minute under 16 foot head to de- 
 velop 400 h. p., the corresponding value of K 5 will be 
 
 nap 100 X 100 X 400 
 
 By examination of Table XXXII it will be found that the Victor 
 Standard Cylinder Gate or the United States Turbine wheels have 
 
To Estimate Probable Results From a Test. 389 
 
 practically this value of K 5 and will therefore fulfill the conditions. 
 Having determined from the calculated value of K 5 the makes and 
 types of the several wheels which will satisfy the requirements, the 
 size of the wheel may immdiately be determined by determining 
 the value >of K 2 for the same series of wheels from Table XXX, 
 Chap. XIV, and calculating the size of the wheel by the use of for- 
 mula 9. 
 
 Thus for the Victor Standard Cylinder Gate wheel the value of 
 K 2 is 0.00205. Therefore from equation (9) 
 
 D * *pLl * JZIJ?OII = 55,2' 
 V K 2 h| ^.00205 X 64 
 
 which is the size of this series of wheels needed to fulfill the as- 
 sumed conditions. 
 
 Having thus selected several possible wheels, tenders for these 
 wheels may be invited from their makers. These tenders should 
 be accompanied by an official report of a Holyoke test for the 
 wheel in question, or, if this is not available at the time, for the 
 next larger and the next smaller wheels of the series which have 
 been tested. From these tests the catalogue values of K 2 and K 5 
 which were used in their selection can be checked. In addition 
 to this the several prospective wheels may be compared as to their 
 operation at part gate, which comparison is equally important 
 for the final choice to be made. 
 
 As the wheels are seldom or never tested for the head under 
 which they are to work, and as tests are not always available for 
 the size of wheel to be used, it is necessary to predict from the test 
 data furnished by the wheel makers the efficiency, power and 
 water-consumption curves which can be anticipated under the 
 given head. This can be done as illustrated in the next two 
 articles. 
 
 1 86. To Estimate the Operating Results of a Turbine under 
 one Head from Test Results secured at another Head. For the 
 purpose of illustrating the methods of calculation, Table l-XX tit 
 may be considered. This table gives the results of certain tests 
 of a 33" special, left-hand turbine wheel, with conical draft tube 
 and balance gate, manufactured by the S. Morgan Smith Com- 
 pany. While the heads in the different experiments of this test 
 vary slightly, they are so nearly uniform that the table may be 
 considered as developed under a uniform head of 17.15 feet. If 
 greater accuracy is desired, however, the square root of the actual 
 head can be considered each time. 
 
39 The Selection of the Turbine. 
 
 Let it be assumed that the wheel is to be operated under a 20 
 foot head and with a speed* of 200 r. p. m. with the average load 
 at about .75 gate. The maximum efficiency at .75 gate is repre- 
 sented by experiment No. 43 of this table. In order that the 
 wheel shall work under the new head with this efficiency, equation 
 (4) must be satisfied. In all of these equations the primed char- 
 acters are used to represent the experimental conditions. The 
 most efficient revolutions under the new head will therefore be 
 determined as follows : 
 
 172.75 X 4.46 
 n = 4 14 = 186 r. p. m. 
 
 The wheel to be chosen must, however, in this case operate at 
 200 revolutions per minute. At 200 r. p. m. the wheel will not 
 run at its maximum efficiency. The actual efficiency at this speed 
 may be determined by finding what speed at the experimental 
 head corresponds with the speed to be used, and noting the effi- 
 ciency corresponding to the same. This is done on the assump- 
 tion that the efficiency remains constant as long as <j> remains 
 constant which is shown to be essentially true by Fig. 214, Chap. 
 XIV. 
 
 The revolutions under 17.16 ft. head corresponding to 200 r. 
 p. m. under 20 feet will be determined as before : 
 
 2GO x 4.14 
 n : 
 
 4.4(5 - - . 
 
 The result, 187 r. p. m., lies between the conditions of experi- 
 ments 41 and 40. By proportion, the efficiency corresponding to 
 187 r. p. m. will be found to be about 83.25 at .75 Jgate. 
 
 If the efficiency corresponding to 187 r. p. m. in the table is now 
 determined from each gate opening, it will be found that at full gate 
 the efficiency will be slightly below that shown in experiment 16, 
 and can be determined by interpolation, or graphically, to be 
 about 81%. At gate .9448 the efficiency can be determined in the 
 same way to be about 82.75%. At gate .883 the results will fall 
 between experiments 69 and 70 and the efficiency will be found to 
 be about 86%. At gate .851 the result falls below experiment 54,. 
 and, by calculation from a graphical diagram or by interpolation, 
 the results are found to be about .86. At gate .702 the revolutions 
 correspond exactly with experiment 56, and the efficiency from the 
 table is found to be 81.01%. At gate .636 the revolutions fall be- 
 tween experiments 24 and 25 and, by proportion, the efficiency is 
 
Effects of Diameter on Results. 
 
 39 1 
 
 found to be 80.25%. At gate .556, the efficiency is found, by pro- 
 portion, to be 77%. To determine the power of the wheel under 
 the new conditions, and for each condition of gate, the power of 
 the wheel as found by the test must be determined for the same 
 value of $. The power of the new head can then be calculated by 
 \ise of formula (n). 
 
 In the same manner the discharge of the turbine can be deter- 
 mined by finding the value of q corresponding to the value of <f> 
 for the experimental head, and from this value so determined the 
 value of q under the 20 foot head can be calculated by formula (7). 
 The results of these calculations, together with the efficiency as 
 determined for 20 foot head and for 200 revolutions per minute, 
 are given in Table XXXVII. 
 
 Having computed a similar table for each of the several pros- 
 pective wheels the one best suited to the given conditions can be 
 chosen. 
 
 TABLE XXXVII. 
 
 Showing Horse Power, Discharge and Efficiency of 33-inch Special Left Hand 
 S. Morgan Smith Turbine, with 20-foot head and 200 R. P. M. 
 
 Calculated from test of 33-inch wheel under a head of 17.15 feet. 
 
 Proportional Gate Opening. 
 
 Horse Power 
 
 Discharge, 
 cubic feet 
 per second. 
 
 Efficiency. 
 
 1 COO . . 
 
 222.1 
 
 120.4 
 
 81.6 
 
 .948 
 
 >>$ . 1 
 
 117.0 
 
 83.2 
 
 .883 
 
 217.7 
 
 111.3 
 
 85.6 
 
 .851 
 
 212.7 
 
 100.2 
 
 86.3 
 
 76o 
 
 188 I 
 
 97 5 
 
 83.2 
 
 702 
 
 1(>5 1 
 
 87.8 
 
 81.3 
 
 .636 
 
 154.7 
 
 81.5 
 
 80.7 
 
 55 1> . . 
 
 136.7 
 
 75.0 
 
 79.0 
 
 
 
 
 
 187. To Estimate the Operating Results of a Turbine of one 
 Diameter from Test Results of Another Diameter of the Same 
 Series. It is always desirable for the purpose of calculations to 
 use the results of a test made on a wheel of the same size and hand 
 as that which is to be used in the installation for which the wheel 
 is being considered. It is seldom, however, that all of the various 
 sizes of wheels in a series of wheels have been tested, and the 
 manufacturers therefore frequently base their estimates and guar- 
 antees of wheels of an untested size on the test of some other 
 wheel of the series which may be larger or smaller than the wheel 
 
392 The Selection of the Turbine. 
 
 offered. Sometimes tests of wheels both larger and smaller than 
 the wheel to be used are available, in which case both sets of tests 
 should be used as a basis of calculation. 
 
 Let it be assumed that a 40" wheel is to be installed of the -same 
 series as the 33" wheel just considered, and that no tests of such 
 a wheel are obtainable. The tests of the 33" wheel may therefore 
 be used as the best information available. Let it be assumed that 
 the 40" wheel is to be operated under a 9 foot head-. For these- 
 calculations formula (3) must be satisfied. 
 
 Let it be assumed that the wheel is to operate at nearly full load* 
 and the best efficiency is desired at about .85 gate. From the 1 tests it 
 will be found that at .85 gate, and with a 17.15 foot head and 191 
 revolutions, the wheel gave 85.97% efficiency and 170.08 horse 
 power. Substituting these values in equation (3) there results : 
 
 33 X 191 40 X n 
 
 T~T7 o ) from which n = 114 r. p. m. 
 
 One hundred and fourteen revolutions per minute is therefore 
 the speed under which the wheel must operate in order to give 
 this maximum efficiency at this gate. 
 
 Let it be assumed, however, that the wheel must be run at 120 
 r. p. m., on account of the class of machinery to be operated 
 By substituting the value n=J2O, in equation (3), it is found 
 that n'=2O2. The experimental efficiency at 202 r. p. m. under 
 the I7-J5 foot head and with the 33" wheel, will therefore, corres- 
 pond to 120 revolutions under a 9 foot head with a 40" wheel, and 
 will indicate the efficiency under which the wheel will operate under 
 these conditions. This is found to be about 81.5 at .85 gate. 
 
 In order to determine the horse power of the wheel under the 
 new conditions, the horse power of the wheel under the test con- 
 ditions must first be determined for that gate; the resulting horse 
 power can then be determined by equation (9). 
 
 For 202 r. p. m. at 17.15 foot head for this 33' wheel P=158- 
 which, substituted in equation (9), gives 
 
 158 P 
 
 33 X 33 X 71 = 40 X 40 X 27 from which P = 88 
 
 Jn the same manner, the discharge of the larger wheel under the 
 lower head can be determined by equation (6), and q is found ta 
 equal 104 cu. ft. per second. 
 
To Estimate Results with Variable Heads. 
 
 393 
 
 In this way the discharge, efficiency and power of the larger 
 wheel under the chosen r. p. m. can be determined for each condi- 
 tion of gate, as shown in Table XXXVIII. 
 
 TABLE XXXVIII. 
 
 Showing Horse Power, Discharge and Efficiency of a 40-inch Special Left Hand 
 
 S. Morgan Smith Turbine, with a 9-Joot hea i and 120 R. P. M. 
 
 Calculated from test of 33-inch wheel under a head of 17.15 feet. 
 
 Proportional Gate Opening. 
 
 Horse 
 Power 
 
 Discharge 
 cubic feet 
 per second. 
 
 Efficiency. 
 
 1 000 
 
 100 
 
 119 
 
 8'? 1 
 
 948 . 
 
 100 
 
 112 
 
 84 2 
 
 .883 
 
 92 
 
 108 
 
 82 5 
 
 .851 
 
 88 
 
 104 
 
 81 5 
 
 .765 
 
 76. 
 
 91. 
 
 78.1 
 
 70? 
 
 68 
 
 83 
 
 77 8 
 
 .36 
 
 64. 
 
 76. 
 
 78.8 
 
 .550 
 
 58 
 
 73 
 
 75 1 
 
 
 
 
 
 1 88. To Estimate the Operating Results of a Turbine under 
 Variable Heads from a Test made under a Fixed Head. Where 
 the variations in the head under which a wheel is to operate are 
 considerable, the variation in <, and consequently in n, are some- 
 times found to be beyond the limits of the test. Where the test 
 conditions are not greatly exceeded, the experiments may be ex- 
 tended graphically without any serious error. 
 
 Let it be assumed that the 33" wheel above considered is to be 
 operated under a maximum head of 25 feet, and that the head will 
 decrease to 16 feet at times of high water; also, that the wheel is 
 to be operated for the major portion of the time under about .75 
 gate. The best condition for operation is shown by test 43, which 
 shows an efficiency of 86.3% at n' = 172.75 r. p. m. 
 
 n may be calculated from equation (4) for the 25 foot head as 
 follows : 
 
 n = 
 
 172.75 X 5 
 4.14 
 
 = 208 r. p. m. 
 
 That is : the best number of revolutions for a 25 ft. working head 
 would be 207 r. p. m. The best number of revolutions for a six- 
 teen foot head would be determined as follows : 
 
 n = 
 
 172.75 X 4 
 4.14 
 
 = 166 r. p. m. 
 
 24 
 
394 The Selection of the Turbine. 
 
 The wheel, for the best efficiency, should be run at a different 
 speed for each head, but under practical conditions of service 
 must be run at a constant speed. 
 
 Let it be assumed that, on account of the machinery operated, 
 it is desirable to adopt for the plant a speed of 200 r. p. m. Let 
 the 25 foot head be first considered. For considering the 25 foot 
 head the equivalent value of n under the test conditions is found 
 as follows: 
 
 =167r.p.m. 
 
 It will be noted from experiment 44 that at 169.25 r. p. m. the 
 efficiency is 85.55. At 167 revolutions per minute the efficiency 
 would therefore be about 85%. Under a sixteen foot head n must 
 also equal 200 r. p. m., hence, for this case, the equivalent value of 
 n' for the test conditions is 
 
 n'= 200X4.14 = 20S revoh . tions . 
 
 Test 39 shows that, with 206.25 revolutions, the efficiency is 
 76.66. At 208 revolutions the efficiency is therefore less than this 
 amount and the probable efficiency under these conditions can 
 be estimated by platting the relation between revolutions and ef- 
 ficiency as shown in Fig. 238. By prolonging the line from the 
 actual experiments, the efficiency indicated for 208 revolutions, 
 under the experimental conditions, is found to be about 76%. 
 As far as efficiency is concerned, therefore, the arrangement is very 
 satisfactory, for a sufficiently high efficiency will be obtained un- 
 der conditions of high water, and when the quantity of water used 
 is immaterial. 
 
 The relations of efficiency to speed, under the experimental con- 
 ditions and at various gate openings, are shown by the points 
 platted on Fig. 238. Through these points mean curves are 
 drawn, which are extended where necessary to intersect the ab- 
 scissa of 167 revolutions, which corresponds to the condition of 
 efficiency for 25 foot head, and to the abscissa of 208 revolutions, 
 which corresponds to the condition of efficiency for a 16 foot head. 
 From these results the relations of efficiency at various gates and 
 at the two heads named are platted in Fig. 239. 
 
 The relations of power to speed are shown by Fig. 240, which 
 has been platted in the same manner as Fig. 238. From Fig. 240; 
 
Estimate of Efficiency with Variable Head. 
 
 395 
 
 ..-_ ISO BOO _., 
 
 RC VOLUTIONS PER Ml MUTE. 
 
 Fig. 238. Curves Showing the Efficiency Obtained at Various Speeds un- 
 der a Test Head of about 17.15 Feet from a 33-Inch Special Left- 
 Hand Wheel with Balance Gate, Manufactured by the S. Morgan 
 Smith Co. 
 
 70 
 
 50 
 
 60 
 
 70 80 
 PER CENT GATE OPENING. 
 
 90 
 
 Fig. 239. Curves Showing Estimated Efficiency at Various Gate Openings 
 and at Two Heads for 33-Inch S. Morgan Smith Wheel. (Taken 
 from Fig. 238.) 
 
39 6 
 
 The Selection of the Turbine. 
 
 the power of the wheel at 25 and 16 feet can be determined by 
 equation (10). 
 
 The power at 25 feet will be 
 
 125 
 
 j = =g-g = l . 77 times the power determined by the exper- 
 
 h'* iment at 17.15 feet and 167 r. p. m. 
 
 The power at 16 feet will be 
 
 64 
 
 = ;=7r~7: = .91 times the power, as determined by the ex- 
 periment at 17.15 feet, and at 216 r. p. m. 
 
 180 
 
 I DO 
 
 180 
 REVOLUTIONS PER MINUTE 
 
 HDD 
 
 220 
 
 Fig. 240. Curves Showing the Power Obtained at Different Speeds under a 
 Test Head of about 17.15 Feet from the S. Morgan Smith 
 33-Inch Wheel. 
 
 .91 times the power, as determined by the experiment at 17.15 feet, 
 and at 216 r. p. m. Curves of the pow r er of this wheel under 25 and 
 1 6 foot heads, and at various gates, as determined in this manner, 
 are shown by Fig. 241. 
 
 The experimental relations of speed and discharge for the wheel 
 are shown in Fig. 242 which was platted in the same manner as 
 the diagrams for efficiency and power. A graphical representa- 
 tion of the discharge under 25 and 16 foot head and at various 
 gates is shown in Fig. 243. 
 
 189. A More Exact Graphical Method for Calculation. The 
 method outlined in section 188 is subject to some error as the re- 
 sults are platted regardless of head. The graphical method is 
 therefore applicable without correction only when the experimen- 
 
A Graphical Method of Calculation. 
 
 397 
 
 tal head remains nearly constant. For a more complete, accurate 
 and satisfactory analysis the discharge, power and revolutions 
 should be reduced to their equivalents i. e. at one foot head 
 
 JL P . _L. h * 
 
 41 Vh, hi Vh 
 
 300 
 
 260 
 
 J220 
 
 80 
 
 140 
 
 100 
 
 GO 
 
 70 
 CENT 
 
 OPENING. 
 
 90 
 
 1QD 
 
 PER CENT GATE 
 
 Tig. 241. Curves Showing Estimated Power Obtained at Various Gate 
 
 Openings and at Two Heads for 33-Inch S. Morgan Smith Wheel. 
 
 (Taken from Fig. 240'.) 
 
 and platted as shown in Fig. 244 where the r. p. m. under one foot 
 head is used as abscissas, and the power, discharge and efficiencies 
 are used as ordinates. The* condition at any given number of 
 revolutions under a given head can be calculated by dividing the 
 given number of revolutions by ttte square root of the head. The 
 
398 
 
 The Selection of the Turbine. 
 
 115 
 
 160 
 
 180 EDO 
 
 REVOLUTIONS PER MINUTE 
 
 220 
 
 Fig. 242. Curves Showing the Discharge at Various Speeds under the Test 
 Head of about 17.15 Feet of ths 33-Inch S. Morgan Smith Wheel. 
 
 140 
 
 120 
 
 u 100 
 
 5 BO 
 
 u 
 en 
 
 60 
 
 50 
 
 60 
 
 70 80 
 
 PER CENT GATE OPENING 
 
 30 
 
 100 
 
 Fig. 243. Curves Showing the Estimated Discharge at Various Gate Open- 
 ings and at Two Heads for the 33-Inch S. Morgan Smith Wheel. 
 Taken from Fig. 242.) 
 
A Graphical Method of Calculation. 
 
 399 
 
 88! 
 
 52 54 
 
 36 38 40 
 
 Fig. 244. Curves of the 33-Inch S. Morgan Smith Wheel for One Foot Head. 
 
 42 44 46 48 50 
 
 R.P.M. UNDER ONE FOOT HEAD. 
 
400 The Selection of the Turbine. 
 
 result is the comparative revolutions under one foot head, and a 
 line drawn vertically at the point so located on the diagram will 
 .give the basis of calculations for power and discharge by multi- 
 plying by hi and ha, respectively, for each gate opening and by 
 reading the efficiency direct. 
 
 For the wheel under 200 revolutions at 25 and 16 foot heads the 
 equivalent speeds on the diagram are 40 and 50, respectively, 
 Lines drawn vertically at these points will intersect the curves of 
 efficiency, power and discharge and if reduced by a similar method 
 will give curves essentially the same as those shown in Figs. 239, 
 241 and 243. This is probably the best method for common use 
 in studying, from test data, the operation of a wheel under a va- 
 riable head. 
 
 190. The Construction of the Characteristic Curves of a Tur- 
 bine. It is frequently desirable to make a more thorough analy- 
 sis, based on the available test, of the conditions under which a 
 wheel can operate. For this purpose, the writer finds the use of 
 what he has termed "the characteristic curve" of a turbine to be 
 the most comprehensive method for such an analysis. 
 
 For this purpose, prepare a diagram on which the ordinates rep- 
 resent the values of <j> and the r. p. in. under one foot head, and 
 the abscissas the discharge of the wheels in cubic feet per second 
 under one foot head. It is also found desirable to show on the 
 upper margin of the diagram the horse power under one font head 
 with 100% efficiency, corresponding to the discharge shown below. 
 For each experimental result the values of <j> and of the discharge 
 under one foot head are determined by formulas (i) and (3). 
 The point representing these values is then platted on the dia- 
 gram, and the efficiency, as determined by the test for that experi- 
 ment, is written closely adjoining the platted point. This is done 
 for each experiment at each condition of gate. After all the ex- 
 perimental points are platted, and the resulting efficiency at each 
 given point is expressed, lines of equal efficiency are interpolated 
 on the drawing, and will indicate the general law of the variation 
 of efficiency as represented by the test. 
 
 It is, of course, possible to reduce the horse power determined 
 for each experiment to the theoretical horse power under one foot 
 head, and record it at the corresponding point, and then interpolate 
 horse power curves, as in the case of the efficiency curves. It has 
 been found by the writer, however, to be more satisfactory to use 
 
The Characteristic Curve. 401 
 
 the horse power scale at the top of the diagram, together with the 
 efficiency lines already drawn, for the calculation and platting of 
 the horse power curves. The horse power at any point will, of 
 course, equal the theoretical horse power expressed at the upper 
 margin, multiplied by the efficiency at the given points. 
 
 In determining the horse power curve, it is best to assume the 
 horse power of the desired curve, and then determine its location 
 in regard to the theoretical horse power from the equation. 
 A. H. P = T. H. P. X Efficiency. 
 
 For example, on Fig. 245, if it is desired to plat the curve rep- 
 resenting 2 A. H. P. it may be done as follows : The line repre- 
 senting two actual horse power will intersect the 70% efficiency 
 line at two points whose abscissae are determined from the T. H. 
 P. scale by the equation 
 
 T . n . p. = 
 
 If, therefore, the two points of intersection of the abscissa 2.86, 
 as indicated on the upper T. H. P. scale, with the 70% efficiency 
 line, are marked, two points will be established on the 2 A. H. P. 
 line. As many of the lines of equal efficiency and equal horse 
 power can be drawn on the diagram as may be desired, but if the 
 lines of the drawing or diagram are too numerous, confusion will 
 result rather than clearness. 
 
 One of the most complete sets of experiments with, or tests of, 
 a turbine water wheel which the writer has been able to obtain 
 is the set of experiments made for the Tremont and Suffolk Mills 
 at the Holyoke Testing Flume, December 3-5,1890, on a 48 inch 
 Victor turbine, with cylinder gate (See ''Notes on Water Power 
 Equipment," by A. H. Hunking), which is given in full in Table 
 LX.* 
 
 From this table, and in the manner above described, a char- 
 acteristic curve of this wheel has been prepared, and is shown by 
 Fig. 245. In this Figure the efficiency curves are shown in black, 
 the horse power curves are shown in red, and the lines showing 
 the relations of discharge and <j> at various gate openings are 
 shown by the dotted lines connecting the experimental points. 
 
 191. The Consideration of the Turbine from its Characteristic 
 Curve: From this characteristic curve the action of the wheel 
 under all conditions of operation within the experimental limits 
 of <f> can be readily determined. The use of the characteristic 
 
 * See Appendix D. 
 
HORSE POWER UNDER ONE FOO 
 
 .7 i.s I.Q e.a s..\ s.z 2.3 a.** e. 
 
 so 
 
 6 17 IB |g 20 21 2 
 
 DISCHARGE IN CUBIC FEET F 
 
 Fig. 245. "Characteristic Curve" of 
 
ME1AD WITH I DO PERCENT EFFICIENCY 
 
 23 S4 25 25 27 28 29 3D 
 SECOND UNDER ONE ROOT MEAD 
 
 18-Tnch Victor Turbine, with Cylinder Gate. 
 
 35 36 
 
404 The Selection of the Turbine. 
 
 curve is based upon the assumption that the efficiency will remain 
 constant for a variable head as long as 4> remains constant. 
 
 The efficiency and horse power lines as interpolated, are sub- 
 ject to errors of interpolation, the extent of which can be readily 
 judged from the diagram made. The conditions of the test are 
 approximately checked by this diagram, for any marked irregulari- 
 ties in these curves must be due to errors in testing, or to poor 
 workmanship. 
 
 By inspection it is possible to decide immediately the value 
 of <f> that must be maintained in order to maintain the maximum 
 efficiency at any particular condition of gate. For example: if 
 the maximum efficiency at full load is desired, < with this wheel 
 should equal about .69. If the maximum efficiency at .75 gate is 
 desired, the value of <j> should be about .65, and for maximum ef- 
 ficiency at .50 gate, < should be reduced to about .64. 
 
 Knowing the head under which the wheel is to operate, the nec- 
 essary number of revolutions at any head can be calculated by 
 formula (i) or by multiplying the r. p. m. at one foot head by the 
 i/h and the conditions of operation, in regard to both power and 
 efficiency at all gates, will be determined by the intersection of a 
 horizontal line through the chosen value of < with the efficiency 
 and horse power lines. If, for example, it is decided that $ shall 
 be .66, a horizontal line running directly through the diagram at 
 < = .66 will, by means of the various points of intersection with 
 the gate opening, efficiency and horse power lines, give all infor- 
 mation desired and from it can be calculated the efficiency, speed, 
 discharge and horse power of the wheel for the head under which 
 it is to operate. The intersection of this .66 </> line with the va- 
 rious efficiency curves will give the relation of efficiency to dis- 
 charge with one foot head. The discharge under the required 
 head can be calculated by equation (9), i. e. by multiplying the dis- 
 charge shown at the bottom of the diagram (cine foot head) by yh. 
 The efficiencies at each gate position will remain unchanged by 
 this change in head since < is fixed at .66. If a 16 foot head be 
 considered, the discharge at any point will be four times the dis- 
 charge read from the diagram. 
 
 The relation of horse power to discharge is aiso shown by the 
 intersection of the <f> line with the horse power curves. The ac- 
 tual horse power under any head can be determined by equation 
 (u) i. e. by multiplying the horse power, as read from the dia- 
 
The Characteristic Curve. 
 
 .-gram (one foot head) by h~. The horse power at 16 foot head will 
 therefore be 64 times that given by the diagram. 
 
 If it is desired to utilize the characteristic curve for the consid- 
 eration of a wheel of another size but of the same series, the power 
 
 D 2 
 .and discharge must be multiplied by the ratio -jj 
 
 All of the various types of curves showing the results of opera- 
 
 80 
 
 40 GO 80 100 
 
 DISCHARGE IN CUBIC FEET PER SECOND . 
 
 120 
 
 Fig. 246. 
 
406 
 
 The Selection of the Turbine. 
 
 tion of the wheel as hitherto described are shown by, or can be 
 calculated from, the characteristic curve. 
 
 Fig. 246, showing the relation of the number of revolutions to the 
 efficiency and discharge of the wheel, is one example of such use. 
 
 192. Other Characteristic Curves. Fig. 247 is the characteristic 
 curve of a 44 inch "Improved New American" turbine showing the 
 
 HORSE POWER UNDER ONE FOOT HEAD WITH 100 PERCENT EFFICIENCY 
 2.0 2.5 3.0 3.5 4.0 4.5 5.0 
 
 18 I* 20 22 24 26 28 30 32 34 36 38 40 42 44 46 4f~ 
 DISCHARGE IN CUBIC FEET PER SECOND UNDER ONE FOOT HEAD 
 
 Fig. 247. Characteristic Curve of a 44-Inch ""-Improved New American' 
 
 Turbine. 
 
The Characteristic Curve. 
 
 407 
 
 operation of the wheel through a considerable range of heads. 
 The outer line entitled "Head at 120 r. p. m., shows the values of <j> 
 and n- L at which the wheel would have to operate to 1 maintain 120 
 r. p. m. at the indicated heads. The location of these points may 
 be determined in two ways : First. By calculating the values of 
 
 Fig. 248. Curves Constructed from Fig. 247 Showing the Power at Two 
 Speeds of Six "Improved New American" Wheels. 
 
 <f> for a given head and number of revolutions, and locating the 
 corresponding point from the scale on the left of the diagram; 
 Second. By dividing the number of revolutions by the square 
 root of the head and fixing the point by the corresponding revolu- 
 tions under one foot head, as shown on the scale of r. p. m. at the 
 right of the diagram. 
 
408 
 
 The Selection of the Turbine. 
 
 At 14 foot head the wheel will operate at about the maximum ef- 
 ficiency. If the head be decreased to 12', the relative efficiencies 
 will still remain fairly satisfactory, but will decrease rapidly at 
 10' as shown by a horizontal line drawn through the corresponding 
 point. It is also evident that at 8' the efficiency becomes very low. 
 and below this head the wheel would probably be unable to main- 
 tain 1 20 r. p. m. 
 
 HORSE POWER UNDER ONE FOOT HEAD WITH 100 PERCENT EFFICIENCY 
 3.4 3.6 3.8 4.0 4. 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 
 
 DISCHARGE IN CUBIC FEET PER SECOND UNDER ONE FOOT HEAD 
 
 Fig. 249. Characteristic Curves of a Wellman-Seaver-Morgan 51-Inch Mc- 
 
 Cormick Wheel. 
 
 The second line at the right shows the value of $ and n, at va- 
 rious heads when operating at 100 revolutions per minute. At 
 this speed the wheel will operate satisfactorily under heads from 
 14' to as low as 7', or even less. The efficiency at 14 foot head in 
 this c'ase will be less than at 120 r. p. m., and the efficiency of oper- 
 ation will increase as the head diminishes to the 9 and 10 foot' 
 point, where the best efficiencies are obtained at 100 r. p. m. Be- 
 low this point the efficiency of operation will gradually decrease. 
 Provided the revolutions per minute are satisfactorily selected, it 
 will be seen that the wheel will meet successfully a wide variation 
 in the operating conditions. 
 
The Characteristic Curve. 
 
 409 
 
 Fig. 248 is a diagram constructed from this characteristic curve 
 and shows the power of six turbines of this series but of 49" diam- 
 eter connected tandem to a horizontal shaft and operated at the 
 various heads and revolutions above discussed. The curves show 
 the condition both at full and at part gates. The gradual change 
 
 145 
 
 140 
 
 HORSE POWER UNDER ONE FOOT HEAD WFTH 100 PERCENT EFFICIENCY 
 1.5 2.0. . .2.5. . . ..-0 3.5. 4.0 4.5 5.0 
 
 25 
 
 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40 4244 
 DISCHARGE IN CUBIC FEET PER SECOND UNDER ONE FOOT HEAD 
 
 Fig. 250. Characteristic Curves of the 99i/,-Inch Tremont Fourneyron Wheel. 
 
410 
 
 The Selection of the Turbine. 
 
 in the relative position of the 100 and the 120 r. p. m. curves, as 
 the head changes, should be noted. 
 
 Fig, 249 shows the characteristic curve of a 51" McCormick tur- 
 bine, as manufactured by Jolly Brothers for the Wellman-Seaver- 
 Morgan Company. At the right of the diagram are shown the 
 relative values of <j> and at the left the values of n for heads from 
 
 HORSE POWER UNDER ONE FOOT HEAD WITH 100 PERCENT EFFICIENCY 
 83 26 27 38 29 30 31 32 33 34 35 36 37 38 39 40 4.1 43 43 44 45 4.6 4.7 48 49 , 
 
 24 25 26 27 28 23 3D .31 32 33 34 33 36 37 38 39 40 4 4Z 43 44 43 
 DISCHARGE IN CUBIC FEET PER SECOND UNDER ONE FOOT HEAD 
 
 Fig. 251. Characteristic Curves of a 45-Inch "Samson" Wheel. (James 
 
 Leftel & Co.) 
 
 16 to 8 feet, at 90 and 100 r. p. m. This curve shows that this 
 wheel will work satisfactorily under a wide range of conditions, 
 if a suitable speed is chosen. 
 
 Fig. 250 is the characteristic curve of the Tremont turbine tested 
 by James B. Francis, and described in the "Lowell Hydraulic Ex- 
 periments." This wheel was a Fourneyron turbine of about 700 
 horse power at 13' head. 
 
 Fig. 251 is the characteristic curve of a 45" Leffel turbine, which 
 has been selected for the Morris Plant of the Economy Light and 
 Power Company, now under construction on the Des Plainas 
 River, about twelve miles south of Joliet, Illinois. It is to be op- 
 erated at 120 revolutions per minute and under variations in head 
 
The Characteristic Curve. 
 
 411 
 
 from 16 to 8 feet. Eight units, each consisting of .eight of these 
 wheels, connected tandem, are to be installed to operate eight 1,000 
 K. W. alternating generators. This diagram was prepared from 
 the test sheet accompanying the bid of the James LefTel & Com- 
 pany. In the construction of the wheels for the plant, an attempt 
 was made to so alter them as to maintain a high efficiency for a 
 
 HORSE POWER UNDER ONE FOOT HEAD WITH 100 PER CENT EFFICIENCY 
 2B 23 3.0 3.2 3.4 3.6 3.8 4.0 4.2 4.4 4.8 4.8 5.0 5.2 
 
 26 28 30 32 34 36 38 40 42 
 
 DISCHARGE IN CUBIC FEET PER SECOND UNDER ONE FOOT HEAD 
 
 46 
 
 Fig. 252. Characteristic Curves of a 45-Inch "Samson" Wheel. (James 
 
 Leffel & Co.) 
 
 greater range of gate conditions than ordinarily obtained. Fig. 
 252 shows a characteristic curve of one of the new wheels as con- 
 structed for this plant. The analysis was made for the purpose of 
 estimating the results which would probably be secured under 
 service. 
 
 In Fig. 253 are shown the discharges, powers, and efficiencies 
 of one unit of eight wheels under all heads from 8 to 16 feet at 
 full and seven-eighths gate. Allowances would have to be made 
 in order to take into account the difference between the operation 
 of the eight wheels in the horizontal position connected in tandem, 
 and in the position in which they were tested ; but the diagram 
 
4 I2 
 
 The Selection of the Turbine. 
 
 shown gives an analysis from which fairly satisfactory conclu- 
 sions can be drawn. 
 
 193. Graphical Analysis as Proposed by Mr. W. A. Waters. 
 A valuable method of graphical analysis is shown in Bulletin No. 
 
 88 
 
 23C3 
 
 2IC3 
 
 ^ 1900 
 
 1700 
 
 1500 
 
 1300 
 
 700 
 
 500 
 
 Fig. 253. Curves Showing the Efficiency and the Maximum and Ordinary 
 Power and Discharge of One Unit of 8 45-Inch Samson Wheels. 
 
 2 of the I. P. Morris Company, in which is discussed the variations, 
 in power and efficiency of a turbine wheel capable of giving 13,500 
 horse power under a head of 65 feet, and at a speed of 107 revolu- 
 tions per minute. This wheel was designed by this Company for 
 the McCall-Ferry Power Company, and was to work under heads 
 varying from 50 to 70 feet. 
 
Graphical Analysis of W. A. Waters. 
 
414 The Selection of the Turbine. 
 
 Figs. 254, 255 and 256 and the following description are taken, 
 with slight alterations, from the above named Bulletin. 
 
 Curve No. I. Fig. 254, shows the power which the wheel will 
 give for heads varying from 70 feet to zero, provided that the revo- 
 lutions are allowed to vary as the square root of the head, and is 
 based on equation (15). 
 
 From Curve No. i, Fig. 254, it will be noted that at 70 foot head 
 the wheel will develop 15,000 horse power, and from Curve No. 6, 
 of the. same Figure, it will be noted that the best speed of the 
 wheel under the conditions of 70 foot head will be in revolutions 
 per minute. It will also be noted from Curve No. I that, under 
 50 foot head, the wheel will develop 9.150 horse power, if it be run 
 at 94 revolutions per minute. That is to say, by keeping a constant 
 ratio between the peripheral speed of the runner and the square 
 root of the head the efficiency of the wheel at varying heads is not 
 changed for any given setting of the gate. 
 
 In order to properly utilize the output of the wheel, it is neces- 
 sary that the speed be kept constant. In order to determine the 
 amount of power that will be lost by keeping the speed constant 
 while the head varies, the curves of Fig. 255 were platted from 
 actual observations. 
 
 Curve No. I, Fig. 254, is the full gate readings of the 10,500 
 horse power turbine, which was installed for the Shawinigan Wa- 
 ter and Power Company. This wheel was designed for 10,500 
 horse power when working under a head of 135 feet, and when 
 running at 180 revolutions per minute. The observations which 
 are platted on this curve were obtained by using the generator as 
 a brake for the wheel, and a water rheostat was used as a means of 
 loading the generator. The speed was then adjusted to 180 revolu- 
 tions per minute at the wide open gate and an observation made. 
 By varying the field of the generator, the speed of the unit was 
 varied without materially affecting the power and without moving 
 the gate of the wheel. Observations were made above and below 
 the normal speed through as wide limits as the rheostat in the 
 field circuit of the .generator would permit. The power output 
 was determined by means of accurately calibrated electrical in- 
 struments. The speed was determined by an accurately calibrat- 
 ed tachometer. The curves on this sheet give the relation between 
 <f> and horse power. 
 
 Referring back to Fig. 254, and taking the 50 foot head condi- 
 tions, it should be noted that for a constant speed of 107 revolu- 
 
Graphical Analysis of W. A. Waters. 
 
 4*5 
 
 <j) Horse Power 
 
 fill/ Gate CuripYo. /, 1830 ffi Ifnif Shstfririigan 
 
 ::%::: Zv 
 
 Fig. 255. Curves of g> and Power of Several I. P. Morris Wheels. (Repro- 
 duced from Bull. No. 2 of I. P. Morris. Co.) 
 
 "^ -. -V J i - - 
 
416 The Selection of the Turbine. 
 
 tions per minute <j> would have to increase from the normal value 
 of about .68 to .08. By referring again to Fig. 255, it will be 
 noted that when <f> was 0.8, with full gate opening, the power 
 .dropped from 10,650 horse power to 10,250 horse power, or about 
 3.3 per cent. From this fact the normal power as shown by Fig. i 
 may be corrected for the new speed of rotation and a point on 
 Curve No. 2, Fig. 254 obtained, giving the actual power which 
 would be developed by the wheel under the 50 foot head, and 
 running at the constant speed of 107 revolutions per minute. 
 Curve No. 2 is platted in this jnanner from Curve No. i. 
 
 As a check to Curve No. 1, Fig. 255, Curves Nos. 5, 6, 7, and 8 
 have been platted, all of which were made from actual observa- 
 tions, in the same manner as Curve No. i. All of these wheels 
 are of the Francis inflow type, and were designed for $-.7, except 
 Curve No. 6, which is an outward flow Fourneyron wheel, and 
 was designed for ^=.5. Curve No. 5 is for a 6,000 horse power 
 wheel with gates in the draft tubes. The shape of the curve 
 shows that the gate was probably not entirely open when the ob- 
 servations were made. 
 
 In Fig. 256 has been platted efficiency curves, which the de- 
 signed wheel would give under varying heads, and running at a 
 constant number of revolutions. Curve No. I is an exact dupli- 
 cate of the efficiency curve which was obtained on a 3,500 horse 
 power wheel working under 210 foot head, and making 250 revolu- 
 tions per minute. The wheel is of the Francis inflow type, with 
 double runners, fitted with movable guide vanes, similar to those 
 which are proposed to be used in the wheels for the McCall-Ferry 
 Power Company. 
 
 It will be noted that the efficiency of the wheel reaches 82.3 per 
 cent, at about seven-eighths power, the efficiency dropping to Si 1 /^ 
 per cent, at full gate. It will be noted that the efficiency is very 
 high at part load. This was accomplished in the design of the wheel 
 by sacrificing a higher efficiency at full load. This curve has. been 
 taken as typical of the efficiency which would be obtained by the 
 wheel proposed for the McCall-Ferry Power Company, when work- 
 ing under a 65 foot head. The efficiency curve of the 10,500 horse 
 power wheel which was supplied by the I. P. Morris Company to 
 the Shawinigan Water and Power Company (See Fig. 236), gives 
 higher results than the curve selected, but it was thought that 
 Curve No. i is the best for a typical curve. 
 
Graphical Analysis of W. A. Waters. 417 
 
 Curve No. i, Fig. 256 was platted by assuming that, at full gate, 
 3,500 horse power corresponded to 13,500 horse power in the 
 wheel to be designed. The part gate points of the curve were ob- 
 tained by proportion. Curve No. 3 represents the efficiency and 
 power of the wheel when working under 50 foot head, and at 94 
 r. p. m. 
 
 Point X on this curve was obtained in the following manner: 
 First, read on Curve No. 1, Fig. 254 the power which the wheel 
 would give under the 50 foot head, and revolutions best suited. 
 This is found to be 9.150 horse power. On Scale B, Fig. 256 a 
 line is drawn from 9,150 horse power to zero, forming Curve No. 
 10. To find what the efficiency would be at 8,000 horse power un- 
 der the 50 foot head, take the point at 8,000 horse power on Scale 
 B, projected horizontally until it intersects Curve No. 10, and 
 11,800 horse power will be read from Scale A. From the effici- 
 ency curve directly over 8,000 horse power on Scale A, the point, X, 
 will be found on Curve No. 3,. which gives the efficiency of the 
 wheel when developing 8,000 horse power under the 50 foot head, 
 and running at the revolutions best suited, namely 94. 
 
 This wheel is to run, however, at 107 revolutions per mirtute, 
 under all conditions of head, and it is necessary to correct Curve 
 No. 3 for the drop in power and efficiency due to the increase in 
 speed. 
 
 Referring to Curve No. I, Fig. 255, it will be noted that the pow- 
 er varies when the speed varies, and in the calculations of effi- 
 ciency in Fig. 256, it has been assumed that the efficiency varies 
 directly as the power. In other words, it has been assumed that 
 the quantity of water does not vary when the revolutions are 
 changed with the constant setting of the gate. This is not strict- 
 ly true but for the observations as platted on Curve No. I, Fig. 255 
 the quantity of water would probably vary only one-half of one 
 per cent., increasing as the revolutions increase from 158 to 201. 
 
 Referring to Fig. 254, and the 50 foot head, it will be noted that 
 when the speed is increased from the best speed of 94 revolutions 
 to the desired speed of 107 revolutions, the power falls 3.3 per 
 cent, and the power and efficiency of the full gate point on Curve 
 No. 3, Fig. 256 can be decreased 3.3 peir cent, resulting in the full 
 gate point on Curve No. 2. 
 
 Referring to Fig. 255, Curves Nos. I, 2, 3, and 4, it will be noted 
 that the slope of these curves between < = 0.7 and <f> --=0.8 is about 
 the same, and, therefore, the power and efficiency of all the points 
 
The Selection of the Turbine. 
 
 Fig. 256. Estimated Efficiency Power Curves of the Proposed McCall-Ferry 
 Wheel. (Reproduced from Bull. No. 2 of 1. P. Morris Co.) 
 
Graphical Analysis of W. A. Waters. 419 
 
 on Curve No. 3, Fig. 256, can be reduced by the same percentage, 
 namely, 3.3 per cent. In this manner Curve No. 2, Fig. 256. is ob- 
 tained, which gives the power and efficiency of the wheel when 
 working under the 50 foot head, and running at the speed of 107 
 revolutions per minute. In the same manner Curves Nos. 5 and 7 
 are platted, Curves Nos. 4 and 6 being deduced therefrom, respec- 
 tively. In the same manner Curve No. 9 is platted, and Curve No. 8 
 deduced therefrom. It will be noted that Curve No. 8 lies on the 
 opposite side of the parent curve to that of the other curves. 
 Curve No. 8 crosses Curve No. 9 at 13,500 horse power on Scale 
 A, and beyond this point would drop below Curve No. 9. The 
 reason Curve No. 8 falls to the left of Curve No. 9, and shows 
 greater efficiency at part gate for the 70 foot head, is because when 
 <j> changes from 0.7 to 0.65, Fig. 255, the partial gate Curves Nos. 2, 
 3, and 4, Fig. 255, show the increase in power and efficiency. 
 These points, however, cannot be very definitely determined, but 
 it does show that the assumption is correct that the designed 
 wheel, working under the head of 70 feet, and running at 107 rev- 
 olutions, will show higher percentage of efficiency at part gate 
 than when running at the 65 foot head and the same powers. 
 
 The curves on Fig. 256 show that the efficiency is not serious- 
 ly affected by keeping the speed of the wheel constant under the 
 varying conditions of head. They do show, however, that the 
 power is seriously affected by keeping the speed of the wheel con- 
 stant under the varying conditions of head. The endings of the 
 various curves show the maximum power, as read on Scale A, 
 which the wheels will give under that head. 
 
 These curves, therefore, give the performance of the wheel when 
 running at a constant number of revolutions, and working under 
 varying heads from 50 to 70 feet. The curves, of course, are not 
 absolutely correct. They show, however, fairly accurately, the 
 amount of variation in efficiency and power which may be ex- 
 pected from the actual conditions obtained with the proposed 
 wheel under the head for which it was designed. 
 
CHAPTER XVII 
 
 THE LOAD CURVE AND LOAD FACTOR, AND THEIR 
 INFLUENCE ON THE DESIGN OF THE POWER 
 PLANT. 
 
 194. Variation in Load. All power plants are subjected to more 
 or less change in load, and this continually changing load has an 
 important bearing on the economy of the plant, and should be care- 
 fully considered in its design and construction. 
 
 If the power output of any plant be ascertained, minute by min- 
 ute or hour by hour, either by means of recording devices or by 
 reading the various forms of power indicators usually provided 
 for such purposes, and a graphical record of such readings be 
 made, a curve varying in height, in proportion as the power varies 
 from time to time, will result. This curve is termed the daily 
 load curve. The load curve itself will vary from day to day as 
 the various demands for power vary, but it usually poss.esses cer- 
 tain characteristic features which depend on the load tributary to 
 each plant and which vary somewhat as the seasons or other con- 
 ditions cause the load to vary. 
 
 The characteristics of the load curve, due to certain demands, 
 can be quite safely predicted. A power plant in a large city, for 
 example, will carry a comparatively small continuous night load. 
 This, in dark weather and in winter, will be increased by the early 
 risers who are obliged to go early to shop and factory. These 
 demands usually begin to affect the load curve about 5 A. M. and 
 may cease wholly, or in part, by 7 A. M., depending on the season 
 and latitude. From 7 to 8 A. M. the motor load begins to be felt. 
 This may reach a maximum from 10 to 12, and usually decreases 
 from 12 to 2 during the lunch hours. The maximum load usually 
 comes in the afternoon when business reaches a maximum, and 
 when the largest amount of power and also light (in the late aftej;- 
 noon) are used. The< load begins to decrease after the evening 
 meal, as the demand for light lessens, and may again increase some- 
 what as the theatres and halls open for evenings' amusements. The 
 character of the load curves, due to various loads, is best under- 
 stood by a study of the actual curves themselves. 
 
Load Curves of Light and Power Plants. 421 
 
 195. Load Curves of Light and Power Plants. The curves 
 shown in Fig. 257 are from the plants of the Hartford Electric 
 Light Co., of Hartford, Conn., and will illustrate variation of the 
 load curve at different seasons of the year. These curves were 
 taken from an article in "The Electrical World and Engineer" of 
 March 8th, 1902. This plant is a combined water and steam pow- 
 er plant, and is provided with a storage battery to assist in equal- 
 izing the load. These curves are described as follows : 
 
 "On a week day in March, 1901, the maximum load was 1720 
 k. w. and the total energy output was 30249 k. w. hours. The aver- 
 age hourly load was then 1260 k. w. or 46 per cent, of the maximum 
 load. On- this same day the battery discharged at the rate of 260 
 k. w. at the peak of the load. In the early morning hours of this day 
 the load on the system, apart from battery charging, reached its 
 minimum at 612 k. w., or only 22.5 per cent, of the maximum load. 
 In June, 1901, the maximum load on a certain week day was 1390 
 k. w., and the minimum 250 k. w., or 18 per cent, of the former. 
 The total output on this day 'was 2505 k. w. hours, so that the 
 average load during the 24 hours was 1046 k. w. or 75 per cent, af 
 the maximum. In January, the maximum load came on between 
 4 and 5 P. M., when lighting was the predominant factor, but in 
 July the greatest demand came on the system in the latter part 
 of the forenoon, and must have been made up in large part by re- 
 quirements for electric power. By December 1901, the maximum 
 load reached 2838 k. w. and the minimum 612 k. w. The approxi- 
 mate capacity of all connected lamps and motors in that month 
 was 8530 k. w. The maximum load for the December day of 2838 
 k.w. is only 33 per cent, of the connected capacity. On this day 
 the total output was 3219 k. w. hours, so that the average load 
 during the 24 hours was 1342 k. w. This average is 15 per cent, of 
 the total capacity." 
 
 Fig. 258 is a combined annual load curve for several years, and 
 not only shows the increase in the electrical output of this system 
 for the years from 1898 to 1905, but also the annual monthly 
 change in load from a maximum in December or January to a 
 minimum in June or July. This variation fortunately accompanied 
 similar variation in the flow of the Farmington River on which 
 most of .the power was developed. 
 
 Up to the middle of 1898. the entire load of this Company was 
 carried by a single water power plant. The natural increase in 
 demand for power necessitated the construction of a second plant 
 
4 22 
 
 The Load Curve. 
 Kilowatts. 
 
Load Curves of Light and Power Plants. 
 
 4*3 
 
 on the same river, and up to January 1905, the two water power 
 plants were able to carry most of the load, steam auxiliaries, how- 
 ever, being occasionally used, as indicated by the dotted line. 
 
 Fig. 259 shows daily load curves from the Christiania Power 
 Stations, of Christiania, Norway. In this figure are shown the max- 
 imum, the minimum, and a mean curve for the entire year. > The 
 
 1000000 
 
 750000 
 
 500000 
 
 250000 
 
 *H 
 
 Jan. Jul. Jan. Jul. Jan. Jul. Jan. Jul. Jan. Jul. Jan. Jul. Jan. JuL Jan. Jul. 
 1898 1899 1900 1901 1902 1908 1904 1905 
 
 Steam 
 
 Water 
 
 Total 
 
 Fig. 258. Energy Output of Hartford Electric Light Co. (From 
 Electrical World and Engineer. ) 
 
 difference between the maximum and minimum curves is here very 
 marked. This is readily ascribed to the high latitude of Christiania 
 as the long twilights of summer render lighting at that season 
 almost unnecessary, while the very short and dark days of winter 
 create not only a high maximum but a high continual demand dur- 
 ing the entire day. No data as to kind of load is available. 
 
 Fig. 260 is a power curve from the New York Edison Company. 
 
 On August ist, 1905, there were connected up to the system of 
 the New York Edison Company an equivalent of 1,651,917 incan- 
 descent lamps, 22,093 arc lamps, 2,539 k. w. in storage batteries 
 
The Load Curve. 
 
 and 99,258 H. P. in motors. The lighting load forms 52.2 per cent, 
 of the connected load. 
 
 The effect of extraordinary conditions on the load curve and the 
 necessity of some kind of storage to provide for the same, is well 
 illustrated by Fig. 261 which shows the effect on the load curve 
 
 1000 
 
 A.M. 
 
 4 6 
 
 P. M. 
 
 Fig. 259. Typical Electric Lighting Load Curves. Christiana, Norway, 
 Power Stations. 
 
 of a lighting plant of a sudden thunderstorm. When such a storm 
 occurs in the late afternoon the light load from schools, offices, 
 stores, etc., may be suddenly thrown on, and the result may be an 
 extraordinary load which the plant must meet. 
 
 196. Factory Load Curves. Shop and factory loads are sup- 
 posed to be the most uniform in character, yet they are subject to 
 great variation, due to the sudden turning on or off of the ma- 
 chines. Fig. 261 shows the load curve of the Pennsylvania Rail- 
 road Shops at Altoona, Pennsylvania. 
 
 The shops of the Pennsylvania Railroad are located in and around 
 Altoona, Pennsylvania, in groups, each group being supplied by its 
 own power station. No data as to the number and power of motors 
 connected up is available, but the following shows to some extent 
 how the load is divided. The Machine Shop power plant embraces 
 
Factory Load Curves. 
 
 425 
 
 2 300 k. w. generators, I Brush arc generator (power unknown), 
 and a 40 H. P. Thompson-Houston arc generator for lighting shop 
 and grounds. At the Car Shops 4-250 k. w. and 1-625 k. w. gen- 
 erators are used. Current is supplied to 75 arc lights in shops and 
 yards. At the Junita shops 3-300 k. w. generators are used for 
 power purposes only. At South Altoona the generating station 
 
 60000 
 
 10 12 
 A. M. M. P. M. 
 
 New York Edison Co., Load Curve, day of Max. load, Dec. 22, 1904. 
 * Including 3100 K. W. delivered directly at 6600 Volts A. C. 
 Fig. 260. Typical Electric Lighting Load Curve. 
 
 embraces 1-50 k. w., and 2-500 k. w., and 2-300 k. w. generators. 
 The loads are quite variable, as would be expected in a railroad 
 shop, there being some very heavy machines in intermittent opera- 
 tion, one planer running as high as 80 H. P., while 20 H. P. motors 
 are numerous. The normal load is less than the maximum, but the 
 latter is frequently reached. 
 
 A, B and C, Fig. 263, are three typical factory lo&d curves which 
 represent types of load curves from three different electric power 
 stations, A in an Eastern, B in a Central, and C in a far Western 
 state. These curves are taken from an article on "The Economics 
 of Electric Power" in Cassier's Magazine for March, 1894. The 
 circuits from these stations are exclusively motor circuits, the num- 
 ber of motors connected being given in the following tables ; 
 
426 
 
 The Load Curve, 
 
 5000 
 
 4000 
 
 3000 
 
 2000 
 
 1000 
 
 A. M. 
 
 10 
 
 Fig. 261. Sharp Thunder Storm Peak, Dickenson St. Station, Manchester, 
 
 Eng. 
 
 
 A 
 
 
 
 B 
 
 
 
 C 
 
 
 Size of 
 Motor 
 <H. P.) 
 
 No. in 
 Use. 
 
 Com- 
 bined 
 H. P. 
 
 Size of 
 Motor 
 (H. P.) 
 
 No. in 
 Use. 
 
 Com- 
 bined 
 H. P. 
 
 Size of 
 Motor 
 (H. P.) 
 
 No. in 
 Use. 
 
 Com- 
 bined 
 H. P. 
 
 i 
 
 3 
 
 H 
 
 I 
 
 3 
 
 I 
 
 i 
 
 4 
 
 1 
 
 
 31 
 
 31 
 
 
 2 
 
 I 
 
 * 
 
 1 
 
 J 
 
 2 
 
 10 
 
 20 
 
 i 
 
 1 
 
 I 
 
 1 
 
 5 
 
 5 
 
 3 
 
 19 
 
 57 
 
 
 15 
 
 15 
 
 2 
 
 3 
 
 6 
 
 5 
 
 10 
 
 50 
 
 2 
 
 14 
 
 28 
 
 3 
 
 4 
 
 12 
 
 7* 
 
 3 
 
 22* 
 
 3 
 
 5 
 
 15 
 
 5 
 
 3 
 
 15 
 
 10 
 
 12 
 
 120 
 
 5 
 
 12 
 
 60 
 
 6 
 
 5 
 
 30 
 
 13 
 
 5 
 
 75 
 
 7* 
 
 12 
 
 90 
 
 8* 
 
 3 
 
 25* 
 
 20 
 
 2 
 
 40 
 
 10 
 
 15 
 
 150 
 
 10 
 
 6 
 
 60 
 
 25 
 
 4 
 
 100 
 
 15 
 
 9 
 
 135 
 
 14 
 
 6 
 
 84 
 
 50 
 
 1 
 
 50 
 
 20 
 
 5 
 
 100 
 
 15 
 
 1 
 
 15 
 
 
 
 
 25 
 
 3 
 
 75 
 
 17i 
 
 1 
 
 
 
 
 
 30 
 
 3 
 
 90 
 
 25 
 
 1 
 
 25 
 
 
 
 
 40 
 
 1 
 
 40 
 
 30 
 
 3 
 
 90 
 
 
 
 
 
 
 
 40 
 
 1 
 
 40 
 
 
 
 
 
 
 
 60 
 
 2 
 
 120 
 
 
 
 
 
 
 
 70 
 
 1 
 
 70 
 
 
 
 
 
 
 
 
 
 
 Total... 
 
 100 
 
 567 
 
 
 100 
 
 799| 
 
 
 50 
 
 616* 
 
 
 
 
 
 
 
 
 
 
Factory Load Curves. 
 
 427 
 
4 28 
 
 The Load Curve. 
 
 7 8 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 
 
 6 7 8 9 10 11 12 1 23 4 5 7 8 9 10 11 12 
 
 7 
 
 V 
 
 
 
 9 10 11 12 1 2 3 4 5 6 7 8 9 10 11 12 
 A. M. M. P. M. 
 
 Fig. 263. Typical Factory Load Curves. (Cassier's Magazine.) 
 
Load Curve of London Hydraulic Company. 
 
 429 
 
 On the circuits covered by the diagram B some of the motors are 
 five miles and more distant from the power stations. 
 
 One deduction which may be made from a study of these curves 
 is that in an electrical power system where a considerable number 
 of motors are employed the initial dynamo plant need not be equal 
 to the total motor load. In the case in hand the curves show that 
 the generator need be but from 25 per cent, to 40 per cent, of the 
 
 14000J 
 
 120000 
 
 Fig. 264. Maximum Days of Pumping. London Hydraulic Supply. (Cas- 
 
 sier's Magazine.) 
 
 rated capacity of the motors connected. In order to check off this 
 phenomenal condition actual meter readings were taken monthly 
 from fifty-three different shops covering a period of from four to 
 six months, current to these shops being sold on the meter basis. 
 The results showed that only 25% per cent, of the nominal capacity 
 of the motors was employed, thus practically checking the condi- 
 tions indicated by the diagrams of the central power stations. 
 
 197. Load Curve of London Hydraulic Supply Company. Fig. 
 264 is a load curve of The London Hydraulic Supply Company, 
 which is rather exceptional in that the power is used almost en- 
 tirely for running elevators and is therefore almost exclusively a 
 26 
 
430 
 
 The Load Curve. 
 
 Kilowatts 
 
 JUNE - 89 -1904 
 
 J 
 
 "^ 
 
 BUFFALO 
 
 BATTERIES 
 
 FALLS POWER BUFFALO, 
 
 ONAWANOA-LOCKPORT 
 
 
 FALLS POWER-TONAWANOA, LOCKPORT AND OLCOTT 
 
 I . . , ! , I . I | I I | I I I I i 
 
 Fig. L'6\ 
 
 12000 
 11000 
 10000 
 9000 
 8000 
 7000 
 6000 
 5000 
 4000 
 3000 
 2000 
 1000 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 DEC 
 
 EM 
 
 3EF 
 
 
 30 
 
 19 
 
 03. 
 
 
 
 
 
 
 
 
 
 
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 BU 
 
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 ^ 
 
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 ^-A.C. STEAM 
 
 yo^^. 
 
 
 
 
 
 
 
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 1 
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 J 
 
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 POWER. 
 
 
 
 
 
 
 
 s 
 
 
 
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 ^ 
 
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 LLS 
 
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 T^ 
 
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 K5= 
 
 C^X 
 
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 ^ 
 
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 AL 
 
 LS 
 
 PO 
 
 AA 
 
 WE 
 
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 R- 
 
 6 
 
 T0> 
 
 A* 
 
 r> 
 
 'AN 
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 3A^ 
 
 A 
 
 LC 
 
 CK 
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 A 
 
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 Lr^ 
 
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 7T 
 
 12 2 4 6 8 10 12 2 4 
 A.M. M. 
 
 6 8 
 P.M. 
 
 10 
 
 12 
 
 Fig. 2C6. Typical Railway Load Curves, International Ry. Co. (From Elec- 
 trical World and Engineer.) 
 
Railway Load Curve. 431 
 
 day load. The London Hydraulic Supply Company furnishes 
 water under a pressure of 750 pounds per square inch through a sys- 
 tem of mains 86 miles long. In 1894, 2915 machines were connected 
 to this system, of which 650 were passenger elevators, 2000 freight 
 elevators and cranes, 90 presses of various kinds, 95 motors, and 
 80 fire hydrants. Each 1000 gallons of water pumped represents 
 8.738 H. P. hours, therefore, the maximum on the diagram repre- 
 sents about 1200 H. P. The preponderant influence of the elevator 
 load is shown in the rapid rise from 6 to 10 A. M. and the some- 
 what slower decline from 4 to 12 P. M. 
 
 198. Railway Load Curves. The power load most subject to 
 violent fluctations is that utilized for railway purposes. The sud- 
 den changes in the demand for power occasioned by stopping and 
 starting of cars, which may, under some conditions, occur simul- 
 taneously are often very rapid and the resulting load fluctuations 
 very great. 
 
 Figs. 265 and 266 show two sets of curves taken from the power 
 charts of the International Railway Company of Buffalo, which 
 may be considered typical for electric railways. Each chart has 
 two sets of curves, one for the city lines, on which the traffic is 
 purely urban in character, and the other for the Tonawanda, Lock- 
 port and Olcott Line, which is an interurban line. In either set the 
 total load at any time is represented by the ordinate to the highest 
 curve in that set. The amount of load carried by any portion of 
 the system is represented by the difference between the ordinates 
 to the curve of that portion and to the curve next below. On the 
 urban lines two peaks will be observed, one at 8 A. M. and one at 
 6 P. M., for both winter and summer, the afternoon peak of the 
 former being nearly 75 per cent greater than the latter, however. 
 The load curve of the interurban line appears to be nearly uniform 
 throughout the year. 
 
 The data, on page 432, concerning these curves are taken from 
 "The Electrical World and Engineer" of December 10, 1904. 
 
 199. Load Conditions for Maximum Returns. It is manifest 
 that no plant will receive its maximum returns without operating 
 at full load all of the time ; that if it operates at less than full load 
 its income will be reduced unless more is charged for power so 
 delivered ; and that if the load carried for a large portion of the 
 time is comparatively small and the returns for such power are not 
 proportionately large the plant may be found to be an unprofitable 
 
432 
 
 The Load Curve. 
 
 investment. On every plant the fixed charges, which include in 
 terest on first cost, depreciation charges and taxes, continue at a 
 uniform rate every hour of the day and every day of the year. The 
 operating expenses increase somewhat with the total amount of 
 power furnished but not in proportion. An increase in the total 
 
 Data from Curves of Figure 265. 
 
 
 PURCHASED POWER. 
 
 STORAGE BATTERIES. 
 
 Grand 
 Total. 
 
 Tonawanda. 
 
 Tonawanda. 
 
 Buffalo. 
 
 Lock- 
 port. 
 Olcott 
 
 Total. 
 
 Buf- 
 falo. 
 
 Lock- 
 port. 
 
 Total. 
 
 Maximum H P 
 
 6,114 
 1,667 
 4, 636 
 111,272 
 83,009 
 
 1,985 
 319 
 1,221 
 29,302 
 21,859 
 
 8,099 
 1,985 
 5,857 
 140,574 
 104,868 
 
 3,752 
 79 
 
 1,262 
 8,406 
 6,271 
 
 635 
 40 
 274 
 3,480 
 2,596 
 
 4,387 
 119 
 1,536 
 11,886 
 8,867 
 
 12,486 
 2,104 
 7,393 
 152, 460 
 113,735 
 
 Minimum H. P 
 
 Average H. P 
 
 H P hours 
 
 K W hours 
 
 
 Maximum number of cars in service in Buffalo, 408. 
 Average volts at D. C. busbars, 592. 
 State of weather: 8 a. m., cloudy; 6 p. m., fair. 
 Temperature: 8 a. m., 66 degrees F.; 6 p. m., 74 degrees F. 
 
 Data from Curves of Figure 26S. 
 
 
 
 PURCHASED POWER. 
 
 STEAM POWER. 
 
 Grand 
 Total. 
 
 Tonawanda. 
 
 Buffalo. 
 
 Lock- 
 port. 
 Olcott 
 
 Total. 
 
 Niag- 
 ara St 
 
 Vir- 
 ginia 
 
 St. 
 
 Total. 
 
 Buf- 
 falo. 
 
 Maximum H. P. ... 
 Minimum H. P 
 Average H. P 
 
 7,622 
 2, 303 
 6,002 
 144,046 
 107,458 
 
 2,025 
 199 
 1,149 
 
 27,584 
 20,578 
 
 9,647 
 2,502 
 7,151 
 171,630 
 128,036 
 
 3,414 
 953 
 2,115 
 38,442 
 28,678 
 
 2,064 
 715 
 1,641 
 4,367 
 3,238 
 
 5,478 
 1,668 
 3,756 
 42,809 
 31,936 
 
 3,970 
 79 
 1,224 
 7,344 
 5,479 
 
 19, 095 
 4,249 
 12, 131 
 221,783 
 165,451 
 
 H. P., hours 
 
 K. W., hours. . 
 
 
 Average volts at D. C. busbars, 592. 
 
 State of weather: 8 a. m., cloudy; 6 p. m., cloudy. 
 
 Temperature: 8 a. m., 20 degrees F.; 6 p. m. 26 degrees F. 
 
 output of a given plant, therefore, means a direct increase in the 
 net earnings of the plant and unless the power plant is constantly 
 operating at its maximum capacity, its earning efficiency is not at 
 the highest point. 
 
The Load Curve in Relation to Machine Selection. 433 
 
 It will be noted at once that if a machine can be operated at its 
 full capacity for the entire time, that the work done will be done 
 under the most economical conditions as far as each unit of output 
 (Horse Power Hour or Kilo-Watt Hour) is concerned. The in- 
 terest on the first cost and other fixed charges will be distributed 
 among the maximum number of power units. The cost of wear, 
 and the repairs, while they increase with the amount of power fur- 
 nished, are not in direct proportion thereto, and decrease per unit 
 as the average load carried reaches nearer the maximum of the 
 machinery used. The same is true of the cost of attendance and 
 most other operating expenses. 
 
 200. The Load Curve in Relation to Machine Selection. A com- 
 parison between the average load carried and the maximum load 
 will show the relation between the machinery which it is necessary 
 to install and the active, work which it has to do, and furnishes a 
 basis for the study of the possible earnings of the plant. 
 
 The ratio between the maximum load and the average load is \ 
 called the "load factor." Some engineers use the term "load factor" 
 as representing the ratio between the average load actually carried 
 and the maximum capacity of the machinery operated. The writer, 
 however, prefers the term "machine factor" to represent this ratio. 
 The same term is also sometimes applied to the ratio of the aver- 
 age load to the machinery in hourly operation, but to this the term 
 "hourly machine factor" seems more applicable. The ratio of the 
 average load to the total capacity of the station would seem best 
 represented by the expression "capacity factor." 
 
 In order to have a plant work at the maximum advantage, it 
 must be designed to fit the contingencies of the load. The opera- 
 tion of a machine at partial load is not only expensive on the basis 
 of fixed charges, but is still more so on account of the decreased 
 efficiency under such conditions. 
 
 With a varying load, efficient operation usually involves the in- 
 stallation of two or more generators of such capacity that a single 
 unit will furnish the power required during the hours of minimum 
 demand and at the same time operate at a fairly efficient rate. As 
 the daily demand for power increases, additional units are started 
 and operated, still under economical conditions, and at the peak 
 of the load one or more additional units may be cut in and operated 
 for the limited time during which the maximum demands prevail. 
 Such an arrangement assures reasonable economy of operation at 
 all times, even when great changes of load are of daily occurrence. 
 
434 The Load Curve. 
 
 201. Influence of Management on Load Curve. The relations of 
 the "load curve," the "load factor," the "machine factor" and the 
 "capacity factor" are, or may be, to an extent controlled by the 
 business management of any plant, and by the selection and the 
 character of the load to be carried, where such selection is possible. 
 Each consumer of power will develop a particular curve due to the 
 character of the work done, and it is frequently possible, by a ju- 
 dicious selection of customers, and especially by a proper grading 
 of rates, to raise the load factor and thereby decrease the cost of 
 operation and increase the net profits from the plant. A study of 
 the probable plant factors is necessary for the judicious selection 
 of machinery in order to attain the most efficient operation and, 
 in a hydraulic plant, in order to properly design it and conserve 
 the maximum energy of the stream that is being developed. 
 
 202. Relation of Load Curve to Stream Flow and Auxiliary 
 Power. Some of the relations between the load factor and the 
 conditions under which a hydraulic plant may have to be operated 
 are shown by Figs. 267, 268 and 269. 
 
 In Fig. 267, diagram A shows a typical daily load curve from the 
 terminal station at St. Louis, a curve quite similar in general char- 
 acter to those previously shown. 
 
 Diagram B shows the power that must be developed by a stream 
 in order to take care of the load represented by this load curve, 
 under conditions where no auxiliary power or storage are available. 
 In this case, it will be noted that the available water power must be 
 equivalent to or greater than the maximum peak load, and that all 
 power represented by the area above the load line, amounting in the 
 case illustrated to about 40 per cent, of the total available power, 
 will be wasted. 
 
 Diagram C illustrates a condition where the average load and 
 water power are equal. In this case, pondage or storage, repre- 
 sented by the cross-hatched area below the average line, may be 
 utilized to furnish the peak power represented by the cross-hatched 
 area above the average line. Without pondage, the cross-hatched 
 area below the average load line will represent the energy wasted, 
 and the cro,ss-hatched area above the average load line will repre- 
 sent the energy which must be supplied by auxiliary power. With- 
 out pondage the power of the stream must be utilized as it passes, 
 and in the diagram B, of Fig. 267, the power represented above the 
 load line under such conditions must be wasted. 
 
Relation of Load Curve to Water Power. 
 
 435 
 
 sue 
 
 400 
 
 300 
 
 ; 800 
 
 100 
 
 500 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f \ 
 
 
 
 
 
 
 
 
 
 
 
 -(/ 
 
 >i 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 \ 
 
 N 
 
 
 
 
 
 
 
 
 
 V 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 \ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f 
 
 
 
 
 
 s A 
 
 VER 
 
 HGE 
 
 2.6 
 
 > 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 -X 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 N 
 
 N 
 
 
 
 
 
 
 
 A 
 
 VER 
 
 GE 
 
 2.9! 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 s r 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r- 
 
 '~ 
 
 
 
 
 
 
 
 
 J N 
 
 
 
 
 
 
 B 
 
 
 
 
 
 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 X* 
 
 
 X| 
 
 A 
 
 VER 
 
 *GE 
 
 2. IB 
 
 ->. 
 
 
 2 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 
 
 
 
 
 -^ 
 
 ^-~ 
 
 
 
 
 ""7^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 s- 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A 
 
 
 
 
 
 
 
 
 
 C 
 
 
 
 
 
 RATIOS. 
 MINIMUM TO AVEBAtC 1 TO 1.7 
 MINIMUM TO MAXIMUM 1 TO .8 
 AVERAGE TO MAXIMUM 1 TO 1.87 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 A.M. f It AM. 
 8 10 12 e 4 6 8 10 IE E 4 
 
 
 
 TYPICAL DAILY LOAD 'CURVE UNION TERMINAL STATION ST. LOUIS. 
 
 WATER POWER REQUIRED WITH 10 AUXILIARY POWER 
 
 STORAGE 
 
 500 
 
 AVERAGE LOAD AND WATER POWER EQUAL. 
 
 STORAGE OR AUXILIARY POWER REQUIRED, 
 
 WATER 
 
 POWER 
 UTILIZED. 
 
 POWER 
 WASTED. 
 
 FIOM 
 
 STORA8E . 
 
 AUXILIARY 
 POWER. 
 
 RELATION OF POWER SUPPLY AND DEMAND 
 Fig. 267. 
 
43$ The Load Curve. 
 
 These same conditions are shown both by diagram C, Fig. 268, 
 and diagram A, Fig. 269. In the latter, with water power above 
 the average load of the plant, the peak load must be supplied by 
 auxiliary power, although more water power than would be suffi- 
 cient to handle it is daily wasted. 
 
 Diagram B, Fig. 268, shows a condition with low water power 
 no storage available, and the power less than the average load. In 
 this case the water power wasted is comparatively small, and the 
 amount, and especially the capacity, of the auxiliary power be- 
 comes large. 
 
 Diagram C, Fig. 268, represents a water power condition, where 
 the power available is less than the average load, where storage 
 is practically unlimited, and some auxiliary power is necessary in 
 order to carry the peak of the load. Under these conditions, the 
 water power, which would otherwise be wasted during the time 
 of minimum load, is impounded, and can be utilized together with 
 the auxiliary power at times of maximum load. The diagram 
 shows a method of utilizing the minimum capacity of auxiliary 
 power by utilizing the stored water power to its greatest advan- 
 tage, and utilizing auxiliary power uniformly throughout the 
 period where auxiliary power is demanded. 
 
 Diagram A, Fig. 269, represents the same conditions where stor- 
 age is limited, and auxiliary power is necessarily required to help 
 out the peak load conditions. In this case only a certain amount 
 of the spare water can be stored, the balance being wasted at times 
 where it cannot be continuously utilized. 
 
 The conditions for reducing the total amount of auxiliary power 
 by utilizing the storage to advantage is shown in the same manner 
 as in diagram C, Fig. 268. 
 
 Diagram B, Fig. 269, shows a method of utilizing the minimum 
 capacity of auxiliary power in a plant where the water power is 
 below the average load and the pondage is practically unlimited. 
 This is accomplished by the continuous operation of the auxiliary 
 plant and the storage of water power during the hours of low con- 
 sumption, for utilization during the hours of peak load. 
 
 A careful and detailed study of the load curve and load factor; 
 the method of increasing the latter and of designing the most 
 economical plant to take care of the condition to be met; and the 
 adjustment of rates to attain equitable returns to the investor at 
 reasonable price to the consumer, are matters of plant design 
 worthy of the best efforts of the engineer. 
 
Relation of Load Curve to Water Power. 
 
 437 
 
 5CU 
 
 400 
 
 300 -i 
 
 ~ aoo 
 
 100 
 
 SOD 
 
 AUXILIARY POWER REQUIRED . NO STORAGE AVAILABLE 
 WATER POWER GREATER THAN AVERAGE LOAD . 
 
 AUXILIARY POWER REQUIRED. NO STORAGE AVAILABLE 
 WATER POWER LE88 THAN AVERAGE LOAD . 
 
 500 
 
 AUXILIARY POWER REQUIRED . STORAGE UNLIMITED 
 WATER POWER LESS THAN AVERAGE LOAD 
 
 WATER 
 PfiWER 
 UTILIZER. 
 
 POWER 
 WASTED 
 
 FROM 
 ITOA(E 
 
 AUXILIARY 
 POWER 
 
 RELATION OF POWER SUPPLY AND DEMAND . 
 
 Fig. 268. 
 
433 
 
 The Load Curve. 
 
 AUXILIARY POWER REQUIRED STORAGE LIMITED 
 WATER POWER GREATER THAN AVERAGE LOAD 
 
 500 
 
 400 
 
 I ""===:? 
 
 r: Z-00 
 
 100 - 
 
 AUXILIARY POWER [MINIMUM REQUIRED] IN CONTINUOUS SERVICE 
 STORAGE UNLIMITED 
 
 WATER 
 
 r\KKXiPowru .*, x 
 
 STORAGE 
 
 POWtB 
 UTILIZED < 
 
 POWER 
 WASTED 
 
 POWER 
 FROM 
 
 STORAGE 
 
 AUXILIARY 
 POWER 
 
 RELATION OF POWER SUPPLY AND DEMAND 
 
 Fig. 269. 
 
Literature on Load Curve. 439 
 
 LITERATURE. 
 REFERENCES OF LOAD CURVES AND LOAD FACTORS. 
 
 1. Load Curves of Electric Central Station. Elektrotechnische Zeitschrift 
 
 Vol. 25, page G8. Jan. 28, 1904. 
 
 2. Influence of Load Factor on the Cost of Electrical Energy. Edmund I*, 
 
 Hill. Electrician (Lon.). Feb. 10, 1905. 
 
 3. Load Factor Its Effect upon an Electricity Station. Alex Sinclair. Elec 
 
 trician, London, June 30, 1905. 
 
 4. Distribution of Power Load of Electricity Works. Electrician (Lon.), 
 
 July 28, 1905. 
 
 5. The Load Factor of Electric Generating Stations. Norberg^Schultz, 
 
 Coustiania. Elektrotechnische Zeitschrift. Vol. 26, p. 919, Oct. 
 5, 1905. 
 
 6. The Effect of Load Factor on Cost of Power. E. M. Archibald. Eng. 
 
 News, Vol. 53, p. 169. Feb. 16, 1905. Elec. Age, Nov. 1906. 
 
 7. Electrical Transmission of Water Power. Alton D. Adams. Chap. I and 
 
 II. New York. McGraw Pub. Co. 1906. 
 
 8. Economy of Continued Railway -and Lighting Plants. Ernest Ganzen- 
 
 bach. St. Ry. Review, Feb. 15, 1906. Elec. World and Engr. 
 Jan. 27, 1906. 
 
 9. Central Station Power. E. P. Espenschied, Jr. Proc. Engrs. Soc. Wes. 
 
 Penn. Mar. 1906. 
 
 10. Relation of Load, Factor to the Evolution of Hydro-Electric Plants. S. B. 
 
 Storer. Am. Inst. Elec. Engrs. Mar. -23, 1906. 
 
 11. Notes on Design of Hydro-Electric Stations (With Reference to the In- 
 
 fluence of Load Factor). David D. Rushmore. Proc. Am. Inst. 
 Elec. Engrs. April, 1906. 
 
 12. Effect of Day Load on Central Station Economy. J. P. Janes. Elec. Re- 
 
 view, N. Y. May 12, 1906.. 
 
 13. Sale and Measurement of Electric Power. S. B. Storer. Electrical Age, 
 
 Aug. 1906. 
 
 14. Sale of Water Power from the Power Company's Point of View. C. E. 
 
 Parsons. Eng. Record, Aug. 11, 1906. 
 
 15. Contracting for Use of Hydro-Electric Power on Railway Systems. G. A. 
 
 Harvey. Elec. Age, Sept. 1906. 
 
 1C. The Sale of Electric Power. Eng. Record, Nov. 3, 1906. 
 17. Flat Rates for Small Water Power Plants. J. S. Codman. Elec. Wld, 
 
 and Engr., Nov. 3, 1906. 
 
CHAPTER XVIII. 
 
 THE SPEED REGULATION OF TURBINE WATER 
 WHEELS. 
 
 203. The Relation of Resistance and Speed. The power delivered 
 by any water wheel may be expressed, in terms of resistance over- 
 come by the wheel through a known distance and in a known time 
 by the formula (See equation i, Section 177, Chap. XVI). 
 
 2x1 w n 
 
 (1) 
 
 P = 
 
 33000 
 
 The second term of this equation may be divided into two fac- 
 tors : first, 
 
 2x1 w 
 
 33000 
 
 which may be called the resistance factor and which is the resist- 
 ance overcome or power produced by the wheel per revolution per 
 
 .UTlONS PCP HINUTC 
 
 Fig. 270. 
 
 minute ; and n, the number of revolutions per minute. The product 
 is the horse power of the wheel. 
 
 ^ In any wheel operating with a fixed gate opening and under a 
 fixed head the speed, n, will always increase as the resistance, w, 
 decreases, and will decrease as the resistance increases. 
 
Self Regulation with Variable Speed and Resistance. 441 
 
 In Fig. 270 the line AB shows the relation of speed to resist- 
 ance in a turbine operated with a single fixed gate opening and 
 for the full range of load conditions (as determined by experiment) 
 from A, at which the resistance, w, was so* great as to hold the 
 motor stationary, to B where the resistance was completely re- 
 moved and the entire energy of the applied water was expended 
 in overcoming the friction of the wheel, or rejected as velocity en- 
 
 HEAD WATER 
 
 Fig. 271. 
 
 ergy in the water discharged therefrom. From this figure it is 
 evident that if, at any fixed gate opening, a wheel 'is revolving at 
 a given speed, n, and the resistance, w, is decreased to w" the speed 
 will increase to n", while if the resistance increases to w' the speed 
 will decrease to n'. 
 
 204. Self-Regulation in a Plant with Variable Speed and Resist- 
 ance. At Connorsville, Indiana, is a pumping plant (Fig. 271) in 
 which a horizontal shaft turbine is directly connected through 
 friction clutches to two rotary pumps. For operation the turbine 
 gates are opened until the pump, or pumps, speeding up to a suit- 
 able r. p. m., produces the desired pressure in the distributing sys- 
 
442 The Speed Regulation of Turbine Water Wheels. 
 
 tem. The work of the pump under these conditions in pumping 
 water at the speed of operation against the desired pressure equals 
 the work done by the quantity of water q passing through the tur- 
 bine, less friction and other losses. If the pressure falls, the loads 
 become unbalanced: i. e., the resistance is reduced and the tur- 
 bine and pump increase in speed until the balance is restored. If 
 the pressure rises the machine slows down until there is again 
 a restoration of balance between the power of the turbine, the 
 purnp load and friction losses. 
 
 IONS pen MINUTE 
 
 Fig. 272. 
 
 To pump water against an increased pressure, it is necessary to 
 increase the gate opening of the turbine. In its regular daily work 
 the varying demand for water is thus supplied by the self-regula- 
 tion of the two machines used and no governor is needed. The 
 conditions of operation are similar to those illustrated in Fig. 
 270. 
 
 205. The Relations Necessary for Constant Speed. Fig. 272 
 is a diagram drawn from experimental or test observations and 
 similar to Fig. 270 except that the relations between speed and de- 
 sistance are shown for various gate openings. 
 
 It is evident that if the wheel must operate at a fixed speed, n, and 
 the resistance, w, increases to w' or decreases to w", it will be neces- 
 sary to increase the gate opening from % gate to full gate in the 
 first case and to decrease it to % gate in the second case in order to' 
 maintain the speed uniform. 
 
The Ideal Governor. 443 
 
 An examination of the load curves described in Chapter XVII 
 shows that changes in load are constantly in progress. For the 
 satisfactory operation of water wheels, under these constant and 
 irregular changes in load, automatic regulation of the turbine gates 
 becomes necessary- This is accomplished through the water wheel 
 governor which regulates the gates through the various classes of ' 
 gate mechanisms described in Chap. XIII. 
 
 206. The Ideal Governor. The power output of a water tur- 
 bine in terms of energy applied to the wheel is expressed by the 
 formula. 
 
 (2) 
 
 q = cu. ft. per second of water used by the wheel. 
 H' = net available head. 
 E = efficiency of the wheel. 
 P = horse power developed. 
 
 Any sudden increase or decrease of load, w, will produce a cor- 
 responding decrease or increa'se, respectively, in the speed, n, of 
 the machine as shown by Fig. 270 unless the energy applied to the 
 turbine is immediately changed to correspond. The ideal turbine 
 governor would effect a change in output by varying only q, thus 
 obtaining perfect water economy by conservmg^ttnneeded water 
 for future use. This is not possible in practice as head, water, and 
 therefore efficiency are usually wasted when operating a wheel un- 
 der other than its normal load and during the change in load. 
 
 207. Present Status, The success of the comparatively recent 
 application of hydraulic power to the operation of alternators in 
 parallel and to the generation of current for electric lighting street 
 railway and synchronous motor loads has been largely dependent 
 upon the possibility of obtaining close speed regulation of the gen- 
 erating units accompanied with good water economy and without 
 undue shock upon machinery and penstocks while working under 
 extremely variable loads. 
 
 The degree of success thus far obtained in the development 
 (necessitated by the above conditions) of automatic turbine gov- 
 ernors, although achieved from the experimental standpoint almost 
 exclusively, has been remarkable. Instances are now by no means 
 uncommon where hydro-electric units working upon variable loads 
 are controlled as , satisfactorily as modern steam driven units. To 
 accomplish this result the conditions must be especially favorable. 
 
444 The Speed Regulation of Turbine Water Wheels. 
 
 Success in this feature of hydro-electric design is by no means 
 uniform, however, and the fre.quent failure to realize satisfactory 
 results can often be ascribed to the lack of proper consideration of 
 the arrangement of the mechanical, hydraulic, and electrical ele- 
 ments of the plant, wheels, and generators, rather than to any in- 
 herent defects in the governor itself. The power plant, the tur- 
 bines, the generators, and the governors are commonly designed by 
 four different parties without proper correlation of study and de- 
 sign. At present neither experimental data nor theoretical formula 
 are available by which the hydro-electric engineer can design hi? 
 plant for an assumed speed regulation, or can predetermine the 
 speed regulation which is possible with a given installation or the 
 
 120 140 
 
 PERCENT OF NC3MAL CANDLE PCWER 
 
 i60 
 
 130 
 
 Fig. 273. 
 
 time required for the return to normal speed, and yet the gov- 
 ernor builder is. commonly required by the engineer to guarantee 
 these operating results. The predetermination oif speed variations 
 'during portions of the steam cycle and at load changes has received 
 careful study in the design of reciprocating steam engines and the 
 desirable per cent of speed regulation is freely guaranteed and 
 readily obtained through careful study and analysis by the designer. 
 The same amount of study is warranted but seldom or never given 
 to the problem of speed regulation in water power work. 
 
 208. Value of Uniform Speed. Uniform, or nearly uniform, 
 speed is of great economic value in the operation of a plant but adds 
 to the first cost and may also result in a waste of water. The cor- 
 rect solution of any given problem of speed regulation involves a 
 compromise between first cost, water economy and speed regula- 
 tion. 
 
 A pecuniary value cannot well be placed upon good speed regu- 
 lation. It differs from poor speed regulation chiefly in procuring a 
 more satisfactory operation of motor driven machinery and in pro- 
 ducing a more constant incandescent light. Fluctuations in the 
 brightness of a light are annoying, and tend to create dissatisfac- 
 tion among consumers. Fig. 273 shows the general way in which 
 
The Problem. 
 
 445 
 
 the candle power of an incandescent light varies with the impressed 
 voltage.* A pressure variation of 5 per cent., and hence also a 
 speed variation of a similar amount, is shown to produce a much 
 larger variation in candle power of the light, in this case about 
 25 to 30 per cent. 
 
 209. The Problem. Where (as in Fig. 271) a turbine is operating 
 under balanced conditions and the resistance changes in magni- 
 tude, the turbine does not at once assume the new speed relations 
 corresponding to the change in resistance. The inertia of the mov- 
 ing parts of the wheel and of the column of water in the penstock, 
 
 Fig. 274. 
 
 Fig. 275. 
 
 turbine and draft tube, tends to maintain uniformity of speed, and 
 the wheel gradually changes in speed to that corresponding to the 
 new conditions. In such cases the speed of operation is not essen- 
 tial and the delay in reaching the speed corresponding to the re- 
 sistance or work the turbine must perform is usually unimportant. 
 
 When, as in Fig. 272, the wheel is designated to operate at a 
 fixed speed, the uniformity of speed becomes a matter of greater 
 or less importance depending on the character of the work the wheel 
 is to perform. In this case the inertia of the wheel and of all rotat- 
 ing parts of other machinery connected thereto tends to maintain 
 a constant speed. On the other hand, the flow of water in penstock, 
 turbine, and draft tube must ,be changed in quantity, (Eq. 2), 
 hence in velocity, and its inertia therefore tends to produce a change 
 in head and to produce effects opposite to those desired for efficient 
 regulation. 
 
 The conditions of installation have a marked effect on the diffi- 
 culties of turbine governing. If (as in Fig. 274) the turbine is in- 
 stalled in an open pit and has only a short draft tube, and the water 
 
 * See American Electrician, Vol. XIII, No. 7. July, 1901, by F. W. Wilcox. 
 
 27 
 
446 The Speed Regulation of Turbine Water Wheels. 
 
 flows to the gates from every direction, the velocity of flow from 
 all directions is very low. The quantity of water which moves at a 
 high velocity in confined to that in the wheel and draft tube and 
 the change in the velocity and momentum, due to a change in the 
 gates, produces no serious effects. If, however, water be con- 
 ducted to and^from the wheel through a long penstock and draft 
 tube (as illustrated by Fig. 275) the conditions become quite differ- 
 ent. In this case a large amount of. energy is stored in the moving 
 column of water and a change in its velocity involves a change in 
 its kinetic energy which may, if an attempt is made at too rapid reg- 
 ulation, leave the wheel deficient in energy when increased power is 
 desired, or, when the power is decreased, may produce such shocks 
 as will seriously affect regulation or perhaps result in .serious in jun- 
 to the penstock and wheel. 
 
 210. Energy Required to Change the Penstock Velocity. An 
 increase or decrease of load requires an ultimate increase or de- 
 crease in velocity of the water in the penstock. Work has to be 
 done upon the water to accelerate it and must be absorbed in order 
 to retard it. The total available power which can be expended for 
 all purposes at any instant during the acceleration is (since vH is 
 proportional to qH)' proportional to the product of the instantane- 
 ous velocity and the supply head. This total power is thus defi- 
 nitely limited and, hence, the work required to accelerate the water 
 must be obtained at the expense of the work done upon the wheel. 
 
 Thus, when an increase of load occurs the gate is opened by the 
 governor, and the immediate result is a decrease in the power out- 
 put of the wheel, even below its original value, and is diametrically 
 opposed to the result desired. This counter effect may last for sev- 
 eral seconds, and, unless sufficient reserve energy in some form 
 is available to partially supply this deficiency, the speed of the 
 wheel may fall considerably before readjustment to normal power 
 can take place. 
 
 In the same way an excess of energy must be absorbed to de- 
 crease the velocity at time of decreasing load. This may be ex- 
 pended upon the wheel thus increasing the speed above normal, or 
 it may be dissipated in one of several ways to be discussed later. 
 
 The water in the draft tube must be accelerated and retarded at 
 each change of gate opening and its kinetic energy changed at the 
 expense of the power output in exactly the same manner as that in 
 the penstock. For this reason it should be included in all calcula- 
 tions as a part of the penstock. One additional precaution must be 
 
Hunting or Racing. 447 
 
 taken : if the draft head is large a quick closure of the turbine gate 
 may cause the water in the draft tube to run away from the wheel 
 (actually creating a vacuum in the draft tube) and then return 
 again causing a destructive blow against the wheel. 
 
 211. Hunting or Racing. The regulation of both steam engines 
 and hydraulic turbines as now accomplished is one of degree only 
 since a departure froim normal speed is necessary before the gov- 
 ernor can act. Since the immediate effect of the gate motion is op- 
 posite to that intended, the speed will depart still further from the 
 normal. This tends to cause the .governor to move the gate too 
 far with the result that the speed will not only return to normal 
 as soon as the inertia of the water and of the rotating parts is over- 
 come, but may rush far beyond normal in the opposite direction. 
 The obvious tendency is thus to cause the speed to oscillate above 
 and below normal to the almost complete destruction of speed reg- 
 ulation. 
 
 A successful governor must therefore "anticipate" the effect of 
 any gate movement. It must move the gate to, or only slightly be- 
 yond, the position which will give normal speed when readjust- 
 ment to uniform flow in the penstock has taken place. A governor 
 with this property or quality is commonly said to be "dead-beat." 
 In Chap. XX several expedients are shown for the automatic elim- 
 ination of excessive racing. 
 
 212. Nomenclature. The following symbols will be used in the 
 mathematical discussions which follow : 
 
 A = cross-sectional area of penstock in sq. ft. 
 
 R V + V 
 ~-^=^ 
 
 c = friction coefficient for flow in pipe lines = (1 -f- f -^ 4- etc.) 
 
 D a = maximum rise of water in standpipe above the forebay when full 
 
 load (v = Vf) is rejected by the wheels. 
 
 D' = drop of water in standpipe below original friction gradient all in- 
 fluences considered. 
 
 D =' ditto, friction in penstock neglected. 
 Db = drop of level in standpipe below forebay. 
 d = diameter of penstock (closed circular) in feet, 
 e 2.71828 = base of natural system of logarithms. 
 F = cross-sectional area of the standpipe in square feet, 
 f "friction factor" in penstock, 
 g = acceleration due to gravity in feet per second. 
 H total available power head in feet. 
 
 H' = effective head at the wheel = H h for any given uniform velocity, 
 V, in the penstock. 
 
448 The Speed Regulation of Turbine Water Wheels. 
 
 h = instantaneous effective head at the wheel during changes of velocity 
 
 in the penstock, 
 hg = head which is effective at any instant in accelerating the water in 
 
 the penstock and draft tube. 
 h F = friction loss in penstock for normal flow with a given head and gate 
 
 opening, 
 hf = variable head lost by friction entrance, etc., in penstock when the 
 
 velocity is v. 
 I = moment of inertia or fly wheel effect of revolving parts in pounds at 
 
 one ft. radius = ft. 8 Ibs. 
 K = energy delivered to the wheel. 
 
 A K = excess or deficient energy delivered to wheel during change of load. 
 A, Ki = excess of deficient energy delivered to wheel due to excess or defic- 
 iency in quantity of water during load change. 
 A 2= ditto, due to energy required to accelerate or retard the water in 
 
 the penstock . 
 A Ka ditto, due to sluggishness of gate movement. 
 
 K' = kinetic energy in foot pounds of revolving parts at speed S. 
 A K' increment (+ or ) in K' due to load change. 
 
 2.31V 
 1 1= length of penstock in feet. 
 
 M = slope of the v-t curve when v = ^-~ (equation 19). 
 
 Po = initial horse power output from the water wheel. 
 
 pi = the horse power output from the water wheel corresponding to the 
 
 new load. 
 Q = discharge of the wheel under normal effective head H' for any given 
 
 load, 
 q = instantaneous discharge of wheel in cubic feet per second during load 
 
 change. 
 
 R = ratio of actual deficient or excess work done on wheel to that com- 
 puted. 
 
 S = normal r. p. m. of the wheel and other rotating parts. 
 A S S Si = temporary change in speed. 
 Si = speed in revolutions per minute after load change. 
 T' = approximate time required lor acceleration or retarding of water 
 
 from velocity v to vi. 
 T" = the time required for the governor to adjust the gate after a change 
 
 of load. 
 
 t = variable time after gate movement. 
 V - normal (and hence maximum possible) velocity in the penstock with 
 
 given head and gate opening, 
 v = instantaneous variable velocity in the penstock while adjusting to a 
 
 new value. 
 
 v = velocity in penstock at the instant of gate change. 
 Vj = velocity in the penstock required for new load. 
 
Water Hammer. 
 
 449 
 
 w = weight of a cubic unit of water in Ibs. 
 
 Y = maximum departure of head, h, from normal with use of stand- 
 pipe, discharge of wheel assumed constant at the abnormal head 
 (see D a and D b ). 
 
 y = variation of water level in the standpipe from forebay level = H h. 
 
 d = speed regulation or per cent variation of speed from normal. 
 
 213. Shock or Water Hammer Due to Sudden Changes in Ve- 
 locity. The acceleration or retardation of a moving body requires 
 an unbalanced force. Since acceleration and retardation are iden- 
 
 Fig. 276. 
 
 tical, except as to sign, the required accelerating force may in all 
 cases be expressed as follows : 
 
 Force = mass X acceleration. 
 
 Acceleration, or the rate at which the velocity increment in- 
 creases per increment of time, is expressed by the formula : 
 
 dv 
 (3) Acceleration r 
 
 The mass of water to be accelerated is 
 
 (4) 
 
 Mass 
 
 Alw 
 
 Figs. 276 and 277 show the conditions existing during an in- 
 crease and decrease of velocity respectively. If the draft tube were 
 closed at the lower end and no water leaving, there would be a 
 total force, equal to the hydraulic pressure over the area of the 
 penstock, or wAH, tending to move the water. 
 
450 The Speed Regulation of Turbine Water Wheels. 
 
 If the water is flowing with a velocity v the turbine offers a re- 
 sistance to flow represented by the effective head, h, at the wheel, 
 and the penstock offers a resisting head h F composed of friction, en- 
 trance, and other losses. If the velocity remains uniform, h=H', 
 and the forces are balanced thus: 
 
 (5) H = H' + h P 
 
 If the opening of the turbine gate is now suddenly increased, the 
 head H' at the wheel, will fall to the value, h, (shown in Fig. 276) 
 which is required to force the given amount of water, Av, through 
 
 Fig. 277. 
 
 the wheel. On the other hand, if the gate opening is decreased the 
 pressure head must rise above H' (as shown in Fig. 277) in order 
 to discharge the water through the wheel. This change h a in the 
 head H' disturbs the equilibrium of forces shown by equation 
 (5) making 
 
 (6) h a = H h h f 
 
 Only the head h a is effective in accelerating or retarding the 
 water and the force resulting from this head is wAh a . Substitut- 
 ing this value and those of equations (3) and (4) in equation (2) 
 we obtain: 
 
 Alw dv 
 
 dt 
 
 or 
 
 (7) 
 
 dv 
 
 of velocity change) 
 
Permissible Rate of Gate Movement. 451 
 
 The value of h a given by formula (7) is a general expression for 
 the change in pressure-head due to a change of velocity or for the 
 head which must be impressed to produce a desired change in 
 velocity. When in excess of the static pressure as shown in Fig. 
 277, it is commonly called "water hammer." (See Appendix A.) 
 
 If the closure of the gates is rapid the value of h a is large and 
 the column of water is set into vibration or oscillation. If the 
 partial closure of gate is sufficiently slow to allow a distribution of 
 each increment of pressure along the pipe, this oscillatory wave is 
 avoided and the pressure produced at, any instant during closure 
 (given by equation (7) is that which is necessary to retard the 
 moving column of water at the rate at which its velocity actually 
 decreases at that instant and can be reduced below any assumed 
 maximum allowable value by a sufficiently slow, gate movement. 
 
 When a penstock is long, these oscillatory waves become a 
 source of great danger to ,the turbines and also to the penstock, 
 especially at bends. The extinction of a velocity of 4 feet per 
 second at a uniform rate in one second in a pipe 1,600 feet in length 
 would create a pressure-head of about 200 feet, or a total longitud- 
 inal thrust on the pipe line at each bend, and upon the wheel gate, 
 if 24" in diameter, of abo ( ut 20 tons. 
 
 These dangers are further augmented by the fact that several 
 waves, if succeeding each other by an interval which is approxi- 
 mately a multiple of the vibration period of the pipe, may pile up, 
 so to speak, crest upon crest and cause a pressure which no possi- 
 ble strength of parts could withstand. 
 
 Fig. 278. 
 
 214. Permissible Rate of Gate Movement. Gate movements 
 must be sufficiently slow to avoid oscillatory waves of dangerous 
 amplitude. No general quantitative rule can be given for the re- 
 quired rate o;f movement. It can be more rapid the shorter the 
 penstock and the smaller the velocity in the same. The danger 
 is much smaller during opening than during closure of a gate and 
 
452 The Speed Regulation of Turbine Water Wheels. 
 
 the rate of gate .movement could well be made much more rapid 
 in the former than in the latter case. 
 
 The rapidity with which a gate should be opened is limited for 
 feeder pipes with an initial flat slope as shown in Fig. 278. 
 
 Let h' be the lowest head obtained in opening the gate at an as- 
 sumed rate and AB, the resulting hydraulic gradient. In case the 
 gate opens so v rapidly as to cause the distance, a, at any point along 
 the pipe to exceed suction limit, the water column m the penstock 
 will separate (the portio,n of the column above A not being able 
 to accelerate as rapidly as that below) and will again reunite with 
 a severe hammer blow. Failure to- observe this precaution probably 
 caused the destruction of the feeder pipe of the Fresno, California, 
 power plant. The rate to be used can be chosen after a determina- 
 tion, by the method discussed in Appendix A, of the pressures re- 
 sulting from several assumed rates of movement. The method is te- 
 dious but justifiable in many cases. 
 
 215. Regulation of Impulse Wheels. It is impracticable, if not 
 impossible, to build a pipe line strong enough and well enough 
 anchored at all points to withstand the enormous pressures and 
 longitudinal thrusts which would result from rapid gate closures 
 in a long closed penstock such as commonly used for impulse 
 wheels. The adjustment of quantity, q, for changes in load % of 
 short duration is hence impossible in such closed penstocks and the 
 expedient usually adopted is to "deflect" the jet from the wheel by 
 changing the direction of discharge of a pivoted nozzle. This re- 
 quires that the "needle valve" (See Fig. 195) or gate maintain a jet 
 sufficient to carry peak loads ; hence causing a waste of water at all 
 other times. This condition is commonly improved somewhat by 
 adjusting the valve about once each hour by means of a slow motion 
 hand wheel for the maximum peak load liable to occur during that 
 hour. 
 
 An automatic governor has recently been invented which moves 
 the needle valve or gate slowly, thus adjusting for changes of load 
 of long duration while it still retains the deflector to provide for 
 abrupt changes in the load curve. (See Fig. 282.) 
 
 Another device proposed fo>r use in this connection is a by-pass 
 nozzle arranged to open as the needle valve rapidly closes, and then 
 automatically close again at a rate sufficiently slow to reduce the ex- 
 cess pressure to safe limits. One advantage in favor of this ar- 
 rangement is that the jet would then always strike the center of 
 the buckets which is found to considerably reduce their wear. 
 
Influence Opposing Speed Regulation. 453 
 
 An automatic relief valve of hydraulic or spring type is nearly 
 always used but serves more as an emergency valve to reduce water 
 hammer pressures than as a by-pass to divert water from the wheel 
 for the purpose of governing? For this latter use the spring type 
 of valve has proven unsatisfactory. 
 
 In some cases the water discharged from high head plants is used 
 below for irrigation and must be kept constant, thus doing away 
 with the necessity of varying the velocity in the feeder pipe for a 
 varying load. 
 
 Mr. Raymond D. Johnson proposes for these high head plants, 
 the use of large air chambers or "Surge Tanks," placed near the 
 wheels, of a sufficient size so that the governor can control the 
 needle valve directly, thus dispensing with the deflector and by- 
 pass and doing away completely with the waste of water occa- 
 sioned by their use. He has derived formulas by which he claims to 
 accurately proportion these tanks for an assumed maximum allow- 
 able range of head fluctuation or surge.* 
 
 216. Influences Opposing Speed Regulation. Abrupt changes 
 in the demand for power of a considerable proportion of the total 
 capacity of a plant, take place at times in modern power plants. 
 Three causes tend to make the change in output of a wheel lag be- 
 hind the change in demand placed upon it; viz.: (i) the fact that 
 the governor, however sensitive, does not act until an appreciable 
 change of speed occurs, and then not instantly; (2) the fact that 
 some time is required for the readjustment of penstock velocity, 
 even after the gate movement is complete ; (3) the necessity of 
 changing the velocity, and hence of overcoming the inertia of the 
 water in the penstock and draft tube at each change of load. 
 
 Each of these influences is directly opposed to speed regulation, 
 as will appear in the succeeding articles, since each causes the 
 power supplied to a wheel, at time of increasing load, .to fall short 
 of the demand, the deficiency being supplied at the expense of the 
 speed from the kinetic energy stored in the rotating parts. The ex- 
 pression for the total deficient work, i. e. footpounds, is: 
 
 (8) A K = A Ki + A K 2 + A K 8 
 
 for which see equations 22 and 23 and Section 221. 
 
 217. Change of Penstock Velocity. Assuming the gate move- 
 ment to take place instantly, we will have the condition illustrated 
 
 * See "The Surge Tank in Water Power Plants," by R. D. Johnson. Trans. 
 Am. Soc. M. E., 1908. 
 
454 The Speed Regulation of Turbine Water Wheels. 
 
 in Figs. 276 or 277, for which equation 7 was derived (See Section 
 
 213). Solving equation (7) for -^- we have: 
 
 dv 2* sr 
 
 (9) Acceleration r = -f- X (accelerating head) = -f- h a 
 
 Qt 1 1 
 
 The accelerating head as shown in equation 6 is H h h f . It 
 is the general principles of hydraulics that the head lost in flow 
 through any opening, pipe, orifice, etc., varies as the square of 
 velocity. 
 
 It was shown in Section 160, Chapter XIV, that the quantity 
 flowing through a turbine varies as the square root of the head. 
 Remembering that the quantity is proportional to the penstock 
 velocity, we have : 
 
 q v Vh 
 
 (10) -Q = y- = /TJ > from which 
 
 XT 2 
 
 h = 
 
 V 2 
 
 12) h f = (l+f. 
 
 2g 
 
 (is) --:---w Or 
 
 (14) h f =4^h F 
 
 From equation (6) 
 
 h. = H-h-h f = H-H'^---h F -IL or 
 
 (15) h a = H (H' + h F )^- 
 
 And from equation (5) 
 
 Hence from equation (9) 
 
 dt 1 V 2 
 
 The integration of this equation as given in Appendix B gives 
 the follpwing equation for the curve of velocity change in the pen- 
 stock a sudden change of gate opening: 
 
 (18) Bantilogk't-1 
 
 Bantilogk't + 1 
 
 As shown in Appendix this value of v approaches but never 
 equals the value of V. The form of the curve for an increasing 
 velocity is shown in Fig. 279. 
 
 * See Merriman's Treatise on Hydraulics, 
 
Effect of Acceleration on Water Supplied to Wheel. 455 
 
 218. Effect of Slow Acceleration on Water Supplied to Wheel. 
 Since velocity in the penstock, discharge of wheel, and loacl 
 are approximately proportional to each other, the ordinates of 
 Fig. 279 may be taken to represent loads. The load demand remains 
 at a constant value v from A to B, where it suddenly increases 
 to YJ, following the line A B C D T. The supply, however, 
 assuming an instantaneous gate movement, follows the line 
 A B D F. Now, the total quantity of water supplied to, and hence 
 
 Fig. 279. 
 
 the work (not power) done by the water upon the wheel, is propor- 
 tional to the area generated by an ordinate to the latter, and the 
 demand upon the wheel to the area generatd by the power curve. 
 The area B C D B therefore represents a deficiency of developed 
 w r ork which must be supplied by the energy stored in the rotating 
 parts. 
 
 For practical purposes this area may be assumed equal to the 
 area L of the triangle B' C' D', where the line B' D' is tangent to 
 
 the curve B M D at the point of mean velocity -o-^ 
 
 The slope of the line B' D' for this mean velocity is readily ob- 
 tained from equation 17. Call it M, then 
 
 pr _ B' C' _ vi v o _ gH |~ (v + vi 
 C' D' ~ T' "Tl 4V 2 
 
 (19) 
 
 and 
 
4 56 The Speed Regulation of Turbine Water Wheels. 
 
 (21) Area B'C'D' = L 
 
 This value of L is expressed in feet and represents the deficiency 
 of lineal distance moved by the water column in the penstock. The 
 deficiency of supplied water in cu. feet is, hence, A L and the de- 
 ficiency of undeveloped work is 
 
 (22) A K, - ALwH = -. ( vi - v ) 2 
 
 219. Value of Racing or Gate Over-Run. At D, Fig. 279, the 
 supply line B D F crosses the load line C D E, and the speed which 
 was lost from B to D begins to pick up again. 
 
 The necessity also for an overrun of the governor is shown by 
 Fig. 279. If the demand line were A B N F and the gate opened 
 to the same place as before, giving the supply line B D F, the sup- 
 ply of power would approach, but theoretically never equal, the 
 demand and the speed would hence never pick up to normal. The 
 
 NORMAL GATE - f> EW LOAD 
 
 _______ NORMAL GATE - OLD LOAD __ 
 
 Fig. 280. 
 
 gate movement should therefore be similar to that shown in Fig. 
 280 in order to give the gate the small overrun which is necessary 
 to bring the speed back to normal. 
 
 220. Energy Required to Change the ,Penstock Velocity. The 
 energy involved in the change of velocity above described results 
 in an excess or deficiency of energy delivered to the wheel (See Sec- 
 tion 210). The amount of this excess or deficient energy is readily 
 determinable. The kinetic energy in foot pounds stored in the 
 
 moving column of water is K 2 = - O r 
 
 , 
 
 The amount which must be diverted from the wheel or dissipated 
 when the velocity changes is therefore 
 
 (23) A K 2 = 0.972 Al (vi 2 v 2 ) 
 
 In this case it should be taken as the combined length of penstock 
 and draft tube. 
 
The Fly- Wheel. 457 
 
 This deficient energy must be supplied, or the excess absorbed, by 
 means of a flywheel or 'the installation of a stand-pipe connected 
 with the penstock closely adjoining the wheel. 
 
 221. Effect of Sensitiveness and Rapidity of Governor. Referring 
 again to Fig. 279, suppose the increase of load to take place at B'" 
 giving the load line AB"' C" E. After -an interval from B'" to B", 
 the speed has dropped an amount depending upon the sensitiveness 
 of the governor. The gate will then begin to open ; the velocity in 
 the penstock accelerating meanwhile along the dotted line B'"Y. 
 The lack of sensitiveness of the governor has therefore added a de- 
 ficient work area of B'" B" C" C'", and the sluggishness of its mo- 
 tion an additional area C"B" B C, approximately. This deficiency 
 A K 3 can be only roughly approximated without the detailed analy- 
 sis given in Appendix B. 
 
 222. The Fly-Wheel. A fly-wheel is valuable for the storage 
 of energy. Work must be done upon it to increase its speed of rota- 
 tion, and it will again give out this energy in being retarded. From 
 the laws of mechanics the number of foot pounds of kinetic energy 
 stored in a body by virtue of its rotation is given by the formula : 
 
 _2X 3.1416' 
 ' ~iW ~ 32~15 X 60* 
 (24) K' = .00017 IS 2 
 
 The amount of energy which must be given to or absorbed from 
 the fly-wheel in order to change the speed is : 
 
 (25) AK' = 000171 (? 2 Si 2 ) 
 
 Thus a fly-wheel can store, energy only by means of a change in 
 speed. By means of a sufficiently large moment of inertia the speed 
 change of a fly-wheel, for any given energy storage, A 1C, can be re- 
 duced to any desirable limit. 
 
 The need of a fly-wheel effect to carry the load of a hydro-electric 
 unit during changes of gate, and while the water is accelerating in 
 the penstock at an increase of load has led to, the development of a 
 type of revolving field generator, whose rotor has a high moment of 
 inertia and is therefore especially adapted for speed regulation usu- 
 ally making the use of a fly-wheel unnecessary. 
 
 Warren* has simplified the expression for AK' (See equation 
 25), substantially as follows: 
 
 * See "Speed Regulation of High Head Water Wheels," by H. E. Warren, 
 in Technology Quarterly, Vol. XX. No. 2. 
 
458 The Speed Regulation of Turbine Water Wheels. 
 
 From equation (24) : 
 
 (ae) |V = ^ = *; Hence, 
 
 K 2 .0001/ I 02 82 
 
 (9-?\ Ki'-K,' _ S^-S 2 2 (Si + SQ (Si -SQ 
 
 K/ ~~S?~ tf*' 
 
 Put Si S 2 = A S 
 and Ki x K 2 X = A K r 
 
 For small differences between S, and S 2 equation (27) becomes 
 approximately : 
 
 A ~LT/ OQ \y AG O \/ A C 
 
 (28) AK 2SXAS = 2XAS Qr 
 
 JV (32 *5 
 
 (29) A K' = ^ 
 
 Or the percentage change in speed is 
 
 (SO) d = 100X 
 
 223. The Stand-Pipe. The function of the stand-pipe is two- 
 fold: (i) to act as a relief valve in case of excess pressures in the 
 penstock ; (2) to furnish a supply of energy to take care of sudden 
 increases of load while the water is accelerating, and to dissipate the 
 excess kinetic energy in the moving water column at time of sudden 
 drop in load. For these purposes it should be of ample diameter and 
 placed as close,to the wheel as possible. 
 
 The analytical determination of the effect of a given stand-pipe 
 upon speed regulation is very difficult if not quite impossible. Fur- 
 thermore, it is not necessary, since the drop in effective head at an 
 increase of load may (except in the case of maximum possible load) 
 be compensated for by an increase of gate opening, hence main- 
 taining a constant power and speed or at least a satisfactory degree 
 of speed regulation. Thus the action of a stand-pipe in storing 
 energy differs radically from that of the fly-wheel as the latter can 
 store or give out energy only by means of a change of speed in 
 the generating unit. 
 
 The determination of the range of fluctuation of water level in an 
 assumed stand-pipe, and the time required for return to normal level 
 for various changes of load on the, wheel, will assist greatly in the 
 design of the stand-pipe. 
 
 Fig. 281 shows the condition when a stand-pipe is used. Assume 
 that the wheel is operating under part load. The water normally 
 stands a height h F below the supply level. If the load suddenly in- 
 creases, the gates open, and the water level begins to fall, thus caus- 
 ing an accelerating head h a = H h -- h f . Equation 9 then applies 
 as before, where h a becomes (h cv 2 ). 
 
The Stand-Pipe. 
 
 459 
 
 If the governor keeps step with the change in head by increasing 
 the gate opening to maintain a constant power then 
 
 (31) 
 
 q h = qi hi 
 
 q (H y) = Avi (H h F ) = Avi (H cvr ) 
 _ Avi (H cvi 8 ) 
 
 or 
 
 H y 
 
 The rate of water consumption by the wheel at any instant is q ; 
 the rate at which the water is supplied by the penstock is Av; and 
 the rate of rise or fall of the water surface in stand-pipe is there- 
 fore : 
 
 ,o 2] dy __ dh _ Av - q _ A T vi (H-cvi 2 ) 1 
 
 dF".~dT- ~F~ "FT H-y 
 
 The solutions of equations 9 and 32, which are necessary for 
 determining the curves of variation of head and velocity, is imprac- 
 
 Fig. 281. 
 
 ticable, if not impossible, hence a different treatment is proposed and 
 considered in Appendix C. 
 
 If q be assumed constant (=Av 1 ) during the adustment of pen- 
 stock velocity and the friction loss, cv 2 , in the penstock be neglected, 
 then equations 9 and 32 simplify and become integrable. The re- 
 sulting equations, showing the variations of v and y, are true har- 
 monics or sine curves. The effect of friction and governor action is 
 to produce a damped or somewhat distorted harmonic as discussed 
 in Appendix C. Any change of load thus starts a series of wave like 
 fluctuations of penstock velocity and stand-pipe level which con- 
 tinue until this wave energy has been entirely expended in friction. 
 
460 The Speed Regulation of Turbine Water Wheels. 
 
 Analogous to all other wave motions these waves may pile up, (if 
 two or more gate movements succeed each other by short intervals 
 which are approximately multiples of the cycle, 2T) causing a very 
 great flucuation in head and velocity. In fact by assuming a proper 
 combination and succession of circumstances no limit can be as- 
 signed to the range of fluctuation or "surge" which may occur. The 
 probable combination of circumstances which will occur in any 
 plant depends largely .upon the character of the load. Overflows 
 from stand-pipes due to these surges have been known to do con- 
 siderable damage and it is desirable to either provide for this over- 
 flow either at the top or by relief valves at the bottom, or build 
 the stand-pipe high enough to prevent it and thus gain the addi- 
 tional advantage of conserving the water which would otherwise 
 waste. 
 
 If the change of load is assumed to occur when the water is at 
 its normal level then the analysis given in Appendix C furnishes the 
 following formulas : 
 
 "A* 
 
 (34) 
 
 (35) D*-2HD= -(vi 8 - 
 
 (36) 
 
 (37) 
 
 The value of T from equation (33) is one-half a wave cycle or 
 the time required for return to normal head after a change of load. 
 It is obtained by neglecting both friction and the compensating 
 effect of the governor. These influences increase T in very nearly 
 the ratio that D exceeds Y. 
 
 Y from equation (34) is the maximum head fluctuation, or maxi- 
 mum value of y, also obtained by neglecting friction and governor 
 action. 
 
 D from equation (35) is the maximum drop in standpipe level 
 corresponding to Y except that governor action is included. If 
 this value of D is added as shown in equation (36) to the initial 
 friction loss, cv 2 , the result agrees very closely with the value of 
 the maximum drop D where friction is included and is much more 
 simple than the more exact equation given in Appendix C. 
 
 A reasonable assumption for determining the probable maximum 
 height to which the water will rise in the stand-pipe is that full 
 
Predetermination of Speed Regulation. 461 
 
 load is instantly thrown off the unit when the normal full load ve- 
 locity v f exists in the penstock. This assumption leads to equa- 
 tion (37). 
 
 The verification of these formulas and some additional ones is 
 given in Appendix C, and an example of their application in sec- 
 tion 230. 
 
 224. The Air Chamber. There is a practical limit to the height 
 to which a stand-pipe can be built. A high stand-pipe is also less 
 effective due to the inertia of the water in the stand-pipe itself which 
 must be overcome at each change of load, thus introducing to a 
 lesser degree the same problem as in a penstock without stand-pipe. 
 For some such cases the top of the tank can be closed and furnished 
 with air by a compressor. The design of air chambers has been in- 
 vestigated by Raymond D. Johnson.* An air chamber is less effec- 
 tive in equalizing the pressure than a standpipe of the same diam- 
 eter. 
 
 225. Predetermination of Speed Regulation for Wheels Set in 
 Open Penstocks. The influences which oppose speed regulation 
 have been partly discussed. At an increase or decrease of load there 
 is a deficiency or excess of developed power due to (i) the inability 
 of the governor to move the gate upon the instant that the load 
 changes; (2) the necessity of accelerating or retarding the water 
 in the penstock and draft tube as previously discussed. If no stand- 
 pipe is used, reliance must be placed upon the fly-wheel effect of 
 turbine, generator and additional fly wheel, if necessary, to absorb 
 or give out the excess or deficiency of input over output of the plant 
 at this time. 
 
 The first influence opposed to speed regulation, that of slow gate 
 movement, is of chief importance (a) where the plant is provided 
 with large open penstocks and short draft tubes ; (b) where an am- 
 ple stand-pipe, placed close to the wheel, and a short draft tube 
 are used; (c) in the regulation of an impulse wheel where no at- 
 tempt is made to change the velocity of water in the feeder pipe. 
 Mr. H. E. Warrenf has analyzed this case essentially as follows: 
 "As long as the output from the wheel is equal to the load, the 
 speed S and kinetic energy K' of the revolving parts will remain 
 constant. The governor is designed to adjust the output of the 
 wheel to correspond with the load, but it cannot do this instanta- 
 
 * See Trans, of Am. Soc. M. E., 1908. 
 
 t See article by H. E. Warren on "Speed Regulation of High Head Water 
 Wheels," previously referred to in Section 222. 
 
 28 
 
462 The Speed Regnlation of Turbine Water Wheels. 
 
 neously. Consequently, during the time T required to make the 
 adjustment of the control mechanism after a load change there will 
 be a production of energy by the water wheel greater or less than 
 the load. The entire excess or deficiency will be added to or sub- 
 tracted from the kinetic energy of the revolving parts, and will be- 
 come manifest by a corresponding change in speed. 
 
 Neglecting friction losses, and assuming that the power of the 
 water wheel is proportional to the percentage of the governor stroke 
 and that the movement of the governor after a load change is at a 
 uniform rate, the excess or deficient energy which goes to or comes 
 from the revolving parts after an instantaneous change of load from 
 L to Lj is measured by the average difference between >the power 
 of the wheel and the new load during the time T", while the gover- 
 nor is moving, multiplied by T" or expressed in foot pounds : 
 
 (38) A K' = P ~ Pl X T" X 550 
 
 From equation 24 the kinetic energy of the rotating parts is : 
 
 K' = .00017 IS 8 
 From equations 24, 30 and 38 
 
 50X(p pi)T*X560 
 
 2X -00017 IS 2 
 
 (39) * = 81, 000, 000 ^5- ( Po - pi) 
 
 226. Predetermination of Speed Regulation, Plant with Closed 
 Penstock. In this case the rotating parts must absorb or deliver 
 up an amount of energy AK' (equation 29), equivalent to that given 
 for AK in formula 
 
 (8) AK = AKi+ AK 2 + AK 3 
 
 where, from equation 22, 
 
 (22) AKl 
 
 M being obtained from equation 
 
 The value of A K 2 is obtained by equation 
 
 (23) AK 8 = 0.972 Al (Vi 3 v 2 ) 
 
 There is no simple way, as discussed in section 221, of determin- 
 ing K 3 . It must be estimated or analyzed graphically as in Appen- 
 dix C. 
 
 From equation 
 
 (24) K' = .00017 IS 2 
 
Predetermination of Speed Regulation. 463 
 
 If R is the proportion of this theoretical energy which is given to 
 the rotating parts at a decrease in load, or which the rotating parts 
 must give out during an increase of velocity and load then 
 
 (40) AK' =RX AK 
 
 and we have from equation 
 
 50 X R X A K 
 
 (30)- AK' = 
 
 K' 
 
 50 x R X A K 
 
 .00017 I 
 (41) 5 = 294,000 
 
 RX AK 
 
 !S S 
 
 Solving for I we find the moment of inertia of the rotating parts, 
 which is necessary to obtain any desired percentage of regulation to 
 be 
 
 (42) 
 
 Although there can be no doubt as to the accuracy of the form of 
 equations 41 and 42 yet their value for other than comparative pur- 
 poses depends upon the accuracy with which we can estimate R. 
 With perfect efficiency of the wheel under all conditions, R would 
 be unity, but in actual cases R must be determined by experiment or 
 by the graphical method given in Appendix B. It will be less for 
 decreasing than for increasing loads since the inefficient operation 
 of the wheel assists speed regulation in the former case, and hinders 
 it in the latter. In addition to this fact, the excess energy at a de- 
 crease of load can be partially dissipated through a relief valve, or 
 a by-pass, etc. For practical cases it is therefore necessary to in- 
 vestigate only the case of increasing load. 
 
 A detailed analysis of a particular problem can be made, as in 
 Appendix B, by which the velocity in the penstock, effective head, 
 power of wheel, speed, etc., can be determined for each instant dur- 
 ing the period of adjustment. From this also the time of return to 
 normal speed can be determined. The method is somewhat tedious, 
 but justifiable nevertheless. 
 
 227. Predetermination ' of Speed, Regulation, Plant with Stand- 
 pipe. If the stand-pipe is of suitable diameter and close to the wheel 
 the speed regulation will approach that obtainable in open penstock 
 and as investigated by Warren in Section 225. Otherwise the prob- 
 lem becomes that of a plant with a closed penstock, of a length equal 
 to that of the draft tube, plus the penstock from stand-pipe to wheel. 
 
464 The Speed Regulation of Turbine Water Wheels. 
 
 228. Application of Method, Closed Penstock. An example of 
 the analysis of a problem in speed regulation is as follows : 
 
 Assume the 48" Victor cylinder gate turbine, whose characteristic 
 curve is shown in Fig. 245, page 402. Suppose it is supplied with 
 water through a penstock whose diameter is 8 feet, jand whose 
 length combined with that of the draft tube is 500 feet. The head 
 is 50 feet which for ^=.664 gives 180 R. P. M. = S. 
 
 Neglecting all losses of head except that in the turbine, we find 
 from the characteristic curve for various loads as follows : 
 
 
 Full load. 
 
 .8 Load 
 
 K Load. 
 
 M Load. 
 
 Brake Hors6 Power 
 
 ll'^O 00 
 
 900 
 
 560 00 
 
 280 00 
 
 Qu&ntity of water p6r S6C ( cu ft 
 
 240 00 
 
 210 
 
 145 00 
 
 97 80 
 
 Velocity in Penstock V. 
 
 4 77 
 
 4 18 
 
 2 88 
 
 1 94 
 
 Efficiency of wheel 
 
 82 
 
 754 
 
 68 
 
 505 
 
 
 
 
 
 
 The above values will be considered as applying to the entire 
 plant since the loss in the penstock is small in this case. 
 
 Assume the load to increase suddenly from one quarter load to 
 0.8 load, while the gate at the same time opens to full load posi- 
 tion. The nujmber of foot pounds of work which must be done to 
 accelerate the water from a velocity of 1.94 feet per second to 4.18 
 feet per second is found from equation 23 to be 
 AK 2 =0.972 Al K 3 v 2 ) 
 
 = 0.972 X 50.3 X 500 (4.18 2 1.94 2 ) 
 = 0.972 X 50.3 X 500 X 13.73 
 = 335,000 foot pounds. 
 
 Referring to section 226, p. 462, to find the amount of deficient 
 work due to insufficient supply of water we have 
 
 
 
 From equation 19, section 226 
 
 32.15X50 
 
 500 V 4 X 4. 
 - 32.15X50 
 500 
 
 = 2.88 
 
 From equation 22, 
 
 -MXJ^^.^. 
 
 = 187, 000 foot pounds. 
 
Predetermination of Speed Regulation. 465 
 
 The total deficiency for which formulas have been derived is 
 hence, 
 
 AK AKj + K 2 + (AK 3 undeterminable) 
 = 335,000 + 137,000 
 = 472, 000 + ft Ibs. 
 
 By means of the detailed graphical analysis given ,in Appendix 
 B this deficiency is found to be 600,000 foot pounds for gate move- 
 ment in one-half second showing that the estimated value should 
 have been increased in this case by 12.7 per cent. (R = 1.127) to 
 compensate for neglecting the effect of slow (% second) gate move- 
 ment, or K 3 . It must be remembered that this quantity, AK, is 
 the deficiency of ^theoretical hydraulic work done upon the wheel. 
 For reasons discussed in Appendix B, it will, however, be found to 
 differ but slightly from the deficiency of wheel output, in this case 
 586,000 ft. pounds. 
 
 To determine the speed regulation which can be obtained, as- 
 sume a generating unit whose rotor has a fly-wheel effect, or mo- 
 ment of inertia, I, of 1,000,000 ,lbs. at one ft. radius. The normal 
 speed S = 180, AK = 472,000 ft. Ibs., and R (in general to be esti- 
 mated, but in this case obtained by the graphical method given in 
 Appendix B, is 1,127. Therefore from equation (43) 
 
 d - 994 000 1 ' 127 X 472 - 000 - 5 42* 
 y4 ' UU 1,000, 000X180*- 
 
 If a fly-wheel is to be designed for a given regulation say 4 per 
 cent., then the required moment of inertia of same is, from equa- 
 tion (42). 
 
 I = 294, 000 ^- 
 
 I ='1,355, 000 ft. 2 Ibs. 
 
 229. Application of Method, Open Penstock. As the penstock 
 and draft tube are shortened, the excess or deficient energy area, 
 A K 3 , .obtained during the gate movement becomes an increasing 
 proportion of the whole until for a large open penstock and short 
 draft tube the developed power ceases to lag and follows practically 
 the same law of change as the gate opening. The estimation of 
 excess i'or deficient energy, and consequently of speed, is then very 
 simple by means of Mr. Warrens equation (39). For illustration: 
 assume the same wheel as in the preceeding section, obtaining the 
 outputs of 280 H. P.=P at one-fourth load and 1120 H. P.= P l at 
 
466 The Speed Regulation of Turbine Water Wheels. 
 
 full load, as in the other installation. Assume the same moment 
 of inertia 1,000,000 and that the gate movement takes place in % 
 second as before. Then T"= % ; S = 180. 
 This gives 
 
 t = 81.000.000 1>000| x 18Q2 (1120 - 280) = 1.05* 
 
 This is a much closer regulation than obtained with the long pen- 
 stock. 
 
 230. Application of Method, Plant with Stand-pipe. Assume a 
 plant where the wheels develop 39,000 H. P. under 375 head, thereby 
 requiring about noo cu. ft. of water per second (assuming 83 per 
 cent, efficiency of the wheels). Assume this water is supplied 
 through four 7' pipes about 4800 feet long, requiring a velocity in the 
 feeder pipes at full load of about 7.15 feet. Suppose four pipes all 
 connected at the lower end to a stand-pipe 30 feet in diameter. If a 
 sudden load change, of about one third of the total is to be provided 
 for this would require an ultimate change of velocity in the penstock 
 from about 4.76 feet per sec. at two^thirds load to 7.15 feet at full 
 load, or v = 4.76, and v = 7.15. Now, 
 
 A = 4 X *-= 154 sq. ft, 
 
 From equation 33 the time required for return to normal head, or 
 the half period of oscillation, is 
 
 T = 
 
 This would perhaps be increased to nearly 100 seconds, due to the 
 use of additional water during this period of low head, as discussed 
 in Appendix C, but the value 82 should be used in equation 35. 
 
 Equation 34 gives for the drop in water level in the stand-pipe, 
 
 Y = J 154 X 480Q (7.15-4.76) 
 ^707 X 32.15 
 
 =1/3275 X 2.39 = 13.6 feet. 
 The more exact equations, 35 and 36, give for D and D, 
 
 igg( 7 .l5^-4.76 2 )+ 37 f * 82 (7- 
 
 D 2 750 D + 11,120 = 
 
Governor Specifications. 467 
 
 Solving this quadratic equation gives 
 
 D - 750 T/750 2 4 X 11,120 
 
 75Q - 719 
 
 Qr 
 
 = 15.5 feet 
 
 D b = 15.5 + c X 4.76 2 = 15.5 + .176 X 4.76 s = 19.5 feet 
 
 No attempt will be made 'to estimate the greatest drop in level 
 which might occur, due to an addition of waves. 
 
 231. Governor Specifications. The present practice of requiring 
 the governor builder to guarantee the speed regulation of a plant, 
 in the design of which he has had no> voice, without even giving 
 him the necessary information regarding the hydraulic elements 
 which are considered in this chapter is wrong. It is partly the out- 
 growth of the modern tendency to specialize, but perhaps more 
 largely due to a lack of understanding on the part of the engineer of 
 the nature of the problem, and a resulting desire to shift the respon- 
 sibility for results upon some one else who is better informed upon 
 the subject and thus protect results financially as well as save his 
 own reputation in case of failure. 
 
 Governor specifications should call for a guarantee of the 
 
 (a) Sensitiveness or per cent load change which will actuate the 
 governor ; 
 
 (b) Power which the governor can develop, and force which it 
 can exert to move the gates ; 
 
 (c) Rapidity with which it will move the gates ; 
 
 (d) Anti-racing qualities, such as number of gate movements re- 
 quired to adjust for a given load change (See figure 280), or per- 
 cent. over-run of the gate, etc. 
 
 (e) General requirements of material, strength, durability, etc. 
 Beyond this point the governor designor has no control. The 
 
 engineer can, however, by choosing a generator whose rotor has a 
 high moment of inertia (which quantity should be stated in tenders 
 for supplying the generators), by the addition of a fly-wheel, if 
 necessary ; by the construction of a stand-pipe ; by means of a re- 
 lief valve, and very largely, also, by the general design of the pen- 
 stocks, draft tubes, etc., greatly improve the governing qualities, 
 and, in fact, reduce the speed variation to any desirable limit which 
 the nature of load to be carried, magnitude of load changes antici- 
 pated, and economy of first cost will warrant. 
 
468 The Speed Regulation of Turbine Water Wheels. 
 
 LITERATURE. 
 
 TURBINE REGULATION. 
 
 1. Williams, Harvey D. A New Method of Governing Water Wheels. Sib. 
 
 Jour, of Engng. March, 1896. 
 
 2. Electric Governors. Eng. News, 1896, vol. 1, p. 276. 
 
 3. Parker, M. S. Governing of Water Power Under Variable Loads. Trans. 
 
 Am. Soc. C. E. June, 1897. 
 
 4. Regulation of Wheels. The Chavanne Nozzle Regulator. Mining & Sci- 
 
 entific Press, Oct. 30, 1897. 
 
 5. Knight, Samuel N. Water Wheel Regulation. Jour, of Elec. Nov., 1S97. 
 
 6. Replogle, Mark A. Speed Government in Water-Power Plants. Jour. Fr. 
 
 Inst., vol. 145, p. 81, Feb., 1898. 
 
 7. Regulation of Water Wheels under High Pressure. Pioneer Electric 
 
 Power Co.'s Wheels. Eng. Rec., Feb. 5, 1898. 
 
 8. Garratt, Allan V. Elements of Design Favorable to Speed Regulation. 
 
 Eng. News, 1898, vol. 2, pp. 51-159. 
 
 9. Modern Practice in Water Wheel Operation. Elec. World, May 5, 1900. 
 
 10. Cassel, Elmer F. Commercial Requirements of Water-Power Governing. 
 
 Eng. Mag., Sept., 1900. 
 
 11. Garratt, Allan V. Speed Regulation of Water Power Plants. Cassier's 
 
 Magazine, May, 1901. 
 
 12. A Water-Wheel Governor of Novel Construction. Eng. News, Nov. 13, 
 
 1902. 
 
 13. Thurso, J. W. Speed Regulation in Water Power Plants. Eng. News, 
 
 1903, vol. 1, p. 27. 
 
 14. Governing Impulse Wheel by an Induction Motor. Eng. News, 1903, vol. 1, 
 
 p. 246. 
 
 15. Garratt, Allan V. Speed Regulation of Water Power Plants. Elec. Age, 
 
 May, 1904. 
 
 16. Goodman, John. The Governing of Impulse Water Wheels. Engng., 
 
 Nov. 4, 1904. 
 
 17. Church, Irving P. The Governing of Impulse Wheels. Eng. Record, 
 
 Feb. 25, 1905. 
 
 18. Gradenwitz, Alfred. The Bouvier Governor for Water Turbines. Mach. 
 
 N. Y. June, 1905. 
 
 19. Henry, Geo. J., Jr. The Regulation of High-Pressure Water-wheels for 
 
 Power Transmission Plants. Am. Soc. of Mech. Engrs. May 1, 
 1906. 
 
 20. Replogle, Mark A. Some Stepping Stones in the Development of a Mod- 
 
 ern Water-Wheel Governor. Am. Soc. Mech. Engrs. May, 1906. 
 
 21. Buvinger, Geo. A. Turbine Design as Modified for Close Regulation. 
 
 Am. Soc. of Mech. Engrs. May, 1906. 
 
 22. Lyndon, Lamar. A New Method of Turbine Control. Proc. Am. Inst. of 
 
 Elec. Engrs. May, 1906. 
 
Literature. 469 
 
 23. Water Wheel Governors. Elec. World. June 30, 1906. 
 
 24. A New Water Wheel Governor. Eng. Rec. Current News Sup. July 14, 
 
 1906. 
 
 25. Warren, H. E. Speed Regulation of High Head Water Wheels. Tech. 
 
 Quar. Vol. 20, No. 2. 
 
 26. Johnson, R. D. Surge Tanks for Water Power Plants, Trans. Am. Soc. M. 
 
 E. 1908. 
 
CHAPTER XIX. 
 
 THE WATER WHEEL GOVERNOR. 
 
 232. Types of Water Wheel Governors. In all reaction turbines 
 and in all impulse turbines, with the exception of tangential wheels, 
 the governor affects regulation, i. e. controls the output, and hence 
 the speed of the wheel, by opening or closing the regulating gates, 
 thus varying the amount of water supplied to the wheel. In tan- 
 gential wheels, under high head, this method of control, for obvious 
 reasons (See section 215), becomes difficult and in extreme cases 
 impossible and in such cases the governor must be arranged to af- 
 fect regulation by the 'deflection of the jet from the bucket. (See 
 Fig. 282). 
 
 Fig. 282. Governing Impulse wheel with Automatic Needle and Deflecting 
 Nozzle (after Warren). 
 
 The force required to move the turbine gates is large (sometimes 
 50,000 Ibs. or more) and it is therefore evident that they cannot be 
 moved by the direct action of the centrifugal ball governors, as with 
 steam engines, but must be moved by a "relay." 
 
 The relay, as its name implies, is a device for transmitting energy 
 from a source of energy independent, as to quantity of the cen- 
 trifugal governor balls but controlled by them in its application. 
 
Types of Water Wheel Governors. 
 
 471 
 
 If the relay is of "mechanical type" the power required to operate 
 it and the gates is transmitted, when needed, from the wheel by 
 means of shafts, gears, friction-clutches, belts and pulleys or other 
 mechanical devices. In mechanical governors the flyballs may 
 actuate pawls, friction gears or other mechanical devices which will 
 bring the relay into action. 
 
 Pig. 283. Woodward Standard Governor. 
 
 If the relay is of the hydraulic type, it usually consists of a piston 
 connected by some mechanical device to the gate rigging and moved 
 by means of the hydraulic 'pressure of water taken from the pen- 
 stock, or other source, or by oil supplied under high pressure from 
 a reservoir. The pressure of the oil in the reservoir is maintained 
 by compressed air supplied by power taken from the wheel itself. 
 The oil thus used in moving the piston is exhausted into a receiver 
 from which it is pumped back into the supply reservoir. The hy- 
 draulic relay is commonly controlled by the ball governor through 
 
472 
 
 The Water Wheel Governor. 
 
 the medium of a small valve which by its motion either admits the 
 actuating water (or oil) directly to the cylinder or to a secondary 
 piston controlling a larger admission valve. 
 
 Electrical methods of actuating the relays controlled by means 
 of governor balls have been used to some extent but are not nearly 
 so common as mechanical or hydraulic devices. 
 
 Pig. 284. Diagramatic Section of Woodward Simple Mechanical Governor. 
 
 233. Simple Mechanical Governors. Fig. 283 is a view and Fig. 
 ,284 a diagramatic section of a simple mechanical governor of the 
 Woodward* Standard type. On the upright shaft are two frictioin 
 pans (a and b). (See also Fig. 287). These pans are loose on the 
 shaft, the upper one being supported in position by a groove in the 
 "hub and the lower one by an adjustable step-bearing. Between 
 these pans, and beveled to fit them, is a double-faced, friction wheel 
 (c) which is keyed to the shaft. This shaft and friction wheel run 
 
 *Woodward Governor Co., Rockford, 111. 
 
Anti-Racing Mechanical Governors. 473, 
 
 continuously and have a slight endwise movement. They are 
 supported by lugs on the ball arm and therefore rise and fall as the 
 position of the balls varies with the speed. 
 
 When the speed is normal, the inner or friction wheel revolves 
 freely between the two outer wheels or pans which remain station- 
 ary. When a change of speed occurs, the friction wheel is brought 
 against the upper or lower pan as the speed is either slow or fast. 
 This causes the latter to revolve and, by means of the bevel 
 gearings, turn the gates in the proper direction until the speed is 
 again normal. As the gate opens, the nut (d) travels along the 
 screw (e) which is driven through gearing by the main governor 
 shaft and as the gate reacts, the nut (d) coming in contact with 
 the lever (f) throws the vertical shaft upward and the governor out 
 of commission. 
 
 This type of governor may be used to advantage where the 
 water wheels operate a number of machines, connected to a main 
 shaft and where, in consequence, the friction or constant load is 
 a considerable percentage of the total load. In such cases the 
 changes in load may not ibe a large percentage of the total load 
 and the temporary variations in speed, which occur at times of 
 changes of load, may not be of sufficient importance to necessitate 
 the installation of a quick acting governor. 
 
 When the water wheel is direct connected tora single machine, 
 and the friction load is comparatively small, the relative change in 
 load, and the consequent possible changes in speed, is much larger. 
 
 In such cases the type of governor above shown will result in 
 a serious hunting or racing (See Section 211) of the wheel during 
 considerable changes of load, and in unsatisfactory regulation. In 
 such cases governors with compensating or anti-racing devices 
 must be used for satisfactory regulation. 
 
 234. Anti-Racing Mechanical Governors. The Woodward Com- 
 pensating Governor. Fig. 285 is a view and Fig. 286 is a dia- 
 gramatic section of a Woodward vertical mechanical governor of 
 the compensating type. 
 
 In the simple Woodward governor (See Figs. 283 and 284) the 
 power necessary to actuate both the centrifugal governor balls and 
 the relay is transmitted through a belt to a single pulley, P. In the 
 Woodward compensating type of governor the relay is operated 
 in a similar manner by ;a single pulley, P, while the centrifugal 
 governor balls are actuated by an independent pulley, q, having an 
 independent belt connected to the wheel shaft or to some other re- 
 
474 
 
 The Water Wheel Governors. 
 
 volving part connected therewith. From the driving pulley, q, 
 power is transmitted to the governor balls through a shaft and 
 gearing. The shaft supporting the centrifugal governor balls 
 is hollow, and on the ball-arms are two lugs which connect with a 
 
 Fig. 285. Woodward Compensating Governor. 
 
 spindle (f), which therefore rises and falls as the positions of the 
 governor balls vary with the speed. 
 
 The movement of the centrifugal governor balls causing the 
 spindle, f, to rise and fall changes the position of the tappet arm, 
 g, to which it is connected, and causes one or the other of the two 
 tappets, tt', to engage a double-faced cam, h. This cam is contin- 
 uously rotated by means of the pulley above it, driven by a belt con- 
 nected with the main vertical shaft of the relay. The tappets are 
 
Anti-Racing Mechanical Governors. 
 
 475 
 
 connected to a common suspension arm to which the vertical spin- 
 dle, f, is attached. The suspension arm is hinged to the lever arm, j. 
 The lever arm is connected to the shaft, K, which can be rotated 
 on its bearings and which is connected with a tension rod, 1, by an 
 eccentric at the bottom. The tension rod, 1, is in turn connected by 
 
 Fig. 286. Diagramatic Section of Woodward Vertical Compensating Mechan- 
 ical Governor, 
 
 a lever, m, with the vertical bearing, e, on which the main shaft of 
 the friction cone rests. This bearing is movable around the ful- 
 crum, n, and is counterbalanced by an arm and weight, u. 
 
 When either of the tappets engages the rotating cam, the resulting 
 movement turns the rocker shaft, K, and, through its connection, 
 raises or lowers the vertical bearing, e, which causes the friction 
 wheel, c, to engage either the upper or the lower of the friction 
 pans, a and b, as in the case of the simple governor. 
 
 The compensating or anti-racing mechanism is just below the 
 rotating cam. It is essentially alike in all of the Woodward com- 
 pensating types of governors and is described in the governor cata- 
 logue as follows : 
 
476 The Water Wheel Governor. 
 
 "On the lower end of the cam shaft is a friction disc, r, (Fig. 286) 
 which rests on a rawhide friction wheel on a diagonal shaft. The 
 hub of the friction wheel is threaded and fits loosely on the diagonal 
 shaft which is normally at rest. The effect of the continually 
 rotating friction disc upon the rawhide wheel is evidently to cause 
 it to travel along the threaded diagonal shaft to the center of the 
 disc. When the governor moves to open or close the gate, the 
 diagonal shaft, which is geared to it, is turned and the friction wheel 
 is caused to travel along the shaft away from the center of the disc 
 
 Fig. 287. Friction Cone and Pans of Woodward Governor. 
 
 and thus raise or lower the cam shaft so as to separate the cam from 
 the tappet which is in action, before the gate has moved too far, 
 thus preventing racing. As soon as the gate movement ceases the 
 disc causes the friction wheel to return to the center of the disc 
 along the threaded shaft." 
 
 To prevent the governor from straining when the gate is fully 
 open or closed, suitable cams are mounted on the stop shaft. 
 "When the gates are completely opened, the cam engages the speed 
 lever and holds it down so that it cannot raise the lower tappet 
 sufficiently to engage the revolving cam ; this does not, however, 
 interfere with the upper tappet, to prevent the closing of the gates, 
 should the conditions demand. The closed gate stop acts in a sim- 
 ilar manner on the upper tappet but does .not interfere with the 
 lower tappet being engaged, should the conditions demand that the 
 gate be opened. In addition to these stops, the governor is pro- 
 vided with a safety stop whose function is to immediately close the 
 gates should the speed governor stop through breakage of the belt 
 or any other cause." 
 
The Woodward Governor. 
 
 477 
 
 235. Details and Applications of Woodward Governors. Fig. 287 
 shows the construction of the friction gearing of the Woodward 
 Mechanical Governor. In the inner friction driving cone, corks 
 are inserted in holes drilled in the rim and these are ground off true 
 so that they project about one-sixteenth inch. This seems to give a 
 very reliable friction surface not readily affected by either water or 
 
 Fig. 288. Woodward Horizontal Compensating Mechanical Governor at Hy- 
 dro-Electric Plant of U. S. Arsenal, Rock Island, 111. 
 
 oil, and it is claimed to be superior to either leather or paper for 
 this purpose. In order to cause the friction wheel to engage 
 smoothly and noiselessly, a plunger attached to the shaft, just 
 below the inner friction wheel, fits rather closely into a dash-pot 
 formed in the lower pan. 
 
 Fig. 288 shows a horizontal compensating type of Woodward 
 governor as installed to control the gates of the turbines in the Hy- 
 draulic Power Plant of the U. S. Arsenal at Rock Island, Illinois. 
 The cables shown at the back of the cut operate the gates of the 
 turbine. On the gate shafts of the latter are sheave wheels to which 
 the cables are attached. These sheave wheels are fitted with 
 29 
 
478 
 
 The Water Wheel Governor. 
 
 clutches so that any gate may be disconnected from the governor. 
 Each gate is provided with an indicator showing its position This 
 provides means of coupling properly, after being disconnected, 
 without closing the gates of the other wheels. Each governor is 
 arranged to control six turbines, belonging to two different units. 
 Two belts are provided so as to drive from either unit. The gover- 
 
 Fig. 289. Lombard-Replogle Mechanical Governor. 
 
 nor can thus be used to control three wheels on either side or all 
 six when the two units are running in multiple. 
 
 236. The Lombard-Replogle Mechanical Governor.* Fig. 289 
 shows a Lombard-Replogle mechanical governor. The principles 
 of operation of this governor are better illustrated in the diagram, 
 Fig. 290. 
 
 In the diagram A is a spherical pulley with its shaft turned down 
 and threaded as at X. B and B are revolving concave discs lined 
 with leather which are continuously revolving in opposite direc- 
 tions. C and C are lignum vitae pins flush with the leather. D 
 and D are compression springs for controlling the pressure between 
 the disks and the sphere. When the spherical pulley A is shifted 
 from its central position in the line of its axis, the springs are 
 
 *The Lombard-Replogle Governor Co., Akron, Ohio. 
 
The Lombard-Replogle Mechanical Governor. 
 
 479 
 
 tightened automatically, causing increased traction as the smaller 
 diameters of the sphere engage the larger diameters of the disc. 
 E and E are the centrifugal governor balls so poised as to require 
 the weight of the pulley A to balance them at normal speed. F is a 
 loose collar to allow independent revolution of the balls EE. G 
 is the point of connection between A and the gates or valve rigging 
 of the wheel to be governed. X is the compensating device, and is 
 
 orernor Ball 
 
 Fig. 290. Diagram of Lombard-Replogle Mechanical Governor. 
 
 for the purpose of reducing and controlling racing. Z is a sta- 
 tionary spindle or connecting link between the collar F and the 
 threaded shaft or pulley A. Z is only stationary in reference to 
 revolution, as it rises or falls with the variations of the governor 
 balls. 
 
 The spherical pulley A is normally at test while the discs BB are 
 continually revolving. A movement of the governor balls raises 
 or lowers the shaft so that the spherical discs rotate the pulley. 
 
 The greater the displacement of the shaft the more rapid the 
 revolution since the circle of contact on the disc is increased. The 
 rotation of the spherical pulley A either shortens or lengthens 
 the distance to collar F by means of thread X. "This shortening 
 causes A to be pulled back to the disc centers, thereby cutting the 
 governor out of action" and preventing the gates from moving 
 too far or racing. 
 
480 
 
 The Water Wheel Governor. 
 
Essential Features of an Hydraulic Governor. 481 
 
 237. Essential Features of an Hydraulic Governor. The essen- 
 tial features of an hydraulic water wheel governor are : 
 
 1. A tank for storing oil under air pressure. 
 
 2. A receiver tank for the collection of oil used by the governor. 
 
 3. A power pump driven from the water wheel shaft. 
 
 4. A hydraulic power cylinder for operating the gates. 
 
 5. A sensitive centrifugal ball system for controlling a valve 
 which either admits oil directly to the power cylinder or to an inter- 
 mediate relay cylinder the piston of which operates the admission 
 valve to the power cylinder. 
 
 6. An anti-racing or compensating mechanism. 
 
 The power pump is continually using power from the wheel to 
 pump the oil from the receiver back to the pressure tank thus 
 gradually storing the energy which is used intermittently to oper- 
 ate the gates. 
 
 Fig. 291 illustrates the Lombard Type "N" Governor and shows 
 -clearly the relations of the various parts of an hydraulic governor. 
 
 The centrifugal governor balls are connected by belt to the wheel 
 shaft. These balls control a small primary or pilot valve of the 
 cylinder type which admits oil from the large pressure tank under 
 about 200 pounds pressure into one side of a cylinder where its pres- 
 sure is exerted against one of two plungers. These plungers control 
 a large valve, also of the cylinder type, which admits oil from the 
 pressure tank to one or the other side of the power piston. The 
 rectilinear motion of the piston is converted, by rack and pinion, into 
 rotary motion for transmission to the wheel gates. The oil used 
 for operating the power pistons and the plungers of the relay is 
 exhausted into the vacuum tank from which it is pumped back into 
 the pressure tank by means of the power pump shown at the left 
 which is driven by belt from the wheel shaft. The speed variation 
 necessary to actuate the governor depends upon the lap of the pilot 
 valve and is adjustable. 
 
 238. Details of Lombard Hydraulic Governor. The details of 
 the Lombard Type N Governor are best shown by the enlarged 
 view of the upper portion of the governor (Fig, 292) and by the sec- 
 tion of the relay valve (Fig. 293). The following description of the 
 operation of this governor is taken from the Directions for Erecting 
 and Adjusting Governors.* 
 
 "The oil from the pressure-tank is supplied to the working cyl- 
 inder 62 through the large relay-valve 106, arranged to discharge 
 
 *PubHshel by The Lombard Governor Co., Ashland, Mass. 
 
482 
 
 The Water Wheel Governor. 
 
 or exhaust oil directly and rapidly into or from either end of the 
 cylinder. The relay-valve 106, through the hydraulic system con- 
 nected therewith, is under the simultaneous control of the reg- 
 ulating-valve 14 and the displacement-cylinder 107- This is 
 
 10 
 
 Fig. 292. Upper Portion of Lombard Type N Governor. 
 
 brought about in the following manner. The relay- valve A 
 (See Fig. 293) is moved hydraulically by plungers B and 
 C contained within cylinders D and E forming parts of 
 the relay-valve heads F and G. Plunger B has about 
 one-half the area of plunger C, consequently plunger C can over- 
 power plunger B. if the pressure in cylinders E and D is nearly 
 
The Lombard Governor. 
 
 483 
 
 equal. The cylinder D is permanently in communication with the 
 main pressure supply through the pipe H which also furnishes liq- 
 uid to the regulating-valve 14. Therefore the tendency of plunger 
 B is always to move valve A towards the relay-valve head G. Cylin- 
 
 Fig. 293. Section Lombard Eelay Valve. 
 
 der E is in communication through pipes I and J with the adjusting- 
 valve 14, and also through the pipes J and K with the displacement- 
 cylinder 107. The regulating valve 14 is capable, when moved 
 in one direction, of admitting liquid under full pressure into the pipe, 
 I, and, when moved in the other direction, of exhausting liquid 
 through the pipe I. In the former case the action is to increase 
 the pressure back of the piston C until it overpowers the piston B, 
 thereby moving valve A towards the relay-valve head F, simulta- 
 neously opening the upper cylinder-port to the main exhaust, and 
 
484 The Water Wheel Governor. 
 
 the lower cylinder-port to the main pressure supply. Instantly the 
 main piston of the governor and with it the displacement-plunger 
 109 are set in motion. 
 
 "As the displacement-plunger begins to move, a space is created 
 back of it, into which a portion of the liquid flowing through the 
 pipe I is diverted. As the motion of the displacement-plunger be- 
 comes more rapid, a condition is reached when all the liquid flowing 
 through I continues on through K into the displacement-chamber. 
 The relay-valve A then ceases to move any further. The motion 
 of the main governor-piston, however, continues as long as the 
 regulating-valve 14 is open. When this valve 14 closes, the relay- 
 valve A is immediately thereafter closed, because the liquid in the 
 cylinder E instantly escapes through the pipes J and K into the 
 space beneath the moving displacement-plunger; thus the whole 
 governor is brought to rest. 
 
 . "When the regulating-valve 14 is moved in the opposite direction 
 by the centrifugal balls so as to allow liquid to escape through the 
 pipe I, there results an immediate loss of liquid in the cylinder E, 
 back of the plunger C ; this allows the plunger B to force the relay- 
 valve A towards the rday-valve head G, thus opening the lower 
 cylinder port to the exhaust, and the upper cylinder-port to the 
 pressure supply. The main governor-piston instantly begins to 
 move down, carrying with it the displacement-plunger, thus forcing 
 liquid through the pipes K and I, reducing the flow outward through 
 J, until finally the downward velocity of the displacement-plunger 
 becomes rapid enough to entirely check the outward flow through J. 
 Relay-valve A then remains stationary until the valve 14 has moved 
 to a new position. As soon as regulating-valve 14 is closed, the liq- 
 uid which has been flowing out through I immediately flows into J 
 and, acting upon the plunger C, restores valve A to its closed posi- 
 tion, stopping further movement of the governor. It will be seen 
 that the governor when moving has a constant tendency to close 
 the relay-valve which keeps it in motion, and this relay-valve can 
 be maintained open only so long as the regulating-valve 14 is add- 
 ing or subtracting oil to or from the system consisting of the pipes 
 I, J, K, and parts connected therewith." 
 
 Fig. 294 shows the Lomard Governor, Type R, the smallest of the 
 various governors made by that company. This is a vertical, self- 
 contained oil pressure machine. The oil is stored in a tank formed 
 by the main frame. The governor is designed to exert 2500 pounds 
 
The Lombard Governor. 
 
 485 
 
 pressure and will make an extreme stroke of eight inches in one 
 second. 
 
 239. Operating Results with Lombard Governor. Fig. 295 is 
 a cut from a speed recorder strip taken from the Hudson River 
 
 Fig. 294. The Lombard Type R Governor. 
 
 Power Transmission Companies plant and shows the regulation of 
 the Lombard Type B Governor regulating S. Morgan Smith tur- 
 bines on an electric railroad load. The cars are large and the 
 change in load rapid and large. 
 
4 86 
 
 The Water Wheel Governor. 
 
 1 ! 
 
 Fig. 296 shows the comparative regula- 
 tion of two generators in the same plant. 
 (See Bulletin No. 107 Lombard Gov- 
 ernor Company.) The load was quite 
 variable on account of beaters which had 
 to be driven from the same shaft as the 
 paper making machinery. The original 
 governor used, the work of which is shown 
 in the upper cut, was replaced by a Lom- 
 bard Type D Governor. The work of 
 the latter is shown in the lower tacho- 
 meter chart, and the improvement in the 
 uniformity of operation is readily seen by 
 a comparison of the tw r o charts. 
 
 240. The Sturgess Hydraulic Gover- 
 nor.* The Sturgess Type "M" Hydrau- 
 lic Governor, with the omission of the 
 pump and storage tank, is shown in Fig. 
 297 and in section in Fig. 298. This gov- 
 ernor consists of a shaft-type centrifugal 
 governor G attached to the top of the ma- 
 chine and operated by a belt and pulley 
 P from the turbine shaft. The governor 
 balls BB in this machine control directly by 
 means of a long vertical lever D a small 
 primary or pilot valve S of cylinder type 
 which admits oil to a cylinder controlling 
 the main admission valve S. The main 
 valves, attached to the side of the cylin- 
 der, admit pressure directly into the cyl- 
 inder S and on either side of the piston* S 
 which, by its motion, rotates the gate 
 shaft by means of the concealed steel rack 
 R and pinion N, shown in the sectional 
 view, Fig. 298. 
 
 The valves for the admission of oil or 
 water, as the case may be, in the cylinder 
 are of the poppet type which avoid lap" 
 and therefore increase the sensitiveness of 
 the governor. The anti-racing mechanism 
 
 *: Sturgess Engineering Dept. of The Ludlow 
 Valve Mfg. Co., Troy,"N. Y. 
 
Operating Results with Lombard Governor. 
 
 487 
 
4 88 
 
 The Water Wheel Governor. 
 
 G 
 
 P 
 
 B 
 
 Fig. 297. Sturgess Type M Hydraulic Governor. 
 
The Sturgess Hydraulic Governor. 
 
 G 
 
 489 
 
 Fig. 298. Section Sturgess Type M Governor. 
 
 consists of a rod A which is attached to the cross head of the 
 governor. At the top of this rod is a projection to which 
 is attached an adjustable piston rod reaching down into the open 
 top dash pot F. The piston rod has a piston attached at its lower 
 end fitting freely into the bore of the dash pot the top of which is 
 
49 
 
 The Water Wheel Governor. 
 
 formed into a cup which receives the excess oil. The bottom of the 
 dash pot is closed and is attached to a tail, piece connected to the 
 counter weighted locker lever, C. 
 
 The piston rod and piston are hollow and near the bottom of the 
 piston is a small by-pass which can be regulated by an adjusting 
 screw which controls the rate of flow of the oil in the dash pot. The 
 lever, C, is fixed on the rocker shaft the opposite end of which car- 
 ries the short arm from which a link is carried to the bottom of the 
 valve lever D which is free to move. Two weights, EE, are 
 
 Speed 
 
 8. A B. TACHOMETER No. 10,205 
 
 ^Revolution* pc-r Miu. 
 
 , Revolution* pi-r Mln. 
 
 L\\\\\\ 
 
 ffffff 
 
 , \ 
 
 \T\T\ \\\\\\\ U \\ \\.\\\\ 
 
 '. 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 11 
 
 
 ''i 
 
 
 
 
 L 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 "- 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Movements of , 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 A 
 
 ll 
 
 ! 
 
 J 
 
 
 In 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 f 
 
 tr 
 
 j 
 
 ; 
 
 ui 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 jvcraor and Gate' 5 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ut 
 
 U 
 
 
 ,i j.,, 
 
 n| 
 
 i.'i-t 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 + 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Closed 
 
 
 (/ 
 
 
 
 
 
 
 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 V, 
 
 
 
 rr 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fig. 299. Test Kesults with Sturgess Governor. 
 
 hung loosely on the rocker shaft but a pin on the shaft engages with 
 either one or the other of the weights and raises them whenever the 
 rocker shaft moves. The function of the weights therefore is to 
 keep the rocker shaft, and consequently the bottom of the valve 
 lever, in normal position. When the main piston moves, it is ob- 
 vious that it will tend to raise or lower the dash pot, F, through 
 its connection to the ro^d I and this movement will swing the lever 
 C and rocker shaft H thus deflecting the bottom of the valve lever 
 D so as to compensate in the correct manner. The same movement 
 raises one of the weights E, but as the dash pot permits a slow 
 movement the weights will finally restore all parts to the middle or 
 
Test Results with Sturgess Governor. 491 
 
 normal position. In the smaller sizes the pilot valve is omitted 
 and the centrifugal governor balls actuate directly through the 
 lever the main valves of the system. 
 
 241. Test Results with Sturgess Governor. The action of any 
 governor in maintaining a uniform speed may be shown graphi- 
 cally by attaching a recording tachometer to the turbine shaft. In 
 order to fully understand and appreciate the action of the governor, 
 the tachometer chart should be considered together with the load 
 curve and a diagram showing the movement of the governor dur- 
 ing the same period. 
 
 Fig. 299 shows a governor test made by Mr. John Sturgess on an 
 1 100 K. W. unit. "The curves were traced by a sp.ecial Schafer & 
 Budenberg tachometer, the readings being sufficiently magnified to 
 bring out the characteristics of the governor. * * * The load 
 changes and governor movements are platted below. Note that when 
 the whole load was thrown off (at 1 :55), the speed accelerated about 
 8 per cent, in an incredibly short time (under i sec.), and the gov- 
 ernor had the gate shut in 14 sees, after the load went off. * * * 
 It is to be noted that after the first quick result at 2 :oo mins. the 
 governor slowly oscillated for about another minute, but with 
 gradually increasing gate opening, the speed and load being prac- 
 tically constant. This was due to the water rising in the forebay, 
 and gradually subsiding in a succession of waves, the governor tak- 
 ing care of these fluctuations, in effective head, in a very intelligent 
 manner."* 
 
 "The plant in which these tests were made was by no means a 
 good one from the regulation standpoint, for it will be noticed that 
 when the whole load was instantly thrown off the momentary rise 
 of speed was about 8 per cent, although the governor shut the 
 gate from full open position in the extremely quick time of 1.4 
 sees. There were five wicket gates, having a total of 96 leaves, and 
 a heavy counter-weight to be moved a considerable distance in this 
 interval. ** 
 
 242. General Consideration. Mechanical governors are cheaper 
 than hydraulic, but, assuming the same gate movement, they are 
 less effective at increasing loads since the power to move the gates 
 must be taken as needed from the wheel itself instead of being taken 
 
 * See American Society M. E., Vol. 27, No. 4, p. 8. 
 
 ** Catalogue of Water Wheel Governors, Sturgess Engineering Department 
 of the Ludlow Valve Co., p. 23. 
 
492 
 
 The Water Wheel Governor. 
 
 from a storage tank as with hydaulic governors. This is a factor 
 of more or less importance in accordance with the degree of regu- 
 lation required. The difference is manifest principally at low loads 
 when the energy taken by the governor relay from the water wheel 
 is a considerable percentage of the total energy being generated. As 
 the power exerted by the relay is usually comparatively small, the 
 difference in action from this cause between the two types of gov- 
 ernors is often unimportant- 
 
 ^4 i 
 
 Fig. 300. Governor Connection by Diaw Rods. 
 
 The hydraulic governor possesses an additional advantage in its 
 ability to start a stationary wheel into action by means of its 
 stored energy. The mechanical governor depending as it does on 
 the power of the wheel itself is only effective after the wheel has 
 been started by other means. 
 
 243. Control From the Switchboard. Electrical devices can now 
 be purchased by which the normal speed of the wheels can be con- 
 trolled from the switchboard in case the governor is so designed 
 that it can be adjusted while in motion, which is true of most high 
 class machines. It is also possible to start and stop the wheels 
 electrically from the switchboard or from a distant station. 
 
Connection of Governors to Gates. 493 
 
 244. Connecton of Governors to Gates. The following discussion 
 of this subject and the accompanying figures are taken with slight 
 changes, from a paper by Mr. A. V. Garratt.* 
 
 * * * rpke most successful method of connecting the cylinder 
 gates of several turbines to the same governor is shown in Fig. 300. 
 In this case each pair of drawrods is connected to a pair of walking 
 beams which carry counterweights on their opposite ends. Each 
 walking beam carries a gear sector which engages a rack on a long, 
 horizontal reciprocating member terminating at the governor. 
 The racks on the reciprocating member are "sleeved" on it, and held 
 in place by pins, which may be removed if it is desired to discon- 
 nect any turbine from the governor. 
 
 "By this method any one, or any combination of turbines, may be 
 handled by the governor or any turbines by hand, at will, by means 
 of a lever shown in the end projection. 
 
 "Fig. 301 shows a good method of connecting a governor to a 
 pair of horizontal wicket-gate turbines. It will be noted that the 
 shaft connecting the two gear sectors on the gate stems goes di- 
 rectly to the governor, and is connected to it through a pin clutch 
 which may be opened, and a hand-wheel on the governor may then 
 be used to move the gates by hand. The only improvement on 
 this design which can be suggested would be to eliminate the coun- 
 ter-shaft between the governor pulleys and the turbine shaft by plac- 
 ing the governor beyond the draught-tube quarter-turn, so that 
 the governor pulleys might belt directly to the turbine shaft. The 
 limitations of available space prevented the location of the governor 
 in this manner on the drawing which shows the design used for 
 three units in a modern power plant. 
 
 "Frequently the only possible location of the governor prevents 
 anything like direct connection between it and the turbines. In 
 such cases experience has shown that it is wisest to avoid the use 
 of several pairs of bevel gears and long shafts, and in their place 
 nse a steel rope drive. This method has great flexibility, and per- 
 mits of governor locations which would otherwise be impossible. 
 Fig. 302 shows a design of this kind. The governor is located in 
 the only available space, and yet its connection to the turbines is 
 perfectly adequate. The steel rope used is small in size, made of 
 very small wire, especially laid up, and its ends are fixed to the 
 grooved sheaves, which are provided with internal take-ups, so 
 
 * See "Speed Regulation of Water Power Plants," by Allan V. Garratt. Cas- 
 sier's Magazine, May, 19'01. 
 
 30 
 
494 
 
 The Water Wheel Governor. 
 
 nnn 
 
 Fig. 301. Governor Connection by Shaft and Sectors. 
 
Relief Valves. 
 
 495 
 
 that the rope may be kept tight as a fiddle string. This general 
 method of connection is in successful use in many plants where 
 the requirements for speed regulation are most exacting. 
 
 "In the above examples the two ends which have governed the 
 design are simplicity and directness. These two factors should 
 never be lost sight of, and the more completely they are embodied 
 in the design, the better will be the speed regulation. To these two 
 may be added another, and that is freedom from lost motion. These 
 
 Fig. 302. Governor Connection by Cable. 
 
 three factors are absolutely necessary if successful results are to be 
 expected. The slightest motion of the governor must be trans- 
 mitted in the simplest and most direct manner, and in the shortest 
 possible interval of time, to the turbine gates/' 
 
 245. Relief Valves. Relief valves are very necessary on long 
 feeder pipes and penstocks to avoid excess pressures of an acci- 
 dental nature as well as those produced by closing of the turbine 
 gates. A group of such valves installed on the end of one of the 
 penstocks of the Niagara Falls Hydraulic Power and Manufactur- 
 ing Co. is shown in 'Fig. 303. Relief valves should be arranged to 
 open with a slight excess of the penstock pressure but should close 
 very slowly in order to avoid oscillatory waves. Spring balanced 
 
49 6 
 
 The Water Wheel Governor. 
 
 relief valves have proven objectionable for this purpose. If set 
 to open at a small excess pressure they are apt not to close on ac- 
 count of the impact of the discharging water against the valve, 
 In order that they may close, the balancing spring must be so strong 
 that a considerable excess is required to open the valve which does 
 not therefore serve the desired purpose. All types of -valves are 
 also hindered by the fact that corrosion is apt to seal the valve so 
 that a considerable excess is required to open it. 
 
 246. Lombard Hydraulic Relief Valve. The Lombard Gov- 
 
 Fig. 303. Relief Valve on end of Penstock. Niagara Falls Hydraulic Power 
 Manufacturing Co. (Electrical World, Jan. 14, 1899.) 
 
 ernor Company have designed a valve in which they claim to have 
 eliminated the difficulties of the spring valve. This valve is shown 
 in Fig. 304* and is described as follows : 
 
 "The valve consists of the following parts, viz : A valve disc, c, 
 capable of motion to or from its seat, b, rigidly connected by means 
 of a rod, i, with the piston, f, in the cylinder, e. The whole valve is 
 bolted to a flange upon the supply pipe, d, wherein the pressure is 
 to be controlled. The area oi piston, f, is somewhat greater than 
 that of the valve disc, c, so that when water at the same pressure 
 is behind the piston and in front of the valve there is a positive and 
 strong tendency to hold the valve closed. For the purpose of al- 
 
 * Lombard Bulletin No. 101. 
 
Lombard Hydraulic Relief Valve. 
 
 497 
 
 lowing the valve disc, c, to open at proper times to relieve excess 
 pressure in the supply pipe, d, there is provided a regulating waste 
 valve, C. This valve is opened or closed by a piston, n, opposed 
 by a very oblong and strong spiral spring, p. Piston, n, is a loose 
 fit in its cylinder, o, so that it moves upward freely in response 
 
 Fig. 304. Lombard Hydraulic Relief Valve. 
 
 to the least excess in pressure upward due to the water in the cylin- 
 der, o, opposed to the downward pressure of the spring, p. * * * 
 The piston, n, is connected by means of the stem, m, with a double- 
 seated balanced valve, d, which of course, opens simultaneously 
 with any upward movement of the piston. Water under existing 
 pressure is admitted into the cylinder, e, through the pipe, k, and 
 throttle valve, i. 
 
498 The Water Wheel Governor. 
 
 "The spring, p, is adjusted by means of the screw, s, and lock-nut, 
 y, so that the effective normal pressure of the water in the chamber 
 is just insufficient to overcome the downward pressure of the 
 spring. The valve, D, will therefore remain closed normally ; con- 
 sequently the main valve disc, c, will also remain closed normally, 
 because water flowing in through the pipe, k, and throttle valve, I, 
 will produce an excess closing pressure upon the piston, f. When 
 thus adjusted any increase in pressure above the normal will 
 immediately force the piston, n, upward, and will thereby open 
 the balanced valve, D. This instantly relieves the pressure back 
 of the piston, f, which of course then gives way to the superior pres- 
 sure back of the piston, f, which of course then gives way to the 
 superior pressure in front of valve, c. In this manner practically 
 the whole pressure in front of the valve disc, c, is available for 
 opening it. * * * Valve disc, c, will continue to open until 
 the limit of its travel has been reached, or the pressure in 
 the supply pipe, d, has been reduced to a point where the 
 piston, n, will close the balanced valve, D. Immediately on the 
 closing of balanced valve, D, water begins to accumulate behind 
 the piston, f, flowing in through the throttle valve, I. This water 
 gradually and surely forces the valve disc, c, to close. The speed of 
 closing is adjustable by the opening through the throttle valve, i, 
 and may be made as slow as several seconds or even minutes. The 
 closing motion is * * uniform and there is not the slightest ten- 
 dency to set up vibrations in the water column, a very serious ob- 
 jection to the ordinary types of spring balanced valves which open 
 and close suddenly and are liable in the latter operation to set up 
 water hammer effects even more dangerous than those which they 
 are designed to relieve." 
 
 247. Sturgess Relief Valves. The Sturgess Engineering De- 
 partment of the Ludlow Valve Manufacturing Company makes two 
 forms or relief valves, the "Automatic" and the "Mechanical." 
 The Automatic Relief Valve is shown in Fig. 305 and is described 
 as follows: 
 
 "The essential element in the Automatic Relief Valves is a large, 
 very sensitive diaphragm o.f special construction. This is under 
 the influence of the water pressure in the pipe-line and its move- 
 ments are communicated to a small pilot valve controlling a hy- 
 draulic cylinder, which in turn operates the relieving valve on the 
 relief valve proper. After the pressure in the pipe-line is restored to 
 normal, the relief valve gradually closes automatically. 
 
Sturgess Relief Valve. 
 
 499 
 
 "The action of this valve is almost instantaneous, and it will 
 iully open on a very small rise of pressure. 
 
 "These valves can either be made in self-contained form, or 
 the sensitive parts (diaphragm, pilot valve, and hydraulic cylin- 
 
 Fig. 305. Sturgess Belief Valve. 
 
 der) may be mounted on a pedestal placed in the power house, 
 and the relief valve proper attached to the penstock or wheel cas- 
 ing, a rod or link being provided to connect the two (as in Fig. 
 305). 
 NOTE. See Appendix for descriptions of two new governors. 
 
CHAPTER XX. 
 
 ARRANGEMENT OF THE REACTION WHEEL. 
 
 248. General Conditions. The reaction turbine may be set or ar- 
 ranged for service in a water power plant in a variety of ways, and 
 the best way may differ more or less with each installation. The 
 arrangement of wheels should always be made with due regard to 
 machinery to be operated, the local conditions that prevail, and es- 
 pecial consideration should be given to securing the greatest 
 economy in the first cost of installation, maximum efficiency and 
 facility in operation, and minimum cost of operation and mainte- 
 nance. 
 
 Impulse water wheels of the tangential type have always been 
 set with their shafts horizontal. An installation with vertical shaft 
 was proposed for one of the first Niagara plants but was not con- 
 sidered on account of the lack of actual experience with such a 
 form of installation. Impulse wheels of the Girard type have been 
 used with both vertical and horizontal shafts. In general, how- 
 ever, because of the high heads under which impulse wheels usually 
 operate, the horizontal shaft arrangement is readily adapted. 
 When an impulse wheel is installed it must be set above the level 
 of maximum tail water, if it is to be operated at all stages of water. 
 The wheel arrangement is therefore dependent principally on the 
 arrangement of the machinery to be operated. By far the greater 
 proportion of such machinery is built with horizontal shafts and 
 hence in most cases where machinery is not special, horizontal 
 shaft arrangements are desirable. 
 
 Reaction wheels are often used on streams where the relative 
 variation in position of the tail-water is considerable, and it is both 
 desirable to utilize the full head and to have the wheel set at an ele- 
 vation at least above the lowest elevation of the tail-water in order 
 that they may be accessible for examination and repairs. By the 
 use of the draft tube this can often be done without the sacrifice 
 of head. If the wheel must be set below tail-water, gates must be 
 provided for the tail-race with pumps for the removal of the water 
 when access to the wheels is necessarv. 
 
Necessary Submergence of Reaction Wheels. 501 
 
 The arrangement of reaction water wheels is susceptible only of 
 general classification, which, however, may assist in the under- 
 standing of the subject and the selection of the best methods to be 
 adopted under any set of local conditions. Wheels may be set 
 vertically or horizontally, as the conditions of operation demand, 
 without materially affecting their efficiency, provided that in each 
 instance the turbine case, draft tubes, etc., are suitably arranged. 
 The improper design of the setting may materially affect the effi- 
 ciency of operation in either case. 
 
 249. Necessary Submergence of Reaction Wheels. In order to 
 prevent the formation of a vortex or whirlpool, which will draw 
 air into the wheel and often seriously affect its power and efficiency, 
 it is necessary that the gate openings of the wheel be placed from 
 one to one and one-quarter wheel diameters below the water 
 surface. The head under which the wheel is to operate, however, 
 greatly affects the formation of the vortex. High velocities of flow 
 will facilitate their formation,; therefore greater heads will require 
 a greater water covering or other means for the prevention of 
 vortex formation. 
 
 As the wheel usually has a greater diameter than the height of 
 the gate it can be set vertically with less danger of air inter- 
 ference than when set horizontally. For this reason the vertical 
 wheels are more readily adapted to low heads and have in the past 
 been more widely used for developments under low and moderate 
 heads. 
 
 With both horizontal and vertical wheels the wheel may be pro- 
 tected from the formation of the vortex by a solid wooden float, or 
 may be partially encased or covered with an umbrella-shaped cover 
 the edges of which can be brought below the level of the upper 
 gates of the turbine thus allowing the wheel to be set near the 
 head water surface without the serious interference above men- 
 tioned. In all such cases the float or cover must be so arranged as 
 to admit the water to the wheel gates without undue velocity in 
 order to prevent the loss of head. If this is done the efficiency and 
 power of the wheel will not be affected (see Appendix E). Arrange- 
 ments of this sort were designed by the writer, in the fall of 
 1906, for the water power plants at Kilbourn and at Dresden 
 Heights. 
 
 250. Arrangements of Vertical Shaft Turbines. Figs. 306 and 
 307 show twelve typical arrangements of reaction turbines. Figs. 
 A, B, C and D of Fig. 306 show typical arrangements of vertical 
 
502 
 
 Arrangement of the Reaction Wheel. 
 
 A 
 
 Fig. 306. 
 
Arrangement of Vertical Shaft Turbine. 503 
 
 wheels. Diagram A is the most common arrangement of the re- 
 action turbine in an open penstock for low head. In this case the 
 wheel is set in a chamber called the wheel pit, the flume, or some- 
 times the penstock, and is connected with the head race from which 
 it should be separated by gates. The wheel pits in the smaller 
 plants have commonly been constructed of timber; but in the larger 
 plant, they are usually built of a more substantial character, 
 often of iron or concrete, usually reinforced. Sometimes two or 
 more wheels are set in a single pit ; but in the better class of con- 
 struction, a pit is supplied for each individual wheel or each unit 
 combination of wheels so that each unit can be cut off from its 
 fellows, disconnected from the transmission mechanism to which 
 it is attached, and examined or repaired without interference with 
 the remainder of the plant. Open pits are commonly used for 
 heads up to 18 or 20 feet and may be used for considerably higher 
 heads under favorable conditions. 
 
 For higher heads, the arrangement shown in diagram B, or some 
 other form similar thereto, is often found more desirable. In this 
 case closed flumes of steel or reinforced concrete are used, and are 
 connected with the head race by metal, wood, or reinforced con- 
 crete pipes to which the term "penstock" is commonly applied. 
 This form of construction permits of the use of vertical wheels 
 with almost any head. In Diagram B the turbine is shown as di- 
 rect connected to an electrical generator of special design with ver- 
 tical shaft. 
 
 In Diagram A the shaft of the turbine is shown as directly at- 
 tached to a crown gear which in turn is connected by a spur gear 
 with a horizontal shaft. This horizontal shaft may be direct-con- 
 nected to a generator as shown in Fig. 325, or may be attached by 
 belting, ropes, cable or other mechanical means with one or more 
 machines which it is designed to operate. 
 
 Diagrams C and D show two vertical types of settings of tan- 
 dem or multiple wheels. Such arrangements are introduced when 
 it is necessary to reduce the diameter of the wheels on account of in- 
 creased speed, and at the same time maintain the power of in- 
 stallation by increasing the number of wheels for the purpose of 
 direct connection to some machine to be operated . 
 
 In all cases where two wheels discharge into a common draft 
 tube sufficient space is necessary between the wheels to prevent 
 interference and consequent loss in efficiency. The arrangement 
 
504 Arrangement of the Reaction Wheel. 
 
 of wheels in this manner therefore requires a considerable amount 
 of vertical space and, under low or moderate head, involves the 
 construction of a wheel pit of considerable depth in order to se- 
 cure proper submergence of the upper wheel. This arrangement 
 results in the lower wheel being often considerably below the tail- 
 water and necessitates the use of tail gates and a pumping plant 
 to remove the water in order to make the lower wheels accessible. 
 With this design the plant is made comparatively narrow but the 
 greater depth of construction means an additional expense in the 
 foundation work. Vertical wheels of all types involve a design 
 of satisfactory vertical bearings which are usually less accessible 
 than in the case of horizontal bearings which can be placed at an 
 elevation above the power house floor, and are consequently more 
 readily accessible. The st$p bearings for single vertical wheels 
 have been long in use and are reasonably satisfactory. The sus- 
 pension bearing, which is involved in the use of large vertical in- 
 stallations, is not universally satisfactory and, in fact, considerable 
 difficulties have been encountered in so designing a bearing that it 
 will operate without undue expense for maintenance. 
 
 251. Arrangement of Horizontal Turbines. Single horizontal 
 wheels of the common type are shown in Diagrams E and F of Fig. 
 306 and in Diagrams A, B, C, and D of Fig. 307. In each case the 
 gates of the turbine must be readily accessible to the entering 
 water without undue velocity, and the wheel pit, or penstock, must 
 be designed with this requirement in view. 
 
 Diagrams E and F, Fig. 306, and A, Fig. 307, show horizontal 
 types of wheels set in an open wheel pit or penstock. 
 
 In Diagram E the wheel has the quarter turn set entirely in the 
 pit, and the main shaft passes through a bulkhead in the wall of 
 the station with a packing gland to prevent the passage of water. 
 In this case the water must flow by the quarter-bend and hence, 
 in order to secure sufficiently slow velocity, the wheel pit must be 
 wider or deeper than in the case shown in Diagram F of Fig. i. 
 Here the gates of the turbine are placed toward the entering water 
 and the flow is interfered with only by the pedestal bearings which, 
 being placed in the center of the crown or cover plate of the wheel, 
 occupy but little space and offer practically no obstruction to flow. 
 
 Diagram A of Fig. 307 is essentially the same in arrangement 
 as Diagram F in Fig. 306, except that in this case instead of a me- 
 tallic quarter-turn and draft-tube, the quarter-turn and draft-tube 
 are constructed in the masonry of the power station and the bulk- 
 
Arrangement of Horizontal Shaft Turbine. 505 
 
 Fig. 307. 
 
506 Arrangement of the Reaction Wheel. 
 
 head is reduced to simply a packing gland through which the shaft 
 enters the power station. 
 
 Diagrams B, C, and D, Fig. 307, illustrate three methods of en- 
 closing a turbine in a closed flume which is connected with the 
 head water by a closed penstock. 
 
 In Diagram B the turbine case is spiral, the water enters tangent 
 to the wheel and at right angles to the shaft and is discharged 
 through a metal quarter-bend into a concrete draft-tube. 
 
 In Diagram C the water enters the metallic flume in which the 
 wheel is placed at right angles to the shaft, and is discharged 
 through a metal quarterrbend and draft-tube. 
 
 In Diagram D the water enters the wheel case parallel to the 
 shaft of the wheel and is discharged through a metal quarter-bend 
 into a concrete draft-tube. 
 
 Figs. E and F of Fig. 307 show methods of setting horizontal 
 shaft wheels in tandem. Diagram F is for setting in an open 
 flume or penstock. The two wheels discharge into a common 
 shaft chest and use a common draft-tube. In Diagram E the wheels 
 have a common closed case or flume connected by a penstock with 
 the head waters and each discharges through an independent quar- 
 ter-turn and an independent draft-tube into the tail-waters beneath. 
 With the closed flume removed, this arrangement can also be used 
 in an open penstock. These diagrams are simply typical of various 
 possible arrangements of wheels that can be adapted with various 
 modifications of detail to meet the local requirements of the en- 
 gineer for any hydraulic plant which he may be called upon to de- 
 sign. 
 
 252. Classification of Wheels. The classification of the arrange- 
 ment of wheels as shown in Figs. 306 and 307 may be reviewed 
 briefly as follows : 
 
 In this review reference is given to various figures in the pre- 
 ceding and following text in which the type of wheel described is 
 illustrated with more or less modifications. 
 
 ist. Vertical single wheel, open wheel pit. (See Diagram A, 
 Fig. 306, also Figs. 329, 331, 333 and 334.) 
 
 2nd. Vertical single or tandem wheels in metal casing con- 
 nected by cylindrical penstock with supply. (See Diagram B, Fig. 
 306, also Figs. 132, 181, 310, 311.) 
 
 3rd. Vertical tandem wheels, two or more wheels in open pit. 
 (See Diagrams C and D, Fig. 306, also Figs. 134, 138, 173, 339.) 
 
Classification of Wheels. 507 
 
 4th. Horizontal turbine, open wheel pit, quarter-bend and draft- 
 tube within wheel pit, quarter bend of metal. (See Diagram E, 
 Fig. 306.) 
 
 5th. Horizontal turbine, open wheel pit, quarter-bend, and draft- 
 tube exterior to pit, quarter-bend may be of metal or concrete 
 construction. (See Diagram F, Fig. 306, also Diagram A, Fig. 
 307 and Figs. 314, 322.) 
 
 6th. Horizontal turbine in spiral case at end of penstock, single 
 or double draft-tube. (See Diagram B, Fig. 307, also Figs. 159, 
 162, 338.) 
 
 7th. Horizontal turbine in cylindrical or conical case at end of 
 penstock. (See Diagrams C and D, Fig. 307, also Fig. 335.) 
 
 8th. Tandem horizontal turbines in open wheel pit, single dis- 
 charge through common or independent draft tubes. (See Diagram 
 F. Fig. 307, also Figs. 315, 319 to 324 inclusive.) 
 
 9th. Tandem horizontal turbine in enclosed cylindrical case with 
 common penstock and common or independent draft-tubes. (See 
 Diagram E, Fig. 307, also Figs. 13, 140, 152, 317.) 
 
 253. Vertical Wheels and Their Connection. The vertical set- 
 ting of single wheels is usually the cheapest in first cost, which 
 fact is an important factor that has been largely instrumental in 
 the adoption of this arrangement in most of the older plants. Ver- 
 tical wheels are most commonly set in open wheel pits. They may, 
 however, be set in a cast iron or steel casing which is then con- 
 nected to the headrace or dam by a proper penstock. Single ver- 
 tical wheels can be connected to the machine they are to drive by 
 various means. Belting, transmission ropes, cables, and shaftings, 
 are in common use for such connections. The shaft is usually placed 
 horizontally and is connected by a crown beveled gear and pinion 
 to the wheel. Frequently belts, ropes, and cables are connected by 
 pulleys or sheaves to a short horizontal shaft driven in the same 
 manner. When the power of a single vertical wheel is insufficient, 
 two or more may be harnessed by gearing to a line shaft which may 
 be directly connected to the machine or machines to be operated, 
 or otherwise connected as convenience and conditions may require. 
 
 254. Some Installations of Vertical Water Wheels. Figs. 329 to 
 332 inclusive, show the plans, elevations, sections, and details of 
 a small plant of vertical water wheels designed by the writer for 
 the Sterling Gas, Light and Power Company of Sterling, Illinois. 
 The details of this plant are clearly shown by the illustrations and 
 will be discussed at some length later. This plant is located on the 
 
5 o8 
 
 Arrangement of the Reaction Wheel. 
 
 oo 
 o 
 
 CO 
 
 to 
 
Some Installations of Vertical Water Wheels. 
 
 5o9 
 
 Sterling side of the Rock River (See Fig. 345) and is next to the 
 last plant on the Sterling Race. The head developed is about eight 
 feet and the power of each wheel is about 115 h. p. under this head. 
 Each wheel of the installation is set in an independent pit -or pen- 
 stock which can be closed by means of a flume gate. The wheels 
 are connected to a common shaft extending into the power house 
 and connected with pulleys and belts to the generator. 
 
 The plan of the South Bend Electric Company at Buchanan, 
 Michigan, is of similar type and is shown on page 544, Fig. 334. The 
 main shaft is here connected with ten turbines and is in turn 
 directlv connected to an electric alternator. 
 
 Fig. 309. Low Head French Water Power Plant. 
 
 The adaptability of the vertical shaft turbine to low head is well 
 shown in Figs. 308 and 309. Fig. 308 shows three turbines manufac- 
 tured by The Trump Manufactnring Company of Springfield, Ohio. 
 These turbines are 61, 56 and 44" respectively, and by suitable gear- 
 ings are connected with a common shaft. These wheels were in- 
 stalled at Bologna, Italy, and operate under a low water head of 42" 
 and under a high water head of 28". It was necessary to set the 
 wheels considerably below the level of the tail water in order that 
 31 
 
Arrangement of the Reaction Wheel. 
 
 the turbines should have a sufficient submergence for operation. 
 Fig. 309 is a similar plant installed at Loches, France. In this 
 case the water is conducted to the turbines by means of a syphon 
 supply pipe in order that the turbine might be placed high enough 
 above tail-water that it be accessible at all times without the 
 __ use of a tail-gate. Air is 
 
 exhausted from the crown 
 of the syphon by use of a 
 steam ejector whenever the 
 plant is to be started up. 
 This plant operates under 
 the low r head of thirty-one 
 inches and is said to work 
 very satisfactorily. 
 
 Fig. 310 shows a vertical 
 shaft turbine of the Victor 
 cylindrical gate type man- 
 ufactured by The Platt 
 Iron Works. This wheel 
 is set in an independent 
 case with provision made 
 for the attachment of a 
 cylindrical penstock con- 
 ducting the w r ater from the 
 head work to the wheel. 
 This figure shows a special 
 design by which the spec- 
 ial generator is set on col- 
 umns resting directly on 
 the wheel case. 
 
 Fig. 311 shows the plant 
 of Trenton Falls, New 
 York, of the Utica Gas and Electric Company. The wheel is a 
 Fourneyron turbine, manufactured by The I. P. Morris Company, 
 operating under a 266 foot head, the water being conducted to the 
 wheel through a penstock the length and arrangement of which are 
 shown in Fig. 353. The wheel is provided with a draft-tube and is 
 regularly connected with the generator above. The moving parts 
 of both machines are carried by a vertical shaft bearing, shown in cut. 
 255. Some Installations of Vertical Wheels in Series. In the 
 last three illustrations wheels are shown of sufficient size and operat- 
 
 Fig. 310. 
 
Some Installations of Vertical Water Wheels. 511 
 
 Fig. 311. The Trenton Falls Plant of the Utica Gas and Electric Co. (I. P. 
 
 Morris Co.) 
 
512 
 
 Arrangement of the Reaction Wheel. 
 
 ing under sufficient head to be suitable for the independent operation 
 of the machine attached to them. In many cases, however, espe- 
 cially with low head, the arrangement shown in Fig. 308 and in 
 Figs. 325 to 329 inclusive, becomes necessary. In such cases 
 considerable loss is entailed by the use of shafts, gearings, and belts. 
 
 Fig. 312. Vertical Turbine for Sewall's Falls Plant of the Concord Electric Co. 
 
 These losses are so large that it is desirable to avoid or reduce 
 them if possible. For this purpose vertical wheels are sometimes 
 placed tandem as shown in Diagrams C and D, Fig. 306. This 
 type of plant is also illustrated by Figs. 312 and 313 which are 
 illustrative of wheels installed in the plant of the Concord Electric 
 Company, at Concord, N. H. 
 
Some Installations of Vertical Wheels in Series. 
 
 513 
 
 Fig. 312 shows tandem wheels for this plant as designed and 
 manufactured by The Allis-Chalmers Company of Milwaukee, 
 .. and are described in further detail on page 
 
 Fig. 313 is a view of a 
 double vertical unit, designed 
 and built for the Concord 
 Electric Company by The S. 
 Morgan Smith Company of 
 York, Pa. This form of in- 
 stallation has the advantage 
 of a greater concentration of 
 the machinery. This type of 
 installation, while quite com- 
 mon in Europe, is somewhat 
 new in this country and pre- 
 sents several novel and desir- 
 able features. 
 
 256. Some Installations 
 of Horizontal Water 
 Wheels. Most machines to 
 be operated by water wheels 
 are built with horizontal shaft, 
 and, as a direct connection of 
 wheels to the machinery to 
 be operated involves a min- 
 imum loss in power and con- 
 sequent greater efficiency 
 than with the various com- 
 plicated arrangements often 
 necessary with vertical 
 wheels, the horizontal wheel 
 becomes desirable and is 
 
 adopted whenever practicable in a modern water power plant. The 
 type of such a plant is well illustrated by the power-plant at Turner's 
 Falls, Massachusetts, shown by Fig. 314. The single horizontal wheel, 
 direct-connected to th*e machinery to be operated, is perhaps already 
 sufficiently described in the preceding pages. The arrangement of 
 two or more wheels for such purposes deserves careful consideration. 
 Figs. 315 and 316 show a plan and section of a double unit, for use in 
 an open penstock, as manufactured by The Dayton Globe Iron 
 Works Company of Dayton, Ohio. These figures show a plain, 
 
 Fig. 313. 
 
5i4 
 
 Arrangement of the Reaction Wheel. 
 
Some Installations of Horizontal Water Wheels. 
 
 cylindrical, draft-chest connected with a common draft-tube. The 
 details of the arrangement can perhaps be better seen from the half- 
 tone, Fig. 320, which illustrates two of these units conneted 
 together tandem. 
 
 Fig. 315. Section Double Wheel with Common Draft Tube. (Dayton, Globe 
 
 Iron Works Co.) 
 
 Fig. 316. Plan. 
 
 Figs. 317 and 318 show a similar double unit manufactured by 
 the same company. This unit is shown set in a closed flume for 
 connection by a penstock of suitable size with the head works. In 
 Fig. 318 the chest, into which the turbines discharge, is designed 
 so as to give a certain independence to- the discharge of the two 
 turbines until they come to the draft-chest below the wheel. The 
 turbine case, shown in Fig, 316, seems to have more room than 
 
516 
 
 Arrangement of the Reaction Wheel. 
 
 necessary in the upper portion of the case in which interference of 
 the two streams and much eddying are possible, all of which is ob- 
 viated in the the design .shown in Fig. 317. The writer knows of 
 no experiments which show conclusively that such loss actually 
 occurred. More information is needed along this line than is now 
 accessible to the engineer. 
 
 Fig. 317. Double Horizontal Turbine in Closed Penstock (Dayton Globe Iron 
 
 Works Co.) 
 
 Fig. 318. Plan. 
 
 Fig. 319 is a cross-section of a double unit of the Samson tur- 
 bine, manufactured by The James Leffel and Company of Spring- 
 field, Ohio. This shows a design in which careful attention is 
 given to the maintenance of a uniform and slowly decreasing ve- 
 locity from the time the water reaches the wheel until it passes 
 from the common draft-chest into the draft-tube below. 
 
Some Installations of Horizontal Water Wheels. 
 
 257. Some Installations of Multiple Tandem Horizontal Wheels. 
 Two double units of the wicket gate type, similar to the double 
 units shown in Fig. 315, are illustrated by Fig. 320. These turbines 
 were manufactured by The Dayton Globe Iron Company of Day- 
 ton, Ohio, and are shown with the upper portion of the case removed 
 so that the arrangement of the wheels and the gate mechanism are 
 clearly visible. The gates are moved by a cylindrical ring to which 
 
 Fig. 319. Double Horizontal Turbine for Open Penstock. (James Leffel & Co.) 
 
 each gate is attached independently. The ring is moved by the 
 link connecting the gate ring to the governor rod which, by its ro- 
 tating, opens or closes the gate as the power needed requires. 
 
 Two double units with cylindrical gate, as manufactured by The 
 S. Morgan Smith Company of York, Pennsylvania, are shown 
 in Fig. 321. The bulkhead casing and the coupling to which the 
 machinery to be operated must be attached, are shown at the left. 
 In this case the governor rods have a horizontal movement, the 
 upper rod moving backward and the lower forward in order to 
 open the cylinder gate. 
 
 Figs. 322 and 323 show a section through one of the main units 
 and a plan of the power house and turbines of The Soiuthern Wis- 
 consin Power Company now under construction at Kilbourn, Wis- 
 consin, on the designs and under the supervision of the writer. 
 This plant consists of four main units, each generator having a 
 capacity, at full load, of 1650 kilow r atts and an overload capacitv 
 of 25 per cent. Each unit is direct-connected to six 57" turbines 
 now under construction by The Wellman-Seaver-Morgan Com- 
 
Arrangement of the Reaction Wheel, 
 
Soir.e Installations of Horizontal Water Wheels. 519 
 
520 Arrangement of the Reaction Wheel. 
 
 pany of Cleveland, Ohiou Each turbine unit is set in a separate 
 penstock controlled by three independent sets of gates. The four 
 center wheels discharge in pairs into common draft-tubes, while the 
 two end wheels have independent draft-tubes. All of the bearings 
 within the flume are accessible by independent wrought iron man- 
 hole casings. 
 
 Fig. 324 shows four pairs of 45" Samson horizontal turbines man- 
 ufactured by The James Leffel and Company of Springfield, Ohio. 
 These wheels have been installed for The Penn Iron Mining Com- 
 pany of Vulcan, Michigan, where two such units are now in opera- 
 tion. Eight similar units, designed -to deliver 1400 H. P. under 14 
 foot head, are now under construction by The James Leffel and 
 Company and are to be installed in the plant designed by the 
 writer for The Economy Light and Power Company at Dresden 
 Heights, Illinois, the general arrangement of which is shown by 
 
 Fig. 350. 
 
 When the head increases above 20 or 30 feet, it may become de- 
 sirable to convey the water from the head-work by means of a 
 closed penstock as shown in the case of the plant of The Winnipeg 
 Electric Railway Company (See Fig. 340). 
 
 In this plant are shown four wheels in tandem, direct connected 
 to a generator. The bell-mouthed entrance to the penstock should 
 be noticed, also the air inlet pipe which is designed to admit the 
 air into the penstock when the same is to be emptied, and to admit 
 the water gradually and without shock when it is again filled. 
 When the head becomes still higher the closed penstock .becomes 
 imperative as in the case with The Shawinigan Water and Power 
 Company's plant shown in Fig. 338 where a head of 135" is utilized. 
 Similar arrangements and connections for single and double wheels 
 with penstock are those of The Dodgeville Electric Light and 
 Power Company, shown in Fig. 337, and that of The Hudson River 
 Power Company's plant at Spier's Falls, as shown in Fig. 335. 
 
 The plant of The Nevada Power and Mining Company shown in 
 Fig. 341, involves tangential wheels operating with needle nozzle 
 and discharging freely into the tail race below. 
 
 In the selection and installation of reaction wheels a con- 
 siderable latitude in the choice and details of arrangement is possi- 
 ble and it is only after a careful examination and consideration of 
 all the conditions of installation that the correct size, speed, and 
 arrangement of the wheels can be obtained. Numerous failures, 
 more or less serious, in the past have fully shown the fact that 
 
Some Installations of Horizontal Water Wheels. ' 521 
 
 CM 
 CM 
 
 CO 
 
 bo 
 
 B 
 
5 22 
 
 Arrangement of the Reaction Wheel. 
 
 
 i 
 
 1 
 
 r 
 
 t: 
 
 ^ y~r^ 
 
 if 
 
 i 
 
 :> '. 
 
 
 
 
 
 ^3 
 
 1 
 
 T-$ 
 
 ' 
 
 - 
 
 
Some Installations of Horizontal Water Wheels. 
 
 523 
 
524 Arrangement of the Reaction Wheel. 
 
 this work demands the most careful attention and investigation of 
 the engineer and should be attempted only after the most thor- 
 ough study and mature deliberation. 
 
 258. Unbalanced Wheels. In installing horizontal wheels it is 
 usually desirable to use them in pairs with two, four, six or eight 
 turbines in tandem. It is, of course, possible to introduce an odd 
 number of wheels and this is frequently done where it seems to be 
 desirable. There is an advantage is an even number of wheels for 
 in this case the wheels may be, and should be, so arranged as to 
 balance the thrust by the union of a right hand and left hand wheel 
 in each pair. Where an odd number of wheels is introduced, an 
 unbalanced condition arises which can only be taken care of by a 
 thrust-bearing which, at the best, is an additional complication 
 often unsatisfactory and should be avoided if possible. 
 
 There is another cause of unbalanced condition which may be 
 here mentioned. If a pair of wheels is so joined together as to 
 use a common draft-tube then, on starting the wheel, the vacuum 
 formed in the draft-tube is co-mmon to both wheels and therefore 
 balanced. If, on the other hand, the wheels have separate draft- 
 tubes, when the wheels are started a partial vacuum is commonly 
 created in one of the draft-tubes in advance of the other, or even 
 when the wheels are in operation the vacuum in one draft-tube is 
 not as great as in the other, creating thereby a thrust in one di- 
 rection or the other which must be balanced by the connection of 
 the two draft-tubes by an air pipe or must be taken up by a thrust- 
 bearing as in the case of a single wheel. 
 
CHAPTER XXI. 
 
 THE SELECTION OF MACHINERY AND DESIGN OF 
 
 PLANT. 
 
 259. Plant Capacity. The selection of machinery for a power 
 plant depends upon numerous conditions. In the first place, for 
 permanent and constant operation, the machinery must be so 
 selected that its total capacity shall be great enough to take care 
 of the maximum load and have at least one unit in reserve so that 
 if it becomes necessary to shut down one unit for examination or 
 repairs, the plant will still be capable of carrying the maximum 
 load for which it was designed. 
 
 The desirable reserve capacity of any plant depends on the con- 
 tingencies of the service or the degree of liability to disabling acci- 
 dent involved in the operation of any plant, and on the relative 
 cost of such reserve capacity and the damages which might be sus- 
 tained if the plant should at any time become disabled as a whole 
 or in part and incapable of furnishing all or any part of the power 
 for which it was designed. In many manfacturing plants the occa- 
 sional delays caused by the entire suspension of power on account 
 of high or low water, or for the necessary repair to machinery, are 
 not serious if cheap power is available for the remainder of the 
 year. For the operation of public utilities, and the furnishing of 
 light and power for diverse municipal and manufacturing purposes, 
 the matter becomes more serious and necessitates a sufficient du- 
 plication of units to practically assure continuous operation. 
 
 For paper mills and other manufacturing purposes water powers 
 are utilized in which the head and consequent power is practically 
 destroyed during high water conditions. For continuous and un- 
 interrupted service such powers are available only with auxiliary 
 power that can be used during such periods. In the same manner 
 reserve capacity may be unnecessary, desirable or absolutely essen- 
 tial as the importance of maintaining uninterrupted power in- 
 creases. 
 
 260. Influence of Choice of Machinery on Total Capacity. A 
 study of the week day load curve of The Hartford Electric Light 
 
 32 
 
526 The Selection of Machinery and Design of Plant. 
 
 Company as shown by Fig. 257, page 422, will show that the load 
 for December, 1901, represents the maximum load which that plant 
 was called upon to carry during the year, and, consequently, was 
 the maximum load for which the machinery must have been se- 
 lected. A considerable variety of unit sizes would be possible 
 which would- fill the requirements of this load curve to a greater 
 or less extent. The maximum or peak load shown in December, 
 1901, was about 3,000 k. w. If a single machine were selected of 
 3,000 k w. capacity for regular operation, then, in order to have 
 one unit in reserve, it would be necessary to purchase two 3,000 
 k. w. machines or a total capacity of about 6,000 k. w. If, on the 
 other hand, machinery should be purchased with units of 500 
 k. w. capacity each, it would be necessary to have six of such units 
 in order to carry the maximum load of 3,000 k. w., and a seventh 
 unit of 500 k. w. capacity would be all that would be needed for the 
 reserve. This would give a total capacity to the plant of 3,500 k. w., 
 giving the capacity of the machine purchased some 2,500 k. w. 
 less than the plant first discussed. 
 
 261. Effect of Size of Units on Cost. The cost of machinery is 
 not in direct proportion to its capacity. The larger machinery is 
 somewhat less in price per kilowatt capacity than the smaller ma- 
 chinery. Hence the cost of the last plant suggested would be more 
 than 35/60 of the cost of the first plant. On the other hand, the in- 
 stallation of such a large number of units complicates the plant and 
 is undesirable. For this plant it would therefore be desirable to 
 select five units of 750 k. w. capacity each, or four units of 1,000 
 k. w. capacity each, giving in one case a total plant capacity of 
 3,750 k. w. and in the other case of 4,000 k. w. 
 
 A plant having units of 750 k. w. or 1,000 k- w. capacity each 
 would have a less total kilowatt capacity and, consequently, a less 
 first cost compared with a plant having units of 3,000 k. w. capacity. 
 Such a plant would also have a less number of units and conse- 
 quently less complication in the arrangement than a plant having 
 units of 500 k. w. capacity. 
 
 262. Overload. In the above consideration no mention is made 
 of overload capacity. The ordinary direct-current machinery can 
 be operated at about 25 per cent, overload for short periods of per- 
 haps one hour at a time without danger to the machinery. Alter- 
 nating machinery can be operated at 50 per cent, overload at similar 
 times or at 25 per cent, overload for two hour periods. In conse- 
 quence of this condition it is frequently possible to purchase ma- 
 
Economy in Operation. 527 
 
 chinery of considerable less capacity than the total load would in- 
 dicate, depending on the overload capacity of the machine for short 
 periods of maximum load. Unless, however, the estimated load 
 curve covers all possible contingencies for maximum power it is 
 desirable to retain this overload capacity as a provision for a second 
 condition which has not been fully covered in the estimate of the 
 daily load curve ; or, in other words, it is desirable to retain the 
 overload capacity as a factor of safety. 
 
 263. Economy in Operation. A second matter that needs the 
 careful consideration of the engineer in the selection of machinery 
 is the question of economic operation under variation in load. A 
 reference to the efficiency curve of most machines will show that 
 the machine will operate most efficiently at some particular load, 
 usually some .75 to full load, and will perhaps give the best results 
 at from .75 to 1.25 load, or to 25 per cent, overload. It therefore 
 becomes important to so select machinery that it will operate effi- 
 ciently at all conditions of Joad. 
 
 An examination of the load curve of The Hartford Electric Light 
 Company for the full week day load in March, June, September 
 and December, will show that for securing the most efficient results 
 at all times in the day, and at all times in the season, units of 500 
 k. w. capacity would apparently be the best. Such units would 
 take care, efficiently, of the minimum loads that occur at 6 :oo 
 A. M., between 12:00 and I :oo P. M., and at about 7:00 P. M. At 
 such times one of these units would operate efficiently; but in 
 most cases the period at which it could be operated singly would 
 be for a few minutes only, or perhaps for an hour at the most, when 
 the additional unit would have to be cut in. A 750 k. w. generator 
 would operate with almost as great an efficiency at these times and 
 it would, with its overload capacity, take care of the load for a much 
 greater period of time each day. The 1,000 k. w. machine would 
 perhaps fulfill these requirements even to a greater degree. While 
 it would be less efficient at the minimum point of the load, it would 
 have the advantage of operating singly for a much wider range of 
 load and the additional advantage that, as a rule, the larger the ma- 
 chine the higher the full load efficiency curve. 
 
 The complications resulting from the numerous machines, and 
 the losses entailed thereby, have also to be considered and must be 
 carefully weighed in this connection. 
 
 The circumstances of operation and many local conditions, which 
 appertain particularly to the plant in question, must be weighed in 
 
528 The Selection of Machinery and Design of Plant. 
 
 connection with the selection of this machinery. There is no defi- 
 nite law by which the selection of machinery for any plant can 
 be reduced to an exact science, and several combinations of ma- 
 chinery are possible in almost any plant and will give reasonable 
 satisfaction. 
 
 In the above discussion only units of a uniform capacity have 
 been considered and it is usually desirable, other things being equal, 
 to have similar machines so that a minimum number of repairs 
 and duplicate parts may be kept in stock. On the other hand, if a 
 long, low night load is probable, it may be desirable to install one 
 or more units of a capacity suitable to carry such load efficiently. 
 
 264. Possibilities in Prime Movers. A third matter for the 
 careful consideration of the designing engineer is the possibility 
 of a prime mover that is to be used for operating the machines in 
 question. If a steam or gas engine is to be used as the motive 
 power, there is a wide range of selection in speed, capacity, and 
 economy of such machinery, and, as a general rule, the prime mover 
 may be selected to conform to the generator or other machine that 
 is to be operated thereby. In the selection of water wheels for 
 prime movers the conditions are radically different and the selection 
 of the size and capacity of the units to be operated is "often modi- 
 fied or controlled by the waterwheels and the conditions under 
 which they will be obliged to operate. 
 
 In the selection of the water wheel one of the most important 
 matters is the head and the range of heads under which the wheel 
 will be called upon to operate. While it is possible to select a wheel 
 so that it will operate at almost any reasonable speed under a con- 
 siderable head, yet the capacity or power of the wheel rapidly de- 
 creases in amount with the speed, and if the speed be too high it 
 will be necessary to join two or more wheels in tandem in order to 
 furnish the power necessary to operate the machinery selected. 
 This is perfectly feasible and is done in a great many cases. 
 
 265. Capacity of Prime Movers. It is important to note that if 
 the generator or other machinery to be operated is to be operated 
 under overload conditions, the maximum power to be generated 
 must be kept fully in mind in the selection of a prime mover. In 
 the case of steam engines, these engines can be commonly operated 
 under overload conditions. They are usually rated at their most 
 efficient capacity and can sometimes be operated to 50 per cent. 
 above their normal rating, although their economy under such con- 
 ditions is apt to materially decrease. Gas engines, on the other 
 
Power Connection. 529 
 
 hand, are commonly rated at very nearly their full capacity and 
 hence the machinery which they are to operate can be operated only 
 to about the normal rated capacity of the engine. 
 
 Water wheels are commonly rated in the catalogues of manu- 
 facturers at very nearly full gate and consequently at full power. 
 In some cases they are rated at about seventh-eighths gate so that 
 a small margin of additional power is availalble. In the selection 
 of a water wheel, therefore, it is important that a careful study 
 be made of the actual power that the wheel can generate under full 
 gate and at minimum head. This should be sufficient to operate the 
 machinery at its maximum load. 
 
 266. The Installation of Tandem Water Wheels. The installa- 
 tion of two wheels set tandem, either horizontally or vertically, 
 and directly connected with the machine by a common shaft, is 
 very common and this may be increased to four, six, or occasionally 
 to eight turbines. Every additional machine, however, involves the 
 introduction of increased diameter in the shaft, of additional bear- 
 ings which must be set and held in alignment, and a complica- 
 tion in the design and construction of the machinery which should 
 be avoided wherever possible. The excuse for the attachment of a 
 number of turbines in tandem arrangement, and the com- 
 plexity of the plant of water wheels installed, lies in the sim- 
 plification of the machinery to be operated by them, and in the de- 
 sign and arrangement of other portions of the plant. The extent 
 to which the application of any principle is to be carried is a matter 
 of judgment and can be answered only by experience and the con- 
 sideration of all of the conditions involved in each particular case. 
 
 267. Power Connection. -With the turbine, as with every other 
 prime mover, it is important to convey the power to the machine 
 or machinery to be operated as directly as possible. The turbines 
 should be connected as directly as possible to the machinery to be 
 driven without any unnecessary intervention of gearing, shafting, 
 bearings, belts, cables, or other still more complicated methods of 
 power transmission. Every shaft, every gear, every belt, every 
 bearing and every other means of transmission that intervenes be- 
 tween the power generated in the wheel and the machine in which 
 the power is to be utilized means an extra loss and a decrease in 
 the efficiency of the plant. The machine to be operated should, 
 therefore, whenever practicable, be direct connected to the shaft 
 of the turbine instead of being connected with the turbine by any 
 intermediate mechanical means. (See Figs. 310, 314 and 322 
 
530 The Selection of Machinery and Design of Plant. 
 
Various Methods of Connection. 531 
 
 Direct connection of machinery and turbine involves a careful selec- 
 tion of both machinery and turbine so that both will work satis- 
 factorily at the same number of revolutions per minute. This 
 frequently involves extra expense that may not be justified in plants 
 for many purposes. 
 
 Other methods of connection or of power transmission are, 
 therefore, frequently necessary. With many low head installations 
 direct connections are impracticable for a number of reasons. 
 Sometimes various machines with diverse revolutions are to be 
 driven by the same wheel and the revolutions of the turbines in- 
 stalled must differ from some or all of the machinery to be operated 
 and some form of connection other than the direct must be used. 
 Even where the importance of the plant makes it desirable to use di- 
 rect connection, it frequently happens that a single turbine gives 
 an insufficient power at the speed desirable for connection to a 
 machine of the desired capacity. Under such conditions it is nec- 
 essary to unite two or more turbines in order to generate sufficient 
 power for the purposes for which the plant is to be designed. The 
 necessity of using a large number of turbines in a single unit may 
 give rise to very long shafts and a large number of bearings, and 
 the loss due to such an arrangement is sometimes considerable, and 
 if poorly arranged will be almost or quite as inefficient as gearings 
 and shafting well maintained. 
 
 268. Various Methods of Connection in Use. The most common 
 form of turbine used is a single vertical turbine, connected by a 
 beveled crown gear and pinion to a horizontal shaft. Several of 
 such turbines are commonly coupled up to the same shaft and may 
 be set in a single or in separate wheel pits. Such types of installa- 
 tion are shown in Figs. 329 to 334. Fig. 325 shows the turbine 
 harness in the plant of The Oliver Plow Works at South Bend, 
 Indiana, installed by The Dodge Manufacturing Company. The 
 arrangement of the wheel is quite similar to that illustrated by 
 Fig. 334. Three or four vertical wheels are here each connected 
 by a gear and pinon with a horizontal shaft, which, in turn, is con- 
 nected to an electric generator. In all such cases more or less 
 energy is lost in transmitting the power through the gearing and 
 numerous bearings to the generator. Sometimes it is found desir- 
 able not to connect the generators directly with the main shaft, 
 but to connect the generator or other machines to be operated by 
 the power plant by belting them to driving pulleys attached to the 
 same horizontal shaft, as shown by Fig. 326, which shows the power 
 
53 2 The Selection of Machinery and Design of Plant. 
 
Various Methods of Connection. 
 
 533 
 
 plant of The Trade Dollar Mining-Company near Silver City, Idaho. 
 This, however, introduces another source of loss through these 
 belts but possesses a certain flexibility due to the ability to thereby 
 drive various small units at a variety of speeds by the simple process 
 of changing the diameter of the pulleys used to drive such machin- 
 ery. Sometimes rope drives can be used to advantage in place of 
 
 Fig. 327. Harness and Driving Sheaves, Southwest Missouri Light Co., 
 
 Joplin, Mo.* 
 
 belts. This is especially true where the distance is great or the 
 alignment other than direct. Examples of such connections are 
 shown by Figs. 327 and 328. 
 
 Direct connected plants are shown in Figs. 310, 314, 322, 335, etc. 
 
 269. Use of Shafting. A shaft connecting a machine to a prime 
 mover, or imposed in any manner in any power transmission, must 
 be carefully designed and constructed. It must be carefully aligned 
 and have its bearings carefully adjusted. Each bearing may be con- 
 sidered as a point in the alignment of a shaft, and, as two points 
 determine the direction of a straight line, it will be seen that each 
 additional bearing is objectionable for it increases the difficulty of 
 obtaining and maintaining a satisfactory alignment. When more 
 than two bearings are used each must be brought and maintained in 
 
 * Dodge Manufacturing Co., . Mishawaka, Ind. 
 
534 Th e Selection of Machinery and Design of Plant. 
 
 the best practicable alignment, both horizonally and vertically. All 
 bearings must be of sufficient size that the limit of bearing pres- 
 sure shall not exceed good practice and they must be sufficiently 
 adjustable so that the shaft shall have as complete and uniform bear- 
 
 Fig. 328. Plan Showing Harness, Rope Drive and Jackshaft. Southwest 
 
 Missouri Light Co.* 
 
 ing as possible over the entire surface of the box. Boxes and bear- 
 ings must be arranged for satisfactory lubrication so that under 
 the hardest service they will not become unduly heated. In order 
 to secure good results the best class of workmanship is necessary 
 and it is also necessary that the plant shall be carefully and prop- 
 
 *Dodge Manufacturing Co. 
 
The Wheel Pit. 535 
 
 erly maintained. A poor shaft, running in poor boxes, poorly 
 aligned, may consume most of the power generated. Shafting, to 
 be reasonably satisfactory, demands frequent and proper inspection, 
 constant lubrication, and proper maintenance or it will soon become 
 a source of great energy loss. 
 
 270. The Wheel Pit. The wheel is usually set in a chamber 
 called the wheel pit, flume, or sometimes the penstock, which is 
 connected with the head-race from which it can be separated by 
 suitable gates. 
 
 The wheel pit in the smaller plants has commonly been con- 
 structed of timber but in the larger plants is usually built of a more 
 substantial character, of concrete, plain or reinforced, stone or 
 iron. 
 
 Open pits are commonly used for heads up to 18 or 20 feet, and 
 may be used for considerably higher heads ; however, for higher 
 heads, closed flumes of reinforced concrete or steel are commonly 
 used, and such construction is usually connected with the head- 
 race by metal, wood or reinforced pipes, to which the term penstock 
 is commonly applied. This latter form of construction admits of 
 the use of wheels with heads of almost any height. 
 
 A number of wheels can be set in the same wheel pit, and are 
 commonly so set, especially where they are used together to 
 operate one machine. It is frequently desirable, however, to sep- 
 arate the turbines and set them in separate pits so that one or 
 more wheels can be shut down at any time without interfering 
 with the operation of the plant. The exent to which this arrange- 
 ment is carried is a matter of policy and depends upon a variety of 
 conditions which the engineer must settle for each particular case. 
 
 271. Turbine Support. The arrangement and construction of the 
 wheel pit must be such as to furnish a proper support for the tur- 
 bine in order to secure satisfactory operation. In many of the 
 earlier plants, the wheel pits were built of timber, with the turbine 
 case resting direc.tly on the timber floor, which was often improp- 
 erly supported. The result of such conditon has been that the tur- 
 bines settle out of alignment and much energy is expended in un- 
 due friction in the transmitting mechanism. The floor or founda- 
 tion on which the wheel case rests should be of a substantial char- 
 acter and of such a nature that it will not readily deteriorate and 
 allow the wheel to settle. It is usually desirable to support the 
 wheel by a column directly below the wheel case, which should rest 
 upon substantial foundations below the bottom of the tail-race, 
 
536 The Selection of Machinery and Design of Plant. 
 
 (See Fig. 331) In all events settlements and vibrations must be 
 prevented or reduced to a minimum in order to eliminate one of the 
 very important causes of loss which is frequently encountered in 
 water power plants. In many cases, due to defects of this kind, 
 water power plants are giving efficiencies of 50 per cent, and below, 
 where 75 or 80 per cent, should be obtained. 
 
 272. Trash Racks. The water entering the wheel pit from the 
 head-race commonly passes through a trash rack consisting of nar- 
 row bars of iron, usually y" by 3" in dimension, spaced i 1 /^" to 2" 
 between and reaching from above the head-waters to the bottom of 
 the wheel pit, the purpose of which is to strain out such floating 
 matter as may be brought by the current down the head-race and 
 which, if not taken out at this point, might float into the wheels 
 and if large and heavy enough, might seriously injure the same. 
 These racks 'have to be raked or cleaned out at intervals depending 
 on the amount of leaves, grass, barks, ice or other floating matter 
 in the stream. In water power plants on some streams where large 
 amounts of such floating matter occurs at certain seasons, it is 
 sometimes necessary to keep a large number of men constantly 
 at work keeping the racks clear. 
 
 The accumulation of material on the racks will sometimes shut 
 off the entire flow of water if attention is not given to keeping them 
 clear; hence it is sometimes necessary to so design the racks and 
 their supports that they may sustain the entire head of water. 
 
 The racks are usually made of barb wire held apart by spools be- 
 tween each pair of bars and held together by bolts passing through 
 the spools and joining together such a number of bars as may be 
 convenient for handling. The spools should usually be placed near 
 the back of the bar so as to allow the rake teeth to pass readily. 
 .The rack should be situated at an angle so as to afford facilities 
 for raking. The deeper the water, the greater should be the in- 
 clination, as with long racks, and especially with high velocities, the 
 clearing of the racks becomes more difficult. 
 
 Chain racks and automatic mechanical racks have been attempted 
 but without satisfactory results. 
 
 Where trouble occurs from ice, involving much winter work, it 
 is frequently desirable to cover the racks with a house in order to 
 protect the workmen. 
 
CHAPTER XXII. 
 
 EXAMPLES OF WATER POWER PLANTS. 
 
 273. Sterling Plant. A rear elevation (Fig. 329) of the plant 
 which was designed by the writer for The Sterling Gas and Electric 
 Company of Sterling, Illinois, shows three 50" vertical Lefrel wheels 
 connected to a common shaft by beveled gearings. 
 
 The general type of harness used is fully shown in the plan and 
 elevation and needs no further description. 
 
 This plant is located on the Sterling race and is next to the last 
 plant on the race on the Sterling side of Rock River. (See Fig. 345.) 
 The head developed at this plant is about 8 feet, and the power of 
 each wheel is about 115 horse power. Each wheel is set in an inde- 
 pendent wheel pit which can be closed by means of a gate, as shown 
 in Fig. 332. In order to make repairs on any wheel without inter- 
 fering with the other wheels, the wheels and harness are well sup- 
 ported from the foundation, a very essential condition for perma- 
 nently maintaining a high efficiency. The discharge pit is of ample 
 size, so that the velocity with which the escaping waters leave the 
 draft tube is reduced to a practical minimum. A rack, to keep 
 coarse floating material from the wheel, is placed in front of the 
 penstock and is shown in Fig. 331, in section, and in Fig- 332, 
 in partial elevation. The shaft ojf this plant is extended into the 
 adjacent building and to it are belted the generators which supply 
 electric current for light and power purposes in the city of Sterling. 
 An engine is also connected to this main shaft and may be utilized 
 in case of extreme low water conditions, where sufficient water for 
 power is not available, or for flood conditions where the head is 
 practically destroyed. 
 
 274. Plant of York-Haven Water Power Company. Figure 333 
 shows the arrangement of the power station of the York-Haven 
 Water Power Company on the Susquehanna River at York, Pa. 
 
 The power house is 478 ft. long and 51 ft- wide. The head-race 
 is 500 ft. long and of an average depth of 20 ft. The wheel pits are 
 19 ft. deep and extend the entire width of the power house, open- 
 
538 
 
 Examples of Water Power Plants. 
 
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Plant of the Sterling Gas and Electric Light Co. 539 
 
 
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54 
 
 Examples of Water Power Plants. 
 
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 Fig. 331. Wheel Pit, Sterling Gas and Electric Light Co.'s Plant. 
 
Plant of the Sterling Gas and Electric Light Co. 541 
 
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 Examples of Water Power Plants. 
 
 ing to the forebay. They are protected by iron racks and are made 
 accessible by large head-gates of structural iron which weigh about 
 eleven tons each. 
 
 Fig. 333 Plant of York Haven Water Power Co. 
 (Electrical Engineer.) 
 
 Each pit contains two 78.5" inward flow turbines, hung from 
 spring bearings just above the runners. The turbines are set on the 
 floor of the pit and are about 6 ft. above the lower water mark. 
 
 The draft tubes are 10 ft. long and extend well under water. The 
 net head under normal conditions is about 21 ft. Float gauges on 
 the switch board show at a glance the height of head and tail 
 water. 
 
Plant of South Bend Electric Company. 543 
 
 The turbines were built by the Poole Engineering Company of 
 Baltimore, Mr., and are rated at 550 H. P. each, or 1,100 H. P. per 
 pair. 
 
 The turbines are of special design, the buckets being made of 
 pressed steel. The shaft extends vertically from the turbines to 
 bevel gears above the main floor and each is encased in a cast iron 
 tube to protect it from the action of the water and to secure long- 
 evity both to the shaft and to the bearings which retain it in line. 
 
 The present installation consists of ten pairs of turbines with 
 ten generators, equipped with Sturgess and Lombard governors. 
 
 The turbine bearings are supplied with oil from a gravity tank 
 located on the switch-board gallery . 
 
 The generators are S. K. C, three-phase, 60 cycle alternators, 
 rated at 875 kilowatts, and generate a 2,400 volt current. The nor- 
 mal speed of the generators is 200 revolutions per minute. Two 250 
 K. W., 125 volt, S. K. C., compound-wound, direct-current exciters 
 furnish the exciter current to the generator fields.* 
 
 275. Plant of South Bend Electric Company. Figure 334 shows 
 the plant of the South Bend Electric Company at Buchanan, Mich- 
 igan, built in 1901. 
 
 The dam, which was constructed in 1895, is of the gravity type, 
 built of wood, with two rows of sheet piling below and one above 
 it. It is about 400 feet long, and affords an average head of 10 feet. 
 This is estimated to furnish a minimum of 2,000 h. p. for from 
 four to six weeks in a year, while the maximum will reach 5,000 h. p. 
 On an average, 2,500 h. p. is available for about three months and 
 4,000 h. p. for the remainder of the year. 
 
 The power house, placed a short distance below the dam, is 273 
 feet long and 40 feet wide. It is built of stone, with concrete foun- 
 dations, and slate roof. It parallels the river so that the water from 
 the turbines is discharged directly into the same. The regulating 
 gates are seven in number, and are operated by racks and pinions. 
 
 The water wheels are Leffel turbines of 68 inch vertical type, 
 300 h. p- each. They are geared to a line shaft, which extends nearly 
 the whole length of the building, and to the end of which the genera- 
 tor is coupled. A 40 inch vertical Leffel wheel is used for driving the 
 exciter, which is belted to an intermediate shaft, driven by gears. 
 The line shaft is divided into three units, so that either four, seven 
 or ten wheels can be used for operating the generator, depending 
 
 * See Electrical World, vol. 49, March 2nd, 1907. 
 
544 
 
 Examples of Water Power Plants. 
 
Spier's Falls Plant Hudson Water Power Co. 
 
 545 
 
 upon the load carried. In addition, the gears on the line shaft can 
 be thrown out of mesh, so that any water wheel can be repaired if 
 necessary. The plant is governed by two Lombard water wheel 
 governors driven from the line shaft. 
 
 A 20 ton hand-operated crane serves all the apparatus in the 
 building. 
 
 Fig. 335. Plant of Hudson Water Power Co. Spier's Falls Plant. Double 
 Horizontal Turbines in Steel Penstock. Central Discharge. (Engine- 
 ering Record.) 
 
 The generator is a 1,500 k. w., 60 cycle General Electric revolving 
 field type alternator supplying three-phase current at a pressure of 
 2,300 volts. The switch-board and transformers are located at one 
 end of the building. There are no high tension switches at the 
 power house. 
 
 The power is largely transmitted to South Bend, Indiana, a 
 distance of 16 miles, where the company has a steam power plant 
 
546 Examples of Water Power Plants. 
 
 which is always kept in such condition as to be put into immediate 
 operation. It is used, however, only in case of extreme low water, 
 at times of a heavy peak, or in case of accident to the transmission 
 line. The steam power house is used as a sub-station and distrib- 
 uting point.* 
 
 276. Spier Falls Plant of The Hudson River Power Transmission 
 Company. A cross section of the Spier Falls Power house is shown 
 in Fig. 335. A head of 75 feet, for operation of this plant, is derived 
 from a granite rubble, ashlar-faced, masonry dam across the Hud- 
 son River between Mount McGregor and the Luzerne Mountains. 
 The dam consists of 817 feet of spillway section, the remainder 
 of the dam, 552 feet, being built about 12 feet higher. Water 
 is admitted through arched gateways to a short intake canal de- 
 signed to carry 6,000 cubic feet per second with a velocity of three 
 feet per second. This canal distributes the water to ten 12' circular 
 steel penstocks which lead about 150 feet to the wheels. 
 
 The power house is divided into three parts with the transformer 
 and switchboard room in one end, the wheel room and generator 
 room being formed by a longitudinal partition wall extending the 
 length of the building, with traveling crane in each. 
 
 Each unit consists of a pair of 42" or 54" cased S. Morgan Smith 
 wheels, governed by Lombard and Sturgess governors and direct 
 connected to 2,000 and 2,500 k. w. 40 cycle, three-phase revolving 
 field generators, built by The General Electric Company. 
 
 The transformer room contains seven 670 k. w. and thirty 833 
 k. w. General Electric air cooled transformers. 
 
 The power is distributed to Glen Falls, Schenectady, Saratoga 
 Springs and Albany, f 
 
 277. Plant of Columbus Power Company. The plant of the 
 Columbus Power Company is shown in Fig. 336. It is situated on 
 the Chattahoochie River just beyond the limits proper of the city 
 of Columbus, Georgia, at a shoal known as Lovers' Leap. At this 
 point a dam of cyclopean or boulder concrete with a cut stone spill- 
 way surface was erected giving a head of 40 feet. The length of the 
 dam is 975 feet 8 inches, with a spillway 728 feet long. 
 
 The power house is located at one end of the dam, so that no pen- 
 stocks are necessary. This applies to power house No. I. Power 
 
 to drive the plant of The Bibb Manufacturing Company is fur- 
 
 . 
 
 *|See Electrical World and Engineer, May 30, 1903 and July 14, 1906. 
 fSee Engineering Record, June 27th, 1903. 
 
Plant of Columbus Power Co. 
 
 547 
 
 nished from power house No. 2, being transmitted to the mill by a 
 rope drive system. The power house is supplied with pressure 
 water by means of penstocks let through the bulk-head wall, which 
 extends from house No. I to the river bank. In both cases the 
 tail water is discharged into the excavated river bed beneath the 
 power houses. Power House No. i is designed to develop 6,000 
 h, p. is six units, and No. 2 about 3,000 h. p. mainly in two units. 
 
 Fig. 336. Plant of Columbus (Ga.) Power Co. Double Horizontal Turbines 
 in Open Penstock. (Engineering News.) 
 
 Power house No. i is 137 feet long and 52 feet wide. It rests on 
 heavy stone foundations, the up-stream portions of which form the 
 heavy bulk-head which is pierced by six large openings for plant No. 
 i, by a smaller opening for the exciter units and a larger one for 
 the penstock leading to power house No. 2. 
 
 The openings for power house No. I are short flumes or chambers. 
 The back end of each of the wheel chambers is closed with a 
 heavy plate or bulkhead of cast iron and steel separating the wheel 
 chamber from the generator room. The racks are of the usual con- 
 
548 Examples of Water Power Plants. 
 
 struction and are supported on a framework of I-beams, giving 
 them an inclination of about 12 with the vertical. The gates to the 
 wheel chambers are of timber and are raised by hand by means of a 
 rack and pinion. 
 
 Each of the main wheel chambers contains a pair of horizontal 
 39 inch Hercules turbines, which discharge into a common draft 
 tube. The center line of the wheels is 15 feet below normal head 
 water level and 25 feet above normal tail water level. Under the 
 total head of 40 feet, each pair of wheels develops 1,484 h. p. at 200 
 r. p. m. The draft tubes are 7% feet in diameter at the turbine cas- 
 ing and 10 feet at the discharge end. 
 
 Each pair of wheels is direct connected to a two-phase alternator 
 built by the Stanley Electric Manufacturing Company. Each ma- 
 chine has a rated capacity of 1,080 k. w. at 6,000 volts and driven at 
 200 r. p. m. gives current at 60 cycles. Each is connected to the 
 wheel shaft by a flexible leather coupling. 
 
 There are two exciters directly connected to a single 18 inch 
 Hercules wheel. Each exciter is of the Eddy type, having a capac- 
 ity of 60 k. w. at 75 volts and running at 450 r. p. m. The exciters 
 are under the control of mechanical governors-* 
 
 278. Plant of The Dolgeville Electric Light and Power Co. In 
 Fig. 337 is shown the plant of The Dolgeville Electric Light and 
 Power Company at High Falls, New York, on what is now known 
 as the Auskerada River. 
 
 The dam is built of limestone masonry. The height at the spill- 
 way is 20 feet, with each abutment 6 feet higher. The total length 
 is about 195 feet. The width at the top is 7 feet and at the boittom 
 26 feet. The upstream side is perpendicular, the downstream side 
 being curved in order to properly receive and discharge the water. 
 The head gate, 12 ft. square and built in two sections, is fitted with 
 a by-pass gate to relieve the pressure when filling the flume. The 
 steel flume extends from the head gate to the power house, 520 feet 
 away. This flume is 10 feet in diameter, and is made of % mcn 
 steel plate, all longitudinal seams being double riveted. Just out- 
 side the dam is a vent pipe which assists in relieving the flume 
 from any sudden strains. 
 
 There are two 36 inch horizontal Victor turbines, each direct 
 connected to one 450 k. w. 2,400 volt two-phase Westinghouse gen- 
 
 * See Electrical World and Engineer, Jan. 23, 1904 or Eng. Record, Jan. 16, 
 1904. 
 
Plant of Dolgeville Electric Light and Power Co. 549 
 
550 Examples of Water Power Plants. 
 
 erator. Each of these wheels will develop 600 h. p. at 300 r. p. m., 
 under the working head of the water, which is 72 feet. They are 
 mounted in cylindrical steel casings, and discharge downward 
 through draft tubes, which extend a few inches below the sur- 
 face of the tail water. Each wheel is supplied with a Giesler elec- 
 tromechanical governor.* 
 
 279. Plant of the Shawinigan Water and Power Company. The 
 power plant of the Shawinigan Water and Power Company is lo- 
 cated on the St. Maurice River, Canada, at a point about 21 miles 
 from Three Rivers, 90 miles from Quebec, and 84 miles from Mon- 
 treal station. Fig. 338 shows a cross-section of their power station. 
 
 The St. Maurice River has a total length of over 400 miles, and is 
 supplied from a great many lakes and streams, the drainage area 
 being about 18,000 square miles. The water flow is very steady 
 throughout the year on account of the dense forest covering this 
 area, and is in the neighborhood of 26,000 cu. ft. per second, seldom 
 going below 20,000 cu. ft. per second. At the crest of the falls the 
 water flows over a natural rock dam and then down over the cas- 
 cade, making a fall of about 100 feet, then on in a narrow gorge 
 through which the water rushes swiftly and in which there is a 
 further fall of 50 feet. 
 
 The intake canal is 1,000 ft. long, 100 ft. wide and 20 ft. deep. Its 
 entrance from the river is located in a rather rapidly flowing stream 
 at the crest of the falls where the water is 20 feet deep, for the reason 
 that at times of rather high water, when the ice is flowing out of the 
 river, the current is expected to carry the ice past the mouth of the 
 canal. The end of the canal where it comes out at the face of the 
 hill is closed by a concrete wall from which the water is led through 
 steel penstock pipes down to the power house 130 feet below. 
 The concrete wall or bulkhead in the canal is 40 feet in height, 
 about 30 feet in thickness at the bottom and 12 feet at the top. 
 On top of this wall are set hydraulic cylinders for lifting the head- 
 gates and on top, covering the cylinders, is a brick gate house- The 
 steel penstocks are 9 feet in diameter. 
 
 The electrical apparatus was supplied by the Westinghouse Elec- 
 tric & Manufacturing Company and the turbines by the I. P. Morris 
 Co. 
 
 The three turbine units of the original installation are horizontal 
 double units of 6,000 h. p. These are direct connected with single 
 
 *See American Electrician, April, 1898, Vol. 10, No. 4. 
 
Plant of the Shawnigan Water Power Co. 
 
552 Examples of Water Power Plants. 
 
 5,000 h. p. generator units of the rotating field type, with twenty 
 poles. They are designed to operate at 180 r. p. m. giving two-phase 
 currents at 30 cycles per' second and 2,200 volts. A later installa- 
 
 Fig. 339. Plant of Concord Electric Co. Sewall's Falls Plant. Vertical Tur- 
 bines Connected in Tandem. (Engineering Record.) 
 
 tion consists of two 10,000 h. p. water wheels each driving a 6,600 
 "k. w. generator. (See Figs. 159 and 236.) 
 
 A separate penstock is provided for the exciter units which con- 
 sist of two 400 h. p. turbines direct connected to exciters.* 
 
 * See references as given: Eng. Rec. Apr. 28, 1900; Can. Engr., Ap-r. 1901, 
 May, 1901, and May, 1902; El. Wld. and Engr., Feb. 8, 1902; Cassier's Mag., 
 June, 1904. 
 
Plant of the Concord Electric Company. 553, 
 
 280- Plant of the Concord Electric Company. This plant, shown 
 in Fig. 339, is situated at Sewall's Falls on the Merrimac 
 River about four miles from the State House in Concord, New 
 Hampshire. The dam is a timber crib-work structure about 500' 
 long and gives a fall varying from 16' to 17'. The addition to the 
 old plant is the one shown in cross-section by Fig. 339 and is of 
 special interest due to the vertical shaft generating units which 
 were here installed. Comparative estimates showed that all other 
 features of the plant, except the machinery could be built cheaper 
 with the vertical shaft installation and the machinery added only 
 a few thousand dollars to the total cost, while other advantages de- 
 ermined its installation. / 
 
 The new installation consists of two units, each consisting of 
 3 55" bronze runners of the Francis type, mounted on a vertical 
 shaft and hung on a step bearing. The machines are of the Escher- 
 Wyss type built by The Allis Chalmers Company, American rep- 
 resentatives of the Escher : Wyss Co. The gates are of wicket pat- 
 tern, controlled by Escher-Wyss mechanical governors, also built 
 by The Allis Chalmers Company. The generators, which are direct 
 connected to the vertical shaft wheels, are of 500 k. w., 3-phase, 
 60 cycle, 2,000 volt, 100 r. p. m., revolving field type. Excitation is 
 furnished by one 75 h. p., 3-phase, 2,600 volt induction motor, direct 
 connected to a 45 k. w., 125 volt, compound wound D. C. generator. 
 The exciter unit runs at 680 r. p. m.* 
 
 281. Plant of Winnipeg Electric Railway Co. In Fig. 340 is 
 shown the power plant of the Winnipeg Electric Railway Company. 
 It is situated on the Winnipeg River at a point a few miles from 
 Lac du Bonnet, which is on a branch line of the Canadian Pacific 
 Railroad, 65 miles distant from the City of Winnipeg. 
 
 To obtain the necessary water, a canal 120 feet wide and with a 
 clear depth of 8 feet at normal low water was cut to the upper river 
 near Otter Falls. The canal is 8 miles long, with a drop of 5 feet 
 to the mile, equaling a total head of 40 feet. At the point where the 
 dam is located there is a natural fall, and the dam crosses almost at 
 the crest. 
 
 With the head and discharge available it is claimed that 30,000 
 electrical horse power can be developed. 
 
 The water wheels are all McCormick turbines regulated by Lorn- 
 bard governors. The turbine pits are protected by racks to keep 
 out ice, logs, etc. 
 
 *See Engineering Record, January 6th, 1906. 
 
554 
 
 Examples of Water Power Plants. 
 
Plant of Nevada Power Mining and Milling Co. 
 
 555 
 
 The electrical units consist of four 1,000 k. w. and five 2,000 k. w. 
 revolving field, 60 cycle, 2,300 volt, three-phase generators and two 
 100 k. w. 125 volt, direct-current exciters, all coupled to turbines, 
 and two 175 k. w. 125 volt direct-current exciters, coupled to three- 
 phase, 2,300 volt induction motors. 
 
 There are 15 transformers, comprising five banks, by means of 
 which the voltage "is stepped up from 2,300 to 60,000 volts for trans- 
 mission to the sub-station at Winnipeg over a distance of 65 miles.* 
 
 Fig. 341 Plant of Nevada Power Mining and Milling Co. 
 (Engineering Record.) 
 
 282. Plant of Nevada Power Mining and Milling Co. Fig. 341 
 shows a section through the plant of The Nevada Power Mining 
 and Milling Company on Bishop Creek, near Bishop, Cal. The 
 equipment of the station consists of two 750 k. w., 60 cycle, 2,200 
 volt, three-phase alternating-current generators, running at 450 
 r. p. m. and a 1,500 k. w. generator running at 400 r. p. m. This 
 latter generator is shown in the sectional drawing. There are two 
 exciters of 60 k. w. each, delivering current at 140 volts pressure. 
 Both exciters are operated by water wheels, and, in addition, one is 
 provided with an induction motor. The water wheels were made 
 by The Pelton Water Wheel Company of San Francisco. The two 
 
 * See Electrical World, June 23, 1906. 
 
556 Examples of Water Power Plants. 
 
 750 k. w. machines have Sturgess governors, and the 1,500 k. w. 
 machine has a type Q Lombard governor. Hand-control mechan- 
 ism is provided for each wheel. Oil is supplied to the governor by 
 two oil pumps operated by water wheels. 
 
 Water is taken from the creek at a small diverting dam and con- 
 veyed along the mountain-side in a pipe line. The pipe line is about 
 12,000 feet long, and consists of 6,700 feet of 42-inch wood-stave 
 pipe, 2,150 feet of 3O-inch wood-stave pipe, and 3,150 feet of 24-inch 
 steel pipe, all diameters being inside measurements. The 42-inch 
 pipe lies on a nearly level grade, the static head at the lower end 
 being about 30 feet. At this point are placed two 3o-inch gate 
 valves, one opening into the 3O-inch pipe and the other provided for 
 a future line. The 3O-inch pipe descends the hill to a point that 
 gives a static head of 265 feet. Here it joins the 24-inch steel pipe, 
 which descends a steep hill to the power house, the total static 
 head being 1,068 feet. 
 
 The power generated at the plant is transmitted, over a line of 
 stranded aluminum, equivalent to No. o copper, to Tonopah and 
 Goldfield, Nev., making a total length of line of 113 miles. In 
 crossing the White Mountains the line reaches an elevation of over 
 10,500 feet.* 
 
 LITERATURE. 
 
 1. Hydro-Electric Development at North Mountain, Cal. Elec. World and 
 
 Engineer, March 4, 1905. 
 
 2. The Northern California Power Company's Systems. Electrical World and 
 
 Engineer, Sept. 10, 1904. 
 
 3. The Power Plants of the Edison Electric Company of Los Angeles. Eng- 
 
 ineering Record, March 18, 1905. 
 
 4. The Fresno Transmission Plant. The Journal of Electricity, April, 1896. 
 
 5. The Edison Company's System in Southern California. Electrical World 
 
 and Engineer, March 11, 1905. 
 
 6. An 83-Mile Electric Power Transmission Plant, Cal. Cassier's Magazine, 
 
 November, 1899. 
 
 7. Bishop Creek, Cal. Hydro-Electric Power Plant. Electrical World, June 
 
 30, 1906. 
 
 8. The Hydraulic Power Development of the Animas Power and Water Com- 
 
 pany. April 14, 1906, Enginering Record. Electrical Review, 
 Jan. 30, 1904. Engineering News, Jan. 4, 1906. 
 
 9. Power Transmission in Pike's Peak Region. Electrical World and Eng- 
 
 ineer, July 26, 1902. Electrical World, May 26, 1906. Engineer- 
 ing Record, May 19, 1906. Engineering Record, July 19, 1902. 
 
 * See Engineering Record, June 30, 1906, or Electrical World of June 30, 
 1906. 
 
Literature. 557 
 
 10. New Water Power Development at New Milford, Conn. Engineering Rec- 
 
 ord, Feb. 13, 1904. 
 
 11. Berkshire Power Company, Canaan, Conn. Electrical Review, Sept 7, 1907. 
 
 12. Plant of Hartford Electric Light Company. American Electrician, March 
 
 1900. 
 
 IS.Hydro-Electric Power Plant and Transmission Lines of the North Georgia 
 Electric Company. Electrical Review, Oct. 20, 1906. 
 
 14. Atlanta Water and Electric Power Company's plant at Morgan Falls, Ga. 
 
 Engineering Record, Apr. 23, 1904. 
 
 15. Plant of The South Bend Electric Company, South Bend, Ind. Electrical 
 
 World and Engineer, May 30, 1903. 
 
 16. Plant at Rock Island Arsenal, Rock Island, 111. Western Electrician, Nov. 
 
 23, 1901. 
 
 17. The Hydraulic Development of the Sterling Hydraulic Company. Engin- 
 
 eering Record, Dec. 16, 1905. 
 
 18. Joliet Water Power of Chicago Drainage Canal. Engineering Record, 
 
 Apr. 19, 1902. 
 
 19. Development of Electric Power at Shoshone Falls, Idaho. Western Elec- 
 
 trician, Mar. 9, 1907. 
 
 20. Chaudiere Falls Power Transmission Company, Maine. Electrical World 
 
 and Engineer, June 15, 1901. Engineering News, May 7, 1903. 
 
 21. Water Power at Portland, Me. Electrical World and Engineer, Jan. 10, 
 
 1903. 
 
 22. Plant at Deer Rips, Me. Electrical World and Engineer, Apr. 8, 1905. 
 
 23. Great Northern Paper Company's New Mill, Me. Engineering Record, 
 
 Dec. 15, 1900. 
 
 24. A Submerged Power Station, Md. Engineering Record, Aug. 24, 1907. 
 
 25. High Pressure Power on the Housantonic, Mass. Electrical World and 
 
 Engineer, Feb. 13, 1904. 
 
 26. Development at Turner's Falls, Mass. Electrical World and Engineer, 
 
 Aug. 12, 1905. 
 
 27. Power on the Blackstone River, Mass. Electrical World and Engineer, 
 
 Oct. 14, 1905. 
 
 28. New Plant of Holyoke Water Power Company. Engineering Record, 
 
 Sept. 15, 1906. 
 
 29. Lowhead Hydro-Electric Developments in Michigan. Engineering Record, 
 
 Oct. 19, 1907. 
 
 30. Plant of the Michigan-Lake Superior Power Company, Sault Ste. Marie. 
 
 American Electrician, August, 1898. Engineering News, Sept. 
 25, 1902. Electrical World and Engineer, Nov. 8, 1902. 
 
 31. Transmission Plant of Kalamazoo Valley Electric Company, Mich. Am- 
 
 erican Electrician, July, 1901. 
 
 32. Water Power Development at Little Falls, Minn., and Its Industrial Re- 
 
 sults. Engineering Record, June 13, 1905. 
 
 33. St. Anthony Falls Water Power Plant, Minn. American Electrician, May, 
 
 1898. 
 
 34 
 
558 Examples of Water Power Plants. 
 
 34. Great Northern Power Company of Duluth, Minn. Electrical World, 
 
 July 28, 1906. 
 
 35. Electric Power Transmission Plant, Butte, Mont. American Electrician, 
 
 February, 1898. 
 
 36. Generating System of The Portland General Electric Company. Engineer- 
 
 ing Record, Aug. 12, 1905. 
 
 37. The Water Power Plant at Hannawa Falls, N. Y. Engineering Record, 
 
 Dec. 7, 1901. 
 
 38. The Water Power Development at Massena, N. Y. Power, December, 1900. 
 
 39. Hudson River Power Plant at Mechanicville, N. Y. American Elec- 
 
 trician, September, 1898. Engineering News, Sept. 1, 1898. Elec- 
 trical World, Nov. 13, 1897. 
 
 40. Hudson River Power Plant at Spier Falls, N. Y. Engineering Record, 
 
 June 27, 1903. Electrical Review, July 21, 1906. 
 
 41. Hydraulic Developments at Trenton Falls, N. Y. Electrical World, May 
 
 19, 1906. 
 
 42. Station of Rochester Gas and Electric Company. Electrical World and 
 
 Engineer, Nov. 13, 1903. 
 
 43. New Hydro-Electric Power Plant of Cornell University. Engineering 
 
 Record, May 20, 1905. 
 
 44. Hydro-Electric Developments in the Adirondacks. Electrical World, Apr. 
 
 26, 1906. 
 
 45. Hydraulic Development, Middletown, N. Y. Electrical World and Eng- 
 
 ineer, Aug. 8, 1903. 
 
 46. Niagara Falls Power Developments. Cassier's Magazine (Niagara Power 
 
 number). Engineering News, 1901, vol. 1, p. 71. 
 
 47. Power Plants of The Portland Railway Light and Power Company, Port- 
 
 land, Ore. Engineering News, June 27, 1907. Engineer, Apr. 
 15, 1907. 
 
 48. Garvin's Falls Plant, Manchester, N. H. Engineering Record, Jan. 24, 
 
 1903. Engineering News, March 19, 1903. Electrical World and 
 Engineer, May 28, 1904. 
 
 49. Concord, N. H. Water Power. Electrical World and Engineer, July 12, 1902. 
 
 50. Plant at Sewall's Falls, N. H. Engineering Record, Jan. 5, 1906. 
 
 51. Water Power at Manchester, N. H. Electrical World and Engineer, Jan. 
 
 17, 1903. 
 
 52. York Haven, Pa. Transmission Plant. Electrical World and Engineer, 
 
 Sept. 19, 1903. Electrical World, March 2, 1907. 
 
 53. Developments at Huntingdon, Pa. Electrical World and Engineer, Dec. 
 
 22, 1906. 
 
 54. Hydro-Electric Plant of the McCall-Ferry Power Company, Pa. Engineer- 
 
 ing Record, Sept. 21, 1907. Electrical Review, June 1, 1907. 
 
 55. The Warriors Ridge Hydro-Electric Plant at Huntingdon, Pa. Engineer- 
 
 ing Record, Dec. 22, 1906. 
 
 56. Hydro-Electric Developments on the Catawba River, South Carolina. 
 
 Electrical World, May 25, 1907. Engineering Record, July 30, 
 
 1904. Electrical World and Engineer, July 23, 1904. 
 
Literature 559 
 
 57. Construction of the Neals Shoals Power Plant on Broad River, S. C. Eng- 
 
 ineering Record, March 3, 1906. 
 
 58. A Large Hydraulic Plant at Columbia, S. C. The Engineering Record, 
 
 Jan. 1, 1898. 
 
 59. Greenville-Carolina Power Company, S. C. Electrical World, June 22, 
 
 1907. 
 
 60. Water and Electric Power Plant of the Utah Sugar Company. Engineer- 
 
 ing News, Apr. 13, 1905. 
 
 61. Bear River Power Plant and Utah Transmission Systems. Electrical 
 
 World and E'ngineer, June 18, 1894. 
 
 62. Plant of the Chittenden Power Company, Rutland, Vt. Engineering Rec- 
 
 ord, Dec. 9, 1905. 
 
 63. Plant of Vermont Marble Company, Proctor, Vt. Electrical World, Feb. 
 
 3, 1906. 
 
 64. Water Wheel Equipment in the Puget Sound Power Company's Plant. 
 
 Electrical World and Engineer, Oct. 22, 1904. 
 
 65. Hydraulic Power Plant on the Puyallup River, near Tacoma. Engineer- 
 
 ing Record, Oct. 1, 1904. Engineering News, Sept. 29, 1904. 
 Electrical World and Engineer, Oct. 1, 1904. 
 
 66. Snoqualmie Falls Water .Power Plant and Transmission System. Eng- 
 
 ineering News, Dec. 13, 1900. Western Electrician, Aug. 20, 1898. 
 Electrical World and Engineer, May 7, 1904. 
 
 67. Apple River Power Plant, Wisconsin. Electrical World and Engineer, 
 
 Dec. 8, 1900. 
 
 68. St. Croix Power Company, Wisconsin. American Institute of Electrical 
 
 Engineers, 1900. Engineering Record, March 3, 1906. Western 
 Electrician, Oct. 27, 1906. 
 
 69. The Lachine Rapids Power Plant, Montreal, P. Q. Engineering News, 
 
 Feb. 18, 1897. 
 
 70. Shawinigan Falls Electrical Development. Electrical World and Eng- 
 
 ineer, Feb. 1, 1902. Cassier's Magazine, June, 1904. Engineer- 
 ing Record, April 28, 1900. Canadian Engineer, April and May, 
 1901 and May, 1902. 
 
 71. 60,000-volt Hydro-Electric Plant, Winnipeg, Manitoba. Electrical World, 
 
 June 23, 1906. 
 
 72. DeCew Falls Power Plant. Engineer, Apr. 2, 1906. 
 
 73. Development of the Montmorency Falls. Electrical World and Engineer, 
 
 June 17, 1899. 
 
 74. The Rheinfelder Power Transmission. Electrician, March 26, 1897. 
 
 75. The Bellinzona, Italy, Hydro-Electric Station. Electrical World and Eng- 
 
 ineer, Sept. 16, 1905. 
 
 76. A Norwegian Water Power Plant. Electrical World and Engineer, Apr. 
 
 4, 1903. 
 
 77. An Italian 40,000-volt Transmission Plant. Electrical World and Eng- 
 
 ineer, Aug. 19, 1905. 
 
 78. Tyrol Hydro-Electric Power Station, Keiserwerke. Electrical World, May 
 
 11, 1907. 
 
560 Examples of Water Power Plants. 
 
 79. The Rome-Tivoli Electric Installation. Cassier's Magazine, March, 1899. 
 
 80. The Tusciano Hydro-Electric Power Station. The Engineer, July 16, 1906. 
 
 81. Hydraulic Station at Gusset, near Lyons, France. Electrical World and 
 
 Engineer, Dec. 9, 1905. 
 
 82. Hydro-Electric Plant of the City of Drammen, Norway. Electrical Re- 
 
 view, March 31, 1908. 
 
 83. The First British Hydro-Electric Power Transmission. Electrical World, 
 
 vol. 47, p. 108. 
 
 84. The Hydro-Electric Sation at Bogota. Engineering Record, Sept. 3, 1904. 
 
 85. The Sill Hydraulic Power Plant near Innsbruck. July 1, 1905. 
 
 86. The Electric Power and Transmission System of Schaffhausen, Switzer- 
 
 land. Electrical World and Engineer, March 19, 1904. 
 
 87. A Bohemian Hydro-Electric Plant. Electrical World, July 21, 1906. 
 
 88. Hydro-Electric Power Installation in lyo, Japan. Electrical World and 
 
 Engineer, July 9, 1904. 
 
 89. Electric Power at Jajce, in Bosnia. Cassier's Magazine, October, 1901. 
 
 90. 26,000-volt Installation at Grenoble, France. Electrical World and Eng- 
 
 ineer, Jan. 31, 1903. 
 
 91. An Unusual Water Power Plant at Kykkelsind, Norway. Engineering 
 
 Record, July 2, 1904. 
 
 92. The Hydro-Electric Plant at Lucerne, Switzerland. Electrical Review, 
 
 Aug. 11, 1906. 
 
 93. The Guanajuato, Mexico, Power Transmission. Electrical World and Eng- 
 
 ineer, Aug. 6, 1904. 
 
CHAPTER XXIII. 
 
 THE RELATION OF DAM AND POWER STATION. 
 
 283. General Consideration. In any water power plant the 
 water must be taken from some source, conducted to the wheels, 
 and discharged from the same at the lower head. To accomplish 
 this object there must be a head-race leading from the source of 
 supply to the plant which may be of greater or less length and in 
 which more or less of the available head may be lost in order to 
 produce the velocity of flow and overcome the frictional resistance. 
 
 Fig. 342. 
 
 After entering the plant the. water is discharged through the 
 turbine T into a tail-race of greater or less extent in which there 
 is also a loss caused by friction and velocity of flow, similar to that 
 already expended in the head-race. In Fig. 342 the total head 
 available is H; the head lost in the head-race is indicated by h ; 
 and the head lost in the tail-race is indicated by h 2 . The net energy 
 of the wheel is h = H h x h s , and a portion of h is also lost in 
 the slip, leakage, and friction of the machinery and transmission- 
 
 The power plant should be located with reference to the dam 
 so that (i) the greatest amount of head may be utilized at the least 
 expense : (2) the plant constructed should be as free as possible 
 from interruptions due to floods or other contingencies ; (3) the 
 location chosen should be at such a point where security of con- 
 struction can be accomplished at the minimum expense. 
 
 Each of these influences is of importance and the relative location 
 of the power plant and dam must depend upon these and various 
 other conditions which must be carefully considered. 
 
562 The Relation of Dam and Power Station. 
 
 284. Classification of Types of Development. For the purpose 
 of a clear understanding of the principles involved, the type of 
 development may be grouped or classified into : 
 
 First : Concentrated fall, in which the plant is built on the dam 
 or closely adjoining thereto, with a short or no race. In this case 
 the entire fall is concentrated by means of the dam and as a rule 
 this class of development is adaptable only to central power sta- 
 tions where one or two plants only are to be installed on the 
 power. 
 
 Second: Diversion type with dam. In this case the fall is de- 
 veloped by means of a dam in the manner conforming to the last 
 type but the water is distributed to one or more plants by means 
 of a long head-race canal through which the water flows to the 
 power station, after which it is discharged either into the stream 
 at some point below the dam or into a tail-race from which it is 
 finally discharged at a point lower down the stream. 
 
 Third: Diversion with or without dam. In this case the develop- 
 ment is installed with or without a dam at the head of the rapids 
 or fall which is to be utilized and the water is conducted through 
 a long head race, if land of a suitable elevation is available, or>, 
 otherwise, through a tunnel to a point immediately above the site 
 of the power station. From the end of the tail-race or tunnel the 
 water is carried to the plant through a metallic penstock. 
 
 Fourth : The fourth type is similar to the third except that where 
 the head-race or tunnel is used (the ground being unfavorable to 
 such construction or the expense of the same being unwarranted) 
 a long penstock of metal is provided to conduct tlie water from 
 the head works to the station. 
 
 Fifth : The fifth type is the tunnel tail-race type and involves con- 
 ducting the water through metallic penstock direct to the wheels 
 located at the minimum level and, after the water is discharged 
 therefrom, the provison of a tunnel tail-race for conducting the 
 water from the turbine to the point where it is to be discharged 
 back into the stream. 
 
 It is important to note in this case, as in the case of all other 
 classifications attempted, that such a classification is for the pur- 
 pose of systematizing the consideration of numerous diversified 
 types and bringing them to a similar basis for examination. In 
 the actual adaptation of plans of development, it is seldom any sin- 
 gle type will be found in its simplicity ; in most cases modifications 
 of the same become desirable or essential. 
 
Classification of Types of Development. 
 
 563 
 
 Fig. 343. 
 
564 The Relation of Dam and Power Station. 
 
 285. Concentrated Fall. In most of the low head water powers 
 the portion of the fall of the river which can be utilized is distrib- 
 uted over minor rapids and small falls and occupies a considerable 
 length of the stream. Where the head is small and the expense of 
 a dam to concentrate the head entirely at one point is permissible, 
 the power house may sometimes be located to advantage in the dam 
 itself. In this case the power house will constitute a part of the 
 dam itself. This is possible only where the length of the spillway 
 remaining is sufficient to pass maximum flood without an undue 
 rise in the head of the water .above the dam. In many such cases 
 this plan, which is represented by Diagram C, Fig. 343, meets 
 economical construction as it may both cheapen the cost of the 
 dam and reduce the excavation necessary for the wheel pit and tail- 
 race. The power house built at such point is, however, usually 
 directly in the line of the current and must be so constructed and 
 protected as to prevent its injury or destruction by floods, ice or 
 other contingencies of river flow. 
 
 In other cases, where the spillway available by the above plan is 
 not sufficient or where the plant is not properly protected by such 
 forms of construction, the plant may be constructed on one side 
 of the dam, receiving its waters from a head-race which joins the 
 river above the dam and discharges it into the river below, as 
 shown by Diagrams C and D, Fig. 343. Or, where the capacity is 
 suitable, the plant itself may receive the water directly from its 
 head gate from the river above the dam and discharge it through 
 a tail-race which will enter the river at some point below the dam, 
 as shown in Diagram A, Fig. 343. 
 
 In other cases, where the power is to be distributed to a number 
 of independent plants, raceways may be constructed on either or 
 both sides of the stream and from the dam, following the stream 
 downward along the bank and more or less approximately parallel 
 thereto as the nature of the conditions demand. The plant drawing 
 the water from this head-race may be distrbuted at various points 
 along the same, and from these plants the water will be discharged 
 after use either directly into the stream itself or into a tail race con- 
 necting such plants with a lower point farther down the stream, as 
 shown in Diagram E, Fig. 343. 
 
 286. Divided Fall. An independent tail-race is usually con- 
 structed to advantage where the dam concentrates only a portion of 
 the head or fall, leaving certain additional portions to be developed 
 by the use of the tail-race, which may, if desirable, enter the stream 
 
Classification of Types of Development, 
 
 565 
 
 Fig. 344. 
 
566 The Relation of Dam and Power Station. 
 
 at a point much farther down the river and at the foot of the rapids. 
 Where the fall of the stream is considerable, and the expense of 
 construction of the dam to suitable height to concentrate the entire 
 fall at a single point is inadvisable, it is often desirable to build a 
 dam to less height at perhaps considerably less expense and develop 
 at the dam only a portion of the total fall. From this dam a head- 
 race may extend to some considerable distance, and the water from 
 this head-race may be delivered to the power plant a mile or two 
 lower down the stream. From this head race, the water, after pass- 
 ing through the wheels, is carried directly into the stream at the 
 lower point, as shown in Diagram G, Fig. 344. 
 
 Under other conditions, where the topography of the country is 
 suitable, the head-race may be much less in extent, and a tail-race 
 substituted for receiving the waters after they have been used in 
 the wheel and then conducted to the river at or near the end of the 
 rapids, as shown in Diagram F, Fig. 344. 
 
 Under still other conditions the plant itself may be located imme- 
 diately at the dam and the tail waters may be conducted from the 
 turbine to a tail-race or tail-water tunnel to the lower end of the 
 rapids, as in Diagram H, Fig. 344. 
 
 The relation of head-race and tail-race is merely a question of 
 developing the power plant at the least cost and securing the max- 
 imum head, and the topographical conditions at the power site will 
 therefore determine which line of development will be best. In a 
 number of cases, where the head or fall is considerable and the 
 power development is large, and where the cost of land for head- 
 races would be almost or quite prohibitive, the stations have been 
 located in the immediate vicinity of the river and have delivered the 
 water into a tail-race tunnel, which frequently empties at a con- 
 siderable distance down the stream and at the lowest point of deliv- 
 ery that is practicable. In other cases it is more economical to run 
 open raceways for a portion of the distance and then conduct the 
 water under pressure by closed pipes to the wheels at the lower 
 point. 
 
 This last method is used particularly under high head and where 
 the water must be conducted for a reasonable distance over an irreg- 
 ular profile. 
 
 The quantity of water to be used, the head available, and the 
 value of power modify the arrangements which must be carefully 
 studied in view of the financial, topographical, and other modifying 
 conditions. 
 
Distribution of Water at Various Plants. 
 
 287. Examples of the Distribution of Water at Various Plants. 
 Fig. 345 is a plan of the power development on the Rock River at 
 Sterling, Illinois. The dam at this point is about 940 feet in length. 
 The power is owned by various corporations and private individuals 
 who have combined their interests in the dam and raceways and 
 
 ROCK 
 
 Sterling Hydraulic Company. 
 
 have organized The Sterling Hydraulic Company, whose function 
 is to maintain the same. The individual plants are owned, installed, 
 and operated by the various owners or by manufacturers who lease 
 the power. At this location races have been constructed at the foot 
 of the rapids, but these rapids continue to a point near the lower 
 end of the tail-race, and the plants farthest from the dam have the 
 highest falls. The fall varies from about 8 to 9% feet. 
 
The Relation of Dam and Power Station. 
 
 Fig. 346 shows the general arrangement of the canal of The Hoi- 
 yoke Water Power Company at Holyoke, Mass. The total fall of 
 the river at this point, from the head water above the dam to the 
 tail water at the lowest point down the stream, is about sixty feet. 
 The fall is divided into three levels by the various canals, marked : 
 ist level canal, 2nd level canal, and 3rd level canal. 
 
 Fig. 346. Canals of Holyoke Water Power Company. 
 
 The first level canal, which has a length of about 6,000 feet, is con- 
 structed as a chord across the bend of the river and is approximately 
 some 3,000 feet from the bend. The canal is about 150' wide near 
 the bulkhead and decreases to about 100' at the lo>wer end. The 
 water depth is about 20' at the upper end and about 10' at the lower. 
 The canals are all walled throughout their length to a height two or 
 three feet above the maximum water surface. The fall from the 
 first level to the second is about 20'. Various mills draw their water 
 supply from the first level as a head-race, and discharge into the 
 second canal as a tail-race. Near the upper end of the canal are a 
 few factories that draw water from the first level and discharge the 
 same into the river with a head of some 35 or 40 feet. 
 
 The second level canal is built parallel to the first and at a dis- 
 tance of about 400 feet nearer the river. The main canal is about 
 6,500 feet in length, but near the left hand of the map is shown to 
 
Distribution of Water at Various Plants. 
 
 569 
 
 Rear devotion of 
 
 Fig. 347. Kilboura Plant of Southern Wisconsin Power Co. 
 
57o 
 
 The Relation of Dam and Power Station. 
 
 sweep round towards the river and attain a reach of about 3,000 
 feet in length parallel thereto. The mills drawing their supply from 
 this canal discharge either directly into the third level or into the 
 river. The water supply from each of the lower levels is the tail 
 water from the next level above, but is also supplemented by over- 
 flows when the mills fed from the level above are not discharging 
 
 Fig. 348. Plant of The Lake Superior Power Co. 
 
 sufficient water to maintain the quantity needed in the lower level. 
 
 The fall from the third level of the river is essentially the same 
 for all the mills drawing water therefrom, but according to the stage 
 of the river ranges from 15 to 27 feet. 
 
 The flow of water in the first level is controlled by gates and its 
 height limited by an overflow of about 200 feet in length which 
 acts as a safety overflow and prevents any great rise in the head 
 water during times of flood. 
 
 288. Head-Races Only. Fig. 347 illustrates the general plan of 
 the hydraulic power development of The Southern Wisconsin Power 
 Company at Kilbourn, Wisconsin. Here the entire cross-section of 
 the stream is necessary in order to pass the maximum volume of 
 
Distribution of Water at Various Plants. 
 
 571 
 
572 
 
 The Relation of Dam and Power Station, 
 
Distribution of Water at Various Plants. 
 
 573 
 
 water, which amounts to about 80,000 second-feet. The plant has 
 therefore been constructed at one side of the river, receives the flow 
 through a series of gates built just above the dam, and discharges 
 the water into the river just below the bend in the river, as shown. 
 The plant now under construction is only a portion of that which 
 it is designed to ultimately install. The proposed future extension 
 of the power plant is shown by the dotted lines. 
 
 
 TWIN FALLS 
 
 Fig. 351. Possible Canal for Peshtigo River Development. 
 
 Fig. 348 shows the water power plant of The Lake Superior 
 Power Company at St. Mary's Falls, Michigan. The canal on the 
 American side begins just above the entrance to the American ship 
 canal and above the Soo rapids. The water is conducted through 
 this canal to a power house located below the rapids at the point 
 shown on the map. On account of the value of the land this canal 
 was designed for a velocity of flow of about 7%' per second with 
 full load of the plant, which was designed for about 40,000 h. p. 
 requiring a capacity with available head of 16.2 feet, of about 4,200 
 cubic feet per second. (See Engineering News of August 4th, 1898.) 
 35 
 
574 The Relation of Dam and Power Station. 
 
 Fig. 349 shows the plan of the hydraulic development of The 
 Economy Light and Power Company at Joliet, Illinois. The entire 
 installation as shown is owned by this company. The fall available 
 is about ii feet and is developed by a concrete dam which creates 
 the upper basin along which the power plant has been constructed. 
 The water flows through the flume gates directly on to the wheels 
 and is discharged into a tail-race built parallel with the river- A 
 
 49 
 
 SO 51 52 S3 54 55 
 
 MILES 
 
 Fig. 352. Profile of Peshtigo River. 
 
 certain amount of water is necessary for feeding the lower level of 
 the canal and this is supplied by a by-pass tunnel shown in dotted 
 line above the dam. This by-pass, which is slightly higher than 
 the elevation of the tail-race, is fed by the discharge of one of the 
 wheels, which operates under a less head than the other wheels in 
 the installation. 
 
 289. Plant Located in Dam. In Fig. 350 is shown the general 
 plan and elevation of the hydraulic plant at Dresden Heights on the 
 Des Plaines River just above its.junction with the Kankakee River. 
 These two streams unite at this point to form the Illinois River. 
 
 In this case the dam is built across a very wide valley and the 
 length of the dam is much greater than necessary or desirable to 
 
High Head Developments. 
 
 575 
 
 \ 
 
 S 
 
 V, 
 
 accommodate the flood flow of the 
 stream which is approximately 25,000 
 second-feet. In consequence, the pres- 
 ent power plant, as well as the pro- 
 posed extension to the power station, 
 will form a part of the 'dam itself and 
 the spillway will occupy only a portion 
 of the entire length of the structure 
 and is so designed as to maintain a sat- 
 isfactory head at times of flood flow 
 The head of the water above the dam 
 is controlled both by the length of 
 spillway and by six tainter gates by 
 means of which the level of the water 
 above the dam can be controlled at all 
 stages of flow. 
 
 290. High Head Developments. 
 Fig. 351 illustrates the general plan of 
 a possible method of development of 
 the Peshtigo River for The Northern 
 Hydro-Electric Company. The fall 
 available is shown by the profile, Fig. 
 352. It is proposed to construct a dam 
 above High Falls of sufficient height 
 to back the water over Twin Falls, and 
 to either develop the. power at High 
 Falls and Johnson' s Falls independently 
 or conduct the water by a canal to Mud 
 Lake, thence to Perch Lake, thence to 
 the head work to be be built above 
 Johnson's Falls, where a head of about 
 110' will be available. If a single de- 
 velopment is chosen the water will be 
 be conducted from the head works 
 through penstocks to the power plant 
 to be built at the base of the bluff below 
 Johnson's Falls. The canal in this case 
 will conduct the head waters with very 
 little fall to the immediate site of the 
 plant, thence by penstocks to the tur- 
 bine located in the gorge below. 
 
576 
 
 The Relation of Dam and Power Station. 
 
 Fig. 354, Niagara Falls Power Development. 
 
Head Developments. 
 
 577 
 
 Fig. 353 is a plant of the power development at Trenton Falls, 
 New York. The upper portion of the fall is developed by a dam 
 about 60' in height, which is connected by an 84" pipe line with the 
 turbine located in the power house about two miles below. The 
 turbines used in this development are the Fourneyron turbines, 
 which are described in Chap. XIX, and are illustrated by Fig. 311. 
 
 Fig. 354 is a general plan of the water power developments at 
 Niagara Falls. The first development was that of The Niagara 
 
 Fig. 355. 
 
 Falls Hydraulic and Manufacturing Company. By means of a 
 canal the water is taken from the upper end of the rapids and con- 
 ducted to the lower bluff on the American side, and distributed, by 
 open canals, to various plants located along this bluff.. 
 
 The second plant constructed was chat of The Niagara Falls 
 Power Company, in which power is developed by the vertical shafts 
 connecting with a tail-water tunnel which discharges into the river 
 just below the new suspension bridge. 
 
578 The Relation of Dam and Power Station. 
 
 On the Canadian side are shown three plants. 
 
 The Ontario Power Company secures its water supply from the 
 upper portion of the rapids, conducting it through steel conduits 
 to a point above the power house and thence by penstocks to the 
 wheel, located in the gorge below the falls. 
 
 In the plants of The Toronto and Niagara Power Company and 
 The Canadian-Niagara Power Company, the water is taken from 
 above the Falls and discharges through penstocks to wheels located 
 at the base of a shaft and thence into tunnels, discharging into the 
 river at a point below the Falls. 
 
 Fig. 355 illustrates the plant of The Niagara Falls Hydraulic and 
 Manufacturing Company, which is supplied by water from the 
 hydraulic canal above mentioned. The water is conducted from the 
 forebay by a vertical penstock to which is attached several wheels 
 which deliver the water into a tail-race tunnel and thence into the 
 gorge below. 
 
 The plant arrangements above described are typical of many now 
 in use both in this country and in Europe. It is at once obvious that 
 in considering this subject each particular location is a problem by 
 itself which must be considered in all its bearings ; but an under- 
 standing of the designs and arrangements already in use forms a 
 satisfactory basis fromi which a judicious selection can be made 
 with suitable modifications to take care of all the conditions of 
 topography and other controlling conditions. 
 
CHAPTER XXIV. 
 
 PRINCIPLES OF CONSTRUCTION OF DAMS. 
 
 291. Object of Construction. A dam is a structure constructed 
 with the object of holding back or obstructing the flow and elevat- 
 ing the surface of water. Such structures may be built for the fol- 
 lowing purposes : 
 
 First : To concentrate the fall of a stream so as to admit of the 
 economical development of power. 
 
 Second : To deepen the water of a stream so as to facilitate nav- 
 igation and to so concentrate the fall that vessels may be safely 
 raised from a lower to an upper level by means of locks. 
 
 Third : To impound or store water so that it may be utilized as 
 desired for water supply, water power, navigation, irrigation, or 
 other uses. 
 
 Fourth : In the form of mine dams or bulk heads to hold back 
 the flow of water which would otherwise flood mines or shafts or 
 cause excessive expense for its removal. 
 
 Fifth: As coffer-dams for the purpose of making accessible, 
 usually for construction purposes, submerged areas otherwise inac- 
 cessible. 
 
 292. Dams for Water Power Purposes. The primary object of 
 a dam constructed for water power purposes is to concentrate the 
 fall of the stream so that it can be developed to advantage at one 
 point and so that the water thus raised can more readily be delivered 
 to the motors through raceways and penstocks of reasonable length. 
 This object is sometimes accomplished in rivers with steep slopes 
 or high velocities by the construction of wing dams which occupy 
 only a portion of the cross-section of the stream, but cause a head- 
 ing up of the water and direct a certain portion of the flow into 
 the channel or raceway through which it flows to the wheels. 
 Usually in streams of moderate slope the dam must extend entirely 
 across the stream in order to concentrate sufficient head to be of 
 practical utility. 
 
580 Principles of Construction of Dams. 
 
 Wing dams can be used at the head of high falls where only a 
 portion of the volume of flow can be utilized, as at Niagara Falls, 
 or in rapid rivers w r here a portion of the flow is to be directed into 
 a narrow channel for utilizing low heads by means of undershot or 
 float wheels as is frequently done for irrigation purposes. Where 
 the full benefit of both head and volume is to be utilized the dam 
 must extend from bank to bank and be constructed of as great a 
 height as possible. 
 
 293. Height of Dam. To utilize a river to the maximum extent 
 the highest dam practicable must be constructed. 
 
 The height of a dam may be limited by the following factors : 
 
 First : The overflow of valuable lands. 
 
 Second: The interference with water power rights above the 
 point of development. 
 
 Third : The interference with other vested or public rights. 
 
 Fourth : The cost of the structure. 
 
 The value of the power that can be developed by means of a pro- 
 posed dam will limit the amount that can be expended in the pur- 
 chase or condemnation of property affected by backwater from the 
 dam and the cost of its construction. These are among the ele- 
 ments of the cost of the project and must be considered together 
 with other financial elements before a water power project can be 
 considered practicable. 
 
 In considering backwater and its effect on riparian rights both 
 high and moderate conditions of flow must be considered. The 
 former condition gives rise to temporary interference, often of little 
 importance when affecting purely farming property, and the real 
 or fancied damages from which can commonly be liquidated by re- 
 leases at small expense. The latter condition will permanently 
 inundate certain low lands which must be secured by purchase or 
 condemnation. In many states where the laws of eminent domain 
 do not apply to the condemnation of property for such purposes it 
 is necessary to secure such property by private purchases before 
 the work is undertaken, and usually before the project becomes 
 known publicly, for in such cases the owner of a single piece of land 
 may delay the project by a demand for exorbitant remuneration, 
 from which demand there is in such cases no escape- In every case 
 it is desirable that riparian and property rights be fully covered 
 before the construction of the project actually begins. 
 
The Foundation of Dams. 581 
 
 294. Available Head. Beside the question of backwater the ques- 
 tion of head at the dam is important both in relation to the question 
 of interference and in relation to the question of power. In relation 
 to interference it is an easy matter with a known length and height 
 of dam to determine by calculation from a properly selected weir 
 formula the height of water above the dam under any condition of 
 flow. To determine the head available under all conditions of flow 
 the weir curve must be studied in connection with the rating curve 
 as discussed in Chapter V. 
 
 Two conditions of flow often require consideration in this con- 
 nection : 
 
 First : Where a considerable portion of the flow is being utilized 
 by the wheels and therefore does not affect the head of the dam. 
 
 Second: Where the water is not being used by the wheels and 
 consequently affects the head of the dam. 
 
 Both of these conditions should be studied and determined in rela- 
 tion to their influence on both backwater conditions and power. 
 
 295. The Principles of Construction of Dams. The general prin- 
 ciples for the construction of all dams are similar, and are as fol- 
 lows : 
 
 First : They must have suitable foundations to sustain the pres- 
 sure transmitted through them, which must be either impervious or 
 rendered practically so. 
 
 Second : They must be stable against overturning. 
 
 Third : They must be safe against sliding. 
 
 Fourth : They must have a sufficient strength to withstand the 
 strains and shocks to which they are subjected. 
 
 Fifth : They must be practically water-tight. 
 
 Sixth : They must have essentially water-tight connections with 
 their beds and banks, and, if bed or banks are pervious, with some 
 impervious stratum below the bed and within the banks of the 
 stream. 
 
 Seventh : They must be so constructed as to prevent injurious 
 scouring of the bed and banks below them. 
 
 The application of the above principles depends on the material 
 .from which the dam is to be built and on local conditions- 
 
 296. The Foundation of Dams. The materials used for the con- 
 struction of dams may be masonry, which includes stone-work and 
 concrete-work, reinforced concrete, timber, steel, loose rock, and 
 earth. Each may be used independently or in combination. 
 Masonry and concrete dams must be built upon foundations which 
 
582 Principles of Construction of Dams. 
 
 are practically free from possible settlement. Small masonry struc- 
 tures may sometimes be safely constructed on piles or grillage 
 foundation based on softer materials ; but the larger and more im- 
 portant structures, if constructed of masonry, can be safely built 
 only upon solid rock. Reinforced concrete is now being extensively 
 used for small structures and is not as seriously affected by slight 
 settlement as in the case of dams of solid masonry. There is, how- 
 ever, little flexibility in structures of this kind, and the foundation 
 
 Fig. 356. Timber Crib Dam at Janes ville, Wis. 
 
 must be selected in accordance with this fact. Timber and steel 
 possess a flexibility not possible in concrete construction and are 
 much better adapted to locations where the foundation may be sub- 
 ject to settlement. 
 
 In construction on rock foundation it is usually desirable to exca- 
 vate trenches therein in order to give a bond between the structure 
 of the dam and its foundation. It is also essential with rock foun- 
 dations to determine whether cracks or fissures in the foundation 
 extend below the structure, and if such are found, they must be 
 completely cut off. 
 
 On earth, sand or gravel foundations, when such must be used, 
 the flow which would take place through these materials and under 
 the structure of the dam must be completely cut off by the use of 
 steel or timber sheet piling, which, if possible, should be driven 
 from the structure to the rock or to some other impervious stratum. 
 If no impervious stratum is accessible, the sheet piling must be 
 
Strength of Dams. 583 
 
 driven to such a distance below the base of the dam that the friction 
 of the flow of water under it will reduce or destroy the head and 
 consequently reduce the flow of water to an inappreciable quantity. 
 297. Strength of Dams. A dam to be built in a flowing stream 
 should be designed with a full appreciation of all the stresses to 
 which it may be subjected. Of these, stresses that are due to static 
 pressure can be readily estimated from the known conditions. The 
 strains due to dynamic forces are not so fully understood or easily 
 
 Fig. 357. Janesville Dam with Moderate Water. 
 
 calculated. Where the structure is constructed to retain a definite 
 head of water without overflow, as in the case of reservoir embank- 
 ments, the problem becomes one largely of statics and the only 
 other stresses to be considered are those due to ice action and the 
 action of waves on the structure. When a dam is constructed in a 
 running stream and is subject to the passage of extensive floods of 
 water over it, frequently accompanied by large masses of floating 
 ice, logs or other material which in many cases may strike the 
 crest of the dam, and bring unknown and violent strains, the prob- 
 lem becomes largely one of experience and judgment. 
 
 298. Flood Flows. The passage of great volumes of water over 
 a dam involves the expenditure of the power so generated upon or 
 immediately adjoining the structure, and unless preparations are 
 made for properly taking care of this immense expenditure of 
 power, the power may be exerted in the destruction of the structure 
 itself. 
 
584 
 
 Principles of Construction of Dams. 
 
 Figs. 356 to 358 show three views of the timber <!rib dam at 
 Janesville, Wisconsin, under various conditions of flow. In Fig. 
 356 the flow of the river is comparatively small and all of the water 
 is being used in the power plant, none passing over the dam. In 
 Fig. 357 the river is at a moderate stage and the greater part of the 
 flow is passing over the crest of the dam. In Fig. 358 some four 
 or five feet of water is passing over the dam and the power that is 
 developed thereby is causing the standing wave and the rough 
 
 Fig. 358. Janesville Dam under High Water. 
 
 water shown in the picture below the dam. At this point the power 
 developed by the fall is being expended in waves and eddies, which, 
 unless properly controlled, will attack and injure or destroy the 
 structure. On rock bottom the rock itself will sustain the impact of 
 flow over small dams. But where the rock is soft, or the bottom is 
 composed of material that can be readily disintegrated, it becomes 
 necessary to extend the structure of the dam itself in the form of 
 an apron to cover and protect the bottom. 
 
 Fig. 359 shows the preliminary design of a dam for the Southern 
 Wisconsin Power Company, now under construction at Kilbourn, 
 Wisconsin. This dam will be about 17 feet in height above low 
 water and will be subject at times to the passage of floods to a 
 depth of 16 feet above its crest. For section of dam as constructed 
 see Fig. 373. The two ends of the dam will rest upon a rock 
 foundation. Cribs are also carried to the rock at the face of the 
 dam and at the edge of the apron. The center of the dam is sus- 
 
Flood Flows. 
 
 585 
 
586 Principles of Construction of Dams. 
 
 tained by piles reaching to rock but surrounded by sand which is 
 retained by the cribs. 
 
 The dam proper is built of cells 6 feet square, the walls of each 
 cell being built of solid timber, and each cell carefully filled with 
 stone and sand. At the face of the dam and at the toe of the apron 
 triple sheeting has been placed and securely fastened to the dam 
 and cribs from the rock up, thus effectively preventing the passage 
 of water below or through the dam. 
 
 During high floods the amount of power which must be wasted in 
 the passage of water over the dam will exceed 100,000 horse power. 
 In order to prevent the expenditure of this power in the destruction 
 of the dam, the dam is extended in an apron of about 100 feet in 
 width., the total width of the structure including the dam and the 
 apron, being about 150 feet. 
 
 To further protect the structure, rip-rap is deposited both above 
 and below the structure itself. The surface of the dam exposed at 
 times of low water is constructed of re-inforced concrete, attached 
 directly to the timber work of steel reinforcement. By this design 
 a structure is obtained having all the advantages of the flexibility of 
 timber, with the lasting qualities of masonry, for the concrete only 
 will be exposed at times of low water, all timber work being sub- 
 merged under every ordinary condition. 
 
 299. Impervious Construction Masonry dams are commonly 
 made impervious by the structure of the masonry itself. 
 
 In timber crib dams ordinarily no attempt is made to make the 
 structure itself water-tight, but the top and upstream side are usu- 
 ally covered with wafer-tight sheeting to prevent the w r ater pass- 
 ing into and through the cribs. Such water as reaches the timber 
 cribs usually passes away readily through the open structure on the 
 down, stream side of the dam. 
 
 In the construction of rock-filled dams the same condition ordi- 
 narily obtains. The dam is fairly porous with the exception of its 
 upper face which is made practically water-tight by the use of con- 
 crete, puddle, or some impervious paving. 
 
 In earthen dams the finer and more water-tight materials are 
 used on the inner slopes of the embankment, and, in addition 
 thereto, it is customary in large and important works to use a core 
 of concrete or puddle to effectively prevent the passage of water 
 through the structure. 
 
 300. The Stability of Masonry Dams. The external forces act- 
 ing on a masonry dam are the water pressure, the weight of the 
 
Stability of Masonry Dams. 587 
 
 masonry, the reaction of the foundation, ice and wave pressure near 
 the top, wind pressure, and back pressure of the water on the down 
 stream side. The action of these forces may cause a dam to fail by : 
 
 (1) Sliding on the base or on any horizontal plane above the 
 base. 
 
 (2) Overturning. 
 
 (3) Crushing the masonry or foundation. 
 
 If the dam be built of rubble masonry there will be no danger of 
 failure by sliding on a horizontal joint above the foundation and 
 experience has shown that where a good quality of mortar is used 
 it can be depended upon to prevent sliding in concrete and stone 
 dams having horizontal bed joints. The joint between the dam and 
 its foundation is a more critical point. In rock foundation steps or 
 trenches should be cut so as to afford good anchorage for the dam. 
 In the case of clay, timber or similar foundations the dam will have 
 to be made massive enough so that the tangent of the angle be- 
 tween the resultant pressure on the base and a vertical line is less 
 than the co-efficient of friction between the materials of the dam 
 and the foundation. 
 
 It is customary in the design of masonry dams to proportion the 
 section so that the lines of resultant pressure at all horizontal 
 joints, for both the conditions of reservoir full and reservoir 
 empty, shall pass through the middle third points of the joints. 
 If this condition is fulfilled, the factor of safety against overturn- 
 ing at every joint will be 2, and there will also be no danger from 
 tensile stresses developing in the faces of the dam. 
 
 Investigation has shown that there is no danger of crushing the 
 masonry except in very high dams, with the consideration of which 
 we are not here concerned- 
 
 301. Calculation for Stability. The general conclusion may there' 
 fore be stated, that, in the case of ordinary masonry and con- 
 crete dams, not over 100 feet in height, to be built on rock foun- 
 dations, the design can be based upon the condition that the lines 
 of pressure must lie within the middle third of the profile 
 This rule must be modified at the top of the dam to resist the 
 stresses due to waves, ice, etc. The force exerted by ice is an in- 
 determinate quantity and the tops of dams must therefore be pro- 
 portioned in accordance with empirical rules. Dams are built with 
 top widths varying from 2 to 22 feet, the broader ones usually 
 
588 
 
 Principles of Construction of Dams. 
 
 carrying a roadway. Coventry suggests the following empirical 
 rules for width of top and height of top above water level : 
 
 (1) b = 4.0 + 0.07H 
 
 (2) y = 1.8 + 0.05 H 
 
 Where b is the width of top, y the height above water level and 
 H the greatest depth of water. Both faces of the dam will be ver- 
 tical until the depth y, is reached, where the resultant force passes 
 through the middle third point. Below this depth the general rule 
 will apply. In computing the water pressure against the dam, it 
 
 Fig. 360. 
 
 is best to consider the water surface level with the top of the dam 
 in order to allow for possible rises due to floods, etc. Having de- 
 termined the top width, b, and assuming a section of the dam one 
 foot long, the height, y, of the rectangular portion can be deduced 
 from the formula 
 
 in which s is the specific gravity of the material of the dam. 
 
 The down-stream face of the dam must now be sloped so as to 
 keep the resultant pressure, with the reservoir full, at the limit of 
 the middle third of the length of any joint Dividing the remainder 
 of the height of the dam into lengths convenient for computation, 
 the length of any joint, (see Fig. 360) as "Gil may be found by the 
 formula 
 
Calculation for Stability. 589 
 
 (4) GIT = l/B + C 8 C 
 
 in which 
 
 B _ 6 m (Area ABFE) + BH ; + ^ 
 
 H~ s^lT 
 
 where m = distance from F of the line of action of the weight of 
 masonry above EF and 
 
 c _ i ["4 (Area ABFE) + ^ 
 The value of n is given by the equation 
 
 ,-x Mom. of ABFE + Mom. of EFHG 
 
 (0) n 
 
 (Area ABHG) 
 
 moments being taken about the point H. 
 
 Equation (4) can be used as long as n is greater than one-third 
 the length of the joint. When this condition can no longer be sat- 
 isfied with a vertical face; it will be necessary to batter the upstream 
 face also, so that the lines of pressure with reservoir full and empty 
 both lie at the limits of the middle third of the length of any joint. 
 
 The length of the joints, as IJ, may now be found by the formula 
 
 (6) IJ = V- 
 
 sHK 
 
 and the value of KJ, is 
 
 tPr _ 2 (Area ABHG) ( IJ 3m) - (~HK X ~GH 8 ) 
 
 {I ) J\.J ==== ^ ^^^z 
 
 6 (Area ABHG) + HK (2GH + IJ) 
 
 In high dams two more stages, governed by the compressive 
 strength of the masonry, would have to be considered, but, within 
 the limit of height set above, the formulas given are sufficient. 
 
 The position of the line of pressure may be readily determined 
 also by graphical methods. 
 
 In the case of overfall dams, which are necessarily subjected to 
 dynamic forces, which are more or less indeterminate, the design 
 cannot be so closely figured- 
 
 302. Further Considerations. The preceding analysis does not 
 take into account the possibility of an upward pressure from below 
 the dam, due to the pervious character of the foundation, or to 
 cracks and fissures, by means of which the pressure of the head 
 water may be transmitted to the base of the dam. This factor is 
 commonly ignored in dam construction, but should be considered, 
 36 
 
590 Principles of Construction of Dams. 
 
 Elevation 
 
 Fig. 361. Cross-section of Dam of Holyoke Water Power Co. 
 
 Fig. 362. Masonry Dam of Holyoke Water Power Co. 
 
Further Considerations. 
 
 59 1 
 
 and, when occasion requires, the foundation should be so prepared 
 as to obviate or reduce it to a minimum. This may usually be done 
 by the careful preparation of the foundation to prevent inflow, or by 
 the construction of drains from the interior of the foundation to the 
 lower face. 
 
 The construction of a dam with a vertical overfall, unless pro- 
 vision is made for the admission of air, will result in the formation 
 of a partial vacuum below the sheet, and a certain extra strain on 
 
 Fig. 363. Holyoke Dam During Flood. 
 
 the structure due to the same. The vertical overfall is also fre- 
 quently objectionable, on account of the action of the falling water 
 on the bed of the stream immediately adjacent to the dam, and 
 on the foundation of the dam itself. It is frequently desirable to give 
 the lower face of the dam a curved outline, in order to guide the 
 water smoothly over the dam, and deliver it approximately tangen- 
 tial to the stream bed. The convex surface of the dam should be 
 of such form that the water will, through gravity, adhere to it. 
 An example of a dam with a curved face is shown by Fig. 361 
 which is a section of the dam of the Holyoke Water Power Com- 
 pany. Two views of the dam, one during low water (Fig. 362) 
 and one with about ten feet of water flowing over the crest (Fig. 
 
59 2 
 
 Principles of Construction of Dams. 
 
 363) are also shown. A section of the McCall's Ferry dam, built of 
 Cyclopean Concrete (height 53 feet) is shown in Fig. 364 and a sec- 
 tion of a small Concrete dam at Danville, 111., is shown in Fig. 365. 
 The curve for dams of this character should be kept at or above the 
 
 Fig. 364. Section of McCall Ferry Dam (Eng. Rec.). 
 
 parabolic path that the water would take in a free fall with the in- 
 itial horizontal velocity corresponding to the depth of water on the 
 dam. 
 
 From equation 50, page 64, the flow over one foot of crest will 
 equal, 
 
 q = vh = ra(f)T/2g hi, tience, 
 v = m 
 
 The abscissa of the parabola is x = vt, .in which t= time in 
 seconds. 
 
 Flash Boards 
 
 Timbers, 6xK" 
 
 
 Fig. 365-Concrete Dam, Danville, 111. 
 
Timber Crib Dam at Butte, Montana. 
 
 593 
 
594 
 
 Principles of Construction of Dams. 
 
 The ordinate is, y = % gt 2 , hence. 
 
 y = -^ x is the equation of the parabola. * 
 
 When a curved face is impracticable or undesirable and the bed 
 of the stream, below the dam, is not of suitable material to resist 
 the impact of the falling water, some form of apron must be pro- 
 vided. Sometimes the dam is divided into steps over which the 
 water falls in numerous cascades. Such a dam is shown in Fig. 
 366. This is the timber crib dam constructed for the Montana 
 
 pi/ma 
 
 . Fig. 367. Timber Dam at Sewall Falls. (Eng. News, vol. XXXI.) 
 
 Power Company, near Butte, Montana. In this case the cells are 
 composed of timber, laid alternately in each direction, with a con- 
 siderable space left between them, instead of being built solid as 
 in the Kilbourn dam. These cells were filled with broken stone, 
 and the upstream side of the dam was planked with sheeting in 
 order to make the structure water-tight. When the water was 
 admitted behind the dam a portion of the structure was forced 
 out of alignment by the crushing of the timbers, at the points of 
 contact. The amount of this displacement and the cause of the 
 same is quite clearly shown in the cut. 
 
 Fig. 367 is a section of the Sewall Falls dam, showing a similar 
 method of resisting the impact of the overflow. 
 
 304. Types and Details of Dams. The types of dams are so nu- 
 merous, and the details of construction vary so greatly with every 
 locality, that an entire volume would be necessary to adequately 
 cover this subject. As the subject isalready well covered in many 
 special treatises and articles, no attempt will be made to discuss 
 this subject in the present edition. Numerous references are given 
 to books and articles in which special forms of construction are 
 discussed and described. 
 
 * Turneaure & Eussell's "Public Water Supplies," Section 446. 
 
Literature. 595 
 
 LITERATURE. 
 
 PRINCIPLES OF CONSTRUCTION OF DAMS. 
 
 1. Turneaure and Russell. Public Water Supplies. Chaps. 16 to 18. John 
 
 Wiley and Sons, 1901. 
 
 2. Church, I. P. Mechanics of Engineering. John Wiley and Sons, 1904. 
 
 3. Wegmann, Edward. The Design and Construction of Dams. John Wiley 
 
 and Sons, 1899. 
 
 4. Leffell, James. Construction of Mill Dams. James Leffell and Company, 
 
 Springfield, Ohio, 1881. 
 
 5*. Follet, W. W. Earthen vs. Masonry Dams. Eng. News, Jan. 2, 1892, 
 et seq. Eng. Rec. May 14, 1892, et seq. 
 
 6. Hall, P. F. Investigation of the Distribution of Pressure on the Base of 
 
 Dams. Trans. Assn. C. E. of Cornell, 1900. 
 
 7. Knight, Frank B. Building an Impounding Dam for Storage Reservoir. 
 
 Mines and Mining, May, 1900, 
 
 8. Schuyler, Jas. Dix. Reservoirs for Irrigation, Water Power and Domes- 
 
 tic Water Supply. New York. Wiley and Sons, 1901. 
 
 9. Gregory, John H. Stability of Small Dams. Eng. Rec. Sept. 21, 1901. 
 
 10. Fielding, John S. Essential Elements in the Design of Dams. Can. 
 
 Ehgr. Jan. 1905. 
 
 11. Wilson, J. S., and Gore, W. Stresses in Dams. Engng. Aug. 4, 1905. 
 
 STABILITY OF MASONRY DAMS. 
 
 1. Coventry, W. B. Design and Stability of Masonry Dams. Proc. Inst. 
 
 C. E. vol. 85, p. 281. 1886. . 
 
 2. Morley, Isaac. On the Determination of the Profile of High Masonry 
 
 Dams. Eng. News, Aug. 11, 1888. 
 
 3. Vischer and Waganer. The Strains in Curved Masonry Dams. Eng. 
 
 News, Mch. 15, 1890; Sept. 27, 1890. 
 
 4. Van Buren, John D. Notes on High Masonry Dams. Trans. Am. Soc. 
 
 C. E. vol. 34, p. 493. Dec. 1895. 
 
 5. Pelletiau, M. Profiles for Masonry Dams. Ann. des Fonts et Chaussees. 
 
 Feb. 1, 1897. 
 
 6. Levy, Maurice. Trapezoidal Formula. Comptes Rendus. May 2, 1898. 
 
 7. Levy, Maurice. The Elastic Equilibrium in a Masonry Dam of Triangu- 
 
 lar Section. Comptes Rendus. July 4, 1898. 
 
 8. Specifications for a Large Concrete Dam. Eng. Rec. Oct. 29, 1898. 
 
 9. Bainet, M. The Computation of Masonry Dams for Reservoirs. Ann des 
 
 Fonts et Chaussees. 2 Trimestre 1898. 
 
 10. Baibet, M. L. The Conditions of Resistance of Masonry Dams for Reser- 
 
 voirs. Ann des Fonts et Chaussees. 1 Trimestre 1899. 
 
 11. Dillman, Geo. L. A Proposed New Type of Masonry Dam. Trans. Am. 
 
 Soc. C. E. vol. 49, p. 94. 1902. 
 
Principles of Construction of Dams. 
 
 12. Wisner, Geo. Y. The Correct Design and Stability of High Masonry 
 
 Dams. Eng. News. Oct. 1, 1903. 
 
 13. Stability of Masonry Dams. Engng. Mch. 31, 1905. 
 
 14. Review of Paper of Atcherly & Pearson on Stability of Masonry Dams. 
 
 Engr., Lond. Mch. 31, 1905. 
 
 15. Unwin, W. C. Note on the Theory of Unsymmetrical Masonry Dams. 
 
 Engng. Apr. 21, 1905. 
 
 16. Unwin, W. C. Further Notes on the Theory of Unsymmetrical Masonry 
 
 Dams. Engng. May 12, 1905. 
 
 17. Unwin, W. C. On the Distribution of Shearing Stresses in Masonry Dams. 
 
 Engng. June 30, 1905. 
 
 18. Pearson, Karl. On the Stability of Masonry Dams. Engng. vol. 80, 
 
 July 14, 1905. 
 
 19. Wisner, Geo. Y., and Wheeler, Edgar T. Investigation of Stresses in 
 
 High Masonry Dams of Short Spans. Eng. News. Aug. 10, 1905. 
 
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 p. 171. Aug. 11, 1905. 
 
 21. The Determination of Pressures on Masonry Dams. Oest. Wochenschr. 
 
 f d Oeff. Baudienst. Aug. 19, 1905. 
 
 22. Bleich, S. D. Internal Stresses in Masonry Dams. Sch. of Mines Qr. 
 
 Nov 1905. 
 
 23. Ende, Maxam. Notes on Stresses in Masonry Dams. Engineering. Dec. 
 
 1905. 
 
 EARTHEN DAMS. 
 
 1. Fitzgerald, J. L. Leakage Through an Earthen Dam at Lebanon, Pa. 
 
 Eng. Rec. May, 1893, pp. 474-5. 
 
 2. LeConte, L. J. High Earthen Dam for Storage Reservoirs. Proc. Am. 
 
 W. Wks. Assn., 1893, and Eng. Rec. Sept. 16, 1893. 
 
 3. Fitzgerald, D., and Fteley, A. Construction of Reservoir Embankments. 
 
 Eng. News. Oct. 26, 1893. pp. 330-1. 
 
 4. Earth Dam of the Honey Lake Valley, California. Eng. News, Mch. 15, 
 
 1894. 
 
 5. Earth Dam at New Britain, Conn. Eng. Rec. June 23, 1894. 
 
 6. Difficulties with Earth Dams in Great Britain. Eng. Rec. Set. 3, 1898. 
 
 7. Strange, W. L. The Construction of High Earth Dams. Eng. Rec. 
 
 Apr. 15, 1899. 
 
 8. The Limiting Heights of Earth Dams. Eng. Rec. Dec. 7, 1901. 
 
 9. A Remarkable Core-wall for an Earth Dam. Eng. Rec. Dec. 21, 1901. 
 
 10. Concerning the Design of Earth Dams and Reservoir Embankments. 
 
 Eng. News, Feb. 20, 1902. 
 
 11. The Tabeaud High Earth Dam, near Jackson, Cal. Eng. News. July 10, 
 
 1902. 
 
 12. Bassell, Burr. The San Leandro Earth Dam of the Oakland Water 
 
 Works. Eng. News, Sept. 11, 1902. 
 
 13. The New Earth Dam for Water Works of Santa Fe, N. M. Eng. News, 
 
 Apr. 13, 1903, p. 346. 
 
Literature. 597 
 
 14. An Earth Dam with Loam Core at Clinton, Mass. Eng. Rec. Aug. 20, 
 
 1904. 
 
 15. Brown, R. H. Grouted Rubble Core Walls for the Weirs of the Delta 
 
 Barrage, Egypt. Eng. News, Feb. 9, 1905. 
 
 16. Walter, Raymond F. Belle Fourche Dam, Belle Fourche Project, S. D. 
 
 Eng. Rec. Mch. 3, 1906. Vol. 53, p. 307. 
 
 17. Herschel, Clemens. Earth Dams with Concrete Core Walls. Eng. News, 
 
 Sept 7 1905. 
 
 18. Leonard, J. A. A Proposed Earth Dam with a Steel Core and a Rein- 
 
 forced Concrete Spillway at Ellsworth, Me. Eng. News, Sept. 7, 
 1905. 
 
 19. Schuyler, J. D. Recent practice in Hydraulic Fill Dam Construction. 
 
 Proc. Am. C. E. Oct. 1906. 
 
 BOCK FILL DAMS. 
 
 1. The Otay Dam. Eng. Rec. Sept. 28, 1895, p. 310. 
 
 2. The Nevada County Electric Power Company's Dam. Min. & Sci. Pr. 
 
 Feb. 8. 1896. 
 
 3. A Rock-fill Dam with a Steel Heartwall at Otay, Cal. Eng. News. Mch. 
 
 10, 1898. 
 
 4. Welles, A. M. The Castlewood Dam. Eng. Rec. Dec. 24, 1898. Vol. 39, 
 
 p. 69. 
 
 5. Hardesty, W. P. The Castlewood Rock-fill Dam and the Canal of the 
 
 Denver Land & Water Co. Eng. & Min. Jour. Feb. 9, 1899. 
 
 6. Parker, H. S. East Canyon Creek Dam, Utah. Eng. Rec. Sept. 2, 1899. 
 
 7. Dumas, A. Rock Dams with Metallic Reinforcement. Genie Civil. Oct, 
 
 21, 1899. 
 
 8. The Goose Neck Canyon Dam. Eng. Rec. Mch. 10, 1900. 
 
 9. The Cascade Rock-fill on the Erie R. R. Eng. News. Dec. 27, 1900, vol. 
 
 44, p. 440. 
 
 10. Hardesty, W. P. A Rock-fill Dam with Steel Core Across East Canyon 
 
 Creek, Utah. Eng. News. Jan. 2, 1902. 
 
 11. Reconstruction of the Castlewood Dam. Eng. Rec. July 12, 1902. 
 
 12. The Plant of the Pikes Peak Power Co. Eng. Rec. July 19, 1902. 
 
 13. Lake McMillan Dam, Pecos River, N. M. Eng. Rec. June 9, 1894. 
 
 MASONKY DAMS. 
 
 1. Ashhurst, F. H. Reconstruction of the Bhim Tal Dam, Kumaon, India. 
 
 Proc. Inst. C. E. vol. 75, p. 202. 1884. 
 
 2. Hill, John W. A Masonry Dam. Trans. Am. Soc. C. E. June, 1887. 
 
 3. Tonsa Dam, Bombay Water Works. Eng. News. June 30, 1892, pp. 646-7. 
 
 Eng. Rec. Dec. 19, 1891, p. 40. 
 
 4. New Croton Dam for the New York Water Supply. Eng. News. June 2, 
 
 1892, pp. 552-3. R. R. Gaz. Oct. 14, 1892. p. 163. 
 
 5. Folsom Dam at Folsom, Cal. R. R. & Eng. Jour. July, 1892. pp. 315-8. 
 
 6. Vyrnwy Dam for the Liverpool Water Works, England. R. R. & Eng. 
 
 Jour. Sept. 1892. 
 
598 Principles of Construction of Dams. 
 
 7. Concrete Masonry Dam of the Butte City Water Company, Montana, 
 
 Eng. News, Dec. 15, 22, 1892, pp. 554 & 584. 
 
 8. Periar Concrete Dam in. India for Irrigation Purposes. Lon. Engr. 
 
 Nov. 25, Dec. 2, 9, 1892. Eng. Rec. Dec. 31, 1892, pp. 92-3. 
 
 9. Report of the Austin Board of Public Works, Austin, Texas. Eng. News 
 
 Jan. 26, 1893, pp. 88-90. 
 
 10. Dam at Austin, Texas. Eng. News. Jan. 26, 1893, pp. 87-88. 
 
 11. McCulloh, Walter. Sodom Dam, New. York. Trans. Am. Soc. C. E. Mch.. 
 
 1893, vol. 28, pp. 185-199. Discussion by Members of Society. 
 Trans. Am. Soc. C. E. May, 1893, vol. 28, pp. 348-351. 
 
 12. McCulloh, Walter. The Construction of a Water Tight Dam. Trans. 
 
 Am. Soc. C. E. Apr. 1893. 
 
 13. Basin Creek Dam for Water-Works of Butte, Mont. Eng. News. Aug. 17,. 
 
 1893, p. 130. 
 
 14. Dam 5 of the Stone Brook Portion of the Boston Water Works. Eng. 
 
 Rec. Nov. 4, 1893, p. 361. 
 
 15. Bettes, Stockwell. Determining Minimum Section for Overfall Masonry 
 
 Dams. Eng. News. Dec. 28, 1893, vol. 30, p. 511. 
 
 16. Masonry Dam at LaGrange, Gal. Eng. News. March 29, 1894. Eng. 
 
 Rec. March 3, 1894. 
 
 17. Pellitveau, Albert. Great Masonry Dam. Ann. des Fonts et Chaussees. 
 
 May, 1894. 
 
 18. Masonry Dam, Chemnitz Water Works, Germany. Eng. Rec. July 28 r 
 
 1894, Jour, f Gasb. u Wasserv. Sept. 1, 1894. Sci. Am. Sup. 
 Nov. 10, 1894. 
 
 19. Snyder, F. E. The Colorado River Dam at Austin, Texas. Eng. News. 
 
 Aug. 2, 1894. Eng. Mag. Nov. 1894. 
 
 20. Dunning's Dam. Eng. News. Oct. 18, 1894. Eng. Rec. Oct. 20, 1894, 
 
 21. Gould, E. S. The Dunning's Dam, Partly of Earth and Partly of Ma- 
 
 sonry. Trans. Am. Soc. C. E. Nov. 1894. 
 
 22. New Masonry Dam at Lonsdale, R. I. Eng. News, Mar. 14, 1895. 
 
 23. Van Buren, John D. High Masonry Dams. Trans. Am. Soc. C. E. voL 
 
 34, No. 6, pp. 495-520. 1895. 
 
 24. Haller, Prof. The Bouzey Dam. Jour. f. Gasb. u. Wasserv. June 22, 
 
 1895, et seq. 
 
 25. Overflow of the Sweetwater Dam. Eng. News. Aug. 15, 1895, vol. 34 r 
 
 p. 111. 
 
 26. Marstrand, O. J. Curved Masonry Dam for Water Works of Remscheid, 
 
 Germany. Eng. News. Jan. 30, 1896. 
 
 27. Firth, Charles. Concrete Dams on the Coosa River, Ala. Eng. News, 
 
 Feb. 20, 1896. 
 
 28. Savage, H. N. Repair and Extension of the Sweetwater Dam. Eng. Rec. 
 
 March 12, 1896. 
 
 29. The Cold Spring, N. Y., Concrete Dam. Eng. Rec. July 11, 1896. 
 
 30. Remscheid and Chemintz Water Works. Eng., Lond. July 31, 1896. 
 
 31. New Arched Dam at Nashua, N. H. Eng. Rec. Aug. 8, 1896. 
 
 32. Dahl, H. M. T. A New Dam at Minneapolis. Eng's. Year Book Univ. of 
 
 Minn., 1897. 
 
Literature. 599 
 
 33. The Proposed Steel-Faced Concrete Arch Dam, Ogden, Utah. Eng. Rec. 
 
 Mch. 6, 1897. 
 
 34. Thompson, Sanford E. The New Holyoke Water Power Dam. Eng. 
 
 News. May 13, 1897. 
 
 35. Homey, Odus C. Concrete Water Power Dam at Rock Island ArsenaL 
 
 Jour. W. Soc. Engs. June, 1897. 
 
 36. Schuyler, James D. The Construction of the Hemet Dam. Jour. Assn. 
 
 Engng. Socs. Sept. 1897. 
 
 37. Schuyler, James D. The Hemet Irrigating Dam. Sci. Am. Sept. 25_ 
 
 1897. 
 
 38. The Muchkundi Dam. Engr. Lond. Oct. 22, 1897. 
 
 39. The Hemet Dam. Eng. News. March 24, 1898. 
 
 40. Richter, Irving. An Unusual Small Masonry Dam. Eng. Rec. Nov. 26,, 
 
 1898. 
 
 41. Rafter, G. W., Greenlach, W., Horton, R. E. The Indian River Dam. 
 
 Eng. News. May 8, 1899. 
 
 42. Crosby, W. O. Geology of the Wachusett Dam and Aqueduct Tunnel. 
 
 Tech. Quar. June, 1899. 
 
 43. The New Masonry Dam at Holyoke. Eng. Rec. July. 22, 1899. 
 
 44. Gould, E. S. Earth Backing for Masonry Dams. Eng. Rec. Dec. 23 r 
 
 1899. 
 
 45. The Bear Valley Dam as an Arch. San Bernardino Co., Cal. Techno- 
 
 graph No. 14, 1899-1900. 
 
 46. The Tariffville Plant Plans of Hartford Elec. Light Company. Etig. Rec. 
 
 Mch. 24, 1900. 
 
 47. The New Water Poweir of the Hartford Electric Light Co. Am. Electri- 
 
 cian. Mch. 1900. 
 
 48. Flinn, Alfred D. The Wachusett Dam. Eng. News. Sept 13. 1900. 
 
 49. The Wachusett Dam. Eng. Rec. Sept. 8, 1900. 
 
 50. A Concrete' Power Dam at Middle Falls, N. Y. Eng. Rec. Oct. 4 1900. 
 
 51. Stewart, J. A. Building of the Great Wachusett Dam. Sci. Am. Sup. 
 
 Dec. 15, 1900. 
 
 52. The Dam & Power Station of The Hudson River Power Company. Eng. 
 
 Rec. Mar. 8, 1902. 
 
 53. Heaman, J. A. Description of a Dam and Accompanying Work Built for 
 
 the Water Commissioners. Can. Soc. of Civ. Engrs. Apr. 24,. 
 1902. 
 
 54. A Concrete Dam Near London, Ontario. Eng. Rec. July 26, 1902. 
 
 55. Frechl, H. Construction of the Lauchenesee/ Dam. Eng. Rec. Aug. 30,. 
 
 1902. 
 
 56. The Spier's Falls Dam of The Hudson River Water Power Company. 
 
 E"ng. News. June 18, 1903. 
 
 57. Morton, Walter Scott. A New Water Power Development at New Mil- 
 
 ford, Conn. Eng. Rec. Feb. 13 and 20, 1904. 
 
 58. Harrison, Chas. L., and Woodard, S. H. Lake Cheesman Dam and Res- 
 
 ervoir. Proc. Am. Soc. C. E. Aug. 1904. 
 
 59. Galliot, M. Reinforcement of the Grosbois Dam. Ann. des Fonts et 
 
 Chaussees, 1905.' 
 
6oo Principles of Construction of Dams. 
 
 60. The Roosevelt Masonry Dam on Salt River, Arizona. Eng. News. Jan. 
 
 12, 1905. 
 
 61. A Quickly Erected Reinforced Concrete Dam at Fenelon Falls, Ont. Eng. 
 
 News. Feb. 9, 1905. 
 
 62. A Concrete Dam on a Pile Foundation at St. John's Lake, Long Island, 
 
 N. Y. Eng. News. Feb. 9, 1905. 
 
 63. Guarini, Emile. Barossa Dam, Southern Australia. Sci. Am. April 1, 
 
 1905. 
 
 64. Hollow Reinforced Concrete Dam at Schuylerville, N. Y. Eng. News. 
 
 April 27, 1905. 
 
 65. Blodgett, Geo. W. -The Wachusett Dam of the Metropolitan Water 
 
 Works. R. R. Gaz., vol. 39, p. 100. Aug. 4, 1905. 
 
 66. Dams for the New Plant of the United Shoe Machinery Company, Bev- 
 
 erly, Mass. Eng. Rec. Sept. 2, 1905. 
 
 67. Shedd, Geo. G. The Garvin's Falls Dam, Canal and Hydro-Electric Plant. 
 
 Jour. Assn. E'ng. Soc. Oct. 1905. 
 
 68. Gowen, Chas. S. Changes at the New Croton Dam. Proc. Am. Soc. C. E. 
 
 Mch. 1906. 
 
 69. The Pedlar River Concrete Block Dam. Lynchburg W. Wks. Eng. Rec. 
 
 May 12, 1906. 
 
 70. The Stresses on Masonry Dams. Editorial Review of Paper by Prof. 
 
 Carl Pearson. Engineering, London, September, 1907. 
 
 71. The McCall's Ferry Hydraulic Electric Power Plant. Eng. News, Sep- 
 
 tember 12, 1907. 
 
 TIMBER DAMS. 
 
 1. Parker, M. S. Black Eagle Falls Dam at Great Falls, Mont. Trans. 
 
 Am. Soc. C. E. July, 1890, vol. 27, pp. 56-59. Eng. Rec. Oct. 8, 
 1892, p. 295. 
 
 2. Sewell Falls Dam Across Merrimac River, near Concord, N. H. Eng. 
 
 News. April 19, 1894. 
 
 3. Parsons, G. W. Closing the Timber & Stone Dam at Bangor, Me. Eng. 
 
 News. July 26, 1894. 
 
 4. Brown, Robert Gilman. Additions to the Power Plant of the Standard 
 
 Consolidated Mining Company. Trans. Am. Inst. Mining Engrs. 
 Sept. 1896. 
 
 5. Ripley, Theron M. The Canyon Ferry Dam, Canyon Ferry, Mont. Jour. 
 
 Assn. Engng. Soc. May, 1898. 
 
 6. The Butte, Montana, Power Plant. Eng. Rec. Mch. 5, 1898. 
 
 7. Carroll, Eugene. Construction of a Crib Dam for Butte City Water Co., 
 
 Butte, Montana. Jour. Assn. Engng. Soc. April, 1899. 
 
 8. The Reconstructed Canyon Ferry Dam, near Helena, Montana. Eng. 
 
 News. Apr. 26, 1900. 
 
 9. A Large Crib Dam. Butte, Mont. Eng. Rec. Feb. 3, 1900. 
 
 10. Harper, Jos. H. The Reconstruction of Big Hole Dam, Big Hole, Mon- 
 tana. Jour. Assn. of Engng. Soc. Apr. 1900. 
 
Literature. 601 
 
 11. Tower, G. W. Timber Dam at Outlet of Chesuncook Lake, Penobscot 
 
 River. Eng. News. Sept. 1, 1904. 
 
 12. Woermann, J. W. A Low Crib Dam Across the Rock River. 
 
 STEEL DAMS. 
 
 1. Fielding, John S. The Use of Steel in the Construction of Dams. Can. 
 
 Arch. Aug. 1897. 
 
 2. Steel Weir, Ash Fork, Arizona. Eng. Rec. Apr. 9, 1898. 
 
 3. Steel Dam at Ash Fork, Arizona. Eng. News. May 12, 1898. 
 
 4. Fielding, John S. Proposed Design for a Steel and Concrete Dam. Eng. 
 
 News. Nov. 16, 1899. 
 
 5. Bainbridge, F. H. Structural Steel Dams. Jour. West. Soc. Eng. 1905. 
 
 6. The Hauser Lake Steel Dam in the Missouri River Near Helena, Mont. 
 
 Eng. New. Nov. 14, 1907. 
 
 7. Wheeler, J. C. A Collapsibe Steel Dam Crest. Eng. News. October 3. 
 
 1907. 
 
 REINFORCED CONCRETE DAMS. 
 
 1. A Large Reinforced Concrete Dam at Ellsworth, Maine. Eng. News. 
 
 May, 1907. 
 
 2. A Hollow Reinforced Concrete Dam at Theresa, New York. Eng. News, 
 
 Nov. 5, 1903. 
 
 3. Reinforced Concrete Dam at Schuylerville, New York. Eng. News, April 
 
 27, 1905. 
 
 4. A Concrete Steel Dam at Danville, Kentucky. Eng. Rec. Dec. 3, 1904. 
 
 5. Reinforced Concrete Dam at Feneloni Falls, Ontario. Eng. News, Feb. 9, 
 
 1905. 
 
 DAM FAILURES. 
 
 1. Washout at the Pecos Dam. Eng. Rec. Aug. 26, 1893. 
 
 2. Failure of the Bouzey Reservoir Dam. Lon. Engr., May 3, 1895, p. 583; 
 
 Eng. News, May 9, 1895, p. 312; Lon. Engr., May 31, 1895, p. 
 383; Eng. News, May 23, 1895, p. 332. 
 
 3. Catastrophe at Lima, Montana. Irrigation Age, July, 1894. 
 
 4. Rickey, J. U. Failure of Dam at Minneapolis, Due to Previous Weaken- 
 
 ing Through Ice Pressure. Eng. News, May 11, 1899. 
 
 5. Failure of Masonry Dams. Annales des Ponts et Chaussees, vol. 7, No. 7, 
 
 pp. 77-89 (1895). 
 
 6. The Johnstown Disaster. Eng. News, June 18, 1899. 
 
 7. Recent Events at the Castlewood Dam, Castlewood, Colo. Eng. Rec. 
 
 May 19, 1900. 
 
 8. The Failure of Two Earth Dams at Providence, R. I. Eng. News, Mch. 
 
 12, 1901. 
 
 9. Destruction of Dams in the South. Eng. Rec. Jan. 11, 1902. 
 
 10. The Failure of the Dam of the Columbus Power Company at Columbus, 
 Ga. Eng. News, Jan. 23, 1902. 
 
602 Principles of Construction of Dams. 
 
 11. Failure of the Lower Tallassee Dam at Tallassee, La. Eng. News, Feb. 
 
 13, 1902. 
 
 12. Johnson, Robert L. Some Thoughts Suggested by the Recent Failure 
 
 of Dams in the South. Eng. News, Mch 20, 1902. 
 
 13. Hill, W. R. A List of Failures of American Dams. Eng. Rec. Sept. 27, 
 
 1902. 
 
 14. The Break in the Utica Reservoir. Eng. Rec. Sept. 27, 1902. 
 
 15. Whited, Willis. The Failure of the Oakford Park and Fort Pitt Dam. 
 
 Eng. News, July 23, 1903. 
 
 16. Robinson, H. F. Construction, Repairs and Subsequent Partial Destruc- 
 
 tion of Arizona Canal Dam. Eng. News, Apr. 27, 1905. 
 
 17. Murphy, E. C. Failure of Lake Avalon Dam, near Carlsbad, N. H. Eng. 
 
 News, July 6, 1905. 
 
CHAPTER XXV. 
 
 APPENDAGES TO DAMS. 
 
 305. Movable Dams. The height of a dam is limited in the man- 
 tier hereinbefore described. It will be noted that the limit is that 
 imposed by high water conditions and that, as a rule, the water sur- 
 face during low stages could be raised to a considerable amount 
 without interference with the riparian owners, if at the same time 
 flood conditions could be provided for. In order to provide such 
 conditions, movable dams are sometimes constructed which will 
 permit of raising or lowering all or a part of the structure as the 
 
 . 368. U. S. Movable Dam on Pile Foundation, McMechen, W. Va. 
 News, vol. 54, page 100.) 
 
 (Bng. 
 
 stage of the water requires. These flexible portions of the dam 
 may consist of a gate or series of gates which can be raised or 
 lowered. Sometimes a considerable portion of the dam is made 
 flexible by the construction of a bear trap leaf, which is usually 
 raised and lowered by hydraulic pressure, and by means of which 
 the head of water can be readily and rapidly controlled. Sometimes 
 
604 
 
 Appendages to Dams. 
 
Movable Dams. 
 
 the entire dam is made movable by the use of Chanoine wickets 
 (see Fig. 368) and similar types of dams, a part of which may be 
 removable while other parts are folded down on the bed of the 
 stream, allowing the flood waters to pass over them. Most of such 
 
 i a - o 
 
 Fig. 370. Tainter Gates for Morris Plant, Economy Light and Power Co. 
 
 constructions are expensive and are used most largely on govern- 
 ment works for the control of rivers for navigation purposes. 
 
 The objection to movable dams for water power purposes is 
 that the reduction in the elevation of the head water by their use 
 commonly so reduces or destroys the head that the continuity of the 
 
 37 4 
 
6o6 
 
 Appendages to Dams. 
 
 power output is interrupted. The same objection also applies to 
 any gate, flash board or other device designed to reduce the head. 
 Such reduction is usually made during conditions of flow under 
 which the natural head that would obtain is already at a minimum. 
 306. Flood Gates. Flood gates are quite commonly used in 
 water power dams to control or modify extreme flood heights. 
 These gates are commonly designed to be raised so as to permit of 
 the escape of the water underneath them. The tainter gate, in 
 
 Fig. 371.' Hoist for Tainter Gates of Northern Hydro Electric Power Co. 
 
 some of its modifications, is perhaps most widely used for this pur- 
 pose. Fig. 369 shows a plan, elevation and section of a tainter 
 gate, designed by L. L. Wheeler, resident engineer of the Illinois 
 and Mississippi Canal, for the U. S. Government dam at Sterling, 
 Illinois. This is one of a series of tainter gates designed for the 
 flood control of the Rock River at that point. The gates are oper- 
 ated by an overhead hoist which can be moved from gate to gate 
 when it is desired to manipulate them. 
 
 Fig. 37 is a section of one of six gates designed by the writer 
 for the Morris plant of the Economy Light and Power Company. 
 
Flood Gates. 
 
 607 
 
 Fig. 372. Tainter Gates at Upper U. S. Gov. Dam, Appleton, Wis. 
 
 Fig. 373. Tainter Gates at Lower U. S. Gov. Dam, Appleton, Wis. 
 
6oS 
 
 Appendages to Dams. 
 
Flashboards. 
 
 609 
 
 These gates are operated by a movable hoist, similar to Fig. 371, 
 which travels on a track on the bridge above. 
 
 Figs. 372 and 373 are views of the steel tainter gates constructed 
 in the upper and lower U. S. Government dams across the Fox 
 River at Appleton, Wisconsin. 
 
 In the dam of the Southern Wisconsin Power Company at Kil- 
 "bourn, Wisconsin, the rise of the flood water is so great (about 16 
 feet) that it was found impracticable to construct lift gates to re- 
 duce the flood heights. In this case the writer has divided the crest, 
 
 Fig. 375. Flash Boards and Supports, Rockford Water Power Co. 
 
 "by piers, into twelve sctions. Between each two piers a twenty- 
 Jive foot gate is placed (see Fig. 374) which can be lowered into the 
 dam six feet, thus reducing the extreme flood height by that amount. 
 These gates are of steel and weigh about seven tons each. They 
 may be operated by an electric motor or may be manipulated by 
 hand, should occasion require. 
 
 307. Flashboards. The control of limited variations in head is 
 -commonly accomplished by means of flash-boards which are widely 
 -used for this purpose. The simplest form of flash-board consists 
 
6io 
 
 Appendages to Dams. 
 
 of a line of boards placed on the crest of the dam (see Fig. 375) 
 usually held in place by iron pins to which the boards are com- 
 monly attached by staples. The object of flash-boards is princi- 
 pally to afford a certain pondage to carry the surplus water from 
 the time of minimum use of power to the time of maximum demand. 
 Incidentally, the head is raised and the power is also increased in 
 this way. The supports of the flashboards should be so arranged 
 that they will withstand only a comparatively low head of water 
 flowing over the boards, and will be carried away if a sudden 
 
 Fig. 376. Automatic Drop-Shutter for Betiva Dam, India. (Eng. News, 
 
 June 4, 1903.) 
 
 flood should raise the head materially above a safe elevation. If 
 the boards are so supported as to withstand the discharge of heavy 
 floods, they will form a permanent portion of the dam and increase 
 its fixed elevation to such an extent as to create damage which their 
 use is supposed to avoid. Sometimes the pins supporting the 
 boards are made so light that they must be held in position by in- 
 clined braces. These braces are sometimes supplied with steel 
 eye-bolts through which is passed a cable. A large steel washer 
 is attached at one end and a winding drum at the other. (See Fig. 
 3/5). Commonly, if a flood is anticipated, the boards are removed 
 and stored for future use. If, however, a sudden flood should arise, 
 the inclined braces are removed by winding up the cable and 
 the pressure on the flash-boards bends the pins and the boards 
 are washed away. The expense involved by the loss of flash-boards. 
 
Head Gates and Head Gate Hoists. 
 
 611 
 
 is not excessive as one set will commonly take care of the entire 
 summer low water period. The expense involved in their use is 
 therefore only the cost of one set of flash-boards per year. 
 
 Sometimes the flash-boards constitute a permanent but adjust- 
 able part of the dam and are lowered automatically during stages 
 of high water. (See Fig. 376). On some dams, especially at 
 waste weirs of canals and reservoirs where the fluctuations in 
 height are inconsiderable, the dam may be provided with a foot 
 bridge which makes the whole crest of the dam accessible at all 
 times arid from which the flash-boards can be readily adjusted. 
 This plan is used on the dam across the Chippewa River at Eau 
 
 Fig. 377. Adjustable Flash Boards at Eau Claire, Wis. 
 
 Claire, although this river is subject to high floods. (See Fig. 377). 
 Ordinarily, on rivers subject to such conditions, this type of con- 
 struction is impracticable. 
 
 In some dams, instead of gates or flash-boards, vertical stop 
 planks or needles are used. These consist of planks or squared 
 timbers that are lowered vertically into position, stopping off the 
 opening partially or wholly, as desired. They are commonly sup- 
 ported by a shoulder at the bottom of the opening and one or more 
 cross beams above. 
 
 308. Head Gates and Head Gate Hoists, It is usually desirable 
 to control the water at the inlets to the headrace by the use of gates 
 which may be closed in emergencies or for the purpose of making 
 
6l2 
 
 Appendages to Dams. 
 
Head Gates and Head Gate Hoists. 
 
614 Appendages to Dams. 
 
 necessary repairs or modifications in the raceway through which 
 the water is diverted to the plant. In northern rivers it is also 
 found desirable to prevent the entrance of ice into the raceway 
 either by the construction of a floating or fixed boom in front of the 
 gates or by constructing a system of submerged arches either in 
 front of, or as a part of, the gateways. By means of such construc- 
 tion the floating ice or other floating material may be diverted from 
 the raceway and passed over the spillway of the dam. 
 
 The head gates must be sufficiently, substantial to allow the race 
 to be emptied under ordinary conditions of water and to protect 
 the raceway under flood conditions. 
 
 Fig. 378 shows an elevation of the head gates, designed by the 
 writer for the power plant at Constantine, Michigan. These are 
 shown in detail ! by Fig. 379. A rear view of these gates from the 
 race side is also shown in Fig. 380. These gates are double wooden 
 gates with concrete gateways and are arched over between the 
 piers so as to permit the passage of men and teams. These gates 
 are designed to pass about 2,000 cubic feet per second. 
 
 Fig. 381 shows a set of double wooden gates, the posts and braces 
 of which are made of structural steel designed by the writer for the 
 power plant of Mr. Wait Talcott, at Rockford, Illinois. 
 
 In the Constantine gates the gate mechanism is geared for fairly 
 rapid operation by two men. The Rockford gate apparatus is very 
 simple, the gate being handled with a capstan bar by a single man 
 but at a much slower speed. 
 
 Fig. 382 shows the movable head gate hoist designed b'y the 
 writer for the operation of the head gates at the Kilbourn plant of 
 the Southern Wisconsin Power Company. 
 
 309. Fish-Ways. In almost every state fishways are required by 
 law in any dam constructed on natural waterways. These fish- 
 ways must be so arranged as to permit the free passage of fish up 
 the stream. 
 
 Fig. 383 shows a concrete fishway built by the writer in con- 
 nection with the ogee concrete dam constructed across the Ver- 
 million River at Danville, Illinois. Fig. 384 is a fishway designed 
 by Mr. L. L. Wheeler and constructed in the dam at Sterling, Illi- 
 nois. The Sterling dam is a timber crib dam and the fishway is 
 constructed of timber. Fig. 385 shows the type of fishway recom- 
 mended by the Fish Commission of the State of Wisconsin and 
 ordinarily used in that state. 
 
Head Gates and Head Gate Hoists. 
 
 615 
 
 o 
 
 00 
 
 CO 
 
 bo 
 
6i6 
 
 Appendages to Dams. 
 
Head Gates and Head Gate Hoists. 
 
 617 
 
 Fig. 382. Head Gate Hoist, Kilbourn, Wis. (Southern Wisconsin Power Co.). 
 
 The purpose of these fishways is to afford a gradual incline 
 through which a continuous stream of water of comparatively low 
 velocity shall flow and against which the fish may readily swim. 
 Both the inlet and outlet should be below low-water and the out- 
 let should be in such a position that the fish, when they ascend the 
 stream and reach the dam, in passing from one side to the other in 
 searching for a passage, are naturally led to the point where the 
 
6i8 
 
 Appendages to Dams. 
 
Fish ways. 
 
 619 
 
 Fig. 384. Timber Fishway in Dam at Sterling, 111. (Eng. News.) 
 
 Fig. 385. Fishway of Fish Commission, State of Wisconsin. 
 
620 
 
 Appendages to Dams. 
 
 flowing water is encountered. The slope of these fishways should 
 not be steeper than one vertical to four horizontal, and the water 
 should be so deflected that the velocity will be reduced as low as 
 possible. A fishway should be entirely automatic and free from 
 all regulating devices. It is usually desirable for the openings in 
 
 EL Fit 933 
 
 SPIL LWAY SECTION. 
 
 PLAN 
 
 SECTION THROUGH LO&-SLUICE 
 
 Fig. 386. Log Way in the Chesuncook Timber Dam. (Eng. Rec., vol. 50, 
 
 p. 70.) 
 
 the bulkheads or baffles to increase progressively from the lower 
 to the upper one in order to insure that the passage of the fishway 
 shall be full of water. The fishway should be so covered as to pre- 
 vent interference, but must be light or it will not be used by the 
 fish. 
 
Log-Ways. 
 
 621 
 
 310. Log- Ways. The free navigation of streams for logging 
 purposes is provided by law in most states and it is therefore neces- 
 sary where logging is practiced to provide ready means for their 
 passage over or through the dam. This is accomplished in the 
 
 Fig. 387. Log Way at Lower Dam, Minneapolis, Minn. 
 
 Kilbourn dam (see Fig. 374) by the lowering of any one of the 
 flood gates. 
 
 Fig. 386 shows a plan and section of the log-sluice constructed in 
 the Chesuncook timber dam on the Penobscot River. A section of 
 the spillway of the dam is also shown in the same figure. 
 
 Fig. 387 is a view of the logway in the lower dam at Minneapolis. 
 This sluice is only six or eight feet in width, and the depth and 
 quantity of water flowing is controlled by a bear trap leaf. 
 
622 Appendages to Dams. 
 
 In most cases, to avoid an excessive waste of water, it is desir- 
 able to build the logway as narrow as possible. Under such condi- 
 tions it becomes necessary to guide the logs into the sluice by tim- 
 ber booms which, leaving the sluice at a law angle, are strung up- 
 stream to such points that the logs in floating down stream shall 
 enter between them and be guided to the sluice opening. 
 
 LITERATURE. 
 
 MOVABLE DAMS, FLASHBOABDS, ETC. 
 
 1. Harcourt, L. V. Fixed and Movable Weirs. Proc. Ins. C. E. Vol. 60, 
 
 p. 24. Jan. 1880. 
 
 2. Chittenden, Hiram M. American Types of Movable Dams. Eng. News, 
 
 Feb. 7, 1895. Vol. 33, p. 84. 
 
 3. Stickney, Amos. Lifting Dam. Jour. Assn. Ehg. Soc. Vol. 16, p. 255. 
 
 June, 1896. 
 
 4. Thomas, B. F. A Design for a Movable Dam. Jour. Assn. Eng. Soc. 
 
 Vol. 16, p. 260. June, 1896. 
 
 5. Chittenden, H. M. Modified Drum Weir. Jour. Assn. Eng. Soc. Vol. 
 
 16, p. 249. June, 1896. 
 
 6. Powell, Archibald 0. Movable Dams, Sluice and Lock Gates of the Bear- 
 
 Trap Type. Jour. Assn. Eng. Soc. Vol. 16, p. 177. June, 1896. 
 
 7. Marshall, W. L. Marshall's Bear-Trap Dams. Jour. Assn. Eng. Soc. 
 
 Vol. 16, p. 218. June, 1896. 
 
 8. Jones, W. A. Bear-Trap Weirs.^ Jour. Assn. Eng. Soc. Vol. 16, p. 238. 
 
 June, 1896. 
 
 9. Johnson, Archibald. Bear-Trap Gates in the Navigable Pass, Sandy Lake 
 
 Reservoir Dam, Minnesota. Jour. Assn. of Eng. Soc. Vol. 16, 
 p. 210. June, 1896. 
 
 10. Martin, Wm. Bear-Trap Gate in Davis Island Dam, Ohio River. Jour. 
 
 Asso. Eng. Soc. Vol. 16, p. 208. June, 1896. 
 
 11. Movable Dams on the Great Kanawha River. Eng. News, vol. 36, p. 426. 
 
 Dec. 31, 1896. 
 
 12. Needle Dams. Ann. des Fonts et Chaussees. Part II. 1897. 
 
 13. Bear-Trap Dam. Chicago Drainage Canal. R. R. Gaz. Feb. 12, 1897. 
 
 14. The Use o Rolling Shutters in Movable Dams. Genie Civil. May 1, 1897. 
 
 15. Larminie, J. C. Falling Shutters, Godavery, Anient. Ind. Eng. Dec. 
 
 18, 1897. 
 
 16. Thomas, B. F. Movable Dams. Trans. Am. Soc. C. E. Vol. 39, p. 431. 
 
 Mar 1898. 
 
 17. Bear-.Trap Dam for Regulating Works, Chicago Drainage Canal. Eng. 
 
 News. Mar. 24, 1898. 
 
 18. The Movable Dam on the Big Sandy River. Genie Civil. May 14, 1898. 
 
 19. Marshall Automatic Movable Dam. Eng. News. May 26, 1898. 
 
Literature. 623 
 
 20. The Management of Non-parallel Motion and Deficient Operating Head 
 
 in Bear-Trap Dams by Auxiliary Constructions. Eng. News, 
 May 26, 1898. 
 
 21. New United States Government Needle Dam at Louisa, Kentucky, on the 
 
 Big Sandy River. Eng. News, vol. 40, p. 2. July 7, 1898. 
 
 22. The Chittenden Drum Dam. Eng. Rec. Vol. 40, p. 356. Sept. 16, 1899. 
 
 23. Claise, M. The Resistance of Dam Framing. Ann des Fonts et Chaus- 
 
 sees. 4 Trimestre, 1899. 
 
 24. A New Automatic Movable Dam. Eng. Rec. Vol. 45, p. 222. March 8, 
 
 1902. 
 
 25. Reconstruction of the Lake Winnibigoshish Dam. Eng. Rec. Vol. 46, 
 
 p. 250. Sept. 13, 1902. 
 
 26. Hilgard, K. E. Roller Dams. Schweizerische Bauzeitung. Bd. 43 s. 
 
 65 u. 86. Feb. 6-13, 1904. 
 
 27. Koechlin, Rene. Large Rolling Dams. Genie Civil, Feb. 27, 1904. 
 
 28. Guarini, Emile. Rolling Dams at Schweinfurt, Bavaria. Eng. News, 
 
 vol. 53, p. 57. Jan. 19, 1905. 
 
 29. Walker, Gilbert S. Pile Foundations for Movable Dam at McMechen, 
 
 W. Va. Eng. News, vol. 54, p. 100. July 27, 1905. 
 
 30. Movable Dam and Lock -of The Rice Irrigation and Improvement Assoc., 
 
 Mermentau River, La. Eng. News, vol. 54, p. 321. Sept. 28, 1905. 
 
 31. Movable Crest Dams at the Water Power Development of the Chicago 
 
 Drainage Canal. Eng. Rec. Vol. 56, p. 194. 
 
 32. Johnston, C. T. Masonry and Steel Head Gates of the Grand Valley Ir- 
 
 rigation Canal. Engineering News, Vol. 50, p. 141. 
 
 33. Hanna, F. W. Electrically Operated Gates for the Roosevelt Dam. Eng. 
 
 News, vol. 57, p. 586. 
 
 34. Hanna, F. W. Hydraulic Gates for Drainage Tunnl, Kern River Plant. 
 
 Eng. News, vol. 51, p. 326. 
 
 35. Leighton, M. O. High Pressure Sluice Gates. Jour. West. Soc. Eng. 
 
 Vol. II, p. 381. 
 
 36. Gillette, H. P. The Rudder Boom. Eng. News, Vol. 47, p. 473. 
 
 FISHWAYS. 
 
 1. Gerhardt, Paul. Fischwege and Fischteiche. Verlag Von Wilhelm En- 
 
 gelmann. Leipzig, 1904. 
 
 2. Leslie, Alexander. Salmon Ladders in Scotland. Institute of C. E. Vol. 
 
 89, p. 304. 
 
CHAPTER XXVI. 
 PONDAGE AND STORAGE. 
 
 331. Effect of Pondage on Power. The terms "Pondage" and 
 "Storage" are quite similar in meaning, both having reference to 
 the impounding of water for future use. The term pondage us- 
 ually refers to the smaller ponds which permit of the impounding 
 of the night flow for use during the working hours of day. Stor- 
 age, on the other hand, is usually applied to the larger impounding 
 reservoirs that enable a sufficient quantity of water to be stored 
 to carry the plant, to some extent at least, through the dry season 
 of the year. Between these limits every variation in capacity is 
 of course possible. 
 
 In Chapter IV, Section 54, the effect of pondage on the power 
 of a stream is briefly outlined and illustrated by hydrographs 
 shown in Figs. 41 and 42. The pondage illustrated by these dia- 
 grams is sufficient to store the entire flow of the river during the 
 parts of the day when the power is not in use and reserve it for 
 those hours of the day when the power is needed. Such a condi- 
 tion can frequently be realized for the low flows during the dry 
 seasons, but the capacity is seldom sufficient to store the larger 
 flows, and if sufficient should be investigated in a different manner 
 to be discussed later. These hydrographs (Figs. 41 and 42) 
 should therefore be examined with these points in view. 
 
 In many water power installations practically no pondage is pos- 
 sible and the power of the stream must be utilized as it flows or 
 otherwise it will be wasted. On continuous service, such as is 
 sometimes required by cotton factories, paper mills, and electro- 
 chemical works that run twenty-four hours per day, pondage is not 
 so essential. With most power loads, such as are shown by the 
 various load curves in Chapter XVII, the night load is small and 
 the pondage of the night flow will frequently permit of more than 
 doubling the power that can be otherwise utilized. 
 
 312. Effect of Limited Pondage on the Power Curve. Fre- 
 quently limited pondage only is possible and its influence on the 
 possible power that can be generated must be carefully investigated. 
 
Effects of Limited Pondage on the Power Curve. 625 
 
 If power is to be used for a limited number of hours each day, the 
 rate at which power can be used for this time without pondage will 
 be the same as for the t continuous power of the stream. 
 
 Such proportions of the otherwise unutilized flow of the stream 
 as can be impounded during periods of light load can be added to 
 the daily output. Thus, if power is used for 12 hours per day, and 
 the night flow can be impounded and utilized during the day, the 
 day power will be increased to double what it otherwise would be. 
 
 If power is used for only ten hours per day, with perfect pondage 
 the day power will be increased to 2.4 of what it would otherwise 
 be. 
 
 In twelve hours there are 43,200 seconds, and in each acre there 
 are 43,560 square feet, it can therefore readily be remembered that 
 for twelve hour pondage there must be practically as many acres 
 one foot deep (or acre feet) in the pond as there are cubic feet per 
 second to be impounded. For ten hour use and fourteen hour 
 storage, the pond area must be increased by one sixth above the 
 capacity needed for twelve hour service. For example: In order 
 to utilize the full flow of the Wisconsin River at Kilbourn in twelve 
 hours, (see Fig. 39) on the day of lowest flow (in August, 1904), a 
 pondage of 3,000 acre feet would have been necessary, and, to util- 
 ize this full flow in ten working hours, would have required a pon- 
 dage of about 3,500 acre feet. 
 
 Where the depth of pondage is considerable the effect of the 
 variation in head on the power should receive careful consideration. 
 
 313. Power Hydrograph at Sterling, Illinois. In 1903 the writer 
 was retained to investigate the probable effect, on the water power 
 at Sterling, Illinois, of the proposed diversion of water for feeding 
 the Illinois and Mississippi or "Hennepen" Canal. 
 
 The pondage formerly available at Sterling, by using eighteen 
 inch flash boards on the dam, was about 42,000,000 cubic feet (al- 
 most 1,000 acre feet). 
 
 The diversion dam at Sterling has been constructed about one 
 mile above the dam of the Sterling Hydraulic Company and has 
 limited the available pondage to an area of about 5,000,000 sq. ft., 
 and a pondage of about 7,000,000 cubic feet. This change has there- 
 fore caused a loss of pondage of about 35,000,000 cubic feet, which 
 represents the night storage (i. e., the storage during the fourteen 
 hours of night), of 700 cubic feet per second, which represents 980 
 hydraulic horse power for the ten hours of day. That is to say, 
 the loss of 35,000,000 cubic feet of storage capacity caused by the 
 
626 
 
 Pondage and Storage. 
 
 QQ 
 
 fcXJ 
 
 s 
 
Effects of Pondage on. Other Power. 627 
 
 construction of the U. S. Government dam near the mouth of the 
 Illinois and Mississippi Canal, has lost to the Sterling Hydraulic 
 Company about 980 hydraulic horse power during such periods as 
 the flow of the river is more than 840 cubic feet per second, and 
 less than the capacity of the wheels installed (i. e., 4,450 cubic feet 
 per second). 
 
 Fig. 388 gives a graphical illustration of the effects of storage on 
 the normal water power^at Sterling and the loss resulting from the 
 loss of storage. The lower flow line is the line of the normal hy- 
 draulic horse power of the Rock River for continuous (twenty-four 
 hour) service. It also shows the total power available for ten-hour 
 service without pondage. The flow line just above the line of 
 normal power, and parallel thereto, shows the additional ten-hour 
 power available from a pondage of 7,000,000 cubic feet. The upper 
 flow line shows the ten-hour power made available by the storage 
 of 42,000,000 cubic feet. The hatched area between lines two and 
 three represents therefore the loss in ten-hour power which has 
 been caused by the loss in storage of 36,000,000 cubic feet. 
 
 From this diagram it will be noted that when the flow of the 
 river is sufficient to supply the wheels, no loss would be occasioned 
 by the loss in pondage, and, as the flow approaches this point, the 
 actual loss decreases. It should also be noted that when the flow 
 of the river is less than 840 cubic feet per second (above the 
 amount diverted by the canal) the total storage of 42,000,000 cubic 
 feet is more than necessary to store the night flow, hence the loss 
 at such times caused by loss of pondage also decreases. 
 
 The approximate total loss of power for the year caused by the 
 loss of 35,000,000 cubic feet of storage, as measured from this 
 diagram, is 980 hydraulic horse power for, approximately, 250 ten- 
 hour days. 
 
 314. Effect of Pondage on Other Power. The pondage of water 
 during the night naturally interferes with the normal flow of the 
 stream and alters the regimen of the river at points below the point 
 of pondage. The effect of such interference on other power, and 
 the effect of other ponds on the plant contemplated, should be 
 carefully considered. 
 
 Fig. 389 is a hydrograph of the Fox River taken from observa- 
 tion by the Government Engineers at Rapid Croche, Wisconsin. 
 Above this point are a number of water power dams. Many of the 
 plants run twenty-four daily, but close down on Sundays. The ef- 
 
Pondage and Storage. 
 
 m h> to in ^t n 
 
 ON033S U3d 133J DI8R3 Nl 33UVH3SIQ 
 
Effect of Limited Storage. 
 
 629 
 
 feet of the Sunday shut-down on the stream flow is well shown in 
 the hydrograph and is evident even during flood periods. 
 
 315. Effect of Limited Storage. When the pondage 'available is 
 more than sufficient to carry the night flow of the low water period 
 over for day use, it becomes possible to equalize, to a greater or less 
 extent, the variation in daily flow and to utilize excess flow to in- 
 crease deficient flows, thus raising the quantity of available contin- 
 uous power. The extent of this equalization depends on the quan- 
 tity of storage and can readily be investigated graphically. 
 
 Fig. 390 shows the estimated daily flow of the Wisconsin River at 
 Kilbourn for July, August, and September, the low water period) 
 1904. From this hydrograph it will be seen that the lowest flow is 
 3,000 cubic feet per second. From Sec. 312 it is seen that in order 
 to utilize the night flow during the twelve hours of day, a pondage 
 of 3,000 acre feet must be available. With such a pondage the 
 
 16,000 
 
 14,000 
 
 12,000 
 
 10,000 
 
 8,000 
 
 6,000 
 
 4.0OO 
 
 2,000 
 
 O 
 
 JULY AUGUST SEPTEMBER 
 
 Fig. 390. Low Water Flow at Kilbourn and Storage Capacity Necessary to 
 Augment it to Various Amounts. 
 
 night flow can ordinarily be distributed so as to be available either 
 for twelve hour constant power or to furnish power for any equiv- 
 alent load curve. 
 
 In Fig. 390 the horizontal spaces each represent a flow of 1,000 
 cubic feet per second, and the vertical spaces, one day. The area 
 of each space therefore, represents 86,400,000 cubic feet, or ap- 
 proximately 2,000 acre-feet. 
 
 To increase the low water flow of the river to 4,000 second feet 
 will require a storage capacity equivalent to that represented by ap- 
 proximately three spaces, or a storage of 6,000 acre-feet in addition 
 to the pondage, or a total storage of about 9,000 acre feet. To in- 
 
630 Pondage and Storage. 
 
 crease the flow to 5,000 second feet, a total storage of 28,000 acre- 
 feet in addition to the pondage would be required; and a flow of 
 6,000 second feet, will require a storage of 90,000 acre feet in addi- 
 tion to the pondage. In this latter case the conditions to Sept. 6th 
 must be considered, for the increased flow from August I2th to I7th 
 is not sufficient to fill the reservoir, although it will reduce the 
 capacity required, as will also the increased flow of August 2oth. 
 
 The reservoir capacity represented by 90,000 acre feet is shown 
 on the diagram both by the curved hatched area above the flow- 
 line and by the rectangular shaded area as well. 
 
 If the reservoir capacity is known, and its equivalent repre- 
 sented on the drawing, its effect on the hydrograph can readily be 
 determined by trial. (See also Fig. 393.) 
 
 316. Effect of Large Storage. When large storage is available, 
 the daily flow of a stream can be equalized and its variations there- 
 fore becomes less important. In such cases the power of a plant 
 depends on the average weekly or monthly flow of the stream and 
 the possible storage capacity. 
 
 S. B. Hill, C. E., has suggested a method of discussing the effect 
 of storage on the flow and power of a stream which is well illus- 
 trated by Figs. 391 and 392. These hydrographs were prepared by 
 the writer to illustrate a report on the probable power of a pro- 
 posed hydraulic development in the South. Figs. 391 represent 
 the mean monthly flow of the river in question for the years 1893 
 to 1906 inclusive. In this case the scale above the zero line shofws 
 both the mean monthly flow of the stream in cubic feet per sec- 
 ond and the mean monthly power of the stream in horse power 
 hours per day with the head available. The available storage is 
 here 51,000 acre feet or 2,221,560,000 cubic feet. This storage is 
 equivalent to a flow of 857 second feet for thirty days, or a stor- 
 age of energy, with the available head, of about 5,000,000 horse 
 power hours. 
 
 The maximum daily continuous power (see A-A, Fig. 391) is 
 determined by the effect of the driest year (viz. 1904) on the stor- 
 age. The effect of the dry periods on the storage is shown by the 
 incisions into the lower or storage line of trie diagram. In the 
 year 1904 the reservoir capacity would have been just exhausted 
 in order to maintain the power during the low flows of September, 
 October and November of that year. The amount of available con- 
 tinuous energy (i. e. the position of the line A-A) is determined 
 
Effect of Auxiliary Power. 631 
 
 by equalizing the deficiency in flow during the dry months with 
 the total reservoir capacity. 
 
 It is important in the study of storage to see that in the inter- 
 vening periods of excessive flow, such flows are sufficient to 
 supply the deficiency occasioned by previous demands on the res- 
 ervoir, otherwise the effect of one dry period must be considered 
 in its relation to subsequent periods in determining the available 
 continuous power (see Fig. 391, 1897 and 1898). 
 
 The daily flow of this river for the year 1904 is shown by the 
 hydrograph, Fig. 393, from which it will be seen that with pondage, 
 but without storage, the available power of this stream would be 
 limited to a minimum of 27,000 horse power hours per day. 
 
 317. Effect of Auxiliary Power. In order to maintain a con- 
 tinuous power greater than that due to the minimum flow of the 
 stream plus the pondage, some source of auxiliary power must be 
 available. If it is desired to increase the power of the stream rep- 
 resented in Fig. 391 by 50,000 horse power hours per day, making 
 the total horse power hours delivered 163,400 (represented by line 
 B-B, Fig. 392), auxiliary power, as represented by the shaded areas 
 on this diagram, would be needed. As at all other times water 
 power would be available, the addition of steam auxiliary power 
 would apparently be warranted. The size of the plant needed to 
 furnish such excess power would depend on the method of power 
 utilization. It is evident that during the dry periods in 1899, 1904 
 and 1905, if the water power was first used to its maximum, and the 
 storage exhausted, an auxiliary plant would be needed of a capacity 
 almost equal to the maximum demand on the plant, and that a 
 plant of less capacity could be utilized satisfactorily only by operat- 
 ing it to a considerable capacity whenever a considerable draft be- 
 gan to be made on the storage. As the extent of the drought, or 
 deficiency of water, could not be anticipated such a use of the 
 auxiliary plant would require a greater expenditure of auxiliary 
 horse power hours than is represented by the shaded areas in Fig. 
 
 392. 
 
 An investigation of the capacity and amount of auxiliary power 
 needed, without pondage or storage, to maintain a given continu- 
 ous power, can be readily made from the hydrograph of daily flow 
 as shown by Figs. 394 and 395 which represent such a study of the 
 Rock River at Sterling, Illinois, before the diversion of water for 
 use in the Illinois and Mississippi canal, and the probable addi- 
 
Fig. 391. Mean Monthly Flow of a Southern Rive 
 
 Fig. 392. Amount of Auxiliary Power Nec< 
 
I3SOOQ 
 08000 
 81000 
 54000 
 27000 
 
 
 U) 
 
 id Effect Thereon of a Given Reservoir Capacity 
 
 2000 
 135000 
 108000 
 81000 
 54000 
 27000 
 
 
 ry to Increase Output by 50,000 H. P. H. 
 
634 
 
 Pondage and Storage. 
 
 O 
 
 cn 
 
 
 
 
 ~ 
 
 QNOD3S Uld 133J 
 
 Nl 39tiVH3SIQ 
 
Calculations for Storage. 
 
 635 
 
 tional auxiliary power required to maintain the same power after 
 such diversion. 
 
 318. Effect of Maximum Storage. As the head increases the 
 quantity of water needed to develop a given amount of power de- 
 creases, and storage becomes of much greater relative value. The 
 storage of comparatively small quantities of water also becomes 
 a more simple matter, but conditions which need little consideration 
 with larger flows and lower heads, then become more important- In 
 such cases, relatively, large reservoir capacity sometimes becomes 
 
 Fig. 394. Hydrograph Showing Auxiliary Power Necessary to Maintain 
 4450 Ten-hour Horse Power at Sterling, 111. 
 
 Fig. 395. Hydrograph Showing Auxiliary Power Needed to Maintain Ca- 
 pacity of Wheels and Probable Increase Due to Diversion of Water 
 for Illinois and Mississippi Canal. 
 
 possible and only the questions of desirability and cost limit the 
 extent to which such storage may be carried. 
 
 319. Calculations for Storage. Rippl has outlined a method of 
 coimputing storage which may occasionally be used to advantage 
 under high head conditions, when- it is desired to utilize the average 
 flow of a series of dry months or years by extensive storage. This 
 method consists in graphically representing the net yield of the 
 
6 3 6 
 
 Pondage and Storage. 
 
 stream during the period of low flow and from the curve of the net 
 flow estimating the quantity of storage necssary for its full utiliza- 
 tion. 
 
 The method suggested may be illustrated as follows : 
 
 From a study of the hydrographic conditions on the water shed 
 
 for a considerable term of year, the period of extreme low flow 
 
 is selected. For this period the observed or estimated flow of the 
 
 stream for each month is reduced by the loss due to evaporation, 
 
 800,000 
 
 700,000 
 
 SCALE OF MONTHS 
 
 Fig. 396. Diagram Illustrating Rippl Method of Calculating Storage. 
 
 seepage, etc. The remainder represents the net quantity of water 
 available for power purposes, The summation of these monthly 
 balances, added one to the other consecutively can be platted in a 
 curve in which the abscissa of each point represents the total time 
 from the beginning of the period ; and the ordinate, the total quan- 
 tity of water available during the same interval. The scale may 
 represent inches on the drainage areas, cubic feet, acre feet, or 
 such other unit as may be desired. Such a curve is represented in 
 Fig. 396 by the irregular curve A-B-OD-E-F. The inclination of 
 Lhe curve at any point indicates the rate of the net flow at that par- 
 
Calculations for Storage. 637 
 
 ticular time. When the curve is parallel to the horizontal axis, the 
 flow at that time will just balance the losses caused by evapora- 
 tion, seepage, etc. A negative inclination of the supply line shows 
 that a loss from the reservoir is taking place. 
 
 In a similar manner the curve of consumption can be platted. 
 For most purposes this can be considered a straight line as the var- 
 iation in the use of power from season to season is a refinement not 
 usually warranted, unless the uses to which the power is to be put 
 at various times of the year are well established. In Fig. 396 a 
 series of straight lines of consumption are drawn, representing the 
 use of water at rates of 100 to 600 acre feet per day. These rates 
 correspond essentially to rates of from 50 to 300 cubic feet per sec- 
 ond. 
 
 The ordinate between the supply and any demand line represents 
 the total surplus from the beginning of the period considered, and 
 when inclination of the supply line is less than that of the demand 
 line, the yield of the drainage area is less than the demand and a 
 reservoir is necessary. 
 
 The deficiency occurring during dry periods is found by drawing 
 lines parallel to the demand line, or lines, and tangent to the curve 
 at the various summits of the supply curve, as at B. 
 
 The maximum deficiency in the supply, and the necessary capac- 
 ity of the reservoir to maintain the demand during the period, is 
 shown by the maximum ordinate drawn from the tangent to the 
 curve itself. The period during which the reservoir would be 
 drawn below the high water line is represented by the horizontal 
 distance between the tangent point and the first point of inter- 
 section of the curve. If the tangent from any summit parallel to 
 any demand line fails to intersect the cu,rve, it indicates that, during 
 that period, the supply is inadequate for the demand. To insure a 
 full reservoir it is necessary that a parallel tangent drawn backward 
 from the low points on the supply curve shall intersect the curve at 
 some point below. For example: The line B-7, representing a daily 
 consumption of 700 acre feet, does not again intersect the curve 
 and is therefore beyond the capacity of the stream. The line B-6 
 intersects the curve at E and is the limit of the stream capacity. 
 Such a consumption will be provided by a storage of about 150,000 
 acre feet as represented by the length of the line 6-D, and such a 
 reservoir will be below the flow line for about twenty-two months 
 during the dry period illustrated in this diagram. That this reser- 
 voir will fill is shown by the intersection of the lower tangent D-A 
 
6 3 S 
 
 Pondage and Storage. 
 
 with the curve near A. The conditions necessary to maintain 
 capacities of 500, 400 and 300 second feet are shown respectively by 
 the tangents B-5, B-4 and B-3, and the verticals 5-D, 4-C and 3-C. 
 If the amount of storage is known, and it is desired to ascertain 
 the maximum demand, that can be satisfied by such fixed capacity, 
 
 ORYEST FIVE CONSEC 
 
 1MT 1M0 IBM 
 
 Fig. 397. Diagram Showing Annual Run-off from Tohickon Creek. 
 
 the rate is determined by drawing various tangent lines from the 
 summits, having the maximum ordinates equal to the fixed storage. 
 320. Method of Storage Calculations. The results of calcula- 
 tions, as outlined in Sec. 319 for various conditions of storage on 
 Tohickon Creek, are shown in Table XXXIX and Fig. 398. To- 
 hickon Creek is one of the possible sources of water supply which 
 has been investigated by the City of Philadelphia for a considerable 
 period. The observed monthly rainfalls and stream flows from the 
 drainage area of this stream (in inches on the drainage area) are 
 given in Tables XL and XLI. The five year period of minimum 
 flow is found by inspection to run from December, 1893, to Novem- 
 ber, 1898, as shown by Fig. 397. The approximate evaporation dur- 
 ing the period is taken from Appendix F. 
 
 The calculations of the mass curves are based on the extreme 
 variations in reservoir area of o to 100 per cent ; that is, on the as- 
 
Method of Storage Calculations. 
 
 639 
 
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 Pondage and Storage. 
 
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 r^ooi^ioost^-oscpcoi^- 
 
 'M CM 
 
 OSCOtOlOt^COCOCOOSCMOSrH 
 
 ' d 
 
 OSOrH-HHiOCOrHT^lOCMCOkO OS 
 IO O CM rH CM CO O CO t^ CO O O CO 
 
 OCOOlOCO( 
 
 Tj-i O t- t> 
 
 rH IO OS O <M 1^ CO 
 
 GO CO CO OS OS OS OS 
 
 O 8 CO CM O 
 
 I I + + 
 
 COOSt^rHCOCO 
 
 rHrHCO' ICOCOCOrH 
 
 grSgrH^gg ct^S^gg^ 
 
 | | 
 
 r_| CQ rH rH rf rH CM 
 
 CO CO CO rH (M Th rH 
 
 ++++++ 1 
 
 CM 1>- "* CO iO 
 
 CO CM CO rH O 
 
 I I I + I 
 
 CO O OS CO 00 CO CO 
 t^ CO iO <M rH t^ rH 
 
 + + + + + 1 + 1 1 1 + 
 
 rH t-~ CO t^ O 
 
 CO CM O O rH 
 
 COCOrHCOrHHHOqOlOOOCO 
 
 8^8coSoS^ 
 
 CO CM CO ' rH CO 
 
 CO -* 
 
 CO OS CO CM O 
 10 CO OS O rH 
 
 rH rH rH CM <M 
 
 C""-! CO ^O ^O CO CO CO CO CO -CO CO 
 
 iOiOOCOCOCOCOCOCCCCCOc^ 
 
 O i iCMTtlCOGCCO^fO'OI^lOCO rHrHCOOSOSCO 1 
 CO CO HH COIO Ot^^ rH CO OS OCO 05 CC CO HS OS O ' 
 
 HH O CO CO rH 
 CM rH CO 
 I I I + I 
 
 rH COCOrHrHrHCMCOrH rH 
 
 + + + +! | | + | + | + 
 
 COCO CN rH CO ^ 
 
 + 4- + + + + | 
 
 CO iO ^ CO CM 
 
 pooooooooooo 
 
 777"T7TTt7TT 
 
 OOOt^OiOiOOiOOCMCO ,OOOt^OOi 
 
 rHrHrHT-tCOHHiOCOlOr^COCM rHrHrHrHCOHHlO 
 I II I I I I I \ \ \ I I I I I I I 
 
 CO CO t~ CO rH 
 IO -*t CO GO I 
 
 co -^ ' co CM' 
 
 t^ CO t^ 
 
 HH HH CO CM CO I> 
 
 (MCOCNCOCOlOCCCO rH.rH 
 
 CO^CiOCOOCOHHGCCXlO^ 
 CDlClO^ft-COrHlOrHrHOCO 
 
 rH CMOS!OiO-HCCCO<MGOGO CCOOCOO-^OS 
 CCCOOSrHlOCOr^COt^rHOr^ Ot^OCOlOOrH 
 
 i CM CM -^ HH r-i CM rH HH CO HH ,_( C3 IO 
 
 CM rH rH CM 
 
 
 fi bi'fr : : 
 
 iii^j 
 
 a :& 
 
 111 
 
 39 
 
 
642 
 
 Pondage and Storage. 
 
 p 
 
 M 
 
 PQ 
 
 B8JBJIOAJ988J 
 #001 WAY 
 
 c jo urns 
 'ranooy 
 
 T i (M lO CO <M 
 C5 r-i (M (M C^I 1C 
 
 sM^s^ 
 
 With 75$ reservoir 
 area. 
 
 2,1 jo tuns 
 umoDv 
 
 O t>- i i CO C^J 
 
 oo cr. Tt o o i>. 
 
 t^- rf CC -^ CO 
 
 kiOjOjO_JJD 'O 
 
 '91 PUB ci 
 
 jo rang 
 
 ^^^0 
 
 T-H T-H 00 rH l f C<J 
 | | 
 
 JO #01 
 
 t^gS 
 r^ r- 1 CC rH Tl 
 1 1 + + 
 
 ' jo $c S 
 
 <M OC C^l 1C <M 
 
 1C r-i O r-i r-l 
 
 With 50$ reservoir 
 area. 
 
 gl jo urns 
 ranooy 
 
 OS C<1 1- QQ O 
 
 ^t 1 r T 1 i 1 Tf CO 
 
 1^ t^ l-^ 1^ t^ 
 
 'SIPUMI 
 jo rang 
 
 O1 t-- lO i I CO 
 
 OS O C5 CO CO 
 
 i I <M rH N 
 1 1 + + 
 
 J ^09 
 
 t rf c: i i cc 
 ^ os ^ cr. o co 
 
 rH C<l rH 
 1 1 + + 
 
 ^ jo #0 
 
 St>. * O O 
 CO O 01 (M 
 
 With 25$ reservoir 
 arear. 
 
 '6 jo rans 
 uinaoy 
 
 o gSSSS 
 
 s^iis 
 
 '8 pu^ Z 
 jo mng 
 
 - r^ co cc oo 
 
 00 
 
 1 1 + + 
 
 fi J fe 
 
 as <M cr. o 
 
 ^ W "* o CO 
 
 M 1 + + 
 
 'S jo ^9Z 
 
 iO 1C '-C CO 1^. 
 
 t^ o >o o * co 
 
 CO 
 
 B8.re JIOAI9 
 -S9J ou qijAY 
 
 g jo rans 
 uinooy 
 
 OS CO ~ O Cl 
 CO O t-<N 
 
 ^ O IO Dp O 
 
 rH rH ^_ ,_i CO 
 
 **-8 
 
 -f O5 r>- I-H co 
 Ci CO o: OCQ 
 lO .... 
 
 7 ^t ^ <M rH 
 
 1 1 + + 
 
 S8SSOJ 
 
 laujjo PUB uorreaodeAg 
 
 ^ SSoSoo 
 
 TIC -f CO <M 
 III! 
 
 saqoui ui IPJUIBH 
 
 CO 1C CO rH CO 
 
 O O O (M to 
 
 "f co co 10 co 
 
 saqoui ui no-un^j 
 
 t^ -* CO O 
 CO O b- O O 1C 
 
 
 
 : ,- , 
 
 jijj 
 
 - 411 1 
 
 2<o 
 
Method of Storage Calculations. 
 
 643 
 
 TABLE XL. 
 
 Toliickon Creek Monthly Rainfall in Inches. 
 
 Year. 
 
 S 
 
 h- ; 
 
 & 
 O> 
 M 
 
 c 
 
 CS 
 
 S 
 
 s_' 
 
 CU 
 < 
 
 >* 
 
 o3 
 *^ 
 
 0; 
 
 d 
 
 H^ 
 
 1-5 
 
 hb 
 
 < 
 
 "a. 
 
 
 
 ^ 
 
 8 
 
 1 
 
 d 
 
 1 
 
 .& 
 
 8 tj 
 pHpii-- 
 
 1886 
 
 4.15 
 4.24 
 5.31 
 4.23 
 2.82 
 6.14 
 5 49 
 
 6.01 
 5.47 
 4.34 
 2.37 
 4.73 
 4.58 
 1.23 
 5.88 
 3.96 
 .96 
 7.90 
 3.10 
 3.38 
 4.75 
 4.08 
 
 4.76 
 3.07 
 5.23 
 3.67 
 6.77 
 4.79 
 4.13 
 2.46 
 1.65 
 3.11 
 5.44 
 2.46 
 2.84 
 6.60 
 4.04 
 
 3.42 
 2.42 
 4.08 
 4.90 
 2.48 
 1.97 
 1.95 
 4.96 
 2.91 
 5.50 
 1.48 
 3.20 
 3.73 
 2.19 
 3.33 
 
 7.14 
 2.59 
 3.03 
 5.41 
 6.30 
 2.83 
 5.55 
 4.98 
 13.50 
 2.99 
 3.18 
 8.90 
 7.62 
 
 9 93 
 
 174 
 
 4.53 
 5.77 
 1.69 
 6.94 
 3.93 
 3.38 
 3.20 
 4.05 
 2.63 
 4.49 
 4.07 
 5.10 
 .76 
 2.74 
 3.95 
 
 5.47 
 8.13 
 3.20 
 12.33 
 5.81 
 7.49 
 4.27 
 2.10 
 2.28 
 3.53 
 8.06 
 8.47 
 4.00 
 3.29 
 5.42 
 
 1.08 
 5.30 
 8.07 
 4.63 
 5.75 
 8.90 
 3.76 
 8.67 
 2.03 
 4.43 
 1.63 
 4.75 
 6.05 
 5.05 
 4.93 
 
 1.30 
 3.36 
 8.32 
 7.92 
 2.98 
 1.37 
 2.91 
 3.20 
 9.44 
 .68 
 5.83 
 1.92 
 2.03 
 6.70 
 4.16 
 
 2.59 
 1.93 
 4.06 
 4.57 
 6.31 
 3.81 
 .64 
 3.72 
 5.18 
 3.86 
 2.67 
 1.83 
 5.21 
 1.39 
 3.71 
 
 5.16 
 1.42 
 3.66 
 8.86 
 1.07 
 1.97 
 7.10 
 4.37 
 3.01 
 2.11 
 4.08 
 5.02 
 3.56 
 2.55 
 3.33 
 
 3.83 
 6.53 
 4.35 
 1.99 
 2.75 
 5.09 
 1.57 
 3.17 
 4.60 
 2.57 
 .94 
 4.64 
 3.49 
 2.34 
 3:78 
 
 49.45 
 50.22 
 55.34 
 68.04 
 51.60 
 52.32 
 41.80 
 50.52 
 53.01 
 38.24 
 46.46 
 50.59 
 46.92 
 43.51 
 49.11 
 
 1887 
 
 1888 
 1889 
 
 1890 
 
 1891 
 
 1892 
 
 1893 
 
 2.96 
 1.82 
 4.19 
 1.18 
 2.20 
 4.19 
 3.68 
 3.64 
 
 1894 
 
 1895 
 
 1896 
 
 1897 
 
 1898 
 
 1899 
 Average 
 
 TABLE XLI. 
 Tohickon Creek Monthly Discharge in Inches on Drainage Area. 
 
 Year. 
 
 oS 
 
 1-5 
 
 J3 
 <D 
 (* 
 
 il 
 oi 
 ^ 
 
 s_' 
 PH 
 < 
 
 !> 
 
 OS 
 
 
 
 6 
 
 G 
 
 >-5 
 
 >> 
 
 -5 
 
 hi> 
 
 < 
 
 <5 
 
 & 
 
 4^ 
 
 
 
 6 
 to 
 
 cj 
 
 & 
 
 t-& 
 
 .2* 
 ^P-g 
 
 1886 
 1887 
 1888 
 
 1889 
 
 4.36 
 5.04 
 6.38 
 4.38 
 2.06 
 6.15 
 6.53 
 2.22 
 .80 
 3.95 
 .54 
 1.81 
 3.70 
 4 7?, 
 
 9.19 
 5.25 
 6.72 
 1.51 
 3.78 
 5.68 
 1.19 
 6.64 
 3.80 
 1.70 
 i.59 
 2.92 
 4.05 
 5.56 
 4.25 
 
 4.28 
 3.84 
 6.27 
 3 86 
 6.37 
 5.03 
 4.87 
 4.54 
 3.09 
 5.37 
 5.48 
 2.19 
 1.83 
 8.99 
 4.70 
 
 4.75 
 1.02 
 
 4.28 
 2.88 
 1.79 
 1.58 
 .84 
 3.22 
 2.28 
 4.65 
 .73 
 1.55 
 2.50 
 1.57 
 2.50 
 
 3.43 
 .93 
 .52 
 1.70 
 3.09 
 .28 
 2.05 
 3.79 
 8.58 
 .66 
 .30 
 4.63 
 5.04 
 .25 
 2.08 
 
 1.41 
 1.21 
 .15 
 2.29 
 .75 
 .17 
 .70 
 .45 
 .53 
 .27 
 .18 
 1.71 
 .19 
 .07 
 .76 
 
 .77 
 1.63 
 .06 
 6.41 
 .87 
 .90 
 .51 
 .10 
 .19 
 .80 
 2.54 
 2.68 
 .07 
 .08 
 1.15 
 
 .09 
 1.96 
 1.77 
 3.75 
 .92 
 8.92 
 .30 
 1.56 
 .12 
 37 
 .19 
 .73 
 .74 
 1.02 
 1.19 
 
 .03 
 .40 
 5.50 
 3.40 
 1.22 
 .94 
 .19 
 .83 
 3.37 
 .03 
 1.12 
 .12 
 .08 
 2.26 
 1.36 
 
 .05 
 .25 
 1.54 
 2.33 
 3.54 
 .46 
 .09 
 .60 
 2.10 
 .09 
 1.06 
 .07 
 .60 
 .19 
 1.20 
 
 1.91 
 .25 
 3.11 
 7.97 
 .69 
 .63 
 3.19 
 2.62 
 2.67 
 .13 
 2.34 
 1.79 
 4.50 
 1.02 
 1.89 
 
 2.38 
 3.20 
 3.47 
 1.92 
 1:51 
 4.27 
 1.67 
 3.10 
 3.57 
 .67 
 .80 
 4.08 
 4.23 
 1.28 
 2 89 
 
 32.65 
 24.98 
 39.77 
 42.40 
 26.59 
 30.01 
 22.13 
 29.67 
 31.10 
 18.69 
 19.87 
 24.28 
 27.53 
 27.01 
 27.58 
 
 1890 
 1891 
 
 1892 
 
 1893 
 
 1894. 
 
 1895 .,.. 
 1896 
 1897 
 1898 
 
 1899 
 
 Average 
 
 3.59 
 
 sumption that the reservoir may occupy from nothing to the en- 
 tire drainage area. 
 
 The conditions on the reservoir area are those due to the equal- 
 ization of the rainfall with the evaporation, seepage and other 
 
644 Pondage and Storage. 
 
 losses. The conditions on the balance of the water shed are given 
 by the run-off and its summation. 
 
 Table XXXIX shows these calculations in detail and the mass 
 curves drawn from columns 6, 10, 14, 18 and 19 are platted in Fig. 
 398. The maximum continuous power which could be maintained 
 throughout this period without storage is shown by the lowest 
 slopes of the zero per cent, mass curve. The possible maximum de- 
 velopment of the stream with various percentages of reservoir area 
 can be determined by an analysis of the lower curves similar to that 
 described in Sec. 319. 
 
 321. Analytical Methods. Graphical methods o;f computation 
 have been heretofore suggested as a means of investigating pondage 
 and storage conditions. Such methods are believed to be advanta- 
 geous in most cases on account of presenting visible evidence which 
 can usually be more clearly understood than an abstract analysis. 
 
 Analytical methods for the consideration of these questions are 
 usually obvious after the graphical methods discussed are under- 
 stood, and such methods should usually be used to check up the 
 graphical deductions. Such methods may be illustrated by the fol- 
 lowing analysis of the effect of low water conditions on- a proposed 
 water power on a Western river on which the writer recently fur- 
 nished a report. 
 
 In this case daily guage readings were available for about ten 
 years, and the rainfall records were available for a considerably 
 longer period. 
 
 From these records it appeared that the year 1905 was the driest 
 year on record, and that the power available during the low water 
 period of that year would have been equalled at least at all times 
 during every year in the past twenty years, and with a probable like 
 result in the future. 
 
 At the proposed plant each cubic foot per second, flowing during 
 a day of twenty-four hours, will, at 80 per cent, efficiency, produce 
 3.63 continuous horse power. In order to develop 8,000 twenty-four 
 hour horse power, it would be necessary, therefore, to have avail- 
 able a continuous flow of 2,200 second feet, while the minimum flow 
 in 1905 was only 1240 second feet. An examination of the gaug- 
 ings shows that during the dry period of 1905 the water was defi- 
 ient in quantity for sixty-eight days. The average flow for this pe- 
 riod was 1,700 second feet, causing an average deficiency of 500 
 second feet. To impound sufficient water to maintain 2,200 second 
 feet would require, therefore, a storage capacity of about 1,000 acre 
 
Literature. 645 
 
 feet for each day of the dry period, or a total reservoir capacity of 
 about 68,000 acre feet. Above the proposed dam site is a lake hav- 
 ing an area of about 60 square miles or 38,400 acres. By raising the 
 level of this lake two feet a storage of 76,800 acre feet would be at- 
 tainable which, with careful manipulation would be sufficient to 
 maintain the desired power. 
 
 If no storage were possible, and auxiliary power was to be es- 
 tablished, the maximum capacity of the auxiliary plant would be 
 determined by the day of lowest flow. During this day there was a 
 deficiency of 960 second feet, equivalent to about 3,500 horse power 
 The average deficiency for the period was 500 second feet, rep- 
 resenting a necessary average of auxiliary power of 1815 horse 
 power, or 43,560 horse power hours per day. The total auxiliary 
 power for this period (68 days) would therefore be about 3,000,000 
 horse power hours. 
 
 In the same manner the total amount of auxiliary power neces- 
 sary during each year could be estimated and the interest and de- 
 preciation on the cost of the plant, plus the average annual operating 
 expenses of the auxiliary plant, when considered in connection with 
 similar elements of the water power installation, would furnish 
 the basis for an estimate of the first cost and operating expenses of 
 the combined plant to develop the required power. 
 
 LITERATURE. 
 
 1. Rippl, W. The Capacity of Storage-Reservoirs for Water Supply. Insti- 
 
 tute of Civil Engineers, vol. 71, p. 270. 
 
 2. Fitzgerald, Desmond. Report on Capacity of the Sudbury River and 
 
 Lake Cochituate Water Sheds in Time of Drought. New Eng. 
 Water Works Asso. 
 
 3. Fitzgerald, Desmond. Methods Used to Determine the Best Capacity to 
 
 Give to Basin No. 5, Boston Water Works. Asso. of Eng. Soc. 
 Vol. X, p. 431. 
 
 4. Greenleaf, J. L. A Method for Determining the Supply from a Given 
 
 Water Shed. Eng. News, vol. 33, p. 238. 
 
 5. Horton, Theodore. A Form of Mass Diagram for Studying the Yield of 
 
 Water Sheds. Eng. Rec. Vol. 36, p. 185. 
 
 6. Turneaure and Russell. Public Water Supplies. Chapter XV. John 
 
 Wiley & Sons. 
 
 7. Mead, Daniel W. Report on the Water Power of the Rock River at Ster- 
 
 ling and Rock Falls, 111. 1904. 
 
CHAPTER XXVII. 
 
 COST, VALUE AND SALE OF POWER. 
 
 322. Financial Considerations. Every engineer who is called 
 upon to advise as to the commercial feasibility of a proposed water 
 power development must carefully consider all financial aspects of 
 the project, for on its financial feasibility the entire commercial suc- 
 cess depends. It is not enough that^the power be constant and suffi- 
 cient in quantity, that the plant be well designed, and that the cost 
 of the same be reasonable ; but there must also be a market in which 
 the power can be utilized to advantage and the price at which the 
 power can be sold in competition with all other sources of power 
 must be sufficient to pay all expenses involved in the construction 
 and operation of the plant and afford a fair return to those who as- 
 sume the risk of the undertaking. 
 
 It is a common belief that any water power development must be 
 profitable. Knowing that an undeveloped water power is a contin- 
 ual waste of energy, it is commonly assumed that the saving of this 
 waste is bound to result in a profit to those who acquire the prop- 
 erty and develop the power. That many water powrs can not be de- 
 veloped at a profit under present conditions is a fact which in many 
 instances is learned by its owner only after a large and unwarranted 
 expense is entailed. 
 
 323. Purpose of Development. Any water power project must 
 be examined in the light of the purposes for which it is to be used 
 or the market it is to supply. The supply must be constant and con- 
 tinuous not only for every day in the year but for every year of its 
 operation unless its use will permit of the discontinuation of the 
 power during droughts, high water, or other contingencies that 
 will decrease or temporarily suspend the generation of power by the 
 plant. 
 
 If its use or market will permit of such interruption, a temporary 
 power may sometimes be developed to advantage. Where the 
 power furnished must be continuous in order to avoid losses or 
 great inconvenience, precautions must be taken to so design the 
 plant with duplication of parts, extra units and suitable pondage or 
 
Cost of Development. 647 
 
 storage or with such sufficient auxiliary sources of power that in- 
 terruptions shall be essentially obviated. 
 
 In some cases considerable losses have been entailed by hydraulic 
 developments constructed without sufficient study or consideration 
 of these questions. In such cases, the plants after completion, were 
 unable to maintain continuous power, without the installation of 
 auxiliary steam plants for use during the temporary interruptions 
 to which the plant was subject, and the income from the sale of 
 power would not warrant the extra expense and hence the plants 
 were commercial failures. 
 
 324. Cost of Water Power, The cost of water power depends on : 
 . First: The investment in real estate, water rights, power plant 
 and equipment, transmision lines, sub-stations, distribution system, 
 etc., and the interest which must be paid thereon. 
 
 Second : On the loss from the depreciation of the various elements 
 of the plant, the cost of maintenance and repairs, the cost of con- 
 tingent damages from floods or other accidents. 
 
 Third : The operating expenses, including labor, oil, waste, and 
 other station supplies and expenses, including also in, hydro-electic 
 plants, the patroling and maintenance of the transmission lines and 
 distribution system. 
 
 Fourth : The expenses for taxes, insurance, etc. 
 
 The total annual cost due to the above sources of expense is the 
 annual cost of the power to be furnished by the plant, be the quan- 
 tity of that power much or little. 
 
 The investment charge should be liberally estimated and should 
 include the entire expense of development including auxiliary power 
 plant, if needed. All contingencies should be carefully considered 
 and estimated. A serious error in the estimate of cost caused by 
 large and unexpected contingencies in construction may mean a 
 commercial failure of the enterprise. The same consideration 
 should be given to the estimate of contingent expenses, deprecia- 
 tion and operating expenses, and each other factor on which the 
 financial life of the plant depends. 
 
 325. Cost of Development. The various conditions under which 
 water power is developed greatly affect the cost of development. 
 As a general rule, other things being comparatively equal, the larger 
 the power developed the smaller the cost of development per unit 
 capacity. This is particularly true when developments of various 
 capacities are considered on the same stream. Many of the features 
 
6 4 8 
 
 Cost, Value and Sale of Power. 
 
 of the development must be essentially the same regardless of the 
 ultimate capacity of the plant. This is especially true of dams 
 and river protection work. The variation in cost per unit capacity 
 of various sized plants is well illustrated by Table XLII. 
 
 TABLE XLII. 
 Estimate of the cost of a Hydro- Electric Plant at Niagara Falls.* 
 
 ITEMS. 
 
 24-HouR POWER CAPACITY. 
 
 50,000 H. P. 
 Development. 
 
 75, 000 H. P. 
 Development. 
 
 100,000 H.P. 
 Develop- 
 ment. 
 
 Tunnel tail-race 
 
 $1,250,000 
 450,000 
 500, 000 
 300,000 
 1,080,000 
 760,000 
 350,000 
 100,000 
 75,000 
 
 $1,250,000 
 450,000 
 700, 000 
 450,000 
 1,440,000 
 910,000 
 525,000 
 100, 000 
 75, 000 
 
 $1,250,000 
 450,000 
 700, 000 
 600,000 
 1,980,000 
 1,400,000 
 700, 000 
 100, 000 
 75,000 
 
 Headworks and canal 
 
 Wheel pit. 
 
 Power house 
 
 Hydraulic equipment 
 
 Electric eouipment 
 
 Transformer station and equipment. . 
 Office building and machine shop. . . . 
 Miscellao eous 
 
 Engineering and contingencies 10 per 
 cent. . . . 
 
 $4,865,000 
 485,000 
 
 $5,900,000 - 
 590,000 
 
 $7,255,000 
 725,000 
 
 Interest, 2 years at 4 per cent 
 Total capital cost 
 
 $5,350,000 
 436, 560 
 
 $6,490,000 
 529,584 
 
 $7,980,000 
 651,168 
 
 $5,786,560 
 
 $7,019,584 
 
 $8,631,168 
 
 Per horse-power 
 
 $114 
 
 $94 
 
 $86 
 
 
 * First report of Hydro-Electric Power Commission of the Province of Ontario, 
 page 15. 
 
 Other things being comparatively equal, the cost of development 
 varies inversely, although not in the same ratio, as the head. The 
 reason of this is evident from the fact that while the power of a 
 stream is directly proportional to the head, the capacity of a turbine 
 increases as the three-halves power of the head. With double the 
 head the power of a wheel is increased almost three times. 
 
 For moderate changes in head, the cost of the turbines will vary 
 in proportion to their size and not their capacity ; so that the cost 
 per unit of capacity will usually decrease considerably with the 
 head. The cost per unit of capacity of other features of water power 
 plants will also frequently decrease as the head increases. This is 
 
Cost of Development. 
 
 649 
 
 particularly true of pondage capacity which increases in value 
 directly as the head increases, although the cost per unit of land 
 overflowed may remain constant. The relative cost of high and 
 low head developments may be illustrated by the comparative cost 
 of two plants recently designed by the writer which were of ap- 
 proximately the same capacity but working under different heads. 
 The comparison is as follows: 
 
 TABLE XLIII 
 Comparative Cost of Water Power Plants. 
 
 
 
 COST OF WATER POWER DEVELOPMENT. 
 
 Capacity. 
 
 Head. 
 
 Without 
 dam. 
 
 With 
 dain. 
 
 With dam 
 and electrical 
 equipment. 
 
 With dam, electrical 
 equipment and 
 transmission line. 
 
 8,000 
 
 18 
 
 63.50 
 
 86 
 
 115 
 
 150 
 
 8,000 
 
 80 
 
 21 
 
 39 
 
 60 
 
 90 
 
 TABLE XLIV. 
 
 Estimates of the cost of developing various Comachian power from Reports of 
 Ontario Hydro- Electric Power Commission. 
 
 Location of Proposed Development. 
 
 Natur- 
 al 
 head. 
 
 Avail- 
 able 
 head. 
 
 Power 
 develop- 
 ed, H. P. 
 
 Estimated 
 capital 
 cost. 
 
 Cost 
 
 ?. 
 
 Cost per 
 H. P. per 
 ft. head. 
 
 (1) Healey's Falls, Lower Trent River . 
 
 
 00 
 
 8000 
 
 $675000 
 
 84 38 
 
 
 Middle Falls, Lower Trent River 
 
 
 30 
 
 5200 
 
 475000 
 
 91 37 
 
 
 Rauney's Fall 
 
 
 35 
 
 6000 
 
 425000 
 
 69 67 
 
 
 Rapids above Glen Miller . . 
 
 
 18 
 
 3200 
 
 3500CO 
 
 109 38 
 
 
 
 Rapids above Trenton 
 
 
 18 
 
 3200 
 
 370000 
 
 115 63 
 
 
 (2) Maitland River 
 
 
 80 (5) 
 
 1600 
 
 325000 
 
 203 12 
 
 
 
 
 40 
 
 1333 
 
 250000 
 
 187 53 
 
 
 Beaver River (Eugenia Falls) 
 
 
 420 
 
 2267 
 
 291000 
 
 128 28 
 
 
 Severn River (Big Chute) 
 
 
 52 (6) 
 
 4000 
 
 350000 
 
 87 50 
 
 
 South River 
 
 
 85 
 
 750 
 
 115000 
 
 153 33 
 
 
 <3) St. Lawrence River, Iroquois, Ont. 
 
 
 12 
 
 1200 
 
 179000 
 
 149 16 
 
 
 Mississippi River,-High Falls, Ont. A 
 
 
 78 (7) 
 
 2400 
 
 195000 
 
 81 25 
 
 
 Mississippi River, High Falls. Ont. B 
 
 
 78 
 
 1100 
 
 123000 
 
 181 82 
 
 * 
 
 Montreal River, Fountain Falls, Ont. 
 
 
 27 
 
 2400 
 
 214000 
 
 89.16 
 
 
 (4) Dog Lake, Kaministiquia River 
 
 347 
 
 310 (8) 
 
 13676 
 
 832000 
 
 61.00 
 
 
 Cameron rapids 
 
 347 
 39 
 
 310 
 
 6840 
 16350 
 
 619700 
 815000 
 
 91.00 
 50 00 
 
 
 
 
 39 
 
 
 8250 
 
 600000 
 
 73 00 
 
 
 Slate Falls 
 
 31 
 
 40 
 
 3686 
 
 357600 
 
 97 00 
 
 
 
 31 
 
 40 
 
 1843 
 
 260000 
 
 141.00 
 
 
 Third Report; (5) Dam rather expensive. (6) Head works and canal less expensive than ordin- 
 ary. (7) With storage developed. (8) Including 3500 feet of head water tunnel. 
 
650 
 
 Cost, Value and Sale of Power. 
 
 t 
 
 i 
 
 OO-Ot^ 
 10 O CO iO 
 -^ i I Ol 
 
 CO r- 
 
 10 C 
 
 O1 O 
 
 CO i i 
 
 iO - O O CO 1C CO CO O 
 
 10" cTcTcxT co'io'co' 
 
 i I i i CM 
 
 i O 
 
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 ^ o 
 o a 
 
 2 j 
 
 
 | 
 
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Cost of Development. 
 
 651 
 
 
 f 
 
 ft c<>-. 
 
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 GO 
 
 
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 i* i i II 
 
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 !!! Ml it 
 
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 il 
 
 lllllg^ 
 
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 Sliff^ -2^.0 
 
 s:S,8s=. ^2P 
 
 of 
 of 
 of 
 n eq 
 t of 
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 ly 12- 
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 re cli 
 favo 
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 statio 
 e cos 
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 5 
 
 Th 
 Th 
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 Th 
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 V 
 
652 Cost, Value and Sale of Power. 
 
 The estimates of The Ontario Hydro-Electric Power Commission 
 of the cost of various hydro-electric plants proposed in Ontario, 
 furnish a good example of the variations in the cost, per unit of 
 power, of various plants under various conditions. These estimates 
 are shown in Table XLIV. 
 
 The actual costs per horse power capacity of various complete 
 American and foreign plants are shown in Tables XLV and XLVI, 
 respectively. 
 
 326. Depreciation. In every operating plant there is in the 
 course of time a certain deterioration or reduction in value due to 
 ordinary operation and the effect of the elements. In the considera- 
 tion of any power plant as an investment, allowance must be made 
 in the annual charges for a sum sufficient to keep the original in- 
 vestment intact. In order to accomplish this an allowance should 
 be made on each feature of the plant for the annual reduction in 
 value or deterioration. The amount of depreciation will vary with 
 the character and use of the machinery or structure and shou,ld be 
 estimated with the best possible knoweldge of the conditions under 
 which the plant will be operated, fully in mind. Such estimates 
 should be sufficiently large to fully cover this item in order that the 
 feasibility of the project may be correctly estimated. 
 
 The allowance for depreciation in an operating plant should be 
 placed in a sinking fund which should be used to replace the vari- 
 ous portions of the plant at the expiration of their useful life. 
 
 327. Annual Cost of Developed Power. As already pointed out 
 the annual cost of operating a plant includes : 
 
 a. Administration and operating expense. 
 
 b. Maintenance and repairs. 
 
 c. Depreciation. 
 
 d. Interest, insurance and taxes. 
 
 Each of these items will vary with the duration and the condi- 
 tions under which the power plant is installed and operated. The 
 method of estimating these charges in shown in the following esti- 
 mates of the cost of operation of the Chicago Sanitary District 
 Hydro-Electric Plant (see Electric World, Feb. 28, 1906). 
 
 Total cost of development and transmission $3, 500, 000.00 
 
 ESTIMATE OF COST. 
 
 Interest on investment at 4 per cent $140,000.00 
 
 Taxes on real estate buildings, etc 7 260 00 
 
 Depreciation on buildings at 1 per cent 3, 650 . 00 
 
Cost of Distribution. 653 
 
 Depreciation on water wheels at 2 per cent 2,027.32 
 
 Depreciation on generators at 2 per cent 1, 824 . 60 
 
 Depreciation on pole line at 3 per cent 2,020.50 
 
 Depreciation on other electrical appliances at 3 per ct. 3,995.52 
 
 Total fixed charges , $161, 137.94 
 
 OPERATING EXPENSES. 
 
 Power and sub-station labor 63, 240.00 
 
 Repairs to machinery and buildings 3, 700.00 
 
 Incidental expenses 1,200.00 
 
 Operating Lawrence avenue pumping station 43, 960.00 
 
 Operating 39th avenue pumping station 120, 380.00 
 
 Interest on investment 39th avenue pumping station. . 15, 599 . 76 
 
 248,079.76 
 
 Total cost to sanitary district , $409, 217.70 
 
 Capacity 15, 500 H. P. Cost per H. P. per annum $26 . 40 
 
 An interesting comparison of the estimated yearly cost of various 
 Hydro-Electric generating plants is given in the various reports of 
 the Ontario Hydro-Electric Power Commission which are repro- 
 duced in Table XLVII- 
 
 328. Cost of Distribution. Having estimated the annual cost of 
 the development of power at the plant, the cost of distributing the 
 power to the customer must also be considered. In many power 
 plants the power is generated at or near the point where it is to 
 be used and the transmission losses and costs will include its trans- 
 mission through shafting, cables, and belts, or by electrical means, 
 to the machine or appliances in which it is to be utilized. In other 
 cases the power has to be transmitted for miles by high voltage 
 electric currents. The units of power for which the power com- 
 pany will receive compensation may or may not include these 
 various transmission losses. Where the power is distributed to a 
 factory, the losses in transmission though shafting, belting, etc., is 
 usually at the consumer's expense ; but the transmission loss in 
 long distance lines is ordinarily assumed by the power company 
 and must be taken into account in the determination of the cost of 
 furnishing power to the consumer. The losses in any system of 
 distribution are a considerable element of the cost of the delivered 
 power and must be carefully estimated. (Sec. 20, page 24, et seq.) 
 
 The losses in the distribution of power in various mills, factories, 
 etc., as determined by Prof. C. H. Benjamin, are given in Table 
 XLVIII. The reports of The Ontario Hydro-Electric Power Com- 
 mission, to which references have already been made, furnish nu- 
 merous clear analyses of the cost of electrical distribution. Table 
 
6 54 
 
 Cost, Value and Sale of Power. 
 
 XLIX shows such an estimate for the delivery of power from a 
 proposed Niagara plant to a proposed sub-station at Hamilton, 
 Ontario. Table L shows the estimate of the Commission on the 
 cost of distributing power from a sub-station to an individual con- 
 sumer not within the local distribution. The variations in the 
 cost of power from the generating plant to the consumer is also 
 well shown by Table LI, taken from the same source. 
 
 TABLE XLVIL 
 
 Estimated yearly operating expenses of generating plant from Reports of 
 Ontario Hydro-Electric Power Commission. 
 
 Location of Plant. 
 
 Horse-power. 
 
 Net H. P. trans- 
 formed for 
 transmisson. 
 
 Operating expen- 
 ses including - 
 administration. 
 
 Maintenance 
 and repairs. 
 
 d 
 
 .0 
 
 a 
 
 
 Q 
 
 Interest at 4 per 
 cent. 
 
 Water rental. 
 
 1 
 
 JO 
 
 o 
 
 j>> 
 
 cS 
 
 o> 
 
 N 
 
 Yearly cost of 
 transformed 
 24-hour power. 1 1 
 
 (1) Niagara plant 
 
 r>oooo 
 
 48750 
 
 $57900 
 
 $115700 
 
 $86800 
 
 $231400 
 
 Sfi^OOn 
 
 fijXM'.JAA 
 
 fill 1C 
 
 (2) Middle Falls. . . 
 
 5000 
 100000 
 
 5200 
 
 73125 
 97500 
 
 4990 
 
 70200 
 86300 
 
 11875 
 
 140400 
 172600 
 
 9500 
 
 105300 
 129500 
 
 9500 
 
 280800 
 345200 
 
 19000 
 
 6oOOO 
 77500 
 
 661700 
 811100 
 
 4W5 
 
 9.05 
 8.32 
 
 10 00 
 
 Healev's Falls 
 
 8000 
 
 7680 
 
 16875 
 
 13500 
 
 13500 
 
 27000 
 
 . . ... 
 
 7087^ 
 
 9 10 
 
 Two above combined 
 
 13200 
 
 12670 
 
 23000 
 
 23000 
 
 23000 
 
 46000 
 
 
 115000 
 
 9 08 
 
 (3) Maitland River 
 
 1600 
 
 
 5665 
 
 2754 
 
 2755 
 
 13000 
 
 
 24174 
 
 
 Saugeen River 
 
 1333 
 
 
 4840 
 
 3247 
 
 3->47 
 
 9984 
 
 
 
 21318 
 
 
 Soutb River . 
 
 750 
 
 
 4100 
 
 2620 
 
 2620 
 
 
 
 
 
 Severn River (Big Chute) 
 Severn and Beaver Rivers 
 combined 
 
 4000 
 6267 
 
 
 
 17483 
 23713 
 
 8571 
 13968 
 
 8571 
 14000 
 
 14000 
 25640 
 
 
 485T5 
 
 77000 
 
 
 (4) St. Lawrence River 
 
 
 1200 
 
 6864 
 
 5119 
 
 5118 
 
 
 
 
 
 Mississippi River High 
 Falls 
 
 
 2400 
 
 9391 
 
 3840 
 
 3841 
 
 7777 
 
 
 9AQAQ 
 
 
 Mississippi River High 
 Falls 
 
 
 1100 
 
 6390 
 
 2491 
 
 2491 
 
 4908 
 
 
 J0280 
 
 
 Montreal River Fount- 
 tain Falls 
 
 
 2400 
 
 9850 
 
 3903 
 
 *21622 
 
 cxqq 
 
 
 
 
 (5) Dog Lake 
 
 
 13675 
 
 13760 
 
 16127 
 
 1 SQ?" 
 
 
 
 
 
 
 
 6840 
 
 13296 
 
 1063 -> 
 
 10 13'^ 
 
 04707 
 
 
 
 
 
 Cameron Rapids 
 
 
 16350 
 
 16375 
 
 173'^7 
 
 16727 
 
 
 
 
 
 
 
 
 82.30 
 
 14390 
 
 11478 
 
 10978 
 
 24008 
 
 
 60854 
 
 
 Slate Falls 
 
 
 368(5 
 
 6000 
 
 H634 
 
 
 1 &'W)'i 
 
 
 
 
 
 
 1843 
 
 6000 
 
 3868 
 
 3669 
 
 10400 
 
 
 23957 
 
 
 
 
 
 
 
 ( 
 
 
 
 
 
 "Including 10-year sinking fund. 
 
 To make the delivered current available for power, a motor 
 must be installed. This is commonly furnished by the consumer. 
 Table LIT shows the estimated cost of induction motor service per 
 horse power per year. 
 
 329. Effect of Partial Load on Cost of Power. The maximum 
 amount of work that any plant can accomplish will be done only 
 when the plant works to its full capacity for twenty-four hours per 
 
Cost of Distribution. 
 
 655 
 
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 a^nmra jad 
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 rHlC^HlN 
 
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 JTt< Ml^f H^. 
 rH CO CO rH CO CO (M OO 
 
 HN r4?> PH|N 
 
 ii C<l (M <M 'M (M Th <M C<J 
 
 <N 
 
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 rH CO <M CO C<> 
 
 laaj 
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 i i 
 
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 rH rH rH 
 
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 : : $ 
 : ' "3 ; 
 
 
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 -* : : : 
 
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 "13 
 
 NATURE OF 
 
 Wire drawing and poll 
 Steel stamping and po 
 Average . . 
 
 Boiler and machine we 
 Bridge machinery .... 
 Heavy machine work 
 Heavy machine work 
 
 Average.. 
 
 Light machine work . 
 
 Manufacture of small 1 
 Manufacture of small 1 
 Sewing machines and 
 
 Sewing machines. .... 
 Screw machines an 1 sc 
 Average 
 
 Steel wood-screws. 
 
 Manufacture of steel n 
 Planing mill 
 Light machine work . 
 
656 
 
 Cost, Value and Sale of Power. 
 
 TABLE XLIX. 
 
 Showing investments, annual charges, and cost of low tension power at sub- 
 station. (Sub-station included.} 
 
 
 Full load. 
 
 % load. 
 
 M load. 
 
 Total horse' power distributed. 
 
 16,000 
 
 12,000 
 
 8 000 
 
 Total investment, including step-down 
 stations and interswitching. 
 
 $450,879 
 
 $404, 879 
 
 $358,379 
 
 Investment per H P delivered 
 
 28 18 
 
 33 73 
 
 44 80- 
 
 Total annual repairs, depreciation, pa- 
 trolling and operation 
 
 22, 496 
 
 19,092 
 
 15,651 
 
 Administration, 10 per cent of repairs, etc. 
 Annual interest, 4 per cent of investment 
 
 2,250 
 18,035 
 
 1,909 
 16, 195 , 
 
 1,565 
 14, 335 
 
 Total annual charges 
 
 $42, 781 
 
 $37,196 
 
 $31,551 
 
 Cost of 24-hour power, including line and 
 step-down sub-station losses 
 
 $12 69 
 
 $12 49 
 
 $12 35- 
 
 Cost of transmitting and transforming. . . . 
 
 2 67 
 
 3 10 
 
 3 94 
 
 Total cost of power 
 
 $15 36 
 
 $15 59 
 
 $16 29- 
 
 
 
 
 
 The above costs of power are based on an assumed rate of $12.00 per 24-hour 
 horse-power per annum for high-tension power at Niagara Falls. 
 
 TABLE L. 
 
 Showing cost of distribution from municipal sub-station to an individual 
 consumer, not covered by local distribution. 
 
 Distance in 
 miles from 
 municipal 
 sub-station. 
 
 COST PER HORSE- POWER PER ANNUM FOR THE DELIVERY 
 OF VARIOUS AMOUNTS OF POWER. 
 
 50 H. P. 
 
 75 H. P. 
 
 100 H.P. 
 
 150 H.P. 
 
 200 H.P. 
 
 250 H.P. 
 
 300 H. P. 
 
 2 
 
 $5 58 
 6 89 
 7 92 
 8 87 
 10 20 
 
 14 10 
 16 12 
 
 18 76 . 
 22 74 
 
 $4 20 
 5 20 
 6 18 
 
 7 18 
 8 24 
 
 10 14 
 12 13 
 
 14 03 
 
 17 08 
 
 $3 53 
 4 41 
 5 20 
 
 5 98 
 
 6 77 
 
 8 40 
 9 54 
 
 11 12 
 
 13 48 
 
 $2 92 
 3 60 
 4 27 
 4 96 
 5 38 
 
 6 97 
 8 31 
 
 $2 74. 
 3 25 
 3 93 
 4 55 
 5 13 
 
 6 24 
 
 $2 60 
 3 10 
 3 72 
 4 32 
 4 60 
 
 5 79 
 6 96 
 
 7 96 
 
 $2 511 
 3 03 | o ; 
 3 86^-g 
 4 17 | g 
 4 43J 
 
 SKJffs 
 6 17 ) 
 
 7 22 ) 8% 
 8 32 ) 1 
 
 3 
 
 4... 
 
 5 
 
 6 . 
 
 8... 
 
 10 
 
 7 68 
 
 8 42 
 9 35 
 
 12 
 
 10 12 
 10 89 
 
 15 
 
 8 84 
 
 
Cost of Distribution. 
 
 657 
 
 TABLE LI. 
 
 COST OF 24-HouR POWER PER H. P. 
 
 PER ANNUM. 
 
 AMOUNT OF POWER DELIVERED. 
 
 At Niagara 
 Falls includ- 
 
 - 
 
 
 
 ing line and 
 
 At 
 
 At 
 
 
 step- down 
 
 sub-station. 
 
 customer. 
 
 
 sub station 
 
 
 
 
 losses. 
 
 
 
 Full load 2 000 H P 
 
 $18 54 
 
 $21 89 
 
 $26 03 
 
 ^ load 1 500 H P 
 
 13 18 
 
 23 54 
 
 29 06 
 
 * load 1 000 H P 
 
 12 85 
 
 27 21 
 
 34 48 
 
 
 
 
 
 TABLE LII. 
 Capital cost and annual charges on motor installations. 
 
 Polyphase 25-cycle, induction motors. 
 
 CAPACITY H. P. 
 
 Capital 
 cost per 
 H. P. 
 installed. 
 
 ANNUAL CHARGES. 
 
 Interest 
 5 per cent. 
 
 Deprecia- 
 tion and 
 repairs, 
 6 per cent. 
 
 Oil, care 
 and 
 operation. 
 
 Total per 
 H. P. per 
 annum. 
 
 5 
 
 $41 00 
 39 00 
 35 00 
 28 00 
 25 00 
 24 00 
 21 00 
 20 00 
 17 00 
 16 00 
 
 $2 05 
 1 95 
 1 75 
 1 40 
 1 25 
 1 20 
 1 05 
 1 00 
 85 
 80 
 
 $2 46 
 2 34 
 2 10 
 1 88 
 1 50 
 1 44 
 1 26 
 1 20 
 1*02 
 96 
 
 $4 00 
 3 00 
 2 50 
 2 00 
 1 75 
 1 50 
 1 25 
 1 00 
 80 
 70 
 
 $8 51 
 7 29 
 6 35 
 5 28 
 4 50 
 4 14 
 3 56 
 3 20 
 2 67 
 2 46 
 
 10 
 
 15 
 
 25 
 
 35 
 
 50 
 
 75 
 
 100 
 
 150 
 
 200 . 
 
 
 day. Thus, if a plant has a capacity of one thousand horse power 
 and is operated continuously during the twenty-four hours, the 
 total output will be twenty-four thousand horse power hours of 
 work. Under such conditions the plant can be built at a minimum 
 expense per unit of output and the cost of operation, fixed charges, 
 interest, etc., will be less per unit of work done than under any 
 other condition of operation. 
 40 
 
658 Cost, Value and Sale of Power. 
 
 For example : If a plant of one thousand horse power be installed 
 at a cost of one hundred thousand dolars, the annual cost of opera- 
 tion, including fixed charges and all other legitimate expenses, may 
 be estimated as follows : 
 
 Interest on $100, 000 at 6 per cent $ 6, 000 
 
 Repairs and depreciation ~.l 5, 300 
 
 Operating expenses 10, 000 
 
 Miscellaneous and contingent expenses 4, 250 
 
 Total annual cost of power $25, 550 
 
 On the above basis the annual cost for each horse power of maxi- 
 mum load will be $25.55. If the plant works at its maximum capac- 
 ity for twenty-four hours per day, the cost per horse power hour 
 will be .292 cts. If, however, the plant is operated to its full capac- 
 ity for 12 hours per day only, the total Cost of power may be reduced 
 to say $23,000 per annum. In this case the cost per horse power 
 of maximum load will be reduced to $23.00 per year, but the cost 
 per horse power hour of energy generated will be increased to 
 .526 cts. In many cases the plant will be used for ten hours per 
 day and for six days per week. Its maximum capacity may be 
 utilized only occasionally, and the demand for power will vary 
 greatly from haur to hour resulting in a load factor of perhaps 50 
 per cent, or less. In this case the annual cost per maximum horse 
 power will still not exceed twenty-three dollars ($23)) per year, 
 .but the annual cost of average ten hour power will be forty-six 
 dollars ($46), and the cost per horse power hour of useful work will 
 be increased approximately to 1.5 cents. The cost of each unit of 
 power under the last condition is over five times as great as in the 
 first case mentioned, and about three times as great as in the second 
 case discussed. It is therefore obvious that unless the conditions 
 of use are carefully studied and conservatively estimated, they may 
 lead to unfortunate investments and financial losses. 
 
 330. Cost of Auxiliary Power, or Power Generated From Other 
 than Water Power Sources. It frequently becomes necessary to es- 
 timate the cost of power plants and of power developed from other 
 than water power sources. This is necessary in order to determine 
 the probable cost of auxiliary power plants and such auxiliary 
 power as may be needed to assist a water power plant at times 
 when the hydraulic power is deficient. It is also necessary to deter- 
 mine the cost of power with which the hydraulic plant may be 
 called upon to compete. 
 
Cost of Auxiliary Power. 
 
 659 
 
 For a correct estimate of such cost, it is necessary to determine 
 the efficiency of the various parts of the plant (see page 31) under 
 all conditions o<f operation in order to correctly determine the actual 
 cost of power due to the conditions of operation. The conditions for 
 maximum efficiencies are seldom met in actual operation, and the 
 cost of generating the power is increased by the irregularities of 
 operating conditions. In all power plants the effect of partial or 
 irregular load affects the cost of power in the same manner as al- 
 ready described in Section 328. 
 
 Fixed Charges 
 
 Operating Expenses. 
 
 1000 1500 
 
 Morse Power of Plarrt-. 
 
 2500 
 
 Fig. 399. Cost of Steam Power per Horse Power per Annum in Various 
 
 Plants. 
 
 By far the largest amount of power generated is from fuel and 
 by steam plants. The cost of the development of steam power is 
 modified by the cost and character of coal used ; the size and char- 
 acter of the machinery operated ; the character of the load (that is, 
 the load factor) ; the number of hours during which the plant is used 
 per year ; and the skill and ability of the engineer and fireman who 
 have charge of the plant. Observations of the actual cost of de- 
 
66o 
 
 Cost, Value and Sale of Power. 
 
 veloping power must therefore form the basis of any accurate esti- 
 mate of the cost of power production. 
 
 Mr. H. A. Foster* made actual tests of twenty-two different 
 power plants, including manufacturing establishments, electric 
 light stations, pumping plants, etc., and determined for each plant 
 the power consumption per annum and its cost, including not only 
 running expenses but fixed charges. The cost per horse power per 
 annum varied from a minimum of $15.69 to a maximum of $233.95. 
 
 TABLE LIU. 
 
 Showing average power developed and its cost per HP. in 22 steam power 
 
 plants. 
 
 OUTPUT. 
 
 Operating ex- 
 penses, per 
 HP. 
 
 Fixed 
 charges, per 
 H. P. 
 
 Total cost, 
 HP. per 
 annum. 
 
 Cost per 
 HP. hr., 
 cts. 
 
 Average HP. 
 developed. 
 
 No. of 
 days per 
 annum. 
 
 12.4 
 
 361 
 
 $147.93 
 
 $25.40 
 
 $173.33 
 
 5.648 
 
 20.9 
 
 365 
 
 123.12 
 
 28.42 
 
 151.54 
 
 ] . 868 
 
 21.5 
 
 361 
 
 90.47 
 
 17.80 
 
 108.27 
 
 2.918 
 
 32.9 
 
 330 
 
 22.56 
 
 5.83 
 
 28.39 
 
 .832 
 
 36.7 
 
 365 
 
 137.25 
 
 96.70 
 
 233.95 
 
 2.811 
 
 42.4 
 
 365 
 
 86.38 
 
 63.20 
 
 149.58 
 
 1.708 
 
 53. 
 
 309 
 
 56.94 
 
 19.51 
 
 76.45 
 
 1-.696 
 
 58.8 
 
 365 
 
 97.30 
 
 33.82 
 
 131.12 
 
 1.613 
 
 70.4 
 
 365 
 
 101.69 ' 
 
 20.78 
 
 122.45 
 
 1.641 
 
 129.3 
 
 365 
 
 30.14 
 
 9.41 
 
 39.55 
 
 .S71 
 
 166.7 
 
 313 
 
 15.19 
 
 4.47 
 
 19.66 
 
 .639 
 
 173. 
 
 313 
 
 22.66 
 
 5.83 
 
 28.39 
 
 3.333 
 
 210.9 
 
 290 
 
 40.33 
 
 7.86 
 
 48.19 
 
 .693 
 
 296.7 
 
 ^97 
 
 45.56 
 
 7.81 
 
 53.37 
 
 .74'.) 
 
 926. 
 
 307 
 
 11.73 
 
 8.77 
 
 20.50 
 
 .691 
 
 1,010.8 
 
 306 
 
 15.70 
 
 7.74 
 
 23.44 
 
 .794 
 
 1,174.8 
 
 306 
 
 10.19 
 
 5.50 
 
 15.69 
 
 .531 
 
 1,278.7 
 
 293 
 
 10.49 
 
 6.23 
 
 16.72 
 
 .590 
 
 1,345.5 
 
 365 
 
 23.28 
 
 9.42 
 
 32.70 
 
 .820 
 
 1,352. 
 
 365 
 
 33.03 
 
 29.41 
 
 62.44 
 
 .713 
 
 1,909.7 
 
 306 
 
 13.40 
 
 6.63 
 
 20.03 
 
 .677 
 
 2,422 
 
 306 
 
 15.67 
 
 6.73 
 
 22 40 
 
 .757 
 
 A summation of the results of these observations is shown in Table 
 LIII and the plotted results of the table are shown in Fig. 399. 
 Mr. R. W. Conant** determined the operating expenses of various 
 street railway power stations and compiled a table (see Table LIV 
 which gives important information bearing on this question. 
 
 * See Trans. Am. Inst. E. E. Vol. 14, p. 385. 
 ** See Engineering News, Vol. 40, p. 181. 
 
Cost of Auxiliary Power. 
 
 66 1 
 
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662 
 
 Cost, Value and Sale of Power. 
 
 An important discussion of the effect of the load factor on the 
 cost of power was recently made by Mr. E. M. Archibald. -f This 
 discussion was accompanied by various diagrams which illus- 
 trate clearly the principles involved. Two of these diagrams are 
 reproduced in Figs. 400 and 401. The diagrams are so complete 
 as to need no further description. The additional diagrams and 
 
 .9 a 
 
 Fig. 400. -Operating Expense of a 900 K. W. Condensing Steam Plant 
 with a 750 K. W. Peak. 
 
 the descriptive matter in the paper itself should be carefully studied 
 in this connection. 
 
 Table LV shows the capital costs of steam power plants of var- 
 ious capacities and the annual cost of power per brake horse power 
 as estimated by The Ontario Hydro-Electric Power Commission. 
 fSee Electrical Age, Nov., 1906. 
 
Market Price of Water Power. 
 
 66 3 
 
 Similar costs for producer gas power are shown in Table LVI from 
 the same source, and the Commission's estimate of the effect on 
 the cost of power oif variations in the price of coal, is shown in 
 Table LVIL 
 
 331. Market Price of Water Power. The market price of water 
 power must be predicated on two considerations: First: The 
 price at which the Power Company can afford to furnish power and 
 insure a fair return of its investment, and, Second : The price that 
 the consumer can afford to pay for the power. The latter amount 
 
 Fig. 401. Ratio of individual Items of Expense to Total Operating Expense 
 of a 900 K. W. Condensing Steam Plant With a 750 K. W. Peak. 
 
 is commonly fixed by what it will cost to produce the power by 
 some other means. 
 
 If, in the preliminary investigation of a water power project, it 
 is found that the cost to the Power Company of generating power 
 will be greater than the price at which the power can be sold, it is, of 
 course, evident that the plant will be a financial failure, and the 
 scheme should at once be abandoned. In introducing a new 
 
66 4 
 
 Cost, Value and Sale of Power. 
 
 TABLE LV. 
 
 Showing capital costs of steam plants installed and annual costs of power 
 
 per brake horse-power. 
 
 SIZE OF PLANT 
 H. P. 
 
 CAPITAL COST OF PLANT PER H. P. 
 INSTALLED. 
 
 Annual cost 
 of 10-hour 
 power per 
 B. H. P. 
 
 Annual cost 
 of 24-hour 
 power per 
 B. H. P. 
 
 Engines, 
 boilers, etc., 
 installed. 
 
 Buildings. 
 
 Total. 
 
 CLASS I. Engines: simple, slide-valve, non-condensing. Boilers: return 
 
 tubular. 
 
 10 
 
 $66 00 
 
 $40 00 
 
 $106 00 
 
 $91 16 
 
 $180 76 
 
 20 
 
 56 00 
 
 37 00 
 
 93 00 
 
 76 31 
 
 151 48 
 
 30 
 
 48 70 
 
 35 00 
 
 83 70 
 
 66 46 
 
 131 68 
 
 40 
 
 44 75 
 
 33 50 
 
 78 25 
 
 59 46 
 
 117 74 
 
 50 . 
 
 43 00 
 
 31 00 
 
 74 00 
 
 53 95 
 
 106 46 
 
 
 
 
 
 
 
 CLASS II. Engines: Simple, Corliss, non-condensing. Boilers: Return tubular. 
 
 30 
 
 $70 70 
 
 $35 00 
 
 $105 70 
 
 $61 14 
 
 $117 70 
 
 40 
 50 
 
 62 85 
 59 00 
 
 33 50 
 31 00 
 
 96 35 
 90 00 
 
 55 50 
 50 70 
 
 107 10 
 97 73 
 
 tiO 
 
 56 00 
 
 30 00 
 
 86 70 
 
 47 42 
 
 91 34 
 
 80 
 
 50 00 
 
 27 50 
 
 77 50 
 
 43 86 
 
 85 41 
 
 100 
 
 44 60 
 
 25 00 
 
 69 60 
 
 40 55 
 
 79 19 
 
 
 
 
 
 
 
 CLASS III. Engines: Compound, Corliss, condensing. 
 
 with reserve capacity. 
 
 Boilers: Return tubular, 
 
 100 
 
 $63 40 
 
 $28 00 
 
 $91 40 
 
 $33 18 
 
 $60 05 
 
 150 
 
 53 70 
 
 24 00 
 
 77 70 
 
 29 83 
 
 54 63 
 
 200 
 
 50 10 
 
 20 00 
 
 70 10 
 
 28 14 
 
 51 72 
 
 300 
 
 45 90 
 
 18 00 
 
 63 90 
 
 26 27 
 
 48 83 
 
 400... 
 500 
 750 
 
 43 55 
 41 25 
 
 40 50 
 
 16 00 
 14 00 
 13 00 
 
 59 55 
 55 25 
 53 50 
 
 24 84 
 23 73 
 23 56 
 
 46 12 
 44 21 
 44 0'? 
 
 1,000 
 
 39 00 
 
 12 00 
 
 51 00 
 
 23 26 
 
 43 71 
 
 
 
 
 
 
 
 CLASS IV. Engines: Compound, Corliss, condensing. Boilers: Water-tube, 
 with reserve capacity. 
 
 300.. 
 400 
 
 $55 20 
 51 50 
 
 $18 00 
 16 00 
 
 $73 20 
 67 50 
 
 $25 77 
 24 18 
 
 $46 32 
 43 61 
 
 500 
 
 49 40 
 
 14 00 
 
 63 40 
 
 23 19 
 
 42 03 
 
 750 
 
 46 80 
 
 13 00 
 
 59 70 
 
 22 88 
 
 41 56 
 
 1,000 
 
 44 30 
 
 12 00 
 
 56 80 
 
 22 47 
 
 41 11 
 
 
 
 
 
 
 
 NOTE. Annual costs include interest at 5 per cent, depreciation and repairs on 
 plant, oil and waste, labor and fuel, (coal at $4.00 per ton). 
 Brake horse-power is the mechanical power at engine shaft. 
 
Cost of Auxiliary Power. 
 
 665 
 
 TABLE LVI. 
 
 Showing capital costs of producer gas plants installed and annual costs of 
 power per brake horse-power. 
 
 SIZE OF PLANT, H. P. 
 
 CAPITAL COST OP PLANT PER 
 H. P. INSTALLED. 
 
 Annual 
 cost of 
 10-hour 
 power per 
 B. H. P. 
 
 Annual 
 cost of 
 24-hour 
 power 
 per 
 B. H. P. 
 
 Machine'y 
 etc. 
 
 Buildings. 
 
 Total. 
 
 10 
 
 $137 00 
 110 00 
 93 00 
 84 50 
 80 00 
 79 00 
 78 20 
 77 50 
 76 00 
 74 00 
 73 00 
 71 50 
 70 00 
 67 50 
 65 00 
 
 $40 00 
 36 00 
 33 00 
 29 00 
 26 00 
 24 00 
 22 00 
 20 00 
 19 00 
 17 00 
 16 00 
 14 00 
 12 00 
 10 00 
 8 00 
 
 $177 00 
 146 00 
 126 00 
 113 50 
 106 00 
 103 00 
 100 20 
 97 50 
 95 00 
 91 00 
 89 00 
 85 50 
 82 00 
 77 50 
 73 00 
 
 $53 48 
 44 47 
 38 73 
 85 05 
 32 27 
 30 49 
 28 70 
 27 05 
 25 87 
 24 95 
 24 24 
 23 41 
 22 54 
 .21 55 
 20 46 
 
 $90 02 
 75 22 
 65 99 
 59 85 
 55 22 
 52 03 
 48 95 
 45 40 
 43 17 
 41 78 
 40 40 
 39 03 
 37 54 
 35 99 
 34 66 
 
 20 
 
 30 
 
 40 
 
 50 ... 
 
 60 
 
 80 
 
 100 
 
 150 
 
 200 
 
 300 
 
 400 .'. 
 
 500 
 
 750 
 
 1 000 
 
 
 NOTE. Annual costs include: interest at 5 per cent, depreciation and repairs 
 on pliant, oil and waste, labor and fuel (Bituminous coal at $4.00 and Anthra- 
 cite coal at $5.00 per ton). 
 
 TABLE LVI1. 
 
 Showing the effect on the cost of power of a variation in the price of coil of 
 
 one-half dollar per ton. 
 
 Size of Plant. 
 
 SUCTION 
 PRODUCER GAS. 
 
 STEAM. 
 
 10 
 Hour. 
 
 24 
 Hour. 
 
 10 Hour. 
 
 24 
 Hour. 
 
 10 
 
 $1 15 
 1 13 
 1 10 
 1 07 
 1 04 
 1 01 
 98 
 96 
 94 
 92 
 90 
 88 
 86 
 82 
 76 
 
 $2 53 
 2 46 
 2 40 
 2 33 
 2 29 
 2 24 
 2 18 
 2 12 
 2 07 
 2 02 
 1 98 
 1 94 
 1 89 
 1 81 
 1 72 
 
 Simple automat- | 
 ic non-condes-<( 
 inof . 
 
 P6 14 
 5 25 
 4 71 
 3 56 
 3 37 
 3 26 
 3 15 
 3 12 
 1 75 
 1 69 
 1 62 
 1 56 
 1 39 
 1 39 
 1 39 
 
 $13 47 
 11 56 
 10 35 
 7 84 
 7 41 
 7 16 
 6 97 
 6 87 
 3 85 
 3 71 
 3 60 
 3 44 
 3 05 
 3 05 
 3 05 
 
 20 
 
 30 . 
 
 40 
 
 50 
 
 60 
 
 80 
 
 100 
 
 Compound con-J 
 densing 1 
 
 150 
 
 200 
 
 300. 
 
 400 
 
 [ 
 
 Compound con- f 
 densing water- ] 
 tube boilers. . . ( 
 
 500 
 
 750 
 
 1000 
 
 
666 Cost, Value and Sale of Power. 
 
 source of power into any community where the power introduced 
 will be obliged to compete with other sources, it can seldom be 
 expected that the power to be so furnished can be sold at the same 
 price as the power already on the market. It is at least only safe 
 to estimate that the power must be sold at a somewhat lower figure. 
 If the power already in use is sold or generated at a profit, a cut 
 in price may be anticipated from the competing company ; and, in 
 the second place, as a considerable expense is necessarily involved 
 in the change of apparatus, etc., necessary to utilize a new source of 
 power, consumers will be slow to make such changes unless they 
 can do so to a considerable financial advantage. 
 
 In calculating the cost of power to a consumer, if he undertakes 
 to generate it himself, the fair cost should be based upon interest, 
 depreciation, operation, etc., of the plant which is necessary to be 
 installed. If, however, the consumer has such a plant already in- 
 stalled, no further investment is necessary, and as the machinery 
 installed can not be sold to advantage, the investment charges or 
 the fixed charges on. such a plant can not be considered, and the 
 consumer will make a change in power only provided the power 
 can be furnished from the new source at or below the actual cost 
 of generation in his own plant, or at such additional cost as the 
 convenient reliability of other desirable features of the new source 
 of power will warrant. 
 
 In estimating the price at which the consumer can afford to pur- 
 chase power, not only the price at which power is no\v sold but 
 any possible decrease in the sale price, due to competition or to 
 other and more economical developments, must be considered. 
 Better and more economical machinery in local plants, or water 
 powers that are nearer the market and that can be developed or 
 operated at less expense, may so reduce the market price as to ser- 
 iously affect the value of power, and hence the probability of 
 the development. 
 
 332. Sale of Power. Attention has already been called to the 
 fact that if the capacity of a plant can be used for only a portion of 
 the time, the cost of the development per unit of power, and there- 
 fore the cost per unit, is very greatly increased. This is a matter 
 of the greatest importance 'which should be kept clearly in mind in 
 the sale power. The load factor of many users is comparatively 
 low. Most companies organized for the general sale of electrical 
 power in municipalities have a load factor of 35% or less. A sale 
 of power to such consumers, to be used under such conditions, is 
 
Sale of Power. 667 
 
 liable to very greatly increase the cost of power to the power com- 
 pany, especially if the maximum power to be furnished is large as 
 compared with the total capacity of the plant. For example: If, 
 in a 3,000 horse power plant, power is sold on a horse power hour 
 basis, with a peak load of 1,000 horse power and a load factor of 
 30%, the average twenty-four hour power furnished to the con- 
 sumer will be only 300 horse power, while the total peak that the 
 power plant will be called upon to carry at any time' will be 1,000 
 horse power or one-third of the total capacity of the power plant. 
 With such sale of power the power plant is likely to be seriously 
 handicapped. With power sold in such large blocks, the overlap- 
 pings of the peak loads can not reasonably be expected to compen- 
 sate for each other. The net results of such a sale will be that the 
 company has tied up one-third of the capacity of its plant but will 
 receive payment for only one-tenth of its capacity. It is evident 
 that unless such conditions are realized and such a charge is made 
 for power as will compensate the power company for the same, 
 the power company may readily tie up its entire out-put and yet 
 not receive 50% of the income that should be reasonably antici- 
 pated. If, on the other hand, the sale of power is made in small 
 blocks, or to small consumers, it is frequently possible to greatly 
 over-sell the total capacity of the plant and yet take care of the 
 consumers in a satisfactory manner. That is, on account of the 
 overlapping of the peak loads and the equalization of the load car- 
 ried throughout the twenty-four hours, the total connected load 
 sold may often considerably exceed the capacity of the plant. For 
 example : In one water power plant, having a total capacity of 
 about 4,000 horse power, the actual connected load is over 10,000 
 horse power. In many power plants the actual connected load is 
 two or three times the plant's capacity. It is evident, however, 
 that such a condition can exist only with small consumers, and that 
 where a single consumer's load is a large fraction of the plant's 
 capacity, it will not only be impossible to overload the power plant, 
 but in addition extra machinery must always be installed to supply 
 the demand should any accident happen to the regular installation. 
 
 Mr. E. W. Lloyd has compiled some valuable data concerning 
 the power loads on various central states from various classes of 
 consumers. This data is given in Table LVIII. 
 
 The increase in the charges for power to consumers on account 
 of the variation in power factor is well illustrated by Fig. 402 taken 
 from the paper of Mr. Archibald before referred to. 
 
668 
 
 Cost, Value and Sale of Power. 
 
 TABLE LVIII. 
 
 Actual conditions under which power is furnished to consumers from Central 
 
 Stations. 
 
 Character of Installations. 
 
 dual 
 p d 
 
 rcentage of aver 
 ge load to con- 
 ected motor 
 
 Bakeries 1582 
 
 Bakeries 705.3 
 
 Boiler shops 326.7 
 
 Boiler shops 1172 
 
 Boots and shoes 3050 
 
 Box making 1555 
 
 Blacksmiths 586 
 
 Brass finishing 5736 
 
 Butchers and packers 1990 
 
 Butchers and packers 1U49 
 
 Breweries 12310 
 
 Carpet cleaning 644 
 
 Cement mixing 2009 
 
 Candy manufactory 1893 
 
 Candy manufactory 796 
 
 Cotton mills 11829 
 
 Carriage works 2091 
 
 Chemical works 4802 
 
 Clothing manufacturing 1 181 
 
 Grain elevators 3842 
 
 Feather cleaners 2447 
 
 General manufacturing 6133 
 
 Engraving and electrotyping 863 
 
 Engraving and electrotyping 2369 
 
 Glass grinding 2760 
 
 Foundries 2057 
 
 Foundries 2419 
 
 Furniture manufacturing 1750 
 
 Flour mills 41276 
 
 Hoisting and conveying 2905 
 
 Hoisting and conveying 0562 
 
 Ice cream 596 
 
 Refrigeration 4645 
 
 Jewelry manufacturing 2526 
 
 Laundries 676 
 
 Marble finishing 1464 
 
 Machine shops I 4006 
 
 Newspapers 3150 
 
 Newspapers 4975 
 
 Ornamental iron works 2771 
 
 Paint manufacturing 281 4 
 
 Printers and bookbinders 1147 
 
 Printers and bookbinders 6215 
 
 Plumbing, manufacturing 3020 
 
 Rubber manufacturing 1051 
 
 Sheet metal manufacturing 1321 
 
 Soap manufacturing 3434 
 
 Seeds 2917 
 
 Structural steel 6514 
 
 Structural steel 77704 
 
 Stone cutting 7425 
 
 Tanners 2466 
 
 Tobacco working 3441 
 
 Wholesale groceries 2005 
 
 Wood working 2306 
 
 Woolen mills 20985 
 
 Averages 3500 
 
 32.8 
 22.5 
 51.4 
 32.2 
 39.7 
 18.1 
 9.4 
 40.5 
 24.8 
 3ti.9 
 94.0 
 14.5 
 37.5 
 26.6 
 29.9 
 99.0 
 24.8 
 
 109.0 
 23.0 
 
 114.4 
 54.4 
 67. H 
 12.4 
 46.3 
 33.5 
 27.7 
 81.1 
 35.7 
 
 148.5 
 70.5 
 
 253.0 
 31.0 
 36.7 
 31.7 
 10.8 
 19.8 
 57.6 
 47.4 
 
 137.0 
 38.4 
 60.4 
 20.4 
 76.8 
 42.4 
 26.0 
 38.8 
 73.0 
 55.1 
 
 176.0 
 
 552.1 
 76.5 
 28.6 
 62.3 
 47 
 39.5 
 
 150.0 
 
 Group 
 Individual 
 G 
 I 
 G 
 G 
 G 
 G 
 G 
 I 
 G 
 G 
 
 G 
 
 I 
 
 G 
 
 G 
 
 G 
 
 G 
 
 G&I 
 G&I 
 G&I 
 
 G 
 
 I 
 
 G 
 
 G 
 
 I 
 
 G 
 
 G 
 
 G 
 
 I 
 
 G&I 
 GGI 
 
 G 
 G&I 
 
 G 
 
 G 
 
 I 
 
 G 
 G&I 
 
 G 
 
 I 
 
 G 
 G&I 
 
 G 
 
 G 
 G&I 
 
 I 
 
 G 
 G&I 
 
 G 
 
 G 
 
 G &I 
 U &I 
 
 2.7 
 3.1 
 2.8 
 5.2 
 5.8 
 4.3 
 2.2 
 7.4 
 2.0 
 6.7 
 4.6 
 1.6 
 1.0 
 3.5 
 7.5 
 3.0 
 3.5 
 5.5 
 4.0 
 3.8 
 5.5 
 6.4 
 2.5 
 
 26.7 
 3.0 
 2.3 
 7 
 3.6 
 3.1 
 6.4 
 
 20.0 
 5.4 
 2 5 
 4.6 
 2.1 
 1.3 
 4.5 
 4.8 
 
 17.3 
 3.6 
 4.6 
 2.6 
 
 24.0 
 4.8 
 
 15.0 
 3.7 
 
 10.0 
 5.8 
 
 16.1 
 
 35.6 
 3.8 
 2.6 
 7.0 
 4.5 
 3.6 
 3.0 
 
 6.08 
 
 27.8 
 19.5 
 33.3 
 20.7 
 42.8 
 45.4 
 34.2 
 45.0 
 36.4 
 18.8 
 33.0 
 30.1 
 24.9 
 33.6 
 16.3 
 60.1 
 35.5 
 23.5 
 44.5 
 32.6 
 25.7 
 33.9 
 46.9 
 22.5 
 36 6 
 43.7 
 21.3 
 35.6 
 48.1 
 28.3 
 13.0 
 35.9 
 53.4 
 31.6 
 34.0 
 51.3 
 34.5 
 38.0 
 15.1 
 41.6 
 26.5 
 39.5 
 26.0 
 21.5 
 24.7 
 27.3 
 27.6 
 24.4 
 18.5 
 31.1 
 34.4 
 54.6 
 37.5 
 26.0 
 33.3 
 71.0 
 
 33.9 
 
An Equitable Basis for the Sale of Power. 
 
 669 
 
 333. An Equitable Basis for The Sale of Power. It is there- 
 fore essential, in order to establish an equitable basis for the sale 
 of power, that some additional factor besides the units of power 
 furnished be considered in determining the basis for the prices 
 charged. One of the most equitable bases for the sale of power 
 
 70 
 
 60 
 
 5.0 
 
 
 30 
 
 t 
 
 I 
 
 Fig. 402. Cost of Steam-Generated Electric Power to the Consumer. 
 
 is apparently: First: A service charge to the consumer of a fixed 
 price, based on the peak load carried ; Second : To this should be 
 added a price for the units of power actually furnished. The fixed 
 price should equal the interest, depreciation, etc., on the capacity 
 that is to be provided or set aside to carry the peak load of the 
 customer. The unit price for power should be an equitable charge 
 for the quantity of power which will actually be sold. Where both 
 
670 Cost, Value and Sale of Power. 
 
 of these quantities are fixed, a net price per horse power per year, 
 or a total price per annum for the power to be furnished, can, of 
 course, be arranged equitably. The main idea in establishing a 
 price for power is to keep clearly in mind the factors that enter 
 into the sale of power, so that in making a contract for the use of 
 power the rights of both power company and consumer shall be 
 duly considered. The sale of power at a profit is one of the most 
 essential features in the management of the power plant, and many 
 plants have been wholly or partially financial failures on account 
 of the ignorance of the basic principle on which power should be 
 sold. 
 
 The method of charging for power outlined above is illustrated by 
 the charges for Electric Current furnished from Niagara Falls, by 
 the Cataract Power & Condu.it Co. of Buffalo, as given in the En- 
 gineering News (May 26th, 1898) as follows : 
 
 "All payments for power are to be made monthly and the amount 
 of each monthly payment will consist of a charge for service, and 
 in addition thereto, a charge for power. The charg,e for service 
 is $i per kilowatt per month, and this charge will depend omly 
 upon the amount of power which the user may require the Catar- 
 act Power & Conduit Company to keep available and ready for his 
 use. The monthly charge for power will depend upon the aggre- 
 gate amount used, as determined by integrating meters installed 
 by the Conduit Company upon the premises of the consumer. The 
 charge for power will be determined from the following schedule : 
 
 Units (K-W. hrs.} used Charge pzr unit 
 
 per month. For current up to For the excess. 
 
 Up to 1,000 1,000 units, 2.0 cts. 2.0 cts. 
 
 l,000to 2,000 1,000 units, 2.0 cts. 1.5 cts. 
 
 2,000 to 3,000 2, 000 units, 1.5 cts. 1.2 cts. 
 
 3,000 to 5,000 3, 000 units, 1.2 cts. 1.0 cts. 
 
 5,000 to 10,000 5, 000 units, 1.0 cts. 0.8 cts. 
 
 10, 000 to 20, 000 10, 000 units, . 8 cts. 0-75 cts. 
 
 20, 000 to 40, 000 20, 000 units, . 75 cts. 0. 70 cts. 
 
 40, 000 to 80, 000 40, 000 units, . 70 cts. . 66 cts. 
 
 Over 80,000 80,000 units, 0.66 cts. 0.64 cts. 
 
 334. Value of Improvements Intended to Effect Economy. In 
 many plants the first cost of an installation is an important matter 
 and must sometimes have a greater effect than the interest and de- 
 preciation charge would seem to warrant. In most cases the plan 
 should be studied in detail and improvements introduced or re- 
 
Value of a Water Power Property. 671 
 
 jected on the basis of their true financial value. Such considera- 
 tion should usually be made on the following basis : 
 
 Dr. 
 
 Invest required to effect improvement. ... $ 
 
 Interest on investment $ 
 
 Depreciation on improvements 
 
 Extra expense of operation and mainten- 
 ance $ 
 
 Total annual cost of improvement . . $ 
 
 .0. 
 
 Saving in power (or in expense) effected 
 
 by improvement $ 
 
 Annual value of saving effected $ 
 
 Net annual gain or loss .due to im- 
 provement $ 
 
 Capitalized value of power (or expense) 
 
 effected by improvement $ 
 
 Net capitalized 'loss or gain effected $ 
 
 335. Value of a Water Power Property. It has frequently be- 
 come necessary in this country to condemn water power privileges 
 on account of the necessity of securing public water supplies or 
 for other public purposes. Under such conditions it frequently be- 
 comes necessary to estimate the value of the water power property. 
 When such matters are brought into court and various witnesses 
 are heard on the subject, it is commonly found that very great dif- 
 ferences of opinion exist as to the value of power- These differ- 
 ences of opinion are largely the result of entirely different points of 
 view. 
 
 To those who have carefully followed the discussion of the hy- 
 drograph, and the estimate of power based thereon, the great var- 
 iations that occur in the potential power of streams at various 
 times in the season, and in the various years, are obvious. 
 
 It is apparent that different engineers, even if they take carefully 
 into account these variations in power, may differ very greatly in- 
 deed as to the extent to which the power can be economically de- 
 veloped. 
 
 The question of pondage as discussed in Chap. XXVI also has 
 a very important bearing on this matter. It is only by a careful 
 study of the whole question and the consideration of the power 
 market that even an approximately correct answer to this question 
 can be given. The value of such a plant may be considered in a 
 
672 Cost, Value and Sale of Power. 
 
 variety of ways: First: Its value if intelligently and recently de- 
 signed, may be represented by the cost of its reproduction plus a 
 certain value for the water power rights; Second. Its value may 
 be computed on the capitalized net income that the plant can or 
 does earn; or, Third: The value of the plant may be considered 
 equal to the capitalized value of the most economical plant that 
 can be installed to furnish power at the point at which the power is 
 to be used. By the term "most economical" is meant not neces- 
 sarily the one lowest in first cost, but the plant that, when consid- 
 ered in the broadest sense, will furnish power, all things consid- 
 ered, at a less cost than from any other source of power. The sub- 
 ject is a very broad one and one that needs careful consideration 
 and study. A number of references are given to discussions of 
 this subject before various engineering societies, to which the en- 
 gineer is referred for further information on this important sub- 
 ject. 
 
 LITERATURE. 
 
 COST AND VALUE OF WATER POWER. 
 
 1. Kimball, Geo. A. Water Power: Its Measurement and Value. Jour. 
 
 Asso. Eng. Soc. 1893. 
 
 2. Main, C. T. The Value of Water Power. Trans. Am. Soc. Mech. Eng. 
 
 Vol. 13, p. 140. Eng. Rec. Vol. 50, p. 694. 
 
 3. Grant, W. H. Calculation of Mean Horse Power of a Variable Stream. 
 
 Trans. Am. Soc. C. E. Vol. 22, p. 389. 
 
 4. Rockwood, G. I. On the Value of a Horse Power. Trans. Am. Soc. M. E. 
 
 Vol. 21, p. 590. 
 
 5. Nagle, A. F. An Analysis of the Commercial Value of Water Power, 
 
 per Horse Power per Annum. Trans. Am. Soc. M. E. 1902. 
 Eng. News, vol. 49, p. 83. 
 
 6. Parker, M. S. Cost of Steam and Water Power in Montana. Jour. Asso. 
 
 Eng. Soc. Vol. 15, p. 26. 
 
 7. Main, C. T. Cost of Steam and Water Power. Trans. Am. Soc. M. E. 
 
 Vol. 11, p. 108. 
 
 8. Manning, C. H. Comparative Cost of Steam and Water Power. Trans. 
 
 Am. Soc. M. E. Vol. 10, p. 499. 
 
 9. Weber, Samuel. The Cost of Water Power. Cassier's Magazine, vol. 8, 
 
 p. 415. 
 
 10. Walbank, W. M. Lachine Rapids Plant and the Cost of Producing 
 
 Power Therefrom. West. Elec. July 9, 1898. 
 
 11. Cost of Niagara Power in Buffalo. Elec. World, April 23, 1898. 
 
Literature. 673 
 
 COST OF POWER. 
 
 12. Jones, C. L. Electrical World, Feb. 18, 1905. 
 
 13. Emery, C, E. Cost of Steam Power. Am. Inst. Elec. Eng. 1895. Trans. 
 
 Am. Soc. C. E. Vol. 12, p. 425. Trans. Am. Inst. Elec. Eng. 
 Vol. 10, p. 119. Eng. Mag. Vol. 8, p. 796. Power, 1895. 
 
 14. Dean, F. W. Reduction in Cost of Steam Power from 1870 to 1897. Am. 
 
 Soc. M. E. Vol. 9, p. 301. Eng. News. Dec. 1897. 
 
 15. Arnold, B. J. Cost of Producing Electrical Energy. Power, Dec. 1894. 
 
 16. Gray, C. C. An Investigation of the Cost of Power. The Engineer, 1902. 
 
 Vol. 39, p. 64. 
 
 17. Perry, N. W. Comparative Cost of Generating Electrical Power. Elec. 
 
 World, vol. 25, p. 274. 
 
 18. Rice, C. W. Analysis of the Cost of the Generation and Distribution of 
 
 a Unit of Electricity. West. Elec. June 25, 1898. 
 
 19. Dreyfus, E. D. Method of Investigating the Cost of Producing Electrical 
 
 Energy. Electrical World, vol. 52, p. 19. 
 
 20. Archibald, -E. M. The Effect of Load Factor on Cost of Power. Elec- 
 
 trical Age. Nov. 1906. 
 
 21. Forest, H. V. Cost of Electrical Power in Small Central Stations. Elec- 
 
 trical World, vol. 48, p. 1246. 
 
 22. Economy of Electric Stations. Report of Committee on Data of the Na- 
 
 tional Electric Light Asso. Eng. Rec. Vol. 36, p. 74. Elec. 
 Eng. Vol. 21, p. 522. 
 
 23. Elecricity Costs and Revenues. Power, May, 1903. 
 
 24. What Does a Steam Power Cost? The American Engineer, 1890. 
 
 THE SALE OF POWEB. 
 
 25. Harvey, G. A. Contracting for Use of Hydro-Electric Power on Railway 
 
 Systems. Electrical Age, Sept. 1906. 
 
 26. Storer, S. B. The Sale and Measurement of Electrical Power. Electri- 
 
 cal World, vol. 47, p. 669. Electrical Age, Aug. 1906. Engineering 
 Record, Nov. 3, 1906. 
 
 27. Parsons, C. E. Sale of Water Power from the Power Company's Point of 
 
 View. Engineering Record, vol. 54, p. 161. 
 
 28. The Principles of Modern Rate Making for Electric Light and Power. 
 
 Electrical World, vol. 49, p. 1086. 
 
 29. Fowler, C. P. Some Fundamental Principles Underlying the Sale of 
 
 Electrical Energy. Electrical World, vol. 50, p. 456. 
 
 30. Burnett, H. R. The Costs of Electricity, Supply, and Their Relation to 
 
 Scale of Charges. Electrical Review, vol. 51, p. 172. 
 
 POWEB TBANSMISSION. 
 
 31. Donaldson, Wm. Transmission of Power by Fluid Pressura E. & F. N. 
 
 Spon, London, 1888. 
 
 32. Unwin, W. C. On the Development and Transmission of Power. Long- 
 
 man, Green & Co., London, 1894. 
 
 33. Kern, E. W. Power and Power Transmission. John Wiley & Son, New 
 
 York, 1902. 
 41 
 
674 Cost, Value and Sale of Power. 
 
 34. Mead, Daniel W. Commercial Transformation of Energy. 111. Soc. Eng. 
 
 & Sur. 1901. Vol. 14, p. 38. 
 
 DEPKECIATION. 
 
 35. Matheson, Ewing. The Depreciation of Factories. E. & F. N. Spon. 
 
 London, 1903. 
 
 36. Mogerisen, Peter. A table for Depreciation or Sinking Fun*d Payments 
 
 with Annual Compounding. Eng. News, vol. 53, p. 226. 
 
 37. Alvord, J. W. Depreciation Proceedings. Am. W. W. Asso. 1903. 
 
 38. Bolton, R. P. Depreciation, Maintenance and Interest Charges. Eng. 
 
 Review. Jan. 1902. 
 
 39. Brayan, W. H. The Appraisal and Depreciation of Water Works. Jour. 
 
 Asso. Eng. Soc. Dec. 1907. 
 
 40. Depreciation of Electrical Apparatus. Elec. World and Eng. Aug. 9, 
 
 1902. Iowa Engineer. July, 1902. 
 
CHAPTER XXVIII. 
 
 THE INVESTIGATION OF WATER POWER PROJECTS. 
 
 336. The Extent of the Investigation. The investigation of any 
 water power project should include a careful study of all available 
 data relating to the physical and meteorological factors that affect 
 the water supply and that obtain on the drainage area of the 
 stream on which the water power development is projected. The 
 present condition of these factors is readily obtainable by careful 
 observations and surveys but the most difficult and yet the most 
 important information needed for the correct understanding of the 
 project is the variations from present conditions that have occurred 
 in the past and that are therefore liable to re-occur in the future. 
 On the correct interpretation of the available data the success of 
 the project or at least the economy of the installation depends, es- 
 pecially if, as is usually the case, it is desired to develop the plant 
 to its economical maximum. 
 
 The extent of the investigation must be governed by the import- 
 ance of the project, and will also depend on whether the investiga- 
 tion and report are to be of a preliminary character, or are to be 
 the basis of a final report on which the feasibility of the project 
 may be decided. 
 
 337. Preliminary Investigation and Report. An examination of 
 the data available in any first class engineering library will gener- 
 ally give the information necessary to form an approximate judg- 
 ment of the probable feasibility of the project in so far as it depends 
 on the flow of the stream. The approximate area drained by the 
 stream can be determined by reference to such maps as may be 
 available and the probable flow and the variations in the same that 
 will occur from day to day and from month to month, can usually be 
 determined by the construction of comparative hydrographs made 
 from either the measured flow of the stream, if such information is 
 available, .(see Literature page 194) or otherwise on the compara- 
 tive flow of similar and adjacent streams as described in Sec. 51, 
 page 83, and Sec. 100, page 184. 
 
676 The Investigation of Water Power Projects. 
 
 From such an investigation together with an appropriate knowl- 
 edge of the available head, an estimate of the probable power of the 
 stream can be made, and from such information an opinion can be 
 formed as to whether it is desirable to carry the investigation fur- 
 ther. Frequently such an investigation will show beyond question 
 the futility of the project, and even an examination of the locality 
 becomes unnecessary. If the preliminary investigation shows that 
 sufficient power is probably available on the stream in question the 
 investigation can be carried into sufficient detail to warrant an 
 opinion as to whether or not the project is feasable in all of its 
 phases. 
 
 338. Study of Run-off. The information of primary importance 
 in a water power project is the amount and variation in the run- 
 off of the stream itself. If this is not available the run-off of neigh- 
 boring streams that have similar physical and meteorological condi- 
 tions prevailing on their drainage area is next in importance. 
 
 As already pointed out, (see Sec. 99, page 181), the hydrograph of 
 the actual flow of the stream itself is the best information for study- 
 ing its variations in flow. Such hydrographs must be available for 
 a considerable term of years, and it is desirable that they should 
 cover all extremes of rain-fall and drought, and other physical and 
 meteorological conditions that influence run-off. 
 
 In the investigation of the hydrographical condition of any 
 stream, a single gauging of the stream is of little or no value. It is 
 however, desirabble to establish a guaging station as early as possi- 
 ble and to take daily gauge readings. It is also important, both for 
 the purpose of an understanding of the guage reading and for the 
 purpose of the study of head, to make stream flow measurements 
 (see Chap. XI) under all large variations in flow, as early as possi- 
 ble in order that a rating curve may be established. 
 
 When no local hydrographs are available, or when such available 
 hydrographs are limited to a few years, it becomes desirable to 
 gather together the flow data of all adjacent and similar streams and 
 to construct comparative hydrographs therefrom, as described in 
 Sec. 100, page 184. A long continued series of hydrographs of a 
 neighboring stream where similar conditions prevail is important 
 and should usually be utilized even if local observations have been 
 made for a few years. The value of comparative hydrographs is 
 dependent on the similarity of conditions, a question that demands 
 careful consideration and a considerable amount of data to deter- 
 mine, and even then can be regarded only as indicative. It is also 
 
Study of Rain-Fall. 677 
 
 essential to make careful comparisons of the relations that exist 
 between the hydrograph of the river under discussion and those of 
 adjoining rivers, for such period as such date may be mutually 
 available on both streams, in order that variations between the 
 areas compared may be determined. 
 
 339. Study of Rain-Fall. The rainfall records of the United 
 States Weather Bureau and, previous to these, the records of the 
 observations of the United States Signal Service (see Literature, 
 page 130) are available from various stations throughout the United 
 States for a long term of years. It is desirable to collect the rain- 
 fall data for the drainage area of the stream under consideration, 
 and also on such other drainage areas as may be used for compara- 
 tive purposes. This information should be classified and studied 
 as outlined in Chapter VI. In investigating rain-fall it is usually 
 especially desirable to make a study of both the annual rain-fall and 
 the periodical rain-fall of the divisions of the water year. (See Sec. 
 77, page 126.) The distribution of the rain-fall of these periods 
 has a greater effect on the low water flow than the total rain-fall 
 for the year. 
 
 The relations between rain-fall and run-off for the period for 
 which complete data is available should be investigated and such 
 relations established as clearly as possible for the drainage areas 
 under conideration. .(See Chapter VIII.) With the information 
 concerning run-off commonly available and the rainfall records for 
 a considerable term of years, it will be possible to draw fairly accu- 
 rate conclusions as to the probable variation and average flow of 
 the stream. The probability of a larger maximum or a smaller min- 
 imum than the stream flow observations themselves indicate can 
 also be determined from such an investigation. 
 
 340. Study of Topographical and Geological Conditions. The 
 topographical and geological conditions may ordinarily be inves- 
 tigated from data available in the publications of the United States 
 Geological Survey, or of the Geological Surveys of the state in 
 which the drainage area may lie. The information sought from this 
 investigation is a knowledge of the conditions that will effect run- 
 off, consequently, such a study is not of particular importance pro- 
 vided sufficient rain-fall and run-off data is available for the purpose 
 of the investigation. 
 
 If. however, the hydrographical condition o'f the areas under 
 consideration, or of other adjacent and similarly located areas have 
 not been previously investigated, and if few or no local observa- 
 
678 The Investigation of Water Power Projects. 
 
 tions of stream flow have been made, the topographical and geolog- 
 ical data may form the basis of a more intelligent opinion in regard 
 to the probable run-off than can be obtained without such considera- 
 tion. In any event, this source of information should be utilized to 
 the full extent warranted, as should all other sources of information 
 that will in any way assist the engineer in an intelligent understand- 
 ing of the problem before him, and the formation of a correct opin- 
 ion as to the possibilities and probabilities of the case in question. 
 
 341. Study of Flood-Flow. It is important to* establish both from 
 information that is usually available in the stream valley under con- 
 sideration, and from information which may be available from 
 adjoining streams, the probable maximum flood-flow of the stream. 
 This must be determined, or at least a safe approximate estimate 
 must be made in order that the dam and other works for the control 
 of the flow can be intelligently designed. (See Sec. 93, page 163.) 
 
 After the rating curve has been established the elevation of the 
 high water marks in the immediate vicinity and the relation of the 
 same to guage heights will usually give a safe basis for the estimate 
 of extreme flood-flows. 
 
 342. Study of the Back-Water Curve. A topographical survey 
 of the proposed site of the dam and of the stream valley above the 
 dam site, to the probable practical limit of the back-water effect, 
 should be carefully made. In order to investigate the probable 
 height of the back-water under all conditions of flow it will be neces- 
 sary to make cross-sections of the river at such intervals and under 
 such conditions as will permit of the division of the river into 
 lengths or divisions having comparatively uniform sections. Gages 
 should then be established at the various stations and observations 
 should be made of the gage heights at each station during various 
 stages of flow (see Chapter X). From the quantity of water flow- 
 ing at any stage, together with the cross sections of the river on the 
 various divisions, the value of the hydraulic elements and especially 
 of the friction coefficients for each division and their variations un- 
 der such condition of flow, can be calculated. (See Sees. 37 to 40, 
 page 44.) After this has been do<ne it is possible to calculate the 
 back-water curve (see Sec. 42, page 58) and to establish the prob- 
 able limit of the back-water flow line under any other conditions of 
 flow in a fairly reliable manner. 
 
 .Study of Head. The consideration of these conditions, the height 
 of the water surface at the dam due to various sections and length 
 of the spill-way and the practicable limit to which flood height in 
 
Study of Storage and Pondage. 679 
 
 the valley above must be restricted, will usually establish the limit 
 of the height to which the dam can or should be built and will in- 
 dicate whether it is necessary or desirable to construct flood gates 
 or to use an adjustable crest, flash boards, or means for regulating 
 and limiting the flood height. When these conditions are estab- 
 lished the variations in head under various conditions of flow can 
 be determined (see Chap. V, page 93) and the effect of such varia- 
 tions on the power which may be developed can be calculated. (See 
 Sec. 62, page 103.) 
 
 343. Study of Storage and Pondage. The topographical survey 
 will also give information concerning the storage and pondage con- 
 dition immediately above the dam. In special cases, reservoirs be- 
 yond the limit of the back-water effect may be desirable and special 
 surveys under such conditions will be necessary. As the conditions 
 of pondage and storage materially effect the amount of power avail- 
 able, these questions frequently become of great importance and 
 should receive the attention of the engineer that their importance in 
 each particular case seems to warrant. After definite information is 
 obtained concerning the extreme permissible limit of flood-flow, and 
 the possibilities of storage and pondage, an estimate of the power 
 of the stream under various conditions of use can be readily matfe. 
 (See Chap. XXVI.) 
 
 344. Study of Probable Load Curve. It is important in consider- 
 ing the power of the stream and especially the desirable condition 
 of pondage, to ascertain as far as practicable the probable necessary 
 distribution of the demand for power throughout the day. The way 
 in which the power is to be used, whether on 10 hour, 12 hour, or 
 24 hour service, and its probable variation during the hours of use, 
 has a most important bearing on the design of the plant. (See Chap- 
 ters XVII and XXI.) If variations in the demand for power 
 throughout the year are also likely to occur, and such variations are 
 likely to effect the requirements for storage, they must also receive 
 consideration. 
 
 A census of the power used in the district, to be supplied from the 
 proposed water power development, is important and should be 
 made in as great detail and with as great care as practicable. An 
 accurate estimate of the amount of power used by a factory or man- 
 ufacturing plant is a matter of considerable difficulty. In some 
 plants where power is electrically distributed, the use of indicating, 
 and sometimes of recording instruments, make it very easy to deter- 
 mine the energy output of the power plant. In most manufacturing 
 
680 The Investigation of Water Power Projects. 
 
 establishments where power is distributed by belts, shafting, and 
 other than electrical means, the amount of power actually developed 
 and utilized is seldom definitely known. The use of the steam engine 
 indicator, if opportunity for such use is offered, will give a knowl- 
 edge of the indicated power of the engine at the time observations 
 are made; and if the probable variations are investigated, a fairly 
 close estimate of power used can often be made by this means. 
 
 The annual quantity of coal used, and a careful study of the con- 
 dition and character of the boiler service, requirements for heating, 
 condition of the engine used, together with a careful examination 
 of the machinery operated, will form the basis of a fairly approxi- 
 mate estimate of power used. Even where the estimate of power 
 used is fairly accurate, it must be remembered that when such 
 power is used and transmitted through a multitude of shafts, belts, 
 etc., that if the electric power is substituted and individual motors 
 used on the machine to be operated, the power then used will be 
 Tery greatly reduced in amount. 
 
 345. Study of Power Development. Having established the 
 probable load curve, the head under all conditions of flow, and the 
 flow as modified by the pondage or storage conditions, the extent of 
 the power development can be determined. All of the questions that 
 have been previously discussed lead up to the consideration of the 
 question of the desirable capacity or extent of the proposed power 
 development. This capacity should always be estimated on a con- 
 servative basis. If, as is usually the case, uncertainties exist as to 
 the probable demand and distribution of power, or the probable min- 
 imum flow of the stream, it is desirable to develop the project to a 
 point below the probable commercial maximum but to keep in mind 
 the probability of the desirability of future enlargements and to 
 consider the plans with the future in view. In this connection the 
 question of auxiliary power, and the capacity of the plant as modi- 
 fied by such power, should receive attention. 
 
 346. Study of Auxiliary Power. The necessity of auxiliary power 
 in connection with the proposed water power development can be 
 determined by an intelligent study of the hydrograph and an inves- 
 tigation of the effects thereon of the storage and pondage available. 
 (See Sec. 317.) As a general principle, it may be stated that a 
 stream can often be developed to commercial advantage to the ex- 
 tent of the power which will be uniformily available for eight or 
 nine months of the dryest year, and that auxiliary power is usually 
 warranted to furnish the power needed for the remainder of the sea- 
 
Study of Plant Design. 68 1 
 
 son. This is a general rule which must be applied with caution. 
 Every proposed development must be carefully investigated for it- 
 self, and no general conclusion should form the basis of a final re- 
 port on the feasibility of such a project. The greater the demand 
 for power, and the greater the cost, of development from other than 
 water power sources, the more expense is warranted for auxiliary 
 service, pondage, etc., and the greater the capacity to which the 
 water power should be ultimately developed. 
 
 347. Study of Site of Dam and Power Station. In addition to 
 the topographical survey previously mentioned, it is necessary to 
 examine in considerable detail the bed and banks of the stream and 
 make all necessary soundings to fully establish all conditions on 
 which the character of the construction recommended must depend. 
 It is important that all conditions be carefully investigated and the 
 type of construction to be recommended carefully considered. The 
 storage of energy almost always involves a hazard which must be 
 met with economical but safe design and construction. The preven- 
 tion of flow under and around the structure requires a detailed 
 knowledge of the local conditions and is one of the most uncertain 
 conditions which, unless carefully and correctly estimated, is apt 
 to result in considerable extra expense. The flood flow is a condi- 
 tion which needs the most careful consideration for it is often the 
 condition of greatest danger and, to assure safe construction during 
 the short period when such conditions obtain, requires special atten- 
 tion and intimate knowledge of the local conditions, and often in- 
 volves considerable expense. 
 
 348. Study of Plant Design. The study of plant design requires 
 an extensive study of the various types of development that are in 
 practical use and the adaptability of such designs to the conditions 
 of the particular locality under consideration. It is seldoim that 
 plans, no matter how successfully carried out in one place, can be 
 duplicated to advantage in another. Each plant should be built to 
 meet the particular conditions under which it is to be installed and 
 operated, and the best ideas from all sources that will apply to the 
 local conditions should be correlated and embodied in the proposed 
 plant. Extensive experience, observation, and study are each desir- 
 able and each essential for the best results. For his own, as well as 
 for his client's good, the engineer should endeavor to secure the very 
 best results possible when all things are carefully weighed and con- 
 sidered. No reasonable amount of conscientious work, painstaking 
 thought, study, labor or expense should stand in the wav of such 
 
682 The Investigation of Water Power Projects. 
 
 results; and anything less than this is a detriment to future pro- 
 fessional attainments which no engineer, young or old, can afford. 
 
 In the previous chapters the general principles underlying the 
 design of the various elements of the plant have been considered. 
 The consideration of these matters has been very brief and the en- 
 gineer must extend his study in all cases to the extensive literature 
 on each subject, reference to some of which has been given at the 
 end of most chapters. Additional references can be found in the En- 
 gineering Index and in the indexes to the various technical publica- 
 tions and the publications of the various engineering societies. A 
 personal visit to and a detailed examination of successful plants is 
 a method for the acquisition of exact knowledge which should not 
 be neglected. New novel and untried designs are frequently de- 
 scribed in engineering publications. If they are successful their suc- 
 cess is often heralded in a similar manner. Their failure is seldom 
 mentioned by the technical press and the only method of ascertain- 
 ing their true value is by personal and confidential inquiry on the 
 ground. 
 
 349. The Estimate of Cost. In order that the preliminary esti- 
 mate shall be made on a safe basis, reasonable allowances should be 
 made for unforeseen and possible contingencies. This is especially 
 desirable in preliminary estimates on which the feasibility of the en- 
 tire project may be based. If a safe estimate of the actual cost of 
 construction, that is an estimate which will surely not be exceeded 
 and will undoubtedly be reduced in construction, makes the feasi- 
 bility of the project doubtful, then, as a general proposition, the 
 project is not worthy of further consideration. If the project is 
 predicated on the basis of an estimate that is known to be safe, it 
 can lead to no unfortunate investments. The owners of a develop- 
 ment are always satisfied if the cost of development is less than the 
 engineer's estimate ; but an increase in cost is often a serious matter. 
 
 The desire to develop a project is sometimes apt to give an opti- 
 mistic coloring to the engineer's report. This is a tendency which, 
 both on account of the interest of his client and his own future repu- 
 tation, he should carefuly guard against. 
 
 If the feasibility of the project is reasonably well established by 
 the preliminary examination, the examination should be still further 
 extended and made fairly complete. Preliminary plans should be 
 outlined in order that a safe detailed' estimate may be made. The 
 expense involved in such preliminary work is well warranted by the 
 results obtained. In many cases plants have been recommended on 
 
The Report. 683 
 
 insufficient examination, and the estimates made with too optimistic 
 a view of the conditions to be met. The latter development of the 
 necessity of increased expense, has made the project less attractive 
 and has resulted in great disappointment both to the owners and to 
 the engineer on whose opinion the work has gone forward. 
 
 350. The Report. As far as practicable the engineer, in making 
 a report on a water power project, should furnish his client with all 
 of the data on which his ^deductions are based. He should discuss 
 this data and its bearing on the project and point out as clearly 
 as possible the reason for the opinions he expresses. In a well' 
 drawn report the engineer can usually so illustrate and describe the 
 conditions by which a project is modified and controlled, that any 
 good business man will understand the basis on which his opinion 
 rests and the degree of probability of any departure from the ex- 
 pected result. While this is not true in regard to the technical de- 
 tails, it is entirely true with the general consideration on which the 
 feasibility of a project rests. If a report can not be so drawn it is 
 due either to insufficient data or to the fact that the engineer him- 
 self does not fully understand and appreciate the logic of the situa- 
 tion. 
 
 In general, a complete report on a water power project should 
 include a careful consideration and discussion of the following: 
 
 First : A general description of the drainage area, including the 
 size and the topographical, geological, and other physical conditions 
 that may have a direct bearing on the feasibility of the project. 
 
 Second : The run-off data available on the streams in question, if 
 any such data exists. 
 
 Third: If local run-off data is available, but only for a brief term 
 of years, the rainfall of the district for as long a period as possible 
 should be collected, and its relations to the available run-off data 
 established. From this the probable modification of the run-off 
 during other years during which the rainfall is found to vary, should 
 be carefully and fully discussed. 
 
 Fourth : The run-off data on adjoining streams, having drainage 
 areas with similar physical, topographical and geological condi- 
 tions, and where the hydrographical conditions of the rainfall and 
 run-off are apparently similar, when the difference therein can be 
 determined and estimated, should be graphically presented and dis- 
 cussed. 
 
 Fifth : The relations of the rainfall and of other conditions on the 
 
684 The Investigation of Water Power Projects. 
 
 comparative areas considered, and their variations from the par- 
 ticular location tinder consideration, should be fully illustrated. 
 
 Sixth : The conclusion in regard to the probable flow from the 
 drainage area, considered on the basis of its run-off, and the run-off 
 of comparative areas should be fully considered. 
 
 Seventh : A general description of the locality at which the dam 
 and power stations are to be constructed, and the physical condi- 
 tions there existing, also the effect of such conditions upon the con- 
 struction of the plant, should be described and the methods of meet- 
 ing them should be carefully and fully outlined. 
 
 Eighth : The head available and the variations under various con- 
 ditions of flow should receive careful consideration. 
 
 Ninth : The probable power available with and without pondage, 
 or with the pondage found by the preliminary survey to be avail- 
 able, should be carefully and fully treated, as this is one of the essen- 
 tial features of the report. 
 
 Tenth : The auxiliary power, if any, necessary to maintain the 
 plant at all times to the capacity recommended, often needs specific 
 discussion. 
 
 Eleventh : An estimate should be made of the probable cost of the 
 development, the probable operating expenses, and the probable 
 cost of maintenance. 
 
 Twelfth : The probable market for the power to be generated, and 
 the probable distribution of the demand for the power through the 
 day and year, and the basis on which such estimates are made, 
 should be given. 
 
 Thirteenth : The sources of power used in the territory which it is 
 proposed to supply, the cost of developing the same, and the prob- 
 able price at which power can be sold, are of primary importance. 
 
 Fourteenth : The report should be accompanied by hydrographs, 
 preliminary plans, and such other drawings as will, with the data 
 furnished, show conclusively that the facts are as the report sets 
 forth. 
 
 Fifteenth : In general it is advisable that the report itself should 
 be clear, concise and definite in its statements and recommenda- 
 tions. Any elaborate discussion of voluminous data should be fur- 
 nished in the form of an appendix to which the main report should 
 refer for confirmation of its findings and recommendations. 
 
APPENDIX A. 
 
 WATER HAMMER. 
 
 In Chapter XVIII, Section 213, it is shown that the pressure head 
 due to a change of velocity in a water column is expressed by the 
 formula 
 
 It is evident that the water hammer head produced by the rapid 
 closing of a gate at the end of a pipe line will be maximum for the 
 
 dv 
 maximum possible value of-j > or that obtained by closing the gate 
 
 instantly. Were it not for the elasticity of water and pipe, instan- 
 taneous gate closure would produce an infinite rate of retardation, 
 
 dv 
 
 -fa> and hence infinite pressure. In reality the water near the gate 
 
 first compresses and the surrounding pipe expands, due to the water 
 hammer pressure, the flow meanwhile continuing undiminished in 
 the remainder of the pipe in order to fill the additional space thus 
 obtained. The point up to which this compression of the water has 
 taken place, as shown by Joukowsky * travels along the pipe from 
 gate to reservoir as a wave with a velocity, A,f equal to that of 
 
 * See the "Memoires of the Imperial Acadainemy of Sciences of St. Peters- 
 burg," vol. IX, No. 5. Ueber den Hydraulipchen Stoss in Wasserleitungsrohren, 
 by N. Joukowsky; published in German and Russian. See also the synopsis 
 of same by O. Simin in The Trans, of the American W. W. Ass'n, 1904. 
 
 t A. varies from about 4,500 to 3,000 feet per second as the size uf the pipe- 
 increases, and can always be obtained by the formula (due to Joukowsky) : 
 
 12 
 
 _ _ _d_ 
 
 where: 
 
 A = velocity of the wave in feet per second. 
 K = volumnar modulus of elasticity of the water = 294, 000 s 
 
 pounds per square inch, 
 e = thickness of the pipe walls in inches. 
 E = modulus of elasticity of the material of the pipe, 
 w, g, and d = as previously defined in Chapter XVIII. 
 
686 Water Hammer. 
 
 sound in the same column of water. The water has not all been 
 brought to rest until the wave reaches the reservoir, which evi- 
 dently requires a timey. Although only an elementary length of 
 the water column is brought to rest at a time, the effect upon the 
 pressure is the same as would result from retarding the whole col- 
 umn as a unit in a time^-. The maximum possible rate of retar- 
 dation is hence 
 
 dv 1 
 
 Max ' dF = v -*- T 
 
 From Equation (i) 
 
 (2) H m = maximum h a . -T- = 
 
 The pressure-head given by this formula varies from about 140 
 to 100 feet per foot of extinguished velocity as the pipe increases 
 in size from 2!' upwards. If the gate is only partially closed by this 
 instantaneous motion, the pressure head is given by the same for- 
 mula in which case v represents the amount of the velocity which is 
 instantaneously extinguished. 
 
 Thus, in the case of instantaneous gate movement, the pressure is 
 not produced at the same instant along the entire pipe, but travels 
 as a wave with a velocity A from the gate to the origin of the pipe 
 and back again to the gate. It then reverses and becomes a wave 
 of rarefaction which travels twice the length of the pipe in the same 
 manner. This continues until the energy of the moving column of 
 water has been dissipated by friction, and the wave gradually sub- 
 sides. This phenomenon is identical with that of the vibrating 
 sound wave in an organ pipe. 
 
 Although equation (2) gives the maximum possible pressure 
 head which can result from the extinction of a given velocity v in 
 a pipe it does not, however, represent the maximum pressure which 
 could be obtained as the result of several successive gate move- 
 ments ; in fact, no limit can be assigned to the pressure which might 
 result in case several water hammer waves were to be produced at 
 intervals differing approximately by multiples of the vibration 
 
 * This formula is the same as that obtained by Joukowsky by two other 
 methods of analysis. His discussion of water hammer phenomena includes 
 all that is known upon the subject and it, or Simin's spnopsis, should be read es- 
 pecially by every engineer interested in high head developments as the subject 
 can only briefly be touched in this book. 
 
Water Hammer. 687 
 
 period of the water column, in which case they are known to "pile 
 up" to enormous indeterminable pressures. 
 
 When the flow in a pipe is shut off by the gradual closure of a 
 gate then equation (i) and also the following equation 
 
 from Chapter XIX, sections 213 and 217, apply as before except that 
 in this case not only v but also V is a variable, its value being differ- 
 ent for each successive position of the gate, and its law of variation 
 depending upon the law and rate of gate movement- The integra- 
 tion of equation (3) in its general form, to obtain the velocity curve 
 is then very difficult if not impossible. 
 
 An approximate curve of v, and hence also of h can be plotted by 
 assuming the gate closure to take place by means of a great many 
 small instantaneous movements, according to any law which may 
 be chosen. The value of.V for each of the many gate positions can 
 then be computed from the known hydraulic data of the wheels 
 and penstock. 
 
 Now, in equation (3), substitute for v the initial velocity in the 
 pipe, and for V the normal velocity (above determined), after the 
 gate has received its first small instantaneous movement. The re- 
 
 dv 
 
 suit will be the initial slope of the v-t curve =^r. Assume this 
 
 at 
 
 rate of decrease in velocity to continue constant for the short in- 
 terval between successive gate movements ; then the actual velocity, 
 v, at the instant of the next gate movement will be 
 
 (4) >.. T -T- J 
 
 where i is the interval between the two movements. 
 
 Assume this new value of v, to be v and using the value of V for 
 the corresponding (or second) gate position, again apply equations 
 (3) and (4), until the gate is completely shut. 
 
 Having thus determined the v-t curve, the head curve can be 
 readily found from equation (i), which gives the excess of head 
 above static or so called water hammer head. 
 
 dv 
 Substituting the value of r from (3) in (1) gives 
 
 (5) h a = : 
 
 Church has investigated this problem by a method described in 
 the Journal of the Franklin Institute for April and May, 1890. 
 
APPENDIX-B. 
 
 SPEED REGULATION, A MORE DETAILED ANALYSIS 
 THAN IN CHAPTER XVIII. 
 
 In Chapter XVIII, Section 217, the following equation was shown 
 to express the rate of acceleration of water in the penstock subse- 
 quent to an instantaneous change in gate opening of the wheel. 
 
 dF^V 1 IT* 
 Separating the variables v and t, gives 
 
 d t = lvs dv 
 
 gH ' V 2 -v 2 
 Integrating we have: 
 
 To determine the constant of integration, C, assume that v v 
 when t = 0, hence 
 
 C = - log e V ~ VO 
 
 Let 
 
 (3) 
 
 (4) B=^ 
 
 V-vo 
 Substituting these values of C, B and k in (2), gives, 
 
 From the definition of a logarithm: if X = log e N, then e x = N 
 hence 
 
 Solving for v we obtain: 
 (7) ^ 
 
 Be kt 4-l 
 
 From the principles of logarithms we have: 
 
 kt ** k/t 
 
 e =10 *-3 = 10 
 
Change of Penstock Velocity. 
 
 689 
 
 hence 
 
 (8-) 
 
 v = V 
 
 BX antilogk't 1 
 
 ' B X antilog k ' t + 1 
 
 Equation (8) is very readily applied to finding the curve of 
 velocity increase or decrease in any pipe line subsequent to a sudden 
 change of gate opening. It has been experimentally demonstrated 
 
 
 
 I 
 
 L 
 
 2 3 
 
 TIME: - SECONDS 
 
 Fig. 403. Curve Showing the Acceleration of Water in a Pipe Line After 
 a Sudden Opening of the Gate. 
 
 for the acceleration of water in the drive pipe of an hydraulic ram, 
 as shown by Fig. 403 which is taken from Bulletin No. 205, Uni- 
 versity of Wisconsin, Engineering Series, Vol. 4, No. 3, "An Investi- 
 gation of the Hydraulic Ram," by the writer. 
 
 The curve is the plot of equation (8) and the experimental points 
 were determined by an especially designed instrument. The fact 
 that they fall commonly below the theoretical curve is due to a 
 systematic friction error in the instrument. The agreement is suf- 
 ficiently close, however, to entirely verify the form of equation (8). 
 Fig. 404 shows the curves determined from equation (8) for 
 42 
 
690 
 
 Speed Regulation. 
 
 the wheel used for illustrative problems in Chap. XVIII, Section 
 228. Acceleration curves are shown for changes from o to the ve- 
 locities of %, %> -9 and full loads ; retardation curves from an initial 
 velocity of 5' per sec. to the above velocities. It will be observed 
 that in each case the actual velocity approaches, but theoretically 
 never equals, the normal value, V, for the given gate position. 
 
 The values of the constants used in computing these v-t curves 
 are given below. B, for accelerating from an initial velocity of 
 zero, is: 
 
 V + v V 
 
 TIME IN SECONDS 
 
 Fig. 404. Curves of Acceleration and Retardation of Water in Penstock for 
 Various Gate Movements. 
 
 The other constants are: H = 50', 1 = 500', and v = 5' for re- 
 tardation curves ; also for the retardation curves B is negative, since 
 v is greater than V. If we always use the positive value of 
 
 V o 
 
 we will obtain two equations: 
 
 For increasing velocities or acceleration 
 
 (9) antilogk't-1 
 antilog k't + 1 
 
 For decreasing or retarding velocities, 
 
 (10) _ y B antilog k't+1 
 
 Bantilogk't- 1 
 
Change of Penstock Velocity. 
 From equations (3) and (4) we obtain the table, 
 
 691 
 
 Load. 
 
 1.0 
 
 .9 
 
 .5 
 
 .25 
 
 V. 
 
 4.77 
 4.49 
 2.88 
 1.94 
 
 B 
 
 41.3 
 19.1 
 3.71 
 2.27 
 
 k' 
 
 .585 
 
 .623 
 
 .975 
 
 1.444 
 
 The computations of v, by equations (9) and (10), for various 
 assumed values of t is very simple if tabulated as below. The 
 computation of the curve of acceleration and retardation of water 
 in the penstock from 0, and from 5 feet per second, respectively, to 
 its value 2.88 ft. per sec. for % load is shown. It is assumed that 
 the gate opens instantly from to its position at % load, and closes 
 to this position instantly when the velocity is 5' per sec., giving 
 the values of velocity in columns v and v', (4) and (6) , respectively. 
 
 Computation of v-t curve.* 
 H = 50', 1 = 500', d = 8', k' = .975, B = 3.71, v = and 5', V = 2.88', 
 
 (1) 
 
 (2) 
 
 (3) 
 
 (4) =v 
 
 (5) 
 
 (6X.-V 1 
 
 t 
 
 k't 
 
 antilog of 
 k't 
 
 <3)-l oo 
 
 (3) X3.71 
 
 (5) + 1 S8 
 
 <3) + l- 
 
 (5)-l~ 
 
 
 
 
 
 
 .0 
 
 .0 
 
 1. 
 
 .0 
 
 3.71 
 
 5.0 
 
 .1 
 
 .0973 
 
 1.261 
 
 .321 
 
 4.64 
 
 4.17 
 
 o 
 
 .1946 
 
 1.565 
 
 .635 
 
 5.81 
 
 4.077 
 
 .4 
 
 .3892 
 
 2.45 
 
 1.210 
 
 9.10 
 
 3.59 
 
 .6 
 
 .5838 
 
 3.835 
 
 1.690 
 
 14.23 
 
 3.31 
 
 .8 
 
 .7784 
 
 6.003 
 
 2.055 
 
 22.27 
 
 3.15 
 
 1.0 
 
 .973 
 
 9.397 
 
 2.327 
 
 34.85 
 
 3.05 
 
 1.2 
 
 1.168 
 
 14.72 
 
 2.513 
 
 54.70 
 
 2.99 
 
 1.4 
 
 1.362 
 
 23.01 
 
 2.64 
 
 85.5 
 
 -.95 
 
 1.7 
 
 1.654 
 
 45.08 
 
 2.753 
 
 167.3 
 
 2.91 
 
 2.0 
 
 1.946 
 
 88.31 
 
 2.81 
 
 328.0 
 
 2.897 
 
 * A number enclosed in parenthesis refers to the value given in the column of 
 that number. 
 
 Referring again to Figure 404 we see that the acceleration curves 
 thus computed all have a common tangent at the origin showing an 
 initial rate of acceleration in each case of, 
 
 dv _ gH 
 ~dtT : ~T~ 
 
 The initial rate of retardation, however, depends upon the gate 
 opening. 
 
692 Speed Regulation. 
 
 As shown by equations (9), (10) and the curves in Figure 404 the 
 velocity never equals, but approaches indefinitely near, to its normal 
 value, V, for a given gate opening. 
 
 To show the application of the foregoing discussion to the change 
 of penstock velocity, power, speed, etc., at a change of load, refer to 
 Figure 405. Here the line A B represents J load, line C C repre- 
 sents full load, line D D .8 load and line H H 45 per cent load for 
 the same wheel discussed above. Lines A 7 B', C' C' and D' D' 
 represent the corresponding hydraulic power input lines. Line 
 abccba represents the line of gate movement from its initial position 
 at 14 to its position at full load and back again to % load. Line O 
 C v C is copied from Figure (404) and represents the curve of velocity 
 increase which would result from a sudden complete opening of the 
 gate. At b the gate begins to open, and the velocity to increase 
 along an estimated curve B v C v . This curve could be more accu- 
 rately determined by the process outlined in Appendix A, but was 
 not so determined here. In the same way curve F B x v A^ w r as taken 
 from Figure 404 and the velocity curve during gate movement, C' v B"' v . 
 was estimated. 
 
 Having thus obtained the velocity curve A v B v C v C-C' V B' v A v , 
 the curve of effective head at the wheel can be readily determined 
 from equation (11) Chapter XVIII, or 
 
 (H) h=^H' 
 
 While the gate is in motion from b to c the valve of V changes, 
 but can be readily estimated by interpolation from the values at 
 !/4 and full gates. From c to c (gate curve) V is constant, and 
 equal to 4.77 ft. per second. Since the friction loss in the pen- 
 stock is slight in the problem under discussion H' is assumed to 
 equal H = 50'. The resulting curve for h is A h B h C h C h C' h B'h A h . 
 
 The curve of hydraulic horse power or input was then determined 
 by applying the equation below to several points along the v and h 
 curves obtaining curve A' B' G Y' X'. 
 
 p _ 9h _ A v h 
 
 8.8 ~ 8.8 
 
 The output power curve A B C Y X was then computed by 
 
 ghE 
 
 8.8 
 
 E or efficiency for each point was obtained from the characteristic 
 curve of the wheel, Figure 245, by first computing from the known 
 
Graphical Analysis. 
 
 693 
 
 values of q, h, and S (= 180) at each point the values of the dis- 
 charge under one foot head and <j>. 
 
 Many interesting facts can now be seen from a study of Figure 405 
 It will be seen that the opening or closing of the gate in order to in- 
 crease, or decrease, the power of the wheel has an 'immediate effect 
 directly opposite to that intended and that in the output curve the 
 
 Fig, 405. Graphical Analysis of Speed Regulation. 
 
 power reduces to practically, if not quite, zero for nearly one-half 
 second. The effective head drops very greatly during acceleration, 
 and rises during retardation. It is evident that the rate of gate 
 movement here used (% second) is too fast for closure, since the 
 head rises to about 165 feet, over three times its normal value. 
 
 Now, since the product of power and time gives energy or work, 
 it is evident that the areas of the figures generated by the ordinates 
 to the various load curves are proportional to the demand for en- 
 
694 Speed Regulation. 
 
 ergy and the areas of the output curves are proportional to the 
 supply. The area between the two curves, therefore, represents a 
 deficiency or excess of work accomplished by the wheel, and can 
 be measured by means of a planimeter or otherwise. The value of 
 one square is % X 200=50 horse power seconds = to Y zzo 
 27,500 foot pounds. 
 
 It was found in this way that the deficient hydraulic energy sup- 
 plied to the wheel, assuming the load demand to increase from 14 
 to full is 
 
 27,500 X areaB' O Y' X' C' B' 
 = 27,500 X 36 
 = 990,000 foot pounds. 
 
 The deficient load output is 
 
 27,500 X areaB C YXCB 
 = 27,500 X 35 = 963,000 foot pounds. 
 
 This deficiency of input over output must be supplied from the 
 energy stored in the rotating parts, or from the fly-wheel effect, 
 and can be accomplished only by a drop in speed of the power unit. 
 Furthermore, in the case considered, the speed can never return to 
 normal as long as the load remains at full value, but suffers a per- 
 manent drop due to the fact that v, q, h and power theoretically 
 approach, but never equal the normal values for the new gate 
 opening. 
 
 The excess energy, when the load again drops to its ^4 value is, 
 27, 500 X area C E F A B C or 
 27,500 X 18 = 495,000 foot pounds. 
 
 It is evident that this excess energy at decreasing load will al- 
 ways be less than the deficient energy at time of increasing load, 
 since the low efficiency of the wheel during the velocity-change 
 tends to decrease the former and increase the latter. 
 
 It is also possible to dissipate the excess energy through a by- 
 pass or relief valve, while no method is available for supplying the 
 deficiency during load increase except at a sacrifice of the kinetic 
 energy of the rotating parts and consequent reduction of speed. 
 
 In Section 226, Chap. XVIII, it was shown that the percentage 
 departure of the speed from normal is 
 
 * = 294,000 R * K 
 
 Since the deficient energy AK is actually measured in this case, 
 the estimated co-efficient R becomes unity. The normal speed, S, 
 of the wheel is 180, and I will be assumed as 1,000,000 ft. 2 Ibs., or 
 1,000,000 pounds at one foot radius, then 
 
Numerical Example. 695 
 
 d - 294 ooo 963 ' 00 
 
 1,000, 000 X ISO 2 
 
 = 8.7 per cent. 
 
 This is a permanent drop in speed. 
 
 In order for the speed to pick up again to normal, the gate must 
 therefore overrun. The condition then is best illustrated by assum- 
 ing in Figure 405 that the load increases only to 0.8 of full load 
 value, following the line A B D D, while the gate movement follows 
 the same line as before. In this case the v, h, wheel imput, and 
 wheel output curves will be unchanged. 
 
 The deficiency of input or of energy in the delivered water is then 
 (by means of planimeter) represented by area B' D' Y' Q B' or 
 
 = 27,500 X 21.8 = 600,000 foot pounds. 
 The deficiency of output, represented by area B D Y C B, is 
 
 27,500 X 21.3 = 586,000 foot pounds, 
 giving a speed regulation of 
 
 The two quantities will probably always agree as closely as the 
 accuracy of the problem demands, and much labor can be saved in 
 an analysis if hydraulic horse power, or input, only is considered. 
 
 At Y the power curve crosses the demand line, D D, and the 
 speed begins to pick up, due to an excess of developed power. The 
 time required for return to normal can be obtained by continuing 
 the two curves until the excess area equals the former deficiency. 
 In this case 8% seconds is required. 
 
 By the successive application of equation (41) Chapter XVIII to 
 narrow vertical strips of the excess or deficient energy area, we 
 may plat the speed curve of the unit. In this way curve MSS , 
 Figure 405, for increase from !/4 to Ml load; curve MSS 2 for in- 
 crease from 14 to .8 load but simultaneous full gate opening ; curve 
 S' S^ for decrease from full to 14 loaci > and curve S' S 2 for decrease 
 from full to 45 per cent, load, were platted. Curves MSS X and 
 S' Si never returned to normal (180 R. P. M.), but curve MSS 2 re- 
 turns in 8!/2 seconds, and curve S' S 2 in 4 seconds- 
 
 It is the belief of the writer that this method of analysis is not too 
 long for a problem in practice and, if not, is therefore better than 
 the method given in Chapter XVIII since the conditions before 
 and during gate movement can be readily included. 
 
APPENDIX C. 
 
 THE STAND-PIPE. 
 
 It was shown in Section 223, Chapter XVIII that the following 
 equations apply to the operation of a plant with standpipe : 
 
 d.V ' ST 2T 
 
 (1) -r- =-y (accelerating head) -y- h a 
 
 (<2\ d dh Av ~ 
 
 dt dt F 
 
 The value of h a in a plant with penstock, is 
 
 h a = y h f 
 
 1 v 3 
 
 Hence = y (1 -j- f ~r -h etc.) = y cv 2 
 
 Equation (2) gives the instantaneous rate of fluctuations of water 
 level in the stand-pipe. 
 
 Equation (3) gives the rate of increase of penstock velocity in 
 terms of the then existing values of y and v. 
 
 The quantity, q, in equation (2), represents the water used by the 
 wheel. This may remain practically constant if the head fluctua- 
 tion is not too large, in which case the speed of the wheel will suffer ; 
 or, by means of an ideal action of the governor, it may be made to 
 fluctuate inversely as the head h, thus maintaining a constant value 
 of the product, qh, and hence of the power input of the wheel. In 
 case this latter assumption is made, then : 
 
 qh =q t h, 
 or q(H-y)=Av 1 (H-cv 1 2 ) 
 
 Substituting this value of q in equation (2) gives : 
 (4) dy_A r YI (H - o v r * n 
 
 dt~FL V (H-y) J 
 
 The solution of the two simultaneous differential equations 2 and 
 3, or 3 and 4, depending upon which assumption is made, is nec- 
 essary in order to determine the exact curve of variation of head 
 and velocity. Their general solution is however, very difficult if not 
 impossible in this form. The equations may be applied successively 
 to short portions of the arc by considering the curves to consist of 
 
Graphical Analysis. 697 
 
 a great many short straight lines. This method is not too long for 
 application to a problem in practice, and will assist in obtaining ap- 
 proximate formulas which will be seen to coincide very closely with 
 the true curves. 
 
 Assume an installation where d = 8', 1 = 500' H = 50, F = 8A. 
 Let the velocities on the penstock at fractional loads be the same as 
 given in the problem considered in Section 228, Chapter XVIII. If 
 the load suddenly increases from *4 to full, the velocity in the pen- 
 stock must accelerate from 1.94 to 4.77 feet per second, or q from 
 97.8 to 240 cu. ft. per sec. 
 
 Estimating f = .018, equation (3) gives 
 dv 32.15 F . 500. 
 
 (5) - = .0643 (y .0331 v 2 ) 
 
 Qt 
 
 and equation (4) gives : 
 
 dy_ _ dh _ v 4 . 77 X 49 . 25 
 "cfiT ~ dt ~~ 8(H y) 
 
 <*}L = _ 29 ' 4 
 dt. 8 H y 
 
 Curves A v and A h , Figure 406, show the curves of velocity, v, and 
 head, h, respectively, obtained by applying equations (5) and (6) 
 alternating to the two curves, considering them to remain straight 
 for the time interval between consecutive points which were taken 
 from % to one second apart depending upon the curvature. The 
 closer these points are taken the more accurate would be the result- 
 ing curves. 
 
 If friction in the penstock, and the action of the governor, in 
 compensating for the fluctuations of h, be neglected then equations 
 (i) and (2) become 
 
 (8) = v,-v 
 
 Dividing (8) by (7): 
 
 dy _ Al[ v, y 
 dv ~~ Fg' y 
 
 Integrating: 
 
 To determine the constant of integration, C ; let v = v when 
 y =^= o, whence : 
 
698 The Stand-pipe. 
 
 Substituting this value in (9) gives : 
 
 (10) y 2 - -- [(v, - v ) 2 - ( Vl - v)*] 
 
 Substituting this value of y in (7) and solving for dt gives 
 
 - y (Tl _ Vo _ fVl _ v) . 
 The integral of (n) is: 
 
 When t = o, v = v 0f hence 
 
 c = 
 
 after which (12) becomes: 
 
 t= 
 
 V T v 
 Solving this equation for v gives: 
 
 (13) v - Vl - ( Vl - v ) cos - 
 
 If this value of v be now substituted in equation (8) the equation 
 for y in terms of t can be obtained as follows : 
 
 When y = o, t = o, hence C o and 
 ^ 04) ' ' v = 
 
 Since this equation is that of a true sine curve it will be readily 
 seen that the maximum ordinate and hence the maximum de- 
 parture of the head from normal is 
 
 (15) Y = - (Vl ~ Vo) ' 
 
 and return to normal head occurs when 
 
 Whence 
 
 (16) T = 
 
Fluctuations of Head and Velocity. 
 
 699 
 
 Equations 13 and 14 may now be revised to read 
 
 (17) 
 
 (18) 
 
 i v ) cos t 
 
 and 
 
 fr* 
 
 These equations, (17) and (18), are shown for a particular prob- 
 lem, by the dotted lines B v and B h in Figure 406. The closeness of 
 their agreement with the curves A v and A h which involve the 
 effect of both friction and governor action shows that the values 
 
 IN FEET PENSTOCK VELOCITY IN FEET PER SECOND 
 o-iuu*>uia>Njco 
 
 . 
 
 
 
 
 
 
 
 
 T 
 
 
 
 
 I 
 
 
 
 
 
 -- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 + 6 
 
 + 4 
 X 
 
 s 
 
 0(0 
 
 UJ 
 
 * 2 < 
 > 
 
 -4 
 -B 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^5" 
 
 
 
 
 
 ^ 
 
 ^ i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 ^ 
 
 X 
 
 
 
 
 
 
 
 
 N 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 
 
 
 
 
 ^ 
 
 ^> 
 
 -F 
 
 
 
 
 
 
 
 
 
 
 s 
 
 k 
 
 
 
 
 
 
 
 
 
 
 
 
 m 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 s^ 
 
 
 
 
 
 
 
 
 
 
 
 i 
 
 ; N 
 
 Of 
 
 _M 
 
 \L 
 
 y 
 
 EL 
 
 DC 
 
 :IT 
 
 Y/ 
 
 
 OR 
 
 
 N 
 
 :w 
 
 
 L 
 
 DA 
 
 D 
 
 j 
 
 \u 
 
 D 
 
 / 
 
 vx 
 
 s 
 
 ^ 
 
 s, 
 
 DF 
 
 
 BIN 
 
 E 
 
 C 
 
 UF 
 
 W 
 
 _ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 s ^ s 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ff 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 X 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 v^. 
 
 
 
 
 
 
 
 > 
 
 < x 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^v 
 
 
 
 . 
 
 
 
 
 
 X 
 
 
 
 
 v, 
 
 
 Nl 
 
 m 
 
 ^_A 
 
 L - 
 
 _y 
 
 EL 
 
 QC 
 
 LT. 
 
 Y_. 
 
 
 
 P_R 
 
 
 
 3fi 
 
 GL 
 
 NA 
 
 L 
 
 _L 
 
 Of 
 
 Q 
 
 
 
 
 
 
 k -. 
 
 ^ 
 
 
 
 
 
 
 ! 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ev 
 
 rf 
 
 
 
 
 
 
 
 "~- 
 
 ^ 
 
 
 
 
 
 
 EFFECTIVE HEAD 
 
 Cv fc Ul Ul 
 
 ^ en CD a ru 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 &f 
 
 
 
 ^ 
 
 
 
 Y 
 
 
 
 
 
 "-^ 
 
 5; 
 
 
 
 S 
 
 ~. 
 
 - 
 
 
 
 _N_C 
 
 R 
 
 ^A 
 
 L 
 
 1 
 
 HEAD 
 
 
 X 
 
 ^N 
 
 D 
 
 ;<- 
 
 t 
 
 L 
 
 xx 
 
 X 
 
 S 
 
 DF 
 
 S 
 
 IN 
 
 E C 
 
 3U 
 
 =IV 
 
 E 
 
 
 
 ^5 
 
 k^ 
 
 
 
 
 
 
 
 
 
 
 ^> 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ^ 
 
 ^ v 
 
 
 
 
 
 
 
 
 
 
 
 
 
 , x 
 
 
 / 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 <<N 
 
 
 
 
 
 Y 
 
 
 
 Db 
 
 
 ^ 
 
 
 rf 
 
 ^ 
 
 ^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 \ 
 
 C^ 
 
 .,. 
 
 
 t 
 
 
 
 2 
 
 ^ 
 
 x' 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 := ~ 
 
 "^^. 
 
 
 
 -" 
 
 ^T 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 ID 
 
 TIME 
 
 SO 
 SINCE 
 
 30 
 OPENING 
 
 40 
 OF SATE 
 
 50 60 
 
 IN SECONDS 
 
 70 
 
 Fig. 406. Curves Showing Fluctuations of Head and Penstock- Velocity 
 in a Plant Avith Standpipe. 
 
 T and Y would commonly be as clo'se to the truth as the estimate 
 could be made of the probable load change (vj v ), for which the 
 stand pipe should be designed. 
 
 More exact formulas can be derived, however, from the stand 
 point of energy as follows : 
 
 Let the time required to reach D' and hence to approximately 
 
 TV 
 
 reach the valve v 1? under exact conditions, be 
 
7oo The Stand-Pipe. 
 
 T" T 
 
 The time -7- will be slightly greater than y' when friction and 
 
 governor action are involved, and the method of determining it will 
 be given later (equation 30). 
 
 It is evident that the number of foot pounds of energy which 
 
 must be supplied by the standpipe in this time ~ is equal to the en- 
 ergy required by the wheel plus that required to accelerate the water 
 in the penstock plus that necessary to overcome the friction of the 
 penstock minus that supplied through the penstock, 
 
 (19) Or E s = Ew + Ea + E, E p 
 Now, 
 
 (20) E s = w F D' H - cv 2 
 
 where D' is the maximum surge below the initial friction gradient 
 for Vo, and is used in place of Y to distinguish it from the value 
 obtained by the other formula: . " 
 Also, 
 
 (21) E w = A v,^w (H CVl 3 ) and 
 
 ' (22) Ea--^- Al(vi 2 -vo 2 ) 
 
 To obtain E f w r e have 
 
 (23) d E, = A v w X cv 2 dt 
 
 where c is the friction coefficient and v is obtained from equation(17). 
 
 rp ' 
 
 The integration of (23) between the limits t = -^ and 0, gives, 
 
 [vi 8 T' 3 T' 
 ~2~ -^ v * 2 (vi-vo) + 
 
 Tf 
 
 Also to find E p we have 
 
 dE p = HAwvdt, 
 
 where v is obtained from equation (17) as before. Integrating be- 
 tween the limits Y and 0, gives 
 
 (25) E p : 
 
 Combining and simplifying: 
 
 F f 2 L ^ 
 
 vi 2 (vi - vo) + M T^ vi (vi - vo) 2 - ^- ( vi - vo) 8 ] + . ~ (vi - vo) 
 
Maximum Drop in Head. 7 O1 
 
 The upward surge can be found by the same equation by a proper 
 change of signs, but is unimportant since it is always less than the 
 downward surge D b for the same change of velocities. 
 
 If friction be omitted and T' be changed to T for reasons men- 
 tioned later, equation (26) reduces to 
 
 (28) D 2 - 2HD = 
 
 
 - ~ ~ 
 
 ~ (vi 2 - vo' 2 ) + ~ (vi - vo) 
 
 To derive an equation for the maximum upward surge D a , when 
 full load is rejected, we may equate the original kinetic energy in 
 the penstock to that expended in friction plus that used in raising 
 water in the standpipe.. The energy lost in friction is found from 
 equation (24) by putting v x = o 
 
 A w c T vo 3 
 or Ef = ^ 
 
 The other quantities are evident. This gives : 
 
 W.A L Awe T vo 3 w FE 
 
 - vo 2 = r . H *- 
 
 or 
 
 Equations (21), (24), (25) and (26) are: all theoretically exact 
 except for the assumption that the velocity change takes place along 
 
 TV 
 
 a simple harmonic in time. The true curve for a half cycle, as 
 used, is scarcely distinguishable from a simple harmonic but its 
 period T' or time for return of water in standpipe to normal level is 
 greater than the value T, given by equation (7). In three cases 
 which the writer has solved by successively applying the differen- 
 tial equations to short positions of the arc he has found that the 
 true value T' may be closely approximated by the following for- 
 mula : 
 
 (30) T' = 5,T 
 
 where T is found from equation (16), 
 Y from equation (15), and 
 D from equation (28). 
 
 The quantity T' is useful in itself as the true time for return to- 
 normal head, but its use in formula (26) for determining D' is not 
 advisable, as the writer has found by solving a number of problems 
 that the value of D', thus found, agrees almost exactly with the 
 value of D found from equation (28), in which equation the value of 
 T from equation (16) is used. Equation (28) is therefore offered as 
 
702 The Stand-Pipe. 
 
 a much simpler substitute for equation (26) and equation (27) 
 becomes : 
 
 (31) D b = D + cvo 2 * 
 
 Like all wave motions, these surge waves are liable to pile up, one 
 upon another, in case several gate movements occur at proper inter- 
 vals and, in fact, no limit can be placed upon the possible amplitude 
 of the surge which can occur in this way. In a plant where large 
 frequent load changes are anticipated the danger from this source 
 should receive careful attention. Some means should be adopted 
 for causing the wave, due to a given gate movement, to rapidly 
 subside in order to lessen the probability of its combination with 
 another wave. One method of accomplishing this result is by ar- 
 ranging the standpipe to overflow at a definite elevation above the 
 forebay. This limits the upward surge and thereby the maximum 
 possible downward surge which could occur under any assumption 
 of gate movements. This method necessitates a waste of water. 
 
 Another methodf is that of imposing a resistance between pen- 
 stock and standpipe. This not only causes the waves to subside 
 more rapidly but also, if properly designed, reduces the amplitude 
 of a single wave. This is of greatest advantage near full load where 
 the downward surge is apt to lower the head sufficiently to make 
 it impossible for the unit to deliver the required power. Another 
 effect of the resistance, however, is to change the form of the curve 
 of effective head so that, instead of a slow sinuous pressure drop 
 after an increase of load, a sudden drop is obtained. This is evi- 
 dently opposed to good speed regulation as it adds to the effective 
 sudden load for which the governor must compensate by requiring 
 a greater q to make up, not only for the increased load, but also for 
 the suddenly decreased head.** 
 
 *Mr. Raymond D. Johnson in Am. Soc. M. E. 1908 has derived an equation for 
 D as follows: 
 
 D' 2 =AL ( Vl __ vo a + C 2 ( Vl8 _ vo .) 
 
 The results obtained by this equation agree quite closely with those obtained 
 by the writer's method and the two entirely independent analyses of the problem 
 are mutually corroborative. 
 
 fSee paper on "Surge Tanks for Water Power Plants" by R. D. Johnson 
 with discussions by the writer and others in the Trans. Am. Soc. of M. E. 1908. 
 
 **For further discussion of this subject and a mathematical analysis of the 
 problem see Mr. R. D. Johnson's paper with discussions as previously re- 
 ferred to. 
 
APPENDIX D. 
 TEST DATA OF TURBINE WATER WHEELS. 
 
 TABLE LIX. 
 
 Test of a 113-inch Boott Center Vent Turbine. Built in \1849 for tfie Boott 
 Cotton Mills, Lowell, Mass., after designs by James B. Francis. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part. 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency =1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1 
 
 0.25 
 0.25 
 0.25 
 0.25 
 0.25 
 0.25 
 0.25 
 0.25 
 
 0.50 
 0.50 
 0.50 
 0.50 
 0.50 
 0.50 
 0.50 
 0.50 
 
 0.75 
 0.75 
 0.75 
 0.75 
 0.75 
 0.75 
 0.75 
 0.75 
 0.75 
 0.75 
 
 1.00 
 .00 
 
 .00 
 .00 
 .00 
 .00 
 .00 
 .00 
 .00 
 .00 
 1.00 
 1.00 
 1.00 
 
 0.603 
 0.577 
 0.5flO 
 0.592 
 0.596 
 0.595 
 0.598 
 0.544 
 
 0.756 
 0.767 
 0.775 
 0.780 
 0.785 
 0.802 
 0.815 
 0.685 
 
 0.852 
 0.876 
 0.893 
 0.910 
 0.913 
 0.920 
 0.922 
 0.921 
 0.925 
 0.818 
 
 1.000 
 1.005 
 1.000 
 1.005 
 1.006 
 1.007 
 1.006 
 1.010 
 1.017 
 1.013 
 0.982 
 0.980 
 0.887 
 
 14.60 
 14.67 
 14.57 
 14.16 
 14.20 
 14.14 
 14.24 
 14.30 
 
 14.29 
 14.23 
 14.20 
 14 19 
 14.19 
 13.78 
 13.61 
 13.95 
 
 13.52 
 13.37 
 13.37 
 13.40 
 13.38 
 13.34 
 13. 32 
 13.33 
 13.30 
 13.70 
 
 13.40 
 13.43 
 13.33 
 13.38 
 13.39 
 13.38 
 13.36 
 13.38 
 13.40 
 13.:-i2 
 13.54 
 13.57 
 13.60 
 
 4 
 
 " 8 
 17 
 12 
 
 7 
 7 
 8 
 
 11 
 10 
 10 
 8 
 14 
 11 
 11 
 8 
 
 7 
 2.5 
 7 
 9 
 12 
 9 
 9 
 9 
 10 
 8 
 
 9 
 6 
 6 
 
 7 
 8 
 8 
 9 
 8 
 8 
 8 
 4 
 2 
 7 
 
 35.6 
 
 5:3.7 
 43.4 
 32.7 
 30.0 
 27.0 
 25.25 
 60.8 
 
 60.6 
 57.6 
 55.9 
 54.1 
 51.4 
 41.6 
 35.9 
 70.6 
 
 66.3 
 59.6 
 54.1 
 49.5 
 47.2 
 44.8 
 43:5 
 42.6 
 41.9 
 75.2 
 
 42.5 
 
 41.9 
 40.7 
 40.3 
 39.6 
 38.9 
 38.1 
 37 4 
 36.8 
 35.5 
 0.0 
 0.0 
 77.0 
 
 67.53 
 64.89 
 66.43 
 66.61 
 67.03 
 66.89 
 67.37 
 61.08 
 
 85.0 
 86.35 
 87.08 
 87.69 
 88.29 
 90.17 
 91.70 
 77.11 
 
 95.76 
 98.49 
 100.42 
 10-'. 42 
 102.82 
 103.52 
 103.77 
 103.69 
 104.23 
 92.02 
 
 112.53 
 112.99 
 112.56 
 113.00 
 113.07 
 113.16 
 113.09 
 113.67 
 114.29 
 113.97 
 110.45 
 110.32 
 99.8 
 
 42.2 
 
 21.94 
 36.4 
 40.8 
 41.1 
 40.0 
 k'J.3 
 0.0 
 
 41.7 
 52.4 
 
 57.8 
 62.7 
 69.5 
 82.0 
 84.4 
 0.0 
 
 35.9 
 65.3 
 87.6 
 102.2 
 107.7 
 111.2 
 112.8 
 114.0 
 114.9 
 0.0 
 
 136.4 
 137.0 
 135.6 
 136.6 
 136.8 
 136.9 
 136.6 
 136.5 
 136.7 
 134.5 
 0.0 
 0.0 
 
 
 37.7 
 20.3 
 33.2 
 38,2 
 38.1 
 37.3 
 27.0 
 0.0 
 
 30.3 
 37.6 
 41.3 
 44.4 
 48.9 
 58.3 
 59.6 
 0.0 
 
 24.5 
 43.7 
 57.6 
 65.7 
 69.0 
 71.0 
 72.0 
 72.8 
 73.1 
 0.0 
 
 79.7 
 79.6 
 79.7 
 79.7 
 79.7 
 79.7 
 79.8 
 79.2 
 78.7 
 78.1 
 0.0 
 0.0 
 0.0 
 
 2 
 
 3 
 4 
 5 
 
 6 
 
 7 
 
 8 
 9 
 
 10 
 
 11 
 
 12 
 18 
 14 
 
 15 
 
 16 ; 
 
 17 
 18 
 19 
 20 
 21 
 
 22 
 23 
 
 2t 
 
 25 
 
 26 
 
 27 
 
 28 
 
 29 
 30 
 
 31 
 
 .32 
 33 
 
 34 
 
 35 
 
 36 
 
 37 
 38 
 
 39 
 
 
704 
 
 Turbine Test Data. 
 
 w A 
 
 3 H * 
 
 o - 
 
 S H 
 
 S*I 
 
 * 
 
 III. 
 
 Ho 
 
 00 B * 
 
 II 
 
 i 
 
 
 1 
 
 - 
 
 II 
 
 111 
 
 ** *"c 
 
 111 
 
 CM 
 
 111 
 
 . 2 
 
 1- t-_ OO 00 O 
 
 00 OC i S3 OO OO 
 
 H CJ i-< Tf IO ' 
 
 i < ck r- - 
 P- & to 
 
 'o4 
 
 ) t~ O> OO CC ?O ^J< IOO O H > O ^ ' 
 
 i o o TH 01 <*< t^ O5 (N co co-g; xo i 
 >ft2lOWU3 CO CO *<'<< Tj< ^ r}< 
 
 Ji-5^*'c4t^*J<pocotc*Cic^4< 
 
 oo< 
 
 {Si 
 
 1 O O Y-H ^ IA t^> 1 
 
 > o> r- * 3 s o i 
 
 > rf 10 lA GO oi 10 c 
 
 ' ^ t^- 1~ t- t~ t- 1 
 
 t>- oo o eo o o o oo n o o oo M o i- 
 
 
 
Victor Turbine. 
 
 705 
 
 OC' 
 
 3 ooooo aoaooocsoaJcScj 
 
 o ' 
 
 t^-t>- o P t> r-- 1> t>- r- r- <o to o 01- S t^cq ^<ioio33o we5*'S^^^ 
 
 * " ' * ' ' ' ' 
 
 eo- ci "eo * ' 'c^i-eo ' co oi eo ' * "c4 *co " * 
 
 6 D to t-' r-' t--" 05 ri cq CO rf' rjJ *' to r-' 06 OO OS C 
 
 :>( o o o 
 
 KggS82 SSsHlli 
 
 l| e '*^Si 
 
 i o _ i-i in 
 
 | = . = s S. ..... s jjj. . . - . . , 
 
 43 
 
7o6 
 
 Turbine Test Data. 
 
 TABLE LXI. 
 
 Test of a 96-inch Fourneyron Turbine Built in 1851 for the Tremont Mills, 
 Lowell, Mass., after designs by James B. Francis. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part. 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency =1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1 
 
 1 
 
 1 01 
 
 12 86 
 
 8 
 
 53 62 
 
 139 42 
 
 161 4 
 
 78 4 
 
 2 
 
 1 
 
 1 01 
 
 12 86 
 
 10 
 
 53 5 
 
 139 42 
 
 159 2 
 
 78 3 
 
 3 
 
 1 
 
 1 01 
 
 12 87 
 
 10 
 
 53 6 
 
 139 47 
 
 159 5 
 
 78 4 
 
 4 
 
 1 
 
 1 13 
 
 12 55 
 
 6 
 
 95 8 
 
 156 65 
 
 60 6 
 
 27 2 
 
 5 ,.. 
 
 1 
 
 1 12 
 
 12 61 
 
 8 
 
 91 9 
 
 154 39 
 
 77 9 
 
 35 3 
 
 6 
 
 1 
 
 1 10 
 
 J2 6-"> 
 
 7 
 
 87 7 
 
 152 27 
 
 94 
 
 43 
 
 7 
 
 1 
 
 1 08 
 
 12 70 
 
 
 8;j () 
 
 149 46 
 
 109 2 
 
 50 7 
 
 g 
 
 o 
 
 1 07 
 
 12 72 
 
 5 
 
 78 5 
 
 147 29 
 
 l''l 5 
 
 57 2 
 
 9 
 
 o 
 
 1 OB 
 
 12 18 
 
 5 
 
 77 4 
 
 146 02 
 
 131 7 
 
 62 2 
 
 10 
 
 o 
 
 1 05 
 
 12 80 
 
 g 
 
 71 
 
 144 81 
 
 140 2 
 
 66 7 
 
 11 
 
 o 
 
 1 04 
 
 12 82 
 
 9 
 
 67 5 
 
 143 91 
 
 147 2 
 
 70 3 
 
 12 
 
 o 
 
 
 
 9 
 
 107 
 
 
 
 
 
 
 13 .... 
 
 o 
 
 1 18 
 
 12 51 
 
 9 
 
 lo7 o 
 
 163 43 
 
 
 
 
 
 14 
 
 o 
 
 1 03 
 
 12 86 
 
 9 
 
 6t 
 
 142 52 
 
 152 6 
 
 73 5 
 
 15 
 
 o 
 
 1 03 
 
 12 89 
 
 9 
 
 61 4 
 
 142 04 
 
 155 8 
 
 75 
 
 16 
 
 o 
 
 1 03 
 
 12 89 
 
 | 
 
 60 
 
 141 98 
 
 157 
 
 75 6 
 
 17 
 
 o 
 
 1 02 
 
 12 90 
 
 9 
 
 58 2 
 
 141 28 
 
 158 3 
 
 76 6 
 
 18 .... 
 
 Q 
 
 ] (J2 
 
 12 8^ 
 
 
 56 7 
 
 140 47 
 
 158 9 
 
 77 4 
 
 19 
 
 o 
 
 1 01 
 
 12 88 
 
 10 
 
 55 4 
 
 140 OS 
 
 159 5 
 
 77 9 
 
 20 
 
 o 
 
 1 01 
 
 12 87 
 
 9 
 
 54 7 
 
 140 01 
 
 159 7 
 
 78 
 
 21 
 22 
 
 .0 
 
 o 
 
 1.01 
 
 1 01 
 
 J2.90 
 12 90 
 
 10 
 14 
 
 54.1 
 53 8 
 
 139.90 
 139 67 
 
 160.0 
 "160 2 
 
 78.1 
 78 4 
 
 23 
 
 (J 
 
 1 17 
 
 12 43 
 
 9 
 
 106 8 
 
 161 69 
 
 
 
 
 
 24 
 
 o 
 
 1 01 
 
 12 90 
 
 9 
 
 53 6 
 
 139 01 
 
 160 5 
 
 78 9 
 
 25 
 26 
 
 .0 
 
 o 
 
 1.01 
 1 
 
 12.90 
 12 89 
 
 13 
 5 
 
 53.1 
 52 5 
 
 139.03 
 138 76 
 
 160.4 
 159 5 
 
 78.8 
 78 6 
 
 27 
 
 28 
 
 .0 
 
 o 
 
 1.0 
 1 
 
 12.90 
 12 91 
 
 14 
 13 
 
 5^.8 
 52 4 
 
 138.85 
 138 87 
 
 160.5 
 160 5 
 
 79.0 
 78 9 
 
 29... 
 
 o 
 
 1 
 
 12 91 
 
 12 
 
 52 
 
 138 51 
 
 160 6 
 
 79 2 
 
 30 
 31 
 
 .0 
 
 o 
 
 1.0 
 1 17 
 
 12.90 
 12 54 
 
 ]2 
 y 
 
 51.1 
 
 106 8 
 
 138! 19 
 162 32 
 
 160.5 
 
 
 79.4 
 
 
 32 
 
 (J 
 
 1 
 
 12 91 
 
 6 
 
 2 
 
 138 27 
 
 160 6 
 
 79 3 
 
 33 
 
 o 
 
 1 
 
 12 93 
 
 10 
 
 48 8 
 
 138 23 
 
 160 6 
 
 79 2 
 
 34 
 
 1 
 
 1 
 
 12 94 
 
 jj 
 
 47 1 
 
 38 09 
 
 160 
 
 78 Q 
 
 35 
 
 1 
 
 1 
 
 12 94 
 
 11 
 
 44 5 
 
 137 71 
 
 158 4 
 
 78 3 
 
 36 
 
 1 
 
 99 
 
 12 96 
 
 jl 
 
 41 7 
 
 136 49 
 
 156 2 
 
 77 9 
 
 37 
 
 1 
 
 98 
 
 12 94 
 
 10 
 
 38 7 
 
 135 14 
 
 152 6 
 
 77 
 
 38 
 
 1 
 
 1 17 
 
 12 5 
 
 9 
 
 107 1 
 
 161 69 
 
 
 
 
 
 39 
 
 1 
 
 98 
 
 12 96 
 
 12 
 
 38 8 
 
 135 34 
 
 153 
 
 76 9 
 
 40 
 41 
 
 1.0 
 1 
 
 0.97 
 97 
 
 12.97 
 12 98 
 
 8 
 11 
 
 36.0 
 31 9 
 
 134.80 
 133 75 
 
 149.3 
 142 7 
 
 75.3 
 72 5 
 
 42 
 
 1 
 
 97 
 
 12 95 
 
 9 
 
 27 3 
 
 133 43 
 
 133 
 
 67 9 
 
 43 
 44 
 
 1.0 
 I 
 
 0.9* 
 98 
 
 12.80 
 12 77 
 
 1.5 
 2 5 
 
 0.0 
 
 
 135.65 
 135 62 
 
 0.0 
 
 
 0.0 
 
 
 45 
 
 1 
 
 I 17 
 
 12 47 
 
 9 
 
 106 9 
 
 162 02 
 
 
 
 
 
 46 
 47 
 
 1.0 
 1 
 
 1.00 
 1 00 
 
 12.95 
 )> 93 
 
 11 
 10 
 
 49.9 
 4Q 
 
 138.62 
 
 1 'Itf nfl 
 
 161.1 
 IfiO 7 
 
 79.1 
 TQ 1 
 
 48 
 
 1 
 
 1 00 
 
 12 95 
 
 11 
 
 48 2 
 
 138 47 
 
 160 5 
 
 78 9 
 
 49 
 
 1 
 
 1 00 
 
 12 95 
 
 12 
 
 47 4- 
 
 ifta 07 
 
 160 3 
 
 78 9 
 
 50 
 51 
 
 1.0 
 75 
 
 1.00 
 1 fl-t 
 
 12.95 
 12 7fi 
 
 11 
 
 j 
 
 46.2 
 
 138.16 
 
 159.8 
 
 78.7 
 
 52 
 
 75 
 
 1 111 
 
 !'* 87 
 
 g 
 
 7* A 
 
 -IQQ 01 
 
 120 fi 
 
 K.Q A 
 
 53 
 
 75 
 
 1 00 
 
 12 91 
 
 9 
 
 
 
 
 K7 ^ 
 
 54. . 
 
 75 
 
 1 00 
 
 12 Q4. 
 
 
 
 
 
 
 55 
 56 
 
 0.75 
 7") 
 
 0.99 
 
 OQH 
 
 12.95 
 
 8 
 
 61.4 
 
 137.00 
 
 145.9 
 
 72.5 
 
 
 75 
 
 
 
 
 
 
 
 
 58 
 
 75 
 
 97 
 
 JO QQ 
 
 
 
 
 
 
 59 
 
 75 
 
 96 
 
 iq An 
 
 
 
 
 
 
 60 
 
 75 
 
 
 
 
 
 
 
 
 61 
 
 75 
 
 OQK 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 148.7 
 
 
Francis' Tremont Turbine. 
 
 707 
 
 TABLE LXL Continued. 
 
 Test of a 96-inch Fourneyron Turbine Built in 1851 for the Tremont 
 Lowell, Mass., after designs by James B. Francis. 
 
 Mills, 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficienc3' = l). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 91 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 62... 
 
 75 
 
 95 
 
 13 04 
 
 9 
 
 46 3 
 
 130 99 
 
 147 9 
 
 76 4 
 
 63 
 
 U 75 
 
 95 
 
 13 03 
 
 8 
 
 42 5 
 
 13(1 89 
 
 145 1 
 
 75 
 
 64 
 
 75 
 
 1 08 
 
 12 72 
 
 U 
 
 103 
 
 
 fl fl 
 
 n (I 
 
 65 
 
 49 
 
 88 
 
 13 17 
 
 H 
 
 92 9 
 
 121 97 
 
 
 
 
 
 66 
 67. .. 
 
 0.49 
 49 
 
 0.86 
 8t 
 
 13.08 
 14 13 
 
 6 
 6 
 
 81.1 
 73 1 
 
 118.55 
 116 1 
 
 52.8 
 78 3 
 
 30.0 
 45 3 
 
 68 
 
 49 
 
 83 
 
 13 18 
 
 g 
 
 65 
 
 114 26 
 
 96 6 
 
 
 69 
 
 49 
 
 82 
 
 13 21 
 
 
 60 2 
 
 113 24 
 
 103 3 
 
 60 9 
 
 70 
 
 49 
 
 81 
 
 13 25 
 
 y 
 
 55 4 
 
 111 52 
 
 
 63 7 
 
 71 
 
 49 
 
 79 
 
 13 2d 
 
 
 50 6 
 
 109 71 
 
 107 8 
 
 65 2 
 
 72 
 73 
 
 0.49 
 49 
 
 0.78 
 78 
 
 13.31 
 13 31 
 
 II 
 
 6 
 
 46.5 
 46 5 
 
 108.05 
 107 95 
 
 106.8 
 107 
 
 65.5 
 65 6 
 
 74 
 
 49 
 
 76 
 
 13 33 
 
 9 
 
 41 2 
 
 105 53 
 
 102 3 
 
 64 1 
 
 75 
 
 49 
 
 75 
 
 13 36 
 
 ( s 
 
 36 9 
 
 103 85 
 
 97 3 
 
 61 9 
 
 76 
 
 49 
 
 73 
 
 13 41 
 
 
 27 4 
 
 100 54 
 
 83 7 
 
 54 8 
 
 77... 
 
 87 
 
 99 
 
 12 88 
 
 
 51 3 
 
 137 36 
 
 156 8 
 
 78 1 
 
 78 
 
 79 
 
 0.87 
 87 
 
 0.99 
 99 
 
 12.90 
 12 91 
 
 7 
 
 7 
 
 49.3 
 47 4 
 
 136.97 
 136 55 
 
 157.0 
 156 6 
 
 78.4 
 78 3 
 
 80 
 81 
 
 0.25 
 25 
 
 0.58 
 57 
 
 13.35 
 13 37 
 
 5 
 6 
 
 74.9 
 
 68 8 
 
 80.45 
 
 78 84 
 
 0.0 
 168 2 
 
 0.0 
 14 i 
 
 82 
 83 
 
 0.25 
 U 25 
 
 0.56 
 0.54 
 
 13.40 
 13 43 
 
 6 
 
 6 
 
 57.6 
 46 3 
 
 76.62 
 74 06 
 
 38.6 
 
 49 7 
 
 33.2 
 44 
 
 84 
 85 
 
 0.2.') 
 0.25 
 
 0.52 
 51 
 
 13.48 
 13 51 
 
 8 
 8 
 
 40.3 
 33 6 
 
 71.87 
 70 01 
 
 50.9 
 
 48 8 
 
 46.3 
 45 5 
 
 86. .'.. 
 
 25 
 
 49 
 
 13 56 
 
 
 27 7 
 
 67 82 
 
 44 4 
 
 42 7 
 
 87 
 
 0.25 
 
 0.47 
 
 13.56 
 
 H 
 
 18 
 
 64.51 
 
 32 7 
 
 33 o 
 
 88 
 
 25 
 
 44 
 
 13 52 
 
 
 
 
 60 36 
 
 
 
 U 
 
 89 
 
 90 
 91 
 
 0.25 
 
 0.087 
 0.087 
 
 0.44 
 
 0.28 
 0.28 
 
 13.53 
 
 13.98 
 14.00 
 
 7 
 7 
 
 0.0 
 
 37.2 
 41.3 
 
 60.42 
 
 38.22 
 38 57 
 
 0.0 
 
 9.09 
 6 23 
 
 0.0 
 
 15.0 
 10 2 
 
 92 ... 
 
 O.U87 
 
 0.27 
 
 14 02 
 
 17 
 
 23 3 
 
 37 17 
 
 14 21 
 
 24 
 
 
 
 
 
 
 
 
 
 
7o8 
 
 Turbine Test' Data. 
 
 TABLE LXII. 
 
 Test of a 57-inch Left Hand McCormick Turbine. Built by J. and W. Jolly, 
 Holyoke, Mass. Testing Flume of the Holyoke Water Power Co. Tested on 
 Conical Draft Tube. Test No. 1156. Oct. 31 and Nov. 1, 1898. 
 
 With the flume empty a strain of IT Ibs. applied 3.6 feet from the center of the shaft, 
 sufficed to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency = l). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 40 
 
 000 
 
 1 Oil 
 
 13 77 
 
 4 
 
 79 87 
 
 244 50 
 
 305 SO 
 
 80 10 
 
 39 
 
 OUO 
 
 1 007 
 
 13 86 
 
 4 
 
 83.25 
 
 244 34 
 
 309 12 
 
 49 
 
 38 
 37 
 
 .000 
 OUO 
 
 1.004 
 1 001 
 
 13.92 
 13 93 
 
 4 
 4 
 
 86.75 
 HO. 25 
 
 244.16 
 243.38 
 
 311.49 
 311.78 
 
 80 82 
 81.10 
 
 36 
 
 OUO 
 
 994 
 
 14 03 
 
 4 
 
 94 62 
 
 242 58 
 
 312 08 
 
 80 86 
 
 35 
 3J 
 
 .000 
 770 
 
 0.934 
 890 
 
 14.10 
 14 69 
 
 4 
 4 
 
 99.87 
 79 37 
 
 240.66 
 222 19 
 
 305.63 
 299 03 
 
 79 43 
 
 80 81 
 
 33 
 32 
 31 
 
 0.770 
 0.770 
 770 
 
 0.886 
 0.883 
 881 
 
 14.72 
 14.73 
 14 75 
 
 4 
 4 
 
 4 
 
 82.87 
 85.75 
 88 75 
 
 221.41 
 
 220.81 
 220 38 
 
 302.63 
 303.24 
 '303 58 
 
 81.89 
 82.22 
 82 36 
 
 30 
 29 
 28 
 
 0.770 
 0.770 
 770 
 
 0.876 
 
 0.868 
 857 
 
 14.76 
 
 14.82 
 14 86 
 
 4 
 4 
 5 
 
 92.00 
 95.50 
 98 90 
 
 219.17 
 217.65 
 215 23 
 
 302.19 
 
 298.75 
 292 57 
 
 82.38 
 81.68 
 80 67 
 
 27 
 
 770 
 
 847 
 
 14 94 
 
 5 
 
 101 50 
 
 213 41 
 
 283 (JO 
 
 78 28 
 
 26... 
 
 615 
 
 762 
 
 15 36 
 
 4 
 
 77 75 
 
 194 56 
 
 261 73 
 
 77 23 
 
 25 
 24 
 
 0.615 
 615 
 
 0.761 
 757 
 
 15.36 
 15 40 
 
 4 
 5 
 
 81.87 
 86 20 
 
 194.25 
 193 52 
 
 266.69 
 269 07 
 
 78.82 
 79 62 
 
 23 
 
 615 
 
 753 
 
 15 39 
 
 4 
 
 89 62 
 
 192 50 
 
 267 55 
 
 79 64 
 
 22 
 21 
 20 
 
 0.615 
 0.615 
 615 
 
 0.745 
 0.739 
 729 
 
 15.45 
 15.47 
 15 52 
 
 4 
 4 
 4 
 
 92.37 
 95.62 
 98 75 
 
 190.92 
 189.30 
 187 15 
 
 262.57 
 257.51 
 251 16 
 
 78.50 
 77.51 
 76 26 
 
 19 
 
 18... 
 17... 
 
 0.615 
 
 0.483 
 483 
 
 0.719 
 
 0.632 
 630 
 
 15.63 
 
 15.90 
 15 87 
 
 4 
 
 4 
 4 
 
 102.25 
 
 78.12 
 
 82 37 
 
 185.14 
 
 164.25 
 163 42 
 
 243.37 
 
 215.69 
 218 46 
 
 74.17 
 
 72.83 
 74 28 
 
 16 
 
 483 
 
 626 
 
 15 85 
 
 4 
 
 8(3 37 
 
 162 32 
 
 17 32 
 
 74 49 
 
 15 
 14 
 13 
 
 12 
 
 0.483 
 0.483 
 0.483 
 483 
 
 0.621 
 0.615 
 0.609 
 603 
 
 15.81 
 15.81 
 15.74 
 15 75 
 
 4 
 4 
 4 
 4 
 
 89.50 
 93.00 
 96.00 
 99 25 
 
 160.80 
 159.31 
 157.40 
 156 03 
 
 213.03 
 208.71 
 20-3.38 
 195 74 
 
 73.90 
 73.07 
 72.04 
 70 y 4 
 
 11 
 
 483 
 
 598 
 
 15 7 
 
 4 
 
 102 37 
 
 154 55 
 
 187*97 
 
 68 23 
 
 10 
 
 483 
 
 59'{ 
 
 15 76 
 
 
 105 50 
 
 153 45 
 
 179 36 
 
 65 41 
 
 9 
 8 
 
 0.360 
 360 
 
 0.500 
 498 
 
 16.27 
 16 37 
 
 4 
 4 
 
 74. 7o 
 
 79 62 
 
 131.52 
 131 26 
 
 161.14 
 163 52 
 
 66.41 
 67 11 
 
 7 
 6 
 5 
 4 
 
 0.360 
 0.360 
 0.360 
 360 
 
 0.495 
 0.492 
 
 0.488 
 
 OAQZ 
 
 16.42 
 16.41 
 16.43 
 
 Ifi 4? 
 
 4 
 4 
 4 
 
 83.75 
 87.12 
 90.37 
 
 130.63 
 129.75 
 
 128.87 
 
 163.46 
 161.15 
 157.94 
 
 67.20 
 66.74 
 65.78 
 R4. 49 
 
 3 
 
 360 
 
 481 
 
 16 45 
 
 
 96 62 
 
 127 21 
 
 14Q -IK 
 
 62 86 
 
 2 
 
 360 
 
 479 
 
 Ifi ^4. 
 
 
 -IAA OX 
 
 128 K^ 
 
 
 611 19 
 
 1 
 
 0.360 
 
 0.474 
 
 16 59 
 
 4 
 
 104.37 
 
 125.70 
 
 134.86 
 
 57.03 
 
Samson Turbine. 
 
 709 
 
 TABLE LXIII. 
 
 Test of 56-inch Right Hand Samson Turbine, built by James Leffel Co.', Spring- 
 field, O. Testing Flume of the Holyoke Water Power Co. Test No. 1257. 
 June 20, 1900. Tested on Conical Cylinder. 
 
 With the flume empty a strain of 22 Ibs. applied 3.6 feet from the center of the shaft, 
 sufficed to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 4 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency = 1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 9 
 
 82.29 
 83.26 
 83. 5* 
 82.79 
 81.68 
 78.94 
 
 83.75 
 84.60 
 
 83. ',13 
 82.50 
 80.63 
 78 94 
 
 84.32 
 85.01 
 
 84.24 
 83 .14 
 8:4.10 
 80.41 
 
 78.75 
 
 84.08 
 83.56 
 82.40 
 81 46 
 K).56 
 79.78 
 
 80.74 
 81.06 
 80.99 
 80.31 
 79.29 
 
 80.06 
 80.36 
 79.85 
 78.70 
 77.01 
 
 78.29 
 78.33 
 78.09 
 77.40 
 75.99 
 73.62 
 
 75.00 
 74.20 
 73.11 
 71.85 
 70.20 
 66.96 
 
 1 
 
 3 
 
 4 
 
 it 
 
 C 
 
 7 
 
 8 
 
 19... 
 
 1.000 
 1.000 
 1.000 
 1.000 
 1.000 
 1. 000 
 
 0.919 
 919 
 0.919 
 0.919 
 0.919 
 0.919 
 
 0.846 
 0.846 
 0.846 
 0.846 
 0.846 
 0.846 
 0.846 
 
 0.771 
 0.771 
 0.771 
 0.771 
 771 
 0.771 
 
 0.696 
 0.696 
 0.696 
 0.696 
 696 
 
 0.626 
 0.626 
 0.626 
 0.626 
 0.626 
 
 0.564 
 0.564 
 0.564 
 0.564 
 564 
 564 
 
 0.497 
 0.497 
 0.497 
 0.497 
 0.497 
 0.497 
 
 0.995 
 0.996 
 1.001 
 0.999 
 0.992 
 0.980 
 
 0.945 
 0.947 
 0.943, 
 0.936 
 0.928 
 0.916 
 
 0>'85 
 0.888 
 0.882 
 0.876 
 0.868 
 0.855 
 843 
 
 0.824 
 0.819 
 0.812 
 0.802 
 0.794 
 0.786 
 
 0.736 
 0.727 
 0.725 
 0.717 
 0.715 
 
 0.663 
 (1.660 
 0.655 
 0.651 
 0.647 
 
 0.603 
 0.600 
 0.598 
 0.592 
 0.587 
 0.581 
 
 0.537 
 0.532 
 0.527 
 0.522 
 0.520 
 0.517 
 
 13.27 
 13.27 
 13.27 
 13.30 
 13.33 
 13.50 
 
 13.52 
 13.50 
 13.52 
 13.56 
 13.63 
 .13.71 
 
 13.80 
 13.79 
 13.80 
 13.82 
 13.91 
 14.09 
 14.11 
 
 14.15 
 14.18 
 14.21 
 14.24 
 14.27 
 14.33 
 
 14.63 
 14.69 
 14.70 
 14.76 
 14.81 
 
 15.11 
 15.12 
 15.16 
 15.13 
 15.17 
 
 15.45 
 15.44 
 15.46 
 15.49 
 15. 5t 
 15.56 
 
 15.91 
 15.95 
 16.00 
 16.04 
 16.04 
 16.07 
 
 3 
 4 
 4 
 4 
 4 
 4 
 
 4 
 4 
 
 4 
 
 4 
 
 4 
 
 4 
 4 
 4 
 4 
 5 
 4 
 4 
 
 4 
 4 
 4 
 4 
 4 
 3 
 
 4 
 4 
 4 
 4 
 4 
 
 4 
 4 
 4 
 4 
 4 
 
 4 
 4 
 4 
 4 
 4 
 4 
 
 4 
 4 
 5 
 4 
 
 4 
 4 
 
 99.67 
 104.00 
 108.62 
 111.75 
 113.50 
 117.00 
 
 99.37 
 104.25 
 107.75 
 110.12 
 132.37 
 115.12 
 
 96.62 
 101.00 
 103.12 
 105.00 
 107.80 
 110.87 
 113.50 
 
 97.50 
 1(10.37 
 102.12 
 104.00 
 106.25 
 109.67 
 
 97.50 
 100.37 
 103.75 
 106.87 
 110.50 
 
 98 25 
 102.00 
 105.00 
 107 37 
 110.75 
 
 95.50 
 98.62 
 102.25 
 105.75 
 109.87 
 114.00 
 
 101.25 
 105.12 
 109.20 
 113.37 
 117.50 
 125.75 
 
 245.41 
 245.75 
 246 86 
 246.69 
 245.26 
 243.81 
 
 2:35.43 
 235.56 
 234.80 
 2X3.37 
 231.98 
 229.82 
 
 222.77 
 223.37 
 2<21.99 
 220.47 
 219.26 
 217.31 
 214.58 
 
 210.02 
 208.95 
 207.29 
 205.01 
 203.03 
 201.51 
 
 190.73 
 188.70 
 188.28 
 186.67 
 166.38 
 
 174.50 
 173.83 
 172.83 
 171.55 
 170.70 
 
 160.63 
 159.54 
 159.11 
 157.75 
 156.65 
 155.30 
 
 145.14 
 143.93 
 142.87 
 141.70 
 140.91 
 140.27 
 
 303.28 
 307.27 
 309.85 
 307.40 
 302.19 
 294.03 
 
 301.69 
 304.47 
 301.52 
 295.43 
 
 *88.50 
 281.48 
 
 293.34 
 296.35 
 292.06 
 286.69 
 283.35 
 278.62 
 269.81 
 
 282.77 
 280.18 
 274.66 
 269.13 
 264.12 
 260.71 
 
 254.95 
 254.28 
 253.68 
 250.42 
 247.67 
 
 238.90 
 239.01 
 236.77 
 231.17 
 225.66 
 
 219.89 
 218.36 
 217.37 
 214.04 
 208.95 
 201.31 
 
 195.99 
 192.77 
 189.13 
 184.80 
 179.56 
 170.82 
 
 18 
 17 
 
 }(j 
 
 15 
 14 
 
 25 
 
 24 
 
 23 
 22 
 
 21 
 
 5>0 
 
 32 
 31 
 
 30 
 
 29 
 
 28 
 27 
 26 
 
 54 
 53 
 
 52 
 
 51 
 
 50 
 
 49 
 
 48 
 47 
 
 46 .. . 
 
 45 
 44 
 
 43 
 
 42 
 41. 
 40 
 
 39 
 
 38 
 
 37 
 
 36 
 35 
 
 34 
 33 
 
 6 
 
 5 
 4 
 
 3 
 2 
 
 \ 
 
 
Turbine Test Data. 
 
 TABLE LXIV. 
 
 Test of a 54-inch Right Hand Special Hercules Turbine. Built by the Holyoke 
 Machine Co., Holyoke, Mass. Testing Flume of the Holyoke Water Power 
 Co. No. 1051. Date Nov. 12, 1897. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 Proportional 
 (discharge 
 discharge 
 at full gate 
 with highest 
 efficiency =1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet, 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 42 
 41 
 
 1.000 
 1 000 
 
 1.004 
 997 
 
 13.98 
 14 07 
 
 5 
 4 
 
 80.40 
 84 12 
 
 230.06 
 
 228 98 
 
 305 38 
 306 94 
 
 83.72 
 
 84 00 
 
 40 
 39 
 
 l.OUO 
 1 000 
 
 .989 
 881 
 
 14.13 
 14 22 
 
 4 
 
 4 
 
 87.00 
 90 50 
 
 227.80 
 26 71 
 
 305.62 
 305 62 
 
 83.71 
 83 58 
 
 38 
 
 1 000 
 
 974 
 
 14 26 
 
 4 
 
 94 00 
 
 225 30 
 
 303 89 
 
 83 26 
 
 37 
 36 
 
 1.000 
 1 000 
 
 .964 
 956 
 
 14.29 
 14 34 
 
 4 
 4 
 
 98.00 
 101 50 
 
 223.16 
 
 221 65 
 
 299.65 
 293 11 
 
 82.83 
 81 31 
 
 35 
 
 1 000 
 
 944 
 
 14 38 
 
 4 
 
 104 87 
 
 219 38 
 
 285 03 
 
 79 66 
 
 34 
 
 800 
 
 881 
 
 14 69 
 
 4 
 
 80 00 
 
 206 93 
 
 287 01 
 
 83 25 
 
 33 
 
 800 
 
 875 
 
 14 73 
 
 5 
 
 83 20 
 
 205 72 
 
 287 19 
 
 83 56 
 
 32 
 31 
 
 .800 
 800 
 
 .868 
 859 
 
 14.80 
 14 87 
 
 4 
 4 
 
 86. 6 J 
 90 25 
 
 204.66 
 202 ^8 
 
 V87.16 
 286 38 
 
 83.59 
 83 65 
 
 30 
 
 800 
 
 852 
 
 14 94 
 
 4 
 
 93 75 
 
 201 77 
 
 284 75 
 
 83 28 
 
 29 
 
 800 
 
 844 
 
 15 01 
 
 4 
 
 97 12 
 
 200 41 
 
 281 78 
 
 82 59 
 
 28 
 
 800 
 
 836 
 
 15 07 
 
 4 
 
 101 00 
 
 198 92 
 
 277 94 
 
 81 75 
 
 27 
 
 SOU 
 
 829 
 
 15 09 
 
 4 
 
 104 87 
 
 197 26 
 
 270 78 
 
 80 20 
 
 26 
 
 800 
 
 820 
 
 15 15 
 
 
 108 40 
 
 195 46 
 
 261 48 
 
 77 85 
 
 25 
 
 650 
 
 749 
 
 15 38 
 
 5 
 
 77 oo 
 
 179 88 
 
 246 9") 
 
 78 70 
 
 24 
 
 650 
 
 745 
 
 15 40 
 
 fj 
 
 81 00 
 
 179 02 
 
 250 4'' 
 
 80 09 
 
 23 
 22 
 
 .650 
 650 
 
 .739 
 734 
 
 15.45 
 
 15 48 
 
 o 
 5 
 
 84.60 
 88 60 
 
 177.87 
 176 85 
 
 251.78 
 252 85 
 
 8(1.78 
 81 43 
 
 21 
 20 
 iy 
 
 .650 
 .650 
 650 
 
 .728 
 .722 
 714 
 
 15.49 
 15.47 
 15 50 
 
 5 
 
 92.80 
 95.80 
 99 25 
 
 175.59 
 173.91 
 172 09 
 
 252.22 
 248.01 
 ''4'* 10 
 
 81.76 
 81.28 
 80 02 
 
 18 
 17 
 
 16 
 
 .650 
 .650 
 
 527 
 
 .705 
 .696 
 
 622 
 
 15.53 
 15.57 
 
 15 97 
 
 5 
 4 
 
 4 
 
 102.40 
 105.75 
 
 74 50 
 
 170.10 
 168.14 
 
 ic9 97 
 
 234.48 
 226.34 
 
 20 49 
 
 78.26 
 76.23 
 
 7Q 40 
 
 15 
 
 .527 
 
 618 
 
 16 01 
 
 4 
 
 78 87 
 
 151 47 
 
 205 79 
 
 74 82 
 
 14 
 13 
 
 .527 
 527 
 
 .612 
 606 
 
 16.03 
 16 09 
 
 4 
 4 
 
 83.12 
 87 25 
 
 150.12 
 
 207.28 
 207 50 
 
 75.94 
 
 12 
 
 527 
 
 597 
 
 16 12 
 
 
 
 
 
 7tt J.7 
 
 11 
 
 527 
 
 591 
 
 16 15 
 
 
 95 37 
 
 145 60 
 
 200 89 
 
 75 32 
 
 10 
 
 527 
 
 584 
 
 16 22 
 
 4 
 
 99 25 
 
 14S 98 
 
 195 57 
 
 70 04. 
 
 y 
 
 527 
 
 578 
 
 16 23 
 
 
 irvj nn 
 
 
 
 79 01 
 
 8 
 
 410 
 
 4QQ 
 
 
 
 
 
 
 
 
 410 
 
 494 
 
 16 63 
 
 
 Sl '" 
 
 
 ifiO t;i 
 
 
 6. .. . 
 
 410 
 
 489 
 
 Ifi t'A 
 
 
 
 
 
 
 5 
 4 
 
 .410 
 410 
 
 .483 
 478 
 
 16.68 
 16 66 
 
 4 
 
 90.50 
 
 04. 7& 
 
 120.82 
 
 159.88 
 
 69.95 
 
 3 
 2 
 
 .410 
 410 
 
 .472 
 467 
 
 16.68 
 
 Ifi 7i 
 
 5 
 
 99.10 
 
 118.20 
 
 148.14 
 
 66.25 
 
 1 
 
 .410 
 
 .460 
 
 16.79 
 
 5 
 
 109.30 
 
 115.53 
 
 129.97 
 
 59.07 
 
McCormick Turbine. 
 
 711 
 
 TABLE LXV. 
 
 Test of a 51-inch Left Hand McCormick Turbine. Built by J. and 
 Holyoke, Mass. Testing Flume of the Holyoke Water Power Co. 
 1444, Feb. 19 and 20, 1903. Tested on Conical Draft Tube. 
 
 W. Jolly, 
 Test No. 
 
 With the flume empty a strain of 37 Ibs. applied 3.6 feet from the center of the shaft, 
 sufficed to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency = 1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 57 
 55 
 
 l.QOO 
 1 000 
 
 1.007 
 1 001 
 
 15.20 
 14 71 
 
 4 
 4 
 
 98.50 
 101 12 
 
 196.58 
 192 30 
 
 293.50 
 278 13 
 
 86.61 
 86 70 
 
 54 
 
 1 ODO 
 
 ij; is 
 
 14 70 
 
 4 
 
 105 50 
 
 191 60 
 
 277 38 
 
 86 84 
 
 53 
 
 1 000 
 
 995 
 
 14 68 
 
 4 
 
 110 00 
 
 191 02 
 
 274 38 
 
 86 28 
 
 52 
 
 1 (100 
 
 989 
 
 14 65 
 
 4 
 
 113 75 
 
 189 58 
 
 268.40 
 
 85 21 
 
 51 
 50 
 
 1.000 
 1 000 
 
 0.974 
 948 
 
 14.74 
 14 86 
 
 4 
 4 
 
 118.25 
 124 25 
 
 187.26 
 183 09 
 
 ','55.10 
 234 54 
 
 81.49 
 76 01 
 
 49 
 
 1 000 
 
 922 
 
 15 04 
 
 4 
 
 130 25 
 
 179 05 
 
 210 74 
 
 69 00 
 
 48 
 
 1 000 
 
 897 
 
 15 15 
 
 4 
 
 136 00 
 
 174 79 
 
 183 37 
 
 61 06 
 
 75.''!!.'.'!!.'! 
 
 0.760 
 0.760 
 
 0.879 
 876 
 
 15.65 
 15 65 
 
 4 
 4 
 
 90.50 
 96 50 
 
 174.22 
 173 55 
 
 259.30 
 263 47 
 
 83.86 
 85 54 
 
 74 
 73 
 
 0.760 
 0.760 
 
 0.871 
 0.861 
 
 15.67 
 15.76 
 
 4 
 .4 
 
 101.75 
 106 00 
 
 172.71 
 171 13 
 
 264.09 
 260 83 
 
 86.04 
 
 85 28 
 
 72 
 
 71 
 
 0.710 
 76d 
 
 0.850 
 840 
 
 15.83 
 15 94 
 
 4 
 4 
 
 110.75 
 114 25 
 
 169.47 
 168 07 
 
 257.58 
 250 32 
 
 84.66 
 82 39 
 
 70 
 69 
 68 
 
 0.760 
 0.760 
 0.760 
 
 0.826 
 0.813 
 0.795 
 
 16.04 
 16.16 
 16.29 
 
 4 
 6 
 3 
 
 118.50 
 123.17 
 129 00 
 
 165.73 
 163.65 
 160 65 
 
 239.66 
 228.35 
 
 208 72 
 
 79.50 
 76.14 
 70 32 
 
 67 
 
 760 
 
 778 
 
 15 74 
 
 4 
 
 132 25 
 
 154 65 
 
 178 31 
 
 64 59 
 
 85 
 
 0.624 
 
 0.767 
 
 15.63 
 
 4 
 
 90.00 
 
 151 93 
 
 218 42 
 
 81 11 
 
 84 
 83 
 
 0.624 
 0.624 
 
 0.764 
 0.756 
 
 15.61 
 15.64 
 
 4 
 4 
 
 94.75 
 100.25 
 
 151.12 
 149.67 
 
 219.73 
 218 97 
 
 82.13 
 
 82 48 
 
 82 
 
 0.624 
 
 0.742 
 
 15.67 
 
 4 
 
 104 25 
 
 147 07 
 
 213 65 
 
 81 75 
 
 81 
 80 
 
 0.624 
 0.6.'4 
 
 0.735 
 0.7^4 
 
 15.73 
 
 15.78 
 
 4 
 4 
 
 108.75 
 114.25 
 
 145.93 
 144.08 
 
 206.74 
 200 26 
 
 79.42 
 77 67 
 
 79 
 
 624 
 
 0.712 
 
 15.86 
 
 4 
 
 119 75 
 
 141 98 
 
 189 71 
 
 74 29 
 
 78 
 
 0.624 
 
 0.698 
 
 15.96 
 
 4 
 
 127.50 
 
 139 76 
 
 171.91 
 
 67 96 
 
 77 
 
 0.624 
 
 0.684 
 
 16.12 
 
 4 
 
 134.75 
 
 137.55 
 
 145 35 
 
 57 80 
 
 47 
 
 500 
 
 656 
 
 15 93 
 
 . 4 
 
 87 00 
 
 131 12 
 
 178 30 
 
 75 27 
 
 46 
 
 0.500 
 
 0.653 
 
 15.96 
 
 ft 
 
 91.83 
 
 13H.61 
 
 179 53 
 
 75 94 
 
 45 
 
 500 
 
 0.648 
 
 16 05 
 
 4 
 
 97 12 
 
 130 11 
 
 180 05 
 
 76 03 
 
 44 
 
 0.5110 
 
 0.640 
 
 16.14 
 
 4 
 
 101.62 
 
 128.70 
 
 178.12 
 
 75 61 
 
 43 .. . . 
 
 0.500 
 
 0.632 
 
 16.19 
 
 4 
 
 106.00 
 
 127 55 
 
 175 08 
 
 74 76 
 
 42 
 
 0.500 
 
 0.624 
 
 16.25 
 
 4 
 
 111.50 
 
 126.04 
 
 169.13 
 
 72 81 
 
 41 
 
 0.500 
 
 0.615 
 
 16.27 
 
 5 
 
 118.20 
 
 124.29 
 
 159.37 
 
 69 49 
 
 40 
 39 
 
 0.500 
 0.500 
 
 0.605 
 0.59t 
 
 16.30 
 16.36 
 
 4 
 5 
 
 124.00 
 129.80 
 
 122.26 
 120.27 
 
 146.29 
 131.26 
 
 64.73 
 58.82 
 
 38 
 
 0.5UO 
 
 U.585 
 
 16.41 
 
 6 
 
 135.50 
 
 118 65 
 
 114.18 
 
 51 71 
 
 
 
 
 
 
 
 
 
 
712 
 
 Turbine Test Data. 
 
 TABLE LXVI. 
 
 Test of a 45-inch Right Hand Victor Turbine. Built by the Plait Iron Works 
 Co., Dayton, Ohio. Testing Flume of the Holyoke Water Power Co. Test 
 No. 1177, March 13 and 14, 1899. Tested on Conical Draft Tube. 
 
 With the flume empty a strain of 10 Ibs. applied 3.6 feet from the center of the shaft, 
 sufficed to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency =1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi 
 
 clency. 
 
 . 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 48 
 47 
 
 .000 
 
 o;K) 
 
 1.012 
 1.000 
 
 15.22 
 15.21 
 
 4 
 
 4 
 
 102.37 
 107.50 
 
 180.69 
 180.24 
 
 252.39 
 
 254.82 
 
 80.92 
 81.96 
 
 46 
 
 000 
 
 1 004 
 
 15.20 
 
 4 
 
 111.50 
 
 179.26 
 
 253.70 
 
 82.10 
 
 45 
 44 
 
 .000 
 000 
 
 0.997 
 0.986 
 
 15.2(5 
 15.31 
 
 4 
 5 
 
 116.67 
 121.60 
 
 178.26 
 176.54 
 
 253.57 
 *51.08 
 
 82.19 
 81.91 
 
 43 
 
 000 
 
 972 
 
 15.35 
 
 4 
 
 126.25 
 
 174.41 
 
 246.10 
 
 81 .05 
 
 42 
 
 .000 
 
 0.954 
 
 15.36 
 
 5 
 
 128.40 
 
 171.19 
 
 235.46 
 
 78.96 
 
 41 
 
 1 000 
 
 0.934 
 
 15.44 
 
 4 
 
 131.50 
 
 167.98 
 
 223.29 
 
 75.91 
 
 40... 
 
 0.900 
 
 0.959 
 
 15.32 
 
 4 
 
 98.37 
 
 171.76 
 
 239.19 
 
 80.15 
 
 39 
 
 0.900 
 
 0.955 
 
 15.32 
 
 4 
 
 103.37 
 
 171.19 
 
 241.52 
 
 81.20 
 
 38 
 37 
 36 
 
 0.900 
 0.900 
 900 
 
 0.949 
 0.942 
 929 
 
 15.36 
 15.39 
 15.50 
 
 4 
 5 
 5 
 
 107.25 
 111.30 
 115.80 
 
 170.19 
 169.23 
 167.41 
 
 240.39 
 239.64 
 238.31 
 
 81.08 
 81.13 
 80.98 
 
 35 
 
 900 
 
 917 
 
 15 54 
 
 4 
 
 119 00 
 
 165 39 
 
 234.39 
 
 80.41 
 
 34 
 33 
 
 0.900 
 900 
 
 0.907 
 896 
 
 15.58 
 15.73 
 
 4 
 4 
 
 122.50 
 127.50 
 
 163.86 
 162.75 
 
 230.47 
 225.15 
 
 79.60 
 77.55 
 
 32 
 30 
 
 0.900 
 800 
 
 0.890 
 888 
 
 15.73 
 15.90 
 
 4 
 4 
 
 133.50 
 97.25 
 
 161.52 
 162.07 
 
 217.62 
 
 228.54 
 
 75.52 
 
 78.20 
 
 29 
 28 
 27 
 
 0.800 
 0.800 
 800 
 
 0.886 
 0.878 
 867 
 
 16.04 
 16.20 
 16 34 
 
 5 
 4 
 4 
 
 105.70 
 111.00 
 118.00 
 
 162.46 
 161.79 
 lliO.41 
 
 238.35 
 239.74 
 241.24 
 
 80.65 
 80.65 
 81 15 
 
 31 
 
 800 
 
 873 
 
 1(5 80 
 
 4 
 
 113 37 
 
 158 91 
 
 231 00 
 
 81 12 
 
 26 
 25 
 
 0.800 
 800 
 
 0.861 
 838 
 
 16.24 
 
 16 28 
 
 4 
 4 
 
 131.35 
 125 25 
 
 157.14 
 154 81 
 
 232.71 
 225.44 
 
 80.32 
 
 78 87 
 
 24 
 
 0.800 
 
 0.826 
 
 16.20 
 
 4 
 
 131.87 
 
 152.24 
 
 214.96 
 
 76.85 
 
 23. . 
 
 700 
 
 802 
 
 16 16 
 
 4 
 
 99 00 
 
 147 56 
 
 205.08 
 
 75.83 
 
 22 
 
 700 
 
 799 
 
 16 15 
 
 4 
 
 104 12 
 
 147 04 
 
 207 20 
 
 76 94 
 
 21 
 
 0.700 
 
 794 
 
 16.17 
 
 4 
 
 109.62 
 
 146.23 
 
 208 47 
 
 77.74 
 
 20 . 
 
 700 
 
 781 
 
 16 12 
 
 4 
 
 114 50 
 
 143 56 
 
 206.09 
 
 78 52 
 
 19 
 
 700 
 
 768 
 
 16 18 
 
 4 
 
 118 00 
 
 141 49 
 
 200 36 
 
 77 17 
 
 18 
 
 17 
 
 0.700 
 700 
 
 0.758 
 747 
 
 16.19 
 16 23 
 
 4 
 3 
 
 122.75 
 130 00 
 
 139.54 
 
 137 72 
 
 184.26 
 185 42 
 
 75.82 
 73 14 
 
 16 
 
 0.600 
 
 0.701 
 
 16 39 
 
 4 
 
 96 00 
 
 129.89 
 
 169.53 
 
 70.21 
 
 15 
 
 600 
 
 702 
 
 16 39 
 
 4 
 
 101 37 
 
 130.02 
 
 172 13 
 
 71 22 
 
 14 
 13 
 
 0.600 
 0.600 
 
 0.696 
 0.683 
 
 16.38 
 16.44 
 
 4 
 4 
 
 106.75 
 111.62 
 
 128.88 
 126.85 
 
 173.29 
 172.85 
 
 72.38 
 73.08 
 
 12 
 
 600 
 
 676 
 
 16 44 
 
 4 
 
 115 50 
 
 125 45 
 
 170 23 
 
 72-78 
 
 11 
 10 
 
 0.600 
 0.600 
 
 0.669 
 0.662 
 
 16.42 
 16.43 
 
 4 
 4 
 
 118.87 
 124.50 
 
 124.06 
 122.81 
 
 165.94 
 160.66 
 
 71.82 
 70.21 
 
 9 
 
 8 
 
 0.600 
 502 
 
 0.656 
 607 
 
 16.44 
 16 60 
 
 4 
 4 
 
 131.25 
 95 25 
 
 121.81 
 113 21 
 
 151.55 
 139 09 
 
 66.73 
 65 26 
 
 7 
 
 0.502 
 
 0.603 
 
 16 60 
 
 4 
 
 100.62 
 
 112.49 
 
 140.10 
 
 66.15 
 
 6 
 
 502 
 
 594 
 
 16 64 
 
 4 
 
 104 62 
 
 110 91 
 
 139 27 
 
 66 54 
 
 5 
 4 
 
 0.502 
 502 
 
 586 
 580 
 
 16.62 
 16 62 
 
 4 
 5 
 
 109.75 
 114 80 
 
 109.32 
 108 25 
 
 138.65 
 136 45 
 
 67.29 
 
 66 87 
 
 3 
 
 0.502 
 
 576 
 
 16 65 
 
 4 
 
 120 00 
 
 107 66 
 
 132 85 
 
 65 35 
 
 2 
 
 502 
 
 574 
 
 16 68 
 
 4 
 
 125 50 
 
 107 30 
 
 127 86 
 
 62 99 
 
 1. . 
 
 502 
 
 570 
 
 16 68 
 
 4 
 
 131 50 
 
 106 59 
 
 120 58 
 
 59 80 
 
 
 
 
 
 
 
 
 
 
Samson Turbine. 
 
 713 
 
 TABLE LXVII. 
 
 Tent of a 45-inch Right Hand Samson Turbine. Built by The James Leffel Co., 
 Springfield, Ohio. Testing Flume of the Holyoke Water Power Co. Test 
 No. 979. Jan. 25 and 26, 1897. Tested with Conical Cylinder 
 
 With the flume empty a strain of 15 Ibs. applied 3.6 feet from the center of the shaft, 
 sufficed to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency = 1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 ;ions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 8 
 
 1 000 
 
 992 
 
 14 94 
 
 5 
 
 127.60 
 
 171.24 
 
 233 49 
 
 80.48 
 
 
 1 000 
 
 1 000 
 
 14 88 
 
 5 
 
 133.40 
 
 172.12 
 
 236 84 
 
 81 54 
 
 6 
 
 1.000 
 
 0.998 
 
 14.92 
 
 4 
 
 138.12 
 
 172.12 
 
 238.65 
 
 81.94 
 
 5 
 4 
 
 1.000 
 1 000 
 
 0.999 ' 
 1 001 
 
 15.00 
 15 02 
 
 4 
 4 
 
 144.00 
 148 75 
 
 172.69 
 173 23 
 
 240.97 
 
 240 82 
 
 82.03 
 81 61 
 
 3 
 
 1 000 
 
 1.002 
 
 15.03 
 
 3 
 
 153.33 
 
 173.38 
 
 239.89 
 
 81 18 
 
 2 
 
 1 000 
 
 998 
 
 15 04 
 
 4 
 
 157 75 
 
 172 81 
 
 236 08 
 
 80 09 
 
 1 
 
 18 
 17 
 
 1.000 
 
 0.832 
 832 
 
 0.986 
 
 0.887 
 892 
 
 15.11 
 
 14.99 
 15.02 
 
 3 
 
 4 
 4 
 
 169.33 
 
 112.50 
 119.75 
 
 171.11 
 
 153.24 
 154.34 
 
 218.85 
 
 208.16 
 215.05 
 
 74.64 
 
 79.90 
 
 81 80 
 
 16 
 15 
 
 0.832 
 0.832 
 
 0.896 
 897 
 
 15.04 
 15.03 
 
 4 
 
 4 
 
 126.12 
 132.25 
 
 155.04 
 155.27 
 
 219.62 
 223.11 
 
 83.05 
 84 30 
 
 14 
 
 832 
 
 896 
 
 15.04 
 
 4 
 
 134.12 
 
 155 03 
 
 223.61 
 
 84 55 
 
 13 
 
 0.832 
 
 0.893 
 
 15.06 
 
 4 
 
 143.00 
 
 154.74 
 
 221.79 
 
 83.92 
 
 12 
 
 832 
 
 888 
 
 15 09 
 
 4 
 
 148.12 
 
 153.93 
 
 219.65 
 
 83 38 
 
 11 
 10 
 9 
 
 27 
 
 0.832 
 0.832 
 0.832 
 
 684 
 
 0.881 
 
 0.874 
 0.847 
 
 0.766 
 
 15.16 
 15.21 
 15.32 
 
 15.19 
 
 4 
 4 
 4 
 
 3 
 
 151.25 
 155.00 
 160.50 
 
 112.67 
 
 153.12 
 152 15 
 148.02 
 
 133.24 
 
 214 01 
 208.77 
 196.52 
 
 183.94 
 
 81.29 
 79.55 
 76.42 
 
 80.14 
 
 26 
 25... 
 
 0.684 
 684 
 
 0.769 
 0.768 
 
 15.12 
 15.11 
 
 3 
 4 
 
 121 33 
 
 127.67 
 
 133.52 
 133.24 
 
 189.83 
 191.06 
 
 82.91 
 83 6S 
 
 24 
 23 
 22 
 
 0.684 
 0.684 
 0.684 
 
 0.762 
 0.756 
 0.745 
 
 15.14 
 15.20 
 15.28 
 
 4 
 4 
 4 
 
 131.50 
 135.50 
 133 00 
 
 132.34 
 131.58 
 130.06 
 
 187 85 
 185.27 
 182 49 
 
 82.67 
 81.68 
 80.97 
 
 21 
 20 
 19 
 
 57 .. 
 
 0.684 
 0.684 
 0.684 
 
 0.568 
 
 0.732 
 
 0.728 
 0.719 
 
 0.641 
 
 15.33 
 15.39 
 15.43 
 
 15.85 
 
 4 
 4 
 4 
 
 5 
 
 141.75 
 147.00 
 156.00 
 
 125.80 
 
 128.02 
 127.52 
 125. b9 
 
 113.89 
 
 178.39 
 176.99 
 169.79 
 
 162.59 
 
 80.15 
 79.52 
 77.01 
 
 79.42 
 
 58 
 59 
 
 0.568 
 0.568 
 
 0.633 
 0.630 
 
 15.88 
 15 85 
 
 4 
 4 
 
 131.50 
 135.75 
 
 112.65 
 112.04 
 
 162.80 
 160.68 
 
 HO. 25 
 79 78 
 
 60 
 
 568 
 
 0.629 
 
 15.83 
 
 4 
 
 139 75 
 
 111.68 
 
 157.81 
 
 78 71 
 
 61 
 62 
 
 0.568 
 568 
 
 0.622 
 0.613 
 
 15.84 
 15.85 
 
 4 
 4 
 
 143.25 
 148.25 
 
 110.45 
 109.02 
 
 152.99 
 146.23 
 
 77.11 
 74 62 
 
 46 
 
 424 
 
 0.500 
 
 16.50 
 
 4 
 
 112.50 
 
 90 70 
 
 123 97 
 
 73 05 
 
 45 
 
 424 
 
 0.499 
 
 16.53 
 
 4 
 
 121.25 
 
 90.59 
 
 127.84 
 
 75.28 
 
 47 
 
 424 
 
 0.499 
 
 16.49 
 
 4 
 
 124.00 
 
 9U.37 
 
 127.79 
 
 75 61 
 
 44 
 49 
 
 0.424 
 424 
 
 0.497 
 497 
 
 16.55 
 16.47 
 
 4 
 
 4 
 
 127 00 
 126 >7 
 
 90.24 
 90.04 
 
 127.86 
 127.73 
 
 75.49 
 75 95 
 
 43 
 
 424 
 
 0.494 
 
 16.55 
 
 4 
 
 131.75 
 
 89.69 
 
 125.47 
 
 74 53 
 
 48 
 4' 
 
 0.424 
 424 
 
 0.487 
 0.479 
 
 16.50 
 16.58 
 
 4 
 
 4 
 
 135.50 
 151 25 
 
 88.24 
 87 01 
 
 121.67 
 113 ig 
 
 73.69 
 69 18 
 
 
 
 
 
 
 
 
 
 
Turbine Test Data. 
 
 TABLE LXVIII. 
 
 Test of a 44-inch Left Hand Improved New American Turbine. Built by the 
 Dayton Globe Iron Works Co., Dayton, Ohio. Testing Flume of the Holyoke 
 Water Power Co. Test. No. 1609. March 21, 1904. Tested on Long Conical 
 Draft Tube. Balanced Gate. 
 
 With the flume empty a strain of 7 Ibs. applied 3.5 feet from the center of the shaft, 
 sufficed to start the -wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part.) 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency = 1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 8 .. 
 
 1.000 
 1.000 
 .000 
 .000 
 .000 
 .000 
 .000 
 .000 
 .000 
 .000 
 
 0.907 
 0.907 
 0.907 
 0.907 
 0.907 
 0.907 
 
 0.823 
 0.823 
 0.823 
 0.823 
 0.823 
 0.823 
 0.823 
 823 
 0.823 
 0.823 
 0.823 
 
 0.684 
 0.684 
 0.64 
 0.684 
 0.684 
 0.684 
 0.684 
 0.684 
 0.684 
 
 0.581 
 0.581 
 0.581 
 0.581 
 0.581 
 0.581 
 0.581 
 
 0.459 
 0.459 
 0.459 
 0.459 
 
 0.4.7.t 
 0.459 
 
 0.986 
 0.988 
 0.992 
 1.001 
 1.014 
 1.011 
 0.999 
 0.98H 
 0.976 
 0.772 
 
 0.944 
 0.948 
 0.949 
 0.952 
 0.945 
 0.935 
 
 0.878 
 0.882 
 0.884 
 0.830 
 0.871 
 0.863 
 0.855 
 0.848 
 0.838 
 0.821 
 0.796 
 
 0.729 
 0.739 
 0.746 
 0.741 
 0.736 
 0.725 
 0.70.5 
 C.6K) 
 0.66v> 
 
 0.628 
 0.633 
 0.633 
 0.614 
 0.58ti 
 0.566 
 0.551 
 
 0.496 
 0.493 
 0.488 
 0.468 
 0.4.50 
 0.441 
 
 15.31 
 15.24 
 15.23 
 15.22 
 15.19 
 15.18 
 15.23 
 15.32 
 15.37 
 16.15 
 
 15.42 
 15.42 
 15.42 
 15.39 
 15.47 
 15.52 
 
 15.61 
 13.59 
 13.56 
 15.57 
 15.61 
 15.67 
 15.79 
 15.75 
 15.74 
 15.82 
 15.94 
 
 16.31 
 16.24 
 16.19 
 16.19 
 16.16 
 16.17 
 16.24 
 16.35 
 16.41 
 
 16,54 
 16.55 
 16.56 
 16.63 
 16.75 
 16.87 
 16.97 
 
 17.02 
 17.03 
 17.04 
 17.10 
 17.11 
 17.08 
 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 5 
 4 
 
 4 
 4 
 4 
 
 4 
 4 
 4 
 
 4 
 5 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 
 3 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 
 4 
 4 
 4 
 4 
 4 
 4 
 4 
 
 4 
 
 4 
 4 
 4 
 4 
 4 
 
 132.25 
 137.75 
 141.75 
 146.50 
 150.50 
 155.00 
 159.00 
 161.75 
 165.40 
 210.25 
 
 '131.50 
 136.00 
 139.00 
 143.50 
 147.75 
 151.00 
 
 115.75 
 121.00 
 131.00 
 135.25 
 138.50 
 142.50 
 147.50 
 151.50 
 156.75 
 161.00 
 164.00 
 
 98.00 
 109.00 
 117.75 
 122.75 
 125.50 
 132.00 
 139.25 
 145.00 
 151.50 
 
 108.50 
 112.00 
 114.50 
 124.25 
 134.50 
 145.00 
 156.25 
 
 99.75 
 107.25 
 112.50 
 128.75 
 143.00 
 152.00 
 
 172.28 
 172.13 
 172.89 
 174.40 
 176.35 
 175.81 
 174.09 
 172 57 
 170.73 
 138.47 
 
 165.47 
 166.15 
 166.27 
 166. 70 
 165.87 
 164.50 
 
 154.80 
 155.32 
 155.60 
 155.05 
 153.55 
 152.60 
 151.67 
 150.20 
 146.45 
 145.80 
 141.85 
 
 131.50 
 132.91 
 134.05 
 133.15 
 132.00 
 130.22 
 126.92 
 122.77 
 119.79 
 
 114.06 
 115.00 
 114.90 
 111.84 
 107.13 
 103.84 
 101 26 
 
 91.31 
 90.75 
 89.87 
 86.39 
 82.01 
 81.30 
 
 228.61 
 231.64 
 233.60 
 236.50 
 237.89 
 234.58 
 2<J4.59 
 217.59 
 205.82 
 
 76.43 
 
 77.86 
 78.22 
 78.56 
 78.31 
 77.50 
 
 72'. 57 
 69.16 
 
 7 
 9 
 
 6 
 
 10 
 5 
 
 4 
 
 3 
 2 
 
 1 
 
 49... 
 
 231.74 
 235.10 
 235.61 
 236.48 
 .233.54 
 228.52 
 
 218.00 
 225.20 
 229.10 
 227.43 
 223.58 
 220.45 
 216.28 
 208.90 
 200.32 
 189.51 
 176.50 
 
 174.68 
 190.62 
 201.96 
 202.28 
 199.95 
 195.33 
 187.33 
 175.56 
 163.04 
 
 160.12 
 169.50 
 169.43 
 167.15 
 158.32 
 146.30 
 131.37 
 
 127. 48 
 129.85 
 128.64 
 125 57 
 115.43 
 102.24 
 
 80.08 
 80.91 
 81.03 
 81.28 
 80.25 
 78.92 
 
 79.55 
 
 82.06 
 83.44 
 83.07 
 82.25 
 81.29 
 79.63 
 77.86 
 75.60 
 72.45 
 68.83 
 
 71.82 
 77.87 
 82.05 
 82.74 
 82.65 
 81.80 
 80.14 
 77.12 
 73.14 
 
 74.84 
 7.53 
 78.52 
 79.24 
 77.80 
 73.64 
 67.41 
 
 72.33 
 74.09 
 74.07 
 74.95 
 71.66 
 64 92 
 
 48 
 47 
 46 
 
 45 
 
 44 
 21 
 
 j>0 
 
 19 
 
 18 
 
 17. .. . 
 
 16 
 
 15 
 
 14 ... 
 
 13 
 
 12 
 
 11 
 29... 
 
 30 
 
 28 
 
 S>7 
 
 26 
 25 
 
 24 
 
 23... 
 
 22 
 
 36 
 
 37 
 
 35 
 34 
 
 33 
 
 32 
 
 31. . 
 
 43 
 42 
 
 41 
 
 40 ... 
 
 39 
 
 38 
 
 
Victor Turbine. 
 
 715 
 
 TABLE LXIX. 
 
 Test of a 43-inch Right Hand Victor Turbine. Built by the Plat Iron Works 
 
 Co., Dayton, Ohio. Testing Flume of the Holyoke Water Power Co. Test 
 
 No. 1707. Tested on Conical Draft Tube. Swing Gate. Nov. 20, 1907. 
 
 With the flume empty a strain of 20 Ibs. applied 3.6 feet from the center of the shaft, 
 
 sufficed to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 Proportional 
 discharge 
 (discharge 
 at full pate 
 with highest 
 efficiency = 1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 6 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1 
 
 1.000 
 
 0.852 
 
 16 19 
 
 3 
 
 Still 
 
 154 79 
 
 
 
 15 
 
 1 000 
 
 946 
 
 15 98 
 
 2 
 
 100 00 
 
 170 72 
 
 203 27 
 
 65 69 
 
 14 
 
 1 000 
 
 969 
 
 15 93 
 
 H 
 
 122 00 
 
 174 gg 
 
 i!31 46 
 
 73 35 
 
 13 
 
 1 000 
 
 985 
 
 15 79 
 
 3 
 
 143 00 
 
 176 80 
 
 247 08 
 
 78 03 
 
 11 
 
 1 000 
 
 989 
 
 15 75 
 
 3 
 
 151 33 
 
 177 23 
 
 251 22 
 
 79 35 
 
 10 
 
 1 000 
 
 9^8 
 
 15 74 
 
 3 
 
 159 67 
 
 178 78 
 
 254 24 
 
 79 66 
 
 12 
 
 000 
 
 1 002 
 
 15 70 
 
 3 
 
 165 00 
 
 179 22 
 
 254 91 
 
 79 87 
 
 9 
 
 g 
 
 .000 
 000 
 
 1.006 
 1 005 
 
 15.82 
 15 86 
 
 4 
 4 
 
 172.25 
 
 178 75 
 
 180.64 
 180 79 
 
 256.77 
 954 35 
 
 79.22 
 78 21 
 
 7 
 
 000 
 
 979 
 
 16 01 
 
 4 
 
 178 75 
 
 176 80 
 
 ''36 18 
 
 73 57 
 
 6 
 5 
 
 .001) 
 000 
 
 0.956 
 93-1 
 
 16.10 
 16 23 
 
 4 
 3 
 
 183.25 
 189 67 
 
 173.26 
 169 33 
 
 217 29 
 192 77 
 
 68.68 
 61 85 
 
 4 
 3 
 
 .000 
 000 
 
 0.878 
 808 
 
 16.39 
 16 60 
 
 3 
 4 
 
 202.67 
 214 25 
 
 160.52 
 148 59 
 
 137.33 
 72 59 
 
 46.02 
 25 95 
 
 2 
 
 .000 
 
 0.762 
 
 16.67 
 
 3 
 
 224.00 
 
 140 43 
 
 
 
 28 
 27 
 26 
 
 0.900 
 0.900 
 900 
 
 0.874 
 0.901 
 908 
 
 15.98 
 15.93 
 15 90 
 
 4 
 4 
 4 
 
 89.75 
 111.75 
 127 00 
 
 157.76 
 162.30 
 163 54 
 
 182.44 
 215.80 
 232 34 
 
 63.80 
 73.59 
 
 78 78 
 
 25. . . 
 
 900 
 
 911 
 
 15 84 
 
 4 
 
 138 50 
 
 163 67 
 
 239 SO 
 
 81 38 
 
 24 
 
 900 
 
 918 
 
 15 81 
 
 4 
 
 150 5 
 
 164 76 
 
 244 34 
 
 82 70 
 
 23 
 
 UOO 
 
 915 
 
 15 81 
 
 4 
 
 158 50 
 
 164 22 
 
 241 64 
 
 82 06 
 
 22 
 21 
 
 0.900 
 900 
 
 0.894 
 877 
 
 15.88 
 15 94 
 
 4 
 4 
 
 160.25 
 164 00 
 
 160.79 
 158 15 
 
 228.02 
 216 69 
 
 78.74 
 75 79 
 
 20.. 
 
 900 
 
 862 
 
 15 94 
 
 4 
 
 168 50 
 
 155 31 
 
 205 51 
 
 73 19 
 
 19 
 
 900 
 
 839 
 
 16 02 
 
 4 
 
 174 00 
 
 151 68 
 
 188 64 
 
 68 45 
 
 18 
 
 900 
 
 798 
 
 16 21 
 
 4 
 
 184 25 
 
 145 14 
 
 156 OD 
 
 58 48 
 
 16.......... 
 
 0.900 
 900 
 
 0.743 
 690 
 
 16.38 
 16 59 
 
 3 
 2 
 
 199.00 
 218 50 
 
 135.86 
 126 81 
 
 101.13 
 
 40.07 
 
 38 
 
 800 
 
 783 
 
 16 32 
 
 3 
 
 60 33 
 
 142 88 
 
 130 34 
 
 49 9 8 
 
 37 
 
 800 
 
 837 
 
 16 15 
 
 
 119 25 
 
 151 91 
 
 218 16 
 
 78 40 
 
 36 
 35 
 
 0.800 
 800 
 
 0.847 
 847 
 
 16.14 
 16 13 
 
 
 135.50 
 146 00 
 
 153 56 
 153 56 
 
 234.12 
 237 42 
 
 as. 29 
 
 84 51 
 
 34 
 33 
 
 0.800 
 800 
 
 0.824 
 807 
 
 16.23 
 16. bO 
 
 
 148.00 
 151 75 
 
 149.80 
 147 12 
 
 225.63 
 215 93 
 
 81.82 
 79 39 
 
 32 
 
 S( 
 
 773 
 
 16 42 
 
 
 161 50 
 
 141 45 
 
 196 97 
 
 74 77 
 
 31 
 
 800 
 
 726 
 
 16 56 
 
 
 173 75 
 
 133 30 
 
 164 82 
 
 65 83 
 
 30 
 
 800 
 
 690 
 
 16 67' 
 
 4 
 
 187 00 
 
 127 18 
 
 126 71 
 
 5'' 69 
 
 29 
 
 800 
 
 627 
 
 16.86 
 
 3 
 
 215 00 
 
 116 21 
 
 
 
 47... 
 
 700 
 
 717 
 
 16 57 
 
 3 
 
 89 33 
 
 131 75 
 
 157 37 
 
 63 56 
 
 48 
 46 
 45 
 
 0.700 
 0.700 
 700 
 
 0.738 
 0.754 
 752 
 
 16.51 
 16.42 
 16 38 
 
 R 
 
 3 
 8 
 
 110.67 
 126.00 
 133 00 
 
 135.45 
 137.95 
 137 41 
 
 189.72 
 209.17 
 21 1 78 
 
 74.80 
 81.42 
 82 96 
 
 44 
 43 
 42 
 41 
 40 
 
 0.700 
 0.700 
 0.700 
 0.700 
 700 
 
 0.732 
 0.708 
 0.678 
 0.650 
 618 
 
 16.44 
 16.53 
 16.63 
 16.70 
 16 82 
 
 8 
 
 4 
 4 
 4 
 4 
 
 136.00 
 142.25 
 150.50 
 160.00 
 179 50 
 
 133.93 
 129.98 
 124.90 
 120.02 
 114 42 
 
 203.73 
 192.77 
 178.46 
 162.62 
 121 63 
 
 81.18 
 79.10 
 75.75 
 71.53 
 55 72 
 
 39 
 
 700 
 
 0.568 
 
 17.02 
 
 3 
 
 209 00 
 
 105 73 
 
 
 
 58 
 
 600 
 
 623 
 
 16 94 
 
 3 
 
 94 67 
 
 115 74 
 
 147 54 
 
 66 35 
 
 57 
 
 56 
 
 0.600 
 600 
 
 0.634 
 643 
 
 16.89 
 16 83 
 
 3 
 3 
 
 105.00 
 116 00 
 
 117.55 
 119 02 
 
 169.08 
 172 Q2 
 
 71.09 
 7fi 11 
 
 55 
 
 HOO 
 
 645 
 
 16 80 
 
 4 
 
 122 50 
 
 119 28 
 
 178 46 
 
 78 52 
 
 54 
 53 
 
 0.600 
 600 
 
 0.625 
 601 
 
 16.81 
 16 90 
 
 4 
 4 
 
 126.50 
 134 'iO 
 
 115.74 
 111 4T 
 
 171.43 
 
 77.66 
 
 52 
 
 600 
 
 582 
 
 16 97 
 
 4 
 
 144 5 
 
 108 20 
 
 ]56 38 
 
 75 09 
 
 51 
 
 50 
 
 0.600 
 600 
 
 O.fi60 
 543 
 
 17.04 
 17 14 
 
 4 
 4 
 
 160.25 
 
 182 50 
 
 104.44 
 
 135.73 
 qo 74 
 
 67.23 
 
 49 
 
 o.'eoo 
 
 0.501 
 
 17.28 
 
 3 
 
 204' 00 
 
 94.03 
 
 
 
Turbine Test Data. 
 
 TABLE LXIX.- Continued. 
 
 Test of a 42-inch Right Hand Victor Turbine. Built by the Plait Iron Works 
 Co., Dai/ton, Ohio. Testing Flume of the Holyoke Water Power Co. Test 
 No. 1707. Nov. 20, 1907. Tested on Conical Draft Tube. Siving Gate. 
 
 With the flume empty a strain of 20 Ibs. applied 3.6 feet from the center of the shaft, 
 sufficed to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency = 1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 ' feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 67 
 
 500 
 
 542 
 
 17 32 
 
 3 
 
 94 33 
 
 101 82 
 
 132 31 
 
 66 15 
 
 66 
 65 
 64 
 
 0.500 
 500 
 0.500 
 
 0.553 
 0.556 
 0.539 
 
 17.24 
 17.19 
 17.25 
 
 3 
 4 
 3 
 
 106.67 
 116.35 
 122.00 
 
 103.59 
 104.06 
 101.02 
 
 144.56 
 149.66 
 144 66 
 
 71.37 
 73.77 
 73 19 
 
 63 
 62. 
 
 0.500 
 500 
 
 0.515 
 509 
 
 17.28 
 17.29 
 
 4 
 
 4 
 
 135.75 
 150 50 
 
 96.66 
 95 61 
 
 137.97 
 127 47 
 
 72.83 
 67 99 
 
 61 
 
 0.500 
 
 0.499 
 
 17.31 
 
 4 
 
 163.00 
 
 93.69 
 
 110 45 
 
 60 04 
 
 60 
 
 500 
 
 0.476 
 
 17.39 
 
 8 
 
 184 33 
 
 89 63 
 
 62 45 
 
 35 33 
 
 59 
 
 5UO 
 
 451 
 
 17 50 
 
 3 
 
 198 33 
 
 85 20 
 
 
 
 
 
 
 
 
 
 
 
 
 NOTE For experiments 2, 16, 29, 39, 49, 59, Jacket Loose. 
 
McCormick Turbine. 
 
 717 
 
 TABLE LXX. 
 
 Test of a 39-inch Left Hand McCormick Turbine. Built by the S. Morgan 
 Smith Co., York, Penn. Testing Flume of the Holyoke Water Power Co* 
 Tested on Conical Draft Tube. Test No. 1191. May 29, 1899. 
 With the flume empty a strain of 6 Ibs. applied 3.2 feet from the center of the shaft, 
 sufficed to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency = 1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 8 . . 
 
 1 000 
 
 1 009 
 
 15 79 
 
 I 
 
 126 00 
 
 117 83 
 
 177 36 
 
 84 15 
 
 
 1.000 
 
 1.006 
 
 15 79 
 
 4 
 
 131 75 
 
 117 46 
 
 178.98 
 
 85.19 
 
 6 
 
 1 000 
 
 1 001 
 
 15 82 
 
 4 
 
 138 00 
 
 116 98 
 
 179 84 
 
 85 78 
 
 5 
 4 
 '6 
 
 1.000 
 1.000 
 1 000 
 
 0.998 
 0.990 
 977 
 
 15.85 
 15.87 
 15 91 
 
 4 
 4 
 
 143.00 
 150.00 
 154 60 
 
 116.73 
 115.89 
 114 53 
 
 179.32 
 177.03 
 171 06 
 
 85.56 
 
 84.27 
 82.87 
 
 2 
 
 1 000 
 
 961 
 
 15 96 
 
 4 
 
 160 25 
 
 112 80 
 
 162 53 
 
 79 70 
 
 1 
 
 1 000 
 
 945 
 
 15 98 
 
 4 
 
 185 75 
 
 110 99 
 
 152 83 
 
 76 07 
 
 43 
 
 796 
 
 903 
 
 15 95 
 
 4 
 
 118.25 
 
 105.98 
 
 159.91 
 
 83 51 
 
 42 
 41 
 
 0.796 
 0.796 
 
 0.8H9 
 0.896 
 
 15.97 
 15.97 
 
 4 
 4 
 
 123.75 
 129.25 
 
 105.51 
 105.02 
 
 161.27 
 162.08 
 
 84.49 
 85 31 
 
 40 
 
 796 
 
 889 
 
 15 99 
 
 4 
 
 133.00 
 
 104 44 
 
 160 24 
 
 84 70 
 
 39 
 
 796 
 
 882 
 
 15 98 
 
 5 
 
 136 60 
 
 103 62 
 
 157 86 
 
 84 11 
 
 38 
 
 796 
 
 874 
 
 16 03 
 
 4 
 
 140.50 
 
 102.78 
 
 155.46 
 
 83.29 
 
 37 
 36 
 
 0.796 
 796 
 
 0.864 
 853 
 
 16.08 
 16.06 
 
 4 
 4 
 
 145.00 
 149.00 
 
 101.72 
 100.45 
 
 151.52 
 146.54 
 
 81.78 
 80.19 
 
 35 
 
 796 
 
 843 
 
 16.11 
 
 4 
 
 153 25 
 
 9i).4l 
 
 141 30 
 
 77 89 
 
 34 
 33 
 32 
 
 0.621 
 0.621 
 621 
 
 0.760 
 0.754 
 
 748 
 
 16.26 
 10.29 
 16.29 
 
 4 
 
 4 
 5 
 
 123.75 
 127.25 
 
 130.80 
 
 89.97 
 89.41 
 
 88. '(3 
 
 136.92 
 135.32 
 133.47 
 
 82.62 
 82.02 
 81.51 
 
 31.. 
 
 621 
 
 742 
 
 16 30 
 
 4 
 
 134 00 
 
 87 94 
 
 130.97 
 
 80 66 
 
 30 
 
 621 
 
 734 
 
 16 34 
 
 4 
 
 138 25 
 
 87 18 
 
 129 17 
 
 80 05 
 
 29 
 
 621 
 
 728 
 
 16.35 
 
 4 
 
 142.25 
 
 86.51 
 
 126.79 
 
 79.13 
 
 28 
 27 
 
 0.621 
 621 
 
 0.716 
 703 
 
 16.37 
 16.40 
 
 4 
 
 4 
 
 147.75 
 156.25 
 
 85.09 
 83.65 
 
 122.61 
 115.26 
 
 77.70 
 74.17 
 
 26... 
 
 0.498 
 
 615 
 
 16.55 
 
 3 
 
 115.00 
 
 77.10 
 
 109.57 
 
 75.80 
 
 25 
 
 498 
 
 640 
 
 16.55 
 
 4 
 
 120.25 
 
 76.47 
 
 110.14 
 
 76.82 
 
 24 
 23 
 
 0.498 
 0.498 
 
 0.636 
 0.63U 
 
 16.55 
 16.56 
 
 5 
 
 4 
 
 123.60 
 127.75 
 
 7o.95 
 75.31 
 
 108.65 
 107.58 
 
 76.30 
 76.15 
 
 22 
 
 0.498 
 
 625 
 
 16.59 
 
 4 
 
 131.75 
 
 74.77 
 
 106.09 
 
 75.50 
 
 21 
 
 0.498 
 
 0.619 
 
 16.60 
 
 4 
 
 136.25 
 
 74.12 
 
 104.69 
 
 75.11 
 
 20 
 
 498 
 
 0.611 
 
 16.69 
 
 4 
 
 143.00 
 
 73.30 
 
 101.09 
 
 72.94 
 
 19 
 18 
 
 17 
 
 0.498 
 0.498 
 
 390 
 
 0.600 
 0.588 
 
 527 
 
 16.71 
 16.78 
 
 16 72 
 
 4 
 4 
 
 4 
 
 150.25 
 
 157.75 
 
 116.75 
 
 72.03 
 70.71 
 
 63.25 
 
 86.13 
 
 87.27. 
 
 83.97 
 
 69.77 
 64.93 
 
 70 09 
 
 16 
 15 
 
 0.390 
 390 
 
 0.522 
 0.516 
 
 16.73 
 16.75 
 
 4 
 4 
 
 121.50 
 125.50 
 
 62.66 
 62.06 
 
 82.90 
 81.77 
 
 69.81 
 69.44 
 
 14 
 13 
 
 0.390 
 0.390 
 
 0.512 
 0.509 
 
 16.78 
 16.77 
 
 4 
 4 
 
 129.50 
 133.00 
 
 61.66 
 61.28 
 
 80.40 
 
 78.48 
 
 68.60 
 67.42 
 
 12 
 
 390 
 
 0.506 
 
 16.76 
 
 4 
 
 135.50 
 
 60.86 
 
 76.63 
 
 66.32 
 
 11 
 10 
 
 0.390 
 390 
 
 0.502 
 0.495 
 
 16.75 
 16.77 
 
 4 
 4 
 
 139.75 
 145.00 
 
 60.38 
 59.60 
 
 73.88 
 70.41 
 
 64.48 
 62.19 
 
 9 
 
 390 
 
 0.489 
 
 16.77 
 
 5 
 
 150.60 
 
 58.81 
 
 64 80 
 
 58 00 
 
 
 
 
 
 
 
 
 
 
7 i8 
 
 Turbine Test Data. 
 
 TABLE LXXI. 
 
 Test of a 3ff-mch Right Hand Swain Turbine. Built by the Swain Turbine and 
 Mfg. Co., Lowell, Mass. Testing Flume of the Holyoke Water Power Co. No. 
 977. Date Jan. 20-21. 1807. 
 
 Number 
 of 
 experi- 
 ment* 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency = 1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 64 
 
 63 
 
 1.000 
 1 000 
 
 1.004 
 995 
 
 IS. 16 
 15 25 
 
 3 
 4 
 
 130.33 
 135 00 
 
 76.49 
 75 98 
 
 111.57 
 111 47 
 
 84 84 
 84 83 
 
 62 
 
 1 000 
 
 984 
 
 15 40 
 
 3 
 
 140 83 
 
 75 52 
 
 111 61 
 
 84 62 
 
 61 
 60 
 
 1.000 
 l.UOO 
 
 .973 
 .966 
 
 15.42 
 15.43 
 
 3 
 
 4 
 
 144.00 
 146.50 
 
 74.74 
 74.19 
 
 110.16 
 108.51 
 
 84.28 
 83 58 
 
 59 
 
 1.000 
 
 954 
 
 15 48 
 
 4 
 
 150 75 
 
 73 45 
 
 107 08 
 
 83 04 
 
 58 
 57 
 
 1.000 
 1 000 
 
 .945 
 
 934 
 
 15.47 
 15 44 
 
 4 
 3 
 
 154.00 
 158 00 
 
 72.73 
 
 71 7t> 
 
 104.72 
 101 68 
 
 82.07 
 80 92 
 
 56 
 
 1 000 
 
 922 
 
 15 33 
 
 4 
 
 161 37 
 
 70 58 
 
 97 97 
 
 79 84 
 
 55 
 54 
 
 .875 
 875 
 
 .932 
 925 
 
 15.16 
 15 15 
 
 3 
 4 
 
 132.00 
 135 75 
 
 70.95 
 70 42 
 
 102.58 
 102 20 
 
 P4.10 
 
 84 47 
 
 53 .. 
 
 875 
 
 916 
 
 15 28 
 
 4 
 
 140 75 
 
 70 01 
 
 102 54 
 
 84 52 
 
 52 
 51 
 
 .875 
 
 875 
 
 .907 
 896 
 
 15.41 
 15 50 
 
 4 
 
 4 
 
 147.00 
 153 50 
 
 69.61 
 68 99 
 
 102.63 
 101 58 
 
 84.37 
 83 75 
 
 50 
 49 
 
 .875 
 750 
 
 .877 
 866 
 
 15.60 
 15 66 
 
 3 
 
 4 
 
 162.33 
 130 00 
 
 67.75 
 67 03 
 
 98.55 
 100 24 
 
 82.22 
 84 20 
 
 48 
 
 750 
 
 857 
 
 15 74 
 
 4 
 
 136 00 
 
 66 52 
 
 100 73 
 
 84 83 
 
 47 
 46 
 
 .750 
 750 
 
 .849 
 844 
 
 15.76 
 15 70 
 
 4 
 2 
 
 141.00 
 146 00 
 
 65.96 
 65 41 
 
 100.16 
 99 28 
 
 84.96 
 85 24 
 
 45 
 44 
 43 
 
 .750 
 .750 
 750 
 
 .838 
 .829 
 826 
 
 15.54 
 15.62 
 15 16 
 
 4 
 3 
 4 
 
 149.75 
 157.33 
 156 75 
 
 64.64 
 64.09 
 62 88 
 
 97.28 
 96.47 
 91 36 
 
 85.39 
 
 84.97 
 84 51 
 
 42 
 
 750 
 
 814 
 
 15 20 
 
 4 
 
 162 75 
 
 6;i 06 
 
 88 ^3 
 
 83 13 
 
 41 
 
 625 
 
 783 
 
 15 30 
 
 
 127 50 
 
 59 90 
 
 85 Q 2 
 
 82 7 
 
 40 
 
 625 
 
 775 
 
 15 38 
 
 4 
 
 134 75 
 
 59 45 
 
 86 72 
 
 83 63 
 
 3tt 
 38 
 
 .625 
 625 
 
 .767 
 
 758 
 
 15.43 
 15 47 
 
 4 
 4. 
 
 142.12 
 149 50 
 
 58.95 
 58 30 
 
 87.15 
 86 23 
 
 84.48 
 84 30 
 
 37 
 
 625 
 
 749 
 
 15 51 
 
 4 
 
 154 50 
 
 57 70 
 
 84 42 
 
 83 18 
 
 36. 
 
 625 
 
 733 
 
 15 58 
 
 4 
 
 162*75 
 
 56 62 
 
 81 02 
 
 80 99 
 
 35 
 
 625 
 
 715 
 
 "15 K5 
 
 
 IRQ -Vl 
 
 55 32 
 
 7fi TS 
 
 77 cc 
 
 34.. 
 
 500 
 
 683 
 
 15 74 
 
 
 123 20 
 
 52 93 
 
 74 PO 
 
 79 09 
 
 33 
 
 500 
 
 676 
 
 15 78 
 
 
 1 m 2^ 
 
 5 9 54 
 
 75 70 
 
 XO ^1 
 
 32 
 31 
 30 
 
 .500 
 .500 
 500 
 
 .668 
 .660 
 652 
 
 15.83 
 15.85 
 
 1 C01 
 
 4 
 
 4 
 
 137.50 
 144.00 
 
 ICf) OC 
 
 51.98 
 51.42 
 
 50 87 
 
 75.13 
 74.31 
 72 98 
 
 80.51 
 80.40 
 79 ^,1 
 
 29 
 
 28 
 
 .50J 
 500 
 
 .644 
 635 
 
 15.95 
 15 96 
 
 4 
 
 157.50 
 163 33 
 
 50.31 
 49 6'-* 
 
 71.72 
 69 41 
 
 78.81 
 71* oq 
 
 26 
 
 375 
 
 CR7 
 
 
 
 -ion 07 
 
 4.2 50 
 
 T.4 08 
 
 70 7- 
 
 25 
 24. 
 
 .375 
 375 
 
 .552 
 545 
 
 15.19 
 
 IK O1 
 
 4 
 
 127.50 
 >oq cr 
 
 42.06 
 41 58 
 
 54.19 
 
 CO AG 
 
 74.78 
 
 74. *S8 
 
 23 
 
 375 
 
 538 
 
 15 1 
 
 4 
 
 130 00 
 
 41 06 
 
 5>> 33 
 
 73 87 
 
 22 
 21. 
 
 .375 
 375 
 
 .531 
 *>24 
 
 15.22 
 
 3 
 
 145.67 
 
 40.53 
 
 51.30 
 49 94 
 
 73.32 
 70 qc 
 
 20 
 27 
 
 .375 
 375 
 
 .514 
 504 
 
 15.30 
 
 1C Of) 
 
 4 
 
 160.25 
 167 20 
 
 39.36 
 38 57 
 
 48.65 
 45 68 
 
 71.23 
 68 25 
 
 19 
 18 
 
 .250 
 250 
 
 .420 
 416 
 
 15.53 
 15 54 
 
 
 113.50 
 120 25 
 
 32.40 
 3'' 11 
 
 36.52 
 36 50 
 
 64.00 
 64 50 
 
 17 
 
 250 
 
 412 
 
 ic C7 
 
 
 noc en 
 
 qi QQ 
 
 36 10 
 
 64 22 
 
 16... 
 
 250 
 
 407 
 
 
 
 
 01 AR 
 
 35 60 
 
 cq qi 
 
 15 
 
 250 
 
 401 
 
 15 60 
 
 
 1^9 50 
 
 '31 00 
 
 34 72 
 
 63 31 
 
 14 
 13 
 12.. 
 
 .250 
 .250 
 250 
 
 .396 
 .386 
 
 378 
 
 15 61 
 15 66 
 
 
 146.25 
 155.75 
 
 30.59 
 29.91 
 
 33.74 
 32.15 
 
 on 7u 
 
 62.31 
 60.52 
 
 11. 
 
 250 
 
 qfi7 
 
 
 
 
 
 
 
 10... 
 
 .250 
 
 AZK 
 
 1* 70 
 
 A 
 
 170 KH 
 
 97 KA_ 
 
 91 KO 
 
 J.J fU 
 
Swain Turbine. 
 
 719 
 
 TABLE LXXL Continued. 
 
 Test of a 36-inch Right Hand Swain Turbine. Built by the Swain Turbine and 
 Mfg. Co., Lowell, Mass. Testing Flume of the Holyoke Water Power Co. No. 
 977. Date Jan. 20-21, 1897. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part) 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with hignest 
 efficiency =1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 9 
 
 125 
 
 257 
 
 16 03 
 
 4 
 
 111 50 
 
 20 06 
 
 16 92 
 
 46 41 
 
 8 
 
 125 
 
 254 
 
 16 01 
 
 4 
 
 119 00 
 
 19 89 
 
 16 62 
 
 46 01 
 
 7 
 
 125 
 
 252 
 
 16 07 
 
 4 
 
 126 75 
 
 19 76 
 
 16 16 
 
 44 88 
 
 6 
 
 125 
 
 249 
 
 16 17 
 
 4 
 
 134 12 
 
 19 62 
 
 15 47 
 
 43 00 
 
 
 125 
 
 247 
 
 16 23 
 
 4 
 
 141 00 
 
 19 45 
 
 14 55 
 
 40 65 
 
 4 
 
 135 
 
 245 
 
 16 18 
 
 4 
 
 146 25 
 
 19 24 
 
 13 32 
 
 37 73 
 
 3..., 
 
 .125 
 125 
 
 .242 
 239 
 
 16.22 
 16 11 
 
 4 
 4 
 
 152.25 
 159 50 
 
 19.07 
 18 73 
 
 12.02 
 9 68 
 
 34.26 
 28 30 
 
 1 . 
 
 067 
 
 161 
 
 16 49 
 
 4 
 
 153 25 
 
 12 80 
 
 
 
 
 
 
 
 
 
 
 
 
720 
 
 Turbine Test Data. 
 
 TABLE LXXII. 
 
 Test of a 36-inch Eight Hand Victor Turbine. Built by the Platt Iron Works 
 Co., Dayton, Ohio. Testing Flume of the Holyoke Water Power Co. Test 
 No. 1061, December 14, 1897. Tested on Conical Draft Tube. Cylinder Gate. 
 With the flume empty a strain of 8 Ibs, applied 3.2 feet from center of the shaft, 
 sufficed to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part). 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency = 1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 
 
 12 
 11 
 10 
 
 1.000 
 1.000 
 1.000 
 
 1.010 
 1.009 
 1.009 
 
 16.75 
 16.76 
 16.74 
 
 3 
 4 
 4 
 
 133.33 
 139.25 
 144.87 
 
 116.38 
 116.38 
 116.27 
 
 175.20 
 176.99 
 177.91 
 
 79.24 
 
 80.01 
 80 59 
 
 9 
 
 1 000 
 
 1 002 
 
 16 79 
 
 4 
 
 150 75 
 
 115 63 
 
 177 73 
 
 80 71 
 
 8 
 
 6 
 
 1.000 
 
 ooo 
 
 0.997 
 992 
 
 16.80 
 16 73 
 
 4 
 
 4 
 
 155.00 
 156 50 
 
 115.04 
 114 30 
 
 176.07 
 172 97 
 
 80.33 
 79 75 
 
 5.'.'.'. .'..'.'.. 
 4 
 
 .'ooo 
 
 .000 
 .000 
 
 0.982 
 0.975 
 965 
 
 16.82 
 16.69 
 16.58 
 
 4 
 4 
 4 
 
 161.75 
 162.75 
 167.00 
 
 113.46 
 112.21 
 110 63 
 
 173.81 
 169.89 
 164 07 
 
 80.30 
 79.98 
 78 87 
 
 3 
 
 000 
 
 953 
 
 16 59 
 
 4 
 
 172 25 
 
 109 31 
 
 158 65 
 
 77 14 
 
 2 
 1 
 53 
 
 .000 
 .000 
 .000 
 
 0.941 
 0.923 
 0.748 
 
 16.65 
 16.70 
 17.33 
 
 4 
 4 
 
 4 
 
 177.25 
 184.00 
 240.50 
 
 108.09 
 106.21 
 87 70 
 
 152.37 
 141.23 
 
 74.65 
 70.20 
 
 52 
 
 0.900 
 
 967 
 
 16 92 
 
 4 
 
 133 75 
 
 112 07 
 
 172 47 
 
 80 19 
 
 51 
 50 
 49 
 
 0.900 
 0.900 
 0.900 
 
 0.965 
 0.959 
 953 
 
 16.99 
 17.01 
 17 04 
 
 4 
 4 
 4 
 
 139.50 
 144.00 
 148 50 
 
 112.07 
 111.37 
 110 76 
 
 174.74 
 174.19 
 173 25 
 
 80.92 
 81.07 
 80 93 
 
 48 
 47 
 46 
 
 0.900 
 0.900 
 0.900 
 
 0.947 
 0.939 
 925 
 
 17.03 
 17.04 
 17 05 
 
 4 
 4 
 4 
 
 152.00 
 157.00 
 164 00 
 
 110 03 
 108.19 
 107 62 
 
 " 171.73 
 170.63 
 
 168 17 
 
 80.81 
 80.86 
 80 81 
 
 45 
 
 900 
 
 914 
 
 17 06 
 
 2 
 
 170 00 
 
 106 32 
 
 161 80 
 
 78 65 
 
 44 
 
 0.801 
 
 900 
 
 17 10 
 
 3 
 
 132 33 
 
 104 79 
 
 160 07 
 
 78 76 
 
 & 
 42 
 41 
 
 0.801 
 0.801 
 801 
 
 0.900 
 0.899 
 892 
 
 17.07 
 17.02 
 17 02 
 
 4 
 4 
 4 
 
 137.75 
 142.25 
 147 00 
 
 104.67 
 104.32 
 103 61 
 
 162.40 
 162.46 
 161 57 
 
 80.14 
 80.64 
 
 80 78 
 
 40 
 
 801 
 
 884 
 
 17 02 
 
 4 
 
 151 25 
 
 102 68 
 
 159 74 
 
 80 59 
 
 39 
 38 
 
 0.801 
 0.801 
 
 0.870 
 863 
 
 17.02 
 16 97 
 
 4 
 4 
 
 155.25 
 159 25 
 
 101.04 
 100 09 
 
 157.29 
 154 50 
 
 80.64 
 80 ' J 
 
 37 
 
 80 I 
 
 816 
 
 16 92 
 
 4 
 
 163 50 
 
 99 18 
 
 150 59 
 
 79 1 
 
 36 
 
 35... 
 34.. . . 
 
 0.801 
 
 0.701 
 701 
 
 0.845 
 
 0.814 
 814 
 
 16.89 
 
 16.89 
 16 90 
 
 4 
 
 3 
 4 
 
 168.25 
 
 125.67 
 133 25 
 
 97.79 
 
 94.25 
 94 25 
 
 144.64 
 
 134.27 
 139 09 
 
 77.21 
 
 74.37 
 76 99 
 
 33 
 
 0.701 
 
 812 
 
 16 89 
 
 4 
 
 138 75 
 
 94 03 
 
 140 58 
 
 78 04 
 
 32 
 
 701 
 
 807 
 
 16 92 
 
 4 
 
 144 25 
 
 93 47 
 
 140 83 
 
 78 51 
 
 31 
 
 701 
 
 7'94 
 
 17 00 
 
 
 
 92 20 
 
 130 75 
 
 78 61 
 
 30. 
 29 
 
 0.701 
 701 
 
 0.787 
 776 
 
 17.07 
 17 15 
 
 5 
 
 153.60 
 158 75 
 
 91.54 
 
 90 52 
 
 137.70 
 134 52 
 
 77.70 
 76 40 
 
 28 
 
 0.701 
 601 
 
 0.768 
 717 
 
 17.15 
 17 24 
 
 4 
 4 
 
 163.25 
 129 00 
 
 89.52 
 83 87 
 
 130.31 
 117 23 
 
 74.84 
 71 49 
 
 26 
 
 601 
 
 714 
 
 17 29 
 
 
 137 00 
 
 CO ce 
 
 120 29 
 
 73 33 
 
 25. 
 
 601 
 
 705 
 
 17 36 
 
 
 
 oo 77 
 
 
 73 04 
 
 24 
 
 601 
 
 6% 
 
 17 41 
 
 4 
 
 148 00 
 
 81 91 
 
 119 05 
 
 73 48 
 
 23 
 
 601 
 
 685 
 
 17 47 
 
 
 
 CM (.) 
 
 116 12 
 
 7 69 
 
 22 
 21 
 
 0.601 
 601 
 
 0.676 
 
 17.53 
 
 4 
 
 159.00 
 
 79.77 
 
 112.28 
 
 70.79 
 fi8 3Q 
 
 20 
 
 502 
 
 622 
 
 17 60 
 
 
 1OO 00 
 
 
 96 93 
 
 66 00 
 
 19 
 18 
 
 0.502 
 502 
 
 0.617 
 609 
 
 17.55 
 17 55 
 
 3 
 3 
 
 131.07 
 138 00 
 
 72.85 
 71 81 
 
 98.64 
 98 29 
 
 68.02 
 
 68 77 
 
 17 
 
 502 
 
 598 
 
 17 56 
 
 3 
 
 
 W'V? 
 
 
 68 41 
 
 10 
 
 502 
 
 592 
 
 17 55 
 
 
 
 fiQ 87 
 
 OQ 1Q 
 
 
 15 
 14 
 
 0.502 
 502 
 
 0.588 
 580 
 
 17.56 
 17 56 
 
 4 
 3 
 
 155.37 
 
 IpO RA 
 
 69.34 
 
 90.63 
 85 34 
 
 65.63 
 62 61 
 
 13 
 
 502 
 
 573 
 
 17 55 
 
 
 
 fi7 R1 
 
 78 4O 
 
 58 26 
 
 
 
 
 
 
 
 
 
 
 For experiment 53, the jacket was removed from the dynamometer. 
 
Special Smith Turbine. 
 
 721 
 
 TABLE LXXIII. 
 
 Test of a 33-inch Special Left Hand Turbine. Built by the S. Morgan Smith 
 Co., York. Penn. Testing Flume of the Holyoke Water Power Co. Test 
 No. 1511. March 25 and 26, 1904. Tested on Conical Draft Tube. Bal- 
 anced Gate. 
 
 With the flume empty a strain of 9 Ibs. applied 3.3 feet from the center, sufficedto start the wheel 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part. 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency=l). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 15 
 
 1 000 
 
 995 
 
 17 01 
 
 4 
 
 196 00 
 
 112 81 
 
 178 22 
 
 81 s'( 
 
 14 
 13 
 
 1.000 
 1 000 
 
 0.998 
 1 000 
 
 16.99 
 16 98 
 
 5 
 4 
 
 203.80 
 208 75 
 
 113.05 
 113 20 
 
 178.92 
 179 34 
 
 82.14 
 
 GO 97 
 
 12 
 
 1 000 
 
 1 003 
 
 16 99 
 
 4 
 
 21'i 50 
 
 113 55 
 
 179 40 
 
 09 nn 
 
 11 
 10 
 
 1.000 
 1 000 
 
 1.004 
 995 
 
 16.95 
 16 94 
 
 4 
 4 
 
 220.00 
 221 50 
 
 113.55 
 112 5" 
 
 177.97 
 173 62 
 
 81.53 
 
 Of) 00 
 
 9 
 
 1.000 
 948 
 
 0.984 
 964 
 
 17.00 
 17 05 
 
 4 
 4 
 
 223.50 
 194 75 
 
 111.46 
 109 42 
 
 168.18 
 mOK 
 
 78.27 
 
 GO 7/) 
 
 5 
 6 
 
 0.948 
 948 
 
 0.967 
 969 
 
 , 17.11 
 17 08 
 
 4 
 4 
 
 201.50 
 204 75 
 
 109.90 
 110 02 
 
 179.43 
 179 75 
 
 84.13 
 
 QA QK 
 
 4 
 
 948 
 
 968 
 
 17 14 
 
 4 
 
 209 75 
 
 110 14 
 
 ISO 20 
 
 84. 17 
 
 3 
 
 948 
 
 959 
 
 17 19 
 
 4 
 
 211 75 
 
 109 30 
 
 175 ''8 
 
 82 26 
 
 2 
 
 948 
 
 952 
 
 17 17 
 
 4 
 
 9 13 00 
 
 108 45 
 
 170 97 
 
 on QA 
 
 1 
 
 948 
 
 949 
 
 17 19 
 
 4 
 
 214. 7*1 
 
 -inu 11 
 
 ICQ 00 
 
 
 8 
 
 948 
 
 939 
 
 17 09 
 
 5 
 
 216 40 
 
 106 69 
 
 162 84 
 
 78 7^ 
 
 71 
 70 
 
 0.883 
 883 
 
 0.909 
 910 
 
 17.29 
 17 25 
 
 4 
 
 4 
 
 181.75 
 185 75 
 
 103.84 
 103 84 
 
 173.24 
 173 56 
 
 85.08 
 ftS 44 
 
 69 
 
 883 
 
 914 
 
 17 93 
 
 4 
 
 193 00 
 
 104 20 
 
 17^ 4Q 
 
 0(1 1Q 
 
 68 
 
 883 
 
 909 
 
 17 24 
 
 4 
 
 197 00 
 
 103 71 
 
 172 95 
 
 85 29 
 
 67 
 66 
 
 0.883 
 883 
 
 0.901 . 
 893 
 
 17.28 
 17 31 
 
 4 
 5 
 
 199.25 
 202 00 
 
 102.90 
 102 09 
 
 168.68 
 164 67 
 
 83.65 
 82 17 
 
 64 
 
 883 
 
 876 
 
 17 36 
 
 4 
 
 208 50 
 
 100 34 
 
 iKt; on 
 
 7Q 42 
 
 54... 
 
 851 
 
 894 
 
 17 15 
 
 4 
 
 191 00 
 
 101 72 
 
 170 08 
 
 OK Q7 
 
 53 
 
 851 
 
 883 
 
 17 19 
 
 4 
 
 193 50 
 
 100 58 
 
 166 24 
 
 Q4 ITU 
 
 52 
 
 851 
 
 875 
 
 17 20 
 
 4 
 
 196 50 
 
 99 77 
 
 162 65 
 
 83 58 
 
 51 
 
 851 
 
 868 
 
 17 27 
 
 4 
 
 200 25 
 
 99 07 
 
 159 48 
 
 82 19 
 
 50 
 
 851 
 
 858 
 
 17 29 
 
 4 
 
 203 25 
 
 98 02 
 
 IKK KA 
 
 of) qr\ 
 
 49 
 
 851 
 
 851 
 
 17 32 
 
 4 
 
 20(5 25 
 
 97 35 
 
 152 62 
 
 79 81 
 
 48 
 47 
 
 0.851 
 851 
 
 0.842 
 836 
 
 17.38 
 17 37 
 
 4 
 4 
 
 210.25 
 212 67 
 
 96.50 
 95 74 
 
 150.30 
 146 70 
 
 79 02 
 
 77 78 
 
 46 .... 
 
 851 
 
 827 
 
 17 42 
 
 4 
 
 215 50 
 
 94 82 
 
 141 90 
 
 75 75 
 
 45 
 
 0.851 
 
 813 
 
 17 44 
 
 4 
 
 218 25 
 
 93 34 
 
 136 86 
 
 74 13 
 
 44 
 43 
 
 0.765 
 765 
 
 0.836 
 823 
 
 17.37 
 17 38 
 
 4 
 4 
 
 169.25 
 172 75 
 
 95.73 
 94 25 
 
 161.32 
 160 33 
 
 85.55 
 86 30 
 
 42 
 
 765 
 
 818 
 
 17 41 
 
 5 
 
 177 60 
 
 93 79 
 
 159 26 
 
 86 00 
 
 41 
 
 0.765 
 
 803 
 
 17 45 
 
 4 
 
 181 75 
 
 92 2o 
 
 153 86 
 
 84 33 
 
 40 
 
 765 
 
 778 
 
 17 48 
 
 4 
 
 192 75 
 
 89 41 
 
 145 04 
 
 81 83 
 
 39 
 63 
 
 0.765 
 702 
 
 0.736 
 764 
 
 17.55 
 17 33 
 
 4 
 3 
 
 206.25 
 159 00 
 
 84.77 
 87 39 
 
 129.34 
 144 57 
 
 76.66 
 84 17 
 
 62 
 
 702 
 
 765 
 
 17 33 
 
 3 
 
 166 67 
 
 87 50 
 
 147 37 
 
 85 69 
 
 61 , 
 
 702 
 
 763 
 
 17 35 
 
 4 
 
 168 50 
 
 87 28 
 
 145 82 
 
 84 91 
 
 60 
 
 702 
 
 750 
 
 17 37 
 
 3 
 
 172 00 
 
 85 95 
 
 143 45 
 
 84 73 
 
 59 
 58 
 
 0.702 
 702 
 
 0.739 
 729 
 
 17.38 
 17 42 
 
 3 
 4 
 
 175.67 
 180 25 
 
 84.66 
 83 56 
 
 139.90 
 136 77 
 
 83.84 
 
 82 85 
 
 57 
 
 702 
 
 720 
 
 17 44 
 
 4 
 
 185 00 
 
 82 57 
 
 133 41 
 
 81 69 
 
 56 
 55 
 
 0.702 
 702 
 
 0.707 
 690 
 
 17.48 
 17 50 
 
 4 
 4 
 
 189.00 
 197 75 
 
 81.18 
 79 34 
 
 130.37 
 124 01 
 
 81.01 
 
 78 75 
 
 31 
 
 30 
 
 0.636 
 636 
 
 0.711 
 705 
 
 17.71 
 17 69 
 
 4 
 4 
 
 162.50 
 166 25 
 
 82.24 
 81 51 
 
 137.57 
 135 53 
 
 83.28 
 
 82 Kft 
 
 29 
 
 636 
 
 696 
 
 17 71 
 
 4 
 
 170 50 
 
 80 43 
 
 133 65 
 
 82 73 
 
 28 
 
 636 
 
 689 
 
 17 69 
 
 4 
 
 173 58 
 
 79 58 
 
 131 65 
 
 82 46 
 
 27 
 26 
 
 0.636 
 636 
 
 0.680 
 670 
 
 17.70 
 
 17 72 
 
 4 
 4 
 
 176.50 
 180 25 
 
 78.60 
 77 54 
 
 129.50 
 126 60 
 
 82.08 
 81 24 
 
 25 
 
 636 
 
 658 
 
 17 74 
 
 4 
 
 187 50 
 
 76 15 
 
 123 46 
 
 80 58 
 
 24 
 
 0.636 
 
 0!659 
 
 17! 73 
 
 4 
 
 209.50 
 
 76^28 
 
 118.24 
 
 77.09 
 
 44 
 
722 
 
 Turbine Test Data. 
 
 TABLE LXXIIL Continued. 
 
 Test of a 33-inch Special Left Hand Turbine. Built by the S. Morgan Smith 
 Co., York, Penn. Testing Flume of the Holyoke Water Power Co. Test 
 No. 1511. March 25 and 26, 190 1*. Tested on Conical Draft Tube Bal- 
 anced Gate. 
 
 With the flume empty a strain of 9 Ibs. applied 3.3 feet from the center, sufficed 
 to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part. 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency = 1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 22 
 
 556 
 
 616 
 
 17 77 
 
 4 
 
 126 25 
 
 71 40 
 
 102 92 
 
 71 53 
 
 23 
 21 
 
 0.556 
 556 
 
 0.638 
 632 
 
 17.75 
 
 17 74 
 
 5 
 4 
 
 153.00 
 156 00 
 
 73.82 
 73 20 
 
 120.89 
 119 35 
 
 81. 35 
 81 04 
 
 20 
 
 556 
 
 619 
 
 17 78 
 
 4 
 
 161 00 
 
 71 73 
 
 116 10 
 
 80 27 
 
 19 
 18 
 
 0.556 
 556 
 
 0.605 
 589 
 
 17.79 
 17 80 
 
 4 
 4 
 
 184.50 
 205 75 
 
 70.10 
 68 33 
 
 109.91 
 103 2 
 
 77.71 
 
 74 83 
 
 17 
 
 556 
 
 564 
 
 17 83 
 
 4 
 
 ^35 00 
 
 65 4 -> 
 
 73 68 
 
 55 70 
 
 
 
 
 
 
 
 
 
 
Victor Turbine. 
 
 723 
 
 TABLE LXXIV. 
 
 Test of a 33-inch Right Hand Victor Turbine. Built by the Platt Iron Works 
 Co., Dayton, Ohio. Testing Flume of the Holyoke Water Power Co. Test 
 No. 1250, May 29 and 31, 1900. Tested on Conical Cylinder, Wicket or Swing 
 Gate. 
 
 With the flume empty a strain of 12 Ibs. applied 3.2 feet from the center of the shaft, 
 sufficed to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor 
 tional 
 part). 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency =1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 3 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 6 
 
 1 000 
 
 998 
 
 16 95 
 
 4 
 
 156 50 
 
 114 36 
 
 146 64 
 
 66 76 
 
 
 1 000 
 
 999 
 
 16 99 
 
 4 
 
 161 25 
 
 114 61 
 
 148 13 
 
 67 13 
 
 5 
 
 1 000 
 
 1 001 
 
 16 96 
 
 4 
 
 163 00 
 
 114 74 
 
 147 74 
 
 67 00 
 
 4 
 
 1 000 
 
 1 002 
 
 16 95 
 
 4 
 
 169 37 
 
 114 86 
 
 147 29 
 
 66 77 
 
 ;{ 
 
 i oon 
 
 1 004 
 
 16 93 
 
 4 
 
 174.25 
 
 114 99 
 
 146 20 
 
 66 27 
 
 2 
 
 1 000 
 
 1 005 
 
 16 93 
 
 4 
 
 181 50 
 
 115 11 
 
 144 50 
 
 65 44 
 
 1 
 
 1 000 
 
 1 Oj6 
 
 16 98 
 
 5 
 
 191 20 
 
 1 15 34 
 
 140 51 
 
 63 32 
 
 19 
 18 
 
 0.878 
 878 
 
 0.977 
 980 
 
 16.96 
 16.93 
 
 4 
 4 
 
 155.75 
 160.87 
 
 112.02 
 112 27 
 
 150.71 
 151 72 
 
 70.01 
 70 44 
 
 17 
 
 878 
 
 981 
 
 16 95 
 
 5 
 
 167 00 
 
 112 40 
 
 152 39 
 
 70 59 
 
 16 
 
 878 
 
 983 
 
 16.94 
 
 4 
 
 173.00 
 
 112 63 
 
 15150 
 
 70 08 
 
 15 
 
 878 
 
 982 
 
 16.98 
 
 5 
 
 101.20 
 
 112 63 
 
 149 81 
 
 69 10 
 
 24... 
 23 
 
 0.785 
 II 785 
 
 .937 
 
 938 
 
 .02 
 03 
 
 5 
 4 
 
 159.20 
 163.25 
 
 107.56 
 107 70 
 
 155.99 
 155 96 
 
 75.20 
 75 04 
 
 22 
 
 7H5 
 
 936 
 
 .08 
 
 4 
 
 169.75 
 
 107 70 
 
 156 9 
 
 75 31 
 
 ''1 
 
 78o 
 
 935 
 
 .07 
 
 4 
 
 177.75 
 
 107 56 
 
 156 75 
 
 75 35 
 
 20 
 
 785 
 
 935 
 
 .06 
 
 4 
 
 191.25 
 
 107.44 
 
 152.26 
 
 73 31 
 
 30 
 29 
 
 0.688 
 688 
 
 .872 
 872 
 
 .15 
 .15 
 
 3 
 5 
 
 162.00 
 167.00 
 
 100.51 
 100.51 
 
 154.77 
 155 46 
 
 79.24 
 79 59 
 
 28 
 X7 
 
 0.688 
 6^8 
 
 .870 
 
 867 
 
 .16 
 
 .18 
 
 4 
 4 
 
 171.50 
 175.50 
 
 100.27 
 100.04 
 
 155.44 
 154.77 
 
 79.73 
 
 79.47 
 
 26 
 
 688 
 
 863 
 
 .20 
 
 4 
 
 181.00 
 
 99 57 
 
 152 97 
 
 78 83 
 
 25 
 
 688 
 
 858 
 
 .22 
 
 4 
 
 187.75 
 
 98.53 
 
 149 47 
 
 77.75 
 
 38 
 37 
 
 0.595 
 595 
 
 .796 
 793 
 
 .53 
 .50 
 
 4 
 4 
 
 152.75 
 158.50 
 
 92.81 
 92.35 
 
 147 80 
 148.51 
 
 80.17 
 81.10 
 
 36 
 
 595 
 
 791 
 
 48 
 
 4 
 
 163.50 
 
 92.02 
 
 148 19 
 
 81 31 
 
 35 
 34 
 
 0.595 
 595 
 
 .784 
 779 
 
 .47 
 .43 
 
 4 
 
 4 
 
 169.00 
 173.50 
 
 91.24 
 90.57 
 
 146.97 
 145.57 
 
 81.37 
 81 38 
 
 33 
 
 595 
 
 773 
 
 .39 
 
 4 
 
 178.25 
 
 89.68 
 
 143 00 
 
 80 92 
 
 32 
 
 595 
 
 .765 
 
 .38 
 
 4 
 
 181.50 
 
 88.75 
 
 138.94 
 
 79.50 
 
 31 
 14 
 
 0.595 
 472 
 
 .756 
 677 
 
 1 .40 
 1 .63 
 
 5 
 
 4 
 
 184.60 
 148.00 
 
 87.76 
 79.15 
 
 135.66 
 126.89 
 
 78.40 
 80.25 
 
 13 
 
 472 
 
 670 
 
 1 .67 
 
 4 
 
 155.25 
 
 78.41 
 
 128 35 
 
 81 76 
 
 12 
 11 
 10 
 
 0.472 
 0.472 
 472 
 
 .662 
 .654 
 .646 
 
 1 .69 
 
 1 .68 
 
 5 
 4 
 4 
 
 160.80 
 164.50 
 170.00 
 
 77.45 
 76.50 
 75.64 
 
 128.02 
 125.93 
 123.89 
 
 82.46 
 82.17 
 81.71 
 
 9 
 
 472 
 
 .639 
 
 1 .68 
 
 4 
 
 177.00 
 
 74.80 
 
 121.40 
 
 81.02 
 
 8 
 
 472 
 
 633 
 
 1 .70 
 
 4 
 
 184.00 
 
 74.17 
 
 118.32 
 
 79 54 
 
 51 
 
 386 
 
 .555 
 
 1 .92 
 
 4 
 
 150.25 
 
 65.43 
 
 101.22 
 
 76 18 
 
 50 
 49 
 48 
 
 0.386 
 0.386 
 386 
 
 .548 
 .547 
 .542 
 
 1 .94 
 1 .95 
 1 97 
 
 5 
 4 
 
 4 
 
 156.40 
 161.25 
 167.75 
 
 64.63 
 64.44 
 63.93 
 
 100.57 
 99.74 
 98.62 
 
 76.55 
 76.10 
 75 76 
 
 47 
 
 0.386 
 
 .539 
 
 17.97 
 
 4 
 
 175.25 
 
 63.54 
 
 96.59 
 
 74.66 
 
 46 
 
 45 
 44 
 
 0.386 
 
 0.304 
 0.304 
 
 .531 
 
 .450 
 .447 
 
 18.00 
 
 18.17 
 18.17 
 
 4 
 
 4 
 
 4 
 
 188.00 
 
 146.25 
 151.25 
 
 62.74 
 
 53.41 
 53.01 
 
 92.11 
 
 78.82 
 77.81 
 
 71.98 
 
 71.68 
 71.29 
 
 43 . 
 
 304 
 
 .445 
 
 18.14 
 
 4 
 
 156.50 
 
 52.74 
 
 76.67 
 
 70.73 
 
 42 
 41 
 40 
 
 0.304 
 0.304 
 (1 304 
 
 .443 
 .442 
 .439 
 
 18.14 
 18.13 
 18.15 
 
 4 
 4 
 4 
 
 162.50 
 168.50 
 17'6.75 
 
 52.54 
 52. 35 
 
 52.10 
 
 75.63 
 74.30 
 71.44 
 
 70.03 
 69.09 
 66 67 
 
 39 
 
 0.304 
 
 .435 
 
 18.15 
 
 4 
 
 187.75 
 
 51.63 
 
 66.69 
 
 62.81 
 
 
 
 
 
 
 
 
 
 
724 
 
 Turbine Test Data. 
 
 TABLE LXXV. 
 
 Test of a 30-inch Special Chase Jonval Turbine. Built by the Chase Turbine 
 Mfg. Co., Orange, Mass. Testing Flume of the Holyoke Water Power Co. 
 No. 256. June 7, 1884. 
 
 With the flume empty a strain of 4 Ibs. applied 2.4 feet from the center of the shaft 
 sufficed to start the wheel. 
 
 Number 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 
 BSKT 
 part. 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency = 1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse- 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 B 
 
 1 :.... 
 8 
 7 
 6 
 
 1.000 
 1.000 
 1.000 
 1 000 
 
 0.960 
 1.008 
 1.004 
 1 004 
 
 14.72 
 14.51 
 14.43 
 14 61 
 
 3 
 3 
 8 
 
 3 
 
 Still. 
 169.67 
 181.67 
 196.33 
 
 39.74 
 41.42 
 41.16 
 41.42 
 
 49.66 
 50.68 
 52 08 
 
 72.98 
 75.36 
 76.00 
 
 5 
 
 1 000 
 
 998 
 
 14 57 
 
 4 
 
 204 75 
 
 41 1(1 
 
 51.50 
 
 75 96 
 
 4 
 
 1 000 
 
 999 
 
 14 41 
 
 3 
 
 215.00 
 
 40.91 
 
 51.13 
 
 76.60 
 
 8 
 2 
 
 1.000 
 1 000 
 
 1.001 
 998 
 
 14.41 
 14.49 
 
 3 
 5 
 
 225.00 
 244. 
 
 41.02 
 40.99 
 
 ^50.42 
 
 50 38 
 
 75.34 
 74.91 
 
 22... 
 
 930 
 
 922 
 
 14 68 
 
 4 
 
 185 75 
 
 38 12 
 
 49.27 
 
 77.76 
 
 21... 
 
 930 
 
 920 
 
 14.72 
 
 6 
 
 194.17 
 
 38.07 
 
 49.73 
 
 78.37 
 
 23 
 
 930 
 
 919 
 
 14 78 
 
 4 
 
 203.75 
 
 38.12 
 
 50 32 
 
 78.88 
 
 24 
 25 
 
 17... 
 
 0.930 
 0.930 
 
 837 
 
 0.916 
 0.913 
 
 831 
 
 14.87 
 14.95 
 
 15 28 
 
 4 
 4 
 
 3 
 
 213.00 
 226.00 
 
 180.00 
 
 38.13 
 
 38.07 
 
 35 07 
 
 50.66 
 50.65 
 
 46 10 
 
 78.90 
 78.59 
 
 75.98 
 
 16.. 
 
 837 
 
 827 
 
 15 42 
 
 4 
 
 191 00 
 
 35 03 
 
 47 17 
 
 77.12 
 
 15 
 
 837 
 
 826 
 
 15 42 
 
 3 
 
 199 67 
 
 35 00 
 
 47.49 
 
 77.71 
 
 18 
 
 837 
 
 823 
 
 15 33 
 
 3 
 
 207 00 
 
 34 75 
 
 47 34 
 
 78.47 
 
 19 
 
 837 
 
 822 
 
 15 28 
 
 4 
 
 215 00 
 
 34.65 
 
 47.20 
 
 78.73 
 
 20 
 
 14... 
 
 0.837 
 674 
 
 0.818 
 666 
 
 15.26 
 16 13 
 
 4 
 4 
 
 228.25 
 163.50 
 
 34.49 
 
 28.85 
 
 46 98 
 35.15 
 
 78.82 
 66.70 
 
 13 
 12.... 
 
 0.674 
 674 ' 
 
 0.663 
 661 
 
 16.14 
 16 07 
 
 4 
 
 174.25 
 
 185 33 
 
 28.75 
 28.61! 
 
 a=>.86 
 
 36 45 
 
 68.25 
 70.04 
 
 11 
 
 6 674 
 
 669 
 
 16.11 
 
 4 
 
 195 50 
 
 28.52 
 
 36.66 
 
 70.46 
 
 10 
 
 674 
 
 655 
 
 16 14 
 
 4 
 
 206 50 
 
 28.40 
 
 36.83 
 
 70.97 
 
 9 
 
 67 i 
 
 650 
 
 16.20 
 
 4 
 
 217.00 
 
 28.25 
 
 36.72 
 
 70.86 
 
 30... 
 
 '0 488 
 
 462 
 
 17 10 
 
 4 
 
 142.25 
 
 20 62 
 
 16.26 
 
 40.74 
 
 29 
 
 488 
 
 460 
 
 17 11 
 
 4 
 
 158 50 
 
 20 55 
 
 16 67 
 
 41.88 
 
 28 
 
 48S 
 
 458 
 
 17 08 
 
 3 
 
 174 33 
 
 20.43 
 
 16.74 
 
 42.38 
 
 27 
 
 488 
 
 459 
 
 17 02 
 
 4 
 
 182 50 
 
 20 43 
 
 16.69 
 
 42.40 
 
 26 
 
 !-- 
 
 lf>s 
 
 17.07 
 
 3 
 
 190.67 
 
 20.43 
 
 16.57 
 
 41.96 
 
 31 
 
 488 
 
 457 
 
 17 09 
 
 5 
 
 206 20 
 
 20 37 
 
 10.03 
 
 40.67 
 
 
 
 
 
 
 
 
 
 
Chase Jonval Turbine. 
 
 725 
 
 TABLE LXXVI. 
 
 Test of a 30-inch Regular Chase Jonval Turbine. Built by the Chase Turbine 
 Mfg. Co., Orange, Mass. Testing Flume of the Holyoke Water Power Co. 
 June 10, 1884. 
 
 With the flume empty a strain of 33 Ibs. applied 2.4 feet from the center of the shaft, 
 sufficed to start the wheel. 
 
 Xumber 
 of 
 experi- 
 ment. 
 
 Gate 
 opening 
 (propor- 
 tional 
 part; . 
 
 Proportional 
 discharge 
 (discharge 
 at full gate 
 with highest 
 efficiency =1). 
 
 Mean 
 head in 
 feet. 
 
 Duration 
 of test in 
 minutes. 
 
 Revolu- 
 tions per 
 minute. 
 
 Dis- 
 charge 
 in sec- 
 ond- 
 feet. 
 
 Horse 
 power 
 devel- 
 oped. 
 
 Percent- 
 age of 
 effi- 
 ciency. 
 
 1 
 
 2 
 
 3 
 
 4 
 
 5 
 
 6 
 
 7 
 
 8 
 
 9 
 
 1 
 
 000 
 
 938 
 
 15.62 
 
 3 
 
 Still. 
 
 33 33 
 
 
 
 6 
 5 
 
 .OOU 
 000 
 
 0.993 
 995 
 
 15.32 
 
 15.29 
 
 3 
 
 3 
 
 194.CO 
 201.67 
 
 34.93 
 34.96 
 
 43.48 
 43.35 
 
 71.70 
 71.58 
 
 4 
 
 000 
 
 996 
 
 15 30 
 
 5 
 
 211 14 
 
 35 00 
 
 43 46 
 
 71 62 
 
 3 
 
 29 
 
 .000 
 .000 
 
 889 
 
 1.001 
 1.007 
 
 894 
 
 15.27 
 15.26 
 
 15 78 
 
 3 
 3 
 
 4 
 
 222.33 
 237.00 
 
 174 75 
 
 35.14 
 35.34 
 
 31 93 
 
 43.72 
 43.36 
 
 41 56 
 
 71.92 
 70.96 
 
 72 80 
 
 2S 
 
 889 
 
 897 
 
 15.77 
 
 4 
 
 190 25 
 
 32 01 
 
 42 64 
 
 74 55 
 
 27 
 20 
 
 0.888 
 889 
 
 0.897 
 0.898 
 
 15.75 
 
 15 80 
 
 4 
 
 4 
 
 200.25 
 211.25 
 
 32.01 
 32.10 
 
 43.05 
 
 43.48 
 
 75.36 
 75.66 
 
 23 
 
 889 
 
 901 
 
 15 77 
 
 3 
 
 220 67 
 
 32.17 
 
 43 40 
 
 75 50 
 
 24 
 
 0.889 
 
 0.903 
 
 15.74 
 
 4 
 
 232.00 
 
 32.20 
 
 43.50 
 
 75.76 
 
 25 
 
 889 
 
 907 
 
 15.72 
 
 3 
 
 242.67 
 
 32.33 
 
 43 29 
 
 75.17 
 
 22 
 
 733 
 
 0.756 
 
 16.30 
 
 4 
 
 184.50 
 
 27.43 
 
 36.28 
 
 71.63 
 
 o* 
 
 733 
 
 0.757 
 
 16.24 
 
 4 
 
 195.25 
 
 27.41 
 
 36 61 
 
 72 59 
 
 20 
 
 9.733 
 
 0.75S. 
 
 16.27 
 
 4 
 
 .'Or.OO 
 
 27.47 
 
 36.92 
 
 72.91 
 
 18 
 
 19 
 
 0.733 
 733 
 
 0.756 
 757 
 
 16.28 
 16.32 
 
 H 
 
 4 
 
 218.67 
 230.50 
 
 27.43 
 2i'.47 
 
 37.00 
 36.90 
 
 73.14 
 72 64 
 
 14 
 13 
 12 
 15 
 
 0.611 
 0.611 
 O.S11 
 
 611 
 
 0.644 
 0.644 
 0.641 
 0.644 
 
 16.65 
 16.65 
 16.68 
 16.77 
 
 5 
 4 
 3 
 3 
 
 175.80 
 
 188.75 
 202.00 
 
 209. as 
 
 23.63 
 23.60 
 23.54 
 23 63 
 
 27.34 
 27.62 
 27.72 
 27 76 
 
 61.33 
 62.05 
 62.16 
 62 21 
 
 ]H 
 
 11.811 
 
 0.644 
 
 16.67 
 
 3 
 
 221.33 
 
 23.64 
 
 27.33 
 
 61 21 
 
 17 
 
 611 
 
 0.647 
 
 16.61 
 
 3 
 
 236.33 
 
 23.71 
 
 27.02 
 
 60 56 
 
 7 
 
 411 
 
 0.469 
 
 17.14 
 
 3 
 
 141 33 
 
 17 47 
 
 12 93 
 
 38 10 
 
 8 
 
 411 
 
 469 
 
 17.20 
 
 4 
 
 157.00 
 
 17.47 
 
 12.92 
 
 37 96 
 
 LI 
 
 411 
 
 0.468 
 
 17.17 
 
 4 
 
 166.00 
 
 17.43 
 
 12 91 
 
 38 06 
 
 ]ti 
 
 0.411 
 
 0.469 
 
 17.13 
 
 4 
 
 184. (HI 
 
 17.43 
 
 12.62 
 
 36.46 
 
 11 
 
 411 
 
 0.471 
 
 17.16 
 
 3 
 
 201). 00 
 
 17.53 
 
 11.89 
 
 34 89 
 
 
 
 
 
 
 
 
 
 
APPENDIX E. 
 
 EFFECT OF AN "UMBRELLA" UPON THE FORMATION 
 
 OF VORTICES. 
 
 Report of Test Made on 30-Inch Horizontal Wheel With "Umbrella" at -the 
 Holyoke Water Power Company's Flume, April 25th to 27th, 1907, by 
 F. Moeller, Engineer Power and Mining Department of the Wellman, 
 Seaver, Morgan Co. for The Southern Wisconsin Power Company. 
 
 The general arrangement of the wheel and testing apparatus is shown by 
 Fig. 407. 
 
 Before begin^ng the test it was desired to note the action of the water 
 without umbrella in place. The penstock was filled, the level of the water 
 being 8' above the center of the shaft, making the total head of water 16.2'. 
 Under this condition, with the head stationary and the wicket gates wide 
 open, a large vortex was formed immediately above the wheel. 
 
 Fig. 407. 
 
Formation of Vortices. 
 
 727 
 
 The umbrella which was first made T in diameter and dished 11", was 
 lowered into the penstock until the edge was 3.1' above the center of the 
 shaft, with the level of the water the same as before. With this arrangement 
 no vortex was formed immediately above the wheel, but there were vortices 
 near the edge of the umbrella, (see Fig. 408). The umbrella was then re- 
 moved and a raft 8' square was built of matched pine about l 1 /^" thick, 
 tongued and grooved and placed as nearly as possible over the center of the 
 wheel on the surface of the water. This did not prevent the formation of 
 vortices. The raft was then increased from 8'x8' to 8'xl2', and placed in po- 
 sition as shown in Figure 409. This entirely prevented the formation of 
 vortices under the same condition of head as before and under all the run- 
 ning conditions of the wheel. 
 
 Regarding these vortices it was observed that all of them were formed at 
 the right hand side of the wheel (standing at the point marked "A," Fig. 408) 
 and towards the upper face of the penstock. The water enters the penstock 
 
 A 
 
 Fig. 408. 
 
 from the left hand side, flows through the wheel and draft tube and off at 
 the right hand side. The most reasonable explanation of this tendency for 
 the vortices to form at the place mentioned was that the wheel, being right 
 hand, the gates at the right hand side of the wheel pointed upward (see Fig- 
 ure 410) and formed a comparatively direct path for the vortex into the 
 wheel, while the gates on the right hand side pointing downward, formed an 
 effectual barrier. An examination of Figure 409 shows that the left hand 
 edge of the large raft does not project beyond the gates so that there was every 
 chance for the vortices to form at this point, yet none formed on this side in 
 any of the experiments. 
 
 As a result of these preliminary trials it was decided to increase the um- 
 brella to 10^' in diameter, and meanwhile a test was run off at full gate 
 and three-quarter gate opening, with the large raft in place, to determine the 
 efficiency of the wheel under this condition. These efficiencies are shown on 
 the report of the Holyoke Water Power Company and are numbered 1 to 18. 
 
 It may be here noted that the Holyoke Water Power Company finds it 
 necessary to use a raft on practically all of the horizontal tests made by 
 
728 
 
 Effect of "Umbrella" Upon Vortices. 
 
 them, the exceptions being only in the case of the smallest wheels, and it is 
 the opinion of the Hydraulic Engineer of that Company, as a result of his 
 observations on the various tests, that the employment of rafts to prevent the 
 formation of vortices does not affect the efficiency of the wheels. This is 
 verified in at least one instance, in the test made of two 33" runners built 
 for the <r Soo," the maximum efficiency obtained was 84%, it being necessary 
 in making this test to use a raft, and this efficiency has not been exceeded 
 by the same wheels when tested in a vertical setting when no raft was used. 
 The next test was made on the wheel with the enlarged umbrella in place, 
 the edge of the umbrella being 2' 2" above the center of the shaft, the center 
 of the umbrella being in the vertical plane of the shaft. The head of the 
 water was 16.2'. With the wheel standing still (with gate wide open), vor- 
 tices formed occasionally, but only for an instant, immediately disappearing. 
 With the wheel allowed to run under the brake, no vortices formed, but the 
 
 Fig. 410. 
 
 surface of the water was disturbed by the formation of whirls, which, how- 
 ever, disappeared without becoming vortices. This action took place at all 
 speeds of full gate opening. The same peculiarities of the action of the 
 water were noticed under three-quarter gate opening, but at no time were 
 any actual vortices formed. 
 
 A test was then made of the wheel with the umbrella in the last named 
 position, and the results of this test are noted under Nos. 19 to 33 in the re- 
 port of the Holyoke Water Power Company. 
 
 It was then decided to suspend the umbrella towards the right side of the 
 wheel. With the umbella in this position there were no whirls or vortices 
 at any gate opening, and the level of the water was entirely smooth ex- 
 cept such disturbances as were created by the current of the water flowing 
 in. With the umbrella in this position it was decided to make a few tests 
 to determine whether or not there was any difference in the efficiencies be- 
 tween the two positions of the umbrella. 
 
 A test was then made with the head lowered about 2' and it was decided 
 to confine the test to only full gate. The action of the water during this test 
 
Comparison of Results. 729 
 
 showed the formation of irregular whirls, but no actual vortices resulted. 
 The results of this test are numbered 38 to 43. 
 
 The head was then lowered about 1'. Under this condition the level of the 
 water was about 15" above the umbrella. No whirls or vortices were formed 
 and there was less disturbance to the water than in previous tests, but owing 
 to the method used for changing the level of the water in the penstock, it 
 was necessary with the water at this head, to allow the incoming water to 
 fall over the gate so that the water when flowing into the wheel was rather 
 full of air 'bubbles. The results of this test are numbered 44 to 49. 
 
 The level of the water was then reduced 2' more so that the top of the 
 umbrella projected II" above the level of the water. Under this condition 
 there were absolutely no disturbances of the water, except that it was full of 
 air bubbles in the head race, and upon examining the water in the tail race it 
 was found that the water there was also full of air bubbles. This condition 
 of the water probably accounts for the lower efficiencies obtained under these 
 conditions. The results of the tests are given in numbers 50 to 58. 
 
 A final test was made with the umbrella raised so that the top was about 
 flush with the level of the water. Under these conditions there were small 
 whirls forming around the edge of the umbrella, but no vortices occurred. 
 The surface of the water on the whole was quieter than with the umbrella 
 placed immediately above the wheel. The results of this test are numbered 
 57 to 65. 
 
 COMPARISON OF RESULTS. 
 
 It must be noted from an examination of all of the tests that the best effi- 
 ciency obtained on this wheel was practically at about .8 gate, so that in 
 making comparisons for similar speeds under different gate openings, this 
 must be allowed for. 
 
 ONE Comparing the results obtained with the raft, numbered 1 to 18, 
 with the results obtained with the umbrella placed immediately above the 
 wheels, numbered 18 to 33: 
 
 Take No. 5 Head 16.09 Revolutions 163 Efficiency 76.18 
 
 No. 24 Head 16.16 Revolutions 161.25 Efficiency 76.51 
 
 Also No. 25 Head 16.19 Revolutions 164.20 Efficiency 76.05 
 
 These show that the umbrella, if anything, is better. 
 
 Take No. 16 Head 16.95 Revolutions 142.25 Efficiency 78.99 
 
 No. 17 Head 16.93 Revolutions 137.5 Efficiency 79.11 
 
 and compare with 
 
 No. 33 Head 16.84 Revolutions 140.5 Efficiency 79.07 
 This also indicates that the umbrella is a little better than the raft. 
 
 TWO Comparing the umbrella at the surface with the umbrella immedi- 
 ately above the wheel: 
 
 Take No. 61 Head 16.48 Revolutions 158.25 Efficiency 78.7 
 No. 25 Head 16.16 Revolutions 157. Efficiency 76.19 
 No. 29 Head 16.8 Revolutions 159.75 Efficiency 74.08, 
 
 show that the umbrella should be placed near the surface of the water. 
 Also 
 
730 Effect of "Umbrella" Upon Vortices. 
 
 Take No. 58 Head 16.53 Revolutions 168. Efficiency 75.73 
 No. 22 Head 16.24 Revolutions 168.75 Efficiency 74.81 
 which indicates the same. 
 
 THREE Comparing the results obtained in tests numbered 38 to 43 with 
 those obtained in tests 1 to 18: 
 
 Take No. 43 Head 14.58 Revolutions 129.75 Efficiency 77.36 with 
 
 No. 17 Head 16.93 Revolutions 137.50 Efficiency 79.11 
 (Giving 137^ revolutions at 16.95 head.) 
 
 This shows a falling off in the efficiency, but as specified above, the point 
 of gate opening for No. 17 is at the point of maximum efficiency of the 
 wheel, whereas the point of gate opening under No. 43 is considerably 
 larger and therefore of itself would be less efficient. 
 Compare No. 40 Head 14.62 Revolutions 148.5 Efficiency 77.14 
 (Giving 156 revolutions at 16.07 head) with 
 No. 6 Head 16.07 Revolutions 154.5 Efficiency 75.98 
 No. 8 Head 16.08 Revolutions 157.6 Efficiency 76.03 
 Also No. 40 (Giving 160 Revolutions at 16.99 Head) with 
 
 No. 12 Head 16.99 Revolutions 159.75 Efficiency 75.09 
 The result of these comparisons would show no loss in efficiency. 
 
 FOUR Comparing numbers 44 to 49 with 1 to 18 tests: 
 No. 47 Head 13.54 Revolutions 138. Efficiency 77.41 
 (Giving 151 Revolutions at 16.08 Head) with 
 No. 7 Head 16.08 Revolutions 150. Efficiency 75.63 
 Also No. 47 (Giving 155 Revolutions at 16.99 Head) with 
 No. 13 Head 15.99 Revolutions 155.5 Efficiency 75.09 
 
 This shows no loss. 
 
 FIVE Comparing tests Nos. 50 to 56 with 1 to 18: 
 Take No. 54 Head 11.5 Revolutions 136. Efficiency 74.92 
 (Giving 161 Revolutions at 16.09 Head) with 
 No. 5 Head 16.09 Revolutions 163. Efficiency 76.18 
 
 This shows a loss, as was to be expected from the condition of the water, 
 as stated above. 
 
 As a result of our calculations from the tests we should say as follows: 
 
 (A) That the use of an umbrella or hood does not reduce the efficiency of 
 the wheel. 
 
 (B) That the hood should be kept as close to the surface of the water as 
 possible. 
 
 (Signed) F. MOELLER. 
 
APPENDIX F. 
 EVAPORATION TABLES. 
 
 Depth of evaporation, in inches, at signal service stations, in thermometer shelt- 
 ers, computed from the means of the tri-daily determination of dew-point and 
 wet-bulb observations.* 
 
 Stations and 
 Districts. 
 
 New England: 
 
 Eastport 
 
 Portland 
 
 Manchester 
 
 Northfield 
 
 Boston 
 
 Nantucket 
 
 Wood's Holl 
 
 Block Island 
 
 New Haven 
 
 New London 
 
 Mid- Atlantic States: 
 
 Albany 
 
 New York City . . . 
 
 Philadelphia 
 
 Atlantic City 
 
 Baltimore 
 
 Washington City. 
 
 Lynchburg 
 
 Norfolk 
 
 So. Atlantic States: 
 
 Charlotte 
 
 Hatteras 
 
 Raleigh 
 
 Wilmington 
 
 Charleston 
 
 Columbia 
 
 Augusta 
 
 Savannah 
 
 Jacksonville 
 
 Florida Peninsula: 
 
 Titusville 
 
 Cedar Keys 
 
 Key West 
 
 0.9 
 1.0 
 0.9 
 0.8 
 1.2 
 1.1 
 0.5 
 1.1 
 1.1 
 1.5 
 
 0.9 
 1.8 
 1.6 
 1.2 
 2.0 
 1.8 
 2.6 
 1.8 
 
 3.5 
 3.3 
 
 3.8 
 
 1.4 
 1.2 
 1.6 
 
 1.0 
 1.6 
 1.1 
 0.8 
 1.1 
 1.6 
 1.3 
 
 1.2 
 1.4 
 2.1 
 1.6 
 2.2 
 1.7 
 2.7 
 1.6 
 
 2.6 
 1.6 
 
 1.8 
 
 2.2 
 2.5 
 2.3 
 2.6 
 2.8 
 2.6 
 
 2.6 
 2.8 
 3.7 
 
 1.5 
 1.8 
 2.2 
 1.5 
 
 1.2 
 1.8 
 1.5 
 
 1.6 
 2 
 2.5 
 1.5 
 2.8 
 2 5 
 3.4 
 2.3 
 
 4.3 
 1.6 
 2.6 
 2 
 
 3 
 
 > 
 
 3.4 
 
 4.1 
 3.8 
 
 / 
 5 
 
 2.6 
 
 4.0 
 
 2.4 
 2.6 
 3 3 
 2.3 
 3.4 
 1.5 
 2.4 
 2.0 
 2.7 
 2.6 
 
 3.3 
 3.4 
 4.4 
 2.4 
 5.1 
 4.2 
 5.2 
 3.5 
 
 6.4 
 2.5 
 
 3.8 
 3 * 
 3 
 
 4.8 
 5 
 
 4 
 4 
 
 3.8 
 46 
 4.5 
 
 2.5 
 1.8 
 3.8 
 25 
 3.1 
 1.8 
 1.8 
 1.8 
 2.7 
 2.8 
 
 4.5 
 2.2 
 4.1 
 3.3 
 3.9 
 4.3 
 4.8 
 4.3 
 4.6 
 
 3.8 
 4.5 
 4.4 
 
 2.7 
 3.3 
 5.0 
 3.4 
 4.7 
 2.1 
 2.7 
 2.6 
 4.1 
 4.0 
 
 4.5 
 4.6 
 5.7 
 3.6 
 5.( 
 6.0 
 5.6 
 4.2 
 
 5.8 
 
 3.0 
 
 5. 
 
 4.3 
 
 4.4 
 
 5.4 
 
 5.0 
 
 4.6 
 
 5.3 
 
 4.3 
 5.1 
 
 4.8 
 
 =^28 kSS 
 
 3 QC fl) GO 
 
 <l^ ! CO'- 
 
 2 2 
 3.8 
 4.1 
 3.5 
 4.4 
 3.3 
 2.7 
 2.5 
 3.7 
 3.4 
 
 5.0 
 5.0 
 5.7 
 2.9 
 6.0 
 5.4 
 4.7 
 4.6 
 
 4 
 
 4.3 
 
 4.5 
 
 4.2 
 
 4.8 
 
 4.2 
 
 5.0 
 
 3.8 
 5.0 
 5.1 
 
 2.9 
 3.9 
 3.3 
 
 9 7 
 
 4.0 
 3.8 
 2.4 
 
 3.9 
 
 4.7 
 5.2 
 5.2 
 
 4.0 
 4.1 
 3.2 
 3.1 
 4.8 
 3.8 
 4.5 
 4.7 
 4.7 
 
 4 3 
 5.5 
 5.1 
 
 2.5 
 3.4 
 2.5 
 2.3 
 3.5 
 3.4 
 2.7 
 2.8 
 3.1 
 3.2 
 
 3.2 
 4.3 
 4.3 
 2.4 
 4.4 
 4.1 
 3.3 
 3.7 
 
 4.6 
 3.8 
 3.0 
 3.9 
 4.2 
 4.2 
 5.1 
 3.4 
 3.8 
 
 4.0 
 4.5 
 4. 
 
 31 
 
 2.6 
 3.0 
 2.8 
 1.8 
 2.7 
 2.7 
 1.2 
 2.6 
 3.2 
 3.1 
 
 3.0 
 4.1 
 4.0 
 18 
 4.3 
 4.2 
 3.4 
 2.9 
 
 4.0 
 3.2 
 2.7 
 3.4 
 4.0 
 3.4 
 4.1 
 3.6 
 3.6 
 
 4.1 
 4.1 
 4.3 
 
 2.2 
 2.5 
 2.4 
 1.1 
 2.2 
 1.8 
 0.8 
 1.8 
 2.4 
 2.4 
 
 2.1 
 3.3 
 3-3 
 
 4.5 
 3.2 
 2.3 
 
 ?. 6 
 2.6 
 2.4 
 2.8 
 3.2 
 3.6 
 3.6 
 3.5 
 3.0 
 
 3.6 
 3.5 
 
 3.8 
 
 1 
 1 
 1 
 1 
 -[ 
 
 1.825.6- 
 
 0. 
 
 1 
 
 1.631.8- 
 
 o 
 
 29.7 
 .433.3 
 .023.9 
 
 34.4 
 
 .5 
 
 2.1 
 
 434. 
 
 1 . 
 
 2. 
 
 2. 
 
 1.5 
 
 2 
 
 2. 
 
 2.645 
 
 1. 
 
 2.7 
 
 2.1 
 
 3.1 
 
 20.3 
 24.0 
 
 31.8 
 
 .8 
 .6. 
 5.0 
 25.2; 
 2.448.1 
 .6 
 .5 
 .1; 
 
 240. 
 245. 
 
 545, 
 
 S 35 . 
 
 2.649.0- 
 1.631 3 
 1.837.0 
 
 38.4 
 
 2.543.7 
 2.4 
 3.1 49.3 
 2.846.0 
 
 45.7 
 
 44.2 
 
 2 649.5 
 3-6516. 
 
 *From Monthly AVeather Review, September, 1888. 
 
732 
 
 Evaporation Tables. 
 
 Depth of evaporation, In inches, at signal service stations Continued. 
 
 Stations and 
 Districts. 
 
 Eastern Gulf States: 
 
 Atlantic 
 
 Pensacola 
 
 Mobile 
 
 Montgomery .... 
 
 Vicksburg 
 
 New Orleans .... 
 
 West. Gulf States: 
 
 Shreveport 
 
 Fort Smith 
 
 Little Rock 
 
 Corpus Christie . 
 Galveston 
 
 West. Gulf State* 
 Continued. 
 
 Palestine 
 
 San Antonio . . . 
 
 Rio Grande Valley: 
 Rio Grande City . . 
 Brownsville 
 
 Ohio Valley and 
 Tennessee: 
 
 'Chattanooga 
 
 Knoxville 
 
 Memphis 
 
 Nashville 
 
 Louisville 
 
 Indianapolis 
 
 Cincinnati 
 
 Columbus 
 
 Pittsburg 
 
 Lower Lake Region. 
 
 Buffalo 
 
 Oswego 
 
 Rochester 
 
 Erie 
 
 Cleveland 
 
 Sandusky 
 
 Toledo 
 
 Detroit 
 
 Upper Lake Region, 
 
 Alpena 
 
 Grand Haven 
 
 Lansing 
 
 Marquette 
 
 Port Huron 
 
 Chicago 
 
 Milwaukee 
 
 Green Bay 
 
 Duluth 
 
 2.9 
 2.6 
 3 
 2.1 
 
 2.8 
 
 1.6 
 2.2 
 2.1 
 1.4 
 1.6 
 
 2.1 
 2.4 
 
 2.7 
 
 1.8 
 
 2.0 
 2.4 
 2.1 
 1.9 
 
 1.4 
 
 0.8 
 0.6 
 
 1.1 
 
 o 
 
 0.8 
 
 o 
 
 1 
 
 
 
 0.5 
 
 2.6 
 2.8 
 2.5 
 3.3 
 2.5 
 2.8 
 
 2.1 
 2.7 
 2.8 
 1.6 
 
 2.8 
 
 3.0 
 3.3 
 
 3.5 
 2.6 
 
 3.3 
 2.6 
 2.3 
 2.1 
 2.1 
 1.4 
 1.8 
 2.0 
 
 1.1 
 1.0 
 1.1 
 1.4 
 1.4 
 1.4 
 1.1 
 1.1 
 
 0.6 
 
 0. 
 
 1.2 
 
 0.8 
 
 1.0 
 
 1.2 
 
 1.0 
 
 0.6 
 
 0.5 
 
 4.0 
 4.1 
 2.8 
 5.1 
 3.6 
 4.1 
 
 3.0 
 3.5 
 3.5 
 3.3 
 3.2 
 
 3.3 
 4.1 
 
 3.5 
 2.9 
 
 3.3 
 3.4 
 3.1 
 3.2 
 2.8 
 2.2 
 2.6 
 2.3 
 2.2 
 
 1.3 
 1.1 
 0.9 
 1.4 
 1.5 
 1.5 
 1.5 
 1.6 
 
 0.9 
 .3 
 ,4 
 ,9 
 
 .1 
 
 .8 
 .1 
 
 0.8 
 0.6 
 
 6.2 
 4.0 
 3.5 
 6.5 
 5.1 
 3 8 
 
 4.8 
 5.3 
 5.5 
 3.0 
 2.9 
 
 4.2 
 
 3.8 
 
 3.6 
 3.0 
 
 5.3 
 5.0 
 5.9 
 5.9 
 5.6 
 
 2.2 
 2.2 
 2.6 
 2.7 
 2.9 
 3.2 
 3.5 
 3.0 
 
 1.6 
 2.6 
 2.7 
 1.7 
 2.6 
 3.2 
 2-4 
 1.7 
 1.5 
 
 4.7 
 4.3 
 3.7 
 5.9 
 
 5.7 
 4.2 
 
 4.9 
 4.4 
 4.8 
 3.2 
 4.3 
 
 4.3 
 4.0 
 
 4.5 
 3.5 
 
 3.7 
 3.5 
 5.3 
 5.0 
 5.4 
 4.8 
 5.2 
 4.8 
 4.2 
 
 3.3 
 2.8 
 3.8 
 3.7 
 3.3 
 3.7 
 3.8 
 4.1 
 
 2.1 
 3.1 
 2.8 
 2.4 
 3.0 
 3.3 
 2.6 
 2.5 
 2.4 
 
 5 
 
 4 
 
 4 
 
 5.8 
 
 4.8 
 
 4.1 
 
 4.2 
 4.H 
 4.1 
 3.9 
 4.2 
 
 4.5 
 4.5 
 
 4.6 
 3.9 
 
 4.3 
 4 
 
 4.8 
 
 5.1 
 
 5.8 
 
 5 
 
 6.4 
 
 5.8 
 
 5.4 
 
 3.9 
 
 3.8 
 
 4 
 4 
 4.4 
 
 4.6 
 
 4.8 
 
 3.6 
 3.8 
 4.0 
 3.3 
 3.8 
 4.8 
 3.8 
 4.1 
 2.5 
 
 >>!>- 
 
 co 
 
 3 CO ~ GO 
 
 4.5 
 5.0 
 4.1 
 
 4-1 
 
 4.9 
 5.6 
 5 4 
 4.4 
 5.3 
 
 5.8 
 6.6 
 
 6.9 
 4.0 
 
 4.3 
 4.9 
 4.9 
 5.5 
 
 6.8 
 7.7 
 6.5 
 6.9 
 6.6 
 
 4.9 
 
 5.5 
 5.2 
 5.4 
 6.0 
 5.9 
 
 3.4 
 4.6 
 5.4 
 4.8 
 5.6 
 3.9 
 
 4.7 
 5.4 
 4.6 
 4.5 
 5.0 
 4.3 
 
 5.2 
 4 6 
 5.9 
 4.3 
 5.2 
 
 4.6 
 
 5.8 
 
 7.0 
 4.1 
 
 5.o 
 5.0 
 5.4 
 6.3 
 7.4 
 6.9 
 6.6 
 6.4 
 5.6 
 
 5.2 
 
 5.2 
 
 3.7 
 3.8 
 3.9 
 3.3 
 4.2 
 5.3 
 3.7 
 4.2 
 3.4 
 
 5.8 
 5.2 
 4.6 
 5.7 
 4.7 
 4.4 
 
 5.0 
 
 4.7 
 
 5. 
 
 4.3 
 
 5.2 
 
 4.8 
 5.2 
 
 5.2 
 3.3 
 
 5.4 
 4.9 
 5.5 
 5.9 
 6.4 
 5.2 
 6.1 
 5.1 
 4.9 
 
 3.9 
 3.6 
 3.8 
 3.1 
 3.8 
 3.7 
 3.7 
 3.4 
 
 2.8 
 2.7 
 2.4 
 3.1 
 3.2 
 4.1 
 3.4 
 3.0 
 3.0 
 
 4.6 
 4.5 
 4 1 
 4.6 
 3.4 
 4.6 
 
 4.1 
 5.9 
 5.2 
 4.1 
 4.7 
 
 4.4 
 5.4 
 
 4.9 
 3.0 
 
 4.2 
 4.0 
 4.9 
 4.1 
 4.7 
 4.0 
 3.4 
 
 2.8 
 2.7 
 2.6 
 2.5 
 3.4 
 3.4 
 3.4 
 2.8 
 
 2.2 
 2.6 
 1.9 
 2.2 
 2.5 
 3.2 
 2.9 
 2.4 
 2.5 
 
 Hi! 
 
 4.2 
 3.6 
 3.4 
 4.3 
 4.0 
 3.7 
 
 3.4 
 3.9 
 4.3 
 3.0 
 4.2 
 
 4.0 
 4.2 
 
 3.6 
 
 2.6 
 
 3.9 
 3.8 
 4.1 
 
 3.1 
 3.3 
 
 2.6 
 
 2.8 
 
 1.9 
 2.2 
 2.2 
 1.9 
 2.4 
 2.2 
 2.4 
 2.0 
 
 1.5 
 1.7 
 1.4 
 1.3 
 1.7 
 2.3 
 1.9 
 1.9 
 1.2 
 
 2.5 
 2.4 
 2.2 
 3.1 
 2.2 
 
 9 s 
 
 oi.o 
 48.8 
 42.1 
 56.6 
 1 
 45.4 
 
 247 
 
 2.445.6 
 2.249.6 
 2.35L.7 
 2.338.8 
 2.4146.0 
 
 2.1 
 3.1 
 
 3.1 
 
 47.1 
 52.4 
 
 53.1 
 
 1.946.4 
 
 2.1 
 
 45.9 
 
 2.4 
 
 50.0 
 50.1 
 1J54.8 
 
 1.648.6 
 
 2.1 
 
 52.0 
 
 1.847.8 
 2.344.5 
 
 1.632.9 
 T028.9 
 
 435.7 
 336.6 
 338.6 
 
 1.336.0 
 
 28.6 
 
 027.6 
 24,5 
 
 029.3 
 
 236.8 
 29.0 
 
 9 28 . 2 
 
 23.0 
 
Evaporation Tables. 
 
 733 
 
 Depth of evaporation, in Inches, at signal service stations Continued. 
 
 Stations and 
 Districts. 
 
 o! GO 
 
 1 
 
 Si 
 
 il 
 
 30 >>GC 
 
 11 
 
 3 
 
 fi 
 
 i| 
 
 si 
 
 1 
 
 l| 
 
 00 
 CO 
 
 
 
 
 ! 
 
 
 "~ 5 i 
 
 ** 
 
 
 
 Extreme Northwest: 
 Moorhead 
 Saint Vincent 
 Bismarck 
 Fort Buford 
 Fort Totten 
 
 Upper Mississippi 
 Valley: 
 St. Paul 
 LaCrosse 
 Davenport 
 DesMoines 
 Dubuque 
 Keokuk .... 
 
 0.2 
 0.3 
 0.4 
 
 1.4 
 0.2 
 
 0.7 
 0.4 
 0.5 
 0.6 
 0.7 
 0.8 
 1.6 
 0.8 
 1.3 
 
 1.1 
 
 1.1 
 0.9 
 1.1 
 0.8 
 0.7 
 1.2 
 0.6 
 3 
 
 1.4 
 0.3 
 0.6 
 0.7 
 0.3 
 
 0.7 
 1.2 
 1.0 
 1.0 
 1.0 
 1.1 
 2.1 
 1.1 
 
 1.6 
 
 1.6 
 1.7 
 1.5 
 1.2 
 1.5 
 1.1 
 1.6 
 0.9 
 0.7 
 
 0.5 
 0.5 
 0.6 
 0.6 
 0.4 
 
 2.2 
 
 1.4 
 1.8 
 1.5 
 1.4 
 2.1 
 2.9 
 2.0 
 2.5 
 
 2.4 
 2.4 
 2. 
 2. 
 1. 
 1. 
 1. 
 1. 
 
 
 2.1 
 
 1.8 
 3.0 
 3.0 
 
 2.2 
 
 2.0 
 3.3 
 3.8 
 3.7 
 2.2 
 4.2 
 5.8 
 4.6 
 5.5 
 
 4.4 
 5.0 
 4.6 
 4.0 
 4.4 
 3.5 
 5.0 
 4.4 
 3 7 
 
 3.6 
 3.8 
 4.3 
 4.7 
 4.6 
 
 2.3 
 3.5 
 3.4 
 3.1 
 2.9 
 3.7 
 4.4 
 3.8 
 4.7 
 
 3.8 
 4.8 
 4.5 
 4.1 
 3.8 
 3.3 
 3.2 
 4.1 
 3 7 
 
 3.8 
 3.9 
 4.1 
 5.0 
 3.8 
 
 4.1 
 4.4 
 4.6 
 4.2 
 4.2 
 4.3 
 4.3 
 4.3 
 5.0 
 
 4.0 
 4.0 
 5.0 
 4.1 
 5.2 
 4.5 
 5.3 
 5.2 
 4 1 
 
 3.7 
 3.1 
 5.6 
 6.2 
 4.2 
 
 5.0 
 5.4 
 6.9 
 6.6 
 6.2 
 7.0 
 5.6 
 5.4 
 7.5 
 
 6.0 
 5.0 
 6.3 
 6.3 
 6.2 
 5.6 
 6.9 
 7.7 
 5 7 
 
 3.3 
 2.6 
 4.2 
 4.9 
 3.7 
 
 3.7 
 4.7 
 6.2 
 
 4.7 
 4.8 
 6.8 
 6.5 
 6.5 
 8.0 
 
 4.6 
 3.4 
 4.5 
 3.5 
 5.2 
 4.7 
 5.0 
 4.9 
 4 9 
 
 3.5 
 2.6 
 4.0 
 
 4.8 
 3.7 
 
 2.8 
 3.0 
 4.4 
 4.1 
 3.3 
 5.0 
 5.1 
 4.5 
 5.9 
 
 3.7 
 3.4 
 4.0 
 3.2 
 4.3 
 3.8 
 5.2 
 5.7 
 4 1 
 
 2.4 
 2.0 
 2.6 
 3-0 
 2.3 
 
 2.4 
 3.0 
 3.0 
 3.3 
 2.8 
 3.8 
 4.5 
 3.5 
 4.9 
 
 3.6 
 3.5 
 3.9 
 3.0 
 4.3 
 3.6 
 3.8 
 3.6 
 3 1 
 
 1.3 
 0.9 
 
 1.2 
 1.7 
 1.4 
 
 1.5 
 1.8 
 2.3 
 2.3 
 1.8 
 2.9 
 3.8 
 2.9 
 3.9 
 
 2.9 
 3.1 
 2.7 
 2.2 
 3.0 
 2.4 
 3.3 
 2.8 
 ?, 4 
 
 0.5 
 0.3 
 0.4 
 0.5 
 0.4 
 
 0.7 
 0.8 
 1.1 
 0.9 
 0.9 
 1.2 
 2.3 
 1.4 
 1.4 
 
 1.5 
 1.4 
 A 
 .4 
 .4 
 .1 
 .5 
 0.7 
 7 
 
 26.3 
 22.1 
 31.0 
 35.5 
 
 27.2 
 
 28.1 
 32.9 
 39.0 
 36.0 
 33.2 
 42.9 
 48.9 
 40.8 
 52.2 
 
 39.6 
 38.3 
 41.6 
 36.1 
 41.7 
 35.5 
 43.8 
 41.9 
 33 
 
 Cairo . . ... 
 
 Springfield, 111. . . . 
 St. Louis 
 
 Missouri Valley: 
 Lamar 
 
 Springfield, Mo. . . 
 Leaven worth 
 Topeka 
 Omaha 
 
 Crete 
 
 Valentine 
 
 Fort Sully 
 Huron 
 
 Yankton 
 
 0.4 
 
 0.8 
 0.6 
 1.1 
 
 1.4 
 
 1.2 
 1.5 
 1.4 
 3 6 
 
 1. 
 
 1. 
 1. 
 1.1 
 
 2 1 
 
 3.3 
 
 3.8 
 5.4 
 3.3 
 6 1 
 
 3.1 
 
 4.1 
 6.8 
 3.2 
 4 3 
 
 4.4 
 
 4.2 
 
 4.9 
 4.6 
 5 5 
 
 4.6 
 
 6.8 
 9.6 
 6.8 
 7.2 
 6.0 
 8.0 
 6.0 
 
 6.7 
 8.3 
 3.0 
 7.3 
 8.3 
 7.6 
 
 4.8 
 9.5 
 11.4 
 9.4 
 
 3.7 
 
 5.5 
 
 8.0 
 4.6 
 
 7.7 
 4.8 
 7.7 
 4.8 
 
 7.2 
 8.5 
 4.0 
 5.2 
 6.6 
 6.2 
 
 7.5 
 
 7.5 
 9.0 
 11.6 
 
 2.9 
 
 4.8 
 6.1 
 3.8 
 6.4 
 4.4 
 8.6 
 3.7 
 
 6.8 
 6.1 
 3.0 
 4.3 
 5.5 
 5.4 
 
 5.1 
 6.2 
 5.9 
 3.9 
 
 3.0 
 
 3.5 
 3.4 
 
 2.8 
 4.3 
 2.5 
 
 5.8 
 2.8 
 
 4.6 
 4.9 
 2.3 
 4.5 
 5.2 
 4.7 
 
 4.2 
 4.5 
 5.2 
 4.0 
 
 2.2 
 
 2.5 
 2.9 
 2.0 
 3.0 
 1.7 
 6.1 
 2.3 
 
 4.2 
 4.2 
 
 2.8 
 3.4 
 4.2 
 4.2 
 
 4.1 
 3.4 
 5.7 
 3.6 
 
 0.8 
 
 1.1 
 1.5 
 1.1 
 2.1 
 0.7 
 3.5 
 1.1 
 
 2.9 
 3.1 
 1.0 
 1.8 
 2.1 
 2.2 
 
 2.0 
 1.7 
 4.9 
 
 3.8 
 
 31.0 
 
 39.5 
 52.0 
 35.8 
 53.4 
 35.4 
 76.5 
 41.3 
 
 59.4 
 69.0 
 26.8 
 47.2 
 54.6 
 55.4 
 
 46.1 
 54.4 
 96.4 
 76.0 
 
 Northern Slope: 
 Fort Assimboine.. 
 Fort Custer 
 
 Fort Maginnis .... 
 
 Poplar River 
 
 0.4 
 3.3 
 
 0.8 
 
 3-0 
 2.8 
 2.1 
 1.3 
 1.4 
 1.3 
 
 1.6 
 1.8 
 5.4 
 3.9 
 
 0.8 
 5.7 
 
 1.8 
 
 3.3 
 3.7 
 1.3 
 2.8 
 2.4 
 1.9 
 
 2.0 
 1.7 
 5.7 
 3.9 
 
 0.8 
 4.0 
 1.8 
 
 4.1 
 3.5 
 1.5 
 
 1.8 
 2.8 
 3.2 
 
 3!l 
 6.7 
 5.2 
 
 2.7 
 
 8.2 
 5.4 
 
 6.7 
 7.6 
 2.1 
 4.8 
 4.1 
 5.1 
 
 3.8 
 4.2 
 8.5 
 7.3 
 
 4.9 
 5.2 
 3.9 
 
 5.6 
 5.8 
 1.8 
 4.3 
 4.6 
 5.4 
 
 4.0 
 5.0 
 11.0 
 9.5 
 
 5.7 
 
 10.4 
 6.9 
 
 4.3 
 
 10.5 
 1.9 
 5.7 
 7.4 
 
 8.2 
 
 4.4 
 
 5.8 
 12.0 
 10.9 
 
 Cheyenne 
 North Platte 
 
 Middle Slope: 
 Colorado Springs. 
 Denver 
 Pike's Peak 
 
 Concordia 
 
 Dodge City 
 Fort Elliott 
 
 Southern Slope; 
 Fort Sill 
 
 Abilene 
 Fort Davis 
 Fort Stanton 
 
734 
 
 Evaporation Tables. 
 
 Depth of evaporation, in inches, at signal service stations Continued. 
 
 Stations and 
 Districts. 
 
 if 
 
 m 
 
 *i 
 
 _ 
 
 11 
 
 B co 
 
 I*! 
 
 ?i 
 
 II 
 
 |i 
 
 si 
 
 11 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 r* 
 
 Southern Plateau: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 El Paso 
 
 4.0 
 
 3.9 
 
 6.0 
 
 8.4 
 
 10.7 
 
 13.6 
 
 9.4 
 
 7.7 
 
 5.6 
 
 5.2 
 
 4.6 
 
 2.9 
 
 82.0 
 
 Santa Fe 
 
 3.0 
 
 3.4 
 
 4.2 
 
 6.8 
 
 8.8 
 
 12.9 
 
 9.2 
 
 9.8 
 
 6.6 
 
 6.7 
 
 5.7 
 
 2.7 
 
 79.8 
 
 Fort Apache .... 
 
 2.6 
 
 3.0 
 
 3.6 
 
 6.8 
 
 9.4 
 
 9.1 
 
 7.1 
 
 6.7 
 
 5.3 
 
 5.2 
 
 4.1 
 
 2.6 
 
 65.5 
 
 Fort Grant 
 
 5.2 
 
 4.8 
 
 6.4 
 
 9.2 
 
 10.2 
 
 13.8 
 
 12.4 
 
 10.5 
 
 9.0 
 
 7.9 
 
 7.2 
 
 4.6 
 
 101.2 
 
 Prescott 
 
 1.4 
 
 2.8 
 
 3.6 
 
 5.4 
 
 6.2 
 
 8.1 
 
 6,6 
 
 6.5 
 
 4.7 
 
 4.9 
 
 3.6 
 
 2.2 
 
 56.0 
 
 Yuma 
 
 4.4 
 
 5.2 
 
 6.6 
 
 9.6 
 
 9.6 
 
 12.6 
 
 11.0 
 
 10.2 
 
 8.2 
 
 8.2 
 
 5.5 
 
 4.6* 
 
 95.7 
 
 Keeler 
 
 3.0 
 
 4.6 
 
 6.3 
 
 8.7 
 
 9.3 
 
 11.9 
 
 12.8 
 
 13.9 
 
 10.6 
 
 8.8 
 
 5.9 
 
 4.8 
 
 100.6 
 
 Middle Plateau: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fort Bidwell .... 
 
 0.8 
 
 1.8 
 
 1.8 
 
 4.6 
 
 5.2 
 
 4.0 
 
 8.8 
 
 8.1 
 
 5.0 
 
 4.6 
 
 2.4 
 
 1.3 
 
 48.9 
 
 Winnemucca .... 
 
 0.9 
 
 2.8 
 
 6.2 
 
 9.1 
 
 9.3 
 
 10.1 
 
 11.5 
 
 12.0 
 
 9.9 
 
 6.6 
 
 3.7 
 
 1.8 
 
 83.9 
 
 Salt Lake City. . . 
 
 1.8 
 
 2.7 
 
 3.6 
 
 7.2 
 
 6.9 
 
 8.9 
 
 9.2 
 
 10.7 
 
 9.6 
 
 6.5 
 
 5.0 
 
 2.3 
 
 7.44 
 
 Montrose 
 
 1.8 
 
 2.7 
 
 3.7 
 
 6.2 
 
 7.0 
 
 11.1 
 
 10.2 
 
 8.3 
 
 6.9 
 
 5.2 
 
 3.4 
 
 2.0 
 
 68.3 
 
 Fort Bridger 
 
 1.6 
 
 2.5 
 
 2.7 
 
 4.3 
 
 4.3 
 
 6.5 
 
 7.7 
 
 6.8 
 
 5.6 
 
 4-2 
 
 5.2 
 
 4.7 
 
 56.1 
 
 Northern Pleat eau: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Boise City 
 
 1.6 
 
 2.5 
 
 3.8 
 
 6.1 
 
 6.5 
 
 6.6 
 
 10.0 
 
 9.2 
 
 7.4 
 
 5.2 
 
 3.2 
 
 1.8 
 
 63.9 
 
 Spokane Falls. . . 
 
 0.7 
 
 1.7 
 
 2.7 
 
 4.4 
 
 5.4 
 
 4.4 
 
 7.7 
 
 6.4 
 
 3.8 
 
 2.5 
 
 1.7 
 
 1.4 
 
 42.8 
 
 Walla Walla.... 
 
 1.1 
 
 2.9 
 
 3.6 
 
 6.2 
 
 7.7 
 
 5.7 
 
 9.9 
 
 7.9 
 
 5.1 
 
 3.4 
 
 1.8 
 
 2.4 
 
 57.7 
 
 No. Pacific Coast:. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fort Canby 
 
 1.2 
 
 1.1 
 
 1.8 
 
 2.1 
 
 2.8 
 
 2.3 
 
 1.8 
 
 2.9 
 
 1.8 
 
 1.8 
 
 1.5 
 
 0.9 
 
 21.1 
 
 Olynipia 
 
 1.3 
 
 1.2 
 
 1.8 
 
 2.5 
 
 4.1 
 
 3.3 
 
 3.2 
 
 3.1 
 
 2.4 
 
 1.5 
 
 1.3 
 
 1.1 
 
 26.8 
 
 Port Angeles .... 
 
 1.0 
 
 0.9 
 
 1.8 
 
 1.8 
 
 2.5 
 
 2.1 
 
 2.1 
 
 1.8 
 
 1.5 
 
 1.2 
 
 1.3 
 
 1.1 
 
 19.1 
 
 Tatoosh Island. . 
 
 1.2 
 
 1.1 
 
 1.8 
 
 1.4 
 
 1.8 
 
 1.8 
 
 1.4 
 
 1.4 
 
 1.4 
 
 1.6 
 
 1.8 
 
 1.4 
 
 18.1 
 
 Astoria 
 
 1.1 
 
 1.0 
 
 1.6 
 
 2.1 
 
 3.0 
 
 2.7 
 
 3.0 
 
 2.9 
 
 2.6 
 
 2.3 
 
 1.8 
 
 1.2 
 
 25.3 
 
 Portland 
 
 0.9 
 
 1.1 
 
 2.4 
 
 3.4 
 
 5.0 
 
 3.2 
 
 5.4 
 
 4.2 
 
 3.4 
 
 2.7 
 
 1.8 
 
 1.2 
 
 34.7 
 
 Roseburg 
 
 1.2 
 
 1.6 
 
 2.7 
 
 3.9 
 
 4.7 
 
 3.5 
 
 5.4 
 
 4.7 
 
 5.0 
 
 3.2 
 
 1.7 
 
 1.6 
 
 39.2 
 
 Middle Pacific 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Coast: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 "Red Bluff 
 
 3.0 
 
 4.6 
 
 5.4 
 
 6.1 
 
 7.0 
 
 6.9 
 
 11.0 
 
 10.7 
 
 10.1 
 
 10.5 
 
 5.9 
 
 3.6 
 
 84.8 
 
 Sacramento 
 
 1.8 
 
 3.1 
 
 3.7 
 
 4.3 
 
 4.2 
 
 5.6 
 
 5.9 
 
 5.6 
 
 6.5 
 
 7.3 
 
 3.9 
 
 2.4 
 
 54.3 
 
 San Francisco. . . 
 
 2.7 
 
 2.7 
 
 3.3 
 
 3.1 
 
 2.8 
 
 3.1 
 
 2.4 
 
 2.5 
 
 3.3 
 
 5.0 
 
 2.8 
 
 3.0 
 
 36.7 
 
 So. Pacific Coast: 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Fresno 
 
 1.8 
 
 2.8 
 
 3.0 
 
 5.6 
 
 6.0 
 
 7.0 
 
 9.1 
 
 10.2 
 
 7.6 
 
 6.7 
 
 3.8 
 
 2.2 
 
 65.8 
 
 Los Angeles 
 
 2.3 
 
 2.0 
 
 2.8 
 
 3.4 
 
 3.0 
 
 3.8 
 
 3.2 
 
 3.5 
 
 3.1 
 
 4.1 
 
 3.0 
 
 3.0 
 
 37.2 
 
 San Diego 
 
 2.9 
 
 2.7 
 
 2.5 
 
 2.7 
 
 3.3 
 
 2.8 
 
 3.2 
 
 3.3 
 
 2.9 
 
 4.3 
 
 3.2 
 
 3.7 
 
 37.5 
 
APPENDIX. G. 
 
 TWO NEW WATER WHEEL GOVERNORS. 
 
 The Glocker- White Turbine Governor. The I. P. Morris Com- 
 pany has built a governor for the Electrical Development Company 
 of Ontario., Canada, which has one novel feature-* A cross section 
 of its distinctive feature is shown in Fig. 411. 
 
 The governor ball is hollow and contains two chambers, a and b, 
 communicating with each other through a small opening, c. 
 
 The balls are partially filled with mercury which, when running 
 at normal speed, the axis of the ball being vertical, is divided be- 
 tween the two chambers. When an increase of speed throws the 
 balls outward, centrifugal force causes a flow of mercury from 
 chamber, a, to chamber, b. This raises the center of gravity of the 
 ball and increases its lever-arm about the knife edge, j, thus increas- 
 ing its effectiveness by making its movement increase in a greater 
 ratio than the speed increases. Similarly a reduction in speed causes 
 the balls to incline inward and the mercury therefore to flow from 
 chamber, b, to chamber, a, which tends to cause a still greater in- 
 ward inclination. 
 
 The charge of mercury hence increases the sensitiveness of the 
 governor balls to small changes in speed. 
 
 The centrifugal force of the balls is resisted through knife edges, 
 K, K, by a spiral spring. This movement is transmitted by levers 
 to a small pilot valve which controls a larger relay valve admitting 
 oil under 250 pounds pressure to the cylinder. The gate to be moved 
 is a cylinder gate opening upward, a force of 15,000 pounds being 
 required for the purpose. The weight of the gate is sufficient to 
 close it and the power-cylinder of the governor is therefore made 
 single acting. The entire governor is not shown as there are no 
 other unusual features. 
 
 The Allis-Chaimers Governor. This Company has recently de- 
 veloped a water wheel governor, the following description of which 
 is taken from their bulletin No. 1612: 
 
 * See "The Glocker-White Turbine Governor" by W. M. White and L. F. 
 Moody in "Power," Aug. 4, 1908. 
 
736 
 
 Two New Water Wheel Governors. 
 
 Fig. 411. Cross-Section of the Glocker-White Governor Head. 
 
The Allis-Chalmers Governors. 
 
 737 
 
 ''The Allis-Chalmers Governor is of the oil pressure type and con- 
 sists of three distinct elements : 
 
 "First Governor Stand (see Fig. 4i2) containing the apparatus 
 
 10 
 
 DISCHARGE 
 
 Fig. 412. View of the Governor Stand of the Allis Chalmer Governor. 
 
 for controlling the time of application of energy for actuating the 
 gates- 
 
 "Second Regulating Cylinder for applying energy. 
 
 "Third Pressure System for supplying energy. 
 45 
 
738 Two New Water Wheel Governor. 
 
 "The Governor Head (i), designed to be a highly sensitive yet 
 stable apparatus and driven from the Turbine Shaft by Pulley (2), 
 forms the basic governing element. Any change in its position 
 moves the Governor Collar (18), thereby shifting the Floating 
 Lever (3), and through it and its connection with the Relay (4) 
 (which momentarily acts as a stationary fulcrum) actuates the Reg- 
 ulating Valve (9). Any movement of this Regulating Valve admits 
 oil from the Pressure System to either the opening or closing side 
 of the Regulating Cylinder and thereby actuates the Turbine gates. 
 The Relay (4) forms a mechanical connection between the Regu- 
 lating Cylinder Piston and the Floating Lever (3), constituting what 
 may be termed a moving fulcrum, so that every movement of the 
 Regulating Piston shifts the fulcrum point and brings the Regu- 
 lating Valve (9) back to mid position, thereby making* the mechan- 
 ism "dead beat." If this movement is adjusted so that the position 
 of these parts have the proper relation, the Governor Collar will 
 practically retain a fixed position. 
 
 'The Regulating Cylinder cannot however, fully open or close 
 the turbine gates instantaneously and the above result can only be 
 obtained within certain limits, a difference of speed occurring be- 
 tween no load and full load that requires a certain movement or 
 travel of the Governor Collar (18). Consequently, the speed of the 
 Turbine at different gate openings will vary slightly and depend 
 upon the speed of the Governor at corresponding positions of the 
 Regulating Piston Stroke. 
 
 "Under favorable conditions (open flume and short penstocks) 
 the opening and closing time of the gates depends solely upon the 
 inertia of the moving masses and "aperiodical regulation" can be 
 obtained; i. e., the stroke of the Regulating Piston and the travel 
 of the Governor Collar correspond in time. Under favorable con- 
 ditions (long penstocks) the closing time is often so influenced by 
 the "critical time," already mentioned, and by other considerations 
 that "aperiodical regulation" is no longer practicable since a travel 
 of Governor Collar would be required that would cause a greater 
 difference in speed between no load and full load than is commer- 
 cially allowable. To meet such conditions, the '"Compensating 
 Dash Pot" (7) is utilized. 
 
 "In the diagram, Fig. 413, the full travel of the Governor Collar 
 is shown as corresponding to a speed change "x"- The Relay 
 Stroke, however, is designed so that only a portion of this travel 
 corresponding to a speed change "y" is utilized; i. e./ within this 
 
The Allis-Chalmers Governor. 
 
 739 
 
 limit the Governor, without other mechanism than the Relay, is 
 ''dead beat" and the Regulating Valve by relay action is returned 
 to mid-position after each movement. The Compensating Dash 
 Pot, (7), consists of a cylinder having an adjustable bypass and 
 containing a compound piston, with auxiliary spring device, the rod 
 of which is connected through a suitable lever to the Governor Col- 
 lar. Arranged so that its piston takes motion from the Relay actu- 
 ating shaft, is a positive displacement pump connected by a pipe to 
 the "Compensating Dash Pot" cylinder. For slight changes of 
 
 Fig. 413. Diagram of Allis-Chalmers Governor. 
 
 load, a negligible displacement of oil takes place and the Dash Pot 
 has a slight damping action only on the governor head, but when 
 any load change occurs of sufficient magnitude to produce a speed 
 variation greater than "y" as shown on the diagram, enough oil dis- 
 placement takes place to bring the auxiliary spring effect of the 
 Dash Pot piston strongly into action until the fluctuation is con- 
 trolled and the Governor Collar is again brought within the limits 
 corresponding to "y" speed variation when action ceases. By this 
 means, a governing element of maximum sensitiveness can be used 
 and the regulation of ordinary slight fluctuations made "aperiodical", 
 even under the most unfavorable conditions. These elements in 
 design, therefore, result in the Allis-Chalmers Governor operating 
 with great quickness and holding the speed variation, due to ordi- 
 nary fluctuations, within the narrowest limits, yet being absolutely 
 safe from hunting or overtravel after heavy load fluctuation, even 
 under the most difficult operating conditions." 
 
APPENDIX H. 
 
 MISCELLANEOUS TABLES. 
 
 TABLE LXXVIIL 
 
 EQUIVALENT MEASURES AND WEIGHTS OF WATER 
 AT 4 CENTIGRADE 39.2 FAHRENHEIT. 
 
 u. s. 
 
 Gallons 
 
 Imperial 
 Gallons 
 
 Liters 
 
 Cubic 
 Meters 
 
 Pounds 
 
 Cubic 
 Feet 
 
 Cubic 
 Inches 
 
 Circular 
 Inch 
 1 Foot 
 Long- 
 
 1 
 
 .83321 
 
 3.7853 
 
 .0037853 
 
 8.34112 
 
 .13368 
 
 231 
 
 24.5096 
 
 1.20017 
 
 1 
 
 4.54303 
 
 .004543 
 
 10.0108 
 
 .160439 
 
 277.274 
 
 29.4116 
 
 .264179 
 
 .22012 
 
 1 
 
 .001 
 
 2.20355 
 
 .035316 
 
 61.0254 
 
 6.4754 
 
 264.179 
 
 220.117 
 
 1000 
 
 1 
 
 2203.55 
 
 35.31563 
 
 61025.4 
 
 6475.44 
 
 .119888 
 
 .099892 
 
 .453813 
 
 .0004538 
 
 1 
 
 .0160266 
 
 27.694 
 
 2.9411 
 
 7.48055 
 
 6.23287 
 
 28.3161 
 
 .0283101 
 
 62.3961 
 
 1 
 
 1728 
 
 183.346 
 
 .0043^9 
 
 .003607 
 
 .0163866 
 
 .0000164 
 
 .0361089 
 
 .0005787 
 
 1 
 
 .10613 
 
 .0408 
 
 .034 
 
 .1544306 
 
 .0001544 
 
 .340008 .005454 
 
 9.4224 
 
 1 
 
 TABLE LXXIX. 
 
 EQUIVALENT UNITS OF ENERGY 
 
 WORK 
 
 HEAT 
 
 ELEC- 
 TRIC 
 
 HYDRAULICS 
 
 'S 
 
 II 
 
 Foot Ton 
 2240 Lbs. 
 
 Kilogram 
 Meter 
 
 is 
 
 
 EHS 
 
 * 
 
 65 il 
 
 e 
 
 "c S 
 wg 
 'E^ bt 
 
 Sti.2 
 
 oc3 
 
 Volt 
 Columb 
 
 d 
 
 ^3 
 
 8* 
 
 feO 
 
 si 
 S.8 
 
 11 
 11 
 
 PL|O 
 
 ^rtf 
 10 
 
 PnU 
 
 1 
 
 .000446 
 
 1383 
 
 .000138 
 
 .001285 
 
 .000324 
 
 .000377 
 
 .12 
 
 .016 
 
 .0519 
 
 .0069 
 
 2240. 
 
 1 
 
 309.688 
 
 .3097 
 
 2.8785 
 
 .7262 
 
 .8439 
 
 268.817 
 
 35.906 
 
 116.414 
 
 15.456 
 
 7.233 
 
 .00323 
 
 1 
 
 .001 
 
 .0093 
 
 .00235 
 
 .00272 
 
 .8673 
 
 .1159 
 
 .3755 
 
 .0499 
 
 7233.18 
 
 3.2291 
 
 1000 
 
 1 
 
 9.302 
 
 2.3452 
 
 2.7241 
 
 867.303 
 
 115.928 
 
 375.516 
 
 49.90 
 
 778. 
 
 .3474 
 
 107.562 
 
 .1076 
 
 1 
 
 .2520 
 
 .2929 
 
 93.28 
 
 12.448 
 
 40.394 
 
 5.368 
 
 3085.34 
 
 1.3774 
 
 426-394 
 
 .4264 
 
 3.9683 
 
 1 
 
 1.1623 
 
 370.17 
 
 49.396 
 
 160.29 
 
 21 . 221 
 
 2655.4 
 
 1.1854 
 
 371.123 
 
 .3671 
 
 3.414 
 
 .8603 
 
 1 
 
 318.39 
 
 42-486 
 
 137.87 
 
 183.23 
 
 8.341 
 
 .00372 
 
 1.1532 
 
 .00115 
 
 .1072 
 
 .0027 
 
 .00314 
 
 1 
 
 .1334 
 
 .4as 
 
 .05754 
 
 62.39 
 
 .02785 
 
 8.6257 
 
 .00863 
 
 .0803 
 
 .00202 
 
 .02353 
 
 7.48 
 
 1 
 
 3.245 
 
 .4312 
 
 19.259 
 
 .00859 
 
 2.6626 
 
 .00266 
 
 .0248 
 
 .00624 
 
 .00726 
 
 2.309 
 
 .3082 
 
 1 
 
 .13-9 
 
 144.92 
 
 .0647 
 
 20.036 
 
 .02004 
 
 .1863 
 
 .04712 
 
 .05457 
 
 17.37 
 
 2.318 
 
 7.524 
 
 1 
 
Theoretical Jet Velocities. 
 
 74 1 
 
 TABLE LXXX. 
 
 Velocities, in feet per second, due to Heads from to 50 feet. 
 
 Head 
 in 
 feet. 
 
 .0 
 
 .1 
 
 .2 
 
 .3 
 
 .4 
 
 .5 
 
 .6 
 
 .7 
 
 .8 
 
 .9 
 
 
 
 0.000 
 
 2.536 
 
 3.587 
 
 4.393 
 
 5.072 
 
 5.671 
 
 6.212 
 
 6.710 
 
 7.178 
 
 7.609 
 
 1 
 
 8.020 
 
 8.412 
 
 8.786 
 
 9.144 
 
 9.490 
 
 9.823 
 
 10.145 
 
 10.457 
 
 10.760 
 
 11.055 
 
 2 
 
 11.342 
 
 11.622 
 
 11.896 
 
 12.163 
 
 12.425 
 
 12.681 
 
 12.932 
 
 13.179 
 
 13.420 
 
 13.658 
 
 3 
 
 13.891 
 
 14.121 
 
 14.347 
 
 14.569 
 
 14.789 
 
 15.004 
 
 15.217 
 
 15.427 
 
 15.634 
 
 15.839 
 
 4 
 
 16.040 
 
 16.240 
 
 16.437 
 
 16.631 
 
 16.823 
 
 17.013 
 
 17.201 
 
 17.387 
 
 17.571 
 
 17.753 
 
 5 
 
 17.934 
 
 18.112 
 
 18.289 
 
 18.464 
 
 18.637 
 
 18.809 
 
 18.979 
 
 19.148 
 
 19.315 
 
 19.481 
 
 6 
 
 19.645 
 
 19.808 
 
 19.970 
 
 20.131 
 
 20.290 
 
 20.448 
 
 20.604 
 
 20.760 
 
 20.914 
 
 21.067 
 
 7 
 
 21.219 
 
 21.370 
 
 21.520 
 
 21.669 
 
 21.817 
 
 21.964 
 
 22.110 
 
 22.255 
 
 22.399 
 
 22.542 
 
 8.'.'.'.'. 
 
 22.685 
 
 22.826 
 
 22.966 
 
 23.106 
 
 23.245 
 
 23.383 
 
 23.520 
 
 23.656 
 
 23.792 
 
 23.927 
 
 9 
 
 24.061 
 
 24.194 
 
 24.326 
 
 24.458 
 
 24.589 
 
 24.720 
 
 24.850 
 
 24.979 
 
 25.107 
 
 25.235 
 
 10 
 
 25.362 
 
 25.489 
 
 25.614 
 
 25.740 
 
 25.864 
 
 25.988 
 
 26.112 
 
 26.235 
 
 26.357 
 
 26.479 
 
 11 
 
 26.600 
 
 26.721 
 
 26.841 
 
 26.960 
 
 27.079 
 
 27.198 
 
 27.316 
 
 27.433 
 
 27.550 
 
 27.667 
 
 12 
 
 27.783 
 
 27.898 
 
 28.013 
 
 28.128 
 
 28.242 
 
 28.356 
 
 28.469 
 
 28.582 
 
 28.694 
 
 28.806 
 
 18 
 
 28.917 
 
 29.028 
 
 29.139 
 
 29.249 
 
 29.359 
 
 29.468 
 
 29.577 
 
 29.686 
 
 29.794 
 
 29.901 
 
 14 
 
 30.009 
 
 30.116 
 
 30.222 
 
 .30.329 
 
 30.435 
 
 30.540 
 
 30.645 
 
 30.750 
 
 30.854 
 
 30.958 
 
 15 
 
 31.062 
 
 31.165 
 
 31.268 
 
 31.371 
 
 31.474 
 
 31.576 
 
 31.677 
 
 31.779 
 
 31.880 
 
 31.980 
 
 16 
 
 32.081 
 
 32.181 
 
 32.281 
 
 32.380 
 
 32.480 
 
 32.579 
 
 32.677 
 
 32.775 
 
 32.873 
 
 32.971 
 
 17 
 
 33.068 
 
 33.165 
 
 33.262 
 
 83.359 
 
 33.455 
 
 33.551 
 
 33.647 
 
 33.742 
 
 33.837 
 
 33.932 
 
 18 
 
 34.027 
 
 34.121 
 
 34.215 
 
 34.309 
 
 34.403 
 
 34.496 
 
 34.589 
 
 34.682 
 
 34.775 
 
 34.867 
 
 19 
 
 34.959 
 
 35.051 
 
 35.143 
 
 35.234 
 
 35.325 
 
 35.416 
 
 35.507 
 
 35.597 
 
 35.688 
 
 35.778 
 
 20 
 
 35.867 
 
 35.957 
 
 36.046 
 
 36.135 
 
 36.224 
 
 36.313 
 
 36.401 
 
 36.490 
 
 36.578 
 
 36.666 
 
 21 
 
 36.753 
 
 36.841 
 
 36.928 
 
 37.015 
 
 37.102 
 
 37.188 
 
 37.275 
 
 37.361 
 
 37.447 
 
 37.532 
 
 22 
 
 37.618 
 
 37.703 
 
 37.789 
 
 37.874 
 
 37.959 
 
 38.043 
 
 38.128 
 
 38.212 
 
 38.296 
 
 38.380 
 
 23 
 
 38.464 
 
 38.547 
 
 38.630 
 
 38.714 
 
 38.797 
 
 38.879 
 
 38.962 
 
 39.014 
 
 39.127 
 
 39.209 
 
 24 
 
 39.291 
 
 39.373 
 
 39.454 
 
 39.536 
 
 39.617 
 
 39.698 
 
 39.779 
 
 39.860 
 
 39.940 
 
 40.021 
 
 25 
 
 40.101 
 
 40.181 
 
 40.261 
 
 40.341 
 
 40.421 
 
 40.500 
 
 40.579 
 
 40.659 
 
 40.738 
 
 40.816 
 
 26 
 
 40.895 
 
 40.974 
 
 41.052 
 
 41.130 
 
 41.209 
 
 41.287 
 
 41.364 
 
 41 .442 
 
 41.520 
 
 41.597 
 
 27 
 
 41.674 
 
 41.751 
 
 41.828 
 
 41.905 
 
 41.982 
 
 42.058 
 
 42.135 
 
 42.211 
 
 42.287 
 
 42.363 
 
 28 
 
 42.439 
 
 42.515 
 
 42.590 
 
 42.666 
 
 42.741 
 
 42.816 
 
 42.891 
 
 42.966 
 
 43.041 
 
 43.116 
 
 29 
 
 43.190 
 
 43.264 
 
 43.839 
 
 43.413 
 
 43.487 
 
 43.561 
 
 43.635 
 
 43.708 
 
 43.782 
 
 43.855 
 
 30 
 
 43.928 
 
 44.002 
 
 44.075 
 
 44.148 
 
 44.220 
 
 44.293 
 
 44.366 
 
 44.438 
 
 44.510 
 
 44.582 
 
 31 
 
 44.655 
 
 44.727 
 
 44.798 
 
 44.870 
 
 44.942 
 
 45.013 
 
 45.085 
 
 45.156 
 
 45.227 
 
 45.298 
 
 3-2 
 
 45.369 
 
 45.440 
 
 45.511 
 
 4?,. 581 
 
 45.652 
 
 45.722 
 
 45.792 
 
 45.863 
 
 45.933 
 
 46.003 
 
 33 
 
 46.073 
 
 46.142 
 
 46.212 
 
 46.281 
 
 46.351 
 
 46.420 
 
 46.489 
 
 46.559 
 
 46.628 
 
 46.697 
 
 31 
 
 46.765 
 
 46.834 
 
 46.903 
 
 46.971 
 
 47.040 
 
 47.108 
 
 47.176 
 
 47.244 
 
 47.312 
 
 47.380 
 
 85 
 
 47.448 
 
 47.516 
 
 47.584 
 
 47.651 
 
 47.719 
 
 47.786 
 
 47.853 
 
 47.920 
 
 47.987 
 
 48.054 
 
 36 
 
 48.121 
 
 48.188 
 
 48.255 
 
 48.321 
 
 48.388 
 
 48.454 
 
 48.521 
 
 48.487 
 
 48.653 
 
 48.719 
 
 37 
 
 48.785 
 
 48.851 
 
 48.917 
 
 48.982 
 
 49.048 
 
 49.113 
 
 49.179 
 
 49.244 
 
 49.310 
 
 49.375 
 
 38 
 
 49.440 
 
 49.505 
 
 49.570 
 
 49.635 
 
 49.699 
 
 49.764 
 
 49.829 
 
 49.893 
 
 49.958 
 
 50.022 
 
 39 
 
 50.086 
 
 50.150 
 
 50.214 
 
 50.278 
 
 50.342 
 
 5D.406 
 
 50.470 
 
 50.534 
 
 50.597 
 
 50.661 
 
 40 
 
 50.724 
 
 50.788 
 
 50.851 
 
 50.914 
 
 50.977 
 
 51.040 
 
 51.103 
 
 51.166 
 
 51.229 
 
 51.292 
 
 41 
 
 51.354 
 
 51.417 
 
 51.479 
 
 51.542 
 
 51.604 
 
 51.667 
 
 51.729 
 
 51.791 
 
 51.858 
 
 51.915 
 
 42 
 
 51.977 
 
 52.039 
 
 52.100 
 
 52.162 
 
 52.224 
 
 52.285 
 
 52.347 
 
 52.408 
 
 52.470 
 
 52.531 
 
 43 
 
 52.592 
 
 52.653 
 
 52.714 
 
 52.775 
 
 52.836 
 
 fi2.87 
 
 w.958 
 
 53.018 
 
 53.079 
 
 53.134 
 
 44 
 
 53.200 
 
 53.26U 
 
 53.321 
 
 53.381 
 
 53.441 
 
 53.501 
 
 53.561 
 
 53.621 
 
 53.681 
 
 53.741 
 
 4) 
 
 53.801 
 
 53.861 
 
 53.921 
 
 53.980 
 
 54.040 
 
 54.099 
 
 54.159 
 
 54.218 
 
 54.277 
 
 54.336 
 
 46 
 
 54.396 
 
 54.455 
 
 54.514 
 
 54.573 
 
 54.632 
 
 54.690 
 
 54.749 
 
 54.808 
 
 54.867 
 
 54.925 
 
 47 
 
 54.984 
 
 55.042 
 
 55.101 
 
 55.159 
 
 55.217 
 
 55.275 
 
 55.334 
 
 55.392 
 
 55.450 
 
 55.508 
 
 48 
 
 55.56H 
 
 55.623 
 
 55.681 
 
 55.739 
 
 55.797 
 
 55.854 
 
 55.912 
 
 55.969 
 
 56.027 
 
 56.084 
 
 49 
 
 56.141 
 
 56.199 
 
 56.256 
 
 56.313 
 
 56.370 
 
 56.427 
 
 56.484 
 
 56.541 
 
 56.598 
 
 56.655 
 
742 
 
 Miscellaneous Tables. 
 
 TABLE LXXXI. 
 
 Table of three-halves (f ) power of. number.* 
 
 Head 
 
 
 
 
 
 
 
 
 
 
 
 in 
 
 .0. 
 
 .1 
 
 .2 
 
 .3 
 
 .4 
 
 .5 
 
 .6 
 
 .7 
 
 .8 
 
 .9 
 
 feet. 
 
 
 
 
 
 
 
 
 
 
 
 0... 
 
 0.0000 
 
 0.0316 
 
 0.0894 
 
 0.1643 
 
 0.2530 
 
 0.3536 
 
 0.4648 
 
 0.5857 
 
 0.7155 
 
 0.8538 
 
 1.... 
 
 1.0000 
 
 1.1537 
 
 1.3145 
 
 1.4822 
 
 1.6565 
 
 1.8371 
 
 2.0238 
 
 2.2165 
 
 2.4150 
 
 2.6190 
 
 2 
 
 2.8284 
 
 3.0432 
 
 3.2531 
 
 3.4881 
 
 3.7181 
 
 3.9529 
 
 4.1924 
 
 4.4366 
 
 4.6853 
 
 4.9385 
 
 3.... 
 
 5.1962 
 
 5.4581 
 
 5.7243 
 
 5.9947 
 
 6.2693 
 
 6.5479 
 
 6.8305 
 
 7.1171 
 
 7.4070 
 
 7.7019 
 
 4 
 
 8.0000 
 
 8.3019 
 
 8.6074 
 
 8.9167 
 
 9.2295 
 
 9.5459 
 
 9.8659 
 
 10.1894 
 
 10.5163 
 
 10.8466 
 
 5.... 
 
 11.1803 
 
 11.5174 
 
 11 8578 
 
 12.2015 
 
 12.5485 
 
 12.8986 
 
 13.2520 
 
 13.6086 
 
 13.9682 
 
 14.3311 
 
 6.... 
 
 14.6960 
 
 15.0659 
 
 15.4379 
 
 15.8129 
 
 16.1909 
 
 16.5718 
 
 16.9557 
 
 17.3425 
 
 17.7322 
 
 18.1248 
 
 
 18.5203 
 
 18.9185 
 
 19.3196 
 
 19.7235 
 
 20.1302 
 
 20.5396 
 
 20.9518 
 
 2i.;i66 
 
 21.7842 
 
 22.2045 
 
 s'.'.'. 
 
 22.6274 
 
 23.0530 
 
 23.4812 
 
 23.9121 
 
 24 3455 
 
 24.7815 
 
 25.2202 
 
 25.6613 
 
 26.1050 
 
 26.5.123 
 
 9.... 
 
 27.0000 
 
 27.4512 
 
 27.9050 
 
 28.3612 
 
 28.8199 
 
 29.2810 
 
 29.7445 
 
 30.2105 
 
 30.6789 
 
 31.1496 
 
 10.... 
 
 31.6228 
 
 32.0983 
 
 32.5762 
 
 33.0564 
 
 33.5390 
 
 31.0239 
 
 34.5111 
 
 35.0006 
 
 35.4924 
 
 35.9865 
 
 11.... 
 
 36.4829 
 
 36 9815 
 
 37.4824 
 
 37.9855 
 
 38.4908 
 
 38.9984 
 
 39 5082 
 
 40.0202 
 
 40.5343 
 
 41 0507 
 
 1*.... 
 
 41.5692 
 
 42.0910 
 
 42.6128 
 
 43.138 s * 
 
 43.6648 
 
 44.1952 
 
 44.7256 
 
 45.2600 
 
 45.7944 
 
 46.3332 
 
 13.... 
 
 4S.8720 
 
 47.4148 
 
 47.9576 
 
 48.5048 
 
 49.0520 
 
 49.6032 
 
 50.1544 
 
 50.7096 
 
 51.2648 
 
 51.*240 
 
 14 
 
 52.3832 
 
 52.9464 
 
 53.5096 
 
 54.0768 
 
 54.6440 
 
 55.2152 
 
 55.7864 
 
 56.3616 
 
 56. 9368 
 
 57.5156 
 
 15. . . . 
 
 58.C944 
 
 58.6776 
 
 59.^608 
 
 59.8472 
 
 60.4336 
 
 61.0244 
 
 61.6152 
 
 62.2096 
 
 62.8040 
 
 63.4020 
 
 16.... 
 
 64.0000 
 
 64.6020 
 
 65.2040 
 
 65.8096 
 
 6B.4152 
 
 67.0244 
 
 67.6336 
 
 68.2464 
 
 H8.S592 
 
 69.4760 
 
 17 
 
 70.0928 
 
 70.7132 
 
 71.3336 
 
 71.9572 
 
 75.5808 
 
 73.2084 
 
 73.H360 
 
 74.4672 
 
 75.0984 
 
 75.7328 
 
 18.... 
 
 76.3672 
 
 77.0056 
 
 77.6440 
 
 78.2856 
 
 78.9272 
 
 79.5724 
 
 80.2176 
 
 80.8684 
 
 81.5152 
 
 82.1672 
 
 19.... 
 
 82.8192 
 
 83.4748 
 
 84 . 1304 
 
 84.7892 
 
 85.4480 
 
 86.1104 
 
 86.7728 
 
 87.43^4 
 
 88.104(1 
 
 88.7732 
 
 20.... 
 
 89.4424 
 
 90.1152 
 
 90.7880 
 
 91.4636 
 
 92.1392 
 
 92.8184 
 
 93.4976 
 
 94.180a 
 
 94.8624 
 
 95.5484 
 
 21.... 
 
 96.2344 
 
 96 9232 
 
 97.6120 
 
 98.3044 
 
 98.9968 
 
 99.6924 
 
 100.3880 
 
 101.0868 
 
 101.7856 
 
 102.4872 
 
 22.... 
 
 103.1883 
 
 103.8940 
 
 104.600S 
 
 105.3076 
 
 106.0160 
 
 106.7276 
 
 107.4392 
 
 108.1540 
 
 108 8688 
 
 109 .58(54 
 
 23. . . . 
 
 110.3040 
 
 111.0248 
 
 111.7456 
 
 112.4700 
 
 113.1944 
 
 113 9216 
 
 114.6488 
 
 115.3788 
 
 116.1088 
 
 116.8420 
 
 24.... 
 
 117. 5752 
 
 118.3128 
 
 119 0496 
 
 119.7876 
 
 1^0.5272 
 
 121.2696 
 
 122.0120 
 
 122.7576 
 
 123.5032 
 
 124.2516 
 
 25.... 
 
 125.0000 
 
 125.7516 
 
 126 5032 
 
 127.2576 
 
 128.0120 
 
 128.7706 
 
 129.5292 
 
 130.2876 
 
 131.0480 
 
 131.8112 
 
 26.... 
 
 132.5744 
 
 133.3408 
 
 134.1072 
 
 134.8764 
 
 135.6456 
 
 136.4180 
 
 13,' 1904 
 
 137.965-2 
 
 188. 7400 
 
 139.5180 
 
 27.... 
 
 140.2960 
 
 141.0768 
 
 I41.a576 
 
 142.6416 
 
 143.4256 
 
 144 2120 
 
 144.9984 
 
 145.7880 
 
 146.5776 
 
 147 3700 
 
 28.... 
 
 148.1624 
 
 148.9572 
 
 149.7520 
 
 150.5500 
 
 151. 34H) 
 
 152.1488 
 
 152.9496 
 
 153.7532 
 
 154.556* 
 
 155.3632 
 
 29.... 
 
 156.1696 
 
 156.9788 
 
 157.7880 
 
 158.6000 
 
 159.4120 
 
 160.2268 
 
 161.0416 
 
 161.858K 
 
 162.6760 
 
 163.4W4 
 
 30.... 
 
 164.3168 
 
 165.1396 
 
 165.9624 
 
 166.7884 
 
 167.6144 
 
 168.4428 
 
 169.2712 
 
 170.1020 
 
 170.9328 
 
 171.7668 
 
 81.... 
 
 172.6008 
 
 173.4372 
 
 174.2736 
 
 175.1128 
 
 175.9520 
 
 176.7940 
 
 177.6360 
 
 178.4804 
 
 179.3-.MH 
 
 180.1720 
 
 32.... 
 
 181.0192 
 
 181.8692 
 
 182.7192 
 
 183.5716 
 
 184.4240 
 
 185.2792 
 
 186.1344 
 
 186.99:iO 
 
 187.8496 
 
 188.7100 
 
 33.... 
 
 189.5701 
 
 1 90. 4336 
 
 191.2968 
 
 192.1624 
 
 93.0280 
 
 193.8960 
 
 194.7640 
 
 195.6318 
 
 19H.5056 
 
 197.3788 
 
 34.... 
 
 198.2520 
 
 199.1460 
 
 200.04dO 
 
 200 9008 
 
 201.7616 
 
 24B.H424 
 
 20:5.5232 
 
 204.4068 
 
 205.29H4 
 
 206.1764 
 
 35.... 
 
 207.0624 
 
 207.9512 
 
 208.8400 
 
 209.7312 
 
 210.6224 
 
 211.5204 
 
 212.4184 
 
 213.3104 
 
 214.2U24 
 
 2:5.1012 
 
 36.... 
 
 216.0000 
 
 216.9012 
 
 217.8024 
 
 218.7060 
 
 219.6096 
 
 220.5760 
 
 221.4224 
 
 222.3312 
 
 223.2400 
 
 224.1512 
 
 37. . . . 
 
 225.0624 
 
 225.976(1 
 
 226.8896 
 
 227.8056 
 
 228.7216 
 
 299.6404 
 
 230.5592 
 
 231.4MX) 
 
 232.40(1* 
 
 233.3244 
 
 38.... 
 
 234.2480 
 
 235.1736 
 
 236.0992 
 
 237.0276 
 
 237.9560 
 
 2*38.8868 
 
 239.8176 
 
 240.7508 
 
 241.^840 
 
 242.6HI6 
 
 39.... 
 
 243.5552 
 
 244.4932 
 
 245.4312 
 
 ^46.3712 
 
 247.3112 
 
 248.2540 
 
 249.196S 
 
 250.1420 
 
 251.0S7 2 
 
 252. OH 18 
 
 40.... 
 
 252.9824 
 
 253.9320 
 
 254.8816 
 
 255.8340 256.7864 
 
 257.7412 
 
 258.6960 
 
 259.6528 
 
 260.KOJ6 
 
 261. SOS* 
 
 41.... 
 
 262.5280 
 
 263.4896 
 
 264.4512 
 
 265.41521 266 3792 
 
 ?R7.345li 
 
 268.3120 
 
 269.2804 
 
 27'0.24H8 
 
 271 2200 
 
 42.... 
 
 272.1912 
 
 273.1644 
 
 274.1316 
 
 275.1132 
 
 276.0888 
 
 277.0672 
 
 278.0456 
 
 279 6252 
 
 2*0.0048 
 
 280. VJ87 2 
 
 43.... 
 
 281.9696 
 
 282.9544 
 
 283.93*2 
 
 284.^264 
 
 285.9136 
 
 286.9028 
 
 287.8920 
 
 288 8836 
 
 289.8752 
 
 29<l. S: 92 
 
 44.... 
 
 291.8632 
 
 292.8597 
 
 293. a5K 
 
 294.8536 
 
 295.8520 
 
 296.8528 
 
 297 8536 
 
 298.8564 
 
 299.8592 
 
 300.W540 
 
 45.... 
 
 301.8688 
 
 302.8764 
 
 303.8840 
 
 304.8936 
 
 305.9032 
 
 306.9148 
 
 307.9264 
 
 308.9404 
 
 309.9544 
 
 310.9708 
 
 46... 
 
 311.9872 
 
 313.0056 
 
 314.0240 
 
 315.0448 
 
 316.0656 
 
 317.0877 
 
 318.1112 
 
 319.0556 
 
 320.0000 
 
 321.1080 
 
 47.... 
 
 322.2160 
 
 323.2452 
 
 324.2744 
 
 325.3060 
 
 326.3376 
 
 327.3716 
 
 328.4056 
 
 3-29.4416 
 
 3H0.4776 
 
 331.5156 
 
 48 
 
 332. 5536 
 
 333.5927 
 
 334.6383 
 
 335.4753 
 
 336.7188 
 
 337.7588 
 
 338.8051 
 
 349.8529 
 
 840.8972 
 
 341.9479 
 
 49. ... 
 
 343.00011 
 
 344.0486 
 
 345.0986 
 
 34B.1500 
 
 347.2079 
 
 348.2622 
 
 349.3179 
 
 350.3750 
 
 351.4336 
 
 352.4-8(5 
 
 50.... 
 
 353.55(10 
 
 354.6128 
 
 355.6720 
 
 356.7376 
 
 357.7996 
 
 358 8681 
 
 359.9329 
 
 360.9992 
 
 362.0719 
 
 363.1409 
 
 'From Water-Supply and Irrigation Paper No. IbO. 
 
Three-Halves Powers. 
 
 743 
 
 TABLE LXXXI Continued. 
 Table of three-halves ( I ) power of number. 
 
 Head 
 
 
 
 
 
 
 
 
 
 
 
 in 
 
 .0 
 
 .1 
 
 2 
 
 .3 
 
 .4 
 
 .5 
 
 .6 
 
 ^ 
 
 .8 
 
 .9 
 
 feet. 
 
 
 
 
 
 
 
 
 
 
 
 51... 
 
 364.2114 
 
 365.2832 
 
 366.3564 
 
 367.4311 
 
 368..J020 
 
 369 5794 
 
 370.6582 
 
 371.7*33 
 
 372 8149 
 
 373.8927 
 
 52.... 
 
 374.9772 
 
 376.0578 
 
 377.1397 
 
 378.2331 
 
 379.3078 
 
 380.3940 
 
 381.4815 
 
 382.5708 
 
 383.6606 
 
 384.7522 
 
 M.... 
 
 3&>.8453 
 
 386.9343 
 
 3H8.0301 
 
 389.1219 
 
 390.2205 
 
 391.3150 
 
 392.4163 
 
 393.5136 
 
 394.6122 
 
 395.7122 
 
 54.... 
 
 396.8136 
 
 397. 9163 
 
 399.0204 
 
 40 J. 1258 
 
 401.2326 
 
 402.3408 
 
 403.4448 
 
 404.5557 
 
 405.6679 
 
 406.7759 
 
 55. . . . 
 
 407.8855 
 
 409.0017 
 
 410.1139 
 
 411.2273 
 
 412.3477 
 
 413.4639 
 
 414.5814 
 
 415.7002 
 
 416.8204 
 
 417.9419 
 
 56. . . . 
 
 419.0648 
 
 420.1833 
 
 421.3089 
 
 422.4257 
 
 423.5583 
 
 424.6879 
 
 425.8131 
 
 426.9453 
 
 428.0732 
 
 429.2080 
 
 57. . . . 
 
 430.3386 
 
 431.4704 
 
 432.6036 
 
 433.7380 
 
 434.8738 
 
 436.0110 
 
 437.1494 
 
 438.2892 
 
 439.4302 
 
 440.5726 
 
 58.... 
 
 441.7106 
 
 442.8556 
 
 443.9961 
 
 445.1438 
 
 446.2869 
 
 447.4372 
 
 448.5830 
 
 449.7300 
 
 450.8842 
 
 452.0359 
 
 59.... 
 
 454.0849 
 
 455.3271 
 
 455.4907 
 
 456.6455 
 
 457.8017 
 
 458.9592 
 
 460.1179 
 
 4*1.2720 
 
 462.4334 
 
 463.5960 
 
 60.... 
 
 464.7540 
 
 465.919,' 
 
 467.0797 
 
 468.2475 
 
 469.4106 
 
 470.5750 
 
 471.7467 
 
 472.9J37 
 
 474.0819 
 
 475.2514 
 
 61.... 
 
 476.4222 
 
 477.3942 
 
 478.7676 
 
 479.9422 
 
 481.1181 
 
 482.2891 
 
 483.4676 
 
 484.6473 
 
 485.8222 
 
 487.0044 
 
 62.... 
 
 488.1880 
 
 489.3666 
 
 490.5465 
 
 491.7339 
 
 492.9163 
 
 494.1000 
 
 495.2912 
 
 496.4774 
 
 497.6648 
 
 498.8536 
 
 83.... 
 
 500.0436 
 
 501.2348 
 
 502.4273 
 
 503.6211 
 
 504.8161 
 
 506. 00*51 
 
 507.2036 
 
 508.4024 
 
 509.5961 
 
 510.7974 
 
 64.... 
 
 512.0000 
 
 513.1974 
 
 514.3960 
 
 515.6024 
 
 516. 8035 
 
 518.0059 
 
 519.2160 
 
 520.4209 
 
 521.6270 
 
 522.8344 
 
 (55. . . . 
 
 524.0430 
 
 525.2528 
 
 526.4639 
 
 527.6762 
 
 528.8898 
 
 530.1046 
 
 531 3120 
 
 532.5313 
 
 533.7498 
 
 534.9630 
 
 66.... 
 
 536.1840 
 
 537.2996 
 
 538.6230 
 
 539.8411 
 
 541.0870 
 
 542.2875 
 
 543.5092 
 
 544.7389 
 
 545.9630 
 
 547.18 C 4 
 
 H7 
 
 548.4151 
 
 549.6429 
 
 550.8720 
 
 552.1022 
 
 553.3337 
 
 554.56r>5 
 
 555.6179 
 
 557.0356 
 
 558.2652 
 
 559.5027 
 
 68.... 
 
 560.7416 
 
 501.974H 
 
 563.2160 
 
 564.4516 
 
 56 >. 6953 
 
 56(5.9334 
 
 568.1795 
 
 r>69.4199 
 
 570.6616 
 
 571.9113 
 
 69.... 
 
 573.1554 
 
 574.4006 
 
 575.6473 
 
 576.8947 
 
 578.1436 
 
 579.3937 
 
 580.6449 
 
 581.8974 
 
 583.1510 
 
 584.4059 
 
 70.... 
 
 585.6620 
 
 586.9122 
 
 588.1707 
 
 589.4303 
 
 590.6841 
 
 591.9462 
 
 593.2023 
 
 594.4668 
 
 595.7253 
 
 596.9921 
 
 71.... 
 
 598.2531 
 
 599.5152 
 
 600.7856 
 
 602.0500 
 
 603.3157 
 
 604.5825 
 
 605.8505 
 
 607.1197 
 
 608.3901 
 
 609.6616 
 
 72.... 
 
 610.9344 
 
 612.2083 
 
 613.4340 
 
 614.7596 
 
 616.0371 
 
 617.3085 
 
 618.5883 
 
 619.8692 
 
 621.0841 
 
 622.4274 
 
 73.... 
 
 623. 71 20 
 
 624.9903 
 
 626.2699 
 
 627.5579 
 
 628.8398 
 
 630.1302 
 
 631.4144 
 
 632.6997 
 
 633.9862 
 
 635.2813 
 
 74.... 
 
 636.5702 
 
 637.8602 
 
 639.1513 
 
 640.4437 
 
 641.7372 
 
 643.0318 
 
 644.3276 
 
 645.6246 
 
 646.9152 
 
 648 2145 
 
 75.... 
 
 649.5150 
 
 6.50.8166 
 
 652.1118 
 
 653.4157 
 
 654.7208 
 
 656.0195 
 
 657.3268 
 
 658.6278 
 
 659.9375 
 
 661.2408 
 
 76 
 
 662.5452 
 
 663.8583 
 
 665.1650 
 
 666.4728 
 
 667.7894 
 
 669.0996 
 
 670.4108 
 
 671.7131 
 
 673.0368 
 
 674.3514 
 
 
 675.6673 
 
 676.9*42 
 
 677.2043 
 
 679.6216 
 
 680.9419 
 
 682.26&J 
 
 683.5784 
 
 684.9021 
 
 686.2271 
 
 687.5454 
 
 78!!! 
 
 WR.8788 
 
 690.2009 
 
 691.5226 
 
 692.8532 
 
 694.1771 
 
 695.5100 
 
 696.8361 
 
 698.8361 
 
 699.1713 
 
 700.8292 
 
 79.... 
 
 702.1599 
 
 703.4995 
 
 704.8324 
 
 706.1665 
 
 707.5016 
 
 708.8379 
 
 710.1752 
 
 711.. '137 
 
 712.8534 
 
 714.1941 
 
 80.... 
 
 715.5360 
 
 716.8789 
 
 718.2230 
 
 719.5683 
 
 720.9146 
 
 722.2540 
 
 723.602ti 
 
 724.9523 
 
 726.2950 
 
 727.6496 
 
 81.... 
 
 729.0000 
 
 730.3460 
 
 731.7613 
 
 733.0495 
 
 7^4.3989 
 
 735.7575 
 
 737.1091 
 
 738.4699 
 
 739.8237 
 
 741.1876 
 
 
 742.5340 
 
 743.K998 
 
 745.2580 
 
 746.6173 
 
 747.9776 
 
 749.3392 
 
 750.7018 
 
 752.0655 
 
 753.4303 
 
 754.1962 
 
 83!!! 
 
 756.1632 
 
 757. 53 12 
 
 758.9004 
 
 760.2624 
 
 761.6338 
 
 763.01)63 
 
 764.3798 
 
 765.7461 
 
 767.1219 
 
 768.4904 
 
 84.... 
 
 T.iQ.8684 
 
 771.2474 
 
 772.6192 
 
 774.0004 
 
 775.3743 
 
 776.7493 
 
 778.1338 
 
 779.5110 
 
 780.8892 
 
 782.2770 
 
 85.... 
 
 783.6575 
 
 785.0389 
 
 686.4215 
 
 787.8052 
 
 789.1984 
 
 790.5843 
 
 791.9712 
 
 793.3591 
 
 794.7482 
 
 796.1383 
 
 86.... 
 
 797.5296 
 
 798.9219 
 
 800.3066 
 
 801.7011 
 
 803.0966 
 
 804.4932 
 
 805.8909 
 
 807.2810 
 
 808.680* 
 
 810.0833 
 
 87. . . . 
 
 811.47'51 
 
 812.8781 
 
 814.2736 
 
 815.6788 
 
 817.0763 
 
 818.4837 
 
 819.8834 
 
 821.2929 
 
 822.6947 
 
 824.1064 
 
 88.... 
 
 H25.5704 
 
 826.9154 
 
 828.3-214 
 
 829.7374 
 
 831.1456 
 
 S: .V>4<) 
 
 833.9652 
 
 835.3765 
 
 836.7890 
 
 838.2025 
 
 89.... 
 
 839.6171 
 
 S41. 0327 
 
 842.4494 
 
 843.8671 
 
 845.2859 
 
 846.7058 
 
 848.1267 
 
 849.5487 
 
 850.9627 
 
 X52.3868 
 
 90. . . . 
 
 853.8120 
 
 855.2382 
 
 856.6564 
 
 858.0847 
 
 859.5051 
 
 860.9355 
 
 862.3670 
 
 863.7905 
 
 865.2241 
 
 8B6.6496 
 
 91.... 
 
 868.0763 
 
 869.5130 
 
 870.9417 
 
 872.3806 
 
 873.8114 
 
 875.2432 
 
 876.6761 
 
 878.1192 
 
 879.5541 
 
 880.9901 
 
 92.... 
 
 882.4272 
 
 883.8652 
 
 885.3044 
 
 886.7445 
 
 888.1857 
 
 889.6280 
 
 891.0712 
 
 892.5156 
 
 893.9609 
 
 895.4073 
 
 93 
 
 896.8518 
 
 898.3032 
 
 899.7528 
 
 901.1946 
 
 902.6456 
 
 904.09X2 
 
 905.5519 
 
 906.9972 
 
 908.4530 
 
 909.9097 
 
 94.... 
 
 911.3582 
 
 912.8170 
 
 914.2675 
 
 915.7284 
 
 917.1809 
 
 918.643'J 
 
 920.0985 
 
 9-21.5541 
 
 923.0202 
 
 924.4778 
 
 95.... 
 
 925.9365 
 
 927.4056 
 
 928.8664 
 
 930.3281 
 
 931.7908 
 
 933.2642 
 
 934.7290 
 
 936.1948 
 
 937.6616 
 
 939.1295 
 
 98.... 
 
 940.5984 
 
 942.0683 
 
 943.5392 
 
 945.0111 
 
 946.4841 
 
 947.9581 
 
 949.4:131 
 
 950.9091 
 
 952.3764 
 
 953.8545 
 
 97 
 
 955.3336 
 
 956.8136 
 
 958.2948 
 
 959.7672 
 
 961.2503 
 
 962.734-> 
 
 964.2099 
 
 965 6961 
 
 967.1 73^ 
 
 968.6617 
 
 98.... 
 
 970.1412 
 
 971.6314 
 
 973.1129 
 
 974.6051 
 
 976.0886 
 
 977. 582^ 
 
 979.0684 
 
 980.5548 
 
 98-2.0522 
 
 983.5407 
 
 93. . . . 
 
 9&J.0302 
 
 986.5206 
 
 988.0220 
 
 989.5145 
 
 991.0080 
 
 992.51(25 
 
 993.9980 
 
 995.4945 
 
 996.9920 
 
 998.4905 
 
 100 
 
 1 OOO.OUOO 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
744 
 
 Miscellaneous Tables. 
 
 TABLE LXXXII. 
 
 Table of Jive-halves (|) powers of number*. 
 
 Head 
 
 
 
 
 
 
 
 
 
 
 in 
 
 .0 
 
 .1 
 
 .2 
 
 .3 
 
 .4 
 
 .5 
 
 .6 
 
 .7 
 
 .8 
 
 .9 
 
 feet. 
 
 
 
 
 
 i 
 
 
 
 
 
 
 
 000 
 
 .003 
 
 .018 
 
 .049 
 
 .101 .177 
 
 .279 
 
 .410 
 
 .572 
 
 .768 
 
 1 
 
 1.000 
 
 1.269 
 
 1.578 
 
 1.927 
 
 2.319 
 
 2.756 
 
 3.238 
 
 3.769 
 
 4.347 
 
 4.976 
 
 2 
 
 5.657 
 
 6.390 
 
 7.179 
 
 8.0*2 
 
 8.923 
 
 9.883 
 
 10.90 
 
 11.880 
 
 13.118 
 
 14.320 
 
 3 
 
 15.589 
 
 16.920 
 
 18.317 
 
 19.784 
 
 21.315 
 
 22.918 
 
 24.588 
 
 26.333 
 
 28.150 
 
 30.038 
 
 4 
 
 32.000 
 
 34.038 
 
 36.149 
 
 38.343 
 
 40.612 
 
 42.957 
 
 45.384 
 
 47.888 
 
 50.477 
 
 53.150 
 
 5 
 
 55.901 
 
 58.736 
 
 61.662 
 
 64.671 
 
 67.765 
 
 70.945 
 
 74.211 
 
 77.671 
 
 81.014 
 
 84.553 
 
 6... 
 
 88.182 
 
 91.903 
 
 95.716 
 
 99.622 
 
 103.622 
 
 107.718 
 
 111.910 
 
 116.198 
 
 120.578 
 
 125.063 
 
 7 
 
 129.642 
 
 134.325 
 
 139.104 
 
 149.086 
 
 148.962 
 
 154.050 
 
 159.235 
 
 164.526 
 
 169.915 
 
 175.420 
 
 8 
 
 181.019 
 
 186.729 
 
 192.544 
 
 198.470 
 
 204.506 
 
 210.647 
 
 216.892 
 
 123.251 
 
 229.724 
 
 236.313 
 
 9 
 
 243.000 
 
 249.804 
 
 256.726 
 
 263.757 
 
 270.908 
 
 278.170 
 
 286.452 
 
 293.047 
 
 300.654 
 
 308.385 
 
 10 
 
 316.228 
 
 324.190 
 
 332.275 
 
 340.477 
 
 343.806 
 
 357.252 
 
 365.817 
 
 374.511 
 
 383.314 
 
 392.258 
 
 11... 
 
 401.311 
 
 410.500 
 
 419.798 
 
 429.242 
 
 438.797 
 
 448.477 
 
 458.293 
 
 468.234 
 
 478.301 
 
 488.507 
 
 18 
 
 49H.820 
 
 509.301 
 
 519.879 
 
 530.610 
 
 541.446 
 
 552.438 
 
 563.548 
 
 574.802 
 
 586.163 
 
 597.696 
 
 13 
 
 6U9.336 
 
 621.137 
 
 633.046 
 
 645.170 
 
 657.297 (569.641 
 
 682.094 
 
 694.727 
 
 707.457 
 
 720.354 
 
 14 
 
 733.365 
 
 746.539 
 
 759.842 
 
 773.301 
 
 786.873 
 
 800.618 
 
 814.476 
 
 828.521 
 
 842.668 
 
 856.988 
 
 15 
 
 871.416 
 
 886.038 
 
 900.767 
 
 915.659 
 
 930.684 
 
 945.872 
 
 961.194 
 
 976.697 
 
 992.303 
 
 1008.092 
 
 16 
 
 1024.000 
 
 1040.092 
 
 1056.305 
 
 1072.703 
 
 1089.200 
 
 1105.896 
 
 1122.724 
 
 1139.708 
 
 1156.831 
 
 1174.144 
 
 17 
 
 1191.578 
 
 1209.192 
 
 1226.945 
 
 1244.856 
 
 1262.909 
 
 1281.140 
 
 1299.514 
 
 1318.066 
 
 1336.744 
 
 1355.621 
 
 18 
 
 1374.606 
 
 1393.809 
 
 1413.121 
 
 1432.634 
 
 1452.257 
 
 1472 082 
 
 1492.055 
 
 1512.194 
 
 1532.482 
 
 1552.956 
 
 19 
 
 1573.561 
 
 1594.373 
 
 1615.296 
 
 1636.428 
 
 1657.691 
 
 1679.145 
 
 1700.751 
 
 1722.529 
 
 1744.459 
 
 1766.583 
 
 20 
 
 1788.840 
 
 1811.312 
 
 1833.918 
 
 1856.719 
 
 1879.636 
 
 1902.769 
 
 1926.059 
 
 1949.526 
 
 1973.130 
 
 1996.953 
 
 21 
 
 2020.914 
 
 2045.075 
 
 2069.374 
 
 2093.875 
 
 2118.536 
 
 2143.378 
 
 2168.381 
 
 2193.588 
 
 2218.935 
 
 2244.465 
 
 22 
 
 2270.136 
 
 2296.057 
 
 2322.142 
 
 2348. 3fi8 
 
 2374.758 
 
 2401.380 
 
 2428.121 
 
 2455.096 
 
 2482.213 
 
 2509.519 
 
 23 
 
 2536.992 
 
 2564.678 
 
 2592.507 
 
 2620.551 
 
 2648.740 
 
 2677.167 
 
 2705.716 
 
 2734.482 
 
 2763.394 
 
 2792.524 
 
 24 
 
 282 1. 800 
 
 2851.343 
 
 2881.010 
 
 2910.848 
 
 2940.859 
 
 2971.115 
 
 3001.495 
 
 3032.123 
 
 3062.874 
 
 3093.875 
 
 25 
 
 3125.000 
 
 3156.375 
 
 3187.876 
 
 3219.627 
 
 3251.505 
 
 3283.661 
 
 3315.942 
 
 3348.402 
 
 3381.038 
 
 3413.905 
 
 26.... 
 
 3446.924 
 
 3480.200 
 
 3513.603 
 
 3547.239 
 
 3581.054 
 
 3615.077 
 
 3649.254 
 
 3683.666 
 
 3718.232 
 
 3753.034 
 
 27 
 
 3787.992 
 
 3823.187 
 
 3858.538 
 
 3894.127 
 
 3929.872 
 
 3985.830 
 
 4001.945 
 
 4038.328 
 
 4074.868 
 
 4111.623 
 
 28 
 
 4148.536 
 
 4ia5.692 
 
 4223.006 
 
 4260.565 
 
 4298.283 
 
 4336.247 
 
 4374.370 
 
 4412 711 
 
 4451.242 
 
 4489.991 
 
 29 
 
 4528.930 
 
 4568.089 
 
 4607.410 
 
 4646.980 
 
 4686.713 
 
 4726.697 
 
 4766.843 
 
 4807.212 
 
 4847.745 
 
 4888.530 
 
 30 
 
 4929.510 
 
 4970.714 
 
 5012.052 
 
 5053.676 
 
 5095.466 
 
 5137.512 
 
 5179.693 
 
 5222.131 
 
 5264.736 
 
 5307.600 
 
 31... 
 32 
 
 5350.631 
 5792.608 
 
 5303.891 
 5887.995 
 
 5137.349 
 5883.552 
 
 5481 .037 i 
 5929.376' 
 
 5524.893 
 5075.888 
 
 5569.011 
 6021 .568 
 
 5613.298 
 6067. 9f,8 
 
 5&57.816 
 6114.638 
 
 5702.535 
 6161.480 
 
 5747.487 
 6208., 559 
 
 33 6255.810 
 
 6303.365 
 
 6351.060 
 
 6398.995 
 
 6447.135 
 
 6495.516 
 
 6544.070 
 
 6592.899 
 
 6641.903 
 
 6691.148 
 
 34 
 
 6740.568 
 
 6790.879 
 
 6841.368 
 
 6890.904 
 
 6940.613 
 
 6991.149 
 
 7041.896 
 
 7092.923 
 
 7144.092 
 
 7195.542 
 
 35 
 
 7247.170 
 
 7299.080 
 
 7351.168 
 
 7403.504 
 
 7456.019 
 
 750S.960 
 
 7562.081 
 
 7615.167 
 
 7668.432 
 
 7722.126 
 
 3f, 
 
 777rt.OOO 
 
 7830.133 
 
 7884.447 
 
 7939.028 
 
 7993.789 
 
 8051 .024 
 
 8104.060 
 
 8159.555 
 
 8215.232 
 
 8271.179 
 
 37 
 
 8327.309 
 
 8383.709 
 
 8440.293 
 
 8497.149 
 
 8554.188 
 
 8611.515 
 
 8669.026 
 
 8726.796 
 
 8784.750 
 
 8842.995 
 
 3H 
 
 8901.424 
 
 8960.114 
 
 9018.989 
 
 9078.157 
 
 9137.510 
 
 9197.142 
 
 9256.959 
 
 9317.056 
 
 9377.339 
 
 9437.902 
 
 39 
 
 9498 653 
 
 9559.684 
 
 9620.903 
 
 9682.388 
 
 9744.061 
 
 9806.033 
 
 9868.193 
 
 9930.637 
 
 9993.271 
 
 0056.189 
 
 40 
 
 10119.296 
 
 0182.673 
 
 0246.240 
 
 0310.110 
 
 10374.171 
 
 10438.519 
 
 0503.058 
 
 0567.869 
 
 0632.872 
 
 0698.164 
 
 41 
 
 10763.648 
 
 0829.423 
 
 089.",. 389 
 
 0961.648 
 
 11028.099 
 
 11094.842 
 
 1161.779 
 
 1228.993 
 
 1296.340 
 
 1364.118 
 
 4-.' 
 
 11432.030 
 
 1502.221 
 
 1568.607 
 
 1637.288 
 
 11706.165 
 
 11775.356 
 
 1844.743 
 
 1939.996 
 
 1984.205 
 
 2054.351 
 
 43 
 
 12124.693 
 
 2195.835 
 
 2266.173 
 
 2337.313 
 
 12408.650 
 
 12480.272 
 
 2552.091 
 
 2624.213 
 
 2696.634 
 
 2769.197 
 
 44 .... 
 
 12841.761 
 
 2915.113 
 
 2988.340 
 
 3062.014 
 
 13135.829 
 
 13209.950 
 
 3284.271 
 
 3358.8*1 
 
 3433.692 
 
 3508.794 
 
 45 
 
 13584.096 
 
 3659.726 
 
 3735.557 
 
 3811.680 
 
 13888.005 
 
 13964.623 
 
 4041.444 
 
 4118.576 
 
 4195.912 
 
 4273.560 
 
 46 
 
 14351.411 
 
 4429.558 
 
 4507.909 
 
 4-86.574 
 
 14665.444 
 
 14744.578 
 
 4823.982 
 
 4899.897 
 
 4976.000 
 
 5059. C65 
 
 47 
 
 15144.152 
 
 5224.849 
 
 5305.752 
 
 5386.974 
 
 15468.402 
 
 15550.151 
 
 5632.107 
 
 5714.?64 
 
 5796.829 
 
 5879.597 
 
 48 
 
 15962.573 
 
 6045.809 
 
 6129.325 
 
 6203.457 
 
 16297.190 
 
 16381.302 
 
 64H5.928 
 
 65*2.036 
 
 6635.7^3 
 
 6722.212 
 
 49 
 50. 
 
 16807.000 
 17677.500 
 
 6892.786 
 
 6978.851 
 
 7065.195 
 
 17152.070 
 
 17238.979 
 
 7326.168 
 
 7413.647 
 
 7501.893 
 
 7589.181 
 
 
 
 
 
 1 
 
 
 
 
 
 
Relation of Rainfall to Stream Flow. 745 
 
 TABLE LXXXIIL 
 
 Showing relation of mean rainfall to the maximum and minimum discharge 
 
 of various rivers. 
 
 DRAINAGE AREA, 500 TO 1,000 SQUARE MILES 
 
 Drainage Mean Annual Discharge Ca Ft 
 
 STREAM AND LOCALITY. Area, Rainfall, pef Sec. 
 
 Sq. Miles Inches per Sq. Mile 
 
 I. AMERICAN STREAMS. MAX. Mw. 
 
 Broad river at Carlton, Ga 762 47.73 22.21 .394 
 
 Coosawattee river at Carters, Ga 532 52.73 15.17 .588 
 
 Des Plaines river at Riverside, 111 630 29.75 14.23 .000 
 
 Etowah river at Canton, Ga 604 52.73 31.50 .405 
 
 Flint river at Molina, Ga 892 52.73 7.37 .062 
 
 French Broad river at Asheville, N. C 987 7 . S8 .660 
 
 Greenbriar river, mouth Howard's cr., W. Va. 810 40.70 .120 
 
 Housatonic river, Massachusetts 790 . 165 
 
 Little Tennessee river at Judson, N. C 675 56.40 .408 
 
 Mahoning river at Warren,* 596 .017 
 
 Mahoning river 967 .026 
 
 Monocacy river at Frederick, ,Md 665 38.77 16.98 .116 
 
 North river at Port Republic, Va 804 38.77 29.78 .220 
 
 North river at Glasgow, Va... 831 38.77 44.80 .180 
 
 Olentangy river at Columbus, 523 .014 
 
 Passaic river at Paterson, N. J 791 45.00 .190 
 
 Potomac river, no. branch at Cumberland, Md. 891 38.77 22.82 .045 
 
 Potomac river at Cumberland, Md 920 38.77 19.46 .022 
 
 Raritan river at Bound Brook, N. J , 879 45.94 59.30 .140 
 
 Schoharie creek at Fort Hunter, N. Y 948 39.25 44.00 
 
 Shenandoah river at Fort Republic, Va 770 38.77 .167 
 
 Tuckasagee river at Bryson, N. C 662 45.30 .603 
 
 II. FRENCH STREAMS. 
 
 Armancon river at Aisy 575 49.20 .011 
 
 Armancon river at Tonnerre 853 .034 
 
 Marne river at St. Pizier 915 30.70 7.73 .101 
 
 Meuse river at Pagny-la-Blanchecote 573 .039 
 
 Meuse river at Chalaines 607 31.51 .041 
 
 Meuse river at Pagny-sur-Meuse 734 .056 
 
 Meuse river at Vignot 817 .085 
 
 Meuse river at Mt. Mihiel 914 .078 
 
 III. GERMAN STREAMS. 
 
 Ihna river at Stargard 672 26.60 15.50 .137 
 
 Jagst river at its mouth 708 29.50 .200 
 
 Kocher river at its mouth - 768 29.50 .221 
 
 Lippe river at Hamm 965 9.75 .235 
 
 Malapane river at Czarnowanz 773 25 . 04 14 35 .274 
 
 Oppa river at Strebowitz 805 24.40 21.95 .256 
 
 Stober river at its mouth.. 620 22.70 3. 05 
 
 *From paper on Water Supply for New York State Canals, Report of State 
 Engineer on Barge Canal, 1901. 
 
746 Miscellaneous Tables. 
 
 TABLE LXXXIIL-Continued. 
 DRAINAGE AREA, 1,000 TO 2,500 SQUARE MILES. 
 
 Drainage Mean Annual Discharge Cu. Ft. 
 
 STREAM AND LOCALITY. 
 
 Area, 
 
 Rainfall, 
 
 per Sec. 
 
 
 
 Sq. Mile. 
 
 Inches 
 
 per Sq. M 
 
 lie. 
 
 I. AMERICAN STREAMS. 
 
 
 
 MAY. 
 
 MIN. 
 
 Androscoggin river at Rumford Falls, Me. . . 
 Broad river at Gaffney, S. C 
 
 2,220 
 1,435 
 
 40.39 
 47.73 
 
 25.00 
 13.05 
 
 .475 
 .550 
 
 Catawba river at Catawba, N . C . 
 
 1,535 
 
 
 34.30 
 
 .553 
 
 Chattahoochee river at Oakdale, Ga 
 
 1,560 
 
 48.91 
 
 21.75 
 
 .432 
 
 Genesee river at Mt. Morris, N. Y 
 
 1,070 
 
 38.09 
 
 39.20 
 
 .094 
 
 Greenbriar river at Aederson, W. Va 
 
 1,344 
 
 44.86 
 
 41.55 
 
 .041 
 
 James river at Buchanan, Va 
 
 2,058 
 
 40.83 
 
 15 56 
 
 .146 
 
 Neuse river at Raleigh, N. C 
 
 1,000 
 
 
 
 .193 
 
 Neuse river at Selma, N. C 
 
 1,175 
 
 
 6.70 
 
 .064 
 
 
 2,425 
 
 49.23 
 
 14.92 
 
 .157 
 
 Oconee river at Carey, Ga 
 
 1,346 
 
 49.31 
 
 7.44 
 
 .283 
 
 Oostannala river at Resaca, Ga 
 
 1,527 
 
 52.47 
 
 14.50 
 
 .389 
 
 Potomac river at Cumberland, Md 
 
 1,364 
 
 35.28 
 
 
 .018 
 
 Saluda river at Waterloo, S. C 
 
 1,056 
 
 
 12.08 
 
 .275 
 
 Schuylkill river at Philadelphia, Pa 
 
 1,800 
 
 
 
 .170 
 
 Schuylkill river at Fairmount, Pa 
 
 1,915 
 
 
 12.17 
 
 .013 
 
 Scioto river at Columbus, O 
 
 1,07.0 
 
 
 
 .004 
 
 Scioto river at Shadeville, O 
 
 1,670 
 
 
 
 .015 
 
 Tar river at Tarboro, N. C 
 
 2,290 
 
 
 6.38 
 
 .074 
 
 Youghiogheny river at Ohio Pyle, Pa 
 
 1,775 
 
 
 
 .060 
 
 II. FRENCH STREAMS. 
 
 
 
 
 
 Aisne river at Biermes 
 
 1,341 
 
 
 - 
 
 .085 
 
 Aisne river at Berry-au-Bac 
 
 2,120 
 
 
 
 .092 
 
 Aisne river at Berry-au-Bac 
 
 2,120 
 
 
 7.58 
 
 
 Loing river at its junction with the Seine. . ^ 
 
 1,785 
 
 28.40 
 
 
 .046 
 
 Lys river , 
 
 1,420 
 
 
 1.74 
 
 .099 
 
 Marne river -at La Chaussee 
 
 2,297 
 
 
 
 .010 
 
 Marne river at Chalons 
 
 2,497 
 
 
 
 .010 
 
 Meuse river at Verdun 
 
 1,219 
 
 28.33 
 
 
 .110 
 
 Oise river at Chauny 
 
 1,575 
 
 
 
 .-104 
 
 Seine river at Troyes 
 
 1,314 
 
 
 
 .051 
 
 III. GERMAN STREAMS. 
 
 
 
 
 
 Bober river at Sagan 
 
 1,638 
 
 39.20 
 
 17.40 
 
 .389 
 
 Drage river at its mouth 
 
 1,234 
 
 
 2.11 
 
 .356 
 
 Ill river at Strasburg 
 
 1,294 
 
 
 9.15 
 
 .327 
 
 Kuddow river at Usch 
 
 1,830 
 
 18.90 
 
 19.30 
 
 .405 
 
 Lahn river at Diez 
 
 2,008 
 
 25.60 
 
 12 80 
 
 .123 
 
 Lippe river at Wesel 
 
 1,890 
 
 
 11.62 
 
 .198 
 
 Main river above mouth of the Regnitz river 
 
 1,725 
 
 27.44 
 
 
 .224 
 
 Netze river at Antonsdorf 
 
 1,086 
 
 
 
 .063 
 
 Netze river above Eicbhorst 
 
 1,130 
 
 
 
 .046 
 
 Oder river at Hoschialkowitz 
 
 1,440 
 
 21.60 
 
 
 .155 
 
 Oder river at Annaberg 
 
 1,800 
 
 24.60 
 
 27.00 
 
 .219 
 
 Oder river at Olsau 
 
 2,250 
 
 24.60 
 
 43.90 
 
 .274 
 
 Obra river at Moschin 
 
 1,325 
 
 
 
 .101 
 
 Ruhu river at Mulheim 
 
 1,728 
 
 
 33.80 
 
 .176 
 
 Saale river at its junction with the Main 
 
 1,070 
 
 27.76 
 
 
 .081 
 
 Welna river at Kowanowko, near mouth . . . 
 
 1,013 
 
 
 3.14 
 
 .077 
 
Relation of Rainfall to Stream Flow. 
 
 747 
 
 TABLE LXXX1IL Continued. 
 
 DRAINAGE AREA, 2,500 TO 5,000 SQUARE MILES. 
 
 Drainage Mean Annual Discharge Cii. Ft. 
 
 STREAM AND LOCALITY. 
 
 Area, 
 
 Rainfall, 
 
 per Sec 
 
 
 
 Sq. Miles. 
 
 Inches. 
 
 per Sq. Mi 
 
 ile. 
 
 I. AMERICAN STREAMS. 
 
 
 
 MAX. 
 
 Mi*. 
 
 Black Warrior river at Tuscaloosa, Ala. . . . 
 
 4,900 
 
 
 38.80 
 
 .018 
 
 Broad river at Alston, S. C r 
 
 4,609 
 
 
 10.26 
 
 .394 
 
 Cape Fear river at Fayetteville, W. Va 
 
 4,493 
 
 
 1.17 
 
 .076 
 
 Catawba river at Rock Hill, S. C 
 
 2,987 
 
 
 21.96 
 
 .445 
 
 Chattahoochee river at West Point, Ga. . . . 
 
 3,300 
 
 52.92 
 
 17.37 
 
 .252 
 
 Connecticut river at Dartmouth, N. H 
 
 3,287 
 
 
 
 .306 
 
 Coosa river at Rome, Ga 
 
 4,001 
 
 52.73 
 
 11.42 
 
 .225 
 
 Crow Wing river, Minnesota 
 
 3576 
 
 30.84 
 
 2.84 
 
 .250 
 
 Dan river at Clarksville, Va 
 
 3,749 
 
 38.28 
 
 8.80 
 
 .107 
 
 Hudson river at Mechanicsville, N. Y 
 
 4,500 
 
 41.61 
 
 15.50 
 
 .189 
 
 Kennebec river at Waterville, Me 
 
 4,410 
 
 
 25.20 
 
 .006 
 
 
 4,085 
 
 
 19.83 
 
 .310 
 
 *Merrimac river at Lawrence, Mass 
 
 4,551 
 
 
 20.00 
 
 .27 
 
 Mohawk river at Rexford Flats, N. Y 
 
 3,384 
 
 
 23.10 
 
 
 Mohawk river at Cohoes, N. Y. 
 
 3,444 
 
 38.65 
 
 
 .232 
 
 Ocanee river at Dublin, Ga 
 
 4,182 
 
 49.31 
 
 6.69 
 
 .021 
 
 Potomac river at Dam No. 5, Md 
 
 4,640 
 
 38.77 
 
 22.15 
 
 .078 
 
 Savannah river at Calhoun Falls, Ga 
 
 2,712 
 
 47.73 
 
 .96 
 
 .518 
 
 Shenandoah river at Millville, W. Va 
 
 2,995 
 
 39.56 
 
 11.44 
 
 .203 
 
 Staunton river at Clarksville, Va 
 
 3,546 
 
 38.28 
 
 10.30 
 
 .157 
 
 Susquehanna river, w. br., Williamsport.Pa. 
 
 4,500 
 
 
 11.60 
 
 .178 
 
 Tallapoosa river at Milstead, Ala 
 
 3,840 
 
 
 9.50 
 
 .091 
 
 Yadkin river at Salisbury, N. C 
 
 3,399 
 
 
 23.55 
 
 .225 
 
 Yadkin river at Norwood, N. C 
 
 4,614 
 
 
 13.70 
 
 .284 
 
 II. FRENCH STREAMS. 
 
 
 
 
 
 Aisne river at Soissons 
 
 3,040 
 
 
 6.43 
 
 .081 
 
 Aisne river, above junction with the Oise rivei 
 
 3,285 
 
 23.50 
 
 5.95 
 
 .096 
 
 Eure rivei* at its mouth 
 
 2,980 
 
 22.30 
 
 2.72 
 
 .076 
 
 Isere river at its mouth 
 
 4,300 
 
 
 21.00 
 
 .780 
 
 Marne river at Chateau Thierry 
 
 3,333 
 
 
 
 .127 
 
 Meuse river at Sedan 
 
 2,560 
 
 28.33 
 
 8.05 
 
 .194 
 
 Meuse river at Fumay 
 
 3,700 
 
 28.33 
 
 4.04 
 
 .191 
 
 Seine river at Bray 
 
 3,750 
 
 
 4.05 
 
 .003 
 
 Seine river at Nogent-sur-Seine 
 
 3,594 
 
 
 
 .103 
 
 Yonne river at Sens 
 
 4,270 
 
 
 9.09 
 
 .106 
 
 Yonne river at Nogent-sur-Seine -. 
 
 4,300 
 
 30.80 
 
 6.37 
 
 .140 
 
 III. GERMAN STREAMS. 
 
 
 
 
 
 Main river, below mouth of the Regnitz river 
 
 4,650 
 
 27.44 
 
 
 .186 
 
 
 3 550 
 
 29.48 
 
 14.92 
 
 .199 
 
 Mur river at Graz 
 
 2,959 
 
 
 12.98 
 
 .243 
 
 Neckar river at Heilbronn , 
 
 3,155 
 
 
 
 .146 
 
 Neckar river at Offenau 
 
 4,770 
 
 
 33.35 
 
 .167 
 
 Oder river at Ratibor 
 
 2,580 
 
 S4.60 
 
 21.20 
 
 .306 
 
 Oder river at Kosel 
 
 3 520 
 
 24.60 
 
 14.10 
 
 .128 
 
 Oder river at Krappitz 
 
 4,150 
 
 24.60 
 
 3.86 
 
 .187 
 
 Regnitz river at its juhc. with the Main river 
 
 2,920 
 
 25.60 
 
 
 .164 
 
 '"Figurrs supplied by Mr. Rich. A. Hale, Lawrence. Mass. 
 
748 Miscellaneous Tables. 
 
 TABLE LXXXIII.- Continued. 
 DRAINAGE AREA, 5,000 AND OVER SQUARE MILES. 
 
 Drainage Mean Annual 
 
 Discnarge Cu. Ft. 
 
 STREAM AND LOCALITY. 
 
 Area, 
 
 Rainfall, 
 
 per Sec. 
 
 
 
 Sq. Miles. 
 
 Inches. 
 
 per Sq. Mile. 
 
 I. AMERICAN STREAMS. 
 
 
 
 MAX. 
 
 MlN. 
 
 Connecticut river at Holyoke, Mass 
 
 8,660 
 
 
 13.26 
 
 .029 
 
 Connecticut river at Hartford, Conn 
 
 10,234 
 
 44.53 
 
 
 .310 
 
 Connecticut river at Hartford, Conn 
 
 10,234 
 
 44.53 
 
 20.27 
 
 .510 
 
 Coosa river at Riverside, Ala 
 
 6,850 
 
 48.08 
 
 10.53 
 
 .197 
 
 Delaware river, New Jersey 
 
 6,750 
 
 
 50.00 
 
 .300 
 
 Delaware river at Stockton, N. J 
 
 6,790 
 
 45.29 
 
 37.50 
 
 .170 
 
 Delaware river at Lambertsville, N. J 
 
 6,855 
 
 45.29 
 
 9.71 
 
 .364 
 
 James river at Richmond, Va 
 
 6,800 
 
 40.83 
 
 
 .191 
 
 Kanawha river at Charleston, W. Va 
 
 8,900 
 
 40.70 
 
 13.49 
 
 .123 
 
 Mississippi river 
 
 7,283 
 
 32.64 
 
 1.49 
 
 .261 
 
 
 36,085 
 
 25.75 
 
 19.73 
 
 .045 
 
 Mississippi river 
 
 164,534 
 
 
 
 .190 
 
 Mississippi river 
 
 526,500 
 
 
 
 .050 
 
 Mississippi river 1 
 
 ,214,000 
 
 
 
 .210 
 
 Missouri river 
 
 17,615 
 
 15.70 
 
 
 .100 
 
 New river at Fayette. W. Va 
 
 6,200 
 
 40.70 
 
 13.49 
 
 .189 
 
 Ohio river at Pittsburg, Pa 
 
 19,990 
 
 
 
 .114 
 
 Ohio river 
 
 200,000 
 
 41.50 
 
 
 .270 
 
 Os.wego river at Oswego, N. Y 
 
 5,013 
 
 37.69 
 
 
 230 
 
 Potomac river at Point of Rocks, Md 
 
 9,654 
 
 39.35 
 
 19.40 
 
 ,083 
 
 Potomac river 
 
 11,043 
 
 38.77 
 
 42.60 
 
 .170 
 
 Potomac river at Georgetown, D. C 
 
 11,124 
 
 38.77 
 
 15.70 
 
 
 Potomac river at Great Falls, Md 
 
 11,427 
 
 45.36 
 
 41.15 
 
 215 
 
 Potomac river at Great Falls, Md 
 
 11,476 
 
 45.36 
 
 15:25 
 
 .093 
 
 Potomac river at Chain Bridge, D. C 
 
 11,545 
 
 38.77 
 
 17.16 
 
 .165 
 
 Red river, Arkansas 
 
 97,000 
 
 39.00 
 
 2.32 
 
 
 Roanoke river at Neal, N. C 
 
 8,717 
 
 38.21 
 
 7.38 
 
 ,229 
 
 St. Croix river, Minnesota 
 
 5,950 
 
 32.58 
 
 6.00 
 
 ,424 
 
 Savannah river at Augusta, Ga 
 
 7,294 
 
 47.73 
 
 42.50 
 
 272 
 
 Susquehanna, w. branch, at Northumberland 
 
 6,800 
 
 
 17.53 
 
 ,074 
 
 Susquehanna river at Harrisburg, Pa 
 
 .24,030 
 
 
 18.88 
 
 .092 
 
 Tennessee river at Chattanooga, Tenn 
 
 21,418 
 
 
 20.78 
 
 .199 
 
 II. FRENCH STREAMS. 
 
 
 
 
 
 Loire river at Nevers 
 
 6,560 
 
 
 23.10 
 
 070 
 
 Loire river, between Maine and Vienne rivers 
 
 9,950 
 
 
 
 255 
 
 Marne river at Charenton 
 
 5,657 
 
 
 
 016 
 
 Marne river at its junction with the Seine. . . 
 
 5,295 
 
 30.70 
 
 4.67 | 
 
 .080 
 
 Meuse river at Maestricht 
 
 8,240 
 
 42.50 
 
 5.51 , 
 
 146 
 
 Meuse river at Maeseyck 
 
 8,480 
 
 42.50 
 
 7.36 
 
 244 
 
 Meuse river above Ruremond 
 
 8,750 
 
 
 3.01 
 
 317 
 
 Oise river at Creil 
 
 5 622 
 
 
 3 14 
 
 194 
 
 Rhone river at Lyons 
 
 18,000 
 
 36.32 
 
 11.83 
 
 333 
 
 Seine river at Port a 1' Anglais 
 
 17,624 
 
 
 
 046 
 
 Seine river at Paris 
 
 20,000 
 
 21.27 
 
 5.80 
 
 085 
 
 Seine river at Mantes 
 
 25,135 
 
 
 3.09 
 
 091 
 
 Seine river at mouth of the Eure river.. . 
 
 28 583 
 
 
 3 09 
 
 
 III. GERMAN STREAMS. 
 
 
 
 
 
 Elbe river at Torgau 
 
 22,000 
 
 27.09 
 
 2.89 
 
 144 
 
 Main river above mouth of Saale river 
 
 5 820 
 
 
 
 18 
 
 Main river below mouth of Saale river 
 
 6,900 
 
 
 
 166 
 
 Main river above mouth of Tauber river 
 
 7,290 
 
 
 
 167 
 
 Main river below mouth of Tauber river 
 
 8,000 
 
 
 
 167 
 
 Main river at Frankfort. . . 
 
 9,610 
 
 
 12.50 
 
 1^1 
 
 Memel river art Tilsit 
 
 38,600 
 
 
 4 02 
 
 813 
 
 Moselle river at Kochem. 
 
 10,253 
 
 
 8 52 
 
 174 
 
 Moselle river at Coblenz 
 
 10,840 
 
 24.76 
 
 13.04 
 
 .166 
 
Relation of Rainfall to Stream Flow. 749 
 
 TABLE LXXXIII. -Continued. 
 DRAINAGE AREA, 5,000 AND OVER SQUARE MILES. 
 
 Drainage Mean Annual Discharge Cu. Ft 
 
 STREAM AND LOCALITY Area Rainfall Per Sec. 
 
 Sq. Miles. Inches. Per S*q. Mile, 
 
 III. GERMAN STREAMS. MAX. MIN. 
 
 Neckar river at Heidelberg 5,321 32. 17 .215 
 
 Neckar river at Mannheim 5,395 31.02 
 
 Oder river at Ohlau 7,750 24.60 4.17 .215 
 
 Oder river at Breslau, below the Ohle river. 8,330 24.60 10.40 .209 
 
 Oder river at Steinau 11,412 24.02 .95 .229 
 
 Oder river below mouth of the Warthe river 28,319 23.62 .61 .212 
 
 Saale river at Rothenburg 7,282 27.76 5.41 .120 
 
 Warthe river at Pogorzelice ... 7,900 .164 
 
 Warthe river at Posen 9,620 6.37 .100 
 
 Warthe river at Landsberg t 20, 020 21 . 65 2 . 56 .192 
 
750 
 
 Miscellaneous Tables. 
 
 TABLE LXXXIV. 
 
 Mean average rainfall, run-off, and evaporation for storage, growing and re- 
 plenishing periods for 12 streams of the United States.* 
 
 Period. 
 
 Muskingum River, 
 from 1888 to 1895, 
 eight years. Catch- 
 ment area, 5,828 
 square miles. 
 
 Genesee River, from 
 1890 to 1898. nine 
 years. Catchment 
 area, 1,070 square 
 toiles. 
 
 Croton River, from 
 1877 to 1899, twenty- 
 three years. Catch- 
 ment area, 338.8 
 square miles. 
 
 Rain. 
 
 Run- 
 off. 
 
 Evap- 
 ora- 
 tion. 
 
 Rain. 
 
 Run- 
 off. 
 
 Evap- 
 ora- 
 tion. 
 
 Rain. 
 
 Run- 
 off. 
 
 Evap- 
 ora- 
 tion. 
 
 Storage 
 
 18.8 
 11.6 
 9.3 
 
 9.6 
 1.7 
 1.8 
 
 9.2 
 9.-9 
 
 7.5 
 
 19.4 
 11.5 
 9.4 
 
 10,5 
 1.7 
 2.0 
 
 8.9 
 9.8 
 7.4 
 
 23.7 
 13.6 
 12.1 
 
 16.8 
 2.6 
 3.4 
 
 6.9 
 11.0 
 
 8.7 
 
 Growing 
 
 Replenishing 
 
 Year 
 
 39.7 
 
 13.1 
 
 26.6 
 
 40.3 
 
 14.2 
 
 26.1 
 
 49.4 
 
 22.8 
 
 26.6 
 
 
 Period. 
 
 Lake Cochituate, 
 from 1863 to 1900, 
 thirty-eight years. 
 Catchment area, 
 18.9 square miles. 
 
 Sttdbu 
 18751 
 six 3 
 men 
 squa 
 
 Rain. 
 
 ry River, from 
 o 1900, twenty - 
 r ears. Catch- 
 ,t area, 78.2 
 re miles. 
 
 Mystic Lake, from 
 1878 to 1895, eighteen 
 years. Catchment 
 area, 26.9 square 
 miles. 
 
 Rain. 
 
 sg- 
 
 Evap- 
 ora- 
 tion. 
 
 Run- 
 off. 
 
 Evap- 
 ora- 
 tion. 
 
 Rain. 
 
 Run- 
 off. 
 
 Evap- 
 ora- 
 tion. 
 
 7.3 
 
 8.6 
 
 8.2 
 
 Storage 
 
 23.1 
 11.6 
 12.4 
 
 14.9 
 2.1 
 3.3 
 
 8.2 
 9.5 
 9.1 
 
 23.6 
 10.7 
 11.9 
 
 17.9 
 1.7 
 3,0 
 
 5.6 
 fl.O 
 
 8.9 
 
 22.4 
 10.9 
 
 10.8 
 
 15.1 
 2.8 
 2.6 
 
 Growing 
 
 Replenishing 
 
 Year 
 
 47.1 
 
 20.3 
 
 26.8 
 
 46.1 
 
 22.6 
 
 23.5 
 
 44.1 
 
 20.0 
 
 24.1 
 
 
 Period. 
 
 Neshaminy Creek, 
 from!884to 1899, six- 
 teen years. Catch- 
 ment area, 139.3 
 square miles. 
 
 Perkiomen Creek, 
 from 1884 to 1899, six- 
 teen years. Catch- 
 in e n t area, 152 
 square miles. 
 
 Tohickon Creek, from 
 1884 to 1898, fifteen 
 years. Catchment 
 area, 102.2 square 
 miles. 
 
 Rain. 
 
 Run- 
 off. 
 
 Evap- 
 ora- 
 tion. 
 
 Rain. 
 
 Run- 
 off. 
 
 Evap- 
 ora- 
 tion. 
 
 Rain. 
 
 Run- 
 off. 
 
 Evap- 
 ora- 
 tion. 
 
 Storage 
 
 23.1 
 13.4 
 11.1 
 
 17.2 
 2.7 
 
 !! 
 
 5.9 
 10.7 
 7.9 
 
 23.2 
 
 13.7 
 11.1 
 
 16.7 
 3.1 
 
 3.8 
 
 6.5 
 10.6 
 7.3 
 
 24.2 
 
 14.6 
 11.3 
 
 20.5 
 3.5 
 4.4 
 
 3.7 
 1L1 
 
 6.9 
 
 Growing 
 
 Replenishing ; 
 
 Year 
 
 47.6 
 
 23.1 
 
 24.5 
 
 48.0 
 
 23.6 
 
 24.4 
 
 50.1 
 
 38.4 i 21.7 
 
 
 Period. 
 
 Hudson River, from 
 1888 to 1901, four- 
 teen years. Catch- 
 ment area, 4,500 
 square miles. 
 
 Pequannock River, 
 from 1891 to 1899, 
 nine years. Catch- 
 ment area, 33.7 
 square miles. 
 
 Connecticut River, 
 from 1872 to 185, 
 eleven years. 
 Catchment area, 
 10,234 square miles. 
 
 Rain. 
 
 Run 
 off. 
 
 Evap- 
 ora- 
 tion. 
 
 4.5 
 9.2 
 
 7.2 
 
 Rain. 
 
 Run- 
 off. 
 
 Evap- 
 ora- 
 tion. 
 
 Rain. 
 
 Run- 
 off. 
 
 Evap- 
 ora- 
 tion. 
 
 Storage 
 
 20.6 
 12.7 
 10.9 
 
 16.1 
 3.5 
 3.7 
 
 33.0 
 12.7 
 11.1 
 
 19.7 
 3.1 
 4.0 
 
 3.3 
 9.6 
 7.1 
 
 18.9 
 13.8 
 10.3 
 
 15.1 
 3.3 
 3.6 
 
 3.8 
 10.5 
 6.7 
 
 Growing 
 
 Replenishing 
 Year .... 
 
 44.2 
 
 23.3 
 
 20.9 
 
 46.8 
 
 26.8 
 
 20.0 
 
 43.0 
 
 22,0 
 
 21.0 
 
 
 *From W. p. and I. Pap?r No. so. Rafter. 
 
Rainfall, Run-off and Evaporation. 
 
 TABLE LXXXV Croton River, 1868-1899, inclusive. 
 L Catchment area=-338,8 square miles.] 
 
 
 
 1868. 
 
 
 
 1869. 
 
 
 
 1870. 
 
 
 Period. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Storage 
 
 23.24 
 
 17 25 
 
 5 99 
 
 21 89 
 
 15 75 
 
 6 14 
 
 28 42 
 
 19 01 
 
 9 41 
 
 Growing 
 
 13.64 
 
 5 75 
 
 7 89 
 
 7 77 
 
 2 01 
 
 5 76 
 
 10 59 
 
 1 56 
 
 9 03 
 
 Replenishing 1 
 
 14.85 
 
 11 06 
 
 3 79 
 
 15 09 
 
 4 39 
 
 10 70 
 
 10 09 
 
 96 
 
 9 13 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 51.78 
 
 34.06 
 
 17 67 
 
 44.75 
 
 22 15 
 
 22 60 
 
 49 10 
 
 21 53 
 
 27 57 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1871. 
 
 
 
 1872. 
 
 
 
 1873. 
 
 
 Storage 
 
 19.83 
 
 9 72 
 
 10 11 
 
 14 57 
 
 10 31 
 
 4 26 
 
 22 19 
 
 18 52 
 
 3 67 
 
 Growing. 
 
 16.04 
 
 2.61 
 
 13.43 
 
 14.33 
 
 3.01 
 
 11 32 
 
 8 65 
 
 1 54 
 
 7 11 
 
 Beplen i sh in g 
 
 11 95 
 
 5 65 
 
 6 30 
 
 10 75 
 
 4 38 
 
 6 37 
 
 12 58 
 
 3 20 
 
 9 38 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 47 82 
 
 17 98 
 
 29 84 
 
 39 65 
 
 17 70 
 
 21 95 
 
 43 42 
 
 23 26 
 
 20 16 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1874. 
 
 
 
 1875. 
 
 
 
 1876. 
 
 
 Storage 
 
 23.74 
 
 22.86 
 
 0.88 
 
 17 10 
 
 14 81 
 
 2 29 
 
 22 64 
 
 19 89 
 
 2 75 
 
 Growing 
 
 12.30 
 
 2.77 
 
 9 53 
 
 16 45 
 
 5 86 
 
 10 59 
 
 7 14 
 
 1 07 
 
 6 07 
 
 Replenishing 
 
 8.68 
 
 1 60 
 
 7 08 
 
 10 33 
 
 3 41 
 
 6 92 
 
 10 11 
 
 1 35 
 
 8 76 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 44.72 
 
 27.23 
 
 17 49 
 
 43 88 
 
 24 08 
 
 19 80 
 
 39 89 
 
 22 31 
 
 17 58 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1877. 
 
 
 
 1878., 
 
 
 
 1879. 
 
 
 Storage . . 
 
 17.49 
 
 12.36 
 
 5.13 
 
 20.99 
 
 14.19 
 
 6 80 
 
 25.17 
 
 20 81 
 
 4 36 
 
 Growing 
 
 13.17 
 
 .96 
 
 12.21 
 
 11.29 
 
 2 57 
 
 8 72 
 
 18 09 
 
 2 63 
 
 15 46 
 
 Replenishing 
 
 18.46 
 
 5 49 
 
 12.97 
 
 16.72 
 
 5 01 
 
 11 71 
 
 6 96 
 
 1 88 
 
 5 08 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 49.12 
 
 18.81 
 
 30.31 
 
 49.00 
 
 21.77 
 
 27 23 
 
 50 22 
 
 25 32 
 
 24 90 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1880. 
 
 
 
 1881. 
 
 
 
 1882. 
 
 
 Storage 
 
 19.78 
 
 12.19 
 
 7.59 
 
 24.53 
 
 14 79 
 
 9 74 
 
 27 91 
 
 16 85 
 
 11 06 
 
 Growing 
 
 11.42 
 
 .68 
 
 10.74 
 
 9 61 
 
 1 95 
 
 7 66 
 
 9 03 
 
 2/06 
 
 6 97 
 
 Replenishing . . 
 
 7.57 
 
 .84 
 
 6.73 
 
 8 96 
 
 97 
 
 7 99 
 
 19 10 
 
 6 21 
 
 12 89 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 38.77 
 
 13.71 
 
 25.06 
 
 43.10 
 
 17.71 
 
 25 39 
 
 56 04 
 
 25 12 
 
 30 92 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1883. 
 
 
 
 1884. 
 
 
 
 1865. 
 
 
 Stora go . .. . .. 
 
 19.03 
 
 11.37 
 
 7.66 
 
 24.81 
 
 16 85 
 
 7 96 
 
 21 86 
 
 15 36 
 
 6 50 
 
 -Growing. . . .. 
 
 12.10 
 
 1.09 
 
 11.01 
 
 15.72 
 
 2 34 
 
 13 38 
 
 12 89 
 
 88 
 
 12 01 
 
 Replenishing 
 
 10.41 
 
 1.28 
 
 9.13 
 
 8.01 
 
 1 87 
 
 6 14 
 
 12 23 
 
 2 92 
 
 9 31 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 41 54 
 
 13 74 
 
 27 80 
 
 48 54 
 
 21 06 
 
 27 48 
 
 46 98 
 
 19 16 
 
 27 82 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1886. 
 
 
 
 1887. 
 
 
 
 1888. 
 
 
 Storage 
 
 25 45 
 
 18.16 
 
 7.29 
 
 23 05 
 
 16 44 
 
 6 61 
 
 30 33 
 
 21 74 
 
 8 59 
 
 Growing 
 
 11 68 
 
 1 53 
 
 10 15 
 
 24 76 
 
 6 71 
 
 18 1)4 
 
 11 25 
 
 2 63 
 
 8 62 
 
 Replenishing 
 
 9 82 
 
 1 23 
 
 8 59 
 
 7 78 
 
 2 60 
 
 5 18 
 
 18 76 
 
 8 23 
 
 10 53 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 46 95 
 
 20.92 
 
 26 08 
 
 55 58 
 
 25 75 
 
 29 83 
 
 60 34 
 
 32 60 
 
 27.74 
 
 
 
 
 
 
 
 
 
 
 
752 
 
 Miscellaneous Tables. 
 TABLE LXXXV Continued. Croton River, 1868-1899, inclusive. 
 
 Period. 
 
 1889. 
 
 law. 
 
 1891. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run_- 
 off. 
 
 Evapo- 
 ration. 
 
 Storage - -- 
 
 22.40 
 17.37 
 18.83 
 
 16.86 
 6.49 
 8.70 
 
 5.54- 
 10.88 
 10.13 
 
 25.31 
 13.31 
 14.60 
 
 19.10 
 2.51 
 
 7.02 
 
 6.21 
 10.80 
 
 7.68 
 
 26.66 
 11.26 
 
 7.78 
 
 21.22 
 1.14 
 1.11 
 
 5.44 
 10.12 
 6.67 
 
 
 Replenishing 
 
 Year r 
 
 58.60 
 
 32.05 
 
 26.55 
 
 53.22 
 
 28.63 
 
 24.59 
 
 46.70 
 
 23.47 
 
 22.23 
 
 
 
 1892. 
 
 1893. 
 
 1894. 
 
 Storage 
 
 22.93 
 15.37 
 10.30 
 
 12.87 
 2.60 
 2.31 
 
 10.06 
 12.77 
 7.99 
 
 27.34 
 12.39 
 11.08 
 
 21.41 
 1.84 
 3.51 
 
 6.93 
 10.56 
 
 7.67 
 
 23.24 
 7.96 
 17.06 
 
 15.65 
 1.88 
 4.41 
 
 7.60 
 6.18 
 12.64 
 
 Growing 
 
 Replenishing 
 
 Year 
 
 48.60 
 
 17.78 
 
 30.82 
 
 50.81 
 
 26.76 
 
 24.06 
 
 48.24 
 
 21.88 
 
 26,,% 
 
 
 
 1895. 
 
 1896. 
 
 1897. 
 
 Storage 
 
 19.55 
 11.19 
 9.54 
 
 14.78 
 1.06 
 1.27 
 
 4.77 
 10.14 
 8.27 
 
 23.18 
 
 24.84 
 12.25 
 11.27 
 
 18.01 
 2.03 
 3.13 
 
 6.88 
 10.22 
 8.14 
 
 20.55 
 20.79 
 8.76 
 
 14.64 
 6.93 
 2.78 
 
 6.91 
 13.86 
 6.08 
 
 25.80 
 
 Growing 
 
 Replenishing 
 
 Year 
 
 40.28 
 
 17.10 
 
 48.36 
 
 23.17 
 
 25. W 
 
 50.10 
 
 24.30 
 
 
 
 1898. 
 
 1899. 
 
 Storage 
 
 28.81 
 17.17 
 13.36 
 
 20.08 
 4.83 
 3.99 
 
 8.73 
 12.34 
 9.37 
 
 22.66 
 12.19 
 10.37 
 
 21,38 
 1.67 
 1.96 
 
 1.2ft 
 10.02 
 8.41 
 
 Growing 
 
 Replenishing 
 
 Year 
 
 59.34 
 
 28.90 
 
 30.44 
 
 45.22 
 
 24.91 
 
 20.31 
 
 
 
 Mean 1868-1876, in- 
 clusive. 
 
 Mean 1877-1899, in- 
 clusive. 
 
 Storage . 
 
 21.51 
 11.88 
 11.61 
 
 16.46 
 2.91 
 
 4.00 
 
 5.05 
 8.97 
 ^T.61 
 
 28.68 
 13.68 
 12.08 
 
 16.83 
 2.57 
 3.42 
 
 C.85 
 11.01 
 
 8.66 
 
 Growing -- 
 
 Replenishing 
 
 Year 
 
 45.00 
 
 23.37 
 
 21.63 
 
 49.33 
 
 22.81 
 
 26.52 
 
 
Rainfall, Run-off and Evaporation. 
 
 753 
 
 TABLE LXXXVI Lake Cochituate, 1863-1900, inclusive. 
 [Catchment area=18.9 square miles, not including catchment of Dudley Pond.] 
 
 
 
 1863. 
 
 
 
 1864. 
 
 
 
 1865. 
 
 
 Period. * 
 
 Rain 
 fall. 
 
 Run 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Storage 
 
 29.49 
 
 16.31 
 
 13.18 
 
 24. 70 
 
 14.44 
 
 10.26 
 
 29. 63 
 
 17.28 
 
 12.35 
 
 Growing 
 
 21.71 
 
 5.15 
 
 16 56 
 
 5.20 
 
 1.58 
 
 3.62 
 
 7.37 
 
 1.27 
 
 6.10 
 
 R eplenishing 
 
 16 49 
 
 5 25 
 
 11 24 
 
 13.47 
 
 3.17 
 
 10.30 
 
 13.43 
 
 2.15 
 
 11.28 
 
 
 
 
 
 
 
 
 
 
 
 Year * 
 
 67 69 
 
 26 "71 
 
 40 98 
 
 43 37 
 
 19 19 
 
 24 18 
 
 50 43 
 
 20 70 
 
 29 73 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1866. 
 
 
 
 1867. 
 
 
 
 1868. 
 
 
 Storage 
 
 22.87 
 
 9.38 
 
 13.49 
 
 27.02 
 
 16.47 
 
 10.55 
 
 23.02 
 
 16.95 
 
 6.07 
 
 Growing 
 
 22.13 
 
 2.94 
 
 19.19 
 
 :20.67 
 
 3.34 
 
 17.33 
 
 12.49 
 
 8.22 
 
 9c27 
 
 Replenishing 
 
 16. 31 
 
 3.26 
 
 13.05 
 
 10.98 
 
 2.43 
 
 8.55 
 
 15.65 
 
 4.76 
 
 10.89 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 61 31 
 
 15 58 
 
 45 73 
 
 58 67 
 
 22 44 
 
 36 43 
 
 51 16 
 
 24 93 
 
 26 23 
 
 
 
 . 
 
 
 
 
 
 
 
 
 
 
 1869. 
 
 
 
 1870. 
 
 
 
 1871. 
 
 
 Storage. .. 
 
 28.91 
 
 12.83 
 
 16.08 
 
 36.50 
 
 23.72 
 
 12.78 
 
 19.77 
 
 10.19 
 
 9 58 
 
 Growing 
 
 8.65 
 
 2.39 
 
 6.26 
 
 9.18 
 
 1.91 
 
 7.27 
 
 11.72 
 
 2.15 
 
 9 57 
 
 Replenishin g 
 
 21.25 
 
 4.77 
 
 16.48 
 
 13.00 
 
 2.85 
 
 10.15 
 
 13. 85 
 
 2 38 
 
 11 47 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 58.81 
 
 19.99 
 
 38.82 
 
 68.68 
 
 28.48 
 
 30.20 
 
 45.34 
 
 14.72 
 
 dO 62 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1872. 
 
 
 
 1873. 
 
 
 
 1874. 
 
 
 Storage 
 
 14.51 
 
 8.88 
 
 5.63 
 
 20.00 
 
 18.51 
 
 1.49 
 
 20.76 
 
 16 23 
 
 4 53 
 
 Growing 
 
 19.58 
 
 2.95 
 
 16.63 
 
 11.63 
 
 2.47 
 
 9.16 
 
 12 78 
 
 3 83 
 
 8 95 
 
 Replenishing - * 
 
 14.20 
 
 6.39 
 
 8.81 
 
 13.27 
 
 4.68 
 
 8.59 
 
 4 64 
 
 1 63 
 
 8 01 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 48.29 
 
 17.22 
 
 31.07 
 
 44.90 
 
 25.66 
 
 19/24 
 
 38.18 
 
 21.69 
 
 16.49 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1875. 
 
 
 
 1876. 
 
 
 
 1877. 
 
 
 Storage 
 
 17.80 
 
 10.76 
 
 7.04 
 
 20.45 
 
 14.91 
 
 5.54 
 
 21.61 
 
 15.65 
 
 5 96 
 
 Growing 
 
 15.34 
 
 2 35 
 
 12.99 
 
 13.28 
 
 1.64 
 
 11.64 
 
 8.76 
 
 2.24 
 
 6 52 
 
 Replenishing 
 
 13 11 
 
 3.75 
 
 9.36 
 
 12.57 
 
 3.22 
 
 9.35 
 
 15.54 
 
 4 31 
 
 11 23 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 46.25 
 
 16.86 
 
 29.39 
 
 46.30 
 
 19.77 
 
 26.53 
 
 45.91 
 
 22.20 
 
 23 71 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1878. 
 
 
 
 1879. 
 
 
 
 1880. 
 
 
 Storage 
 
 23.38 
 
 19.08 
 
 4.30 
 
 19.96 
 
 16.83 
 
 3.13 
 
 18.47 
 
 8.55 
 
 9 92 
 
 Growing 
 
 13.74 
 
 2.07 
 
 11.67 
 
 13.95 
 
 2.05 
 
 11.90 
 
 12.06 
 
 .62 
 
 11 44 
 
 Replenishing 
 
 12.36 
 
 3.09 
 
 9.27 
 
 5.62 
 
 1.93 
 
 3.69 
 
 6.34 
 
 1.56 
 
 4 78 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 49.48 
 
 24.24 
 
 25.24 
 
 39.53 
 
 20.81 
 
 18.72 
 
 36.87 
 
 10.73 
 
 26.14 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1881. 
 
 
 
 1882. 
 
 
 
 1883. 
 
 
 Storage 
 
 22.23 
 
 12.74 
 
 9.49 
 
 23.10 
 
 12.39 
 
 10.71 
 
 16.62 
 
 8.31 
 
 8.31 
 
 Growing 
 
 8.74 
 
 1.56 
 
 7.18 
 
 6.50 
 
 .75 
 
 5.75 
 
 5.08 
 
 .16 
 
 4.92 
 
 Replenishing . 
 
 8.85 
 
 1.25 
 
 '7.60 
 
 12.35 
 
 2.39 
 
 9.96 
 
 8.53 
 
 1.62 
 
 6.91 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 39 82 
 
 15 55 
 
 24 27 
 
 41 95 
 
 15 53 
 
 26 42 
 
 30 23 
 
 10 09 
 
 20 14 
 
 
 
 
 
 
 
 
 
 
 
 46 
 
754 
 
 Miscellaneous Tables. 
 
 TABLE LXXXVL Continued. Lake Cochituate, 1863-1900, inclusive. 
 
 Period. 
 
 1884. 
 
 1885. 
 
 1886. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration . 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Storage 
 
 24.79 
 12.79 
 5.82 
 
 15.70 
 
 1.54 
 1.09 
 
 9.09 
 11.25 
 4.73 
 
 22.80 
 11.70 
 12.15 
 
 11.90 
 .76 
 3.09 
 
 10.90 
 10.94 
 9.06 
 
 24.14 
 8.26 
 11.12 
 
 18.97 
 .57 
 1.92 
 
 5.17 
 7.69 
 9.20 
 
 Growing 
 
 Replenishing 
 
 Year . 
 
 43.40 
 
 18.33 
 
 25.07 
 
 46.65 
 
 15.75 
 
 30.90 
 
 43.52 
 
 21.46 
 
 22.06 
 
 
 
 1887. 
 
 1888. 
 
 1889. 
 
 Storage 
 
 26.97 
 10.05 
 6.53 
 
 19.91 
 2.87 
 1.83 
 
 7.06 
 7.18 
 4.70 
 
 24.22 
 10.06 
 20.79 
 
 15.44 
 1.94 
 9.09 
 
 8.78 
 8.12 
 11.70 
 
 21.79 
 16.84 
 14.56 
 
 17.26 
 6.24 
 
 6.65 
 
 4.53 
 10.60 
 7.91 
 
 Growing 
 
 Replenishing T 
 
 Year ,.... 
 
 43.55 
 
 24.61 
 
 18.94 
 
 55.07 
 
 .26.47 
 
 28.60 
 
 53.19 
 
 30.15 
 
 23.04 
 
 
 
 1890. 
 
 1891. 
 
 1892. 
 
 Storage 
 
 23.42 
 7.48 
 17.82 
 
 17.17 
 2.20 
 6.29 
 
 6.25 
 5.23 
 11.53 
 
 27.73 
 11.68 
 9.10 
 
 28.21 
 1.99 
 2.88 
 
 -0.48 
 9.69 
 6.72 
 
 21.11 
 10.49 
 9.43 
 
 12.47 
 
 1.38 
 2.26 
 
 16.11 
 
 8.64 
 9.11 
 
 __UT 
 
 24.92 
 
 Growing 
 
 Replenishing 
 
 Year. . 
 
 48.67 
 
 25.66 
 
 23.01 
 
 48.51 
 
 32.58 
 
 15.93 
 
 41.03 
 
 
 
 1893. 
 
 1894. 
 
 1895. 
 
 Storage * 
 
 22.84 
 11.01 
 7.58 
 
 12.40 
 1.90 
 2.51 
 
 10.44 
 9.11 
 5.07 
 
 21.00 
 7.79 
 10.94 
 
 39.73 
 
 10.25 
 1.24 
 2.04 
 
 13.63 
 
 10.76 
 6.65 
 8.90 
 
 20.18 
 11.79 
 18.66 
 
 11.29 
 1.45 
 6.17 
 
 8.89 
 10.34 
 12.49 
 
 Growing 
 
 Replenishing 
 
 Year . 
 
 41.43 
 
 16.81 
 
 24.62 
 
 26.20 
 
 50.63 
 
 18.91 
 
 31.72 
 
 
 
 1896. 
 
 1897. 
 
 18k 
 
 Storage .. 
 
 20.91 
 7.69 
 14.74 
 
 15.96 
 1.55 
 3.70 
 
 4.95 
 6.14 
 11.04 
 
 19.87 
 12.34 
 9.92 
 
 11.05 
 2.57 
 
 2.58 
 
 8.82 
 9.77 
 7.34 
 
 26.61 
 12.71 
 16.76 
 
 16.15 
 245 
 
 4.26 
 
 10.46 
 10.26 
 
 12.50 
 
 Growing 
 
 Replenishing 
 
 Year . . . 
 
 43.34 
 
 21.21 
 
 22.13 
 
 42.13 
 
 16.20 
 
 25.93 
 
 56.08 
 
 22.86 
 
 33.22 
 
 
 
 1899. 
 
 1900. 
 
 Storage. . , 
 
 22.31 
 8.16 
 10.01 
 
 18.38 
 .23 
 1.63 
 
 3.93 
 7.93 
 
 8.38 
 
 28.30 
 9.25 
 13.01 
 
 14.09 
 1.49 
 2.72 
 
 14.21 
 7.76 
 10.29 
 
 Growing . 
 
 Replenishing.. . 
 
 Year _ 
 
 40.48 
 
 20.24 
 
 20.24 
 
 50.56 
 
 18.30 
 
 32.26 
 
 
 
 Mean for 5 years, 
 1896-1900, inclusive. , 
 
 Mean for 38 years 
 1863-1900, inclusive. 
 
 Storage 
 
 23.60 
 10.03 
 12.89 
 
 15. 13 
 
 1.66 
 2.98 
 
 8.47 
 8.37 
 9.91 
 
 23.15 
 11.59 
 12.38 
 
 14.92 
 2.08 
 3.32 
 
 8.23 
 ' 9.51 
 9.05 
 
 Growing 
 
 Replenishing 
 
 Year 
 
 46.52 
 
 19.77 
 
 20.75 
 
 47. 13 
 
 20.32 
 
 26.81 
 
 
Rainfall, Run-off and Evaporation. 
 
 755 
 
 TABLE LXXXVII Neshaminy Creek, 1884-1899, inclusive. 
 
 [Catchment area=139.3 square miles.] 
 
 
 
 1884 
 
 
 
 1885. 
 
 
 
 1886. 
 
 
 Period. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run-v, 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Storage . 
 
 25 77 
 
 25 61 
 
 16 
 
 20 13 
 
 17 85 
 
 2 28 
 
 26 61 
 
 21 45 
 
 5 16 
 
 Growing 
 
 13.71 
 
 1.85 
 
 11.86 
 
 10.25 
 
 1.08 
 
 9.17 
 
 12.67 
 
 1.87 
 
 10.80 
 
 Replenishing 
 
 7.05 
 
 .45 
 
 6.60 
 
 11.22 
 
 1.73 
 
 9.49 
 
 7.60 
 
 .66 
 
 6.94 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 46.53 
 
 27.91 
 
 18.62 
 
 41.60 
 
 20.66 
 
 20.94 
 
 46.88 
 
 23.98 
 
 22.90 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1887. 
 
 
 
 1888. 
 
 
 
 1889. 
 
 
 Storage 
 
 21.88 
 
 15.92 
 
 5.96 
 
 26.48 
 
 21.17 
 
 5.31 
 
 22.32 
 
 13.44 
 
 8.88 
 
 Growing 
 
 19.26 
 
 4.44 
 
 14.82 
 
 11.83 
 
 1.01 
 
 10.82 
 
 22.42 
 
 10.00 
 
 12.42 
 
 Replenishing 
 
 7.59 
 
 1.03 
 
 6.58 
 
 14.18 
 
 6.02 
 
 8.16 
 
 22.18 
 
 12.37 
 
 9.81 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 48 73 
 
 21 39 
 
 27 34 
 
 52 49 
 
 28 20 
 
 24 29 
 
 66 92 
 
 35 8l 
 
 31 11 
 
 
 
 
 
 
 
 
 
 
 
 
 . 
 
 1890. 
 
 
 
 1891. 
 
 
 
 1892. 
 
 
 Storage 
 
 22.06 
 
 14.85 
 
 7.21 
 
 23.48 
 
 17.74 
 
 5.74 
 
 22.55 
 
 15.01 
 
 7.54 
 
 Growing. 
 
 14.28 
 
 2.15 
 
 12.13 
 
 15.90 
 
 2. 53 
 
 13.37 
 
 11.58 
 
 1.31 
 
 10.27 
 
 Replenishing . . . 
 
 10.23 
 
 3.33 
 
 6.93 
 
 8.08 
 
 2. ay 
 
 5.70 
 
 10.13 
 
 1.94 
 
 8.19 
 
 
 
 
 
 
 
 
 
 
 
 Year . 
 
 46.57 
 
 20.33 
 
 26.24 
 
 47.46 
 
 22.65 
 
 24.81 
 
 44.26 
 
 18.86 
 
 26.00 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1893. 
 
 
 
 1894. 
 
 
 
 1885. 
 
 
 Storage 
 
 22 16 
 
 18 52 
 
 3 64 
 
 26 68 
 
 18 16 
 
 8 52 
 
 20 97 
 
 15 84 
 
 5' 13 
 
 Growing 
 
 12.21 
 
 1.70 
 
 10.51 
 
 8.95 
 
 1.82 
 
 7.13 
 
 11.41 
 
 2.07 
 
 9.34 
 
 Replenishing 
 
 11.07 
 
 3.74 
 
 7.33 
 
 16.45 
 
 6.12 
 
 10.33 
 
 6.21 
 
 .24 
 
 5.97 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 45.44 
 
 23.98 
 
 21.48 
 
 52.06 
 
 26.10 
 
 25.98 
 
 38.59 
 
 18.15 
 
 20.44 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1896. 
 
 
 
 1897. 
 
 
 Storage 
 
 
 
 
 20.52 
 
 11.54 
 
 8.98 
 
 19.28 
 
 10.60 
 
 8.68 
 
 Growing 
 
 
 
 
 10.80 
 
 1.65 
 
 9.15 
 
 17.70 
 
 6.50 
 
 11.20 
 
 Replenishing 
 
 
 
 
 12 65 
 
 3 41 
 
 9 24 
 
 9 06 
 
 3 11 
 
 6 95 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 
 
 
 43.97 
 
 16.60 
 
 27.37 
 
 46.04 
 
 19.21 
 
 26 83 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1898. 
 
 
 
 1899. 
 
 
 Storage 
 
 
 
 
 25.68 
 
 16.87 
 
 8.81 
 
 33.09 
 
 20.60 
 
 2 59 
 
 Growing 
 
 
 
 
 12.34 
 
 1.69 
 
 10.65 
 
 9.41 
 
 1.76 
 
 7.66 
 
 Replenishing 
 
 
 
 
 12.80 
 
 3.33 
 
 9.47 
 
 10.91 
 
 1 96 
 
 895 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 
 
 
 50. 82 
 
 21.89 
 
 28.93 
 
 43.41 
 
 24.22 
 
 19.19 
 
 
 
 
 
 
 
 
 
 
 
756 
 
 Miscellaneous Tables. 
 
 TABLE LXXXVIII Perkiomen Creek, 1884-1899, inclusive. 
 [Catchment area=152 square miles.] 
 
 
 
 1884. 
 
 
 
 1885. 
 
 
 
 1886. 
 
 
 Period. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Storage 
 
 25.25 
 
 25.19 
 
 0.06 
 
 20.47 
 
 15.29 
 
 5.18 
 
 26.03 
 
 19.74 
 
 6.29 
 
 Growing 
 
 15.53 
 
 4.07 
 
 11.46 
 
 9.83 
 
 1.68 
 
 8.15 
 
 11.76 
 
 3.35 
 
 8.41 
 
 Replenish! ng 
 
 7.54 
 
 1.59 
 
 5.95 
 
 9.49 
 
 2.3& 
 
 7.11 
 
 9.00 
 
 2.02 
 
 6.98 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 48.32 
 
 30.85 
 
 17.47 
 
 39.79 
 
 19.35 
 
 20.44 
 
 46.79 
 
 25.11 
 
 21.68 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1887. 
 
 
 
 1888. 
 
 
 
 1889. 
 
 
 Storage 
 
 21.63 
 
 14.66 
 
 6.97 
 
 27.48 
 
 19.67 
 
 7.81 
 
 22.99 
 
 14.28 
 
 8,71 
 
 Growing 
 
 17.28 
 
 4.26 
 
 13.00 
 
 12.42 
 
 2.17 
 
 10.25 
 
 23.38 
 
 10.02 
 
 13.36 
 
 Replenishing 
 
 6.70 
 
 1.45 
 
 5.25 
 
 14.18 
 
 7.40 
 
 6.78 
 
 20.45 
 
 11.81 
 
 8.64 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 45.59 
 
 20.37 
 
 25.22 
 
 54.08 
 
 29,24 
 
 24.84 
 
 66*82 
 
 36.11 
 
 30.71 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1890. 
 
 
 
 1891. 
 
 
 
 1892. 
 
 
 Storage .. 
 
 24.68 
 
 18.15 
 
 6.53 
 
 22.89 
 
 17.35 
 
 5.54 
 
 23.64 
 
 15.89 
 
 7.75 
 
 Growing 
 
 14 35 
 
 3 11 
 
 11 24 
 
 18 32 
 
 &25 
 
 15 07 
 
 11 06 
 
 2 3a 
 
 8 68 
 
 Replenishing 
 
 10 31 
 
 4 52 
 
 5 79 
 
 8 15 
 
 2 69 
 
 5 46 
 
 9 33 
 
 2 66 
 
 6 67 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 49.34 
 
 25.78 
 
 23.56 
 
 49.36 
 
 23.29 
 
 26.07 
 
 44.03 
 
 20.93 
 
 23.10 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1893. 
 
 
 
 1894. 
 
 
 
 1896. 
 
 
 Storage 
 
 22 16 
 
 17 21 
 
 4 95 
 
 24 37 
 
 15 77 
 
 8 60 
 
 23 22 
 
 15 51 
 
 7 71 
 
 Growing 
 
 12 20 
 
 1 82 
 
 10 38 
 
 8 77 
 
 2 05 
 
 6 72 
 
 10 88 
 
 1 32 
 
 9 56 
 
 Replenishing 
 
 10 18 
 
 3 33 
 
 6 85 
 
 15 40 
 
 5 18 
 
 10 22 
 
 6 25 
 
 75 
 
 5 50 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 44 54 
 
 22 36 
 
 22 18 
 
 48 54 
 
 23 00 
 
 25 54 
 
 40 35 
 
 17 58 
 
 22 77 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1896. 
 
 
 
 1897. 
 
 
 Storage 
 
 
 
 
 19 99 
 
 10 26 
 
 9 73 
 
 20 00 
 
 12 37 
 
 7 63 
 
 Growing 
 
 
 
 
 15 05 
 
 2 83 
 
 12 22 
 
 13 69 
 
 3 08 
 
 10 61 
 
 Replenishing . 
 
 
 
 
 14 62 
 
 4 19 
 
 10 43 
 
 10 07 
 
 2 26 
 
 7 81 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 
 
 
 49 66 
 
 17 28 
 
 32 38 
 
 43 76 
 
 17 71 
 
 26 05 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1898. 
 
 
 
 1899. 
 
 
 Storage 
 
 
 
 
 24 24 
 
 15 74 
 
 8 50 
 
 22 79 
 
 20 49 
 
 2 30 
 
 Growing 
 
 
 
 
 9 98 
 
 1 39 
 
 8 59 
 
 14 12 
 
 2 46 
 
 11 66 
 
 Replenishing ,. 
 
 
 
 
 13.85 
 
 3 90 
 
 9 95 
 
 11 36 
 
 4 01 
 
 7 35 
 
 
 
 
 
 
 
 
 
 
 
 Year , 
 
 
 
 
 48 07 
 
 21 03 
 
 27 04 
 
 48 27 
 
 26 96 
 
 21 31 
 
 
 
 
 
 
 
 
 
 
 
Rainfall, Run-off and Evaporation. 
 
 757 
 
 TABLE LXXXIX Tohickon Creek, 18S4-1898, inclusive. 
 [Catchment area=102.2 square miles.] 
 
 
 
 1884. 
 
 
 
 1885. 
 
 
 
 1886. 
 
 
 Period. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Rain- 
 fall. 
 
 Run- 
 off. 
 
 Evapo- 
 ration 
 
 Rain- 
 fall.' 
 
 Run- 
 off. 
 
 Evapo- 
 ration. 
 
 Storage 
 
 26.06 
 
 27.27 
 
 -1.21 
 
 21.86 
 
 19.45 
 
 2.41 
 
 28.54 
 
 27.79 
 
 0.75 
 
 Growing 
 
 17.52 
 
 6.53 
 
 10.99 
 
 11.31 
 
 1.54 
 
 0.7? 
 
 11.10 
 
 2.27 
 
 8.83 
 
 Replenishing 
 
 7.97 
 
 1.35 
 
 6.62 
 
 10 
 
 2.94 
 
 7.06 
 
 9.05 
 
 2.04 
 
 7.01 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 51 55 
 
 35 15 
 
 16.40 
 
 43 17 
 
 23 93 
 
 19 24 
 
 48 69 
 
 32 10 
 
 16 59 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1887. 
 
 
 
 1888. 
 
 
 
 1889. 
 
 
 Storage . . . , > 
 
 21.60 
 
 18.44 
 
 3.16 
 
 28.52 
 
 27. i7 
 
 1.15 
 
 25.13 
 
 17.82 
 
 7.31 
 
 Growing 
 
 19."19 
 
 4.80 
 
 14.39 
 
 12.96 
 
 1.99 
 
 10.97 
 
 23.90 
 
 12.45 
 
 11.45 
 
 Replenishing 
 
 6.71 
 
 .91 
 
 5.80 
 
 16.04 
 
 10.14 
 
 5.90 
 
 21.34 
 
 18.70 
 
 7.64 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 47,50 
 
 24.15 
 
 23.35 
 
 57.52 
 
 39.50 
 
 18.02 
 
 70.37 
 
 43 97 
 
 26.40 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1890. 
 
 
 
 1891. 
 
 
 
 1892. 
 
 
 Storage 
 
 25.09 
 
 19.01 
 
 6.08 
 
 23.07 
 
 20.23 
 
 2.84 
 
 23 43 
 
 19 76 
 
 3 67 
 
 Growing 
 
 15.49 
 
 2.54 
 
 12.95 
 
 19.77 
 
 4.99 
 
 14.78 
 
 11 22 
 
 1 52 
 
 9 70 
 
 Replenishing 
 
 10.20 
 
 5.45 
 
 4.75 
 
 7.16 
 
 2.03 
 
 5.13 
 
 10 65 
 
 3 47 
 
 7 18 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 50.78 
 
 27 
 
 23.78 
 
 50 
 
 27.25 
 
 22.75 
 
 45.30 
 
 24.75 
 
 20.55 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1893. 
 
 
 
 1894. 
 
 
 
 1895. 
 
 
 Storage ... 
 
 22.82 
 
 22.05 
 
 0,77 
 
 27.04 
 
 21.65 
 
 5.39 
 
 21.35 
 
 19.91 
 
 1 44 
 
 Growing 
 
 14.82 
 
 2.10 
 
 12.72 
 
 6.95 
 
 .84 
 
 6.11 
 
 12.45 
 
 1.46 
 
 10 99 
 
 Replenishing 
 
 11.81 
 
 4.06 
 
 7.25 
 
 17.63 
 
 8.11 
 
 9.52 
 
 6.63 
 
 .28 
 
 6 35 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 48.95 
 
 28.21 
 
 20.74 
 
 51.62 
 
 30.60 
 
 21.02 
 
 40.43 
 
 21.65 
 
 18.78 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1896. 
 
 
 
 1897. 
 
 
 
 1898. 
 
 
 Storage 
 
 21.69 
 
 12.30 
 
 9.39 
 
 20.82 
 
 13.93 
 
 6.89 
 
 26.40 
 
 21 30 
 
 5 20 
 
 Growing 
 
 13.76 
 
 2.91 
 
 10.85 
 
 17.32 
 
 5.12 
 
 12.20 
 
 10.87 
 
 1 
 
 9 87 
 
 Replenishing . ^ 
 
 12.58 
 
 4.52 
 
 8.06 
 
 8.78 
 
 1.98 
 
 6.80 
 
 13.80 
 
 5.19 
 
 8 61 
 
 
 
 
 
 
 
 
 
 
 
 Year 
 
 48 03 
 
 19 73 
 
 28 30 
 
 46 92 
 
 21 03 
 
 25 89 
 
 51 07 
 
 27 39 
 
 23 68 
 
 
 
 
 
 
 
 
 
 
 
\ 
 
 
INDEX 
 
 PAGE 
 
 Abbe, evaporation relations 141 
 
 Acceleration, 
 
 and retardation of water in 
 
 penstock 690 
 
 curve of 689 
 
 effect of, on water supplied 
 
 to wheel 455 
 
 of gravity 06 
 
 Action, turbines (see Impulse 
 
 Turbines) 244 
 
 Adam's, A. L., Values of coeffi- 
 cients for wood stave pipe .... 60 
 
 Air chamber 461 
 
 Air, energy in 22 
 
 Allis Chalmers Co., 
 
 Sewalls Falls turbines 512 
 
 turbine governor 735 
 
 Turner's Falls power plant.. 514 
 Altitude, effect of on rainfall ... 124 
 American turbines. 11, 13, 249, 256, 266 
 
 buckets of 275 
 
 Fourneyron 250 
 
 Francis 2 48 
 
 impulse 275 
 
 Jonval 252 
 
 practice of various manufac- 
 turers in measuring the di- 
 ameter of 28G 
 
 reaction, type, efficiency of. . 247 
 catalogue relations of diam- 
 eter and speed of 326 
 
 relations of diameter and 
 
 discharge of 339 
 
 relation of power and diam- 
 eter of 342 
 
 relation of speed and dis- 
 charge in 346 
 
 ! American Turbines Con. PAGE 
 
 relation of speed and power 
 
 in 350 
 
 specific speed of 350 
 
 Ampere 33 
 
 Aprons for dams, preliminary 
 
 study of, for dam at Kilbourn. . 585 
 Archibald, E. M., discussion of 
 effect of load factor on cost of 
 
 power 622 
 
 Atkins' wheel and case 273 
 
 Atlantic drainage, hydrographs. . 190 
 Auxiliary power, 
 
 cost of 65S 
 
 effects of 631 
 
 hydrograph showing amount 
 of, necessary to maintain 
 
 power at Sterling, 111 635 
 
 necessary to maintain fixed 
 
 power on a southern river 633 
 study of, for report on water 
 power 680 
 
 B. 
 
 Back water curve 58 
 
 literature on 78 
 
 study of, for report on water 
 
 power 678 
 
 Barker's mill 5, 239 
 
 Bazin's formula 50, 69 
 
 diagram for solution of. ... 51 
 Bearings, 
 
 Geylin glass suspension 290 
 
 horizontal lignum vitae 295 
 
 hydraulic balancing piston of 
 Niagara Falls Power Co. 
 
 293, 294 
 of horizontal turbines 292 
 
760 
 
 Index. 
 
 Bearings Con. PAGE 
 
 vertical cross or hanging 
 bearings of Niagara Falls 
 
 Power Co 293 
 
 vertical turbine 289 
 
 Belt losses 30 
 
 Bends in a stream, effect of on 
 
 distribution of velocity 212 
 
 Betiva Dam, India, automatic 
 
 drop shutter for 610 
 
 Bmn<ie, Alexander A 125 
 
 Borda turbine 241 
 
 Boyden, Uriah A 9 
 
 diffuser 305, 307 
 
 Fourneyron turbine of. . 249, 251 
 
 turbine of 250 
 
 turbine tests of 360 
 
 Brake wheel, W. O. Weber 376 
 
 Breast water wheels 3 
 
 British thermal unit 32 
 
 equivalents of 34 
 
 per minute, equivalents of . . 35 
 
 Brown, Ralph T 275 
 
 Buckets, 
 
 American 276 
 
 Dodd's 274 
 
 Ellipsoidal 274 
 
 Hug's 274 
 
 Knight's 274 
 
 Moore's 274 
 
 Pelton 274 
 
 modern changes in 13 
 
 of tangential or impulse 
 water wheels 274 
 
 C. 
 
 Cadiat's turbine 239 
 
 Canals, 
 
 determination of economic 
 
 cross section 54 
 
 of Holyoke Water Power 
 
 Company 568 
 
 for Peshtigo River develop- 
 ment 573 
 
 Capacity, 
 
 influence of choice of machin- 
 ery on 525 
 
 of each part of a system... 25 
 of prime movers'. . . 528 
 
 Capacity Con. PAGE 
 
 Case Turbine Manufacturing 
 
 Company, 
 tests of a 30" regular turbine 725 
 
 tests of a 30" special 724 
 
 Channel condition, effect of on 
 
 gradient 203 
 
 Channel grade, effects of on the 
 
 hydraulic gradient of a stream 204 
 Characteristic curve, 
 
 consideration, of a turbine 
 
 from 401 
 
 of Tremont-F ourneyron 
 
 wheel 409 
 
 of a 45" Samson wheel.. 410-411 
 of a turbine, construction of 400 
 
 of a Victor turbine 402-403 
 
 of Improved New American 
 
 turbine 406 
 
 of Wellman-Seaver-Morgan 
 
 51" turbine 408 
 
 Chase, Mr. Stewart, agent of 
 
 Holyoke Water Power Co 361 
 
 Chestnut Hill reservoir, evapora- 
 tion from water surface of... 143 
 
 Chesuncock log way 620 
 
 Chezy's formula 46 
 
 applied to pipes 60 
 
 diagram for the solution of 52-53 
 
 Chinese Nora 1 
 
 Chippewa River . , 165 
 
 Christiana Power Station, Nor- 
 way, typical electrical lighting 
 
 load curve 424 
 
 Chute case, the 297 
 
 Closed penstock, predetermina- 
 tion of speed regulation with 
 
 462,464 
 
 Cochituate basin, relations be- 
 tween precipitation, evapora- 
 tion, run-off and temperature 
 
 on 149-150 
 
 Coefficients, 
 
 of discharge for weirs 65,74 
 
 of discharge through sub- 
 merged orifices and tubes 45 
 
 of entrance losses 42 
 
 relation of to hydraulic ra- 
 dius on Wisconsin River.. 199 
 
Index. 
 
 761 
 
 PAGE 
 
 Columbus Power Company, plant 546 
 Combes, tests of reaction wheels 359 
 
 Compound motion 37 
 
 Conant, R. W., estimate of operat- 
 ing expenses of various rail- 
 way power stations 660 
 
 Concord Electric Company, plant 
 
 of 55?, 
 
 Connecticut River, table showing 
 relation of rainfall to run-off 
 on the storage, growing and re- 
 plenishing period 159 
 
 Connections of, 
 
 governor to gates 493 
 
 by cable 477, 495 
 
 by draw rods 492 
 
 by shafts and sectors... 494 
 turbines to machinery, vari- 
 
 ious methods ' 531 
 
 vertical wheels to generator 507 
 Connorsville, Indiana, regulation 
 
 of pumping plant 441 
 
 Conservation, laws of energy 21 
 
 Constantine, Michigan, 
 
 details of head gates at 613 
 
 elevation of head gates at. . 613 
 rear view of head gates at. . 613 
 
 Contractions 42 
 
 Control of governor from switch- 
 board 492 
 
 Conversion of, 
 
 energy units 33 
 
 power 26 
 
 Cornell Hydraulic Laboratory, 
 experiments on float measure- 
 ments by Kuichling, Williams, 
 
 Murphy and Boright 229 
 
 Cost, 
 
 effect of size of units on .... 526 
 
 of auxiliary power 658 
 
 of coal, effect of on the cost 
 
 of power 665 
 
 of developed water power... 652 
 of development of various 
 American water power 
 
 plants 650 
 
 of development of various 
 foreign water power plants 651 
 
 Cost Con. PAGE 
 
 of development of water 
 
 power 647 
 
 of distribution of power 653 
 
 of gas power, estimate of . . . 685 
 
 of motor installation 657 
 
 of operation, estimate of for 
 various proposed Canadian 
 
 plants 654 
 
 of operation of various street 
 
 railway power stations. . . 661 
 of water power development, 
 relation of capacity to .... 648 
 
 relation of head to 649 
 
 of water power plant, esti- 
 mate of Canadian 649 
 
 Cost of power, 
 
 effect of cost of coal on.... 665 
 effect of partial load on.... 654 
 
 from sub-station 656 
 
 literature on 672-673 
 
 per H. P. per annum in, vari- 
 ous plants 659 
 
 transmission 656 
 
 steam at 22 power plants. . . . 660 
 
 steam, estimate of 664 
 
 steam generated electric 
 power to the consumer... 669 
 
 water power 647 
 
 Cost, value and sale of power... 646 
 
 Coulomb 33 
 
 Crest, effect of changes in lengths 
 
 on head 100 
 
 Crops, daily consumption of water 
 
 by 135 
 
 Cross section, and slope, estima- 
 tion of flow from 219 
 
 Croton River, rainfall, run-off and 
 
 evaporation 751 
 
 Cubic foot, equivalents of 34 
 
 Current meter, 
 
 methods of computation for 227 
 observations and computation 223 
 
 Price's electric 222 
 
 rating curve 224 
 
 rating station at Denver, Col- 
 orado 223 
 
 readings, method of making 225 
 the use of . . . 221 
 
762 
 
 Index. 
 
 PAGE 
 
 Current wheels 1, 241 
 
 Cylinder gates 299-300 
 
 diagram showing eddies 
 caused by 302 
 
 D. 
 
 Dam and power plant, relations 
 
 of 561 
 
 Dam at, 
 
 Holyoke during flood 591 
 
 Danville, Illinois, section of 592 
 Kilbourn, Wisconsin, with 
 
 movable crest 60S 
 
 McCall's Ferry, section of. . 592 
 
 Sewell's Falls, timber 594 
 
 of Holyoke Water Power 
 
 Company 590 
 
 of The Montana Power Com- 
 pany, near Butte 593 
 
 Dams, 
 
 appendages to 603 
 
 aprons for 585 
 
 calculations for stability of 587 
 consideration of various fac- 
 tors in 589 
 
 effect of design of, on head 100 
 
 flood flows over 583 
 
 for water power purposes. . . 579 
 
 foundations of 581. 
 
 heights of 580 
 
 impervious construction of. . 586 
 
 literature on 595 
 
 movable 100, 603 
 
 object of construction of. ... 579 
 
 overturning of 586 
 
 plants -located in 574 
 
 preliminary study of dam 
 for Southern Wisconsin 
 
 Power Co 585 
 
 principles of construction of 
 
 579-581 
 
 sliding on base 586 
 
 stability of masonry 586 
 
 timber crib at Janesville, 
 
 Wis 582 
 
 types and details 594 
 
 Danaide turbine.. . 241 
 
 PAGE 
 Danville, Illinois, concrete and 
 
 timber fishway at 619 
 
 Danville, Illinois, section of con- 
 crete dam at 592 
 
 Dayton Globe Iron Works Com- 
 pany 256 
 
 American turbine, develop- 
 ment of 258 
 
 increase in speed of.... 259 
 
 runner of 260 
 
 characteristic curve of an 
 Improved New American 
 
 turbine 406 
 
 double horizontal wheel 515 
 
 double horizontal wheel in 
 
 closed penstock 516 
 
 test of a 44" turbine 714 
 
 two pairs of turbine units in 
 
 tandem 518 
 
 Deflecting nozzle, governing im- 
 pulse wheel with 470 
 
 Denver, Colorado, current meter 
 
 rating station ~ 223 
 
 Depreciation 652 
 
 literature on 674 
 
 Developed power, annual cost of 562 
 Development of, 
 
 American turbine 25S 
 
 capacity, speed and power of 
 
 a 48" turbine 257 
 
 Leffel's wheel 260 
 
 potential energy 19 
 
 the turbine 4 
 
 water power in the U. S. . . . 14 
 Diameter, 
 
 graphical relations of dis- 
 charge to 338 
 
 of runner 285 
 
 of a turbine, expression for 
 
 relations of power to.... 338 
 of a turbine, relation of dis- 
 charge to 337 
 
 of turbine water wheels, prac- 
 tice of various manufac- 
 turers in measuring 286 
 
 Diameter and discharge of vari- 
 ous American turbines.. . 339 
 
Index. 
 
 763 
 
 PAGE 
 
 Diameter and power, 
 
 graphical relation of in tur- 
 bines of homogeneous de- 
 sign 341 
 
 of various American tur- 
 bines 342 
 
 Diffuser, Boyden 305-307 
 
 Discharge and speed of various 
 
 American turbines. 346 
 
 Discharge curve 95 
 
 of Potomac River 232 
 
 Discharge, curves of at various 
 gate openings under given 
 speed, calculated from 
 actual tests 398 
 
 graphical relations of dia- 
 meter to 338 
 
 measurement of 372 
 
 of a turbine at a fixed "gate 
 opening 332 
 
 of certain American and 
 European rivers, rates of 
 maximum flood 168 
 
 of rivers, relation to rainfall 745 
 
 of thirteen water wheels of 
 homogeneous design and 
 different diameters 337 
 
 of turbine proportional to 
 square root of head 332 
 
 of turbines, relation of speed 
 to 345 
 
 of various Michigan rivers.. 188 
 
 of various turbines at full 
 gate, graphically ex- 
 pressed 333 
 
 of wheel under fixed gate con- 
 ditions, equation for 332 
 
 over weirs, comparative .... 68-69 
 
 relation of diameter to, in 
 American turbines 339 
 
 relation of power to diameter 
 of a turbine 337 
 
 relations of speed to for a 
 12 inch Smith-McCormick 
 
 turbine 335 
 
 Distribution of, 
 
 power, cost of 653 
 
 rainfall . ill 
 
 Distribution of Con. PAGE 
 total annual rainfall in Wis- 
 consin 114-115 
 
 velocity, effects of ice cover- 
 ing 215 
 
 water at various plants, ex- 
 amples of 567 
 
 weekly rainfall in Wisconsin 117 
 Dix, J, L. & S. B., Jonval turbine 255 
 
 Doble, ellipsoidal bucket 274 
 
 needle nozzle 302-306 
 
 nozzle, stream from 307 
 
 runner 277 
 
 tangential wheel 248 
 
 Dodd bucket 274 
 
 Dodge Manufacturing Co., instal- 
 lation by 533-534 
 
 Dolgeville Electric Light and 
 
 Power Co., plant of 548 
 
 Draft Tube, the 302-304 
 
 Drainage area, relations to flood 
 
 discharge 168 
 
 Drop-shutter, automatic for 
 
 dam 610 
 
 Duration curves of: 
 
 Ausable River 187 
 
 Grand River at Grand Rap- 
 ids 187 
 
 Grand River at North Lans- 
 ing 187 
 
 Kalamazoo River 187 
 
 St. Joseph River 187 
 
 Thunder Bay River 187 
 
 various Michigan rivers for 
 
 1904 187 
 
 Dynamo, efficiency of 24 
 
 E. 
 
 Earthen dams, literature on 596 
 
 Eastern Gulf drainage, hydro- 
 graphs of 190 
 
 Eau Claire, adjustable flash- 
 boards at 61 L 
 
 Economy, 
 
 principles of 32 
 
 value of improvements in- 
 tended to effect 670 
 
 Economy in operation of power 
 Plant .527 
 
764 
 
 Index. 
 
 PAGE 
 
 Economy Light and Power Co., 
 
 Joliet plant of 571 
 
 Morris plan,t of 572 
 
 tainter gates for Morris plant 605 
 wheels of 410-411 
 
 Eddies, 
 
 as caused by cylinder gate.. 302 
 as caused by partial closure 
 
 of register gates 305 
 
 through opening and par- 
 tially closed wicket gate.. 304 
 
 Efficiency 21, 375 
 
 definition of 23 
 
 natural limit to 21 
 
 of a combined plant 24 
 
 of a dynamo 24 
 
 of turbines, relative 246 
 
 of a Fourneyron turbine.... 247 
 
 of a furnace 22 
 
 of American type of reaction 
 
 turbine 247 
 
 of an hydro-electric plant... 24 
 
 of a shaft 24 
 
 of a steam engine 24 
 
 of canal section 54 
 
 of Jonval turbine 247 
 
 of pumping engine.... 23 
 
 of tangential turbines 247 
 
 of the machine 23 
 
 practical limits to 23 
 
 relations of q> and 329 
 
 Electric lighting load curve 424 
 
 Electric lighting, losses in hy- 
 draulic plant for 25 
 
 Electric units 32 
 
 Emerson, James, 
 
 testing of turbines by 361 
 
 tests by 364 
 
 Energy 23 
 
 conservation, laws of 21 
 
 definition of 19 
 
 differentiation of 20 
 
 equivalent units of 740 
 
 exertion of by, 
 
 momentum 41 
 
 weight ; 41 
 
 pressure 41 
 
 in the air. . 22 
 
 Energy Con. PAGE 
 
 literature of 39 
 
 losses in an hydraulic plant 25 
 losses in a pumping plant.. 25 
 losses in steam power plant. 24 
 mathematical expression of 40 
 
 no waste of in nature 20 
 
 of fuel 19 
 
 potential and kinetic 3'J 
 
 potential 20 
 
 thermal 20 
 
 required to change penstock 
 
 velocity 446, 456 
 
 transmission and transforma- 
 tion of 23 
 
 units, conversion of 33 
 
 units of 32 
 
 Enlargements, sudden 42 
 
 Entrance head 42 
 
 Equivalent measures and weights 
 
 of water 740 
 
 Equivalents of energy 740 
 
 Escher, Wyss and Company:.... 280 
 double turbines at Chivres 
 
 near Geneva 282 
 
 Jonval turbine at Geneva 
 
 Water Works 281 
 
 Estimate of cost, for report on 
 
 water power 682 
 
 European practice in, 
 
 turbine construction 280 
 
 water wheel design 278 
 
 European type of turbine 249 
 
 European vertical turbine, steps 
 
 of 290 
 
 Evaporation, 137 
 
 and temperature on Lake 
 
 Cochituate, relations of. . 150 
 annual in the United States 
 
 138-139 
 
 from water surface in inches, 
 Chestnut Hill reservoir... 143 
 
 literature on 144 
 
 monthly from free water sur- 
 faces, 
 
 Augusta, Ga., Cincinnati, 
 Ohio, Des Moines, Iowa, 
 Detroit, Mich., Helena, 
 Mont., Little Rock, Ark., 
 
Index. 
 
 765 
 
 Evaporation Con. PAGE 
 
 monthly from free water sur- 
 facesCon. 
 
 Montgomery, Ala., New 
 Haven, Conn., Olympia, 
 Wash., Palestine, Texas, 
 Sacramento, Cal., Spo- 
 kane, Wash., Topeka, 
 Kans., Winnemucca, Nev., 
 Yuma, Ariz., and at vari- 
 ious points in the U. S.. . 140 
 
 of water 20 
 
 precipitation, run-off and 
 temperature, relations of 
 on upper Hudson, River... 154 
 rainfall and run-off for vari- 
 ous periods 750 
 
 relation to precipitation, run- 
 off and temperature, on 
 
 Lake Cochituate 149 
 
 tables ... .732 
 
 F. 
 
 Factory friction tests, data an^d 
 
 results of 655 
 
 Factory load curves 424, 42S 
 
 Faesch and Picard 252 
 
 Failures of Dams, literature on. . 601 
 
 Fairbairn 3 
 
 Fairmont pumping station 252 
 
 Falling stream, effects of on gra- 
 dient 201 
 
 Fanning, J. T 15 
 
 Financial considerations of water 
 
 power development 646 
 
 Fishways : 614 
 
 in dam at Danville, Illinois,.. 618 
 in timber dam at Sterling, 
 
 111 619 
 
 of Fish Commission State of 
 
 Wisconsin 619 
 
 literature on 632 
 
 Fitzgerald, Desmond. On evap- 
 oration 137 
 
 Fitz Water Wheel Company. 
 
 overshot water wheels of 243 
 
 Five-halves powers of numbers.. 744 
 Flash boards, 100, 609 
 
 Flash Boards Con. PAGE 
 
 adjustable at Eau Claire, 
 
 Wis 611 
 
 and supports, Rockford Wa- 
 ter Power Company 609 
 
 literature on 622 
 
 Float Measurements 226 
 
 at Lowell by Francis 229 
 
 Float Wheels, 1-3 
 
 London water works 1 
 
 Flood discharge, American and 
 
 European rivers 168 
 
 of rivers, relation to rainfall 745 
 Flood Flow, study of for report 
 
 on water power 678 
 
 Flood flows, data on 583 
 
 Flood gates 606 
 
 Flood over Holyoke dam 592 
 
 Flow, 
 
 comparative mean monthly 
 of Wisconsin and Rock 
 
 Rivers 178 
 
 distribution of velocity dur- 
 ing various conditions of. . 212 
 
 effects of low water 107 
 
 estimates of, 
 
 from cross sections and 
 
 slope 219 
 
 by weirs 219 
 
 in open channels, methods 
 
 for the estimate of 219 
 
 in open; channels, literature 
 
 of 198 
 
 in reaction wheels 317-320 
 
 in tangential wheels 316 
 
 measurements of by the de- 
 termination of velocity . . . 221 
 mean monthly of various 
 Eastern streams, in chron- 
 ological order 172 
 
 mean monthly of various 
 streams, arranged in order 
 
 of magnitude 173 
 
 of water in pipes 59 
 
 of water through orifices. ... 64 
 
 over weirs 64 
 
 power of a stream as affected 
 
 by 79 
 
 relations of guage height to 208 
 
766 
 
 Index. 
 
 PAGE 
 
 Flow and head, relations of 83 
 
 Fly-ball governor, first used . . 3 
 
 Fly wheel 457 
 
 Foot pound 32 
 
 Foot, cubic foot per minute, 
 
 equivalents of 36 
 
 Foot, cubic foot per second, 
 
 equivalents of 35 
 
 Foot gallon, equivalents of 34 
 
 Foot pound, equivalents of. ... 34 
 Foot pounds per minute, equiva- 
 lents of 35 
 
 Forests, effect on, evaporation .... 136 
 Foster, H. A., tests of steam 
 
 power plant 660 
 
 Foundations of dams... 581 
 
 Fourneyron turbine, 11, 239, 250, 305 
 
 characteristic curve of 409 
 
 data of 706 
 
 diagram of double turbine 
 of the Niagara Falls Water 
 
 Power Company 253 
 
 efficiency of 247 
 
 Fox River, hydrograph at Rapid 
 
 Croche 628 
 
 Francis, J. B 11, 378 
 
 float measurements at Low- 
 ell 229 
 
 formula for dam on the Mer- 
 
 rimac River 69 
 
 inward flow wheel 256 
 
 tests by 359 
 
 turbine at Boott Mills, test 
 
 data of 703 
 
 turbine, original 12 
 
 Fraser River, high water dis- 
 charge at Mission Bridge 170 
 
 Friction loss 44 
 
 in asphalt coated pipe 02 
 
 in lap-riveted pipe 63 
 
 in wood stave pipe 63 
 
 Friction in pipes, conduits and 
 
 channels, first principles 44 
 
 Friction loads in factories 655 
 
 Friction of reaction wheels, 
 
 losses by ' 315 
 
 Frizell's formula for sharp cres- 
 ted weirs 
 
 PAGE 
 
 Fuel, energy of 19 
 
 Furnace efficiency 22 
 
 G. 
 
 Ganguillet and Kutter's formula 47 
 Garratt, A. C., discussion of connec- 
 tion of governors to gates.... 493 
 Gas plant, estimate of capital 
 
 cost and annual cost 665 
 
 Gate hoists and head gates. . 611, 617 
 Gate movement, permissible rate 
 
 of 451 
 
 Gate opening, discharge of a tur- 
 bine at various 332 
 
 Gates and guides of Girard Im- 
 pulse turbine 306 
 
 Gates, 
 
 cylinder 300 
 
 details and operating devices 
 of Snoqualmie Falls tur- 
 bine 303 
 
 flood 606 
 
 for overshot and breast 
 
 wheels 3 
 
 register 301 
 
 wicket 300-301 
 
 Guage heights, 
 
 and heads available at Kil- 
 
 bourn, Wis 99 
 
 fluctuations in 200 
 
 relations at various stations 
 on the Wisconsin river. . . . 206 
 
 relation of to flow 208 
 
 Gears and shafting, losses in. ... 2i) 
 Generators and motors, ordinary 
 
 efficiency of 31 
 
 Generation and transmission of 
 
 energy, power losses in 27 
 
 Generation of power from poten- 
 tial source 26 
 
 Genesee River, run-off diagram.. 155 
 
 Geneva, Switzerland, 280 
 
 water works, Jonval turbine 
 
 at 281 
 
 Geological conditions, 
 
 effects on run-off 177 
 
 study of for report on water 
 power . . 677 
 
Index. 
 
 767 
 
 PAGE 
 
 Geylin Glass suspension bearing 290 
 
 Geylin-Jonval turbine 
 
 249, 254, 290, 299 
 
 of Niagara Falls Paper Mill 
 
 Company 256 
 
 Girard turbines, 
 
 current 239 
 
 Gates and guides of 306 
 
 general view of 280 
 
 impulse 278 
 
 longitudinal section of.. 279 
 
 runners of 284 
 
 with draft tube 278 
 
 runner of 280 
 
 Girard type for partial tur- 
 bine 273 
 
 type of water wheels 
 
 269, 276, 307 
 
 Glocker-White turbine governor 735 
 Governing, 
 
 impulse wheels with deflect- 
 ing nozzles 470 
 
 regulation with variable 
 
 speed and resistance 441 
 
 water wheels, present status 
 
 of 443 
 
 Governor, 
 
 Allis Chalmers hydraulic 735 
 
 anti-racing mechanical 473 
 
 calculations, nomenclature 
 
 for 447 
 
 connections, 
 
 by cable 477, 495 
 
 by draw rods 492 
 
 by shaft and sectors. . . . 494 
 control from switchboard. . . . 492 
 details and application of 
 
 Woodward 477 
 
 diagram of Lombard-Replogle 
 
 mechanical 479 
 
 effect of sensitiveness and 
 
 rapidity of 457 
 
 essential features of an hy- 
 draulic 481 
 
 for water wheels first used 3 
 general consideration of.... 491 
 Glocker-White . . 735 
 
 Governor Con. PAGE 
 Lombard-Replogle mechan- 
 ical 478 
 
 Lombard type "N" hydraulic 480 
 operating results with Lom- 
 bard 485 
 
 problem of water wheel 445 
 
 section and plans of Wood- 
 ward 476 
 
 section of Woodward vertical 
 compensating mechanical 475 
 
 simple mechanical 472 
 
 Sturgess hydraulic 486 
 
 the ideal 443 
 
 Woodward compensating. . . . 474 
 
 Woodward standard 471 
 
 specifications 467 
 
 Grade, effect of change in 205 
 
 Gradient, effect of channel con- 
 ditions on 203 
 
 effects of rising or falling 
 
 stream on 201 
 
 Granid River, at Lansing Mich- 
 igan 165 
 
 Graphical, 
 
 analysis of relation of power, 
 head and flow at Kilbourn, 
 
 Wisconsin 105 
 
 determination of stream flow 
 
 from measurements 230 
 
 investigation of the rela- 
 tions of power to head and 
 
 and flow 103 
 
 relation of energy and veloc- 
 ity in reaction turbines... 321 
 
 representation of head 97 
 
 representation of the laws of 
 
 motion 38 
 
 study of head 104 
 
 study of power at Kilbourn 104 
 
 Gravity wheels 237, 233 
 
 Great Lakes, hydrograph of dis- 
 charge of the 180 
 
 Growing period 157 
 
 Guides and buckets of Tremont 
 
 turbine 251 
 
 Gulf drainage, hydrographs of.. 
 
 190, 192 
 
768 
 
 Index. 
 
 H. 
 
 PAGE 
 
 Hand of water wheels 289 
 
 Hanging bearing, the Niagara 
 
 Falls Power Company 293 
 
 Harness and driving sheaves, 
 Southwestern Missouri Light 
 
 Co 533 
 
 Harper, John L., tests of Leffel 
 
 turbines at Niagara 380 
 
 Harrington, N. W., effect of for- 
 ests on rainfall and evapora- 
 tion 133 
 
 Hartford Electric Light Co., 
 
 increase in sale of energy 
 
 of 423 
 
 load curve of 422 
 
 Head, at Kilbourn dam 581 
 
 showing changes in.... 99 
 under various conditions 97 
 effect of design of dam on 
 
 available 100 
 
 entrance 42 
 
 friction 44 
 
 graphical representation of . . 97 
 
 graphical study of 104 
 
 measurements of 373 
 
 on turbines, relation to speed 
 
 and diameter 324 
 
 study of for report on water 
 
 power 67S 
 
 variations in 93 
 
 velocity 41 
 
 velocity in feet per second 
 
 due to 741 
 
 Head and flow, 
 
 importance of for power pur- 
 poses 79 
 
 relations of 83 
 
 variations of 83 
 
 Head and power, 
 
 effect of number of wheels 
 
 on 108 
 
 selection of turbine for uni- 
 form 38? 
 
 Head gates, 
 
 at Constantine, Michigan 612, 613 
 details of for Mr. Wait Tal- 
 cott, Rockford, Illinois.. . 616 
 
 Head Gates Con. PAGE 
 
 rear view of, at Constantine, 
 
 Michigan 613 
 
 Head race, plants with 570 
 
 Head water curve 96 
 
 Heat, 
 
 solar, 20 
 
 units of, 32 
 
 Heights of dams, limit of 580 
 
 Henry, Professor, conclusions on 
 the reliability of rainfall rec- 
 ords 125 
 
 Henschel turbine 233 
 
 Hercules turbine, test of a 54 inch 710 
 
 High head developments 575 
 
 High head or type "B" runner.. 268 
 High water, Fraser River at Mis- 
 sion, Bridge, B. C 170 
 
 History of water power develop- 
 ment 1, 14, 16 
 
 Hoist for tainter gates 606 
 
 Holyoke Machine Company, test 
 
 of a 54 inch turbine 710 
 
 Holyoke testing flume, 364, 370 
 
 arranged for horizontal tur- 
 bines 367 
 
 plan of 366 
 
 Holyoke Water Power Company, 
 
 canals of 568 
 
 view of dam during flood. . . . 591 
 view of masonry dam of.... 590 
 
 Horse power, 32 
 
 and efficiency of proposed tur- 
 bines for McCall Ferry 
 
 Power Company 418 
 
 equivalents of 34 
 
 speed relation of from tests 415 
 
 Horse power hour 33 
 
 Houck Falls power station, test 
 of Victor high pressure turbine 
 
 at 382 
 
 Howd-Francis turbine 249 
 
 Howd, Sanruel B 11 
 
 wheel of 256 
 
 Hudson River, 
 
 discharge arranged in chrono- 
 
 ical order 172 
 
 arranged in order of 
 magnitude 174 
 
Index. 
 
 769 
 
 Hudson River Con. PAGE 
 
 run-off diagram of 155 
 
 table showing relation of 
 rainfall to runoff for the 
 storage, growing and re- 
 plenishing period 158 
 
 Hudson River Power Transmis- 
 sion Company, 
 speed records from plant of 48G 
 
 Spier's Falls plant of 546 
 
 Hug bucket 274 
 
 Hunking, A. W., notes on water 
 
 power equipment 338 
 
 Hunting or racing of water 
 
 wheels 447 
 
 Hunt-McCormick runner 267 
 
 Hunt runner of The Rodney Hunt 
 
 Machine Company 269 
 
 Hurdy-Gurdy wheel 241 
 
 Hydraulics, general literature on 75 
 Hydraulic governor, 
 
 Allis Chalmers 735 
 
 details of Lombard 481 
 
 essential features of 481 
 
 Glocker-White 735 
 
 Sturgess type "N" 488 
 
 Sturgess, the 486 
 
 Hydraulic gradient, 
 
 effects of channel grade and 
 
 obstructions on 204 
 
 effects of variable flow on... 200 
 of a stream, 
 
 after construction of dam 94 
 effects of variable flow on 202 
 under various conditions 
 
 of flow 93 
 
 Hydraulic plant, energy losses 
 
 in 25 
 
 Hydraulics, 40 
 
 of the turbine... 309 
 
 Hydraulic type of relay 471 
 
 Hydro-electric plant, 
 
 efficiency of 24 
 
 losses in 26 
 
 Hydrographs, 80 
 
 as power curves 89 
 
 available at some other point 
 
 on the river 82 
 
 available on other rivers 83 
 
 47 
 
 Hydrographs Con. PAGE 
 
 comparative from different 
 hydrological divisions of 
 
 the U. S 184, 189 
 
 continuous 24 hour theoreti- 
 cal power at Kilbourn .... 88 
 for full range of conditions 
 of rainfall and temperature 82 
 
 when none are available 85 
 
 of, 
 
 Alcovy River 191 
 
 Atlantic and Eastern 
 
 Gulf Drainage 190 
 
 Ausable River 186 
 
 Bear River, Utah 193 
 
 Chittenango River 191 
 
 Clear Creek 192 
 
 Coosa River 190 
 
 Discharge of Great Lakes 180 
 
 Fox River 628 
 
 Grand River 
 
 at Grand Rapids... 
 
 186, 191 
 at North Lansing.. 186 
 
 Hood River 193 
 
 Iron River, Michigan... 191 
 
 Kalamazoo River 186 
 
 Kalawa River 193 
 
 Kennebec River 19$ 
 
 Kern River 193 
 
 Licking River 190 
 
 Meramec River 192 
 
 Mississippi Valley and 
 
 Gulf Drainage 191 
 
 Niobrara River 192 
 
 Ohio Valley and St. Law- 
 rence Drainage 191 
 
 Otter Creek 192 
 
 Passaic River 1^82-183 
 
 Perkiomen Creek 190 
 
 Rio Grande River 192 
 
 Salt River 192 
 
 San Gabriel River 193 
 
 Seneca River 190 
 
 Spokane River 193 
 
 St. Joseph River 186 
 
 Tennessee River 191 
 
 Thunder Bay River 186 
 
 Walker River, California 193 
 
770 
 
 Index. 
 
 Hydrographs Con. PAGE 
 
 Western drainage 193 
 
 Wisconsin River, 
 
 at Kilbourn, based 
 on measurements 
 
 at Necedah 86 
 
 at Necedah, Wis. 81,192 
 
 Yadkin River 190 
 
 Yellowstone River 192 
 
 power hydrographs at, 
 
 Kilbourn 90-91 
 
 Sterling, Illinois 623 
 
 reliability of comparative. .. 87 
 showing continuous power 
 at Kilbourn, with actual 
 
 head 101 
 
 showing power of plant as 
 influenced by variable head 110 
 
 study of a stream from 181 
 
 use of comparative 83 
 
 use of local 83 
 
 when none are available 87 
 
 when available 82 
 
 Hydrological divisions of the U. 
 S., comparative hydro- 
 graphs from 189 
 
 I. 
 
 Ice conditions, 
 
 maximum velocities in a ver- 
 tical plane 217 
 
 rating curve for... 217 
 
 with overshot and breast 
 
 wheels 3 
 
 Ice covering, effects of, on distri- 
 bution of velocity 215 
 
 Illinois River basin, comparison 
 of mean monthly rainfall 
 
 and run-off 147 
 
 Improved New American tur- 
 bine 257, 259, 300 
 
 calculations from character- 
 istic curves of 407 
 
 characteristic curve of 406 
 
 sectional plan of 262 
 
 Impulse and reaction turbines.. 311 
 
 relative advantage of 245 
 
 conditions of operations of. . 215 
 
 PAGE 
 
 Impulse turbines (see also Tan- 
 gential Wheels) 
 
 237,241,244,246,301,313 
 
 angle of discharge 310 
 
 early development of 261) 
 
 efficiency of 247 
 
 governing of 470 
 
 regulation of 452 
 
 J. 
 
 James Leffel and Company 266 
 
 characteristic curve of a 45 
 
 inch Samson wheel... 410-411 
 curve showing efficiency, 
 power and discharge, un- 
 der various heads, calcu- 
 lated from characteristic 
 
 curves 412 
 
 double horizontal turbine. . . . 517 
 double horizontal turbine 
 
 manufactured by 265 
 
 double runner of 26'i 
 
 four pairs of 45 inch Samson 
 
 horizontal turbines 523 
 
 tests of wheel at Niagara. . . . 380 
 Janesville, Wisconsin : 
 
 dam during high water 583 
 
 dam during moderate flow.. 583 
 
 dam showing low water 582 
 
 Joliet plant of Economy Light 
 
 and Power Company 571 
 
 Joliet, water power at 22 
 
 Jolly, J. & W., Holyoke, Mass.,.. 248 
 test of a 57 inch turbine. . . . 70S 
 
 test of a 51 inch turbine 711 
 
 Jonval, 8 
 
 turbine, 239-255 
 
 efficiency of 247 
 
 at the Geneva Water Works 281 
 
 tests of a 30 inch 725 
 
 tests of a 30 inch special 724 
 
 the American . . 252 
 
 K. 
 
 Kennebec River discharge, 
 
 arranged in order of magni- 
 tude 17.! 
 
 chronologically arranged... 172 
 
Index. 
 
 771 
 
 Kilbourn dam, 
 
 diagram showing changes in 
 
 head at 99 
 
 head under various condi- 
 tions of flow 97 
 
 Kilbourn, Wisconsin: 
 
 guage heights and head 
 
 available at 99 
 
 graphical study of power at 104 
 
 head gate hoists at 617 
 
 hydrograph showing continu- 
 ous power with actual head 101 
 hydrograph showing 24 hour 
 
 horse power 88 
 
 hydrograph of Wisconsin 
 River based on flow at Ne- 
 
 cedah, Wis 86 
 
 plant of Southern Wisconsin 
 
 Power Company 521, 569 
 
 power hydrograph 90 
 
 power hydrograph, H. P. 
 
 hours with pondage 10, 19 
 
 power of the wheels under 
 
 variations in flow 106 
 
 rainfall above 129 
 
 Kilowatt hour 33 
 
 Kinetic energy 33, 34, 36 
 
 Knight bucket 274 
 
 Koechlin 8 
 
 Kuichling, Emil: 
 
 discussion of rainfall and 
 
 run-off 162 
 
 graphical relations of dis 
 charge area for maximum 
 flood, American and Euro- 
 pean rivers 168 
 
 Kutter's coefficient "n" 47 
 
 Kutter's formula 47 
 
 diagrams for the solution of 48-49 
 
 L. 
 
 Lake Cochituate, rainfall, run-off 
 
 and evaporation 763 
 
 Lake Superior Power Company, 
 
 pJant of 570 
 
 Lap-riveied pipe, friction losses 63 
 Laws: of energy conservation... 21 
 of motion, graphical repre- 
 sentation of . . 38 
 
 Laws Con. PAGE 
 
 of motion, Newton's 36 
 
 Laxy overshot water wheels (see 
 
 frontispiece) 14 
 
 Leffel and Company, the James 
 (See also James Leffel & 
 
 Co) 13 
 
 tests of a 56 inch turbine... 709 
 test of a 45 inch Samson tur- 
 bine 713 
 
 Leffel turbine, 249 
 
 diagram of efficiency, dis- 
 charge and power at Niagara 380 
 
 tests of, at Logan, Utah 379 
 
 Lighting, losses in generation and 
 transmission of power for.... 30 
 
 Limit turbines. 244 
 
 Lippincott, J. B. and S. G. Ben- 
 nett, relations of rainfall to 
 
 run-off in California 177 
 
 Literature: 
 
 back water and interference 78 
 
 causes of rainfall 131 
 
 concerning dams 595 
 
 descriptive of hydraulic and 
 
 hydro-ejectric plants 556 
 
 disposal of rainfall 144 
 
 effect of altitude on rainfall 132 
 
 evaporation 144 
 
 floods 190 
 
 flow of water over weirs. ... 77 
 flow of water through pipes 76 
 
 general hydraulic. 75 
 
 measurement of rainfall 132 
 
 power and energy 39 
 
 percolation 144- 
 
 relations of rainfall and 
 
 stream flow 195 
 
 results of stream flow meas- 
 urements 194 
 
 stream gauging 233 
 
 turbines 353 
 
 turbine testing 383 
 
 water power development . . 16 
 Lloyd, E. W., data concerning the 
 power load on various central 
 stations, due to various classes 
 of consumers . 667 
 
772 
 
 Index. 
 
 PAGE 
 
 Load conditions for maximum re- 
 turns 431 
 
 Load curve 420 
 
 factory 424 
 
 for sharp thunder storm peak 426 
 in relation to machine selec- 
 tion 433 
 
 New York Edison Company, 
 
 for day of maximum load. . 425 
 of Hartford Electric Light 
 
 Company 422 
 
 of light and power plant 421 
 
 literature on 439 
 
 maximum days of pumping, 
 
 London Hydraulic Co 429 
 
 Pennsylvania railroad shops 427 
 relation of power, supply and 
 
 demand, diagrams of 435 
 
 relation of, to stream flow 
 
 and auxiliary power 434 
 
 study of, for report on water 
 
 power 679 
 
 typical factory 42S 
 
 typical railway 430 
 
 Load factor, 
 
 definition of 433 
 
 effect of on cost of power, Ar- 
 chibald 662 
 
 effect of on cost of steam- 
 generated electric power to 
 
 the consumer 669 
 
 influence of on operating ex- 
 penses 662 
 
 literature on 439 
 
 Logan, Utah, tests of Leffel tur- 
 bines at 370 
 
 Log way 621 
 
 at Lower Dam, Minneapolis, 
 
 Minn 62 1 
 
 in the Chesuncook timber 
 
 dam 620 
 
 Lombard governor, 
 
 operating results with 485 
 
 details of 481 
 
 type "R" 484 
 
 type "N" 480 
 
 Lombard hydraulic relief valves 496 
 Lombard relay valve. . . 483 
 
 PACK 
 Lombard-Replogle mechanical 
 
 governor 478, 479 
 
 London Hydraulic Supply Com- 
 pany, maximum days of pump- 
 ing 429 
 
 London water wheels, float 
 
 wheels 1 
 
 London Water Works, undershot 
 
 wheel used in 14 
 
 Losses, 
 
 in an hydro-electric plant. ... 26 
 
 in belts 30 
 
 in\ machinery 23 
 
 in turbines 27,371 
 
 Low heads, vertical shaft tur- 
 bine for 509 
 
 Low water flow, effects of 107 
 
 Machine factor, definition of.... 433 
 
 Machine, ideally perfect 23 
 
 Machine selection, load curve in 
 
 relation, to 433 
 
 Machinery, losses in 23 
 
 Madison, Wisconsin, diagram of 
 fluctuations of monthly rain- 
 fall at 122 
 
 Manchester, England, sharp thun- 
 der storm peak 426 
 
 Maps of, 
 
 average annual rainfall in 
 
 the United States 112-113 
 
 average annual rainfall in 
 
 Wisconsin 115 
 
 rainfall conditions in the 
 
 United States, July 16-17 118 
 weekly distribution of rain- 
 fall in Wisconsin 117 
 
 Manufacturing purposes, losses in 
 
 utilization of energy for 30 
 
 Market price of water power.... 663 
 Masonry dams, 
 
 literature on 597 
 
 stability of 586 
 
 Mass 36 
 
 Mass diagram showing run-off 
 
 from Tochickon Creek 639 
 
 Mathon, DeCour 5 
 
 McCall's Ferry dam, section of . . . 592 
 McCormick, John B 13,266 
 
Index. 
 
 773 
 
 PAGE 
 
 McCormick turbine, 267, 269 
 
 test of a 57 inch 708 
 
 test of a 51 inch 711 
 
 test of a 39 inch 717 
 
 Mechanical governor, 
 
 anti-racing, Woodward 473 
 
 Lombard-Replogle 478 
 
 simple, Woodward 472 
 
 Mechanical type of relay 471 
 
 Merrill, Wisconsin, rainfall above 129 
 Merrimac River discharge, 
 
 arranged in chronological 
 
 order 172 
 
 arranged in order of magni- 
 tude 174 
 
 Meter, the wheel as a 365 
 
 Michigan drainage area 185 
 
 Michigan rivers, 
 
 comparative hydrographs of 
 
 various 186 
 
 discharge in cubic feet per 
 second per square mile of 
 
 drainage area 18<8 
 
 Mississippi Valley Drainage, hy- 
 drographs of 192 
 
 Missouri River, variations in the 
 cross-section of, near Omaha, 
 
 Neb 210 
 
 Momentum, exertion of, energy 
 
 by 41 
 
 Moore bucket 274 
 
 Morin, tests in 1838 359 
 
 Morris Company, I. P 252, 268 
 
 diagram of double Fourney- 
 
 ron turbine 253 
 
 estimate for turbine for Mc- 
 
 Call-Ferry Power Co 412 
 
 graphical diagram of rela- 
 tions of power and head. . . 413 
 graphical diagram of test of 
 wheel of The Shawinigan 
 
 Power Company 382 
 
 Shawinigan Falls turbine... 270 
 Trenton Falls plant of The 
 Utica Gas and Electric Co. 511 
 
 Morris, Elwood, 9 
 
 first systematic tests of tur- 
 bines in U. S.. . . 359 
 
 PAGE 
 Morris plant of Economy Light 
 
 and Power Co 572 
 
 Motion, 
 
 compound 37 
 
 laws of 36 
 
 uniform 37 
 
 uniformly varied 37 
 
 Motor installation, capital cost 
 
 and annual charge on ..... 657 
 
 ordinary efficiency of 31 
 
 Movable crest for dam at Kil- 
 
 bourn, Wisconsin 608 
 
 Movable dams 100, 603 
 
 at McMechan, W. Va 603 
 
 literature on 622 
 
 Mullin's formula (used by East 
 
 India engineers) 69 
 
 Murphy, E. C., methods of current 
 
 meter computation 227 
 
 Muskingum River, run-off dia- 
 gram of 156 
 
 table showing relations of 
 rainfall to run-off for vari- 
 ious periods 156 
 
 Necedah, Wisconsin, 
 
 hydrograph of the Wiscon- 
 sin River at 96 
 
 rainfall above 129 
 
 rating curve of Wisconsin 
 
 River at 96 
 
 Needle nozzle, Doble, cross section 
 
 of 306 
 
 Neshaminy Creek, 167 
 
 rainfall, run-off and evapora- 
 tion 754 
 
 Nevada Mining and Milling Com- 
 pany, plant of 555 
 
 New American turbine 257 
 
 test of a 44 inch 714 
 
 runner of 260 
 
 Newell, F. H., estimates of rela- 
 tion of rainfall to run,'-off 174 
 
 Newton's laws of motion 36, 38 
 
 Niagara Falls, 
 
 estimate of the cost of hydro- 
 electric plant at 643 
 
774 
 
 Index. 
 
 Niagara Falls Con. PAGE 
 
 first power at 15 
 
 power development 576 
 
 water power at 22 
 
 Niagara Falls Hydraulic Power 
 and Manufacturing Company 
 
 255, 266 
 
 Niagara Falls Paper Company. . . 254 
 Niagara Falls Power Company, 
 the vertical bearing used by 291 
 double horizontal Leffel tur- 
 bine of the 265 
 
 tests of wheels of 380 
 
 Niagara River, hydrograph of dis- 
 charge of 179 
 
 Niagara Falls Water Power Com- 
 pany 252 
 
 Niagara Fourneyron turbine 290 
 
 Nomenclature for, 
 
 governor .calculations 447 
 
 turbine discussion 310 
 
 Nora, Chinese 1 
 
 Northern Hydro-Electric Power 
 Company, hoists for tainter 
 
 gates for 606 
 
 Northern rivers, monthly rainfall 
 
 and run-off 165 
 
 Nunn, P. N., turbine tests at Lo- 
 gan, Utah 379 
 
 O. 
 
 Oberchain, Matthew and John.. 267 
 Obstructions, 
 
 effect of change in 205 
 
 effects on channel grade, and 
 
 on the hydraulic gradient 204 
 Ogden pipe line, experiments on 60 
 Ohio Valley drainage, hydro- 
 graphs of 191 
 
 Oliver Power Plant, wheel har- 
 ness of 530 
 
 Ontario Hydro-Electric Power 
 
 Commission, estimates by 
 
 648, 649, 654, 656, 657, 664 
 Open channels, flow in, literature 
 
 of 198 
 
 Open penstocks, 
 
 application of method to 465 
 
 predetermination of speed 
 
 Open Penstocks Con. PAGE 
 
 regulation for wheels set 
 
 in 461 
 
 Operation, economy in 527 
 
 Operating expenses, 
 
 effect of load factor on...,. 662 
 estimate of for various pro- 
 posed Canadian plants.... 654 
 ratio of individual items to 
 
 total 660 
 
 Orifices, 
 
 flow of water through 01 
 
 submerged 43 
 
 Oscillatory waves in long pen- 
 stock 451 
 
 Outward radial flow turbines... 244 
 
 Overload 526 
 
 Overshot water wheels 3, 243 
 
 Laxy 14 
 
 P. 
 
 Pacific Coast, development of 
 
 wheels on 275 
 
 Paddle wheels 241 
 
 Paris water works, undershot 
 
 wheel used in 14 
 
 Partial load, effect of on cost of 
 
 power 651 
 
 Partial turbines 244 
 
 Passaic River, 
 
 hydrographs of 182-18S 
 
 rainfall on drainage area of 
 
 182-18a 
 
 relations of rainfall to ruii'- 
 
 off 182-183 
 
 rim-off diagrams of 155 
 
 Pel ton, 
 
 bucket 274 
 
 tangential water wheel run- 
 ner 27d 
 
 Water Wheel Company 275-276 
 
 wheel 276, 307 
 
 Penstock velocity, 
 
 change of 453 
 
 energy required to change 
 
 446-456 
 
 Percolation, literature on 144 
 
 Periods, growing 15? 
 
Index. 
 
 775 
 
 Periods Con. PAGE 
 
 replenishing 157 
 
 storage 157 
 
 Pcrkiomen Creek,,. 167 
 
 rainfall, run-off and evapora- 
 tion 75G 
 
 Peshtigo River development, pro- 
 file of 574 
 
 Philadelphia, water wheel tests 
 
 in 1860 at 360 
 
 Pile foundations for dams.. 603, 608 
 
 Piobert and Tardy 8 
 
 Pipe> 
 
 Chezy's formula 60 
 
 Darcy's formula 60 
 
 flow of water in 59 
 
 literature on flow of water in 76 
 
 losses in asphalt coated 62 
 
 Plant capacity 525 
 
 Plant design, study of for report 
 
 on water power 681 
 
 Plant of, 
 
 Columbus Power Company.. 546 
 Hudson River Transmission 
 
 Company at Spier's Falls 546 
 Nevada Mining and Milling 
 
 Company 555 
 
 South Bend Electric Company 546 
 Sterling Gas and Electric 
 
 Company 537 
 
 The Concord Electric Com- 
 pany 553 
 
 The Dolgeville Electric Light 
 
 and Power Company 548 
 
 The Lake Superior Power 
 
 Company 570 
 
 The Niagara Falls Paper 
 
 Company 257 
 
 The Shawinigan Water and 
 
 Power Company 550 
 
 Winnipeg Electric Railway 
 
 Company 553 
 
 York Haven Water Power 
 
 Company 537 
 
 Plants, 
 
 Located in dams 574 
 
 with concentrated fall 564 
 
 with divided fall 564 
 
 with head race only.. . 570 
 
 PAGE 
 
 Platt Iron Works Company 
 
 . . .267, 268, 276, 295, 300, 301, 308 
 characteristic curves of a Vic- 
 tor turbine 402-403 
 
 graphical diagram of test of 
 25 inch Victor high pres- 
 sure turbine 382 
 
 relations of efficiency to dis- 
 charge at various revolu- 
 tions 405 
 
 the Snoqualmie Falls reac- 
 tion turbine 272-273 
 
 test data of 48 inch turbine 704 
 
 test of a 42 inch turbine 715 
 
 test of a 45 inch turbine 712 
 
 tests of a 36 inch turbine 720 
 
 tests of a 33 inch turbine 723 
 
 Poncelet's wheel 4, 241 
 
 Pondage, 
 
 effect of limited, on the power 
 
 curve 624 
 
 effect of on power 624 
 
 hydrograph on Fox River 
 showing effect of Sunday 
 shutdown of hydraulic 
 
 plants 628 
 
 hydrograph showing effect of 
 
 626 
 
 study of for report on water 
 
 power 679 
 
 Pondage and storage, 
 
 analytical method for calcu- 
 lating 644 
 
 Potential energy, 20, 33 
 
 development of 19 
 
 generation of power from. ... 26 
 Potomac River, 
 
 discharge arranged in chronr 
 
 ological order 172 
 
 discharge arranged in order 
 
 magnitude 174 
 
 discharge, velocity and area 
 
 curve of 232 
 
 Power, 
 
 actual conditions under 
 which same is furnished 
 to consumers from central 
 stations . 668 
 
776 
 
 Index. 
 
 Power Con. PAGE 
 
 at Kilbourn, graphical study 
 
 of .104 
 
 charges for by Cataract 
 Power and Conduit Co. of 
 
 Buffalo 670 
 
 conversion of 26 
 
 development of 
 
 at Niagara Falls 576 
 
 study of for report on 
 
 water power 680 
 
 effect of on pondage 624 
 
 from municipal sub-station, 
 
 estimated cost of 656 
 
 literature on 672 
 
 measurment of 375 
 
 of the Kilbourn wheels un- 
 der variations in; flow 106 
 
 of plant as influenced by var- 
 iable head, hydrograph 
 
 showing 110 
 
 of plant, effect of head on . . 100 
 
 of steam 33 
 
 of stream as affected by flow 79 
 
 of turbine, 325 
 
 expression for 336 
 
 of homogeneous design . . 341 
 
 proportional to hi 8v>5 
 
 of water 33 
 
 relation of to head in a 12 
 inch Smith-McCormick tur- 
 bine 33G 
 
 sale of 666 
 
 transmission of 26 
 
 utilization of 26 
 
 Power and diameter, 
 
 graphical relations of in tur- 
 bines of homogeneous de- 
 sign 341 
 
 of various American turbines 342 
 Power and energy, literature on.. 39 
 Power and speed of turbines, 
 
 relations of 347 
 
 various American 350 
 
 Power curve, 
 
 effects of limited pondage 624 
 
 hydrograph as a 89 
 
 Power, head, and flow, relation 
 of at Three Rivers, Michigan 103 
 
 PACK 
 
 Power hydrograph at Kilbourn 91 
 Power hydrograph at Sterling, 
 
 Illinois C25 
 
 Power losses in generation and 
 
 transmission of energy 27 
 
 Power plant at Turner's Falls. . . . 514 
 Power station, 
 
 and dam, relation of 561 
 
 study of site of for report on 
 
 water power 681 
 
 Power transmission, 
 
 estimate of investment, an- 
 nual charges and costs. . . . 656 
 
 literature on 673 
 
 Precipitation, 
 
 in United States, types of 
 
 monthly distribution 123 
 
 relation of evaporation, run- 
 off and temperature to, on 
 
 Lake Cochituate 140 
 
 run-off, evaporation and tem- 
 perature, relations on Siid- 
 
 bury River basin 151 
 
 run-off, evaporation and tem- 
 perature, relations of on 
 
 Upper Hudson River 154 
 
 variations at stations closely 
 
 adjoining 125 
 
 Pressure, exertion of energy by. . 41 
 Pressure or reaction turbines. . . . 244 
 Price's electric current meter. . . . 222 
 Prime movers, possibilities of. ... 528 
 
 Prony brake, W. O. Weber 377 
 
 Pumping engine, efficiency of. ... 23 
 Pumping plant, 
 
 at Connorsville, Indiana, reg- 
 ulation of 441 
 
 energy losses in steam and 
 electric 25 
 
 R. 
 Raceways, 
 
 of Holyoke Water Power 
 
 Company 56S 
 
 of Sterling Hydraulic Com- 
 pany 567 
 
 Racing or hunting of water 
 wheels , 447 
 
Index. 
 
 777 
 
 PAGE 
 
 Racing, value of 456 
 
 Racks, trash 536 
 
 Rafter and Williams, experi- 
 ments of. 65 
 
 Rafter, George W., 
 
 discussion of rain fall 125 
 
 discussion of Vermuele's for- 
 mula 148 
 
 graphical comparison of dis- 
 charge over weirs 68, 69 
 
 graphical diagram showing 
 discharge over weirs with 
 
 irregular crest 72-73 
 
 report to the Board of Engi- 
 neers on Deep Waterways 65 
 
 Railway load curve, typical 430 
 
 Rainfall, 
 
 accuracy of records of ........ 122 
 
 at Merrill, Wis ,120 
 
 annual at, 
 
 Augusta, Ga 120 
 
 Cincinnati, 120 
 
 Des Moines, Iowa 120 
 
 Detroit, Mich 120 
 
 Helena, Mont 120 
 
 Little Rock, Ark 120 
 
 Madison, Wis 120 
 
 Montgomery, Ala 120 
 
 Moorhead. Minn 120 
 
 New Haven, Conn 120 
 
 Phoenix, Ariz 120 
 
 Sacremento, Cal 120 
 
 San Antonio, Texas 120 
 
 Spokane, Wash 120 
 
 Tacoma, Wash 120 
 
 Topeka, Kans 120 
 
 Winnemucca, Nev 120 
 
 annual, local variations and 
 
 periodic distribution of 121 
 
 conditions in the United 
 
 States 118 
 
 data, availability of 87 
 
 disposal of 133 
 
 distribution of Ill 
 
 in United States, types of 
 monthly distribution of... 123 
 
 literature on 130 
 
 literature on disposal of.. . 144 
 
 Rainfall Con. PAGE 
 
 maps and records, accuracy 
 
 of 122 
 
 monthly mean at, 
 
 Augusta, Ga 127 
 
 Cincinnati, 127 
 
 Des Moints, Iowa. 127 
 
 Detroit, Mich... 127 
 
 Helena, Mont 127 
 
 Little Rock, Ark 127 
 
 Montgomery, Ala 127 
 
 Moorhead, Minn 127 
 
 New Haven, Conn 127 
 
 Sacramento, Cal 127 
 
 San Antonio, Tex 127 
 
 Spokane, Wash 127 
 
 Tacoma, W r ash 127 
 
 Topeka, Kans 127 
 
 Tucson, Ariz 127 
 
 various points in United 
 
 States 127 
 
 Winnemucca, Nev 127 
 
 observations, accuracy in... 126 
 on the drainage area of the 
 
 Wisconsin river 129 
 
 records, value of extended.. 124 
 relations of annual to run off 177 
 
 study of, Ill 
 
 as affecting run-off 126 
 
 for report on water 
 
 power 677 
 
 rate or intensity of 133 
 
 relation to river discharge.. 745 
 run-off and evaporation, for 
 
 various periods 750 
 
 variations of at stations 
 
 closely adjoining 125 
 
 Rainfall and Altitude 124 
 
 Rainfall to run-off 
 
 monthly relation of 162 
 
 on southern rivers 166 
 
 on Northern rivers 165 
 
 on Sudbury River for each 
 
 period of the water year. . 161 
 on upper Hudson River for 
 each period of the water 
 
 year 160 
 
 relations between monthly 
 depth of 161 
 
77 8 
 
 Index. 
 
 Rainfall to run-off Con. PAGE 
 
 relations between, on the 
 
 Passaic river 182-183 
 
 relation of, for various per- 
 iods on the Connecticut 
 
 River 159 
 
 relations of, for various per- 
 iods on the Hudson River 158 
 relations of, on the Hudson 
 and Genesee River, dia- 
 gram of 155 
 
 relation of periodic 159 
 
 Rating curve, 
 
 changes in head due to 
 changes in cross section.. 96 
 
 current meter 221 
 
 for Wallkill River, ice and 
 
 open conditions 217 
 
 for Wisconsin River at Kil- 
 
 bourn, Wisconsin 209 
 
 influence of stream cross sec- 
 tion on 95 
 
 Rating or discharge curve 95 
 
 Rating station for current meters, 
 
 Denver, Colorado 223 
 
 Reaction and impulse turbines.. 311 
 
 relative advantages of 245 
 
 Reaction turbine, 237, 239, 316 
 
 American type 256 
 
 arrangement of 500 
 
 condition of operation of.... 245 
 
 diagrams of 240 
 
 economical operation of 31$ 
 
 friction of 318 
 
 general conditions of opera- 
 tion 500 
 
 graphical relation of energy 
 
 and velocity in. . 321 
 
 graphical relation of velocity 
 
 and energy in flow through 320 
 minimum residual velocity 
 
 of water in leaving buckets 319 
 necessary submergence of... 501 
 
 path of jet 317 
 
 relative velocity of the bucket 318 
 residual velocity of water 
 
 from 31S 
 
 Snoqualmie Falls 272,273 
 
 PAGE: 
 
 Register gates 301, 301 
 
 diagram showing eddying 
 
 caused by 305- 
 
 Regulation of impulse wheels... 452: 
 Regulation of turbines, compara- 
 tive 487 
 
 Reinforced concrete dams, litera- 
 ture on 601 
 
 Relay, 
 
 hydraulic type of 471 
 
 mechanical type of 471 
 
 Relay Valve, Lombard 483" 
 
 Relief valves, 495-498- 
 
 Lombard hydraulic 49ft 
 
 on end of penstock 49f> 
 
 Sturgess 49S 
 
 Rennie 3- 
 
 Replenishing period 15T 
 
 Report of water power, general 
 
 outline of 683 
 
 Resistance and speed, relation of 44ft 
 Retardation of water in penstock 690 
 
 of on gradient 201 
 
 Rising or falling stream, effects 
 
 Risler, M. E., estimate of daily 
 
 consumption of water by differ- 
 
 erent kinds of crops 135 
 
 Rivers, 
 
 comparative hydrograph of 
 
 various in Michigan 18f> 
 
 hydrographs of, 
 
 Alcovy River 190 
 
 Bear River, Utah 19S 
 
 Clear Creek 192 
 
 Chittenango Creek 191 
 
 Coosa River 19ft 
 
 Grand River at Grand 
 
 Rapids 191 
 
 Hood River 193 
 
 Iron River 193" 
 
 Kalawa River 193 
 
 Kennebec River 19ft 
 
 Kern River 193 
 
 Licking River 191 
 
 Meramec River 192 
 
 Niobrara River 192 
 
 Otter Creek.. . 192 
 
Index. 
 
 779 
 
 Rivers, hydrographs of Con. PAGE 
 
 Perkiomen Creek 191 
 
 Rio Grande River 192 
 
 Salt River 192 
 
 San Gabriel River 193 
 
 Seneca River 191 
 
 Spokane River 193 
 
 Tennessee River 191 
 
 Walker River 19;! 
 
 Wisconsin River at Ne- 
 
 cedah, Wis 192 
 
 Yadkin River 190 
 
 Yellowstone River 192 
 
 monthly discharges in cub. 
 ft. per sec. per square mile, 
 
 Ausable River 183 
 
 Grand River at Grand 
 
 Rapids 188 
 
 Grand River at Lansing, 
 
 Mich 1S8 
 
 Kalamazoo River 1 88 
 
 Manistee River 188 
 
 Muskegon River 188 
 
 St. Joseph River 18S 
 
 Thunder Bay River 188 
 
 White River 188 
 
 relation of rainfall and run- 
 off on 165 
 
 Reek-fill dams, literature on 597 
 
 Rockford, Illinois, 
 
 details of head gates for Mr. 
 
 Wait Talcott 610 
 
 flashboards and supports at. . 609 
 Rock River, 
 
 at Rockton, Illinois 165 
 
 comparison of mean monthly 
 
 flow with Wisconsin River 178 
 Rodney Hunt Machine Company 
 
 267-268 
 
 Rome, water wheels in 14 
 
 Rotary converters, losses in 29 
 
 Rotation of water wheels, direc- 
 tion of 289 
 
 Rou6 a Cuves 8 
 
 Rou6 Volant 8 
 
 Runner, 
 
 details of 28C 
 
 its material and manufacture 2j84 
 Improved New American.... 261 
 
 Runner Con. PAGE 
 
 of Girard turbine 280 
 
 Run-off (see also Stream Flow), 
 
 relations between monthly 
 depth 164 
 
 study of for report on water 
 power 676 
 
 and rainfall, monthly rela- 
 tion of 162 
 
 and rainfall, monthly rela- 
 tions on Southern Rivers.. 16(5 
 
 and rainfall, monthly rela- 
 tions of on Northern Rivers left 
 
 diagrams 
 
 of Hudson and Genesee 
 
 River 155 
 
 of the Muskingum River 156 
 of the Passaic River.... 155 
 
 effects of area on 179 
 
 effects of geological condi- 
 tions on 177 
 
 effects of rainfall on 126 
 
 influence of storage on the 
 distribution, of 179 
 
 influen.ce of various factors 
 on 14S 
 
 mean annual of the rivers of 
 the U. S 152-153 
 
 precipitation, evaporation and 
 temperature, relations of 
 on Upper Hudson River.. 154 
 
 precipitation, run-off and tem- 
 perature, on Sudbury River 
 basin, relations of 151 
 
 rainfall, and evaporation, 
 for various periods 750 
 
 relation of periodic rainfall 
 to 159 
 
 relation of annual rainfall to 
 
 175-177 
 
 relation to precipitation, eva- 
 poration and temperature 
 on Lake Cochituate.. . 149 
 
 S. 
 
 Sale of power, 646-666 
 
 an equitable basis for 669 
 
 literature on?. . . 673 
 
Index. 
 
 PAGE 
 
 Saline River, cross section at 
 
 guaging station 225 
 
 Samson turbine, 265 
 
 section and plan of 263 
 
 test of a 56 inch. . : 709 
 
 test of a 45 inch 713 
 
 top and outside view of run- 
 ner of 261 
 
 characteristic curve of a 45 
 
 inch 410-411 
 
 Schiele turbine 239 
 
 Science of hydraulics 40 
 
 Scotch turbine 7, 239 
 
 Seattle and Tacoma Power Com- 
 pany, The 268 
 
 Sewall's Falls, vertical turbines 
 
 for 512 
 
 Shafting, efficiency of 24 
 
 use of 533 
 
 Shawinigan Falls turbine... 268, 270 
 
 runner of 271 
 
 efficiency and discharge dia- 
 gram of 381 
 
 Shawinigan) Water and Power 
 
 Company, plant of 550 
 
 Shock, due to sudden changes in 
 
 velocity 449 
 
 Shutter, automatic drop at Ba- 
 
 tavia, India 610 
 
 Site of dam for power station, 
 study of for report on. 
 
 water power ' 681 
 
 Slope, estimates of flow from 210 
 
 Smeaton's experiments on water 
 
 wheels 357 
 
 Smith, Hamilton, Jr's., coefficients 
 
 of discharge for weirs 74 
 
 Smith-McCormick turbine, 
 
 relations of head to discharge 
 
 of 334 
 
 relations of power to head in, 
 
 a 12 inch 336 
 
 runner- of 267 
 
 Smith turbine 267 
 
 S. Morgan Smith Company, 267 
 
 curve of relations of dis- 
 charge and speed from ac- 
 tual tests. . . .393 
 
 S. Morgan Smith Co. Con. PAGE 
 
 curve of turbine from actual 
 
 t(ysts 399 
 
 relation of efficiency to speed 
 
 in a 33 inch wheel 395 
 
 relation of power ami speed 
 from actual turbine tests.. 396 
 
 test of a 33 inch turbine 717 
 
 tests of a 33 inch special tur- 
 bine 7.21 
 
 turbine, relations of speed 
 
 and efficiency in 329 
 
 turbines for Contcord Electric 
 
 Co 513 
 
 two pairs of turbine units in 
 
 tandem 519 
 
 Snoqualmie Falls reaction tur- 
 bine 272, 273 
 
 diagram showing relation of 
 
 gate guides and buckets.. 303 
 diagram showing rigging for 
 opening and operating 
 
 . gates : 303 
 
 thrust bearing of 296 
 
 Solar energy 19, 20 
 
 South Bend Electric Company's 
 
 plant 546 
 
 Southern Wisconsin Power Com- 
 pany, 
 dam with.. movable crest at 
 
 Kilbourn, Wis 60S 
 
 head gate hoists for 617 
 
 Kilbourn plant of 521-569 
 
 preliminary study of dam for 585 
 Southwestern Missouri Light Co., 
 
 harness and sheaves of. ... 533 
 Special New American runner. . 261 
 
 Specifications for governor 467 
 
 Specific speed or system curve of 
 
 turbines 349 
 
 Speed, 
 
 economical speed of any 
 
 wheel 329 
 
 relation) necessary for con- 
 stant 442 
 
 relation of turbine speed to 
 
 diameter and head 324 
 
 Speed and discharge of various 
 American turbines. . .... 34J 
 
Index. 
 
 7 8i 
 
 PAGE 
 
 Speed and power of turbines, 
 
 relation of 347 
 
 Speed and power, selection of a 
 
 turbine for, under fixed heads. . 387 
 Speed and power of various Am- 
 erican turbiixes 350 
 
 Speed and resistance, relation of 440 
 Speed, cp and horse power, ex- 
 perimental curve showing rela- 
 tion of 415 
 
 Speed of rotation, measurements 
 
 of 373 
 
 Speed of turbines, relation of 
 
 discharge to 345 
 
 Speed records from Hudson, River 
 
 Power Transmission Co 486 
 
 Speed regulation, 
 
 detailed analysis of 688 
 
 for plant with open penstock, 
 
 predetermination of 461 
 
 plant with closed penstock.. 462 
 
 plant with stand pipe 463 
 
 graphical analysis of '. 693 
 
 influences opposing 453 
 
 Speed relations, graphical expres- 
 sion, of 329,331 
 
 Special New American turbine. . . 257 
 Spier's Falls plant of Hudson 
 River Power Transmission Co. 546 
 
 Spouting velocities of water 741 
 
 Stability of masonry dams, litera- 
 ture on 505 
 
 Stand pipe, 453 
 
 discussion of relative speed 
 
 regulation 696 
 
 fluctuation of head in 699 
 
 numerical problem 466 
 
 predetermination of speed 
 
 regulation with 463 
 
 St Clair River, 
 
 drainage and guage heights 
 
 on 200 
 
 hydrograph of discharge of 
 
 the 180 
 
 variations in velocity in the 
 
 cross section of 211 
 
 Steam and electric pumping 
 plant, energy losses in 25 
 
 PAGE 
 
 Steam engine, efficiency of 24 
 
 Steam plant, capital cost and an- 
 nual cost of per brake H. P... 664 
 
 Steam power 33 
 
 Steam power plant, energy losses 
 
 in 24 
 
 Steel dams, literature on 601 
 
 Sterling Gas and Electric Com- 
 pany plant 537 
 
 Hydraulic Company, race- 
 ways of 567 
 
 power hydrograph.... 625 
 
 tainter gates in U. S. dam at 604 
 timber fishway in dam at... 619 
 St. Lawrence drainage, hydro- 
 graphs of 179, 191 
 
 St. Mary's River, hydrographs of 
 
 discharge of the 180 
 
 Storage, 624 
 
 calculations for 635, 636 
 
 diagram showing effect of 
 
 large storage capacity 633 
 
 effects of limited 629 
 
 effect of maximum 635 
 
 influence of on distribution 
 
 of run-off 179 
 
 limited, effect on low water 
 
 flow at Kilbourn 629 
 
 literature on 645 
 
 study of for report on water 
 
 power 67$ 
 
 period of 157 
 
 Stout, Mills and Temple 13, 25G 
 
 Strabo, reference on water wheels 14 
 Stream flow, 
 
 broad knowledge of neces- 
 sary for water power pur- 
 poses SO 
 
 estimates of 169 
 
 factors of 79 
 
 graphical determination of, 
 
 from measurements 230 
 
 literature on 19S 
 
 maximum 16:> 
 
 measurements, necessity of. . 21S 
 
 relation of load curve to 434 
 
 value of single observations 80 
 
782 
 
 Index. 
 
 Stream flow Con. PAGE 
 
 variation of from year to 
 
 year 82 
 
 Stream guaging, 
 
 application of 231 
 
 cable station for 228 
 
 Stream, study of from its hydro- 
 graphs 181 
 
 Sturgess governor, test results 
 
 with 491 
 
 hydraulic governor 486 
 
 Type N, section of 489 
 
 relief valves 498 
 
 Submerged orifices 43 
 
 Submergence of reaction wheel.. 501 
 Sub-stations, estimated cost of 
 
 power from 65C 
 
 Sudbury River, rainfall and run- 
 off of for each period of the 
 
 water year 161 
 
 Sudden enlargements 42 
 
 Swain turbine 13, 249 
 
 test of a 36 inch 718 
 
 Switchboard, control of governors 
 from m 492 
 
 Tailwater curve 9.3 
 
 Tainter Gates, 
 
 for Morris Plant of Economy 
 
 Light and Power Co 605 
 
 in U. S. dams at Appleton, 
 
 Wis 607 
 
 in U. S. dam at Sterling, Il- 
 linois 604 
 
 Talladega Creek 166 
 
 Tangential wheels (see also Im- 
 pulse Wheels) 241 
 
 angle of discharge from buck- 
 ets of 3H 
 
 Atkin's wheel and case...,. 273 
 
 early forms of g 
 
 effect of angle of discharge 
 
 on efficiency 315 
 
 efficiency of 247 
 
 maximum work... 314 
 
 path of jet 316 
 
 runners of 284 
 
 Tangential wheels Con. PAGE 
 Telluride double, 2,000 H. P. 275 
 Tate, Professor Thomas, on evap- 
 oration 141 
 
 Taylor, J. W., turbine 300 
 
 Telluride double tangential wheel 275 
 Telluride transmission plant, the 276 
 Temperature an/i evaporation, re- 
 lations of on Lake Cochituate 
 
 basin 150 
 
 Temperature, precipitation, run- 
 off and evaporation, rela- 
 tions of, 
 
 on Sudbury River basin 151 
 
 on the Upper Hudson River 154 
 
 on Lake Cochituate 149 
 
 Test data of turbine water wheels 703 
 
 Testing turbines 355 
 
 purpose of 370 
 
 flumes for at Holyoke 364 
 
 machinery for, importance of 355 
 
 by James Emerson. 361 
 
 early methods 359 
 
 literature on 383 
 
 plan of apparatus for by 
 
 James B. Francis 374 
 
 illustration of methods and 
 
 apparatus 378 
 
 Test results with Sturgess gov- 
 ernor 491 
 
 Tests, 
 
 curve showing discharge and 
 
 speed of wheel from actual 398 
 factors that influence the re- 
 sults of 371 
 
 of water wheels, 
 
 at Philadelphia in 1860. . 360 
 by Messrs. Samuel Weber 
 
 and T.' G. Ellis 362 
 
 in place 379 
 
 the value of 369 
 
 Thermal energy 20 
 
 Thermal units, British 32 
 
 Thompson's turbine 239 
 
 Three-halves powers of numbers. 742 
 Three Rivers, Michigan, variation 
 
 in power at 103 
 
 Thrust bearing at Snoqualmie 
 Falls . . 295 
 
Index. 
 
 PAGE 
 
 Thunder Bay River 165 
 
 Thurso, J. W 279 
 
 Tidal mill..... 14 
 
 Timber dam, 
 
 at Janesville 582 
 
 at Sewell's Falls 594 
 
 of the Montana Power Com- 
 pany, near Butte 593 
 
 Timber fishway, 
 
 of Fish Commission State of 
 
 Wisconsin 619 
 
 in dam at Sterling, Illinois.. 619 
 
 Tohickon Creek 167 
 
 diagram showing annual run- 
 off from 638 
 
 mass curve of run-off of 639 
 
 monthly discharge from 
 
 drainage area of 643 
 
 monthly rainfall in inches on 
 
 drainage area of 643 
 
 rainfall, run-off and evapora- 
 tion 757 
 
 Topographical condition, 
 
 relation of run-off to 175 
 
 study of for report on water 
 
 power 677 
 
 Traction purposes, transmission 
 
 of power for 26 
 
 Trade Dollar Mining Company, 
 
 power plant of 532 
 
 Transformation of energy 23-33 
 
 Transformers, losses in 29 
 
 Transmission of energy 23 
 
 losses in 27 
 
 for traction purposes 26 
 
 literature on 673 
 
 Transverse curves of mean veloc- 
 ity in stream cross sections... 211 
 
 Trash racks 53C 
 
 Tremont-Fourneyron wheel, 
 
 characteristic curve of 409 
 
 diagram of 21 
 
 efficiency of 247 
 
 guides and buckets of 251 
 
 Trenton Falls, N. Y., plan of 
 
 power development at 575 
 
 Tub wheel . . 8 
 
 PAGE 
 Turbines, 
 
 American, Francis 11 
 
 Cadiats, Fourneyron, Fran- 
 cis, Girard Current, Hen- 
 schel, Jonval, Schiele, 
 
 Scotch, Thompson's 239 
 
 advantages of 9 
 
 arrangement of, 
 
 horizontal 504 
 
 reaction 500 
 
 vertical shaft 501 
 
 axial flow 244 
 
 bearings of, 
 
 horizontal 292 
 
 vertical 239 
 
 calculation of, 
 
 a more exact graphical 
 
 method for 396 
 
 graphical method, effi- 
 ciency and speed at 
 various heads and gates 395 
 diagram of estimated 
 
 power at various heads 397 
 to estimate operating re- 
 sults under one head 
 from test results at 
 
 another head 389 
 
 to estimate results of one 
 diameter from tests of 
 
 another 391 
 
 capacity of, 
 
 power and speed of a 40" 
 wheel under 16' head 260 
 
 characteristic curve of 400 
 
 classification of 243,506 
 
 complete 244 
 
 connection of, to load 531 
 
 conditions of operation of 
 
 245,384 
 
 constants of 310, 351 
 
 design of, first principles. . . . 311 
 details and appurtenances.. 284 
 
 development of 4 
 
 in Europe 277 
 
 in United States.. 24S 
 
 discharge, 
 
 measurement of.. . 372 
 
784 
 
 Index. 
 
 Turbines Con. PAGE 
 
 at fixed gate opening 332 
 
 fundamental ideas of 5 
 
 gates of 290 
 
 history of 8,9 
 
 horizontal 244 
 
 horizontal, multiple tandem. 517 
 
 hydraulics of, practical o09 
 
 impulse or action^ 244 
 
 installations of, 
 
 horizontal 513 
 
 tandem 529 
 
 vertical 507, 510 
 
 inward radial flow 244 
 
 limit 244 
 
 literature on 353 
 
 mixed flow 244 
 
 number of, effect on head and 
 
 power 108 
 
 partial 244 
 
 outward radial flow 244 
 
 power of modern, increase in 13 
 
 power of 335 
 
 practice, modern changes in 13 
 
 radial flow 244 
 
 reaction, or pressure 244 
 
 regulation, comparative 487 
 
 relations 321 
 
 of discharge to diameter 
 
 in various wheels 339 
 
 of diameter and speed.. 326 
 of discharge to diameter 337 
 of efficiency and speed of 
 
 33" turbine, graphical. 395 
 of efficiency and speed of 
 
 a 48" Victor, curve of 322 
 of <p and discharge 
 (graphical) at full gate 
 for various wheels.... 333 
 of head to discharge of a 
 
 12" Smith-McCormick. 331 
 homogeneous series, di- 
 ameter and speed 326 
 
 homogeneous series, pow- 
 er and diameter.. 340,341 
 to estimate results for 
 variable head from 
 tests under fixed head 393 
 of power to diameter uh- 
 
 Turbines Con. PAGE 
 der unit head (graphi- 
 cal) 344 
 
 of power and speed of 
 
 a 33" wheel 396 
 
 of power and speed, 48" 
 
 Victor (graphical)... 323 
 of power and head, I. P. 
 
 Morris Co 415 
 
 of speed to diameter and 
 
 head 324 
 
 of speed to discharge... 345^ 
 of speed to discharge for 
 a 12" Smith-McCormick 3'tt 
 
 of speed and power 347 
 
 runners of, 
 
 built up 284 
 
 cost 281 
 
 details of 28G 
 
 how made 284 
 
 Shawinigan Falls 272 
 
 Scotch 7 
 
 selection of 38 1 
 
 basis for. .-. 385- 
 
 for speed and power to 
 work under a fixed 
 
 head 38T 
 
 uniform head and power 287 
 
 Shawinigan Falls 270 
 
 speed, increase of 259 
 
 speed relations of 330 
 
 support of 53* 
 
 Swain 13 
 
 testing of 355- 
 
 tests, 
 
 by James Emerson 361 
 
 literature on 383" 
 
 methods and apparatus 
 
 for , 378" 
 
 plan of apparatus for, by 
 
 Francis 374 
 
 value of 270,369 
 
 vertical 244 
 
 vertical and horizontal 244 
 
 vertical shaft for low heads. . oOO 
 Unwin's estimate of losses in 26" 
 units, two pairs in ; tandem 
 
 519, 523 
 Turner's Falls power plant 514 
 
Index. 
 
 785 
 
 PAGE 
 
 Tutton's formula 62 
 
 Tweeddale's report to the Kansas 
 
 State Board of Agriculture ... 136 
 
 Tyler, Benjamin 6 
 
 Tympanum, Egyptian 14 
 
 U. 
 
 Umbrella covering, 
 
 tests of 729 
 
 to prevent vortices 725 
 
 Unbalanced wheels 524 
 
 Undershot wheels 2 
 
 early application to mine 
 
 drainage 16 
 
 Uniform motion 37 
 
 Uniform speed, value of 444 
 
 Uniform varied motion 37 
 
 United States, 
 
 annual evaporation in the 138-139 
 average rainfall of, map 112-113 
 comparative hydrographs 
 from different hydrological 
 
 divisions 189 
 
 development of water power 
 
 in 14 
 
 first wheel in 9 
 
 mean annual run-off of the 
 
 rivers of 152-153 
 
 rainfall conditions in, July 
 
 16th and 17th 118 
 
 Units of, energy 32 
 
 heat 3:> 
 
 potential energy 34 
 
 University of Wisconsin, 
 
 experiments on 12" S. Mor- 
 gan-Smith wheel 329 
 
 experiments on submerged 
 
 orifices at 43 
 
 Unwin, Professor . . . 26 
 
 Upadachee River 166 
 
 Utica Gas and Electric Co., Tren- 
 ton Falls plant of 511 
 
 V. 
 
 Valves, relief 498 
 
 Velocities, position of mean and 
 maximum in a vertical plane 
 under ice .- 217 
 
 48 
 
 Velocity, PAGE 
 
 changes of penstock. ....... 453 
 
 effects of ice covering on dis- 
 tribution, of.. , ... 215 
 
 energy required to change 
 
 penstock 446, 456 
 
 measurements of flow by the 
 
 determination of. 221 
 
 relative, of the bucket in re- 
 action wheels. 318 
 
 residual, in reaction wheels 318 
 shock due to sudden changes 
 
 in 449 
 
 variations in the cross sec- 
 tion of a stream. 210 
 
 Velocity curves, 
 
 for open and ice covered 
 streams, comparative mean 
 
 vertical 216 
 
 ideal vertical 213 
 
 of Potomac River. .. . ... 232 
 
 Velocity head ;..,... -It 
 
 Vermuele, C. C. 148 
 
 formula for the relation be- 
 tween annual evaporation, 
 precipitation and run-off. . 148 
 Vertical Geylin-Jonval turbine, 
 
 diagram of 251 
 
 Vertical turbine, 
 
 arrangement of 501 
 
 for low heads 509 
 
 for Sewall's Falls... 512 
 
 bearings of 289 
 
 Vertical thrust or hanging bear- 
 ing of The Niagara Falls Power 
 
 Co 293 
 
 Vertical turbines, some installa- 
 tions of 507 
 
 Vertical turbines and their con- 
 nection ......... 507 
 
 Vertical turbines in series, some 
 
 installations of 510 
 
 Vertical suspension, ball bearing 291 
 Vertical suspension oil pressure 
 
 bearing 292 
 
 Vertical velocity curves, in 
 
 streams 211, 213, 214, 215 
 
 Victor turbine, 
 
 characteristic curves of. .402-405 
 
Index. 
 
 Victor turbine Con. 
 
 efficiency-speed curve of a 48" 322 
 relation of efficiency to the 
 
 number of revolutions 405 
 
 runner of 267,268 
 
 teats of, 
 
 data of a 48* 704 
 
 test of a 45" 712 
 
 of a 42" 713 
 
 f *36" 720 
 
 of a 33" 723 
 
 VitruvUw' description of water 
 
 wheels 14 
 
 Volt 33 
 
 Volt, coulomb, equivalents of 34 
 
 Vortices, effect of an umbrella up- 
 on the formation of . . 72 tf 
 
 W. 
 
 River, rating curve for 217 
 Warren. H. B., ou predetermina- 
 tion of spaed regulation 462 
 
 Waste of energy, none in nature 20 
 Water, 
 
 circulation of 20 
 
 evaporation of 20 
 
 Water hammer 685 
 
 due to sudden changes in ve- 
 locity 449 
 
 Water power 33-79 
 
 chronological development of 15 
 
 sort of development 647 
 
 development in the U. S 14 
 
 market price of 663 
 
 sources of 79 
 
 Water power development, 
 
 examples of 537 
 
 financial consideration of... 646 
 
 history of 1-14-16 
 
 investigation of 675 
 
 purposes of 646 
 
 relation of capacity to cost. . 648 
 
 classification of types 562 
 
 costs of various, 
 
 American $50 
 
 Canadian $49 
 
 Foreign 651 
 
 Water power property, value of. 671 
 
 PAGE 
 
 Water power purposes, dams for 580 
 Water supplied to wheel, effect of 
 
 slow acceleration on 455 
 
 wheels (.see also Turbines) 237 
 
 Barker's Mill 5 
 
 breast 3 
 
 Chinese Nora 1 
 
 classification of L 10 .7 
 
 current 1 
 
 early types of 1 
 
 float 1-3 
 
 horizontal, some installations 
 
 of 
 
 installation of ta.ndem W 
 
 Laxy overshot ou Isle of Man 14 
 
 overshot I, M3 
 
 Poncelet 4 
 
 Roue* a Cuves 8 
 
 Rou6 Volant 8 
 
 Smeaton's experiments on. . . :r>7 
 
 testing of 3 "HI 
 
 tests at Philadelphia in, IS- 
 
 tub 8 
 
 undershot 2 
 
 use of 241 
 
 wry fly 6 
 
 Water wheel governors t see 
 
 Governors) 470-735 
 
 problem of 445 
 
 types of 470 
 
 Water year, the MR 
 
 rainfall and runoff of the 
 Hudson River for each 
 
 period of 1*0 
 
 rainfall and run-off of the 
 Sudbury River for each 
 
 period of 161 
 
 rainfall and run-off of vari- 
 ous rivers 7o< 
 
 Waters, W. A., graphical analysis 
 
 as proposed by 412 
 
 Watt, the equivalents of 
 
 Weber, Samuel 13 
 
 and T. O. Ellis, turbine tests 
 
 by 
 
 Weber, W. a, 
 
 plan of brake wheel 576 
 
 plan of prony brake 377 
 
Index. 
 
 787 
 
 PAGE 
 
 Weekly rainfall in Wisconsin, 
 
 distribution of 117 
 
 Weight, exertion of energy by. . 41 
 Weights of water, equivalent 
 
 measures and 740 
 
 Weirs, 
 
 coefficients 65 et seq. 
 
 formulas for 64 
 
 measurements of flow by 219 
 
 comparative discharge over 68-69 
 comparative discharge with 
 
 irregular crest 72-73 
 
 flow over 64 
 
 literature on flow of water 
 
 over 77 
 
 Wellmari-Seaver-Morgan C o m- 
 
 pany 299-300 
 
 characteristic curve of 51" 
 
 wheel 408 
 
 Western drainage, hydrograph of 193 
 Wheeler, L. L., 
 
 design of fish way by 614 
 
 tainter gates designed by... 606 
 Wheel harness of Oliver power 
 
 plant 530 
 
 Wheel pit 535 
 
 Wheels (see Turbines), 
 
 Atkins' wheel and case 273 
 
 effects of number on head and 
 
 power 108 
 
 gravity 237 
 
 impulse 237-301-313 
 
 other American 266 
 
 reaction 237 
 
 Whitlaw, James 6 
 
 Wicket gate 300-301 
 
 diagram showing condition of 
 flow through open and par- 
 tially closed 304 
 
 Winnipeg Electric Railway Com- 
 pany, plant of 553 
 
 Wisconsin, 
 
 diagram of fluctuations of 
 monthly rainfall at Madi- 
 
 Wisconsin Con. PAGE 
 
 son 122 
 
 distribution of average an- 
 nual rainfall in 116 
 
 distribution of total annual 
 
 rainfall in lltJ 
 
 distribution of weekly rain- 
 fall in 117 
 
 maps of annual rainfall in 
 
 114-115 
 rainfall on drainage area of 
 
 Wisconsin River 129 
 
 Wisconsin River, 
 
 comparative flow of 85 
 
 comparison of mean monthly 
 
 flow with Rock River 173 
 
 drainage area of 84 
 
 hydrograph at Kilbourn, 
 based on observations at 
 
 Necedah 86 
 
 hydrograph in 1904 81 
 
 monthly rainfall and run-off 165 
 rainfall on the drainage area 
 
 of 129 
 
 rating curve at Kilbourn . . . 209 
 rating curve at Necedah .... 96 
 relations of coefficient to hy- 
 draulic radius 199 
 
 relations of gauge heights at 
 
 various stations on 206 
 
 Wood, R. D., and Company 254 
 
 Geylin-Jonval turbine 266 
 
 Wood stave pipe friction losses.. 63 
 Woodward governors, 
 
 compensating 474 
 
 details and applications of. . 477 
 
 standard 471 
 
 Work 32 
 
 Wry fly wheel 6 
 
 Y. 
 
 York Haven Water Power Com- 
 pany, plant of .537 
 
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