OS* 
 
 
 REESE LIBRARY 
 
 OF THE 
 
 UNIVERSITY OF CALIFORNIA. 
 
 Received^. . _ . ^*&.&$L $dLt_ _ _ i88/_, 
 
 Shelf No.___ ^ /_-/-- 
 
 ' ' Tzi 
 
HYDRAULIC ENGINEERING 
 
 AND 
 
 MAN UAL 
 
 FOR 
 
 WATER SUPPLY ENGINEERS. 
 
PUBLIC FOUNTAIN, CINCINNATI. 
 
PRACTICAL TREATISE 
 
 ON 
 
 WATER-SUPPLY ENGINEERING: 
 
 RELATING TO THE 
 
 HYDROLOGY, HYDRODYNAMICS, AND PRACTICAL 
 
 CONSTRUCTION OF WATER-WORKS, IN 
 
 NORTH AMERICA. 
 
 WITH NUMEROUS 
 
 TABLES AND ILLUSTRATIONS, 
 
 BT 
 
 J. T. FANNlM^ v C.Bf,/y^ 
 
 MEMBER OF THE AMERICAN 
 
 SECOXD EDITIOIST. 
 
 NEW YORK: 
 D. VAN NOSTRAND, PUBLISHER, 
 
 23 MURRAY STREET & 27 WARREN STREET. 
 
 1878. 
 
^ 
 
 v 
 
 COPYKIGHT, 1877, 
 
 BY 
 
 J. T. FANNING. 
 // 
 
 Electrotyped by Printed by 
 
 SMITH & McDOTJGAL. H. J. HEWETT 
 
PREFACE TO THE SECOND EDITION. 
 
 THE author having been informed by the Publisher of this 
 treatise that he has already had the sheets of a second 
 edition struck off, and is about to hand them to the binder, gladly 
 avails himself of the opportunity to thank his professional friends 
 in practice and in training for the honor they have conferred, by 
 taking up the first edition ere it is scarce six months out of the 
 press, and to thank the scientific press generally for their kind 
 criticisms and commendations; and he is especially glad to have 
 opportunity so early to call attention to some typographical errors 
 in the first edition, and to ask the purchasers to make the proper 
 corrections therein, viz. : 
 
 In 423, p. 423, equation 28, one h t was omitted. It should 
 read, 
 
 P l = $w 9 \Ji, sec <f> (7i, 3 tan 2 < + c 2 2 )* f 2 . 
 
 In the Appendix, p. 597, the decimal point in the weight per 
 cubic inch of metals is one place too far to the left; thus, the 
 weight of aluminum is printed .00972, but should read .0972. 
 
 No one can regret so much as the author that other duties have 
 prevented a thorough revision and improvement of the work, so 
 that it may be more worthy of so generous a reception. 
 
 J. T. F. 
 
WATER SUPPLY ENGINEERING. ERRATA. 
 
 Page 225. In line 10 the equation should read 
 
 v 
 
 249. The eighth line from the bottom should read : 
 In which h" = the resistance head in feet. 
 
 " 266. In equation 19 insert the sign + before m in 
 each of the three equations of v. 
 
 " 273. In line 15, after the word equation, strike out 
 the words, " double the subdivisor 9," and sub- 
 stitute, to find the new value of v. Also, in line 
 20 strike out the word " zero," and substitute 
 the word unity. 
 
 " 289. In the foot note, after the word deduct, substi- 
 tute the following : from the total length, in feet, 
 'an amount equal to one-tenth the head upon 
 the weir, in feet. Reduce the total length a 
 like amount for each end contraction. 
 
 ' 380. In table 80 the two equations of Q at heads of 
 columns, are to change places. 
 
 " 487. In equation 20 place a decimal point before the 
 
 divisor, thus : .33338. . 
 
 528. In table 108, in the four columns of cubic feet 
 per minute, on this page, remove the decimal 
 point one place further to the right. 
 
PREFACE. 
 
 fT^HERE is at present no sanitary subject of more general 
 -- interest, or attracting more general attention, than that 
 relating to the abundance and wholesomeness of domestic water 
 supplies. 
 
 Each citizen of a densely populated municipality must of 
 necessity be personally interested in either its physiological or 
 its financial bearing, or in both. Each closely settled town and 
 city must give the subject earnest consideration early in its ex- 
 istence. 
 
 At the close of the year 1875, fifty of the chief cities of the 
 American Union had provided themselves with public water sup- 
 plies at an aggregate cost of not less than ninety-five million 
 dollars, and two hundred and fifty lesser cities and towns were 
 also provided with liberal public water supplies at an aggregate 
 cost of not less than fifty-five million dollars. 
 
 The amount of capital annually invested in newly inaugurated 
 water-works is already a large sum, and is increasing, yet the 
 entire American literature relating to water-supply engineering 
 exists, as yet, almost wholly in reports upon individual works, 
 usually in pamphlet form, and accessible each to but compara- 
 tively few of those especially interested in the subject 
 
 . Scores of municipal water commissions receive appointment 
 each year in the growing young cities of the Union, who have to 
 inform themselves, and pass judgment upon, sources and systems 
 
vi PREFACE. 
 
 of water supply, which are to become helpful or burdensome to 
 the communities they are intended to encourage accordingly as 
 the works prove successful or partially failures. 
 
 The individual members of these "Boards of Water Commis- 
 sioners," resident in towns where water supplies upon an extended 
 scale are not in operation, have rarely had opportunity to observe 
 and become familiar with the varied practical details and appa- 
 ratus of a water supply, or to acquaint themselves with even the 
 elementary principles governing the design of the several different 
 systems of supply, or reasons why one system is most advanta- 
 geous under one set of local circumstances and another system 
 is superior and preferable under other circumstances. 
 
 A numerous band of engineering students are graduated each 
 year and enter the field, many of whom choose the specialty of 
 hydraulics, and soon discover that their chosen science is great 
 among the most noble of the sciences, and that its mastery, in 
 theory and practice, is a work of many years of studious acquire- 
 ment and labor. They discover also that the accessible literature 
 of their profession, in the English language, is intended for the 
 class-room rather than the field, and that its formulae are based 
 chiefly upon very limited philosophical experiments of a century 
 and more ago but partially applicable to the extended range of 
 modern practice. 
 
 Among the objects of the author in the compilation of the 
 following pioneer treatise upon American Water-works are, to 
 supply water-commissioners with a general review of the best 
 methods practised in supplying towns and cities with water, and 
 with facts and suggestions that will enable them to compare in- 
 telligently the merits and objectionable features of the different 
 potable water sources within their reach ; to present to junior and 
 assistant hydraulic engineers a condensed summary of those ele- 
 mentary theoretical principles and the involved formulas adapted 
 to modern practice, which they will have frequently to apply, 
 together with some useful practical observations ; to construct 
 and gather, for the convenience of the older busy practitioners, 
 
PREFACE. vii 
 
 numerous tables and statistics that will facilitate their calcula- 
 tions, some of which would otherwise cost them, in the midst of 
 pressing labors, as they did the author, a great deal of laborious 
 research among rare and not easily procurable scientific treatises ; 
 and also to present to civil engineers generally a concise reference 
 manual, relating to the hydrology, hydrodynamics, and practical 
 construction of the water-supply branch of their profession. 
 
 This work is intended more especially for those who have 
 already had a task assigned them, and who, as commissioner, 
 engineer, or assistant, are to proceed at once upon their recon- 
 noissance and surveys, and the preparation of plans for a public 
 water supply. To them it is humbly submitted, with the hope 
 that it will prove in some degree useful. Its aim is to develop 
 the bases and principles of construction, rather than to trace the 
 origin of, or to describe individual works. It is, therefore, prac- 
 tical in text, illustration, and arrangement ; but it is hoped that 
 the earnest, active young workers will find it in sympathy with 
 their mood, and a practical introduction, as well, to more pro- 
 found and elegant treatises that unfold the highest delights of the 
 science. 
 
 Good design, which is invariably founded upon sound mathe- 
 matical and mechanical theory, is a first requisite for good and 
 judicious practical engineering construction. We present, there- 
 fore, the formulae, many of them new, which theory and practical 
 experiments suggest as aids to preliminary studies for designs, 
 and many tables based upon the formulas, which will facilitate the 
 labors of the designer, and be useful as checks against his own com- 
 putations, and we give in addition such discussions of the elemen- 
 tary principles upon which the theories are founded as will enable 
 the student to trace the origin of each formula ; for a formula is 
 often a treacherous guide unless each of its factors and experience* 
 coefficients are well understood. To this end, the theoretical dis- 
 cussions are in familiar language, and the formulas in simple ar- 
 rangement, so that a knowledge of elementary mathematics only 
 is necessary to read and use them. 
 
viii PREFACE. 
 
 We do by no means intimate, however, that an acquaintance 
 with elementary theories alone suffices for an accomplished en- 
 gineer. It is sometimes said that genius spurns rules, and it is 
 true that untutored genius sometimes grapples with and accom- 
 plishes great and worthy deeds, but too often in a bungling 
 manner, not to be imitated. 
 
 In kindly spirit we urge the student to bear in mind that it is 
 the rigorously trained genius who oftenest achieves mighty works 
 by methods at once accurate, economical, artistic, and in every 
 respect successful and admirable. 
 
 J. T. F. 
 
 BOSTON, November, 1876. 
 
CONTENTS. 
 
 SECTION I. 
 
 COLLECTION AND STORAGE OF WATER, AND ITS 
 IMPURITIES. 
 
 CHAPTER I. 
 
 INTRODUCTORY. PAGE 25. 
 
 Art. i, Necessity of Public Water Supplies. 2, Physiological Office of Water. 
 3, Sanitary Office of Water Supplies. 4, Helpful Influence of Public 
 Water Supplies. 5, Municipal Control of Public Water Supplies. 6, 
 Value as an Investment. 7, Incidental Advantages. 
 
 CHAPTER II. 
 
 QUANTITY OF WATER REQUIRED. PAGE 31. 
 
 Art. 8, Statistics of Water Supplied. 9, Census Statistics. 10, Approximate 
 Consumption of Water. n, Water Supplied to Ancient Cities. 12, Water 
 Supplied to European Cities. 13, Water Supplied to American Cities. 
 14, The Use of Water Steadily Increasing. 15, Increase in Various Cities. 
 16, Relation of Supply per Capita to Total Population. 17, Monthly 
 and Hourly Variations in the Draught. 18, Ratio of Monthly Consump- 
 tion. 19, Illustrations of Varying Consumption. 20, Reserve for Fire 
 Extinguishment. 
 
 CHAPTER III. 
 
 RAINFALL. PAGE 45. 
 
 Art. 21, The Vapory Elements of Water. 22, The Liquid and Gaseous Succes- 
 sions. 23, The Source of Showers. 24, General Rainfall. 25, Review of 
 Rainfall Statistics. 26, Climatic Effects. 27, Sections of Maximum Rain- 
 fall. 28, Western Rain System. 29, Central Rain System. 30, Eastern 
 Coast System. 31, Influence of Elevation upon Precipitation. 32, River 
 Basin Rains. 33, Grouped Rainfall Statistics. 34, Monthly Fluctuations 
 
x CONTENTS. 
 
 in Rainfall. 35, Secular Fluctuations in Rainfall. 36, Local Physical 
 and Meteorological Influences. 37, Uniform Effects of Natural Laws. 
 38, Great Rain Storms. 39, Maximum Ratios of Floods to Rainfalls. 40^ 
 Volume of Water from given Rainfalls. 41, Gauging Rainfalls. 
 
 CHAPTER IV. 
 
 FLOW OF STREAMS. PAGE 65. 
 
 Art. 42, FJtood Volumes Inversely as the Areas of Basins. 43, Formulas for 
 Flood Volumes. 44, Table of Flood Volumes. 45, Seasons of Floods. 
 46, Influence of Absorption and Evaporation upon Flow. 47, Flow in Sea- 
 sons of Minimum Rainfall. 48, Periodic Classification of available Flow. 
 49, Sub-surface Equalizers of Flow. 50, Flashy and Steady Streams. 
 51, Peculiar Watersheds. 52, Summaries of Monthly Flow Statistics. 
 53, Minimum, Mean, and Flood Flow of Streams. 54, Ratios of Monthly 
 Flow in Streams. 55, Mean Annual Flow of Streams. 56, Estimates of 
 Flow of Streams. 57, Ordinary Flow of Streams. 58, Tables of Flow, 
 Equivalent to given Depths of Rain. 
 
 CHAPTER V. 
 
 STORAGE AND EVAPORATION OF WATER. PAGE 84. 
 
 STORAGE. Art. 59, Artificial Storage. 60, Losses Incident to Storage. 61, 
 Sub-strata of the Storage Basin. 62, Percolation from Storage Basins. 
 63, Rights of Riparian Owners. 64, Periodical Classification of Riparian 
 Rights. 65, Compensations. EVAPORATION. 66, Loss from Reservoir 
 by Evaporation. 67, Evaporation Phenomena. 68, Evaporation from 
 Water. 69, Evaporation from Earth. 70, Examples of Evaporation. 71, 
 Ratios of Evaporation. 72, Resultant Effect of Rain and Evaporation. 
 73, Practical Effect upon Storage. 
 
 CHAPTER VI. 
 
 SUPPLYING CAPACITY OF WATER-SHEDS. PAGE 94. 
 
 Art. 74, Estimate of Available Annual Flow of Streams. 75, Estimate of 
 Monthly available Storage Required. 76, Additional Storage Required. 
 /7, Utilization of Flood Flows. 78, Qualification of Deduced Ratios. 79, 
 Influence of Storage upon a Continuous Supply. 80, Artificial Gathering 
 Areas. 81, Recapitulation of Rainfall Ratios. 
 
 CHAPTER VII. 
 
 SPRINGS AND WELLS. PAGE 102. 
 
 Art. 82, Subterranean Waters. 83, Their Source, the Atmosphere. 84, Po- 
 rosity of Earths and Rocks. 85, Percolations in the Upper Strata. 86, 
 The Courses of Percolation. 87, Deep Percolations. 88, Subterranean 
 
CONTENTS. 
 
 Reservoirs. 89, The Uncertainties of Subterranean Searches. 90, Re- 
 nowned Application of Geological Science. 91, Conditions of Overflow- 
 ing Wells. 92, Influence of Wells upon each other. 93, American Ar- 
 tesian Wells. 94, Watersheds of Wells. 95, Evaporation from Soils.-^ 
 96, Supplying Capacity of Wells and Springs. 
 
 CHAPTER VIII. 
 
 IMPURITIES OF WATER. PAGE 112. 
 
 Art. 97, The Composition of Water. 98, Solutions in Water. 99, Properties 
 of Water. zoo, Physiological Effects of the Impurities of Water. 101, 
 Mineral Impurities. 102, Organic Impurities. 103, Tables of Analyses 
 of Potable Waters. 104, Ratios of Standard Gallons. 105, Atmospheric 
 Impurities. 106, Sub-surface Impurities. 107, Deep-well Impurities. 
 108, Hardening Impurities. 109, Temperature of Deep Sub-surface 
 Waters. no, Decomposing Organic Impurities. in, Vegetal Organic 
 Impurities. 112, Vegetal Organisms in Water-pipes. 113, Animate Or- 
 ganic Impurities. 114, Propagation of Aquatic Organisms. 115, Purify- 
 ing Office of Aquatic Life. 116, Intimate Relation between Grade of 
 Organisms and Quality of Water. 117, Animate Organisms in Water- 
 pipes. 118, Abrasion Impurities in Water. 119, Agricultural Impuri- 
 ties. 120, Manufacturing Impurities. 121, Sewage Impurities. 122, 
 Impure Ice in Drinking- Water. 123, A Scientific Definition of Polluted 
 Water. 
 
 CHAPTER IX. 
 
 WELL, SPRING, LAKE, AND RIVER SUPPLIES. PAGE 139. 
 
 WELL WATERS. Art. 124, Locations for Wells. 125, Fouling of Old Wells. 
 SPRING WATERS. 126, Harmless Impregnations. 127, Mineral Springs. 
 LAKE WATERS. 128, Favorite Supplies. 129, Chief Requisites. 130, 
 Impounding. 131, Plant Growth. 132, Strata Conditions. 133, Plant 
 and Insect Agencies. 134, Preservation of Purity. 135, Natural Clarifi- 
 cation. 136, Great Lakes. 137, Dead Lakes. RIVER WATERS. 138, 
 Metropolitan Supplies. 139, Harmless and Beneficial Impregnations. 
 140, Pollutions. 141, Sanitary Discussions. 142, Inadmissible Polluting 
 Liquids, 143, Precautionary Views. 144, Speculative Condition of the 
 Pollution Question. 145, Spontaneous Purification. 146, Artificial Clari- 
 fication. 147, A Sugar Test of the Quality of Water. 
 
xii CONTENTS. 
 
 SECTION II. 
 
 FLOW OF WATER THROUGH SLUICES, PIPES, AND 
 
 CHANNELS. 
 
 CHAPTER X. 
 
 WEIGHT, PRESSURE, AND MOTION OF WATER. PAGE 161. 
 
 Art. 148, Special Characteristics of Water. 149, Atomic Theory. 150, Molec- 
 ular Theory. 151, Influence of Caloric. 152, Relative Densities and 
 Volumes. WEIGHT OF WATER. 153, Weight of Constituents of Water. 
 154, Crystalline Forms of Water. 155, Formula for Volumes at Differ- 
 ent Temperatures. 156, Weight of Pond Water. 157, Compressibility 
 and Elasticity of Water. 158, Weights of Individual Molecules. 159, In- 
 dividual Molecular Actions. PRESSURE OF WATER. 160, Pressure Propor- 
 tional to Depth. 161, Individual Molecular Reactions. 162, Equilibrium 
 destroyed by an Orifice. 163, Pressures from Vertical, Inclined, and Bent 
 Columns of Water. 164, Artificial Pressure. 165, Pressure upon a Unit 
 of Surface. 166, Equivalent Forces. 167, Weight a Measure of Pressure. 
 168, A Line a Measure of Weight. 169, A Line a measure of Pressure 
 upon a Surface. 170, Diagonal Force of Combined Pressures Graphically 
 Represented. 171, Angular Resultant of a Force Graphically Repre- 
 sented. 172, Angular Effects of a Force Represented by the Sine and 
 Cosine of the Angle. 173, Total Pressure. 174, Direction of Maximum 
 Effect. 175. Herizontal and Vertical Effects. 176, Centres of Pressure 
 and of Gravity. 177, Pressure upon a Curved Surface, and Effect upon 
 its Projected Plane. 178, Centre of Pressure upon a Circular Area. 
 179, Combined Pressures. 180, Sustaining Pressure upon Floating and 
 Submerged Bodies. 181, Upward Pressure upon a Submerged Lintel. 
 182, Atmospheric Pressure. 183, Rise of Water into a Vacuum. 184, 
 Siphon. 185, Transmission of Pressure to a Distance. 186, Inverted 
 Syphon. 187, Pressure Convertible into Motion. MOTION OF WATER. 
 188, Flow of Water. 189, Action of Gravity upon Individual Molecules. 
 190, Frictionless Movement of Molecules. 191, Acceleration of Motion. 
 192, Equations of Motion. 193, Parabolic Path of Jet. 194, Velocity of 
 Efflux Proportional to the Head. 195, Conversion of the Force of Grav- 
 ity from Pressure into Motion. 196, Resultant Effects of Pressure and 
 Gravity upon the Motion of a Jet. 197, Equal Pressures give Equal 
 Velocities in all Directions. 198, Resistance of the Air. 199, Theoretical 
 Velocities. 
 
 CHAPTER XI. 
 
 FLOW OF WATER THROUGH ORIFICES. PAGE 194. 
 
 Art. 200, Motion of the Individual Particles. 201, Theoretical Volume of 
 Efflux. 202, Converging Path of Particles. 203, Classes of Orifices. 
 
CONTENTS. xiii 
 
 204, Form of Submerged Orifice Jet. 205, Ratio of Minimum Section of 
 Jet. 206, Volume of Efflux. 207, Coefficient of Efflux. 208, Maximum 
 Velocity of the Jet. 209, Factors ol the Coefficient of Efflux. 210, Prac- 
 tical Use of a Coefficient. 211, Experimental Coefficients. (From Michel- 
 otti, Abbe Bosset, Rennie, Castel, Lespinasse, General Ellis.) 212, Co- 
 efficients Diagramed. 213, Effect of Varying the Head, or the Proportions 
 of the Orifice. 214, Peculiarities of Efflux from an Orifice. 215, Mean 
 Velocity of the Issuing Particles. 216, Coefficients of Velocity and 
 Contraction. 217, Velocity of Particles Dependent upon their Angular 
 Positions. 218, Equation of Volume of Efflux from a Submerged Orifice. 
 219, Effect of Outline of Geometrical Orifices upon Efflux. 220, Vari- 
 able Value of Coefficients. 221, Assumed Mean Value of Efflux. 222, 
 Circular Jets, Polygonal do., Complex do. 223, Cylindrical and Divergent 
 Orifices. 224, Converging Orifices. 
 
 CHAPTER XII. 
 
 FLOW OF WATER THROUGH SHORT TUBES. PAGE 213. 
 
 Art. 225, An Ajutage. 226, Increase of Coefficient. 227, Adjutage Vacuum, 
 and its Effect. 228, Increased Volume of Efflux. 229, Imperfect Va- 
 cuum. 230, Divergent Tube. 231, Convergent Tube. 232, Additional 
 Contraction. 233, Coefficients of Convergent Tubes. 234, Increase and 
 Decrease of Coefficient of Smaller Diameter. 235, Coefficient of Final 
 Velocity. 236, Inward Projecting Ajutage. 237, Compound Tube. 
 238, Coefficients of Compound Tubes. 239, Experiments with Cylindri- 
 cal and Compound Tubes. 240, Tendency to Vacuum. 241, Percussive 
 Force of Particles. 242, Range of Eytelwein's Table. 243, Cylindrical 
 Tubes to be Preferred. 
 
 CHAPTER XIII. 
 
 FLOW OF WATER THROUGH PIPES, UNDER PRESSURE. 
 
 PAGE 223. 
 
 Art. 244, Pipe and Conduit. 245, Short Pipes give Greatest Discharge. 246, 
 Theoretical Volume from Pipes. 247, Mean Efflux from Pipes. 248, Sub- 
 division of the Head. 249, Mechanical Effect of the Efflux. 250, Ratio 
 of Resistance at Entrance to the Pipe. RESISTANCE TO FLOW W*THIN 
 A PIPE. 251, Resistance of Pipe-Wall. 252, Conversion of Velocity into 
 Pressure. 253, Coefficients of Efflux from Pipes. 254, Reactions from the 
 Pipe-Wall. 255, Origin of Formulas of Flow. 256, Formula of Resist- 
 ance to Flow. 257, Coefficient of Flow. 258, Opposition of Gravity and 
 Reaction. 259, Conversion of Pressure into Mechanical Effect. 260, 
 Measure of Resistance to Flow 261, Resistance Inversely as the Square 
 of the Velocity. 262, Increase of Bursting Pressure. 263, Acceleration 
 and Resistance. 264, Equation of Head Required to Overcome the Re- 
 sistance. 265, Designation of h" and /. 266, Variable Value of m. 267, 
 Investigation of Values of m. 268, Definition of Symbols. 269, Experi- 
 
xiv CONTENTS. 
 
 mental Values of the Coefficient of Flow. 270, Peculiarities of the Coeffi- 
 cient (m)of Flow. 271, Effects of Tubercles. 272, Classification of Pipes 
 and their Mean Coefficients. 273, Equation of the Velocity Neutralized 
 by Resistance to Flow. 274, Equation of Resistance Head. 275, Equation 
 of Total Head. 276, Equation of Volume. 277, Equation of Diameter. 
 278, Relative Value of Subdivisions of Total Head. 279, Many Popular 
 Formulas Incomplete. 280. Formula of M. Chezy. 281, Various Pop- 
 ular Formulas Compared. 282, Sub-heads Compared. 283, Investiga- 
 tions by Dubuat, and Coloumb, and Prony. 284, Prony's Analysis. 285, 
 Eytelwein's Equation of Resistance to Flow. 286, D'Abuisson's Equation 
 of Resistance to Flow. 287, Weisbach's Equation of Resistance to Flow. 
 288, Transpositions of an Original Formula. 289, Unintelligent Use of 
 Partial Formulas. 290, A Formula of more General Application. 291, 
 Values of v for Given Slopes. 292, Values of h and h! for Given Velocities. 
 293, Classified Equations for Velocity, Head, Volume, and Diameter. 
 294, Coefficients of Entrance of Jet. 295, Mean Coefficients for Smooth> 
 Rough, and Foul Pipes. 296, Mean Equations for Smooth, Rough, and 
 Foul Pipes. 297, Modification of a Fundamental Equation of Velocity. 
 298, Values of c 1 . 299, Bends. 300, Branches. 301, How to Economize 
 Head. 
 
 CHAPTER XIV. 
 
 MEASURING WEIRS, AND WEIR GAUGING. PAGE 277. 
 
 Art. 302, Gauged Volumes of Flow. 303, Form of Weir. 304, Dimensions. 
 305, Stability. 306, Varying Length. 307, End Contractions. 308, 
 Crest Contractions. 309, Theory of Flow over a Weir. 310, Formulas 
 for Flow, without and with Contractions. 311, Increase of Volume due 
 to Initial Velocity of Water. 312, Coefficients for Weir Formulas. 313, 
 Discharges for Given Depths. 314, Vacuum under the Crest. 315, Ex- 
 amples of Initial Velocity. 316, Wide-crested Weirs. 317, Triangular- 
 Notch Weirs. 318, Obstacles to Accurate Measures. 319, Hook Gauge. 
 320, Rule Gauge. 321, Tube and Scale Gauge. 
 
 CHAPTER XV. 
 
 FLOW OF WATER IN OPEN CHANNELS PAGE 299. 
 
 Art. 322, Gravity the Origin of Flow. 323, Resistance to Flow. 324, Equa- 
 tions of Resistance and Velocity. 325, Equation of Inclination. 326, Co- 
 efficients of Flow for Channels. 327, Observed Data of Flow in Channels. 
 328, Table of Coefficients for Channels. 329, Various Formulas of Flow 
 Compared. 330, Velocities of Given Films. 331, Surface Velocities. 
 332, Ratios of Surface to Mean Velocities. 333, Hydrometer Gaugings. 
 334, Tube Gauges. 335, Gauge Formulas. 336, Pitot Tube Gauge 337, 
 Woltmann's Tachometer. 338, Hydrometer Coefficients. 339, Henry's 
 Telegraphic Moulinet. 340, Earlier Hydrometers. 341, Double Floats. 
 342, Mid-depth Floats. 343, Maximum Velocity Floats. 344, Relative 
 Velocities and Volumes due to Different Depths. 
 
CONTENTS. 
 
 SECTION III. 
 
 PRACTICAL CONSTRUCTION OF WATER-WORKS. 
 
 CHAPTER XVI. 
 
 RESERVOIR EMBANKMENTS AND CHAMBERS. PAGE 333. 
 
 Art. 345, Ultimate Economy of Skillful Construction. 346, Embankment Foun- 
 dations. 347, Springs under Foundations. 348, Surface Soils. 349, Con- 
 crete Cut-off Walls. 350, Treacherous Strata. 351, Embankment Core 
 Materials. 352, Peculiar Pressures. 353, Earthwork Slopes. 354, Re- 
 connaissance for Site. 355, Detailed Surveys. 356, Illustrative Case. . 
 357, Cut-off Wall. 358, Embankment Core. 359, Frost Covering. 360, 
 Slope Paving. 361, Puddle Wall. 362, Rubble Priming Wall. 363, A 
 Light Embankment. 364, Distribution Reservoirs. 365, Application of 
 Fine Sand. 366, Masonry Faced Embankment. 367, Concrete Paving. 
 368, Embankment Sluices and Pipes. 369, Gate Chambers. 370, Sluice 
 Valve Areas. 371, Stop-valve Indicator. 372, Power required to Open 
 a Valve, 373, Adjustable Effluent Pipe. 374, Fish Screens. 375, Gate 
 Chamber Foundations. 376, Foundation Concrete. 377, Chamber 
 Walls. 
 
 CHAPTER XVII. 
 
 OPEN CANALS.-PAGE 370. 
 
 Art. 378, Canal Banks. 379, Inclinations and Velocities in Practice. 380, 
 Ice Covering. 381, Table of Dimensions of Supply Canals. 382, Canal 
 Gates. 383, Miners' Canals. 
 
 CHAPTER XVII I. 
 
 WASTE WEIRS. PAGE 377. 
 
 Art. 384, The Office and Influence of a Waste-Weir. 385, Discharges over 
 Waste-Weirs. 386, Required Lengths of Waste- Weirs. 387. Forms of 
 Waste-Weirs. 388, Isolated Weirs. 389, Timber Weirs. 390, Ice-Thrust 
 upon Storage Reservoir Weirs. 391, Breadths of Weir-Caps. 392, Thick- 
 nesses of Waste-Weirs and Dams. 393, Force of Overflowing Water. 
 394, Heights of Waves. 
 
 CHAPTER XIX. 
 
 PARTITIONS AND RETAINING WALLS. PAGE 390. 
 
 Art. 395, Design. 396, Theory of Water-Pressure upon a Vertical Surface. 
 397, Water Pressure upon an Inclined Surface. 398, Frictional Stability 
 
xvi CONTENTS. 
 
 of Masonry. 399, Coefficients of Masonry Friction. 400, Pressure Lever- 
 age of Water. 401, Leverage Stability of Masonry. 402, Moment of 
 Weight Leverage of Masonry. 403, Thickness of a Vertical Rectangular 
 Wall for Water Pressure. 404, Moments of Rectangular and Trapedoidal 
 Sections. 405, Graphical Method of Finding the Leverage Resistance. 
 406, Granular Stability. 407, Limiting Pressures. 408, Table of Walls for 
 Quiet Water. 409, Economic Profiles. 410, Theory of Earth Pressures. 
 411, Equation of Weight of Earth Wedge. 412, Equation of Pressure of 
 Earth Wedge. 413, Equation of Moment of Pressure Leverage. 414, 
 Thickness of a Vertical Rectangular Wall for Earth Pressure. 415, Sur- 
 charged Earth Wedge. 416, Pressure of a Surcharged Earth Wedge. 
 417, Moment of a Surcharged Pressure Leverage. 418, Pressure of an 
 Infinite Surcharge. 419, Resistance of Masonry Revetments. 420, Final 
 Resultants in Revetments. 421. Table of Trapezoidal Revetments. 422, 
 Curved-face Batter Equation. 423, Back Batters and their Equations. 
 424, Inclination of Foundation. 425, Front Batters and Steps. 426, 
 Top Breadth. 427, Wharf Walls. 428, Counterforted Walls. 429, Ele- 
 ments of Failure. 430, End Supports. 431, Faced and Concrete Revet- 
 ments. 
 
 CHAPTER XX. 
 
 MASONRY CONDUITS. PAGE 431. 
 
 Art. 432, Protection of Channels for Domestic Water Supplies. 433, Examples 
 of Conduits. 434, Foundations of Conduits. 435, Conduit Shells. 436, 
 Ventilation of Conduits. 437, Conduits under Pressure. 438, Protection 
 from Frost. 439, Masonry to be Self-sustaining. 440, A Concrete Con- 
 duit. 441, Example of a Conduit under Heavy Pressure. 442, Mean 
 Radii of Conduits. 443, Formulas of Flow for Conduits. 444, Table of 
 
 Conduit Data. 
 
 
 
 CHAPTER XXI. 
 
 MAINS AND DISTRIBUTION PIPES. PAGE 446. 
 
 Art, 445, Static Pressures in Pipes. 446, Thickness of Shell resisting Static 
 Pressure. 447, Water-Ram. 448, Formulas of Thickness for Ductile 
 Pipes. 449, Strengths of Wrought Pipe Metals. 450, Moulding of Pipes. 
 451, Casting of Pipes. 452, Formulas of Thickness for Cast-iron Pipes. 
 453, Thicknesses found Graphically. 454, Table of Thicknesses of Cast- 
 iron Pipes. 455, Table of Equivalent Fractional Expressions. 456, Cast- 
 iron Pipe-Joints. 457, Dimensions of Pipe-Joints. 458, Templets for 
 Bolt Holes. 459, Flexible Pipe-Joint. 460, Thickness Formulas Com- 
 pared. 461, Formulas for Weights of Cast-iron Pipes. 462, Table of 
 Weights of Cast-iron Pipes. 463, Interchangeable Joints. 464, Charac- 
 teristics of Pipe Metals. 465, Tests of Pipe-Metals. 466, The Preserva- 
 tion of Pipe Surfaces. 467, Varnishes for Pipes and Iron Work. 468, 
 Hydraulic Proof of Pipes. 469, Special Pipes. 470, Cement-lined and 
 
CONTENTS. xvii 
 
 Coated Pipes. 471, Methods of Lining. 472, Covering. 473, Cement 
 Joints. 474, Cast Hub Joint. 475, Composite Branches. 476, Thickness 
 of Shells for Cement Linings. 477, Gauge Thickness and Weights of 
 Rolled Iron. 478, Lining, Covering, and Joint Mortar. 479, Asphaltum- 
 Coated Wrought-iron Pipes. 480, Asphaltum Bath, for Pipes. 481, 
 Wrought Pipe Plates. 482, Bored Pipes. 483, Wyckoff's Patent 
 Pipe. 
 
 CHAPTER XXI I. 
 
 DISTRIBUTION SYSTEMS, AND APPENDAGES. PAGE 493. 
 
 Art. 484, Loss of Head by Friction. 485, Table of Frictional Heads in Pipes. 
 486, Relative Discharging Capacities of Pipes. 487, Table of Relative 
 Capacities of Pipes. 488, Depths of Pipes. 489, Elementary Dimensions 
 of Pipes. 490, Distribution Systems. 491, Rates of Consumption of 
 Water. 492, Rates of Fire Supplies. 493, Diameter of Supply Main. 
 494, Diameters of Sub-mains. 495, Maximum Velocities of Flow. 496, 
 Comparative Frictions. 497, Relative Rates of Flow for Domestic and 
 Fire Supplies. 498, Required Diameters for Fire Supplies. 499, Duplica- 
 tion Arrangement of Sub-Mains. 500, Stop-Valve Systems. 501, Stop- 
 Valve Locations. 502, Blow-off and Waste Valves. 503, Stop-Valve De- 
 tails. 504, Valve Curbs. 505, Fire Hydrants. 506, Post Hydrants. 507, 
 Hydrant Details. 508, Flush Hydrants. 509, Gate Hydrants. 510, High 
 Pressures. 511, Air Valves. 512, Union of High and Low Services. 513, 
 Combined Reservoir and Direct Systems. 514, Stand Pipes. 515, Fric- 
 tional Heads in Service-Pipes. 
 
 CHAPTER XXII I. 
 
 CLARIFICATION OF WATER. PAGE 530. 
 
 Art. 516, Rarity of Clear Waters. 517, Floating Debris. 518, Mineral Sedi- 
 ments. 519, Organic Sediments. 520, Organic Solutions. 521, Natural 
 Processes of Clarification. 522, Chemical Processes of Clarification. 523, 
 Charcoal Process. 524, Infiltration. 525, Infiltration Basins. 526, Ex- 
 amples of Infiltration. 527, Practical Considerations. 528, Examples 
 of European Infiltration. 529, Example of Intercepting Well. 530, 
 Filter Beds. 531, Settling and Clear-Water Basins. 532, Introduction 
 of Filter-Bed System. 533. Capacity of Filter Beds. 534, Cleaning of 
 Filter Beds. 535, Renewal of Sand Surface. 536, Basin Coverings. 
 
 CHAPTER XXIV. 
 
 PUMPING OF WATER. PAGE 557. 
 
 Art. 537, Types of Pumps. 538, Prime Movers. 539, Expense of Variable 
 Delivery of Water 540, Variable Motions of a Piston. 541, Ratios of 
 Variable Delivery of Water. 542, Office of Stand-Pipe and Air- Vessel. 
 
xviii CONTENTS. 
 
 543, Capacities of Air -Vessels. 544, Valves. 545, Motions of Water 
 through Pumps. 546, Double-Acting Pumping Engines. 547, Geared 
 Pumping Engines. 548, Costs of Pumping Water. 549, Duty of 
 Pumping Engines. 550, Special Trial Duties. 551, Economy of a High 
 Duty. 
 
 CHAPTER XXV. 
 
 SYSTEMS OF WATER SUPPLY. PAGE 585. 
 
 Art. 552, Permanence of Supply Essential. 553, Methods of Gathering and 
 Delivering Water. 554, Gravitation. 555, Choice ot Water. 556, 
 Pumping with Reservoir Reserve 557, Pumping with Direct Pres- 
 sure. 
 
LIST OF TABLES. 
 
 Table No. Page 
 
 1. Population, Families, and Dwellings in Fifty American Cities. ....... 32 
 
 2. Water Supplied, and Piping in several Cities 38 
 
 3. Water Supplied in years 1870 and 1874 39 
 
 4. Average Gallons of Water Supplied to each Inhabitant 40 
 
 5. Ratios of Monthly Consumption of Water in 1874 43 
 
 6. Mean Rainfall in different River Basins 51 
 
 7. Rainfall in the United States 53 
 
 8. Volumes of Rainfall per minute for given inches of Rain per twenty- 
 four hours 62 
 
 9. Flood Volumes from given Watershed Areas 67 
 
 10. Summary of Rainfall upon the Cochituate Basin 72 
 
 11. Summary of Rainfall upon the Croton Basin 72 
 
 12. Summary of Rainfall upon the Croton West-Branch Basin 73 
 
 13. Summary of Percentage of Rain Flowing from the Cochituate Basin. . . 73 
 
 14. Summary of Percentage of Rain Flowing from the Croton Basin 73 
 
 15. Summary of Percentage of Rain Flowing from the Croton West-Branch 
 
 Basin 74 
 
 16. Summary of Volume of Flow from the Cochituate Basin 74 
 
 17. Summary of Volume of Flow from the Croton Basin 74 
 
 18. Summary of Volume of Flow from the Croton West- Branch Basin 75 
 
 19. Estimates of Minimum, Mean, and Maximum Flow of Streams 75 
 
 20. Monthly Ratios of Flow of Streams 76 
 
 21. Ratios of Mean Monthly Rain and Inches of Rain Flowing each Month 77 
 
 22. Equivalent Volumes of Flow for given Depths of Rain in One Month. 82 
 
 23. Equivalent Volumes of Flow for given Depths of Rain in One Year. . . 83 
 
 24. Evaporation from Water 89 
 
 25. Mean Evaporation from Earth 89 
 
 26. Monthly Ratios of Evaporation from Reservoirs 92 
 
 27. Multipliers for Equivalent Inches of Rain Evaporated 92 
 
 28. Monthly Supply to and Draft from a Reservoir (with Compensation). . 96 
 
 29. Monthly Supply to and Draft from a Reservoir (without Compensation) 97 
 
 30. Ratios of Monthly Rain, Flow, Evaporation, and Consumption 101 
 
 31. Percolation of Rain into One Square Mile of Porous Soil m 
 
 32. Analyses of Various Lake, Spring, and Well Waters 117 
 
 33. Analyses of Various River and Brook Waters 118 
 
 34. Analyses of Various Streams in Massachusetts 120 
 
 35. Analyses of Various Water Supplies from Domestic Wells 121 
 
xx LIST OF TABLES. 
 
 Table No. p age 
 
 36. Artesian Well Temperatures 1 1 1 1 4 , , , 4 4 127 
 
 37. Analyses of Various Mineral Spring Waters 143 
 
 38. Weights and Volumes of Water at Different Temperatures 166 
 
 39. Pressures of Water at Stated Depths 172 
 
 40. Correspondent Heights, Velocities, and Times of Falling Bodies 190 
 
 41. Coefficients from Michelotti's Experiments with Orifices 198 
 
 42. Coefficients from Bossut's Experiments with Orifices 199 
 
 43. Coefficients from Rennie's Experiments with Orifices 199 
 
 44. Coefficients from Lespinasse's Experiments with Orifices 201 
 
 45. Coefficients from General Ellis's Experiments with Orifices 203 
 
 46. Coefficients for Rectangular Orifices (vertical) 205 
 
 47. Coefficients for Rectangular Orifices (horizontal) 206 
 
 48. Castel's Experiments with Convergent Tubes 217 
 
 49. Venturi's Experiments with Divergent Tubes 219 
 
 50. Eytelwein's Experiments with Compound Tubes 220 
 
 51. Coefficients of Efflux (c) for Short Pipes 227 
 
 52. Experimental Coefficients of Flow (m) by Darcy 237 
 
 53. Experimental Coefficients of Flow (m) by Fanning 238 
 
 54. Experimental Coefficients of Flow (m) by Du Buat 238 
 
 55. Experimental Coefficients of Flow (m) by Bossut 238 
 
 56. Experimental Coefficients of Flow (m) by Couplet 239 
 
 57. Experimental Coefficients of Flow (m) by Provis 239 
 
 58. Experimental Coefficients of Flow (m) by Rennie 239 
 
 59. Experimental Coefficients of Flow (m) by Darcy 240 
 
 60. Experimental Coefficients of Flow (m) by General Greene and others. . 240 
 
 61. Tabulated Series of Coefficients of Flow (m) 242 
 
 62. Coefficients for Clean, Slightly Tuberculated, and Foul Pipes 248 
 
 63. Various Formulas for Flow of Water in Pipes 254 
 
 64. Velocities (v) for given Slopes and Diameters 259 
 
 65. Tables of h and K due to given Velocities 264 
 
 66. Values of c v and c for Tubes 267 
 
 66a. Sub-coefficients of Flow (*:') in Pipes. 271 
 
 67. Coefficients of Resistance in Bends 274 
 
 68. Experimental Weir Coefficients 288 
 
 69. Coefficients for given Depths upon Weirs 289 
 
 70. Discharge for given Depths upon Weirs 290 
 
 71. Weir Coefficients by Castel , 291 
 
 72. Series of Weir Coefficients by Smeaton and others 291 
 
 73. Coefficients for Wide Weir-crests 294 
 
 74. Observed and Computed Flows in Canals and Rivers 307 
 
 75. Coefficients (m) for Open Channels 308 
 
 76. Various Formulas for Flow in Open Channels 310 
 
 77. Weights of Embankment Materials 341 
 
 78. Angles of Repose, and Frictions of Embankment Materials 345 
 
 79. Dimensions of Water Supply and Irrigation Canals 373 
 
 80. Waste-Weir Volumes for given Depths 380 
 
 81. Lengths and Discharges of Waste-Weirs 381 
 
f ' '" 
 
 LIST OF TABLES , xxi 
 
 Table No. Page 
 
 82. Thicknesses of Masonry Weirs and Dams 387 
 
 83. Heights of Reservoir and Lake Waves 388 
 
 84. Coefficients of Masonry Frictions 396 
 
 85. Computed Pressures in Masonry 403 
 
 86. Limiting Pressures upon Masonry 404 
 
 87. Dimension of Walls to Retain Water 406 
 
 88. Dimension of Walls to Sustain Earth 420 
 
 89. Thicknesses of a Curved-face Wall 422 
 
 90. Hydraulic Mean Radii for Circular Conduits 442 
 
 900. Coefficients (m) for Smooth Conduits 444 
 
 91. Conduit Data 445 
 
 92. Tenacities of Wrought Pipe Metals 451 
 
 93. Thicknesses of Cast-iron Pipes 455 
 
 930;. Thicknesses of Cast-iron Pipes as used in several Cities 456 
 
 94. Parts of an Inch and Foot expressed Decimally 457 
 
 95. Dimensions of Cast-iron Water-pipes 461 
 
 96. Flange Data of Flanged Cast-iron Pipes 462 
 
 97. Various Formulas for Thicknesses of Cast-iron Pipes 466 
 
 98. Weights of Cast-iron Pipes 468 
 
 980;. Weights of Cast-iron Pipes as used in several Cities 469 
 
 99. Thicknesses of Wrought-iron Pipe Shells 486 
 
 100. Thicknesses and Weights of Iron Plates 488 
 
 101. Frictional Head in Pipes 495 
 
 102. Relative Discharging Capacities of Pipes ; 5 
 
 103. Depths to lay Water-pipes in different Latitudes 502 
 
 104. Elementary Dimensions of Pipes 54 
 
 105. Maximum Advisable Velocity of Flow in Pipes 508 
 
 106. Diameters of Pipes to supply given Numbers of Hose Streams 510 
 
 107. Experimental Volumes of Fire Hydrant Streams. 520 
 
 108. Frictional Head in Service Pipes 528 
 
 109. Dimensions of Filter-beds for given Volumes 554 
 
 no. Piston Spaces for given Arcs of Crank Motion ... 562 
 
 in. Ratios of Piston Motions for given Crank Arcs 5 6 4 
 
 112. Costs of Pumping in Various Cities 575 
 
 113. Special Trial Duties of Various Pumping Engines 580 
 
 114. Comparative Consumptions of Coal at Different Duties 581 
 
 115. Fuel Expenses for Pumping compared on Duty Bases 581 
 
 116. Comparison of Values of Pumping-Engines on Fuel Bases 583 
 
LIST OF FULL PAGE ILLUSTRATIONS. 
 
 PAGE 
 
 Public Fountain, Cincinnati 2 
 
 Gateway, Chestnut Hill Reservoir, Boston 24 
 
 Pumping Station, Toledo 31 
 
 Diagram of Pumping, Annual 43 
 
 Pumping Station, Millwaukee 45 
 
 Diagrams of Rainfall 55 
 
 Diagrams of Rainfall 57 
 
 Diagrams of Secular Rainfall 59 
 
 Section and Plan of Pump-House 65 
 
 Reservoir Embankment, Norwich 84 
 
 Intercepting Well, Prospect Park, Brooklyn 102 
 
 Pumping Station, New Bedford 139 
 
 Stand-Pipe, Boston 160 
 
 Pumping Station, Manchester. 213 
 
 Compound Duplex Pumping Engine 223 
 
 Measuring Weir, for Turbine Test 277 
 
 Fairmount Turbines and Pumps, Philadelphia 332 
 
 Distributing Reservoir. 333 
 
 Compound Inverted Pumping-Engine 377 
 
 Conduit Sections 431 
 
 Cylindrical Penstock 440 
 
 Forms of Pipe-Sockets and Spigots 446 
 
 Branch, Reducer and Bend 478 
 
 Double-Faced Stop-Valves 493 
 
 Plan of a Pipe System 505 
 
 Flush Fire Hydrants 521 
 
 Pumping-Engine, No. 3, Brooklyn 557 
 
 Cornish Plunge-Pump 563 
 
 Compound Beam Pumping-Engine, Lynn 567 
 
 Geared Pumping-Engine, Providence 573 
 
 Hydraulic Power Pumping Machinery, Manchester 585 
 
 Jonval Turbine 593 
 
 WHOLE NUMBER OF ILLUSTRATIONS 180 
 
APPENDIX. 
 
 Page 
 
 Metric Weights and Measures 593 
 
 Table of French Measures and United States Equivalents 594 
 
 Cubic Inch, and Equivalents 595 
 
 Gallon, and Equivalents 595 
 
 Cubic Foot, and Equivalents 595 
 
 Imperial Gallon, and Equivalents 596 
 
 Cubic Yard, and Equivalents 596 
 
 Table of Units of Heads and Pressures of Water, and Equivalents 596 
 
 Table of Average Weights, Strengths, and Elasticities of Materials 597 
 
 Formulas for Diameters and Strengths of Shafts 599 
 
 Trigonometrical Expressions 599 
 
 Trigonometrical Equivalents 600 
 
 Table of Sines, Tangents, &c 601 
 
 What Constitutes a Car Load 602 
 
 Lubricating Compounds for Gears 602 
 
 Compound for Cleaning Brass 602 
 
 Iron Cement, for Repairing Cracks in Castings 602 
 
 Alloys, Table of 603 
 
 Velocities of Flow in Channels, that Move Sediments 604 
 
 Tensile Strengths of Cements and Mortars 605 
 
 Dimensions of Bolts and Nuts 606 
 
 Weights of Lead and Tin-lined Service-Pipes 607 
 
 Meters and Meter Rates - 608 
 
 Resuscitation from Death by Drowning 609 
 
if LIBRA RY X 
 
 1 UNIVERSITY OF jj 
 
 I CALIFORNIA. 
 
 ./' 
 
 SECTION I. 
 
 COLLECTION AND STORAGE OF WATER, AND ITS IMPURITIES, 
 
 CHAPTER I. 
 
 INTRODUCTORY. 
 
 1. Necessity of Public Water Supplies. A new or 
 
 an additional water supply is an inevitable necessity when- 
 ever and wherever a new settlement establishes itself in an 
 isolated position ; again whenever the settlement receives 
 any considerable increase ; and again when it becomes a 
 great metropolis or manufacturing centre. 
 
 In all the wonderful and complex transformations in 
 Nature, in the sustenance of all organized beings, and in 
 the convenience and delight of man, water is appointed to 
 perform an important and essential part. 
 
 Life cannot long exist in either plant or animal, unless 
 water, in some of its forms, is provided in due quantity. 
 
 Wholesome water is indispensable in the preparation of 
 all our foods ; clear and soft water is essential for promot- 
 ing the cleanliness and health of our bodies; and pure 
 water is demanded for a great variety of the operations of 
 the useful and mechanic arts. 
 
 2. Physiological Office of Water. Of the three 
 essentials to human life, air, water, and food, the one now 
 
26 INTRODUCTORY. 
 
 to be specially considered, water ^ has for its physiological 
 office to maintain all the tissues of the body in healthy 
 action. 
 
 If the water received into the system is unfit for such 
 special duty, all the animal functions suffer and are weak- 
 ened, air then but partially clarifies the blood, food then is 
 imperfectly assimilated, and the body degenerates. 
 
 Vigor is essential to the uniform success and happiness 
 of every individual, and strength and happiness of the 
 people are essential to good public morals, good public 
 government, and sound public prosperity. 
 
 Sanitary improvements are, therefore, among the first 
 and chief duties of public officers and guardians, and have 
 ever been the objects of the most earnest thought and labor 
 of great public philanthropists. 
 
 3. Sanitary Office of Public Water Supplies. 
 Water has thus far proved the most effectual and econom- 
 ical agent, as sanitary scavenger, in the removal from our 
 habitations of waste slops and sewage, and also the most 
 effectual * and economical agency in the protection of life 
 and property from destruction by fire. 
 
 The necessity of a judiciously executed system of public 
 water-supply increases as the population of a town increases; 
 as the mass of buildings thickens ; as the lands upon which 
 the town is built become saturated with sewage, and the 
 individual sources within the town are polluted; as the 
 atmosphere over and within the town is fouled by gases 
 
 * We need refer to but one of many experiences, viz. : At Columbus, 
 Ohio, the average loss by fire for the four years preceding the completion of 
 the public water- works was -f 3 ^ of one per cent, of the valuation. The average 
 loss during the first four years after the completion of the works was y 1 ^, and 
 during the fifth year, from April 1, 1875, to April 1, 1876, was yW of the valu- 
 ation. These statistics show a probable saving in the first four years of upward 
 of one-half million dollars, and in five years of more than the entire cost of the 
 water-works. 
 
f ' ' 
 
 HELPFUL INFLUENCE OF PUBLIC WATER SUPPLIES. 27 
 
 arising therefrom ; and as the dangers of epidemics, fevers, 
 and contagious diseases increase. 
 
 4. Helpful Influence of Public Water Supplies. 
 No town or city can submit to a continued want of an 
 adequate supply of pure and wholesome water without a 
 serious check in its prosperity. 
 
 Capital is always wary of investment where the elements 
 of safety and health are lacking, and industry dreads fre- 
 quent failures and objectionable quality in its water supply. 
 
 It is true that considerations of profit sometimes induce 
 the assembling of a town where potable waters are procur- 
 able with difficulty, but in such cases the lack is sure to 
 prove a growing hindrance to its prosperity, and before the 
 town arrives at considerable magnitude, its remedy will 
 present one of the most difficult problems with which its 
 municipal authorities are obliged to cope. 
 
 In the experience of all large and thriving cities, there 
 has come a time when an additional or new and abundant 
 water supply was a necessity, terribly real, that would not 
 be talked down, or resolved out of existence by public 
 meetings, or wait for a more convenient season; a time 
 when it was not possible for every citizen to supply his 
 household or his place of business independently, or even 
 for a majority of the citizens to do so, and when prompt, 
 united, and systematic action must be taken to ensure the 
 health, prosperity, and safety of the people. Such stern 
 necessity often appears to present difficulties almost insur- 
 mountable by the available mechanical and financial re- 
 sources of the citizens. 
 
 Out of such simple but positive necessities have grown 
 the grandest illustrations, in our great public water sup- 
 plies, of the benefits of co-operative action, recorded in the 
 annals of political economy. Out of such simple necessi- 
 
28 INTRODUCTORY. 
 
 ties grew some of the most magnificent and enduring con- 
 structions of the powerful empires of the Middle Ages, the 
 architectural grandeur of which the moderns have not 
 attempted to surpass. 
 
 5. Municipal Control of Public Water Supplies. 
 The magnitude of the labors to be performed and the 
 amount of capital required to be invested in the construc- 
 tion of a system of water supplies invariably brings into 
 prominence the question, Shall the construction, operation, 
 and control of these works be entrusted to private capital, 
 or shall they be executed under the patronage of the muni- 
 cipal authorities and under the direction of a commission 
 delegated by the people? The conclusion reached in a 
 majority of the American cities has been that the works 
 ought to be conducted as public enterprises. They have 
 been believed to be so intimately connected with the public 
 interests and welfare as to be peculiarly subjects for pub- 
 lic promotion ; and that, under the direction of a commis- 
 sion appointed by the people to study and comprehend all 
 their needs, to consider, with the aid of expert advice, and 
 to suggest plans, the works would be projected on such a 
 liberal and comprehensive scale as would best fulfil the 
 objects desired to be attained, and that the true interests of 
 the people would not be subordinated to mere considera- 
 tions of profit. 
 
 Further, that if the works when complete were operated 
 under municipal care, their standard and effectiveness would 
 more certainly be maintained; their extension into new 
 territory might keep pace with and encourage the growth 
 of the city ; they might not, by excessive rates, be made to 
 oppress important industries ; their advantages might more 
 surely be kept within the reach of the poorer classes ; they 
 might more economically be applied to the adornment of 
 
INCIDENTAL ADVANTAGES. 29 
 
 the public buildings and grounds ; and that they might, 
 when judiciously planned, constructed, and managed, be- 
 come a source of public revenue. 
 
 Nearly all the objects desirable to be attained in a pub- 
 lic water supply have, however, been accomplished, in 
 numerous instances that might be cited, under the auspices 
 of private enterprise. 
 
 6. Value as an Investment. The necessary capital 
 honestly applied to the construction of an intelligently and 
 judiciously planned effective public water supply has 
 almost invariably proved, both directly and indirectly, a 
 remunerative investment. 
 
 Many, though not all, of our American Water-supply 
 Reports, show annual incomes from water-rates in excess 
 of the combined annual operating expenses and interest on 
 the capital expended. In addition to this cash return, there 
 are in all cases benefits accruing to the public, usually 
 exceeding in real value that of the more generally recog- 
 nized money income. 
 
 7. Incidental Advantages. The construction of water- 
 works is almost sure to enhance the value of property along 
 its lines, under its protection, and availing of its conve- 
 niences. There is, also, a perpetual reduction* in the 
 
 * In a recently adopted schedule of the National Board of Underwriters, 
 there are additions to a minimum standard rate in a standard city, which is 
 provided with good water supply, fire alarm, police, etc., as follows, termed 
 deficiency charges : 
 
 Minimum standard rate of insurance of a standard building. . 25 cents. 
 
 If no water supply add 15 
 
 If only cisterns, or equivalent " 10 
 
 If system is other than gravity " 05 
 
 If no fire department " 25 
 
 If no police organization " 05 
 
 If no building law in force " 05 
 
 The financial value of the enhanced fire risk, as deduced by the Board from 
 an immense mass of statistics, and the additional premium charged on the 
 
30 INTRODUCTORY. 
 
 yearly rates of insurance. The substitution of soft water 
 for hard water, as almost all waters are, results in a mate- 
 rial reduction in the daily waste accompanying the prepa- 
 ration of foods, in laundry and cleansing operations, in the 
 production of steam power, and in many of the processes 
 employed in the useful arts. 
 
 There are many industries, the introduction of which are 
 of value to a community, that cannot be prosecuted with- 
 out the use of tolerably pure and soft water. To save the 
 annual aggregate of labor required to convey water from 
 wells into and to the upper floors of city tenements or resi- 
 dences, is a matter of no inconsiderable importance ; but 
 paramount to all these is the value of the sanitary results 
 growing out of the maintenance of health, and the induce- 
 ment to cleanliness of person and habitation, by the con- 
 venience of an abundance of water delivered constantly in 
 the household, and the enhanced safety to human life and 
 to property from destroying flames, accompanying a liberal 
 distribution of public fire hydrants under adequate pressure 
 throughout the populous districts. 
 
 most favorable buildings, is 60 per cent, without good water- works, and 40 per 
 cent, if only fire cisterns are provided. 
 
?;:;:) 
 
f I, I B R A R Y 
 
 UNIVKUS1TY OF 
 
 CHAPTER II. 
 
 QUANTITY OF WATER REQUIRED. 
 
 8. Statistics of Water Supplied. One of the first 
 duties of a Commission to whom has been assigned the 
 task of examining into and reporting upon a proposed 
 supply of water for a community, is to determine not only 
 what is a wholesome water, but what quantity of such 
 wholesome water will be required, and adequate for its 
 present and prospective uses. 
 
 In many cases, this problem is parallel with the deter- 
 mination of a product from two factors, one of which only 
 is a known quantity. Oftea all factors must be assumed. 
 
 The total number of inhabitants, the total number of 
 dwellings, and the total number of manufacturing and 
 commercial firms can be obtained without great difficulty, 
 and it can safely be assumed that eighty per cent, of all 
 these within reach of a new and improved water supply 
 will be among its patrons within a few years after the intro- 
 duction of the new supply ; but how much water will be 
 required for actual use, or will be wasted, per person, per 
 dwelling, or per firm, is always quite uncertain. 
 
 Rarely can any data worthy of confidence respecting 
 these quantities be obtained. The practice, therefore, gen- 
 erally is, to obtain statistics from towns and cities already 
 supplied, and to attempt to reduce these to some general 
 average that will apply to the case in hand. 
 
 9. Census Statistics. In a small portion of the water- 
 supply reports there is given, in addition to the total quan- 
 
32 
 
 QUANTITY OF WATER REQUIRED. 
 
 tity of water supplied, the number of families supplied ; in 
 other reports, the number of dwellings, or the number of 
 fixtures of the several classes supplied, and occasionally 
 the population supplied, or the total population of the 
 municipality. 
 
 In the investigations for facts applicable to a new sup- 
 ply, when information must necessarily be culled from 
 various water reports, it is often desirable to know the 
 populations of the places from which the reports are re- 
 ceived, their number of families, persons to a family, num- 
 ber of dwellings and persons to a dwelling, so as to be able 
 to reduce their water-supply data to a uniform classifica- 
 tion. We therefore present an abstract from the United 
 States Census for the year 1870, giving such information 
 respecting fifty prominent American cities : 
 
 TABLE No- 1 . 
 
 POPULATION, FAMILIES, AND DWELLINGS IN FIFTY AMERICAN CITIES, 
 IN THE YEAR 1 870. 
 
 CITIES. 
 
 SIZE.* 
 
 POPULATION. 
 
 FAMILIES. 
 
 DWELLINGS. 
 
 Number. 
 
 Persons 
 to a 
 family. 
 
 Number. 
 
 Persons 
 to a 
 dwelling 
 
 Albany N. Y 
 
 20 
 23 
 
 6 
 7 
 3 
 ii 
 
 33 
 26 
 
 47 
 
 69,422 
 53,180 
 267,354 
 250,526 
 396,099 
 117,714 
 
 39,634 
 48,956 
 28,323 
 298,977 
 216,239 
 
 14,105 
 10,147 
 49,929 
 48,188 
 80,066 
 22,325 
 
 7,897 
 9,098 
 
 6,i55 
 59,497 
 42,937 
 
 4.92 
 
 5-24 
 
 5-35 
 5.20 
 
 4-95 
 5-27 
 5.02 
 
 5.38 
 4.60 
 
 5-3 
 5-4 
 
 8,748 
 
 8,347 
 40,35 
 29,623 
 
 45,834 
 18,285 
 
 6,348 
 6,861 
 
 4,396 
 44,620 
 
 24,55 
 
 7-94 
 
 6.37 
 6.63 
 8.46 
 8.64 
 
 6-44 
 6.24 
 7.14 
 6.44 
 6.70 
 
 8.81 
 
 Allegheny, Penn 
 
 Baltimore, Md 
 
 Boston Mass 
 
 Brooklyn N. Y 
 
 Buffalo, N. Y 
 
 Cambridge, Mass 
 
 Charleston S C 
 
 Charlestown, Mass .... 
 Chicago 111 
 
 Cincinnati, Ohio 
 
 
 * This column expresses the order of size as numbered from largest to 
 smallest ; New York, the largest, being numbered 1. 
 
STATISTICS OF FIFTY AMERICAN CITIES. 33 
 
 POPULATION, ETC., IN FIFTY AMERICAN CITIES (Continued). 
 
 CITIES. 
 
 SIZE. 
 
 POPULATION. 
 
 FAMILIES. 
 
 DWELLINGS. 
 
 Number. 
 
 Persons 
 to a 
 family. 
 
 Number. 
 
 Persons 
 to a 
 dwelling 
 
 Cleveland Ohio .... 
 
 15 
 
 42 
 
 44 
 
 18 
 
 5 
 34 
 
 27 
 
 17 
 
 38 
 45 
 14 
 3i 
 49 
 32 
 
 *9 
 
 39 
 13 
 
 2 5 
 
 9 
 
 i 
 
 37 
 
 2 
 
 16 
 41 
 
 21 
 36 
 24 
 
 22 
 10 
 48 
 
 35 
 4 
 29 
 40 
 28 
 46 
 
 12 
 
 43 
 30 
 
 92,829 
 3l>274 
 30,473 
 
 79*577 
 26,766 
 37,180 
 48,244 
 82,546 
 32,260 
 28,921 
 
 J oo,753 
 40,928 
 28,233 
 40,226 
 71,440 
 32,034 
 105,059 
 50,840 
 191,418 
 942,292 
 
 33*579 
 674,022 
 86,076 
 
 3i4 I 3 
 68,904 
 
 33*930 
 51,038 
 62,386 
 
 149*473 
 28,235 
 
 35' 92 
 310,864 
 
 43*05! 
 3i*5 8 4 
 46,465 
 28,804 
 109,199 
 30,841 
 41,105 
 
 18,411 
 
 5*790 
 6,109 
 
 I5* 6 36 
 
 5,216 
 
 7,427 
 9,200 
 
 16,687 
 
 5*585 
 5*287 
 
 J 9,!77 
 7,649 
 6,100 
 7,824 
 14,226 
 6,301 
 21,631 
 10,482 
 39*13^ 
 185,789 
 7*048 
 127,746 
 16,182 
 6,632 
 
 J 4,775 
 6,932 
 9,792 
 12,213 
 
 30,553 
 5, OI 3 
 6,642 
 
 59,43i 
 8,677 
 
 6,457 
 9,302 
 
 5*793 
 2i,343 
 
 5*8o8 
 8,658 
 
 5.04 
 5-40 
 4-99 
 5.09 
 5.13 
 
 , 5.oi 
 
 ' 5-24 
 4-95 
 5.78 
 
 5.47 
 5.25 
 5-35 
 4.63 
 5.H 
 5.02 
 5.o8 
 4.86 
 4.85 
 4.89 
 5.07 
 4.76 
 5.28 
 5.32 
 4.74 
 4.66 
 
 4.89 
 5.21 
 5-" 
 
 4.89 
 5.63 
 
 5.28 
 
 5.23 
 4.96 
 4.89, 
 5.00 
 
 4.97 
 5.12 
 
 5-31 
 4-74 
 
 16,692 
 
 5* 011 
 5,6n 
 14,688 
 2,687 
 6,688 
 7,820 
 9,867 
 5*424 
 3,443 
 14,670 
 6,362 
 4,625 
 6,408 
 13,048 
 5,738 
 14,350 
 8,100 
 33,656 
 64,044 
 4,653 
 112,366 
 14,224 
 4,836 
 9,227 
 6,294 
 
 8,033 
 11,649 
 
 25,905 
 4,56i 
 5,646 
 
 39*675 
 7,088 
 6,069 
 5,893 
 4,799 
 '9*545 
 5*398 
 4,922 
 
 5.56 
 6.24 
 
 5-43 
 5-42 
 9.96 
 
 5.56 
 6.17 
 
 8.37 
 
 5-95 
 8.40 
 6.87 
 
 6.43 
 6.10 
 6.28 
 5.48 
 5.58 
 7.32 
 6.28 
 
 5-69 
 14.72 
 7.22 
 6.01 
 6.05 
 6.50 
 746 
 5-39 
 6.35 
 5.36 
 
 5-77 
 6.19 
 
 6.21 
 
 7-84 
 6.07 
 5.20 
 7.88 
 6.00 
 5-59 
 5-7 1 
 8-35 
 
 Columbus Ohio 
 
 Dayton, Ohio 
 
 Detroit, Michigan 
 
 Fall River Mass 
 
 Hartford, Conn 
 
 Indianapolis Ind 
 
 Jersey City NT 
 
 Kansas City Mo 
 
 Lawrence, Mass 
 
 Louisville, Ky 
 
 Lowell, Mass 
 
 Lynn, Mass 
 
 Memphis, Tenn. . . . 
 
 Milwaukee, Wis 
 
 Mobile, Ala 
 
 Newark, N. J 
 
 New Haven, Conn 
 New Orleans, La. . 
 
 New York, N. Y 
 
 Paterson, N. J 
 
 Philadelphia, Pa 
 
 Pittsburg, Pa 
 
 Portland, Me 
 
 Providence, R. I 
 
 Reading, Pa. . 
 
 Richmond Va 
 
 Rochester, N Y 
 
 San Francisco, Cal .... 
 Savannah, Ga 
 
 Scranton, Pa 
 St. Louis, Mo 
 
 Syracuse, N. Y 
 
 Toledo, Ohio 
 
 Troy, N. Y 
 
 Utica NY .... 
 
 Washington, D. C 
 
 Wilmington Del . . 
 
 Worcester Mass 
 
 
34 QUANTITY OF WATER REQUIRED. 
 
 1O. Approximate Consumption of Water. In 
 
 American cities, having well arranged and maintained sys- 
 tems of water supply, and furnishing good wholesome 
 water for domestic use, and clear soft water adapted to the 
 uses of the arts and for mechanical purposes, the average 
 consumption is found to be approximately as follows, in 
 United States gallons : 
 
 (a.) For ordinary domestic use, not including hose use, 
 20 gallons per capita per day. 
 
 (b.) For private stables, including carriage washing, 
 when reckoned on the basis of inhabitants, 3 gallons per 
 capita per day. 
 
 (c.) For commercial and manufacturing purposes, 5 to 
 15 gallons per capita per day. 
 
 (d.) For fountains, drinking and ornamental, 3 to 10 
 gallons per capita per day. 
 
 (e.) For fire purposes, -f$ gallon per capita per day. 
 
 (/.) For private hose, sprinkling streets and yards, 
 10 gallons per capita per day, during the four dryest 
 months of the year. 
 
 (g.) Waste to prevent freezing of water in service-pipes 
 and house-fixtures, in Northern cities, 10 gallons per capita 
 per day, during the three coldest months of the year. 
 
 (h.) Waste by leakage of fixtures and pipes, and use 
 for flushing purposes, from 5 gallons per capita per day 
 upward. 
 
 The above estimates are on the basis of the total popu- 
 lations of the municipalities. 
 
 There will be variations from the above approximate 
 general average, with increased or decreased consumption 
 for each individual town or city, according to its social and 
 business peculiarities. 
 
WATER SUPPLIED TO ANCIENT CITIES. 35 
 
 The domestic use is greatest in the towns and cities, and 
 in the portions of the towns and cities having the greatest 
 wealth and refinement, where water is appreciated as a 
 luxury as well as a necessity, and this is true of the yard 
 sprinkling and ornamental fountain use, and the private 
 stable use. 
 
 The greatest drinking-fountain use, and fire use, and 
 general waste, will ordinarily be in the most densely- 
 populated portions, while the commercial and manufactur- 
 ing use will be in excess where the steam-engines are most 
 numerous, where the hydraulic elevators and motors are, on 
 the steamer docks, and where the brewing and chemical 
 arts are practiced. 
 
 The ?atio of length of piping to the population is greater 
 in wealthy suburban towns than in commercial and manu- 
 facturing towns. 
 
 Some of these peculiarities are brought out in a follow- 
 ing table of the quantity of water supplied and of piping in 
 several cities, which is based upon the census table hereto- 
 fore given and upon various water-works reports for the 
 year 1870. 
 
 The general introduction of public water- works, on the 
 constant-supply system, with liberal pressures in the mains 
 and house-services, throughout the American towns and 
 cities, has encouraged its liberal use in the households, so 
 that it is believed that the legitimate and economical domes- 
 tic use of water is of greater average in the American cities 
 than in the cities of any other country, at the present time, 
 and its general use is steadily increasing. 
 
 11. Water Supplied to Ancient Cities. The sup- 
 plies to ancient Jerusalem, imperial Rome, Byzantium, and 
 Alexandria, were formerly equal to three hundred gallons 
 per individual daily ; and, later, the supplies to Nismes, 
 
36 
 
 QUANTITY OF WATER REQUIRED. 
 
 Metz, and Lyons, in France, and Lisbon, Segovia, and 
 Seville, in Spain, were most liberal, but a small proportion 
 only of the water supplied from these magnificent public 
 works was applied to domestic use, except in the palaces 
 of those attached to the royal courts. 
 
 12. Water Supplied to European Cities. In the 
 year 1870, the average daily supply to some of the leading 
 European cities was approximately as follows : 
 
 CITIES. 
 
 IMP. GALLONS. 
 
 London, England 
 
 2Q 
 
 Manchester " ....... 
 
 *7 
 
 2/1 
 
 Sheffield " 
 
 2Q 
 
 Liverpool, " 
 
 ^y . 
 
 27 
 
 Leeds, " 
 
 21 
 
 Edinburgh Scotland . . 
 
 ?o 
 
 Glasgow " . 
 
 o w 
 4.O 
 
 
 7Q 
 
 
 40 
 
 
 30 
 
 Geneva Switzerland 
 
 16 
 
 
 16 
 
 
 18 
 
 
 * r- 
 
 In the year 1866, public water supplies * were, in vol- 
 ume, as follows, in the cities named : 
 
 CITIES. 
 
 POPULATION. 
 
 SUPPLY PER CAPITA. 
 
 Hamburg Prussia . 
 
 2OO,OOO 
 
 34. sfals. 
 
 Altona " 
 
 C2,OOO 
 
 20 " 
 
 Tours France 
 
 42.OOO 
 
 22 " 
 
 Ansrers. " 
 
 
 
 Toulouse, " 
 
 IOO,OOO 
 
 13-5 " 
 
 Nantes " 
 
 II2,OOO 
 
 13.6 " 
 
 Lyons, " 
 
 ^OO.OOO 
 
 22 " 
 
 
 
 ///Ji.6 
 
 * Vide Kirkwood's " Filtration of River Waters." Van Nostranfl, N. Y., 1869. 
 
WATER SUPPLIED TO AMERICAN CITIES. 
 
 37 
 
 Prof. Rankine gives,* as a fair estimate of the real daily 
 demand for water, per inhabitant, amongst inhabitants of 
 different habits as to the quantity of water they consume, 
 the following, based upon British water supply and con- 
 sumption : 
 
 RANKINE'S ESTIMATE FOR ENGLAND. 
 
 
 IMP. 
 
 GALLONS PER 
 
 DAY. 
 
 
 Least. 
 
 Average. 
 
 Greatest. 
 
 Used for domestic purposes 
 
 7 
 
 I O 
 
 
 Washing streets, extinguishing fires, sup- 
 plying fountains, etc 
 
 
 
 
 Trade and manufactures 
 
 
 
 
 Waste under careful regulations, say .... 
 Total demand 
 
 2 
 
 
 2 
 22 
 
 !* 
 
 
 
 
 2 7? 
 
 13. Water Supplied to American Cities. The lim- 
 ited use of water for domestic purposes in many of the 
 European cities during the last half century, led the engi- 
 neers who constructed the pioneer water-works of some of 
 the American States to believe that 30 gallons of water per 
 capita daily would be an ample allowance here ; and in 
 their day there was scarce a precedent to lead them to 
 anticipate the present large consumption of water for lawn 
 and street sprinkling by hand-hose, or for waste to prevent 
 freezing in our Northern cities. 
 
 The following tables will show that this early estimated 
 demand for water has been doubled, trebled, and in some 
 instances even quadrupled ; and this considerable excess, 
 to which there are few exceptions, has been the cause of 
 much annoyance and anxiety. 
 
 * " Civil Engineering," London, 1872, p. 731. 
 
38 
 
 QUANTITY OF WATER REQUIRED. 
 
 In the year 1870, the average daily supply to some of 
 the American cities was as follows, in United States gallons : 
 
 TAB LE No. 2. 
 WATER SUPPLIED AND PIPING IN SEVERAL CITIES, IN THE YEAR 1870. 
 
 CITIES. 
 
 POPULA- 
 TION 
 IN 1870. 
 
 SUPPLY 
 
 PER 
 
 PERSON, 
 DAILY 
 AVERAGE 
 
 SUPPLY 
 
 PER 
 
 FAMILY, 
 DAILY 
 AVERAGE. 
 
 SUPPLY 
 
 PER 
 
 DWELLING, 
 DAILY 
 
 AVERAGE. 
 
 TOTAL 
 DAILY SUPPLY, 
 AVERAGE. 
 
 TOTAL MILES 
 OF PIPE MAINS. 
 
 MILES OF PIPE 
 
 PER 1,000 
 
 INHABITANTS. 
 
 Baltimore 
 Boston 
 
 267,354 
 2 CO C 26 
 
 Gallons. 
 52.81 
 
 60 T C 
 
 Gatfons, 
 282.53 
 
 7 T 2 >rft 
 
 Gallons. 
 
 SS^S 
 co8 87 
 
 Gattons. 
 14,122,032 
 T C O7O AOO 
 
 Miles. 
 214 
 IOA 
 
 Miles. 
 0.80 
 
 7& 
 
 Brooklyn .... 
 Buffalo 
 
 ^G U ,0^ IJ 
 396,099 
 117 7 I A. 
 
 JU. l^j 
 
 47.16 
 
 c.8 08 
 
 3 1 ^-7 
 233-44 
 206 08 
 
 5 uo -7 
 407.46 
 
 2*7/1 QA 
 
 A 0> U / U ,T- UU 
 18,682,219 
 6 8^8 7O7 
 
 1 y4 
 
 *s8 
 
 c6 
 
 0.65 
 
 o 48 
 
 Cambridge . . . 
 Charlestown. . 
 Chicago . 
 
 1 A /,/ x ^f 
 
 39,634 
 28,323 
 208 0.7*7 
 
 43-90 
 43-90 
 
 62 "^2 
 
 220.38 
 201.94 
 
 2 T -2 A T 
 
 O/ T-^T- 
 273-94 
 282.72 
 A -1 *J A 
 
 U J O <J JO W O 
 
 J ,739869 
 1,243,380 
 
 T R ()% ? r>oo 
 
 o u 
 60 
 
 25 
 24.0 
 
 1.64. 
 0.90 
 o 81 
 
 Cincinnati . . . 
 Cleveland 
 Detroit 
 
 ^yjy// 
 216,239 
 92,829 
 
 7Q C77 
 
 40.OO 
 33- 2 4 
 
 f\A 2/1 
 
 o 1 o-47 
 201.60 
 
 167.53 
 
 2^6 08 
 
 4 i /-54 
 352.40 
 184.81 
 -jxig 18 
 
 10,812,609 
 3,085,559 
 51 T 2 A.Q "? 
 
 132 
 5 
 
 I 2Q 
 
 0.6 1 
 
 o-54 
 i 61 
 
 Hartford 
 
 / yo / / 
 
 27 180 
 
 **H*^ 
 
 6c 81 
 
 32Q 71 
 
 26 C QO 
 
 , j. j.^,q.y^ 
 
 2 Ad.7 OOO 
 
 ^y 
 
 4.8 
 
 T SO 
 
 Jersey City. . . 
 Louisville .... 
 Montreal, Can. 
 
 O/> i<JW 
 82,546 
 
 ^,753 
 117, coo 
 
 83.66 
 28.95 
 
 4.Q.OO 
 
 o^y-/ i 
 
 414.12 
 
 I 5 I -99 
 
 o^o-y 
 700.23 
 
 198.89 
 
 i ,^-'4-/5 l -"-' w 
 6,906,056 
 2,817,300 
 572O ^?o6 
 
 ^.J 
 
 70 
 
 58 
 
 06 
 
 J..^<- 
 0.85 
 
 o.5& 
 0.8 1 
 
 Newark 
 New Haven . . 
 New Orleans . 
 New York . . . 
 Philadelphia . 
 Salem 
 
 105,059 
 50,840 
 191,418 
 942,292 
 674,022 
 
 2A. 1 17 
 
 *Vy*** 
 
 2O.20 
 59.00 
 30.19 
 9O.20 
 
 55-n 
 
 4.1 4.6 
 
 98.17 
 286.15 
 147-63 
 457.31 
 290.98 
 
 147.86 
 
 370-52 
 171.78 
 
 i,327-74 
 33L2I 
 
 2,121,842 
 
 3,000,000 
 
 5,779,317 
 
 85,000,000 
 
 37^45,385 
 
 I OOO OOO 
 
 52 
 
 53 
 
 5 
 346 
 488 
 
 -2C. 
 
 0.50 
 1.04 
 0.30 
 
 o-37 
 0.71 
 i 04. 
 
 St. Louis 
 Washington . . 
 Worcester. . . . 
 
 310,864 
 109,199 
 41,105 
 
 35.38 
 I27.0O 
 48.65 
 
 185.04 
 650.24 
 230.60 
 
 277.38 
 709.93 
 406.23 
 
 11,000,000 
 
 13,868,273 
 
 2,000,000 
 
 OO 
 
 I0 5 
 1 02 
 
 45 
 
 0.34 
 o-93 
 1.09 
 
 /. 
 
 The average quantity of water supplied to some of the 
 same cities in 1874 is indicated in the following table, show- 
 ing also the extensions of the pipe systems, and the increase 
 in the average daily consumption of water per capita, from 
 year to year : 
 
INCREASE IN VARIOUS CITIES. 
 
 TAB LE No. 3. 
 WATER SUPPLIED IN YEARS 1870 AND 1874. 
 
 CITIES. 
 
 AVERAGE 
 DAILY SUPPLY 
 PER CAPITA. 
 
 TOTAL AVERAGE DAILY SUPPLY. 
 
 TOTAL 
 MILES OF PIPES. 
 
 1870. 
 
 I874 . 
 
 i8 7 a 
 
 i8 74 . 
 
 1870. 
 
 1874. 
 
 Boston 
 
 60 
 
 47 
 58 
 44 
 44 
 64 
 40 
 32 
 64 
 84 
 29 
 20 
 
 55 
 41 
 127 
 
 49 
 49 
 
 60 
 
 f 
 60 
 
 54 
 62 
 
 84 
 45 
 45 
 87 
 86 
 24 
 38 
 58 
 55 
 138 
 80 
 66 
 
 15,070,400 
 18,682,219 
 6,838,303 
 1,739,869 
 1,243,380 
 18,633,000 
 10,812,609 
 3,085,559 
 
 5, II2 ,493 
 6,906,056 
 2,817,300 
 2,121,842 
 
 37^45,385 
 1,000,000 
 13,868,273 
 2,000,000 
 5,720,306 
 
 18,000,000 
 24,772,467 
 8,509,481 
 2,300,000 
 7,643,017 
 38,090,952 
 13,600,596 
 5,625,150 
 
 9, OI 3,35 
 10,421,001 
 
 3,598,730 
 4,73 2 ,7 l8 
 42,111,730 
 1,380,000 
 18,000,000 
 3,000,000 
 8,395,8io 
 
 194 
 258 
 I 6 
 
 60 
 
 25 
 240 
 I 3 2 
 
 5 
 129 
 
 70 
 58 
 52 
 488 
 
 35 
 
 102 
 
 45 
 96 
 
 262 
 
 323 
 87 
 
 76 
 132 
 386 
 
 156 
 81 
 177 
 in 
 9 1 
 
 112 
 625 
 40 
 141 
 
 63 
 
 114 
 
 Brooklyn 
 
 Buffalo 
 
 Cambridge. . 
 
 Charlestown . . . 
 Chicago . 
 Cincinnati 
 
 Cleveland 
 
 Detroit 
 jersey City ... 
 
 Louisville 
 
 Newark 
 
 Philadelphia . . . 
 Salem .... 
 
 Washington .... 
 Worcester 
 
 Montreal 
 
 
 14. The Use of Water Steadily Increasing. The 
 
 legitimate use of water is steadily being popularized, calling 
 for an increased average in the amount of household appa- 
 ratus, increased facilities for garden irrigation and jets 
 d'eau, increased street areas moistened in dusty seasons, 
 and increased appliances for its mechanical use ; from all 
 which follows increased waste of water. 
 
 15. Increase in Various Cities. The following table 
 is introduced to show the average daily supply in various 
 cities through a succession of years : 
 
40 
 
 QUANTITY OF WATER REQUIRED. 
 
 TABLE No. 4. 
 AVERAGE GALLONS WATER SUPPLIED TO EACH INHABITANT DAILY IN 
 
 YEAR. 
 
 | 
 
 Buffalo. 
 
 d 
 
 >> 
 
 Cleveland. 
 
 Cincinnati. 
 
 Chicago. 
 
 Detroit. 
 
 Jersey City. 
 
 Louisville. 
 
 Montreal. 
 
 Jsj 
 
 o 
 
 >H 
 
 te 
 
 4) 
 
 
 Philadelphia. 
 
 1 
 
 1856 
 
 i8c7 
 
 
 
 
 
 
 
 8 
 
 
 
 
 
 55 
 4.6 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1858 . . 
 
 
 
 
 8 
 
 
 22 
 
 16 
 
 71; 
 
 
 
 
 
 
 1859 
 1860 .... 
 1861 . 
 
 
 
 
 
 
 
 ii 
 
 14 
 16 
 
 
 
 OO 
 40 
 
 43 
 
 4."? 
 
 48 
 
 52 
 
 r-2 
 
 / D 
 
 77 
 
 
 
 
 
 
 
 
 
 
 1862 .... 
 
 
 
 17 
 
 IQ 
 
 ?Q 
 
 T-O 
 
 4.4. 
 
 JO 
 
 r8 
 
 
 14. 
 
 
 
 
 
 186* 
 
 
 
 A / 
 22 
 
 ^y 
 
 2 I 
 
 oy 
 
 AJ 
 
 D^ 
 
 r8 
 
 
 12 
 
 
 
 
 
 1864 
 i86c 
 
 
 
 
 
 26 
 2Q 
 
 22 
 22 
 
 
 
 TO 
 41 
 
 4.2 
 
 
 
 57 
 
 c c 
 
 77 
 
 14 
 
 17 
 
 
 
 62 
 
 
 
 
 
 1866 . . . 
 
 ee 
 
 
 *y 
 3? 
 
 22 
 
 
 4.-? 
 
 a 
 60 
 
 / / 
 
 A / 
 17 
 
 
 
 
 
 1867 
 1868 
 1869 
 1870 
 1871 
 
 Oo 
 
 59 
 62 
 62 
 60 
 
 4. 
 
 58 
 ci 
 
 oo 
 36 
 
 43 
 46 
 
 47 
 ^6 
 
 24 
 
 25 
 27 
 
 33 
 
 76 
 
 40 
 
 TO 
 
 5 
 f 
 
 62 
 
 63 
 
 73 
 
 64 
 6 7 
 
 61 
 
 64 
 
 7^ 
 
 84 
 
 A / 
 
 J 5 
 16 
 18 
 29 
 
 IQ 
 
 49 
 
 cc 
 
 62 
 
 68 
 84 
 90 
 
 8"; 
 
 4 6 
 
 5 1 
 5 1 
 
 55 
 cc 
 
 127 
 
 I^O 
 
 1872 . . 
 
 ce 
 
 61 
 
 so 
 
 4.O 
 
 60 
 
 75 
 
 8? 
 
 QQ 
 
 22 
 
 ce 
 
 88 
 
 CA 
 
 174. 
 
 i873 
 1874 
 
 DO 
 
 58 
 60 
 
 60 
 60 
 
 
 
 55 
 
 r8 
 
 43 
 
 A r 
 
 dC 
 
 / 
 
 75 
 
 81 
 
 90 
 
 87 
 
 86 
 
 22 
 24. 
 
 t 
 
 60 
 
 66 
 
 104 
 
 56 
 
 r8 
 
 138 
 
 T-?,8 
 
 *Y/*r' 
 
 
 
 
 
 TO 
 
 T-D 
 
 
 "/ 
 
 
 
 
 
 
 
 
 16. Relation of Supply per Capita to Total Pop- 
 ulation. In the larger cities there are generally the great- 
 est variety of purposes for which water is required, and 
 consequently a greater average daily consumption per cap- 
 ita. Exceptions to this general rule may be found in a few 
 suburban towns largely engaged in the growth of garden 
 truck, and plants, and shrubs for the urban markets, in 
 which there is a large demand for water for purposes of 
 irrigation. 
 
 In the New England towns and cities the average daily 
 consumption and waste of water according to population is 
 approximately as follows : 
 
MONTHLY AND HOURLY VARIATIONS. 41 
 
 Places of 10,000 population, 35 to 45 gallons per capita. 
 " " 20,000 " 40 to 50 " 
 
 " " 30,000 " 45 to 65 " 
 
 " " 50,000 " 55 to 75 
 
 Places of 75,000 population and upward, 60 to 100 gal- 
 lons per capita. 
 
 1 7. Monthly and Hourly Variations in the Draught. 
 The data heretofore given relating to the daily average 
 consumption of water have referred to annual quantities 
 reduced to their daily average. The daily draught is not, 
 however, uniform throughout the year, but at times is 
 greatly in excess of the average for the year, and at other 
 times falls below. 
 
 It may be twenty to thirty per cent, in excess during 
 several consecutive weeks, fifty per cent, during several 
 consecutive days, and not infrequently one hundred per 
 cent, in excess during several consecutive hours, independ- 
 ently of the occasional heavy drafts for fires. Diagrams of 
 this daily consumption of water in the cities usually show 
 two principal maxima and two principal minima. The 
 earliest maximum in the year occurs, in the Eastern and 
 Middle States, about the time the frost is deepest in the 
 ground and the weather is coldest, that is, between the 
 middle of January and the first of March, and in New 
 England cities this period sometimes gives the maximum of 
 the year. The second maximum occurs usually during the 
 hottest and dryest portion of the year, or between the mid- 
 dle of July and the first of September. The two principal 
 minima occur in the spring and autumn, about midway 
 between the maxima. Between these four periods the pro- 
 file shows irregular wavy lines, and a profile diagram 
 continued for a series of years shows a very jagged line. 
 
 To illustrate the irregular consumption of water, we 
 
FIG. 1. 
 
 Chicago. 
 
 Brooklyn. 
 
 Cincinnati. Montreal 
 
 -uiaip lad suo^S uoiitiui jo 'o NJ 
 
RATIO OF MONTHLY CONSUMPTION. 43 
 
 
 
 have prepared the diagrams, Fig. 1, of the operations of the 
 pumps at Chicago, Brooklyn, Cincinnati, and Montreal, 
 during the years 1871, 1872, 1873, and 1874. 
 
 18. Ratio of Monthly Consumption. The varia- 
 tions in draught, as by monthly classification, in several 
 prominent cities, in the year 1874, have been reduced to 
 ratios of mean monthly draughts for convenience of compar- 
 ison, and are here presented ; unity representing the mean 
 monthly draught for the year : 
 
 TABLE No. 5. 
 RATIOS OF MONTHLY CONSUMPTION OF WATER IN 1874. 
 
 CITIES. 
 
 c 
 
 4J 
 
 6 
 fe 
 
 1 
 
 I 
 
 I 
 
 jj 
 
 >> 
 
 "3 
 i > 
 
 bi> 
 
 P 
 < 
 
 & 
 
 
 
 $ 
 
 > 
 
 o 
 % 
 
 1 
 
 Brooklyn. . . 
 
 1.029 
 
 I.I32 
 
 971 
 
 .892 
 
 .941 
 
 1.008 
 
 1.069 
 
 1.034 
 
 1.044 
 
 .987 
 
 .919 
 
 974 
 
 Buffalo. . . 
 
 1.008 
 
 I.OO7 
 
 .0.60 
 
 .941 
 
 983 
 
 9 6 3 
 
 996 
 
 1.020 ,1.044 
 
 I.OII 
 
 1.040 
 
 1. 000 
 
 Cleveland. . 
 
 .883 
 
 .901 
 
 .850 
 
 .871 
 
 .992 
 
 1.180 
 
 1.181 
 
 .206 
 
 1.058 
 
 I.OOI 
 
 .942 
 
 915 
 
 Detroit 
 
 .856 
 
 .80 7 
 
 90S 
 
 .844 
 
 1.029 
 
 1.065 
 
 1.051 
 
 .I6 7 
 
 1.171 
 
 1.115 
 
 .987 
 
 1.003 
 
 Philadelphia 
 
 .850 
 
 .844 
 
 834 
 
 .898 
 
 1.056 
 
 1,199 
 
 1.289 
 
 145 
 
 1.091 
 
 .990 
 
 952 
 
 .853 
 
 Chicago . . . 
 
 .862 
 
 .844 
 
 .904 
 
 .904 
 
 .942 
 
 .942 
 
 1.171 
 
 193 
 
 1.162 
 
 1.039 
 
 .966 
 
 1.029 
 
 Cincinnati.. 
 
 .792 
 
 .762 
 
 .778 
 
 .80 
 
 I.OII 
 
 1.217 
 
 1.207 
 
 .257 
 
 1.302 
 
 1.058 
 
 .960 
 
 799 
 
 Louisville. . 
 
 .842 
 
 .819 
 
 .848 
 
 .841 
 
 .960 
 
 1.192 
 
 1.207 
 
 .223 
 
 1.202 
 
 1.138 
 
 940 
 
 .876 
 
 Montreal. . . 
 
 .864 
 
 959 
 
 943 
 
 1.025 
 
 .916 
 
 .907 
 
 I.IOI 
 
 151 
 
 1.096 
 
 1.043 
 
 .971 
 
 1.023 
 
 Mean. . . 
 
 .887 
 
 .897 
 
 .888 
 
 .897 
 
 .960 
 
 1-075 
 
 1.144 
 
 I.I55 
 
 I.I30 
 
 1.042 
 
 .964 
 
 .941 
 
 There is also a very perceptible daily variation in each 
 week, and hourly variation in each day, in the domestic 
 consumption of water. 
 
 The Brooklyn diagram shows that the average draught 
 in the month of maximum consumption was in 1872, fifteen 
 per cent, in excess of the average annual draught ; in 1873, 
 seventeen per cent, in excess ; in 1874, thirteen per cent, in 
 excess. 
 
 A Boston Highlands direct pumping diagram lying "be- 
 fore the writer shows that the average draught at nine 
 o'clock in the forenoon was thirty-seven per cent, in excess 
 
44 
 
 QUANTITY OF WATER REQUIRED. 
 
 of the average draught for the three months, and that at 
 eight o'clock A.M. on the Mondays the draught was sixty 
 per cent, in excess of the average hourly draught for the 
 three months. 
 
 The maximum hourly draught indicated by the two 
 diagrams taken together is nearly seventy -five per cent, in 
 excess of the average throughout the year. 
 
 19. Illustrations of Varying Consumption. In 
 illustration, we will assume a case of a suburban town re- 
 quiring, say, an average daily consumption for the year of 
 1,000,000 United States gallons of water, and compute the 
 maximum rate of draught on the bases shown by the above- 
 named diagrams, thus: 
 
 
 GALLONS 
 PER DAY. 
 
 GALLONS 
 
 PER MlN. 
 
 CUBIC FEET 
 
 PER MlN. 
 
 Average draught per year 
 
 I OOO OOO 
 
 6o4 A. 
 
 02 8 
 
 Add 17 per cent, for max. monthly average 
 draught making 
 
 I,OI7,OOO 
 
 7O6 2 
 
 Q-7 I 
 
 Add to the last quantity 10 per cent, for the 
 max weekly average draught making. . 
 
 I O27 I7O 
 
 7iq 2 
 
 QC q 
 
 Add to the last quantity 37 per cent, for the 
 max hourly average draught making 
 
 I <1O7 222 
 
 Q72 2 
 
 I2O O 
 
 Add to the last quantity 23 per cent, for the 
 max. hourly av. draught on Mondays, making 
 
 1,730,883 
 
 1,202.0 
 
 i*yy 
 
 160.7 
 
 The experience of nearly every water-supply shows that 
 the maximum draught, aside from fire-service, is at times 
 more than double the average draught. 
 
 2O. Reserve for Fire Extinguishment. In addi- 
 tion to the above, there should be an ample reserve of water 
 for fire service, and extra conduit and distribution capacity 
 for its delivery. There is a possibility of two or three fires 
 being in progress at the same time, in even the smaller 
 cities, requiring at least twelve hydrant streams, or say 300 
 cubic feet of water per minute, for each fire. 
 
PUMPING STATION, MILWAUKEE. 
 
CHAPTER III. 
 
 RAINFALL. 
 
 21. The Vapory Elements. The elements of water 
 fill the ethereal blue above and the earth crust beneath. 
 They, with unceasing activity, permeate the air, the rocks, 
 the sand, the fruits we eat, and the muscles that aid our 
 motion. 
 
 Since first "there went up a mist from the earth," the 
 struggle between the ethereal elements and earth's internal 
 fire, between the intense cold of space and direct and 
 radiated heat enveloping the face of the earth, has gone 
 on unceasingly. 
 
 22. The Liquid and Gaseous Successions. If we 
 hold a drop of water in the clear sunshine and watch it 
 intently, soon it is gone and we could not see it depart ; if 
 we expose a dish of water to the heat of fire, silently it 
 disappears, and we know not how it gathered in its activity ; 
 if we leave a tank of water uncovered to the sun and wind, 
 it gradually disappears, and is replenished by many showers 
 of summer, still it departs and is replenished by snows of 
 winter. Under certain extreme conditions it may never be 
 full, it may never be exhausted, the rising vapor may equal 
 the falling liquid, as where " the rivers flow into the sea, yet 
 the sea is not full." 
 
 23. The Source of Showers. Physical laws whose 
 origin we cannot comprehend but whose steady effects we 
 observe, lift from the saline ocean, the fouled river, the moist 
 earth, a stream of vapor broad as the circuit of the globe, 
 
46 RAINFALL. 
 
 but their solid impurities remain, and the flow goes up with 
 ethereal clearness. 
 
 From hence are the sources of water supply replenished. 
 From hence comes the showers upon the face of the earth. 
 
 24. General Rainfall. But there is irregularity in 
 the physical features of the earth, and unevenness in the 
 temperature about it, and the showers are not called down 
 alike upon all its surface. Upon the temperate zone in 
 America enough water falls in the form of rain and snow 
 to cover the surface of the ground to an average depth of 
 about 40 inches, in the frigid zone a lesser quantity, and in 
 the torrid zone full 90 inches, and in certain localities to 
 depths of 100 and 150, and at times to even 200 inches. 
 
 We recognize in the rain an ultimate source of water 
 supply, but the immediate sources of local domestic water 
 supply are, shallow or deep wells, springs, lakes, and rivers. 
 The amplitude of their supply is dependent upon the avail- 
 able amount of the rainfall that replenishes them. In 
 cases of large rivers, and lakes like the American inland 
 seas, there can be no question as to their answering all 
 demands, as respects quantity, that can be made upon them, 
 but often upon watersheds of limited extent, margins of 
 doubt demand special investigations of their volumes of 
 rainfall, and the portions of them that can be utilized. 
 
 25. Review of Rainfall Statistics. Looking broadly 
 over some of the principal river valleys of the United States 
 we find their average annual rainfalls to be approxi- 
 mately as follows : Penobscot, 45 inches ; Merrimack, 43 ; 
 Connecticut, 44 ; Hudson, 39 ; Susquehanna, 37 ; Koanoke, 
 40; Savannah, 48; Appalachicola, 48; Mobile, 60; Mis- 
 sissippi, 46 ; Rio Grande, 19 ; Arizonian Colorado, 12 ; Sac- 
 ramento, 28 ; and Columbia, 33 inches ; but the amount 
 of rainfall at the various points from source to mouth of 
 
WESTERN RAIN SYSTEM. 47 
 
 river is by no means uniform ; as, for instance, upon 
 the Susquehanna it ranges from 26 to 44 inches ; on the 
 Eio Grande, from 8 to 37 inches ; and on the Columbia, 
 from 12 to 86 inches. 
 
 26. Climatic Effects. The North American Continent 
 presents, in consequence of its varied features and reach 
 from near extreme torrid to extreme polar regions, almost 
 all the special rainfall characteristics to be found upon the 
 face of the globe ; and even the United States of America 
 includes within its limits the most varied classes of climato- 
 logical and meteorological effects, in consequence of its range 
 of elevation, from the Florida Keys to the Rocky Mountain 
 summits, and its range of humidity from the sage-bush 
 plains between the Sierras and Wahsatch Mountains, and 
 the moist atmosphere of the lower Mississippi valley, and 
 from the rainless Yuma and Gila deserts of southern Cali- 
 fornia to the rainy slopes of north-western California and of 
 Oregon, where almost daily showers maintain eternal verdure. 
 
 27. Sections of Maximum Rainfall. The maxi- 
 mum recorded rainfall, an annual mean of 86 inches, occurs 
 in the region bordering upon the mouth of the Columbia 
 River and Puget Sound. A narrow belt of excessive hu- 
 midity extends along the Pacific coast from Vancouver's 
 Island southerly past the borders of Washington Territory, 
 Oregon and California, to latitude 40. 
 
 Next in order of humidity is the region bordering upon 
 the Delta of the Mississippi River and the embouchure of 
 the Mobile, whose annual mean of rain reaches 64 inches. 
 
 Next in order is a section in the heart of Florida of 
 about one-half the breadth of the State, whose mean annual 
 rain reaches 60 inches. 
 
 28. Western Rain System. The great northerly 
 ocean current of the Pacific moves up past the coast of 
 
RAINFALL. 
 
 China and the Aleutian Islands and impinges upon the 
 North American shore, then sweeps down along the coast 
 of Washington Territory, Oregon and California ; and from 
 its saturated atmosphere, flowing up their bold western 
 slopes, is drawn the excessive aqueous precipitations that 
 water these regions. 
 
 Their moist winds temper the climate and their condensed 
 vapors irrigate the land, so that the southerly portion of the 
 favored region referred to is often termed the garden of 
 America. 
 
 Fig. 2 is a profile, showing a general contour across the 
 Worth American Continent, along the thirty-ninth parallel 
 of latitude. 
 
 FIG. 2. 
 
 A. Pacific Ocean. 
 
 B. Coast Ran'ge. 
 
 C. Sierra Nevada. 
 
 D. Wahsatch Mountains. 
 
 E. Rocky Mountains. 
 
 F. Mississippi River. 
 
 G. Alleghany Mountains. 
 H. Blue Ridge. 
 
 I. Atlantic Ocean. 
 
 ELEVATION. 
 feet. 
 
 a. Sacramento City 82 
 
 b. Carson City 4,629 
 
 c. Salt Lake Region 4,382 
 
 d. Colorado River 
 
 e. Colorado City 6,000 
 
 f. St. Louis 481 
 
 g. Cincinnati 582 
 
 h. Washington 70 
 
 The California coast range and the western slope of the 
 Sierra Nevadas are the condensers that gather from the 
 prevailing westerly ocean breezes their moisture. From 
 thence the winds pass easterly over the Sierra summit 
 almost entirely deprived of moisture, and yield but rarely 
 any rain upon the broad interior basin stretching between 
 the bases of the Sierra and Wahsatch Mountains. Upon the 
 
CENTRAL RAIN SYSTEM. 49 
 
 arid plains of this region, above the Gulf of California, 
 whose average annual rainfall reaches scarce 4 inches, the 
 winds roll down like a thirsty sponge. 
 
 Further to the east, the western slopes of the Wahsatch 
 and Eocky Mountains lift up and condense again the west- 
 ern winds, and gather in their storms of rain and snow. 
 In the lesser valley "between these mountains, 12 to 20 
 inches of rain falls annually, and the tributaries of the 
 Colorado Eiver gathers its scanty surplus of waters and 
 leads them from thence around the southerly end of the 
 Wahsatch Mountains past the Yuma Desert to the Gulf. 
 
 Over the summit of the Eocky Mountains onward moves 
 the westerly wind, again deprived of its vapor, and down it 
 rolls with thirsty swoop upon the Great American Desert, 
 skirting the eastern base of the mountains. Farther on, it 
 is again charged with moisture by the saturated wind-eddy 
 from the Caribbean Sea and Gulf of Mexico. 
 
 The great Pacific currents of water and wind, and the 
 extended ridges and furrows of the westerly half of our 
 Continent lend their combined influence, in a marked man- 
 ner, to develop its special local and its peculiar general 
 climatic and meteorological systems. 
 
 29. Central Rain System. A second system of anti- 
 trade winds bears the saturated atmosphere of the Gulf of 
 Mexico up along the great plain of the Mississippi. Its 
 moisture is precipitated in greatest abundance about the 
 delta, and more sparingly in the more elevated valleys of 
 the Eed and Arkansas rivers upon the left, and the Tennes- 
 see and Ohio rivers upon the right. Its influence is per- 
 ceptible along the plain from the Gulf to the southern bor- 
 der of Lake Michigan, and easterly along the lower lakes 
 and across New England, where the chills of the Arctic 
 polar current sweeping through the Gulf of St. Lawrence 
 4 
 
50 RAINFALL. 
 
 and down the Nova Scotia coast into Massachusetts Bay, 
 throws down abundantly its remaining moisture. 
 
 30. Eastern Coast System. A third system en- 
 velops Florida, Georgia, and the eastern Carolinas, espe- 
 cially in summer, with an abundance of rain. 
 
 A fourth subordinate system shows the contending 
 thermic and electric influences of the warm and moist 
 atmosphere from the Gulf Stream, flowing northerly past, 
 and of the cooler atmosphere from the polar current flowing 
 southerly upon the New England coast, where an abundant 
 rain is distributed more evenly throughout the seasons than 
 elsewhere upon the Continent. 
 
 31. Influence of Elevation upon Precipitation. 
 
 The influence of elevation above the sea-le/el is far less 
 active in producing excessive rain uponao 
 
 ranges and high river sources than upon other continents 
 and some of the mountainous islands, being quite subordi- 
 nate to general wind currents. 
 
 Upon the mountainous island of Guadaloupe, in latitude 
 16, for instance, a rainfall of 292 inches per annum at an 
 elevation of 4500 feet is recorded. 
 
 Upon the Western Ghauts of Bombay, at an elevation 
 of 4,500 feet, an average rainfall for fifteen years is given as 
 254 inches. 
 
 On the southerly slope of the Himalayas, northerly of 
 the Bay of Bengal, at an elevation of 4,500 feet, the rainfall 
 of 1851 was 610 inches. These localities all face prevailing 
 saturated wind currents. 
 
 32. River-basin Rains. A study of some of our 
 principal river valleys independently, reveals the fact that 
 their rainfall gradually decreases from their outlets to their 
 more elevated sources. 
 
RIVER-BASIN RAINS. 
 
 51 
 
 In illustration of this fact, we present the following river- 
 valley statistics relating to the principal basins along the 
 Atlantic, Gulf, and Pacific coasts. 
 
 TABLE No. 6. 
 
 MEAN RAINFALL ALONG RIVER COURSES, SHOWING THE DECREASE 
 IN PRECIPITATION OF RAIN AND MELTED SNOW FROM THE 
 RIVER MOUTHS, UPWARD. 
 
 ST. JOHN'S RIVER. 
 
 NAME OF STATION. 
 
 SUMMER. 
 
 WINTER. 
 
 YEAR. 
 
 DISTANCE FROM MOUTH. 
 
 
 St. Johns 
 
 Inches. 
 IO 
 
 Inches. 
 14 
 
 Inches. 
 ci 
 
 Miles (approximate). 
 c ) Distances from 
 
 Average ra.in 
 
 Fort Kent.. 
 
 12 
 
 10 
 
 16 
 
 * the Atlantic 
 
 A.I inches. 
 
 MERRIMACK RIVER. 
 
 Newburyport . 
 
 Lawrence 
 
 Manchester . , 
 Concord . . 
 
 12 
 
 19 
 II 
 II* 
 
 12 
 II 
 II 
 
 9 
 
 41 
 45 
 45 
 41 
 
 25 I ^/^P* Average rain, 
 43 inches. 
 
 CONNECTICUT RIVER. 
 
 
 i-i 
 
 iq 
 
 4Q 
 
 4~) 
 
 Middletown. ...... 
 
 ii 
 
 12 
 
 46 
 
 oe 
 
 Hartford 
 
 IO 
 
 II 
 
 44 
 
 4O 
 
 Hanover 
 
 i i 
 
 
 4O 
 
 1 80 
 
 
 II 
 
 8 
 
 16 
 
 21* 
 
 Sound. 
 
 44 inches. 
 
 HUDSON RIVER. 
 
 New York City 
 
 Poughkeepsie 
 
 Hudson 
 
 Albany 
 
 12 
 12 
 10 
 
 9 
 
 10 
 9 
 
 8 
 
 44 
 40 
 
 35 
 36 
 
 81 
 
 re Distances from 
 _' J > the Atlantic 
 "5 I Ocean. 
 145 J 
 
 Average rain, 
 39 inches. 
 
 SUSQUEHANNA RIVER. 
 
 Havre de Grace .... 
 Harrisburg 
 
 13 
 
 12 
 
 10 
 
 g 
 
 44 
 
 AQ 
 
 5 
 
 7O 
 
 Lewi sb u rg 
 
 II 
 
 8 
 
 e vy 
 
 7Q 
 
 
 William sport 
 
 IO 
 
 7 
 
 1Q 
 
 I4O 
 
 Owego 
 
 8 
 
 6 
 
 24. 
 
 2OO 
 
 Elmira. . 
 
 7 
 
 4 
 
 26 
 
 200 
 
 ram, 
 37 inches. 
 
RAINFALL. 
 
 MEAN RAINFALL ALONG RIVER COURSES (Continued). 
 MISSISSIPPI RIVER. 
 
 NAME OF STATION. 
 
 SUMMER. 
 
 WINTER. 
 
 YEAR. 
 
 DISTANCE FROM MOUTH. 
 
 
 Delta 
 
 Inches. 
 
 20 
 20 
 
 18 
 
 14 
 
 II 
 8 
 ii 
 13 
 14 
 ii 
 ii 
 
 Inches. 
 
 18 
 16 
 
 15 
 16 
 
 15 
 15 
 
 12 
 
 8 
 5 
 3 
 T 
 
 Inches. 
 
 60 
 60 
 60 
 56 
 
 55 
 42 
 42 
 42 
 38 
 30 
 
 25 
 
 Miles 
 IO^ 
 
 95 
 190 
 240 
 
 350 
 560 
 700 
 850 
 
 1 100 
 1200 
 IW> 
 
 approximate). 
 
 Distances from 
 - the Gulf of 
 Mexico. 
 
 Average rain, 
 46 inches. 
 
 
 Baton Rouge 
 
 June, of Red River . . 
 Vicksburg 
 
 Memphis 
 
 Cairo 
 
 St Louis 
 
 Dubuque 
 
 Lacrosse 
 
 St. Paul's . . 
 
 Brownsville 
 
 June. Peeos River 
 
 El Paso 
 
 Albuquerque 
 
 Astoria 
 
 Walla-Walla 
 Boise City . . 
 Fort Hall .... 
 
 RIO GRANDE. 
 
 37 
 18 
 
 12 
 
 3 
 
 Distances from 
 
 Mexico. 
 
 Average rain, 
 19 inches. 
 
 COLUMBIA RIVER. 
 
 86 
 
 44 
 
 5 
 
 6 
 
 20 
 
 13 
 12 
 
 275 I Distances from Average rain, 
 600 
 
 Pacific Ocean. 
 
 33 inches. 
 
 Reference to the above, from among the principal river 
 valleys, is sufficient to show that the oft-made statement, 
 that "rain falls most abundantly on the high land," is 
 applicable, in the United States, to subordinate watersheds 
 only, and in rare instances. 
 
 33. Grouped Rainfall Statistics. The following 
 table gives the minimum, maximum, and mean rainfalls, 
 according to the most extended series of observations, at 
 various stations in the United States. They are grouped by 
 territorial divisions, having uniformity of meteorological 
 characteristics. 
 
RAINFALL IN THE UNITED STATES. 
 
 TABLE No. 7. 
 RAINFALL IN THE UNITED STATES. 
 
 (Front Records to 1866 inclusive.) 
 GROUP 1. Atlantic Sea-coast from Portland to Washington. 
 
 STATION. 
 
 LAT. 
 
 LONG. 
 
 HEIGHT 
 
 ABOVE 
 
 SEA. 
 
 YEARS 
 
 OF 
 
 RECORD 
 
 MlN. 
 
 ANNUAL 
 RAIN. 
 
 MAX. 
 
 ANNUAL 
 RAIN. 
 
 MEAN 
 ANNUAL 
 RAIN. 
 
 Oardiner Me. 
 
 44.lo' 
 
 6O4</ 
 
 76 
 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 
 
 *A 
 
 
 
 26 38 
 
 5i-47 
 
 i!'S 
 
 Worcester, Mass 
 Cambridge " 
 
 43 54 
 42 ID 
 
 7i 49 
 
 52 7 8 
 
 26 
 
 34.60 
 
 75-64 
 61.83 
 
 44.00 
 46.92 
 
 Boston " 
 
 
 
 
 11 
 
 
 
 46-39 
 
 New Bedford " .... 
 
 
 
 
 
 ao 68 
 
 CO T , 
 
 44-99 
 
 
 
 
 
 
 
 
 41.42 
 
 Flatbush, N. Y 
 Fort Hamilton, " 
 Fort Columbus, " 
 
 40 37 
 40 36 
 
 74 02 
 74 02 
 
 54 
 25 
 
 36 
 
 19 
 
 32.14 
 
 2 9'75 
 
 54-17 
 58.92 
 
 41-54 
 43-52 
 42-55 
 
 New York City, " 
 West Point, " 
 
 40 43 
 
 74 oo 
 
 1 
 
 l67 
 
 31 
 2O 
 
 34-79 
 
 62.87 
 
 6l -fl 
 
 43-24 
 43.00 
 
 Newark N. J. 
 
 
 
 
 
 
 
 47.65 
 
 Lambertville, " 
 
 
 
 tf 
 
 23 
 
 
 
 44-5 
 
 Philadelphia, Peon 
 Baltimore Md 
 
 39 57 
 
 75 ii 
 
 60 
 
 s 
 
 29-57 
 
 57-37 
 62.94 
 
 43-99 
 44-05 
 
 Fort McHenry, " 
 
 
 
 16 
 
 
 
 
 42-33 
 
 Washington, D. C 
 
 og C4. 
 
 
 
 28 
 
 
 
 
 
 
 
 
 
 
 
 37-S 2 
 43-44 
 
 GROUP 2. Atlantic Sea-coast, Virginia to Florida. 
 
 Fortress Monroe, Va. 
 
 oo / 
 
 76i8' 
 
 3 
 
 Charleston, S. C 
 
 32 47 
 
 
 
 Fort Moultrie, " 
 
 32 46 
 
 7Q CT 
 
 oe 
 
 Savannah Ga 
 
 
 8? 05 
 
 J 
 
 Fort Brooke, Fla 
 
 28 oo 
 
 82 28 
 
 42 
 2O 
 
 
 
 
 
 23 
 
 19. 
 
 35-93 
 
 47-04 
 
 53-63 
 47.63 
 
 GROUP 3. Hudson River Valley, Vermont, Northern and Western 
 
 New York. 
 
 Newburgh, N. Y 
 Poughkeepsie, " 
 Kingston, " 
 Hudson, " 
 Kinderhook, " 
 Albany, " 
 Watervliet Arsenal, " . ... 
 Lansingburg, " 
 Granville, " 
 Hanover, N. H 
 
 4i3i / 
 4i 4 1 
 4i 55 
 42 13 
 
 42 22 
 
 42 39 
 42 43 
 42 47 
 43 20 
 
 745 / 
 73 55 
 74 02 
 73 46 
 73 43 
 73 44 
 73 43 
 73 4 
 73 17 
 
 150 
 
 "188 
 150 
 125 
 130 
 50 
 30 
 250 
 
 20 
 IS 
 19 
 15 
 
 11 
 
 17 
 2O 
 
 15 
 
 25.04 
 
 31.92 
 27.50 
 
 55-63 
 
 50-97 
 44-93 
 
 cc'oS 
 
 36.61 
 40.36 
 
 35-iQ 
 34-52 
 36.48 
 40.52 
 34.65 
 33-31 
 3i-52 
 
 Burlington, Vt .... 
 
 
 
 530 
 
 
 
 
 
 Fairfield N Y 
 
 
 
 ii8e 
 
 
 
 
 34- J 5 
 
 Clinton, " 
 
 
 
 
 
 . . . . 
 
 ***** 
 
 
 Utica " 
 
 
 
 
 22 
 
 
 
 c6 60 
 
 
 Lowville " 
 
 
 
 473 
 
 
 
 
 
 Gouverneur, " 
 
 
 
 
 22 
 
 
 
 
 Potsdam " 
 
 
 
 
 
 
 
 28 63 
 
 Cazenovia, " .... 
 
 
 
 394 
 
 20 
 
 ***** 
 
 ***** 
 
 
 Oxford, " 
 
 
 
 06 1 
 
 
 * 
 
 
 06 36 
 
 Pompey, " 
 
 
 75 3 2 
 
 
 16 
 
 
 45.08 
 
 
 Auburn " 
 
 
 76 28 
 
 * 
 
 
 
 
 
 Ithaca, " 
 
 
 
 
 
 
 
 34.71 
 
 
 
 
 
 
 f 
 
 
 
 Penn Yan " ... 
 
 
 
 
 
 IQ 66 
 
 
 28.42 
 
 Rochester, " . 
 
 43 08 
 
 
 5i6 
 
 
 24.97 
 
 43*03 
 
 32.56 
 
 Middlebury, " .... 
 
 
 78 10 
 
 800 
 
 
 
 
 30.44 
 
 Fredonia, " 
 
 
 
 
 16 
 
 
 
 36.55 
 
 
 
 
 
 
 
 
 34-99 
 
RAINFALL. 
 
 RAINFALL IN THE UNITED STATES (Continued). 
 
 GROUP 4. Upper Mississippi, part of Iowa, Minnesota, and 
 Wisconsin. 
 
 STATION. 
 
 LAT. 
 
 LONG. 
 
 HEIGHT 
 
 ABOVE 
 
 SEA. 
 
 YEARS 
 
 OF 
 
 RECORD 
 
 MlN. 
 
 ANNUAL 
 RAIN. 
 
 MAX, 
 
 ANNUAL 
 RAIN. 
 
 MHAN 
 ANNUAL 
 RAIN. 
 
 Fort Ripley , Minn 
 
 46IQ / 
 
 04 I Q' 
 
 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 Fort Snelling, " .... 
 
 
 
 820 
 
 
 
 
 
 Dubuque, Iowa 
 
 42 9.O 
 
 
 666 
 
 
 
 
 
 Milwaukee, Wis 
 
 
 8? 
 
 
 
 
 AA 86 
 
 
 
 41 20 
 
 9 1 5 
 
 sse 
 
 IQ 
 
 2* 
 
 27.66 
 
 
 42.88 
 
 Fort Madison, " 
 
 
 
 600 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 33.27 
 
 GROUP 8. Ohio River Valley, "Western Pennsylvania to Eastern 
 
 Missouri. 
 
 Marietta, 
 Cincinnati, 
 Portsmouth, 
 Athens, 111. 
 St. Louis Ar; 
 St. Louis, 
 
 irsenal, Penn 
 , Ohio 
 
 4o32' 
 4 2 5 
 
 8o02 / 
 
 80 41 
 
 704 
 070 
 
 23 
 
 37 
 
 25.62 
 28.02 
 
 47-79 
 57.28 
 
 35-23 
 41.48 
 
 
 39 2"? 
 
 wv ^ 
 
 8l 2Q 
 
 580 
 
 48 
 
 32.46 
 
 53.54 
 
 42.70 
 
 u 
 
 oy *y 
 39 06 
 
 u ~y 
 
 84 2 1 ? 
 
 givv 
 582 
 
 QI 
 
 2 "5. 49 
 
 65.18 
 
 44.87 
 
 <( 
 
 38 42 
 
 04 ^3 
 
 82 
 
 468 
 
 le 
 
 *0'*ry 
 
 25.50 
 
 56.79 
 
 *rr*'-'/ 
 
 38.33 
 
 
 OQ CO 
 
 80 56 
 
 5 
 800 
 
 16 
 
 2"5.I2 
 
 48.17 
 
 39.62 
 
 senal, Mo 
 
 jy o* 
 38 40 
 08 -17 
 
 oy ^v 
 
 90 10 
 oo 16 
 
 450 
 481 
 
 19 
 
 28 
 
 3M 
 
 24.08 
 27.OO 
 
 7 I -54 
 68.83 
 
 < 
 42.63 
 
 42.18 
 
 tracks, " 
 
 O J/ 
 
 38 28 
 
 y\j AU 
 
 oo 15 
 
 472 
 
 21 
 
 *./.\^s 
 29.18 
 
 55.13 
 
 40.88 
 
 
 o w 
 
 yv- J-^ 
 
 
 
 
 
 
 
 
 
 
 
 
 
 40.88 
 
 GROUP 6. Indian Territory and Western Arkansas. 
 95 3' 56o 
 
 Fort Gibson, Ind. Ten. 
 
 Fort Smith. Ark 
 
 Fort Washita, Ind. Ter. 
 
 3S48' 
 35 23 
 34 14 
 
 18.84 
 24-34 
 
 21.81 
 
 55-82 
 
 61.03 
 64.29 
 
 36.37 
 40.36 
 38.04 
 
 GROUP 7. Lower Mississippi and Red Rivers; part of Kentucky. 
 
 Springdale, Ken. 
 
 o807 / 
 
 85 24' 
 
 570 
 
 24 
 
 30.91 
 
 67.10 
 
 48.58 
 
 Washington Ark 
 
 O w ^/ 
 00 A A 
 
 QO HI 
 
 660 
 
 22 
 
 41.40 
 
 70.40 
 
 54.50 
 
 Vicksburg, Miss. . 
 
 JO T-T- 
 32 2^ 
 
 yj ^^ 
 90 56 
 
 350 
 
 16 
 
 37.21 
 
 60.28 
 
 49.30 
 
 Natchez " 
 
 OT 1A 
 
 91 25 
 
 ^9 
 264 
 
 18 
 
 31.09 
 
 78.73 
 
 53-55 
 
 
 O A JT 1 
 
 y A ^D 
 
 
 
 
 
 
 
 
 
 
 
 
 
 51.48 
 
 GROUP 8. Mississippi Delta, and Coast of Mississippi and Alabama. 
 
 New Orleans, La 
 
 Mt. Vernon Arsenal, Ala 
 
 Baton Rouge, La 
 
 295/ 
 
 3 I 12 
 
 30 26 
 
 9002' 
 
 88 02 
 91 18 
 
 41.92 
 51-49 
 4L34 
 
 67.12 
 106.57 
 116.40 
 
 51.05 
 66.14 
 60. 16 
 
 59.12 
 
 GROUP 9. Pacific Coast, Bay of San Francisco to Alaska. 
 
 San Francisco, Cal 
 
 3748 / 
 
 I2226' 
 
 170 
 
 18 
 
 ".73 
 
 36.03 
 
 21.69 
 
 Sacramento, " - 
 Fort Vancouver, W. Ter 
 
 38 35 
 45 4 
 
 121 28 
 122 30 
 
 82 
 50 
 
 18 
 16 
 
 11.15 
 25.91 
 
 27.44 
 56.09 
 
 19.56 
 38.84 
 
 Fort Steilacoom, " 
 
 47 I0 
 
 122 25 
 
 300 
 
 16 
 
 25-75 
 
 70.21 
 
 43-98 
 
 Sitka, Alaska 
 
 57 3 
 
 135 18 
 
 20 
 
 16 
 
 58.68 
 
 95.81 
 
 83-39 
 
 
 
 
 
 
 
 
 41.49 
 
No. 2. 
 
 No. 1. 
 
 
 C-g 
 
 s 
 
 il, 
 
 J J A 80 N D J 
 
 .70 
 
 CURVES OF ANNUAL FLUCTUATIONS IN RAINFALL. 
 
56 RAINFALL. 
 
 34. Monthly Fluctuations in Rainfall. Our gener- 
 alizations thus far have referred to the mean annual rainfall 
 over large sections. There is a large range of fluctuation in 
 the average amount of precipitation through the different 
 seasons of the year, in different sections of the United 
 States. It will be of interest to follow out this phase of the 
 question in diagrams 3 and 4, in which type curves * of 
 monthly means are drawn albout a line of annual mean 
 covering a series of years, in no case less than fifteen. 
 
 The letters J, F, M, &c., at the heads of the diagrams, 
 are the initials of the months. The heavy horizontal lines 
 represent means for the year, which are taken as unity. 
 Their true values may be found at the foot of their respect- 
 ive groups in the above table. About this line of annual 
 mean is drawn by free-hand the type curve of mean rain- 
 fall through the successive months, showing for each month 
 its percentage of the annual mean. 
 
 Each type curve relates to a section of country having 
 uniform characteristics in its annual distribution of rain. 
 
 Curve No. 1, for Group No. 1, includes the section of 
 country bordering upon the Atlantic sea-coast from Port- 
 land to Washington. The average fluctuation of the year 
 in this section is forty per cent. Its maximum rainfall 
 occurs oftenest in August, and its minimum oftenest in 
 January or February. 
 
 Curve No. #, for Group No. 2, includes the Atlantic 
 coast border from Virginia to Florida. The average fluc- 
 tuation of the year is one hundred and ninety-eight per 
 cent. Its maximum rainfall occurs oftenest about the first 
 of August, and nearly equal minima in April and October. 
 
 * Reduced from a diagram by Chas. Schott, C. E. , Smithsonian Contribu- 
 tion, Vol. XVIII, p. 16. The tables of American rainfall arranged by Mr. 
 Schott, and published in the same volume, are exceedingly valuable. 
 
J F 
 
 N D J 
 
 V A M J J A SO 
 
 CURVES OF ANNUAL FLUCTUATIONS IN RAINFALL, 
 
68 RAINFALL. 
 
 Curve No. 3, for Group No. 3, includes the upper Hud- 
 son River valley, and northern and western New York. 
 The average fluctuation of the year is sixty-six per cent. 
 Its maximum rainfall occurs oftenest near the first of July 
 and its minimum oftenest about the first of February. 
 
 Curve No. h for Group No. 4, includes a part of Iowa, 
 central Minnesota, and part of Wisconsin, in the upper 
 Mississippi valley. The average fluctuation of the year is 
 one hundred and nine per cent. Its maximum rainfall 
 occurs oftenest in the latter part of June and its minimum 
 oftenest about the first of February. 
 
 Curve No. 5, for Group No. 5, includes the Ohio River 
 valley, from western Pennsylvania to eastern Missouri. 
 The average fluctuation of the year, is seventy -three per 
 cent. Its maximum rainfall occurs oftenest about the first 
 of June and its minimum oftenest in the latter part of 
 January. 
 
 Curve No. 6, for Group No. 6, includes the Indian Ter- 
 ritory and Western Arkansas. The average fluctuation of 
 the year is ninety-one per cent. Its maximum rainfall 
 occurs oftenest about the first of May and its minimum 
 oftenest at the opening of the year. 
 
 Curve No. 8, for Group No. 8, includes the Mississippi 
 Delta and Gulf coast of Alabama and Mississippi. The 
 average fluctuation of the year is seventy -five per cent. Its 
 maximum rainfall occurs oftenest in the latter part of July 
 and its minimum oftenest early in October. 
 
 A similar type curve for Group No. 9, the region border- 
 ing upon the Pacific coast from the Bay of San Francisco 
 to Puget's Sound, would show an average annual fluctua- 
 tion through the seasons of two hundred and thirty-two 
 per cent. The fluctuations here have nothing in common 
 with the Mississippi and Atlantic types. The maximum 
 
FIG. 5. 
 
 ail 2 V 
 
 l> 
 
 1864 
 
 1860 
 
 1856 
 
 1852 
 
 1848 
 
 1844 
 
 1840 
 
 1832 
 
 1824 
 
 1820 
 
 1816 
 
 1812 
 
 
 ; 
 
 CURVES OF SECULAR FLUCTUATIONS IN RAINFALL. 
 
60 RAINFALL. 
 
 rainfall here occurs oftenest in December and the minimum 
 oftenest in July. 
 
 35. Secular Fluctuations in Rainfall. Diagram 5 
 
 illustrates the secular fluctuations in the rainfall through a 
 long series of years in the Atlantic system and in the central 
 Mississippi system. It presents the successions of wet and 
 dry periods as they vibrate back and forth about the mean 
 of the whole period. 
 
 The extreme fluctuation is in the first case twenty-eight 
 per cent., and in the second case thirty per cent. 
 
 36. Local, Physical, and Meteorological Influ- 
 ences. The above statistics give sufficient data for deter- 
 mining approximately the general average rainfall in any 
 one of the principal river-basins of the States. 
 
 There are local influences operating in most of the main 
 physical divisions, analogous to those governing rainfall in 
 the grand atmospheric systems. 
 
 Referring to any local watershed, and the detailed study 
 of such is oftenest that of a limited gathering ground tribu- 
 tary to some river, we have to note especially the mean 
 temperature and capacity of the atmosphere to bear vapor, 
 the source from which the chief saturation of the atmos- 
 phere is derived, the prevailing winds at the different sea- 
 sons, whether in harmony with or opposition to the direction 
 of this source, and if any high lands that will act as con- 
 densers of the moisture lie in its path and filch its vapors, 
 or if guiding ridges converge the summer showers in more 
 than due proportion in a favored valley. A careful study 
 of the local, physical, and meteorological influences will 
 usually indicate quite unmistakably if the mean rainfall of 
 a subordinate watershed is greater or less than that of the 
 main basin to which its streams are tributary. There is 
 rarely a sudden change of mean precipitation, except at the 
 
GREAT RAIN STORMS. 61 
 
 crest of an elevated ridge or the brink of a deep and narrow 
 ravine. 
 
 37. Uniform Effects of Natural Laws. When 
 studies of local rainfalls are confined to mean results, 
 neglecting the occasional wide departures from the influence 
 of the general controlling atmospheric laws, the actions of 
 nature seem precise and regular in their successions, and in 
 fact we find that the governing forces hold results with a 
 firm bearing close upon their appointed line. 
 
 But occasionally they break out from their accustomed 
 course as with a convulsive leap, and a storm rages as 
 though the windows of heaven had burst, and floods sweep 
 down the water-courses, almost irresistible in their fury. 
 If hydraulic constructions are not built as firm as the ever- 
 lasting hills, their ruins will on such occasions be borne 
 along on the flood toward the ocean. 
 
 38. Great Rain Storms. In October, 1869, a great 
 storm moved up along the Atlantic coast from Virginia to 
 New York, and passed through the heart of New England, 
 with disastrous effect along nearly its whole course. Its 
 rainfall at many points along its central path was from 
 eight to nine inches, and its duration in New England was 
 from forty to fifty-nine hours. 
 
 In August, 1874, a short, heavy storm passed over east- 
 ern Connecticut, when there fell at New London and at 
 Norwich twelve inches * of rain within forty-eight hours, 
 five inches of which fell in four hours. Such storms are 
 rare upon the Atlantic coast and in the Middle and West- 
 ern States. 
 
 Short storms of equal force, lasting one or^two hours, 
 are more common, and the flood effects from them, on hilly 
 
 * From data supplied by H. B. Winship, Supt. of Norwich Water-works. 
 
62 
 
 RAINFALL. 
 
 watersheds, not exceeding one or two square miles area, 
 may be equally disastrous, and waterspouts sometimes 
 burst in the valleys and flood their streams. 
 
 39. Maximum Ratios of Floods to Rainfalls. 
 When the surface of a small watershed is generally rocky, 
 or impervious, or, for instance, when the ground is frozen 
 and uncovered by snow, the maximum rate of volume of 
 flow through the outlet channel may reach two-thirds of the 
 average rate of volume of rain falling upon the gathering- 
 ground. 
 
 40. Volume of Water from given Rainfalls. The 
 rates of volume of water falling per minute, for the rates of 
 rainfall per twenty-four hours, indicated, are given in cubic 
 feet per minute, per acre and per square mile, in the follow- 
 ing table : 
 
 TABLE No, 8. 
 
 VOLUME OF RAINFALL PER MINUTE, FOR GIVEN INCHES PER TWENTY- 
 FOUR HOURS. 
 
 RAINFALL PER 
 24 HOURS. 
 
 VOLUME PER 
 MINUTE ON 
 ONE ACRE. 
 
 VOLUME PER 
 MINUTE ON 
 ONE SQ. MILE. 
 
 RAINFALL 
 
 PER 
 
 24 HOURS. 
 
 VOLUME PER 
 MINUTE ON 
 ONE ACRE. 
 
 VOLUME PER 
 MINUTE ON 
 ONE SQ. MILE. 
 
 Inches. 
 
 Cu.feet. 
 
 Cu.feet. 
 
 Inches. 
 
 Cu. feet. 
 
 Cu.feet. 
 
 O.I 
 
 .252 
 
 l6l.33 
 
 I 
 
 2.521 
 
 1613.33 
 
 .2 
 
 -54 
 
 322.67 
 
 2 
 
 5.042 
 
 3226.67 
 
 3 
 
 .756 
 
 484.01. 
 
 3 
 
 7-563 
 
 4840.00 
 
 -4 
 
 1.008 
 
 645-33 
 
 4 
 
 10.084 
 
 6453-33 
 
 5 
 
 1.264 
 
 806.67 
 
 
 12.605 
 
 8066.65 
 
 .6 
 
 I-5IS 
 
 968.00 
 
 6 
 
 15.126 
 
 9689.99 
 
 7 
 
 I-765 
 
 1122.73 
 
 7 
 
 17.647 
 
 II2 93-33 
 
 .8 
 
 2.IO7 
 
 1290.67 
 
 8 
 
 20.168 
 
 12906.66 
 
 9 
 
 2.269 
 
 I450.OO 
 
 9 
 
 22.689 
 
 14529.99 
 
 
 
 
 10 
 
 25.210 
 
 i6i33-33 
 
 41. Gauging Rainfall. A pluviometer, Fig. 6, is used 
 to measure the amount of rain that falls from the sky. It is 
 a deep, cylindrical, open-topped dish of brass. Its top 
 
GAUGING RAINFALL. 
 
 63 
 
 FIG. 6. 
 
 edge is thin, so it will receive just the rain due to the sec- 
 tional area of the open top. 
 
 A convenient size is of two inches diameter at a, and at 
 b of such diameter that its sectional 
 area is exactly one-tenth the sec- 
 tional area at #, or a little more 
 than one-half inch. 
 
 When extreme accuracy is re- 
 quired, the diameter at a is made 
 ten inches and at b a little more 
 than three inches, still maintaining 
 the ratio of sectional areas ten to 
 one, the displacement of the meas- 
 uring-rod being allowed for. 
 
 This rain-gauge should be set 
 vertically in a smooth, open, level 
 ground, and the grass around be 
 kept smoothly trimmed in summer. 
 The top of a ten-inch gauge is set 
 at about one foot above the surface 
 of the ground, and of smaller 
 gauges, clear of the grass surface. 
 
 The gauge should be placed sufficiently apart from 
 buildings, fences, trees, and shrubs, so that the volume of 
 rain gathered shall not be augmented or reduced by wind- 
 eddies. 
 
 If such a situation, secure from interference by animals 
 or by mischievous persons, is not obtainable, the gauge 
 may be set upon the flat roof of a building, and the height 
 above the ground noted. 
 
 The measuring-rod for taking the depth of rain in b is 
 graduated in inches and tenths of inches, so that when the 
 sections of a and b are ten to one, ten inches upon the rod 
 
64 RAINFALL. 
 
 corresponds with one inch of actual rainfall, and one inch 
 on the rod to one-tenth inch of rain, and one-tenth on the 
 rod to one-hundredth of rain. 
 
 Snow is caught in a cylindrical, vertical-sided dish, not 
 less than ten inches diameter, melted, and then measured as 
 rain. Memorandums of depths of snow "before melting, 
 with dates, are preserved also. 
 
 It has been observed at numerous places, that elevated 
 pluviometers indicated less rain than those placed in the 
 neighboring ground. When there is wind during a shower, 
 the path of the drops is parabolic, being much inclined in 
 the air above and nearly vertical at the surface of the 
 ground. A circular rain-gauge, held horizontally, presents 
 to inclined drops an elliptic section, and consequently less 
 effective area than to vertical drops. 
 
 The law due to height alone is not satisfactorily estab- 
 lished, though several formulae of correction have been 
 suggested, some of which were very evidently based upon 
 erroneous measures of rainfall. 
 
 The observed rainfall at Greenwich Observatory, Eng- 
 land, in the year 1855, is reported, at ground level, 23.8 
 inches depth ; at 22 feet higher, .807 of that quantity, and 
 at 50 feet higher, .42 of that quantity. 
 
 The observed rainfall at the Yorkshire Museum, Eng- 
 land, in the years 1832, 1833, and 1834, is reported, for 
 yearly average, at ground level, 21.477 inches ; at 44 feet 
 higher, .81 as much, and at 213 feet higher, .605 as much. 
 
 Unless vigilantly watched during storms, the gauges are 
 liable to overflow, when an accurate record becomes impos- 
 sible. Overflow cups are sometimes joined to rain-gauges, 
 near their tops, to catch the surplus water of great storms. 
 
OHAPTEE IT. 
 
 FLOW OF STREAMS. 
 
 42. Flood Volume Inversely as the Area of the 
 Basin. A rain, falling at the rate of one inch in twenty- 
 four hours, delivers upon each acre of drainage area about 
 2.5 cubic feet of water each minute. 
 
 If upon one square mile area, with frozen or impervious 
 surface, there falls twelve inches of rain in twenty-four 
 hours, and two-thirds of this amount flows off in an equal 
 length of time, then the average rate of flow will be 215 
 cubic feet per second. 
 
 Any artificial channel cut for a stream, or any dam 
 built across it, must have ample flood-way, overfall, or 
 waste-sluice to pass the flood at its maximum rate. 
 
 The rate of flood flow at the outlet of a watershed is 
 usually much less from a large main basin than from its 
 tributary basins, because the proportion of plains, storage 
 ponds, and pervious soils is usually greater in large basins 
 than in small, and the flood flow is consequently distrib- 
 uted through a longer time. 
 
 In a small tributary shed of steep slope the period of 
 maximum flood flow may follow close after the maximum 
 rainfall ; but in the main channel of the main basin the 
 maximum flood effect may not follow for one, two, three, or 
 more days, or until the storm upon its upper valley has 
 entirely ceased. 
 
 43. Formulae for Flood Volumes. The recorded flood 
 measurements of American streams are few in number, but 
 
 5 
 
66 FLOW OF STREAMS. 
 
 upon plotting such data as is obtained, we find their mean 
 curve to follow very closely that of the equation, 
 
 Q = 200 (M)*, (I) 
 
 in which M is the area of watershed in square miles and Q 
 the volume of discharge, in cubic feet per second, from the 
 whole area. 
 
 Thus the decrease of flood with increase of area is seen 
 to follow nearly the ratio of two hundred times the sixth 
 root of the fifth power of the area expressed in square 
 miles. 
 
 Among the Indian Professional Papers we find the fol- 
 lowing formula for volume, in cubic feet per second : 
 
 Q = cx27(M). (2) 
 
 in which c is a co-efficient, to which Colonel Dickens has 
 given a mean value of 8.25 for East Indian practice. 
 
 Testing this formula by our American curve, we find the 
 following values of c for given areas : 
 
 Area in sq. miles. . . 
 Value of c 
 
 i. 
 7.41 
 
 z. 
 9-33 
 
 3- 
 10.68 
 
 4- 
 11.76 
 
 6. 
 13.46 
 
 8. 
 
 14.83 
 
 10. 
 
 15.96 
 
 IS- 
 18.26 
 
 20. 
 20.11 
 
 30- 
 23.02 
 
 40. 
 25-33 
 
 5- 
 27.28 
 
 75- 
 31.26 
 
 100. 
 
 34.38 
 
 
 Mr. Dredge suggests, also in Indian Professional Papers, 
 the following formula : 
 
 Q ts 1300 ^| (3) 
 
 in which L is the length of the watershed, and M the area 
 in square miles. 
 
 Our formula, modified as follows, gives an approximate 
 flood volume per square mile, in cubic feet per second : 
 
 
 
TABLE OF FLOOD VOLUMES. 
 
 67 
 
 in which M is the area of the given watershed in square 
 miles. 
 
 44. Table of Flood Volumes. Upon the average 
 New England and Middle State basins, maximum floods 
 may be anticipated with rates of flow, as per the following 
 table: 
 
 TABLE No. 9. 
 FLOOD VOLUMES FROM GIVEN WATERSHEDS. 
 
 AREA OF WATER- 
 SHED. 
 
 FLOOD DISCHARGE 
 FOR WHOLE AREA, 
 
 Q = 200 (M)*' 
 
 FLOOD DISCHARGE PER 
 SQUARE MILE, 
 
 200 (M)* 
 M. 
 
 FLOOD DISCHARGE 
 PER ACRE. 
 
 Sg. Miles. 
 
 Cu. Feet per Second. ' Cu. Feet per Second. 
 
 Cu. Feet per Minute. 
 
 
 
 
 0-5 
 
 112 
 
 225.00 
 
 21.15 
 
 i 
 
 2OO 
 
 2OO.OO 
 
 18.75 
 
 2 
 
 356 
 
 178.20 
 
 l6 -75 
 
 3 
 
 500 
 
 166.53 
 
 ^.65 
 
 4 
 
 635 
 
 IS9-2S 
 
 14.96 
 
 6 
 
 890 
 
 148.37 
 
 J 3-94 
 
 8 
 
 II 3 I 
 
 141.42 
 
 13.29 
 
 10 
 
 I3 6 3 
 
 136.26 
 
 12.80 
 
 *5 
 
 IQIO 
 
 127-33 
 
 11.97 
 
 20 
 
 2428 
 
 I2I.4O 
 
 11.41 
 
 25 
 
 2925 
 
 Iiy.OO 
 
 II. OO 
 
 30 
 
 3404 
 
 H3-47 
 
 10.66 
 
 40 
 
 4326 
 
 108.15 
 
 10,16 
 
 5 
 
 5208 
 
 104.16 
 
 9.82 
 
 75 
 
 734 
 
 97-39 
 
 9- I 5 
 
 IOO 
 
 9282 
 
 92.82 
 
 8.72 
 
 200 
 
 16542 
 
 82.71 
 
 7-77 
 
 300 
 
 23190 
 
 77.30 
 
 7.26 
 
 400 
 
 29480 
 
 73.70 
 
 6.93 
 
 500 
 
 355 
 
 71.00 
 
 6.67 
 
 600 
 
 41320 
 
 68.87 
 
 6.46 
 
 800 
 
 5 2 5 20 
 
 65-65 
 
 6.16 
 
 IOOO 
 
 63260 
 
 63.26 
 
 5-94 
 
 1500 
 
 88680 
 
 59.12 
 
 5-55 
 
 2000 
 
 112600 
 
 56.30 
 
 5-29 
 
 3000 
 
 158000 
 
 52.67 
 
 4.94 
 
 400O 
 
 200800 
 
 50.20 
 
 4.72 
 
 5000 
 
 241800 
 
 48.36 
 
 4-54 
 
68 FLOW OF STREAMS. 
 
 45. Seasons of Floods. Great floods occur only 
 when peculiar combinations of circumstances favor such, 
 result. 
 
 A knowledge of the magnitude of the floods upon any 
 river, and of their usual season, is invaluable to the director 
 of constructions upon that stream, to enable him to take such 
 precautionary measures as to be always prepared for them. 
 Such knowledge is also requisite to enable him to compute 
 the storage capacity required to save and utilize such flood, 
 or to calculate the sectional area of waste weir required 
 upon dams to safely pass the same. 
 
 Long rivers, having their sources upon northern moun- 
 tain slopes, have usually well-known seasons of flood, de- 
 pendent upon the melting of snows ; but small watersheds 
 in many sections of America are subject to flood, alike, at 
 all seasons. 
 
 46. Influence of Absorption and Evaporation 
 upon Flow. The rainfall upon the Atlantic coast and 
 upon the Mississippi valley appears comparatively uniform 
 when noted in its monthly classification, but the ability of 
 any one of their watersheds to supply, from flow of stream, 
 a domestic demand equal to its mean flow is by no means 
 as uniform. 
 
 We have seen that, according to the statistics quoted, 
 the consumption of water is not as uniform, when noted by 
 monthly classification, as is the monthly rainfall. When 
 lesser classifications of rainfall and consumption are com- 
 pared, there is scarce a trace of identity in their plotted 
 irregular profiles. 
 
 Evaporation, though comparatively uniform in its 
 monthly classification, is very irregular as observed in its 
 lesser periods. 
 
 In the spring and early summer, when vegetation is in 
 
CLASSIFICATION OF RAINFALL AVAILABLE IN FLOW. 69 
 
 most thrifty growth, the innumerable rootlets of flowers, 
 grasses, shrubs, and forests, gather in a large proportion of 
 rainfall, and pass it through their arteries and back into 
 the atmosphere beyond reach for animal uses. 
 
 47. Flow in Seasons of Minimum Rainfall. In 
 gathering, basins having limited pondage or available 
 storage of rainfall, the flow from minimum annual, and 
 minimum periodic rainfall demands especial study. Occa- 
 sionally the annual rainfall continues less than the general 
 mean through cycles of three or four years, as is indicated 
 in the above diagram of curves of secular rainfall. The 
 mean rain of such cycles of low-rainfall is occasionally less 
 than eight-tenths of the general mean. 
 
 We have selected for data upon this point the rainfall 
 records of twenty-one stations, of longest observation in the 
 United States, at various points from Maine to Louisiana 
 and from California to Sitka. The computation gives the 
 annual rainfall of the least three-year cycle at any one of 
 these points as .67 of the general mean annual rain at the 
 same point, and annual rainfall of the greatest three-year 
 low cycle as .97 of the general mean at the same point. An 
 average of all these stations gives the three-year low cycle 
 rainfall as .81 of the average mean annual rainfall. 
 
 48. Periodic Classification of Rainfall Available 
 in Flow. Next, the rainfall and the portion of it that can 
 be made available, demands especial study in its monthly, 
 or less periodic classification. It is desirable to know the 
 ratio of each month' s average fall to the mean monthly fall 
 for the year, and the percentage of this fall that is exempted 
 from absorptions by vegetation and evaporations into the 
 atmosphere, and that flows from springs, and in the streams, 
 since it is ordained by Nature that the lily and the oak 
 with their seed, shall first be supplied and the atmospheric 
 
70 FLOW OF STREAMS. 
 
 processes be maintained, and the surplus rain be dedicated 
 to the animal creation, as their necessities demand and 
 ingenuities permit them to make available. 
 
 49. Sub- surface Equalizers of Flow. The inter- 
 stices of the soils and the crevices of the rocks were filled 
 long ages ago, and now regularly aid in equalizing the flow 
 of the springs and streams without, to any considerable 
 extent, affecting the total annual flow, yet their influence is 
 observable in cycles of droughts when the sub-surface water 
 level is drawn slowly down. 
 
 The substructure of each given watershed has its indi- 
 vidual storage peculiarities which may increase or diminish 
 the monthly flow and degree of regularity of flow of its 
 streams to an important extent. 
 
 If a porous subsoil of great depth and storage capacity 
 is overlaid with a thin crust of soil through which water 
 percolates slowly, a great flood-rain may fall suddenly over 
 the nearly exhausted sub-reservoir and be run off to the 
 rivers without replenishing appreciably the waning springs, 
 or increasing their flow as would an ordinary slow rainfall. 
 
 On the other hand, if its surface soil is open and absorb- 
 ent, it may be able to receive nearly the whole flood and 
 distribute it gradually from its springs. 
 
 The early sealing over of the subsoil by winter frosts 
 before the usual subterranean storage has accumulated 
 from winter storms, or a shedding of the melting snows in 
 spring by a like frost-crust, may result in a diminished flow 
 of the deep springs in the following summer. 
 
 Subsoils that exhaust themselves in ordinary seasons 
 are comparatively valueless to sustain the flow in the second 
 and third years of cycle droughts. 
 
 Steep and impervious earths yield no springs, but gather 
 their waters rapidly in the draining streams. 
 
SUMMARIES OF MONTHLY FLOW STATISTICS. 71 
 
 50. Flashy and Steady Streams. Upon the steep 
 and rocky watersheds of northern New Hampshire, we find 
 extreme examples of ''flashy" streams that are furious in 
 storm and vanish in droughts. 
 
 Upon the saturated sands of Hempstead Plains on Long 
 Island, N. Y., we find an opposite extreme of constant and 
 even flow, where a great underground reservoir co-extensive 
 with its supplying watershed, feeds its streams with remark- 
 able uniformity. 
 
 Almost all degrees of constancy and fickleness of flow 
 are to be found in the several sub-section streams of any 
 one of our great river basins. 
 
 51. Peculiar Watersheds. The extremes or results 
 from peculiar watersheds, are in all cases to be considered 
 as extremes when their individual merits and capacities of 
 supply are investigated, and the investigation may often 
 take the direction of determining the relations of its results 
 to results from a general mean, or ordinary watershed, 
 especially as respects its mean temperature, its mean hu- 
 midity of atmosphere, the direction from whence its storms 
 come, the frequency of its storm winds, the extent of its 
 storms in the different seasons, the imperviousness or the 
 porosity of its soils and rocks, the proportions of its steep, 
 gently undulating, and flat surfaces, and also it is to be 
 observed if it can be classed among those rare instances in 
 which one watershed is tributary as giver to or receiver 
 from another basin, involving an investigation of its geo- 
 logical substructure. 
 
 53. Summaries of Monthly Flow Statistics. 
 We have analyzed some valuable statistics of monthly 
 rainfalls, and measured flow of streams in Massachusetts 
 and New York State, which are too voluminous for repro- 
 duction here, and present the deduced results. The records 
 
72 FLOW OF STREAMS. 
 
 are, first, from a report by Jos. P. Davis, C. E., relating to 
 the watershed of Cochituate Lake, which has. supplied the 
 city of Boston with water until supplemented in 1876 from 
 the Sudbury River watershed ; second, from a table com- 
 piled by Jas. P. Kirkwood, C. E., relating to the watershed 
 of Croton River above the Croton Dam ; and third, from a 
 paper read by J. J. R. Croes, C. E., before the American 
 Society of Civil Engineers, July, 1874, relating to the water- 
 shed of the West Branch of the Croton River. 
 The summaries are as follows : 
 
 TABLE No. 1O. 
 SUMMARY OF RAINFALL UPON THE COCHITUATE BASIN. 
 
 Average annual, 55.032 inches ; average monthly, 4.586 inches. 
 
 
 d 
 
 
 t 
 
 | 
 
 1 
 
 i 
 
 1 i 
 
 !> 
 
 H- 
 
 5 
 
 < 
 
 
 
 t 
 
 
 
 g 
 
 1 
 
 
 
 
 
 
 
 
 
 
 in 
 
 
 in 
 
 
 Mean 
 Minimum 
 
 3-69 
 
 4-03 
 .08 
 
 5-35 
 
 4.58 
 
 5.69 
 
 2 66 
 
 3-9 
 .58 
 
 5-23 
 I. O6 
 
 4.91 
 
 3.81 
 .64 
 
 5-86 
 
 5.26 
 
 2.6^ 
 
 3-52 
 
 Maximum 
 
 7-85 
 
 Jo 
 
 8.44 
 
 "34 
 
 8.25 
 
 5.96 
 
 14.12 
 
 12.36 
 
 8.49 
 
 9-50 
 
 8,S4 
 
 5.98 
 
 Ratio of monthly 
 mean... 
 
 .806 
 
 .878 
 
 1.167 
 
 .008 
 
 I.24.I 
 
 .67* 
 
 1. 141 
 
 1.070 
 
 .8qi 
 
 I.^OO 
 
 1. 147 
 
 .768 
 
 TABLE No. 11. 
 SUMMARY OF RAINFALL UPON THE CROTON BASIN. 
 
 Average annual, 46.497 inches ; average monthly, 4.227 inches. 
 
 
 c 
 
 > > 
 
 1 
 
 
 
 VH 
 Pi 
 
 < 
 
 1 
 
 o 
 
 i , 
 
 ^>> 
 
 *3 
 i i 
 
 fci 
 
 3 
 <5 
 
 
 U 
 
 C/D 
 
 |j 
 
 
 
 > 
 o 
 
 fc ' 
 
 1 
 
 Mean 
 Minimum.. 
 
 in. 
 *'$ 
 
 in. 
 
 3- J 5 
 
 in. 
 
 ?% 
 
 in. 
 
 3.12 
 
 2 4.8 
 
 in. 
 6.40 
 
 A 78 
 
 in. 
 
 4.58 
 
 /. 
 4-31 
 
 /. 
 6.03 
 
 in. 
 5-30 
 
 in. 
 
 4.70 
 
 in. 
 3-83 
 
 r*. 
 
 3-60 
 i 86 
 
 Maximum 
 
 4 .?8 
 
 5-03 
 
 5.6? 
 
 4-32 
 
 TO. 18 
 
 2.51 
 6.19 
 
 8.12 
 
 .9.21 
 
 13.35 
 
 8.7! 
 
 5.36 
 
 6.86 
 
 Ratio of monthly 
 mean 
 
 .625 
 
 
 
 
 
 
 
 
 
 
 
 8<u 
 
 
 
 
 
 
 
 
 
 1 . 
 
 
 
 
 
SUMMARIES OF MONTHLY FLOW STATISTICS. 
 
 73 
 
 TA B L E No. 12. 
 SUMMARY OF RAINFALL UPON CROTON WEST-BRANCH BASIN. 
 
 Average annual, 44.429 inches ; average monthly, 4.039 inches. 
 
 
 1 
 
 .0 
 
 4> 
 & 
 
 & 
 
 tj 
 
 Q, 
 <3 
 
 >, 
 
 
 i, 
 
 >, 
 
 3 
 
 ! 
 
 1 
 
 a 
 
 i 
 fc 
 
 1 
 
 Mean 
 
 in. 
 
 -\ 16 
 
 /, 
 
 in. 
 
 in. 
 
 , 84 
 
 in. 
 
 c og 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 *. 
 
 in. 
 o jg 
 
 Minimum 
 Maximum 
 
 1.44 
 4.5i 
 
 1.22 
 6.40 
 
 2.55 
 4.27 
 
 3.01 
 5-45 
 
 2.30 
 8.79 
 
 4-32 
 2.06 
 5-73 
 
 3-43 
 5-5 2 
 
 5-10 
 10.04 
 
 1.44 
 3.69 
 
 2.15 
 9.46 
 
 2-43 
 4-35 
 
 1.49 
 5.96 
 
 Ratio of monthly 
 mean 
 
 .733 
 
 .767 
 
 1.296 
 
 .718 
 
 1-633 
 
 1.136 
 
 1.070 
 
 1-257 
 
 951 
 
 .818 
 
 793 
 
 783 
 
 TAB L E No. 13. 
 
 SUMMARY OF PERCENTAGE OF RAINFALL FLOWING FROM THE COCHIT- 
 
 UATE BASIN. 
 
 Average percentage of average annual rainfall flowing off, 45.6. 
 
 
 I 
 
 1 
 
 S3 
 
 ij 
 
 a 
 <J 
 
 
 
 1 
 
 H- > 
 
 !>> 
 
 "3 
 i, 
 
 to 
 I 
 
 .1 
 
 1 
 
 1 
 
 y 
 
 Q 
 
 
 in. 
 
 in. 
 
 in. 
 
 in. 
 
 80 s 
 
 in. 
 
 *. 
 
 in. 
 
 in. 
 
 iV*. 
 
 in. 
 
 26 ; 
 
 in. 
 
 27 8 
 
 in. 
 64 i 
 
 Minimum 
 Maximum 
 
 33 
 79 
 
 %' 
 159 
 
 44 
 153 
 
 39 
 124 
 
 20 
 76 
 
 8? 
 
 9 
 39 
 
 14 
 27 
 
 J 3 
 39 
 
 10 
 
 80 
 
 20 
 42 
 
 ^ 
 
 Ratio of monthly 
 
 
 
 i =;6 
 
 
 
 
 
 
 
 ,c8 
 
 .61 
 
 1.41 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 TABLE No. 14. 
 
 SUMMARY OF PERCENTAGE OF RAINFALL FLOWING FROM THE CROTON 
 
 BASIN. 
 
 Average percentage of average annual rainfall flowing off, 57.47- 
 
 
 i 
 
 Xi 
 
 i 
 
 J3 
 
 !M 
 
 OH 
 
 ! 
 
 | 
 
 d 
 
 i 
 
 ^, 
 
 "3 
 i 
 
 t# 
 
 ! 
 
 1 
 
 > 
 
 o 
 K 
 
 o 
 
 Q 
 
 Mean 
 
 in. 
 
 70 68 
 
 in. 
 
 in, 
 
 86.72 
 
 . 
 
 80.60 
 
 in. 
 
 48. 4.5 
 
 in. 
 
 4S-O2 
 
 in. 
 
 21. 02 
 
 z. 
 19.45 
 
 in. 
 30.10 
 
 in. 
 81.13 
 
 in. 
 60.40 
 
 in. 
 62.12 
 
 Minimum 
 Maximum 
 
 49.0 
 123.4 
 
 62.1 
 lOJ.O 
 
 21.9 
 147.4 
 
 53-5 
 125.7 
 
 42.8 
 ,S6.4 
 
 18.6 
 67.4 
 
 8-5 
 29.6 
 
 8.4 
 42.2 
 
 IO.2 
 
 92.0 
 
 7.6 
 366.5 
 
 36.3 
 94-i 
 
 39-o 
 94-5 
 
 Ratio of monthly 
 mean . . 
 
 i 386 
 
 
 
 
 .840 
 
 .783 
 
 .369 
 
 .338 
 
 5 2 4 
 
 1.412 
 
 1.051 
 
 1.081 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
74 
 
 FLOW OF STREAMS. 
 
 TABLE No. 15. 
 
 SUMMARY OF PERCENTAGE OF RAINFALL FLOWING FROM THE CROTON 
 WEST-BRANCH BASIN. 
 
 Average percentage of average annual rainfall flowing off, 70.98. 
 
 
 d 
 
 rt 
 
 H> 
 
 1 
 
 cj 
 Jv* 
 
 < 
 
 | 
 
 i 
 i > 
 
 >, 
 
 3 
 
 H- > 
 
 bb 
 
 3 
 < 
 
 1 
 
 ti 
 
 o 
 
 i 
 * 
 
 1 
 
 
 
 
 
 
 
 in 
 
 in 
 
 
 
 
 
 ir 
 
 Mean 
 
 102.8 
 
 71.1 
 
 158.9 
 
 II7.2 
 
 80.5 
 
 44-8 
 
 19.0 
 
 24.6 
 
 26.6 
 
 30.4 
 
 78.9 
 
 97.0 
 
 Minimum.., 
 Maximum 
 
 17.7 
 186.6 
 
 59- 
 103.9 
 
 103.0 
 209.1 
 
 93- 2 
 158.4 
 
 46.7 
 100.3 
 
 !}.6 
 71.2 
 
 7-3 
 3i-4 
 
 & 
 
 3-3 
 39-8 
 
 II. 2 
 56.3 
 
 4-5 
 
 1 10. 2 
 
 65-6 
 140.8 
 
 Ratio of monthly 
 mean 
 
 1.448 
 
 I.OOI 
 
 2.238 
 
 1.651 
 
 i.i34 
 
 .636 
 
 .267 
 
 347 
 
 375 
 
 . 42 8 
 
 1. 112 
 
 1.367 
 
 TABLE No. 16. 
 
 SUMMARY OF VOLUME OF FLOW OF RAINFALL FROM THE COCHITUATE 
 BASIN (in cubic feet per minute per square mile). 
 
 
 I 
 
 ,Q 
 
 
 
 1 
 
 
 
 O 
 
 >, 
 a 
 
 c5 
 
 N- 
 
 j>> 
 
 3 
 
 1 > 
 
 bb 
 
 3 
 
 < 
 
 "cL 
 
 
 
 8 
 
 
 
 > 
 
 
 
 
 
 g 
 
 Q 
 
 Mean .... 
 
 cu.ft. 
 99.17 
 
 37-99 
 245.12 
 
 cu.ft. 
 
 150.42 
 
 58.29 
 301.90 
 
 cu.ft. 
 
 174.76 
 
 91.60 
 
 242.52 
 
 cu.ft. 
 
 169.80 
 
 70.44 
 369.40 
 
 cu.ft. 
 131.80 
 67.14 
 321.11 
 
 cu.ft. 
 
 44.27 
 18.28 
 85.49 
 
 cu.ft. 
 
 45.27 
 21.34 
 154-57 
 
 cu.ft. 
 
 49-15 
 21.34 
 109.29 
 
 cu.ft. 
 
 42.84 
 4-30 
 99.48 
 
 cu.ft. 
 
 62.45 
 36-43 
 123.34 
 
 cu.ft. 
 75-9 
 47-32 
 I0 5-39 
 
 ,*.//. 
 
 78.94 
 40.07 
 164.98 
 
 Minimum 
 Maximum 
 Ratio of monthly 
 mean 
 
 1.058 
 
 1.605 
 
 1.865 
 
 1.812 
 
 1.406 
 
 .472 
 
 .483 
 
 524 
 
 457 
 
 .666 
 
 .809 
 
 .842 
 
 
 TABLE No. 17. 
 
 SUMMARY OF VOLUME OF FLOW OF RAINFALL FROM THE CROTON 
 BASIN (in cubic feet per minute per square mile). 
 
 
 d 
 
 
 i > 
 
 cu.ft. 
 
 91.48 
 48.08 
 127.71 
 
 1 
 
 cu.ft 
 
 147.69 
 40.65 
 293.01 
 
 1-317 
 
 1 
 
 < 
 
 1 
 
 cu.ft. 
 164.49 
 108.25 
 
 298.98 
 
 i 
 
 lj 
 
 cu.ft. 
 115.12 
 34-9 
 224-33 
 
 j>> 
 3 
 
 H-> 
 
 cu.ft. 
 
 48.37 
 
 10.46 
 
 81.76 
 
 $ 
 
 <J 
 
 
 
 
 
 I 
 
 g 
 
 g 
 
 Q 
 
 Mean 
 
 cu.ft. 
 
 177.02 
 79-05 
 25.709 
 
 cu.ft 
 
 132.63 
 87-43 
 
 188.95 
 
 cu.ft. 
 70.22 
 13.12 
 202.19 
 
 r.//. 
 
 85-99 
 12.91 
 
 275-95 
 
 CK../3?. 
 
 81.08 
 18.05 
 141.14 
 
 <:.//. 
 124.92 
 61.41 
 201.30 
 
 C */'' 
 100.23 
 
 72.08 
 146-24 
 
 .948 
 
 
 Maximum 
 
 Ratio of monthly 
 mean 
 
 .816 
 
 i-579 
 
 1.183 
 
 1.467 
 
 1.027 
 
 431 
 
 .627 
 
 .767 
 
 .7=3 
 
 1.114 
 
 
MINIMUM, MEAN, AND FLOOD FLOW OF STREAMS. 75 
 
 TABLE No. 18. 
 
 SUMMARY OF VOLUME OF FLOW OF RAINFALL FROM THE CROTON 
 WEST-BRANCH BASIN (in cubic feet per minute per square mile). 
 
 
 I 
 
 1 
 
 1 
 
 a 
 < 
 
 >, 
 
 A 
 
 8 
 i) 
 
 >, 
 
 s 
 
 fcJb 
 
 g 
 < 
 
 tl 
 
 & 
 
 o 
 
 > 
 
 o 
 
 fe 
 
 
 
 Q 
 
 Mean 
 
 cu.ft. 
 
 158.95 
 35.08 
 347-88 
 
 1.041 
 
 cu.ft\cu.ft. cu.ft. 
 185.191290.56 272.60 
 47.16 203.58 146.04 
 
 378.90 390.83 463.98 
 
 cu.ft. 
 161.60 
 26.19 
 394.92 
 
 cu.ft. 
 
 103.86 
 45.18 
 
 202.02 
 
 cu.ft. 
 40.02 
 
 19.26 
 
 _8*56 
 
 .262 
 
 cu.ft. 
 
 103.12 
 9.06 
 281.04 
 
 .676 
 
 cu.ft. 
 
 *47-59 
 5-i6 
 477-22 
 
 .967 
 
 cu.ft. 
 96.26 
 27-48 
 277.26 
 
 cu.ft. 
 
 107.85 
 
 5-92 
 
 203.28 
 
 c*.//. 
 
 164.07 
 50.88 
 299.16 
 
 1.075 
 
 
 Maximum . . 
 Ratio of monthly 
 mean 
 
 1.213 
 
 1.904 
 
 1.786 
 
 1.059 
 
 .680 
 
 .631 
 
 .707 
 
 
 53. Minimum, Mean, and Flood Flow of Streams. 
 
 An analysis of the published records of volumes of water 
 flowing in the streams in all the seasons has led to the fol- 
 lowing approximate estimate of volumes of flow in the aver- 
 age Atlantic coast "basins : 
 
 The minimum refers to a fifteen days' period of least 
 summer flow. 
 
 The mean refers to a one hundred and twenty days' 
 period, covering usually July, August, September, and 
 October, beginning sometimes earlier, in June, and ending 
 sometimes later, in November. 
 
 The maximum refers to flood volumes. 
 
 TABLE No. 19. 
 ESTIMATES OF MINIMUM, MEAN, AND MAXIMUM FLOW OF STREAMS. 
 
 
 Mm. in cu. ft. per 
 sec. per sq. mi. 
 
 Mean in cu. ft.'per 
 sec. per sq. mi. 
 
 Max. in cu ft. per 
 sec. per sq. mi. 
 
 Area of 
 
 watershed, i 
 
 sq. mi. 
 
 083. 
 
 I.OO 
 
 2OO 
 
 tt tt 
 
 10 
 
 ii 
 
 .1 
 
 99 
 
 I 3 6 
 
 tt it 
 
 2 5 
 
 tt 
 
 .11 
 
 .98 
 
 117 
 
 tt it 
 
 5o 
 
 n 
 
 .14 
 
 97 
 
 104 
 
 it n 
 
 100 
 
 " 
 
 .18 
 
 95 
 
 93 
 
 it it 
 
 " 250 
 
 ti 
 
 2 5 
 
 .90 
 
 80 
 
 if ii 
 
 500 
 
 it 
 
 30 
 
 .87 
 
 7 1 
 
 it ti 
 
 " IOOO 
 
 ii 
 
 35 
 
 .82 
 
 63 
 
 it it 
 
 " 1500 
 
 n 
 
 38 
 
 .80 
 
 59 
 
 it ii 
 
 " 2000 
 
 n 
 
 79 5 6 
 
76 
 
 FLOW OF STREAMS. 
 
 This table refers to streams of average natural pondage 
 and retentiveness of soil, Ibut excludes effects of artificial 
 storage. The fluctuations of streams will be greater than 
 indicated by the table when prevailing slopes are steep and 
 rocks impervious, and less in rolling country with pervious 
 soils. 
 
 54. Ratios of Monthly Flow in Streams. A care- 
 ful analysis of the published records of monthly flow of the 
 average Atlantic coast streams leads to the following ap- 
 proximate estimate of the ratio of the monthly mean rain- 
 fall that flows down the streams in each given month of the 
 year, in which due consideration of the evaporation from 
 soils and foliage in very dry seasons has not been neglected. 
 
 TABLE No. 2O. 
 MONTHLY RATIOS OF FLOW OF STREAMS. 
 
 
 I 
 
 1 
 
 1 
 
 _j 
 
 I 
 
 < 
 
 
 
 i 
 
 i 
 
 h 
 
 s 
 
 bb 
 1 
 
 i 
 
 V) 
 
 i 
 
 i 
 
 si 
 
 Q 
 
 Ratio of flow . 
 
 1.65 
 
 1.50 
 
 1.65 
 
 i-45 
 
 .85 
 
 75 
 
 35 
 
 25 
 
 30 
 
 45 
 
 i. 20 
 
 1.60 
 
 Here unity equals the mean monthly flow, or one-twelfth 
 the mean annual flow. 
 
 To compute, approximately, the inches depth of rain 
 flowing in the streams each month, one-twelfth the mean 
 annual rain, at the given locality, may be multiplied by the 
 ratios in the following table. For illustration, a mean 
 annual rain of 40 inches depth, giving 3.333 inches mean 
 monthly depth, is assumed, and the available flow of stream 
 expressed in inches depth of rain is added after the ratios. 
 
MEAN ANNUAL FLOW OF STREAMS. 
 
 77 
 
 TABLE No. 21. 
 
 RATIOS OF MEAN MONTHLY RAIN, AND INCHES OF RAIN FLOWING 
 
 EACH MONTH. 
 
 
 4 
 
 1 
 
 1 
 
 (X 
 
 ci 
 
 
 
 c 
 
 3 
 
 i > 
 
 *3 
 
 bb 
 
 3 
 
 ft 
 
 
 
 1 
 
 1 
 
 Ratios of mean 
 
 
 
 
 
 
 
 
 
 
 
 
 
 monthly rain 
 Inches of rain 
 
 .825 
 
 750 
 
 .825 
 
 725 
 
 425 
 
 375 
 
 .175 
 
 .125 
 
 ISO 
 
 .225 
 
 .600 
 
 .800 
 
 flowing 
 
 2.75 
 
 2.50 
 
 2-75 
 
 2.41 
 
 I.4I 
 
 1.25 
 
 0.59 
 
 0.41 
 
 0.50 
 
 0.75 
 
 2.OO 
 
 2.66 
 
 Eight - tenths 
 of same 
 
 2.20 
 
 2.00 
 
 2. 2O 
 
 i-93 
 
 ...3 
 
 I.OO 
 
 0.47 
 
 0-33 
 
 0.40 O.6o 
 
 1. 60 
 
 2.13 
 
 For low-cycle years, use eight-tenths ( 47) the available 
 monthly depth of rain flowing. 
 
 tf 55. Mean Annual Flow of Streams. When month- 
 ly data of the flow of any given stream is not obtainable, it 
 may ordinarily be taken upon average drainage areas, for 
 an annual flow, as equal to fifty per cent, of the annual 
 rainfall. 
 
 Or, for different surfaces, its ratio of the annual rain, 
 including floods and flow of springs, is more approximately 
 as follows : 
 
 From mountain slopes, or steep rocky hills 80 to .90 
 
 Wooded, swampy lands 60 to .80 
 
 Undulating pasture and woodland 50 to .70 
 
 Flat cultivated lands and prairie 45 to .60 
 
 Since stations for meteorological observations are now 
 established in or near almost all the populous neighbor- 
 hoods, and some of the stations have already been estab- 
 lished more than a quarter of a century, it is easier to obtain 
 data relating to rainfall than to the flow of streams. In 
 fact, the required data relating to a given stream is rarely 
 obtainable, and the estimates relating to the capacity and 
 
78 FLOW OF STREAMS. 
 
 reliability of the stream to furnish a given water-supply 
 must necessarily be quite speculative. 
 
 56. Estimates of Flow of Streams. In such case, 
 an estimate of the capacity of a stream to deliver into a 
 reservoir, conduit, or pump-well is computed according to 
 some scheme suggested by extended observations and study 
 of streams and their watersheds, and long experience in the 
 construction of water supplies. 
 
 The first reconnoissance of a given watershed by an ex- 
 pert in hydrology will ordinarily enable him to judge very 
 closely of its capacity to yield an available and suitable 
 water supply ; for his comprehension at once grasps its 
 geological structure, its physical features and its usual 
 meteorological phenomena, and his educated judgment 
 supplies the necessary data, as it were, instinctively. 
 
 If the estimate of flow of a stream must be worked up 
 from a survey of the watershed area and the mean annual 
 rainfall, as the principal data, then recourse may be had to 
 the data and estimates given above, relating to the question, 
 for average upland basins of one hundred or less square 
 miles area. 
 
 In illustration, let us assume a basin of one square mile 
 area, having a forty-inch average annual rainfall, and then 
 proceed with a computation. This is a convenient unit of 
 area upon which to base computations for larger areas. 
 
 The ratios of the three-year low rain cycles gives their 
 mean rainfall as about eight-tenths of the general mean 
 rainfall. We assume it to be eighty per cent. The mean 
 annual flow of the stream we assume to be fifty per cent, of 
 the annual rainfall. Eight-tenths of fifty per cent, gives 
 forty per cent, of the annual rainfall as the annual available 
 flow of the stream, and forty per cent, of the forty inches 
 rainfall gives an equivalent of sixteen inches of rainfall 
 
ESTIMATES OF FLOW OF STREAMS. 
 
 79 
 
 flowing down the stream annually. The monthly average 
 flow is then taken as one-twelfth of sixteen, or one and one- 
 third inches. Our estimated monthly percentage of mean 
 flow, as given above ( 54), is sometimes much in excess 
 and sometimes less than the monthly average. Flows less 
 than the mean are to be compensated for by a proportion- 
 ate increase of storage above the mean storage required. 
 The monthly computations are as follows : 
 
 _ 40 inches x 50 percent, x .8 
 
 = 1.333 
 
 12 months 
 
 inches average available rain monthly. This average mul- 
 tiplied by the respective ratios of flow in each month gives 
 the inches depth of available rain flowing in the respective 
 months, thus: 
 
 MEAN MONTHLY 
 RAINFALL. 
 
 January.. 1.333 
 
 February 
 
 March 
 
 April 
 
 May 
 
 June 
 
 July 
 
 August 
 
 September 
 
 October ,.. 
 
 November 
 
 December . . 
 
 INCHES DEPTH OF 
 AVAILABLE RAIN 
 FLOWING EACH 
 MONTH. 
 
 
 Again, uniting the constants, we have - ^ =.0333, 
 
 which, multiplied by the respective ratios of monthly flow, 
 thus : Jan., .0333 x 1.65 = ,055, etc., gives directly the mean 
 ratio of the low cycle annual rainfall that is available in the 
 stream each month. 
 
80 
 
 FLOW OF STREAMS. 
 
 Jan 
 Feb. . . 
 March. 
 April . 
 May. . . 
 June.. 
 July... 
 Aug... 
 Sept. . . 
 Oct.... 
 Nov. . . 
 Dec.. 
 
 40 nches 
 
 FLOW IN Cu. FT. PER 
 MINUTE PER SQ. Mi. 
 
 IN EACH MONTH. 
 
 055 = 
 
 2.20 inches depth = 
 
 116.60 
 
 .050 = 
 
 2.00 
 
 = 
 
 106.00 
 
 055 = 
 
 2.20 
 
 
 
 116.60 
 
 .0483 = 
 
 1-93 
 
 = 
 
 102.29 
 
 .0283 = 
 
 1.13 
 
 = 
 
 59-89 
 
 .025 - 
 
 1. 00 
 
 = 
 
 53-oo 
 
 .012 = 
 
 47 
 
 = 
 
 24.91 
 
 .0083 = 
 
 33 
 
 = 
 
 17.49 
 
 .OIO = 
 
 .40 
 
 
 
 21.20 
 
 .015 = 
 
 .60 
 
 = 
 
 31.80 
 
 .040 
 
 i. 60 
 
 = 
 
 84.80 
 
 0533 = 
 
 2.14 
 
 = 
 
 II342 
 
 Total, 
 
 16.00 inches. Mean, 
 
 70.67 cu. ft. 
 
 57. Ordinary Flow of Streams. Mr. Leslie has 
 proposed* an arbitrary rule for computing the "average 
 summer discharge" or " ordinary" flow of a stream, from 
 the daily gaugings, as follows : 
 
 " Range the discharges as observed daily in their order 
 of magnitude. 
 
 "Divide the list thus arranged into an upper quarter, a 
 middle half, and a lower quarter. 
 
 " The discharges in the upper quarter of the list are to be 
 considered as floods, and in the lower quarter as minimum 
 flows. 
 
 " For each of the gaugings exceeding the average of the 
 middle half, including flood gaugings, substitute the average 
 of the middle Jialf of the list, and take the mean of the 
 whole list, as thus modified, for the ordinary or average 
 discharge, exclusive of flood-waters" 
 
 This rule applied to a number of examples of actual 
 measurements of streams in hilly English districts gave 
 computed ordinary discharges ranging from one-fourth to 
 
 * Minutes of Proceedings of Institution of Civil Engineers, Vol. X, p. 327. 
 
TABLES OF FLOW. 81 
 
 one-third of the measured mean discharge, including 
 floods. 
 
 The ordinary flow of New England streams is, at an 
 average, equivalent to about one million gallons per day 
 per square mile of drainage area, which expressed in cubic 
 feet, equals about ninety-two cubic feet per minute per 
 square mile. 
 
 The above computation for the average flow in low cycle 
 years gives a little less than eight-tenths of this amount, or 
 seventy-one cubic feet per minute per square mile as the 
 average flow throughout the year, and a little less than one- 
 fourth this amount as the minimum monthly flow.* 
 
 58. Tables of Flow Equivalent to Given Depths 
 of Rain. To facilitate calculations, tables giving the 
 equivalents of various depths of monthly and annual rain- 
 falls, in even continuous flow, in cubic feet per minute per 
 acre, and per square mile, are here inserted. 
 
 Greater or less numbers than those given in Tables 22 
 and 23 may be found by addition, or by moving the decimal 
 point ; thus, from Table 22, for 40.362 inches depth, take 
 
 Depth, 30 inches = 1590.204 cu. ft. 
 
 10 " = 530.068 " 
 
 .3 = 15.902 
 
 .06 " = 3.180 " 
 
 .002 " = .106 " 
 
 40.362 inches = 2139.460 cu. ft. 
 
 To reduce the flows in the two tables to equivalent vol- 
 umes of flow for like depths of rain in ONE DAY, divide the 
 flows in Table 22 by 30.4369 (log. = 1.483400), and divide 
 the flows in Table 23 by 365.2417 (log. = 2.562581). 
 
 * Some useful data relating to the flow of certain British and Continental 
 streams may be found in Beardmore's " Manual of Hydrology," p. 149 (Lon- 
 don, 1862). 
 
FLOW OF STREAMS. 
 
 TABLE No. 22. 
 
 EQUIVALENT VOLUMES OF FLOW, FOR GIVEN DEPTHS OF RAIN IN 
 
 ONE MONTH.* 
 
 DEPTHS OF RAIN 
 IN ONE MONTH. 
 
 EQUIVALENT FLOW IN 
 CUBIC FEET PER 
 MINUTE PER ACRE. 
 
 EQUIVALENT FLOW IN CU- 
 BIC FEET PER MINUTE 
 PER SQUARE MILE. 
 
 EQUIVALENT FLOW IN CU- 
 BIC FEET PER MONTH PER 
 SQUARE MILE. 
 
 Inches. 
 
 
 
 
 .01 
 
 .00083 
 
 530 
 
 23,232 
 
 * .02 
 
 .O0l66 
 
 1. 060 
 
 #6,464 
 
 03 
 
 .00248 
 
 1.590 
 
 69,696 
 
 .04 
 
 .00331 
 
 2.I2O 
 
 92,928 
 
 5 
 
 .00414 
 
 2.650 
 
 Il6,l6o 
 
 .06 
 
 .00497 
 
 3.180 
 
 I39.392 
 
 .07 
 
 .00580 
 
 3.710 
 
 162,624 
 
 .08 
 
 .00662 
 
 4.240 
 
 185,856 
 
 .09 
 
 .00745 
 
 4.770 
 
 209,088 
 
 .1 
 
 .00828 
 
 5-3007 
 
 232,320 
 
 .2 
 
 .01656 
 
 IO.60I4 
 
 464,640 
 
 3 
 
 .02484 
 
 15.9020 
 
 696,960 
 
 4 
 
 .03312 
 
 21.2027 
 
 929,280 
 
 5 
 
 .04140 
 
 26.5034 
 
 I,l6l,6oo 
 
 .6 
 
 .04968 
 
 31.8041 
 
 i,393>9 20 
 
 7 
 
 .05796 
 
 37-I048 
 
 1,626,240 
 
 .8 
 
 .06624 
 
 42.4054 
 
 1,858,560 
 
 9 
 
 .07452 
 
 47.7061 
 
 2,090,880 
 
 1.0 
 
 .0828 
 
 53.0068 
 
 2,323,200 
 
 2 
 
 .1656 
 
 106.0136 
 
 4,646,400 
 
 3 
 
 .2484 
 
 159.0204 
 
 6,969,600 
 
 4 
 
 3312 
 
 212.0272 
 
 9,292,800 
 
 5 
 
 .4140 
 
 265.0340 
 
 11,616,000 
 
 6 
 
 .4868 
 
 318.0408 
 
 13,939.200 
 
 7 
 
 5796 
 
 371.0476 
 
 16,262,400 
 
 8 
 
 .6624 
 
 424.0544 
 
 18,585,600 
 
 9 
 
 7452 
 
 477.0612 
 
 20,908,800 
 
 10 
 
 .828 
 
 530.068 
 
 23,232,000 
 
 20 
 
 1.656 
 
 1060.136 
 
 46,464,000 
 
 3 
 
 2.484 
 
 I59O.204 
 
 69,696,000 
 
 * One month is taken equal to 30.4369 days. 
 
TABLES OF FLOW. 
 
 83 
 
 TABLE No. 23. 
 
 EQUIVALENT VOLUME OF FLOW, FOR GIVEN DEPTHS OF RAIN IN 
 
 ONE YEAR.* 
 
 DEPTHS OF RAIN 
 IN ONE YEAR. 
 
 EQUIVALENT FLOW IN 
 CUBIC FEET PER 
 MINUTE PER ACRE. 
 
 EQUIVALENT FLOW IN CU- 
 BIC FEET PER MINUTE 
 PER SQUARE MILE. 
 
 EQUIVALENT FLOW IN CU- 
 BIC FEET PER YEAR PER 
 SQUARE MILE. 
 
 Inches. 
 
 
 
 
 .01 
 
 .000069 
 
 .0442 
 
 23,232 
 
 .02 
 
 .000138 
 
 .0883 
 
 46,464 
 
 03 
 
 .000207 
 
 1325 
 
 69,696 
 
 .04 
 
 .000276 
 
 .1767 
 
 92,928 
 
 5 
 
 .000345 
 
 .2209 
 
 Il6,l6o 
 
 .06 
 
 .000414 
 
 .2650 
 
 X 39>39 2 
 
 .07 
 
 .000483 
 
 .3092 
 
 162,624 
 
 .08 
 
 .000552 
 
 3534 
 
 185,856 
 
 .09 
 
 .OOO62I 
 
 3976 
 
 209,088 
 
 .1 
 
 .00069 
 
 .4417 
 
 232,320 
 
 .2 
 
 .00138 
 
 .8834 
 
 464,640 
 
 3 
 
 .002O7 
 
 1-3252 
 
 696,960 
 
 4 
 
 .00276 
 
 1.7669 
 
 929,280 
 
 5 
 
 00345 
 
 2.2086 
 
 1,161,600 
 
 .6 
 
 .00414 
 
 2.6503 
 
 I >393>9 2 <> 
 
 7 
 
 .00483 
 
 3.0921 
 
 1,626,240 
 
 .8 
 
 .00552 
 
 3.5338 
 
 1,858,560 
 
 9 
 
 .OO62I 
 
 3-9755 
 
 2,090,880 
 
 I.O 
 
 .0069 
 
 4.4172 
 
 2,323,200 
 
 2 
 
 .0138 
 
 8.8345 
 
 4,646,400 
 
 3 
 
 .0207 
 
 13-2517 
 
 6,969,600 
 
 4 
 
 .0276 
 
 17.6689 
 
 9,292,800 
 
 5 
 
 0345 
 
 22.0862 
 
 11,616,000 
 
 6 
 
 .0414 
 
 26.5034 
 
 1 3>939>2oo 
 
 7 
 
 .0483 
 
 30.9206 
 
 16,262,400 
 
 8 
 
 055 2 
 
 35-3379 
 
 18,585,600 
 
 9 
 
 .0621 
 
 39-755 1 
 
 20,908,800 
 
 10 
 
 .069 
 
 44.1723 
 
 23,232,000 
 
 20 
 
 .T 3 8 
 
 88.3447 
 
 46,464,000 
 
 30 
 
 .207 
 
 132.5170 
 
 69,696,000 
 
 40 
 
 .276 
 
 176.6894 
 
 92,928,000 
 
 50 
 
 345 
 
 220.8617 
 
 116,160,000 
 
 60 
 
 .414 
 
 265.0340 
 
 139,392,000 
 
 * One year is taken, equal to 365 days, 5 hours, 49 minutes. 
 
CHAPTEE V. 
 
 STORAGE AND EVAPORATION OF WATER. 
 STORAGE. 
 
 59. Artificial Storage. The fluctuations of the rain- 
 fall, flow of streams, and consumption of water in the differ- 
 ent seasons of the year, require almost invariably that, for 
 gravitation and hydraulic power pumping supplies, there 
 shall be artificial storage of the surplus waters of the sea- 
 sons of maximum flow, to provide for the draught during 
 the seasons of minimum flow. A grand exception to this 
 general rule is that of the natural storage of the chain of 
 great lakes that equalizes the flow of the St. Lawrence 
 River, which furnishes the domestic water supply of the 
 City of Montreal and the hydraulic power to pump the same 
 to the reservoir on the mountain. 
 
 When the mean annual consumption, whether for do- 
 mestic use, or for power and domestic use combined is 
 nearly equal to the mean annual flow of the supplying 
 watershed, the question of ample storage becomes of su- 
 preme importance. The chief river basins of Maine present 
 remarkable examples of natural storage facilities, since 
 they have from six to thirteen per cent., respectively, of 
 their large watershed areas in pond and lake surfaces. 
 
 60. Losses Incident to Storage. There are losses 
 incident to artificial storage that must not be overlooked ; 
 for instance, the percolation into the earth and through the 
 embankment, evaporation from the reservoir surface and 
 from the saturated borders, and in some instances constant 
 draught of the share of riparian owners. 
 
RIGHTS OF RIPARIAN OWNERS. 85 
 
 61. Sub- strata of the Storage Basin. The structure 
 of the impounding basin, especially when the water is to 
 fill it to great height above the old bed, is to be minutely 
 examined, as the water at its new level may cover the edges 
 of porous strata cropping out above the channel, or may 
 find access to fissured rocks, either of which may lead the 
 storage by subterranean paths along the valley and deliver 
 it, possibly, a long distance down the stream, or in a mul- 
 titude of springs beyond the impounding dam. If the 
 water carries but little sediment of a silting nature, this 
 trouble will be difficult to remedy, and liable to be serious- 
 ly chronic. 
 
 62. Percolation from Storage Basins. Percolation 
 through the retaining embankment is a result of slighted or 
 unintelligent construction, and will be discussed when con- 
 structive features are hereafter considered. (See Reservoir 
 Embankments.) 
 
 63. Rights of Riparian Owners. The rights of 
 riparian owners, ancient as the riparian settlements, to the 
 use of the water that flows, and its most favored piscatory 
 produce, is often as a thorn in the impounded s side. What 
 are those rights 1 The Courts and Legislatures of the man- 
 ufacturing States have wrestled with this question, their 
 judges have grown hoary while they pondered it, and their 
 attorneys have prospered, and yet who shall say what 
 riparian rights shall be, until the Court has considered all 
 anew. 
 
 Beloe mentions* that it is a "common (British) rule in 
 the manufacturing districts to deduct one-sixth the average 
 rainfall for loss by floods, in addition to the absorption and 
 evaporation, and then allow one-third of the remainder to 
 
 * Beloe on Reservoirs, p. 12. London, 1872. 
 
86 , STORAGE AND EVAPORATION OF WATER. 
 
 the riparian owners, leaving two-thirds to the impounders. 
 In some instances this is varied to the proportion of one- 
 quarter to the former and three-quarters to the latter." 
 
 The question can only be settled equitably upon the 
 basis of daily gaugings of flow, through a long series of 
 years. A theoretical consideration involves a thorough 
 investigation of its geological, physical, and meteorological 
 features. There is no more constancy in natural flow at any 
 season than in the density of the thermometer's mercury. 
 The flow increases as the storms are gathered into the chan- 
 nel, it decreases when the bow has appeared in the heavens ; 
 it increases when the moist clouds sweep low in the valleys, 
 it decreases under the noonday sun ; it increases when the 
 shadows of evening fall across the banks, it decreases when 
 the sharp frosts congeal the streams among the hills. 
 
 64. Periodical Classification of Riparian Rights. 
 The riparian rights subject to curtailment by storage 
 might be classified by periods not greater than monthly, 
 though this is rarely desirable for either party in interest, 
 but they should be based upon the most reliable statistics 
 of monthly rainfall, evaporation, and flow, as analyzed and 
 applied with disciplined judgment to the particular locality 
 in question. 
 
 65. Compensations. In the absence of local statistics 
 of flow, it may become necessary, in settling questions of 
 riparian rights, or adjusting compensation therefor, to esti- 
 mate the periodic flow of a stream by some such method as 
 is suggested above in the general discussion upon the flow 
 of streams, after which it remains for the Court to fix the 
 proportion of the flow that the impounders may manipulate 
 for their own convenience in the successive seasons, and the 
 proportion that is to be passed down the stream regularly 
 or periodically. 
 
EVAPORATION PHENOMENA. 87 
 
 EVAPORATION. 
 
 66. Loss from Reservoir by Evaporation. Losses 
 by evaporations from the surfaces of shallow storage reser- 
 voirs, lakes and ponds are, in many localities, so great in the 
 summer and autumn that their areas are omitted in compu- 
 tations of water derivable from their watersheds. This is a 
 safe practice in dry, warm climates, in which the evapora- 
 tions from shallow ponds may nearly or quite equal the 
 volume of rain that falls directly into the ponds. Marshy 
 margins of ponds are profligate dispensers of vapor to the 
 atmosphere, usually exceeding in this respect the water 
 surfaces themselves. 
 
 67. Evaporation Phenomena. Evaporation is the 
 most fickle of all the meteorological phenomena, and its 
 action is so subtle that we cannot observe its processes. Its 
 results demonstrate that the constituents of water are con- 
 stantly changing their state of existence from that of gas to 
 liquid, liquid to gas, liquid to solid, and solid to gas. The 
 action takes place as well upon polar ice fields or mountain 
 snows, as upon tropical lagoons, though less in degree. 
 The active vapors that form within the waters or porous ice, 
 silently emerge through their surfaces and proceed upon 
 their ethereal mission, and are not again recognizable until 
 they have been once more united into cloud and condensed 
 into rain. 
 
 The rapidity with which water, snow, and ice are con- 
 verted into vapor and pass off by evaporation is depend- 
 ent upon the temperature of the water and atmosphere, but 
 more especially upon their relative temperatures, and upon 
 the dryness and activity of the atmosphere. The formation 
 of vapor in a body of water is supposed to be at its mini- 
 mum when the atmosphere is moist and the atmosphere 
 
88 STORAGE AND EVAPORATION OF WATER. 
 
 and water are quiet and of an equal low temperature, and 
 most active when the atmosphere is dryest and hottest and 
 the wind brisk and water warm. 
 
 M. Aime Drian observed that "when the temperature 
 of the dew point is higher than that of the evaporating sur- 
 face, water is deposited on that surface," which action he 
 styles negative evaporation. 
 
 Undoubtedly the cool surfaces of deep waters condense 
 moisture in summer from warm moist atmospheres wafted 
 across them, and thus at times are gaining in volume while 
 popularly supposed to be losing by evaporation. When 
 winds blow briskly across a water surface, large volumes 
 of unsaturated air are presented in rapid succession to 
 attract its vapors, and the wave motion increases the agita- 
 tion of the body and permits its vapors to escape freely. 
 
 The atmosphere has, however, its limit of power to ab- 
 sorb vapor for each given temperature, and when it is fully 
 saturated it can receive no more without depositing an equal 
 amount, or until its temperature is raised. 
 
 68.' Evaporation from Water. In an instructive 
 paper upon rainfall and evaporation, by Mr. A. Golding, 
 State Engineer at Copenhagen, quoted* by Beardmore, we 
 find some valuable measurements of evaporation in the 
 different seasons, from which the following, relating to 
 evaporation at Emdrup, is extracted. 
 
 * Vide Beardmore's Hydrology, p. 269 d. London, 1862. 
 
EVAPORATION FROM EARTH. 
 
 89 
 
 TABLE No. 24. 
 EVAPORATION FROM WATER AT EMDRUP, DENMARK. 
 
 N. Lat. S54 I// ? E - Long i234 // from Greenwich. 
 
 YEAR. 
 
 d 
 
 ci 
 
 1 
 
 
 < 
 
 Ijl 
 
 ! 
 
 bJD 
 P 
 
 i 
 
 g 
 
 o 
 
 1' 
 
 3 
 
 o 
 
 
 In. 
 
 In. 
 
 In. 
 
 In. 
 
 In. \ In. 
 
 In. 
 
 In 
 
 In. 
 
 In 
 
 In 
 
 In. 
 
 In 
 
 1849 
 1850 
 
 i.i 
 i.i 
 
 o-3 
 0-3 
 
 1.8 
 
 1.2 
 
 2.5 
 
 4.1 | 5-8 
 4-5 5-6 
 
 tl 
 
 4.0 
 4.8 
 
 2.6 
 
 2.4 
 
 i.i 
 1.6 
 
 0.9 
 0.9 
 
 0.6 
 
 O.2 
 
 29-5 
 29.1 
 
 1851 
 1852 
 
 o.S 
 0.7 
 
 0.4 
 o.S 
 
 0. 7 
 
 0.8 
 
 2.4 
 
 4.2 4.8 
 3-8 4.6 
 
 e 
 
 4-5 
 
 2-7 
 2-7 
 
 5 
 7 
 
 0.6 
 0.8 
 
 0-5 
 0-5 
 
 28.4 
 29.4 
 
 1853 
 1854 
 1855 
 1856 
 1857 
 
 o-5 
 
 I.O 
 
 o.S 
 0.7 
 
 O.I 
 
 0.9 
 i.i 
 
 0.6 
 
 0.7 
 0.9 
 0.5 
 
 1.2 
 
 0.6 
 
 I.O 
 
 3-2 
 
 1.2 
 2.1 
 
 4.1 6.2 
 
 3-3 4-5 , 
 2.6 4.1 
 2.8 4.6 
 4.1 6.6 
 
 5.1 
 
 
 
 4.3 
 
 5-9 
 
 4-2 
 
 4-3 
 4.1 
 4.0 
 4-3 
 
 2.8 
 2.6 
 2.8 
 2.O 
 
 3.2 
 
 .1 
 
 .2 
 
 4 
 0.9 
 4 
 
 0.6 
 0.7 
 0.9 
 0.6 
 0.7 
 
 0.1 
 
 0.7 
 o-5 
 0.4 
 
 26.9 
 27.9 
 25-1 
 24.0 
 29.9 
 
 1858 
 
 0.4 
 
 0.7 
 
 1.2 
 
 3-i 
 
 5.1 6.1 
 
 4.9 
 
 5-6 
 
 2.8 
 
 .6 
 
 0.7 
 
 0.4 
 
 30.6 
 
 1859 
 
 
 o-5 
 
 0.7 
 
 
 4-3 5-8 
 
 5-3 
 
 3-8 
 
 1.8 
 
 I.O 
 
 0.7 
 
 o-3 
 
 26.4 
 
 Mean . . 
 
 0.7 
 
 o.5 
 
 0.9 
 
 2.0 
 
 3-7 5-4 
 
 5-2 
 
 4-4 
 
 2.6 
 
 1-3 
 
 0.7 
 
 0-5 
 
 27.9 
 
 Ratio . . 
 
 .301 
 
 .215 
 
 .387 
 
 .860 
 
 1.592 , 2.323 
 
 2-37 
 
 1.892 
 
 1.118 
 
 559 
 
 .301 
 
 .215 
 
 
 Mean.. 
 
 Mean Evaporation from Short Grass, 1852 to 1859 inclusive. 
 0.7 | 0.8 | 1.2 1 2.6 | 4.1 | 5.5 | 5.2 | 4.7 | 2.8 | 1.3 | 0.7 
 
 0.5 | 30.1 
 
 Mean Evaporation from Long Grass, 1849 to 1856 inclusive. 
 Mean.. | 0.9 1 0.6 | 1.4 | 2.6 | 4.7 | 6.7 | 9.3 | 7.9 | 5.2 | 2.9 | 1.3 
 
 Mean Rainfall at same Station, 1848 to 1859 inclusive. 
 Mean.. | 1.5 | 1.7 ] i.o | 1.6 | 1.5 | 2.2 | 2.4 | 2.4 | 2.0 | 2.3 | 1.8 
 
 21.9 
 
 TABLE No. 25. 
 
 69. Evaporation from Earth. MEAN EVAPORATION FROM 
 EARTH, AT BOLTON LE MOORS,* LANCASHIRE, ENG., 1844 TO 
 1853, INCLUSIVE. 
 
 Lat. 533o" N. ; Height above the Sea, 320 Feet. 
 
 
 c 
 
 ci 
 h- 
 
 jd 
 
 <u 
 
 
 
 | 
 
 
 
 * 
 
 i 
 
 3 
 
 _>> 
 
 3 
 
 H- > 
 
 $ 
 
 i 
 
 $ 
 
 1.28 
 599 
 
 i 
 
 1 
 
 i 
 
 25.65 
 
 Mean . . 
 Ratio. . . 
 
 0.64 
 .299 
 
 0-95 
 .444 
 
 1-59 
 739 
 
 2.59 
 
 I.2I2 
 
 4.38 
 2.049 
 
 3.84 
 1.796 
 
 4.02 
 
 1.887 
 
 3.06 
 I-43I 
 
 2.02 
 
 945 
 
 0.81 
 379 
 
 0.47 
 
 .220 
 
 Mean Rainfall at same Station, 1844 to 1853 inclusive. 
 Mean..] 4.63 | 4.03 j 2.25 | 2.22 | 2.23 | 4 7 | 4-32 | 4-77 [ 3-79 [ S-o? | 4.64 | 3-94 | 45-96 
 
 * Beardmore's Hydrology, p. 325. 
 
90 
 
 STORAGE AND EVAPORATION OF WATER. 
 
 MEAN EVAPORATION FROM EARTH, AT WHITEHAVEN, CUMBERLAND, 
 ENG., 1844 TO 1853 INCLUSIVE. 
 
 Lat. 54 30" N. ; Height above the Sea, 90 feet. 
 
 
 1 
 
 4 
 
 h 
 
 | 
 
 tgi 
 & 
 
 < 
 
 t>> 
 
 <u 
 a 
 
 3 
 H- > 
 
 _>, 
 
 3 
 
 H- > 
 
 
 
 <J 
 
 i 
 
 S 
 
 > 
 
 
 
 fe 
 
 8 
 
 Q 
 
 "3 
 5 
 
 Mean. 
 Ratio . . 
 
 0.95 
 39 
 
 I. 01 
 
 4 J 5 
 
 1.77 
 .727 
 
 2.71 
 1.113 
 
 4.11 
 
 1.689 
 
 4-25 
 1.746 
 
 4- I 3 
 1.697 
 
 3-29 
 1-352 
 
 2 . 9 6 
 i. 216 
 
 i. 7 6 
 723 
 
 1.25 
 
 513 
 
 1.02 
 .419 
 
 29.21 
 
 Mean Rainfall. at same Station, 1844 to 1853 inclusive. 
 Mean..] 5.1 [ 3.4 [ 2.5 ] 2.2 [ 1.9 | 3.1 | 4.3 | 4.3 | 3.! [ 5.3 | 4.5 [ 3.8 | 43 . 5 
 
 7O. Examples of Evaporation. Charles Greaves, 
 Esq., conducted a series of experiments upon percolation 
 and evaporation, at Lee Bridge, in England, .continuously 
 from 1860 to 1873, and has given the results * to the Insti- 
 tution of Civil Engineers. The experiments were on a large 
 scale, and the very complete record is apparently worthy 
 of full confidence. 
 
 The evaporation boxes were one yard square at the sur- 
 face and one yard deep. Those for earth were sunk nearly 
 flush in the ground, and that for water floated in the 
 river Lee. The mean annual rainfall during the time was 
 27.7 inches. The annual evaporations from soil were, mini- 
 mum 12.067 inches ; maximum 25.141 inches ; and mean 
 19.534 inches : from sand, minimum 1.425 inches ; maxi- 
 mum 9.102 inches; and mean 4.648 inches: from water, 
 minimum 17.332 inches ; maximum 26.933 inches ; and 
 mean 22.2 inches. 
 
 Some experimental evaporators were constructed at 
 Dijon on the Burgundy canal, and are described in Annales 
 des Fonts et CTiausses. They are masonry tanks lined 
 with zinc, eight feet square and one and one-third feet deep, 
 
 * Trans. Inst. Civil Engineers, 1876, Vol. XLV, p. 33, 
 
RATIOS OF EVAPORATION. 91 
 
 and are sunk in the ground. From 1846 to 1852, there was 
 a mean annual evaporation of 26.1 inches from their water 
 surfaces against a rainfall of 26.9 inches. At the same time 
 a small evaporator, one foot square, placed near the larger, 
 gave results fifty per cent, greater. 
 
 Observations of evaporation from a water surface at the 
 receiving reservoir in New York indicated the mean annual 
 evaporation from 1864 to 1870 inclusive as 39.21 inches, 
 which equaled 81 per cent, of the rainfall. 
 
 On the West Branch of the Croton River, an apparatus* 
 was arranged for the purpose of measuring the evaporation 
 from water surface, consisting of a box four feet square and 
 three feet deep, sunk in the earth in an exposed situation 
 and filled with water. The mean annual evaporation was 
 found to be 24.15 inches, or about fifty per cent, of the 
 rainfall. The observations were made twice a day with 
 care. The maximum annual evaporation was 28 inches. 
 
 Evaporations from the surface of water in shaDow tanks 
 are variously reported as follows : 
 
 At Cambridge, Mass., one year, 56.00 inches depth. 
 
 " Salem, " " " 56.00 " 
 
 " Syracuse, N. Y., " " 50.20 " 
 
 * " Ogdensburgh, N. Y., " " 49.37 " 
 
 " Dorset, England, three " 25.92 " 
 
 " Oxford, " five " 31.04 " 
 
 " Demerara, three " 35.12 " 
 
 " Bombay, five " 82.28 " 
 
 71. Katios of Evaporation. In the eastern and mid- 
 dle United States, the evaporation from storage reservoirs, 
 having an average depth of at least ten feet, will rarely 
 exceed sixty per cent, of the rainfall upon their surface. 
 
 * Vide paper on " Flow of the West Branch of the Croton River," by J. Jas. 
 R. Croes. Traus. Am. Soc. Civ. Engrs., July, 1874, p. 83. 
 
92 STORAGE AND EVAPORATION OF WATER. 
 
 The ratio of evaporation in each month to the monthly aver- 
 age evaporation, or one-twelfth the annual depth, is esti- 
 mated to be, for an average, approximately as follows : 
 
 TABLE No. 26. 
 MONTHLY RATIOS OF EVAPORATION FROM RESERVOIRS. 
 
 
 a 
 
 i 
 
 35 
 
 ctf 
 
 
 
 6 
 
 u 
 
 c 
 
 3 
 
 H- , 
 
 jA 
 
 "3 
 
 > ) 
 
 
 
 < 
 
 2.00 
 
 ! 
 
 1 
 
 > 
 o 
 fe 
 
 cJ 
 
 Q 
 35 
 
 Mean ratio.. .. 
 
 3 
 
 50 
 
 .80 
 
 MS 
 
 I. 7 
 
 1.85 
 
 1.45 
 
 75 
 
 5 
 
 The following ratios of the annual evaporation from 
 water surfaces are equivalent to the above monthly ratios, 
 and may be used' as multipliers directly into the annual 
 evaporation to compute an equivalent depth of rain in 
 inches upon the given surface in action. Beneath the ratios 
 are given the equivalent depths for each month of 40 inches 
 annual rain, assuming the annual evaporation to equal 
 sixty per cent, of the rainfall, or 24 inches depth. 
 
 TABLE No. 27. 
 MULTIPLIERS FOR EQUIVALENT INCHES OF RAIN EVAPORATED. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 , 
 
 
 
 
 i 
 
 ij 
 
 
 
 1 
 
 c 
 3 
 i , 
 
 >> 
 
 3 
 t 
 
 be 
 I 
 
 1 
 
 $ 
 
 
 
 i 
 
 * 
 
 1 
 
 H 
 
 Ratio of annual evapora- 
 tion 
 
 
 
 
 .0667 
 
 .1208 
 
 
 
 1667 
 
 1208 
 
 
 
 
 
 Equivalent depth of rain 
 
 6 
 
 
 1.0 
 
 i 6 
 
 
 
 
 
 
 
 
 
 2 AIM 
 
 
 
 
 
 
 
 
 
 
 
 
 I.O 
 
 
 
 12. Kesultant Effect of Kaiii and Evaporation. 
 
 For the purpose of comparing the effects upon a reservoir 
 replenished by rain only, let us assume the available rain- 
 fall to be eight-tenths of 40 inches per annum, and the 
 ratios of mean monthly rain, and the ratios of annual rain 
 in inches depth, to be as per the following table : 
 
PRACTICAL EFFECT UPON STORAGE. 
 
 93 
 
 
 1 
 
 t 
 
 1 
 
 
 
 < 
 
 
 
 1 
 
 i 
 
 3 
 
 > i 
 
 t 
 
 < 
 
 ! 
 
 g 
 
 > 
 o 
 fe 
 
 1 
 
 Ratio of aver. 
 
 
 
 
 
 
 
 
 
 
 
 
 
 monthly rain 
 
 75 
 
 .83 
 
 .00 
 
 I.IO 
 
 1.30 
 
 i. 08 
 
 1. 12 
 
 1.20 
 
 I. 00 
 
 95 j -93 
 
 .84 
 
 Ratio of .8 of 
 
 
 
 
 
 
 
 
 
 
 1 
 
 
 annual rain. 
 
 .0625 
 
 .0692 
 
 .0750 
 
 .0917 
 
 .1083 
 
 .0900 
 
 0933 
 
 .1000 
 
 .0833 
 
 .0792 
 
 .0775 
 
 .0700 
 
 Equiv. inches 
 
 
 
 
 
 
 
 
 
 
 
 
 
 of rain 
 
 2.00 
 
 2.21 
 
 2.40 
 
 2-93 
 
 3.47 
 
 2.88 
 
 2.99 
 
 3-20 
 
 2.67 
 
 .2.53 
 
 2.48 
 
 224 
 
 Comparing, in the two last tables, and their lowest 
 columns, the inches of gain by rainfall upon the reservoir, 
 supposing the sides of the reservoir to be perpendicular, and 
 the inches of loss from the same reservoir by evaporation, 
 we note that the gain preponderates until June, then the 
 loss preponderates until in November. 
 
 73. Practical Effect upon Storage. Since the prac- 
 tical value of storage is ordinarily realized between May 
 and November, the excess of loss during that term is, 
 practically considered, the annual deficiency from the reser- 
 voir chargeable to evaporation. We compute its maximum 
 in the following table, commencing the summation in June, 
 all the quantities being in inches depth of rain. 
 
 
 I 
 
 1 
 
 3* 
 
 i 
 
 I 
 
 >- 
 
 I 
 
 ! 
 
 1 
 
 3 
 
 > 
 
 o 
 
 25 
 
 1 
 
 Gain by rain- 
 
 
 
 
 
 
 
 
 
 
 
 
 
 inches 
 
 2.00 
 
 2.21 
 
 240 
 
 2.93 
 
 347 
 
 2.88 
 
 2.99 
 
 3.20 
 
 2.67 
 
 2.53 
 
 2.48 
 
 2.24 
 
 Loss by evapo- 
 
 
 
 
 
 
 
 
 
 
 
 j 
 
 ration inches 
 Diff eren c e 
 
 .60 
 
 .70 
 
 1 .00 
 
 i. 60 
 
 2.90 
 
 3-40 
 
 3-70 
 
 4.00 
 
 2.90 
 
 1.50 
 
 1. 00 
 
 0.70 
 
 inches 
 Max. deficiency 
 
 -)-I.40 
 
 + I.SI 
 
 + 1.40 
 
 + I-33 
 
 +0-57 
 
 0.62 
 
 0.71 
 
 0.80 
 
 -0.23 
 
 +0.97 
 
 + 1.48 
 
 + 1.54 
 
 after June 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0.62 
 
 1-33 
 
 2.13 
 
 2.36 
 
 1.39 
 
 + 0.09 
 
 .... 
 
 
 
 
 
 
 
 If the classification is reduced to daily periods instead 
 of monthly, the maximum deficiency, according to the 
 above basis, will in a majority of years exceed three inches. 
 
CHAPTEE VI. 
 
 SUPPLYING CAPACITY OF WATERSHEDS. 
 
 74. Estimate of Available Annual Flow of Streams. 
 
 Applying our calculations in the last chapter, of available 
 flow of water from the unit of watershed, one square mile, 
 and modifying it by the elements of compensation, storage, 
 evaporation, and percolation, we then estimate mean annual 
 quantities of low-cycle years, applicable to domestic con- 
 sumption, as follows : 
 
 Assumed mean annual rainfall 40 inches. 
 
 Flow of stream available for storage, 40 per cent, of mean rain = 16 inches of rain. 
 
 This available rain is applied to : 
 
 ist. Compensation to riparian owners, say 16.8 p. c. of mean rain = 6.72 in. of rain. 
 
 2d. Evaporation from surface of storage reservoir, u 2.4 " " " " = .96 " " " 
 3d. Percolation from storage reservoir, " 2.4 " " ' " = .96 " " " 
 
 4th. Balance available for consumption, 18.4 4t " " " = 7 . 3 6 u " u 
 
 Total 40 per cent. 16 inches. 
 
 The 7.36 inches of rain estimated as available from a 
 40-inch annual rain equals 17,098,762 cubic feet of water, 
 which is equivalent to a continuous supply of seven cubic 
 feet per day (= 52.36 gals.) each, to 6,692 persons. 
 
 By applying to the annual results the monthly ratios, 
 and thus developing the monthly surpluses or deficiencies 
 of flow, we shall have in the algebraic sum of the deficien- 
 cies the volume of storage necessary to make forty per cent, 
 of the rainfall available, and this storage must ordinarily 
 approximate one-third of the annual flow available for 
 storage. 
 
MONTHLY AVAILABLE STORAGE REQUIRED. 95 
 
 75. Estimate of Monthly Available Storage Re- 
 
 quired. Computation of a supply, and the required 
 storage ; applied to one square mile of watershed as a unit 
 of area. 
 
 Assumed data: Population to be supplied. 6,500 per- 
 sons, consuming 7 cubic feet per capita daily,. each ; 
 
 Mean annual rainfall, 40 inches, and eight-tenths = 
 32 inches of rain, in the low-cycle years ; 
 
 Available flow of stream, fifty per cent. . of eight-tenths 
 of rain = 16 inches ; 
 
 Compensation each month, .168 of one-twelfth the mean 
 annual depth of rain = .56 inches each month uniformly ; 
 
 Evaporation annually from the reservoir surface , only, 
 sixty per cent, of the depth of mean annual rain, or 24 
 inches ; and monthly, sixty per cent, of one-twelfth the 
 annual evaporation = 2 inches. 
 
 Area of storage reservoir, .04 square mile,* or 25.6 acres, 
 with equivalent available draught of ten feet for that sur- 
 face. The evaporation of two inches from four hundredths 
 of a square mile = .08 inch from one square mile. 
 
 Volume of percolation assumed to equal volume of 
 evaporation from the reservoir surface. 
 
 The monthly ratios will be multiplied into 
 
 P " = '<* - ^r the monthly flow. 
 
 40 in. mean rain 
 
 =- = 3.3333 in. for monthly compensation. 
 
 * 
 
 .04 x - - ' ' - = .08 in. for monthly evaporation from reservoir. 
 12 months 
 
 " = .08 in. for monthly percolation from reservoir. 
 
 6500 x 7 cu. ft. x 30.4369 days = 1,384,879 cu. ft. for monthly con- 
 
 sumption. 
 
 * A unit of reservoir area, for each square mile unit of watershed. 
 
96 
 
 SUPPLYING CAPACITY OF WATERSHEDS. 
 
 TABLE No. 28. 
 MONTHLY SUPPLY TO, AND DRAFT FROM, A STORAGE RESERVOIR. 
 
 MONTH. 
 
 Jan. | 
 Feb. | 
 
 Mar. j 
 
 Apr. j 
 (* 
 
 May | 
 June -j 
 July | 
 Aug. ] 
 Sept. | 
 Oct. -j 
 Nov. | 
 Dec. | 
 
 MONTHLY 
 FLOW. 
 
 cubic feet. 
 
 MONTHLY 
 COMPEN- 
 SATION. 
 
 cubic feet. 
 
 MONTHLY 
 EVAPORA- 
 TION FROM 
 RESER- 
 VOIR. 
 cubic feet. 
 
 MONTHLY 
 PERCOLA- 
 TION FROM 
 RESER- 
 VOIR. 
 cubic Jeet. 
 
 MONTHLY 
 DOMESTIC 
 CONSUMP- 
 TION. 
 
 cubic feet. 
 
 SURPLUS. 
 cubic feet. 
 
 DEFICIENCY. 
 cubic feet. 
 
 Gain, 
 
 Ratio, 1.65 
 5,111,040 
 
 Ratio, 1.50 
 4,646,400 
 
 Ratio, 1.65 
 5,111,040 
 
 Ratio, 1.45 
 4490,746 
 
 Ratio, .85 
 2,632,186 
 
 Ratio, .75 
 2,323,200 
 
 Ratio, .35 
 1,084,934 
 
 Ratio, .25 
 773,626 
 
 Ratio, .30 
 929,280 
 
 Ratio, .45 
 1,393,920 
 
 Ratio, 1.20 
 3,717,120 
 
 Ratio, i. 60 
 4,955,386 
 
 Loss. 
 Ratio, .168 
 1,300,992 
 
 .168 
 1,300,992 
 
 .168 
 1,300,992 
 
 .168 
 1,300,992 
 
 .168 
 1,300,992 
 
 .168 
 1,300,992 
 
 .168 
 1,300,992 
 
 .168 
 1,300,992 
 
 .,68 
 
 I,3OO,992 
 
 .168 
 I,3OO,992 
 
 .168 
 I,3OO,992 
 
 .168 
 1,300,992 
 
 Loss. 
 Ratio, .30 
 
 55,757 
 
 35 
 65,050 
 
 5 
 92,928 
 
 .80 
 148,685 
 
 i-45 
 269,491 
 
 1.70 
 315,955 
 1.85 
 343,834 
 
 2.OO 
 371,712 
 
 L45 
 269,491 
 
 75 
 I39,39 2 
 
 So 
 92,928 
 
 35 
 65,050 
 
 Loss. 
 Ratio, .30. 
 
 55,757 
 
 35 
 65,050 
 
 So 
 92,928 
 
 .80 
 148,685 
 
 i.45 
 269,491 
 
 1.70 
 315,955 
 1.85 
 343,834 
 
 2.00 
 371,712 
 
 i-45 
 269,491 
 
 75 
 139,392 
 
 5 
 92,928 
 
 35 
 65,050 
 
 Used. 
 
 Ratio, 1.05 
 1,454,123 
 
 1. 10 
 
 1,523,367 
 
 .90 
 
 1,246,391 
 
 .85 
 1,177,147 
 
 .90 
 1,246,391 
 
 1.00 
 
 1,384,879 
 
 1.20 
 1,661,855 
 
 1.25 
 1,731,099 
 1.05 
 1,454,123 
 .90 
 1,246,391 
 
 85 
 1,177,147 
 
 95 
 1,315,635 
 
 2,311,507 
 1,691,941 
 
 2,447,497 
 1,715.237 
 
 
 
 
 
 454,119 
 994,581 
 2,565,581 
 3,037,889 
 2,364,817 
 1,432,247 
 
 
 
 
 
 
 1,053.125 
 2,208,659 
 
 
 Totals 
 
 37,272,270 
 
 T5,6lI,9O4 
 
 2,232,072 
 
 2,232,072 
 
 16,618,548 
 
 11,427,966 
 
 10,849,234 
 
 From certain localities no claim will arise for diversion 
 of the water, or the diversion may be compensated for by 
 the payment of a cash bonus, in which case the proportion 
 of rainfall applicable to domestic consumption will be a 
 little more than doubled, and approximately as follows, 
 neglecting percolation from the storage reservoir. 
 
MONTHLY AVAILABLE STORAGE REQUIRED. 
 
 97 
 
 The monthly ratios will here be multiplied into, 
 
 40 in. x .8 x .^o p. c. /- 
 
 - = 1.3333 m - for tne monthly flow. /, / 
 12 months , ^ / /J 
 
 40 in. x .60 p. c. 
 .04 x - = .08 m. for monthly evaporation fronvfraservoir. .<! 
 
 12 months * y,, fy 
 
 13,500 persons x 7 cu. ft. x 30.4369 days = 2,876,467! cu. ft 6$, x < 
 
 monthly consumption. ftp J" 
 
 TABLE No. 29. <\V 
 
 MONTHLY SUPPLY TO, AND DRAFT FROM, A STORAGE RESERVOIR 
 (without compensation). 
 
 MONTH. 
 
 MONTHLY 
 FLOW. 
 
 cubic feet. 
 
 MONTHLY 
 EVAPORATION 
 
 FROM 
 
 RESERVOIR. 
 cubic feet. 
 
 MONTHLY 
 DOMESTIC 
 CONSUMPTION. 
 
 cubic feet. 
 
 SURPLUS. 
 cubic feet. 
 
 DEFICIENCY. 
 cubic feet. 
 
 Jan. | 
 
 Gain. 
 
 Ratio, 1.65 
 5, 180,736 
 
 Loss. 
 Ratio, .30 
 
 Used. 
 
 Ratio, 1.05. 
 i Q2O 2QO 
 
 2 IO2 889 
 
 
 Feb. | 
 
 Ratio, 1.50 
 4,646,400 
 
 35 
 
 1. 10 
 
 3,164 114 
 
 1,417,2^6 
 
 
 Mar. -j 
 
 Ratio, 1.65 
 5,180,736 
 
 50 
 Q2,Q28 
 
 .90 
 2,588,820 
 
 2,4Q8,o88 
 
 
 April -j 
 
 Ratio, 1.45 
 4,400,746 
 
 .80 
 
 148 68^ 
 
 .85 
 2 4.4.4. QQ7 
 
 I 897 064 
 
 
 May | 
 
 Ratio, .85 
 2,632,186 
 
 1-45 
 260,401 
 
 .90 
 
 2 588 82O 
 
 
 226 125 
 
 June -j 
 
 Ratio, .75 
 2,323,200 
 
 1.70 
 
 I.OO 
 
 2,876,467 
 
 
 869 222 
 
 July | 
 
 Ratio, .35 
 1,084,934 
 
 1.85 
 343,834 
 
 i. 20 
 
 3,451,760 
 
 
 2 7IO 660 
 
 Aug. -j 
 
 Ratio, .25 
 737,626 
 
 2.00 
 371,712 
 
 
 
 3,22Q,67O 
 
 Sept. | 
 
 Ratio, .30 
 
 Q2Q 28O 
 
 1-45 
 
 260 401 
 
 1.05 
 7 O2O 2QO 
 
 
 2 360 5OI 
 
 Oct. | 
 
 Ratio, .45 
 l.^Q^,Q2O 
 
 75 
 iqn -JQ2 
 
 .90 
 2 588,820 
 
 
 
 Nov. -j 
 
 Ratio, 1.20 
 3717 1 2O 
 
 5 
 Q2 928 
 
 .85 
 
 2 AAA QQ7 
 
 I 179 195 
 
 
 Dec. | 
 
 Ratio, 1.60 
 4,955,386 
 
 35 
 65,050 
 
 95 
 2,732,644 
 
 2,157,692 
 
 
 Totals, 
 
 37,272,270 
 
 2,232,072 
 
 34,517,603 
 
 11,253,064 
 
 10,730,470 
 
98 SUPPLYING CAPACITY OF WATERSHEDS. 
 
 76. Additional Storage Required. Forty inches 
 of rainfall on one square mile equals a volume of 92,928,000 
 cubic feet. The deficiency as above computed is nearly 
 twelve per cent, of this quantity, and calls for an available 
 volume of water in store early in May, or at the beginning 
 of a drought, equal to about one-eighth the mean annual 
 rainfall. 
 
 The calculations of supply and draught in the two 
 monthly tables given above refer to mean quantities of low- 
 cycle years, and not to extreme minimums. The seasons of 
 minimum flow, which are also, usually, the seasons of 
 maximum evaporation from the storage reservoirs and of 
 maximum domestic consumption, are in the calculations 
 supposed to be tided over by a surplus of storage provided 
 in addition to the mean storage required for the series of 
 low-cycle years. The storage should therefore be in excess 
 of the mean deficiency as above computed at least twenty- 
 five per cent., or should equal at least fifteen per cent, of the 
 mean annual rainfall. 
 
 If the storage is less than fifteen per cent., the safe 
 available supply is liable to be less than the calculations 
 given. 
 
 If the area of the storage reservoir is greater per square 
 mile of watershed than assumed above, the loss by evapo- 
 ration from the water surface will be proportionately in- 
 creased, and must be compensated for by increased storage. 
 
 77. Utilization of Flood Flows. The calculations 
 as above assume that fifty per cent, of the annual rainfall 
 is the available annual flow in the stream. The remaining 
 fifty per cent, is assumed to be lost through the various 
 processes of nature and by floods. If the storage is still 
 further increased, an additional portion of the flood flow 
 can be utilized, and sometimes fifty per cent, or even sixty 
 
INFLUENCE OF STORAGE. 99 
 
 per cent, of the annual rainfall utilized for domestic con- 
 sumption, or made applicable at the outlet of the reservoir 
 for power. Hence, when it is desired to utilize the greatest 
 possible portion of the flow, the storage should equal twenty 
 or twenty-five per cent, of the mean annual rainfall. 
 
 78. Qualification of Deduced Ratios. The ratios 
 of flow, evaporation, and consumption, as above used in 
 the calculations, are not assumed to be universally appli- 
 cable, but are taken as safe general average ratios for the 
 Atlantic Coast and Middle States. The winter consump- 
 tion will be less in the lower Middle and Southern States, 
 and also in very efficiently managed works of Northern 
 States ; but the summer consumption tends to be greater in 
 the lower Middle and Southern States, where the evapora- 
 tion and rainfall are greater also. 
 
 The results upon the Pacific slope can scarcely be gen- 
 eralized to any profit, since within a few hundred miles it 
 presents extremes, from rainless desert to tha maximum 
 rainfall of the continent, and from vaporless atmosphere to 
 constant excessive humidity. 
 
 79. Influence of Storage upon a Continuous 
 Supply. A safe general estimate of the maximum contin- 
 uous supply of water to be obtained from forty inches of 
 annual rain upon one square mile of watershed, provided 
 the storage equals at least fifteen per cent, of the rainfall, 
 gives 7 cubic feet (= 52.36 gals.) per capita daily, to from 
 13000 to 15000 persons, dependent upon the amount of 
 available storage of winter and flood flows ; or say, three- 
 quarters of a million gallons of water daily. 
 
 The same area and rain, with but one month's deficiency 
 storage, can be safely counted upon to supply but about 
 3,000 persons with an equal daily consumption, or 157,000 
 gallons of water daily. From the same area and rain, with 
 
100 SUPPLYING CAPACITY OF WATERSHEDS. 
 
 no storage, a flashy stream may fail to supply 1,000 persons 
 to the full average demand in seasons of severe drought. 
 
 Hence the importance of the storage factor in the calcu- 
 lation. 
 
 The above estimates are based upon mean rainfalls of 
 low-cycle ( 47) years ; therefore the results may be ex- 
 pected to be twenty per cent, greater in years of general 
 average rainfall. 
 
 80. Artificial Gathering Areas. When resort is 
 necessarily had to impervious artificial collecting areas for 
 a domestic water supply, as when dwellings are located 
 upon vegetable moulds or low marsh areas, bituminous 
 rock surfaces, limestone surfaces, or, as in Venice, where 
 the sheltering roofs are the gathering areas of the house- 
 holds, the proportion of the rainfall that may be run into 
 cisterns is very large. If such cisterns are of sufficient 
 capacity and their waters protected from evaporation, eighty 
 per cent, of the rainfall upon the gathering areas may thus 
 be made available., though special provisions for its clarifi- 
 cation will be indispensable. 
 
 In such case, a roof area equivalent to 25 feet by 100 
 feet might furnish from a forty-inch rainfall a continuous 
 supply of 3 cubic feet (=22.44 gallons) per day to six per- 
 sons, which would be abundant for the household uses for 
 that number of persons. 
 
 81. Recapitulation of Rainfall Ratios. Recapitu- 
 lating, in the form of general average annual ratios, relating 
 to the mean rainfall upon undulating crystalline or diluvial 
 surface strata, as unity, we have : 
 
 Ratio of mean annual rainfall '. i.oo 
 
 Ratio of mean rainfall of lowest three-year cycles 80 
 
 Ratio of minimum annual rainfall 7O 
 
 Ratio of mean annual flow in stream (of the given year's rain) 60 
 
RAINFALL RATIOS. 
 
 101 
 
 Ratio of mean summer flow in stream (of the given year's rain) 25 
 
 Ratio of low summer flow in stream " 05 
 
 Ratio of annual available flow in stream 50 
 
 Ratio of storage necessary to make available 50 per cent, of annual rain. .15 
 Ratio of general evaporation from earths, and consumption by the pro- 
 cesses of vegetation 40 
 
 Ratio of percolation through the earth (included also in the flow of 
 
 streams) 25 
 
 Ratio of mean rainfall collectible upon impervious artificial or primary 
 
 rock surfaces 80 
 
 The monthly ratios of these annual ratios are to be taken 
 in ordinary calculations of water supplies, and each annual 
 ratio to be subjected to the proper modification adapting it 
 to a special local application. 
 
 T A BL E No- SO. 
 RATIOS OF MONTHLY RAIN, FLOW, EVAPORATION, AND CONSUMPTION. 
 
 
 
 JQ 
 
 u 
 
 g 
 
 
 
 | 
 
 
 
 * 
 
 J 
 
 a~' 
 
 > 
 
 g 
 
 
 
 
 
 % 
 
 <5 
 
 s 
 
 3 
 
 3 
 
 <J 
 
 $ 
 
 
 I 
 
 Q 
 
 Ratios of average monthly rain 
 Ratios of av. monthly flow of streams. 
 Ratios of av. monthly evap. from water 
 Ratios of average monthly consump- 
 
 .: 
 
 .30 
 
 8 3 
 1.50 
 
 35 
 
 50 
 
 1. 10 
 
 3 
 
 1. 08 
 75 
 1.70 
 
 1.12 
 
 sits 
 
 1.20 
 25 
 2.00 
 
 I.OO 
 
 30 
 
 i-45 
 
 95 
 45 
 75 
 
 93 
 
 1.20 
 50 
 
 .84 
 i. 60 
 35 
 
 tion of water .... 
 
 
 I.ZO 
 
 qo 
 
 gc 
 
 .00 
 
 I.OO 
 
 i. 20 
 
 1.25 
 
 1.05 
 
 9 
 
 gr 
 
 95 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
OHAPTEE VII. 
 
 SPRINGS AND WELLS. 
 
 82. Subterranean Waters. A portion of the rain, 
 perhaps one-fourth part of the whole, distilled upon the 
 surface of the earth, penetrates its soils, the interstices of 
 the porous strata, the crevices of the rocks, and is gathered 
 in the hidden recesses. These subterranean reservoirs were 
 filled in the unexplored past, and their flow continues in 
 the present as they are replenished by new rainfalls. 
 
 83. Their Source the Atmosphere. We find no 
 reason to suppose that Nature duplicates her laboratory of 
 the atmosphere in the hidden recesses of the earth, from 
 whence to decant the sparkling springs that issue along the 
 valleys. On the other hand, we are often able to trace the 
 course of the waters from the storm-clouds, into and through 
 the earth until they issue again as plashing fountains and 
 flow down to the ocean. 
 
 The clouds are the immediate and only source of supply 
 to the subterranean watercourses, as they are to the sur- 
 face streams we have just passed in review. 
 
 The subterranean supplies are subject indirectly to at- 
 mospheric phenomena, temperatures of the seasons, surface 
 evaporations, varying rainfalls, physical features of the 
 surface, and porosity of the soils. Especially are the shal- 
 low wells and springs sensitively subject to these influences. 
 
 84. Porosity of Earths and Rocks. Respecting the 
 porosity and absorptive qualities of different earths, it may 
 be observed that clean silicious sand, when thrown loosely 
 together, has voids between its particles equal to nearly 
 
FIG. 131. 
 
 INTERCEPTING WELL, PROSPECT PARK, BROOKLYN. 
 
THEIR SOURCE THE ATMOSPHERE. 103 
 
 one-third its volume of cubical measure ; that is, if a tank 
 of one cubic yard capacity is filled with quartzoid sand, 
 then from thirty-to thirty -five per cent, of a cubic yard of 
 water can be poured into the tank with the sand without 
 overflowing. 
 
 Gravel, consisting of small water- worn stones or pebbles, 
 intermixed with grains of sand, has ordinarily twenty to 
 twenty-five per cent, of voids. 
 
 Marl, consisting of limestone grains, clays, and silicious 
 sands, has from ten to twenty per cent, of voids, according 
 to the proportions and thoroughness of admixture of its 
 constituents. 
 
 Pure clays have innumerable interstices, not easily 
 measured, but capable of absorbing, after thorough drying, 
 from eight to fifteen per cent, of an equal volume of water. 
 
 The water contained in clays is so fully subject to laws 
 of molecular attraction, owing to the minuteness of the 
 individual interstices, that great pressure is required to give 
 it appreciable flow. 
 
 Water flows with some degree of freedom through sand- 
 stones, limestones, and chalks, according to their textures, 
 and they are capable of absorbing from ten to twenty per 
 cent, of their equal volumes of water. 
 
 The primary and secondary formations, according to 
 geological classification, as for instance, granites, serpen- 
 tines,- trappeans, gneisses, mica-slates, and argillaceous 
 schists, are classed as impervious rocks, as are, usually, 
 the several strata of pure clays that have been subjected to 
 great superincumbent weight. 
 
 The crevices in the impervious rocks, resulting from 
 rupture, may, however, gather and lead away, as natural 
 drains, large volumes of the water of percolation. 
 
 The free flow of the percolating water toward wells or 
 
104 SPRINGS AND WELLS. 
 
 spring, is limited and controlled, not only by the porosity 
 of the strata which it enters, but also by their inclination, 
 curvature, and continuous extent, and by the impervious- 
 ness of the underlying stratum, or plutonic rock. 
 
 85. Percolations in the Upper Strata. Shallow 
 well and spring supplies are, usually, yields of water from 
 the drift formation alone. Their temperatures may be va- 
 riable, rising and falling gradually with the mean tempera- 
 tures of the surface soils in the circuits of the seasons, and 
 they may not be wholly freed from the influence of the 
 decomposed organic surface soils. Their flow is abundant 
 when evaporation upon the surface is light, though slack- 
 ened when the surface is sealed by frost. 
 
 A variable spring, and it is the stream at its issue that 
 we term a spring, indicates, usually, a flow from a shallow, 
 porous surface stratum, say, not exceeding 50 feet in depth, 
 though occasionally its variableness is due to peculiar 
 causes, as the melting of glaciers in elevated regions, and 
 atmospheric pressure upon sources of intermittent springs. 
 
 Porous strata of one hundred feet in depth or more give 
 comparatively uniform flow and temperature to springs. 
 
 86. The Courses of Percolation. Gravitation tends 
 to draw the particles of water that enter the earth directly 
 toward the center of the earth, and they percolate in that 
 direction until they meet an impervious strata, as clay, 
 when they are forced to change their direction and follow 
 along the impervious surface toward an outlet in a valley, 
 and possibly to find an exit beneath a lake or the ocean. 
 
 When the underlying impervious strata has considerable 
 average depth, it may have been unevenly deposited in 
 consequence of eddies in the depositing stream, or crowded 
 into ridges by floating icebergs, or it may have been worn 
 into valleys by flowing water. Subsequent deposits of 
 
SUBTERRANEAN RESERVOIRS. 105 
 
 sand and gravel would tend to fill up the concavities and 
 to even the new surface, hiding the irregularities of the 
 lower strata surface. 
 
 The irregularities of the impervious surface would not 
 be concealed from the percolating waters, and their flow 
 would obey the rigid laws of gravitation as unswervingly 
 as do the showers upon the surface, that gather in the chan- 
 nels of the rocky hills. 
 
 Springs will appear where such subterranean channels 
 intercept the surface valleys. The magnitude of a spring 
 will be a measure of the magnitude of its subterranean 
 gathering valley. 
 
 87. Deep Percolations. The deep flow supplies of 
 wells and springs are derived, usually, from the older 
 porous stratifications lying below the drift and recent clays. 
 The stratified rocks yielding such supplies have in most 
 instances been disturbed since their original depositions, 
 and they are found inclined, bent, or contorted, and some- 
 times rent asunder with many fissures, and often intercepted 
 by dykes. 
 
 88. Subterranean Reservoirs. Subterranean basins 
 store up the waters of the great rain percolations and 
 deliver them to the springs or wells in constant flow, as 
 surface lakes gather the floods and feed the streams with 
 even, continuous delivery. A concave dip of a porous 
 stratum lying between two impervious strata presents favor- 
 able conditions for an " artesian" well, especially if the 
 porous stratum reaches the surface in a broad, concentric 
 plane of great circumference, around the dip, forming an 
 extensive gathering area. 
 
 Waters are sometimes gathered through inclined strata 
 from very distant watersheds, and sometimes their course 
 
106 SPRINGS AND WELLS. 
 
 leads under considerable hills of more recent deposit than 
 the stratum in which the water is flowing. 
 
 The chalks and limestones do not admit of free percola- 
 tion, and are unreliable as conveyers of water from distant 
 gathering surfaces, since their numerous fissures, through 
 which the water takes its course, are neither continuous nor 
 uniform in direction. 
 
 89. The Uncertainties of Subterranean Searches. 
 The conditions of the abundant saturation and scanty 
 saturation of the strata, and their abilities to supply water 
 continuously, are very varied, and may change from the 
 first to the second, and even alternate, with no surface indi- 
 cations of such result ; and the subterranean flow may, in 
 many localities, be in directions entirely at variance with 
 the surface slopes and flow. 
 
 Predictions of an ample supply of water from a given 
 subterranean source are always extremely hazardous, until 
 a thorough knowledge is obtained of the geological posi- 
 tions, thickness, porosity, dip, and soundness of the strata, 
 over all the extent that can have influence upon the flow at 
 the proposed shaft. 
 
 Experience demonstrates that water may be obtained in 
 liberal quantity at one point in a stratum, while a few rods 
 distant no water is obtainable in the same stratum, an 
 intervening " fault" or crevice having intercepted the flow 
 and led it in another direction. Sometimes, by the exten- 
 sion of a heading from a shaft in a water-bearing stratum, 
 to increase an existing supply, a fault is pierced and the 
 existing supply led off into a new channel. 
 
 90. Renowned Application of Geological Science. 
 Arago's prediction of a store of potable water in the deep- 
 dipping greensand stratum beneath the city of Paris, was 
 one of the most brilliant applications of geological science 
 
INFLUENCE OF WELLS UPON EACH OTHER. 107 
 
 to useful purposes. He felt keenly that a multitude of his 
 fellow-citizens were suffering a general physical deteriora- 
 tion for want of wholesome water, for which the splendors 
 of the magnificent capital were no antidote. With a fore- 
 sight and energy, such as displays that kind of genius that 
 Cicero believed to be "in some degree inspired," he pre- 
 vailed upon the public Minister to inaugurate, in the year 
 1833, that notable deep subterranean exploration at Gre- 
 nelle. By his eloquent persuasions he maintained and 
 defended the enterprise, notwithstanding the eight years of 
 labor to successful issue were beset with discouragements, 
 and all manner of sarcasms were showered upon the pro- 
 moters. In February, 1841, the augur, cutting an eight- 
 inch bore, reached a depth of 1806 feet 9 inches, when it 
 suddenly fell eighteen inches, and a whizzing sound an- 
 nounced that a stream of water was rising, and the well 
 soon overflowed. 
 
 91. Conditions of Overflowing Wells. An over- 
 flow results only when the surface that supplies the water- 
 bearing stratum is at an elevation superior to the surface of 
 the ground where the well is located, and the water-bearing 
 stratum is confined between impervious strata. In such 
 case, the hydrostatic pressure from the higher source forces 
 the water up to the mouth of the bore. 
 
 92. Influence of Wells upon Each Other. The 
 success of wells, penetrating deep into large subterranean 
 basins, upon their first completion, has usually led to their 
 duplication at other points within the same basin, and the 
 flow of the first has often been materially checked upon the 
 commencement of flow in the second, and both again upon 
 the commencement of flow in a third, though neither was 
 within one mile of either of the others. The flow of the 
 famous well at Grenelle was seriously checked by the open- 
 
 
108 SPRINGS AND WELLS. 
 
 ing of another well at more than 3000 yards, or nearly two 
 miles distant. 
 
 The successful sinking of deep wells in Europe began at 
 Artois, in France, in the year 1126. The name " Artesian," 
 from the name of the province of Artois, has been familiarly 
 associated with such wells from that date, notwithstanding 
 similar works were executed among the older nations many 
 years earlier. Since the success at Artois, this method has 
 been adopted in many towns of France, England, and Ger- 
 many, where the geological structure admitted of success. 
 The French engineers have recently sunk nearly one hun- 
 dred successful wells in the great Desert of Sahara ; and 
 Algeria and Northern Africa are beginning to bloom in 
 waste places in consequence of being watered by the pre- 
 cious liquid sought in the depths of the earth. 
 
 93. American Artesian Wells. Not less than 21 
 -yielding wells have been sunk in Chicago varying in depth 
 from 1200 to 1640 feet, the most successful of which is five 
 and one half inches diameter at the bottom, yielding about 
 900,000 gallons of water per 24 hours. The usual depth of 
 the Chicago wells is reported to be from 1200 to 1300 feet, 
 and the average cost of a five-and-a-half-inch well $6000, and 
 for a four-and-a-half-inch well $5000, for depth of 1200 feet. 
 
 A well for the Insane Asylum at St. Louis has reached 
 a depth of 3850 feet, or 3000 feet below the level of the sea. 
 
 Along the line of the Union Pacific Railroad, water is 
 obtained at certain points by means of Artesian wells, for 
 supplying the necessities of the road. 
 
 A few Artesian wells have been sunk in Boston, but the 
 water obtained has rarely been of satisfactory quality for 
 domestic purposes. 
 
 94. Watersheds of Wells. The watershed of a deep 
 subterranean supply is not so readily distinguishable as is 
 
WATERSHEDS OF WELLS. 
 
 that of a surface stream, that usually has its limit upon the 
 crown of the ridge sweeping around its upper area. 
 
 The subterranean watershed may possibly lie in part 
 beyond the crowning ridge, where its form is usually that 
 of a concentric belt, of varying width and of varying sur- 
 face inclination. A careful examination of the position, 
 nature, and dip of the strata only, can lead to an accurate 
 trace of its outlines. 
 
 The granular structure of the water-bearing stratum, as 
 a vehicle for the transmission of the percolating water, is to 
 be most carefully studied ; the existence of faults that may 
 divert the flow of percolation are to be diligently sought 
 for ; and the point of lowest dip in a concave subterranean 
 basin or the lowest channel line of a valley-like subterra- 
 nean formation, is to be determined with care. 
 
 A depressed subterranean water basin, when first dis- 
 covered, is invariably full to its lip or point of overflow. 
 Its extent may be comparatively large, and its watershed 
 comparatively small, yet it will be full, and many centuries 
 may have elapsed since it was moulded and first began to 
 store the precious showers of heaven. A few drops accu- 
 mulated from each of the thousand showers of each decade, 
 may have filled it to its brim many generations since ; yet 
 this is no evidence that it is inexhaustible. If the perennial 
 draught exceeds the amount the storms give to its replen- 
 ishment, it will surely cease, in time, to yield the surplus. 
 
 Coarse sands will, when fully exposed, absorb the 
 greater portion of the showers, but such sands are usually 
 covered with more or less vegetable soil, except in regions 
 where showers seldom fall. 
 
 Fissured limestones and chalks will also absorb a large 
 portion of the storms, if exposed, but they are rarely en- 
 tirely uncovered except upon steep cliff faces, where there 
 
110 .SPRINGS AND WELLS. 
 
 is little opportunity for the storms that drive against them 
 to secure lodgement. 
 
 95. Evaporation from Soils. Vegetable and surface 
 soils that do not permit free percolation of their waters 
 downward to a depth of at least three feet, lose a part of 
 it by evaporation. On the other hand, evaporation opens 
 the surface pores of close soils, so that they receive a por- 
 tion of the rain freely. 
 
 96. Supplying Capacity of Wells and Springs. 
 Percolation in ordinary soils takes place in greatest part 
 in the early spring and late autumn months, and to a lim- 
 ited extent in the hot months. In cold climates it ceases 
 almost entirely when the earth is encased with frost. 
 
 Permanent subterranean well or spring supplies receive 
 rarely more than a very small share of their yearly replen- 
 ishment between each May and October, their continuous 
 flow being dependent upon adequate subterranean storage. 
 
 Such storage may be due to collections in broad basins, 
 to collections in numerous fissures in the rocks, or to very 
 gradual flow long distances through a porous stratum where 
 it is subject to all the limiting effects of retardation included 
 under the general term, friction. 
 
 In the latter case a great volume of earth is saturated, 
 and a great volume of water is in course of transmission, 
 and the flow continues but slightly diminished until after 
 a drought upon the surface is over and the parched surface 
 soils are again saturated and filling the interstices of perco- 
 lation anew. 
 
 For an approximate computation of the volume of per- 
 colation into one square mile of porous gathering area, 
 covered with the ordinary superficial layer of vegetable soil, 
 and under usual favorable conditions generally, let us 
 assume that the mean annual rainfall is 40 inches in depth, 
 
SUPPLYING CAPACITY OF WELLS AND SPRINGS. Ill 
 
 and that in the seasons of droughts, or the so-called dry 
 years, 60 per cent, of the mean monthly percolation will 
 take place. 
 
 TABLE No. 31. 
 PERCOLATION OF RAIN INTO ONE SQUARE MILE OF POROUS SOIL. 
 
 Assumed Mean Annual Rain 40 Inches Depth. 
 
 
 d 
 
 H 
 
 > > 
 
 j 
 
 
 
 .796 
 
 2.653 
 .40 
 
 1.061 
 637 
 
 
 
 5 
 
 9*736 
 
 i 
 
 Q, 
 
 <1 
 
 
 
 1.462 
 
 4-873 
 .055 
 
 .268 
 ,i6 7 
 
 I 
 
 CO 
 
 2,552 
 
 1 
 
 l- 
 
 .964 
 
 3.213 
 
 .02 
 .06 4 
 .038 
 
 1 
 
 8 
 581 
 
 j>, 
 
 "5 
 H- i 
 
 1.077 
 
 3-59 
 
 .01 
 
 .036 
 
 .022 
 O 
 
 5> 
 336 
 
 1 
 
 1.251 
 
 4.170 
 .005 
 
 .021 
 .013 
 
 199 
 
 ! s 
 
 > 
 
 O 
 
 fe 
 
 o 
 
 Q 
 
 Ratios of T \ of mean 
 annual rain 
 Inches of rain each 
 
 737 
 
 2.457 
 SO 
 
 1.228 
 
 737 
 
 1 
 cT 
 
 t*. 
 
 11,264 
 
 1.070 
 3-567 
 
 45 
 1.605 
 
 963 
 
 1 
 
 t** 
 
 1 
 
 14,719 
 
 .814 
 
 2.713 
 15 
 
 .407 
 .244 
 
 3.729 
 
 1.015 
 3-383 
 
 .01 
 
 034 
 
 .020 
 305 
 
 x.076 
 
 3-587 
 
 .20 
 .717 
 430 
 
 6,572 
 
 937 
 
 3-123 
 50 
 
 1.561 
 937 
 % 
 
 f 
 
 14,321 
 
 .801 
 
 2.670 
 .70 
 
 1.869 
 
 1. 121 
 
 s 
 
 1 
 
 eT 
 I7,i33 
 
 Ratios of Percolation. . . 
 Mean inches of Rain 
 Percolating 
 Sixty per cent, of do. in 
 dry years 
 
 Volume of Percola-J ^ 
 tion in dry years. 1 . 
 
 [* 
 
 No. of persons it would 
 supply at 5 cu. ft. each 
 daily 
 
 
 From springs, with the aid of capacious storage reser- 
 voirs, it might be possible to utilize fifty per cent, of the 
 above volume of percolation. From wells, it would rarely 
 be possible to utilize more than from ten to twenty per cent, 
 of the volume. 
 
 Fifty per cent, of the above total estimated volume of 
 percolation would be equivalent to a continuous supply of 
 5 cubic feet per day each, to 3391 persons, or 126,823 gal- 
 lons per diem ; and ten per cent, of the same volume would 
 be equivalent to a like supply (37.4 gals, daily) to 678 
 persons, or 25,357 gallons per diem. 
 
 Wells sunk in a great sandy plain bordering upon the 
 ocean, or bordered by a dyke of impervious material, would 
 give greater and more favorable results, for in such case the 
 conditions of subterranean storage would be most favorable, 
 but such are exceptional cases. 
 
CHAPTEK VIII. 
 
 IMPURITIES OF WATER. 
 
 97. The Composition of Water. If a quantity of 
 pure water is separated, chemically, the constituent parts 
 will be two in number, one of which weighing pne^iinth as 
 much as the whole will be hydrogen, and the other part 
 oxygen ; or if the parts of the same quantity be designated 
 by volume, two parts will be hydrogen and one part oxygen. 
 
 These two gases, in just these proportions, had entered 
 simultaneously into a wondrous union, the mystery of 
 which the human mind has not yet fathomed. In fact, 
 many years of intense intellectual labor of such profound 
 investigators as Cavendish, Lemery, Lavoisier, V olta, Hum- 
 boldt, Gray Lussac, and Dumas were consumed before the 
 discovery of the proportions of the two gases that were 
 capable of entering into this mystic union. 
 
 98. Solutions in Water. If two volumes of oxygen 
 are presented to two volumes of hydrogen, one only of the 
 oxygen volumes will be capable of entering the union, and 
 the other can only be diffused through the compound, water. 
 
 When alcohol is poured into water it does not become 
 a part of the water, but is diffused through it. 
 
 This we are assured of, since by an ingenious operation 
 we are able to syphon the alcohol out of the water by a 
 method entirely mechanical. If we put some sugar, or 
 alum, or carbonate of soda into water, the water will cause 
 the crystals to separate and be diffused throughout the 
 liquid, but they will not be a part of the water. The water 
 
PROPERTIES OF WATER. 113 
 
 might be evaporated away, when the sugar, or alum, or 
 soda would have returned to its crystalline state. In these 
 cases, the surplus hydrogen, the alcohol, and the constitu- 
 ents of the crystalline ingredient are diffused through the 
 water as impurities. 
 
 If in a running brook a lump of rock salt is placed, the 
 current will flow around it, and the water attack it, and will 
 dissolve some of its particles, and they will be diffused 
 through the whole stream below. A like effect results when 
 a streamlet flows across a vein of salt in the earth. In like 
 manner, if water meets in its passage over or through the 
 earth, magnesium, potassium, aluminium, iron, arsenic, or 
 other of the metallic elements, it dissolves a part of them, 
 and they are diffused through it as impurities. In like 
 manner, if water in its passage through the air, as in 
 showers, meets nitrogen, carbonic acid, or other gases, 
 they are absorbed and are diffused through it as impurities. 
 
 99. Properties of Water. Both oxygen gas and 
 hydrogen gas, when pure, are colorless, and have neither 
 taste nor smell. Water, a result of their combination, when 
 pure, is transparent, tasteless, inodorous, and colorless, 
 except when seen in considerable depth. 
 
 The solvent powers of water exceed those of any other 
 liquid known to chemists, and it has an extensive range of 
 affinities. This is why it is almost impossible to secure 
 water free from impurities, and why almost every substance 
 in nature enters into solution in water. There is a property 
 in water capable of overcoming the cohesive force of the 
 particles of matter in a great variety of solids and liquids, 
 and of overcoming the repulsive force in gases. The par- 
 ticles are then distributed by molecular activities, and the 
 result is termed solution. 
 
 Some substances resist this action of water with a large 
 
114 IMPURITIES OF WATER. 
 
 degree of success, though not perfectly, as rock crystals, 
 various spars and gems, and vitrified mineral substances. 
 
 1OO. Physiological Effects of the Impurities of 
 Water. When we remember that seventy-five per cent, of 
 our whole body is constituted of the elements of water, that 
 not less than ninety-five per cent, of our healthy blood, and 
 not less than eighty per cent, of our food is also of water, 
 we readily acknowledge the important part it plays in our 
 very existence. 
 
 Water is directly and indirectly the agency that dissolves 
 our foods and separates them, and the vehicle by which the 
 appropriate parts are transmitted in the body, one part to 
 the skin, one to the finger-nail, one to the eye-lash, to the 
 bones phosphate of lime, to the flesh casein, to the blood 
 albumen, to the muscles fibrin, etc. When the stomach is 
 in healthy condition, nature calls for water in just the 
 required amount through the sensation, thirst. Good 
 water then regulates the digestive fluids, and repairs the 
 losses from the watery part of the blood by evaporation 
 and the actions of the secreting and exhaling organs. 
 Through the agency of perspiration it assists in the regula- 
 tion of heat in the body ; it cools a feverish blood ; and it 
 allays a parching thirst more effectually than can any fer- 
 mented liquor. Water is not less essential for the regula- 
 tion of all the organs of motion, of sight, of hearing, and 
 of reason, than is the invigorating atmosphere that ever sur- 
 rounds us, to the maintenance of the beating of the heart. 
 
 If from a simple plant that may be torn asunder and yet 
 revive, or a hydra that may be cut across the stomach or 
 turned wrong side out and still retain its animal functions, 
 the water is quite dried away; if but for an instant, man, 
 with his wonderful constructive ability, and reason almost 
 

 MINERAL IMPURITIES. 115 
 
 divine, cannot restore that water so as to return the activity 
 of life and the power of reproduction. 
 
 The human stomach and constitution become toughened 
 in time so as to resist obstinately the pernicious effects of 
 certain of the milder noxious impurities in water, but such 
 impurities have effect inevitably, though sometimes so grad- 
 ually that their real influence is not recognized until the 
 whole constitution has suffered, or perhaps until vigor is 
 almost destroyed. 
 
 Note the effect of a few catnip leaves thrown into drink- 
 ing water, which will act through the water upon the nerves ; 
 or an excess of magnesia in the water will neutralize the free 
 acids in the stomach, or lead in the water will act upon the 
 gums and certain joints in the limbs, or alcohol will act 
 upon the brain ; and so various vegetable and mineral solu- 
 tions act upon various parts of the body. 
 
 It would be fortunate if the pernicious impurities in 
 water affected only matured constitutions, but they act with 
 most deplorable effect in the helplessness of youth and even 
 before the youth has reached the light. These impurities 
 silently but steadily derange the digestive organs, destroy 
 the healthy tone of the system, and bring the living tissues 
 into a condition peculiarly predisposed to attack by malig- 
 nant disease. 
 
 * 1O1. Mineral Impurities. The purest natural waters 
 found upon the earth are usually those that have come 
 down in natural streams from granite hills ; but if a thou- 
 sand of such streams are carefully analyzed, not one of them 
 will be found to be wholly free from some admixture. This 
 indicates that in the economy of nature it has not been 
 ordained to be best for man to receive water in the state 
 chemically called pure. A United States gallon of water 
 weighs sixty thousand grains nearly. Such waters as phy- 
 
116 IMPURITIES OF WATER. 
 
 sicians usually pronounce good potable waters have from 
 one to eight of these grains weight, in each gallon, of certain 
 impurities diffused through them. These impurities are 
 usually marshalled into two general classes, the one derived 
 more immediately from minerals, the other derived directly 
 ' or indirectly from living organisms. The first are termed 
 mineral impurities, and the other organic impurities. 
 
 The mineral impurities may be resolved by the chemist 
 into their original elementary forms, and they are usually 
 found to be one or more of the most generally distributed 
 metallic elements, as calcium, magnesium, iron, sodium, 
 potassium, etc. If as extracted they are found united with 
 carbonic acid, they are in this condition termed carbonates ; 
 if with sulphuric acid, sulphates ; if with silicic acid, sili- 
 cates ; if with nitric acid, nitrates ; if with phosphoric acid, 
 phosphates, etc. ; if one of these elements is formed into a 
 compound with chlorine, it is termed a chloride; if with 
 bromine, it is termed a bromide, etc. A few metallic ele- 
 ments may thus be reported, in different analyses, under a 
 great variety of conditions. 
 
 1O2. Organic Impurities. There are a few elements 
 that united form organic matter, as carbon, oxygen, hydro- 
 gen, nitrogen, sulphur, phosphorus, potassium, calcium, 
 sodium, silicon, manganese, magnesium, chlorine, iron, and 
 fluorine. Certain of these enter into each organized body, 
 and their mode of union therein yet remains sealed in mys- 
 tery. In the results we recognize all animated creations, 
 'from the lowest order of plants to the most perfect quadru- 
 peds and the human species. All organic bodies may, 
 however, upon the extinction of their vitality, be decom- 
 posed by heat in the presence of oxygen, and by fermenta- 
 tion and putrefaction. 
 
 The metallic elements are, in the impurities of good 
 

 ANALYSES OF POTABLE WATERS. 
 
 117 
 
 
 potable waters, usually much, in excess of the organic ele- 
 ments, but the contained nitrogenized organic impurities 
 indicate contaminations likely to be much more harmful to 
 the constitution, and especially if they are products of ani- 
 mal decompositions. 
 
 1O3. Tables of Analyses of Potable Waters. We 
 will quote here several analyses of running and quiet waters 
 that have been used, or were proposed for public water 
 supplies, indicating such impurities as are most ordinarily 
 detected by chemists in water. For condensation and for 
 convenience of comparison they are arranged in tabular 
 form. 
 
 TABLE No. 32. 
 ANALYSIS OF VARIOUS LAKE, SPRING, AND WELL WATERS. 
 
 
 1 Jamaica Pond, near 
 Brooklyn, L. I. 
 
 Flax Pond, near 
 Lynn, Mass. 
 
 Sluice Pond, near 
 Lynn, Mass. 
 
 Breeds Pond, near 
 Lynn, Mass. 
 
 Reeds' Lake, near 
 Grand Rapids, Mich. 
 
 Lake Konomac, near 
 New London, Conn. 
 
 Loch Katrine, near 
 Glasgow, Scotland. 
 
 1 
 
 a 
 It 
 
 
 
 wU 
 
 Well at Highgate, 
 England. 
 
 Artesian Well, at 
 Hatton, ( England. 
 
 4 
 
 i"; 
 
 Jig 
 
 <5J3 
 
 6 
 5.420 
 
 I.IOI 
 
 5.921 
 
 Carbonate of Lime 
 Magnesia . 
 " Soda 
 
 1.092 
 .408 
 
 .700 
 .692 
 
 .400 
 .320 
 
 .600 
 .612 
 
 4.65 
 1-13 
 
 .096 
 
 *.'ai6 
 
 12.583 
 11.658 
 
 
 1.768 
 734 
 12.677 
 
 Protocarbonate of Iron. . 
 
 
 
 
 
 
 
 
 
 'Chloride of Sodium 
 " Magnesia . . . 
 Calcium. ... 
 Potassium 
 
 244 
 328 
 1 20 
 
 .612 
 
 .408 
 
 54 
 
 .... 
 
 2.18 
 trace 
 
 .... 
 
 9-556 
 
 8.032 
 
 7-745 
 
 3-553 
 
 
 
 
 
 
 
 4-930 
 
 .... 
 
 
 
 
 1.62 
 
 
 
 
 Sulphate of Lime 
 " Magnesia... 
 Potash 
 " Potassa. . . 
 Soda 
 
 I2O 
 
 288 
 
 .300 
 '.'064 
 
 .300 
 .070 
 
 .270 
 .050 
 
 .... 
 
 1.29 
 
 :$ 
 
 12.775 
 
 
 .... 
 
 3-798 
 
 
 
 
 
 14.217 
 
 trace 
 
 2.160 
 
 4.811 
 trace 
 
 '.880 
 
 
 
 
 5 662 
 
 
 .080 
 
 .086 
 
 
 
 
 8.776 
 
 7-935 
 
 8.719 
 trace 
 
 Phosphate of Lime 
 
 
 trace 
 
 
 
 Nitrate of Lime 
 " Magnesia. . 
 
 
 
 
 
 
 
 
 33-457 
 
 Oxide of Iron 
 Ammonia 
 
 .044 
 
 .840 
 
 trace 
 
 .096 
 
 85 
 
 035 
 
 trace 
 
 
 14.231 
 
 
 559 
 
 "Silica 
 'Organic Matter 
 
 .008 
 2.652 
 
 .156 
 2.208 
 
 .144 
 i-344 
 
 .120 
 2.184 
 
 5-3I6 
 
 & 
 
 3S 
 
 .170 
 .900 
 
 2.244 
 
 .200 
 
 3-4*9 
 
 747 
 
 .042 
 
 Total Solids 
 
 Soluble Organic Matter. 
 Hardness, Degrees by 
 Clark's Scale 
 
 5-652 
 
 3.072 
 
 17.750 
 
 7-831 
 
 64.629 
 
 83-549 
 
 35-685 
 
 27-323 
 392 
 
 
 
 
 
 
 
 o 80 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
118 
 
 IMPURITIES OF WATER. 
 
 TABLE 
 
 ANALYSIS OF VARIOUS 
 
 The quantities are expressed in 
 grains per U. S. Gallon of 231 cubic 
 inches, or 58,372 j 1 ^ grains. 
 
 Hudson River, above 
 Albany, N. Y. 
 
 Hudson River, above 
 Poughkeepsie, N. Y. 
 
 Connecticut River, 
 above Holyoke, Mass. 
 
 Connecticut River, 
 above Springfield, Mass. 
 
 Schuylkill River, above 
 Philadelphia, Pa. 
 
 Croton River, above 
 Croton Dam, N. Y. 
 
 <a> 
 
 JS& 
 
 ii 
 
 feS 
 
 &M 
 
 *0 
 
 o>* 
 
 il 
 
 o^; 
 
 Saugus River, near 
 Lynn, Mass. 
 
 Carbonate of Lime 
 
 
 1.050 
 
 8* 
 
 .00 
 
 1.56 
 
 2 67 
 
 
 
 " Magnesia 
 
 
 
 rfi 
 
 
 
 60 
 
 
 84. 
 
 
 " Soda 
 
 
 2.126 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 361 
 
 108 
 
 676 
 
 
 
 ' 
 
 
 .QQ 
 
 
 .juj 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 86 
 
 
 
 " Potassium 
 
 
 
 .070 
 
 83 
 
 
 
 
 
 " and Sodium 
 
 
 
 
 
 
 
 
 
 
 080 
 
 
 
 156 
 
 
 jcg 
 
 
 280 
 
 " Magnesia 
 
 
 
 
 
 
 
 
 
 " Potash 
 
 
 
 
 
 
 
 
 028 
 
 " Potassa 
 
 
 
 
 
 
 
 
 
 " Soda 
 
 
 2.785 
 
 
 
 .48 
 
 
 
 
 Silicate of Potassa 
 
 
 
 
 
 
 
 
 
 " Soda 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Oxide of Iron 
 
 
 
 jr6 
 
 .168 
 
 
 trace 
 
 
 
 Iron Alumina and Phosphates 
 
 
 
 
 
 
 
 
 
 Ammonia . t ... .... 
 
 
 
 
 
 
 
 
 
 Silica 
 
 408 
 
 
 
 
 
 62 
 
 A.6 
 
 
 Organic Matter .... 
 
 ,4<jo 
 6qo 
 
 .776 
 
 I 728 
 
 T 'So 
 
 
 67 
 
 
 2 880 
 
 
 
 
 
 
 
 
 
 
 Total Solids ... 
 
 2 68n 
 
 
 
 
 
 
 
 6 624 
 
 Soluble Organic Matter 
 
 
 
 
 
 
 
 
 
 Solid residue obtained on evaporation 
 
 
 
 
 
 
 
 
 
 Free Carbonic Acid . . .... 
 
 
 
 
 
 
 
 
 
 Hardness, Degree by Clarke's Scale. .. 
 
 3'35 
 
 
 43 
 
 5 1 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 * Notwithstanding the exceeding importance of an intelligent microscopi- 
 cal examination of each proposed domestic water supply, in addition to the 
 chemical analysis, no record of such examination is found accompanying the 
 reports upon the waters herein enumerated. Lenses of the highest microscop- 
 ical powers should be used for such purpose, and immersion lenses are required 
 in many instances. 
 
 To obtain specimens of sedimentary matters, the sample of water may first 
 
ANALYSIS OF POTABLE WATERS. 
 
 
 No. 33. 
 
 RIVER AND BROOK WATERS.* 
 
 Chickopee River, near 
 Springfield, Mass. 
 
 Mill River, near 
 Springfield, Mass. 
 
 Grand River, above 
 Grand Rapids, Mich. 
 
 White River, in Filter 
 Wells on Bank, at 
 Indianapolis, Md. 
 
 Fallkill Greek, near 
 Poughkeepsie, N. Y. 
 
 g tf 
 
 en S 4 
 
 3 
 
 C M 
 
 fi 
 
 U5 
 
 Thames River, above 
 London, Eng. 
 
 Dee River, near 
 Aberdeen, Scotland. 
 
 I 
 
 
 
 rf 
 
 r 
 
 <u 
 
 Hampstead Water Co/s 
 Supply, England. 
 
 Cowley Brook, near 
 Preston, Eng. 
 
 Loud Scales, Preston',"^ 
 England. x * <N v 
 
 Dutton Brook, near 
 Preston, Eng. 
 
 .65 
 
 ..jo 
 
 7-8 
 
 10.02 
 
 51 
 
 6.221 
 
 334 
 
 I3.X3 
 
 .709 
 
 6.521 
 
 4.128 
 
 .575 
 218 
 
 6.131 
 066 
 
 i.343 
 .217 
 
 
 7 
 
 - * 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .242 
 
 .152 
 
 .532 
 
 .865 
 
 .... 
 
 4.70 
 
 1.20 
 
 trace 
 
 .... 
 
 1.56 
 
 .... 
 
 1.442 
 
 5.662 
 
 938 
 
 55 
 
 .970 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 T -38 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 559 
 
 
 
 
 
 
 
 260 
 
 
 
 
 
 
 
 
 
 
 
 
 .105 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .394 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 026 
 
 i 167 
 
 287 
 
 
 .150 
 
 
 
 
 
 trace 
 
 
 .150 
 
 
 
 1.242 
 
 12.625 
 
 
 780 
 
 .171 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .348 
 
 
 
 
 
 
 
 
 
 
 
 
 
 .058 
 
 
 
 
 trace 
 
 trace 
 
 
 
 i 66 
 
 8<u 
 
 .167 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 trace 
 
 trace 
 
 
 
 
 
 
 
 
 
 
 
 
 
 trace 
 
 trace 
 
 
 
 
 .12 
 
 1.104 
 
 trace 
 3-864 
 
 1.37 
 
 18.75 
 
 5 
 
 trace 
 
 15 
 
 05 
 trace 
 
 275 
 .417 
 
 .27 
 2.37 
 
 .... 
 
 .417 
 2.327 
 
 .058 
 1-535 
 
 .425 
 
 334 
 
 .401 
 
 4.516 
 
 7-339 
 
 31.24 
 
 20.99 
 
 6.74 
 
 "459 
 
 1.727 
 
 20.19 
 
 
 16.496 
 
 29.678 
 
 3-317 
 1.167 
 
 1-774 
 
 1.168 
 
 3.912 
 .785 
 
 
 
 
 
 
 
 
 
 
 
 2"5. "527 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 30 
 
 
 
 
 
 
 
 
 
 
 9.8 
 
 1.25 
 
 12 
 
 I.5O 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 rest a day in a deep, narrow dish, and then have its clear upper water syphoned 
 off . The remainder of the water may then be poured into a conical glass, such 
 as, or similar to, the graduated glasses used by apothecaries, and then again 
 allowed to rest until the sediment is concentrated, when the greater part of the 
 clear water may be carefully syphoned off and the sediment gathered and 
 transferred to a slide, where it should be protected by a thin glass cover. 
 
120 
 
 IMPURITIES OF WATER. 
 
 TABLE No. 34. 
 ANALYSIS OF STREAMS IN MASSACHUSETTS.* 
 
 (Quantities in Grains per U. S. Gallon.) 
 
 
 
 SOLID RESIDUE OF 
 FILTERED WATER. 
 
 
 FREE 
 AMMONIA. 
 
 ALBUMINOID 
 AMMONIA. 
 
 INORGANIC. 
 
 ORGANIC AND 
 VOLATILE. 
 
 >j 
 J 
 
 CHLORINE. 
 
 Merrimac River Mean of n ex- 
 aminations above Lowell 
 
 0.0027 
 .0026 
 .0018 
 
 .105 
 .024 
 
 .004 
 0035 
 .0030 
 .0026 
 .0047 
 .0027 
 .0027 
 .0064 
 
 0.0066 
 .0064 
 .0074 
 .015 
 .012 
 
 .008 
 .0096 
 .0107 
 .0115 
 .0158 
 .0097 
 .0158 
 .0175 
 
 1.38 
 1.41 
 
 i-54 
 1.98 
 2.62 
 
 1.66 
 2.26 
 1.63 
 
 2.22 
 1. 80 
 
 2.85 
 1.40 
 
 2.10 
 
 I .OI 
 
 .98 
 1.05 
 1.98 
 i-75 
 
 .21 
 .07 
 50 
 31 
 .42 
 
 59 
 .98 
 
 77 
 
 2-39 
 2.39 
 2-59 
 3-96 
 4-37 
 
 2.87 
 3-33 
 4-13 
 3-53 
 3.22 
 4.44 
 3.38 
 3-87 
 
 0.08 
 .12 
 .11 
 
 50 
 37 
 
 .21 
 
 23 
 23 
 .18 
 .20 
 .26 
 .29 
 30 
 
 Merrimac River Mean of 12 ex- 
 aminations above Lawrence 
 Merrimac River Mean of n ex- 
 aminations below Lawrence 
 Blackstone River, near Quinsig- 
 amund Iron \Vorks . 
 
 Blackstone River, just above Mill- 
 bury. . .. 
 
 Blackstone River, below Black- 
 
 Charles River at \Valtharn . 
 
 Sudbury River, above Ashland. . . . 
 Sudbury River ajt Concord 
 
 Concord River at Concord 
 
 Concord River at Lowell 
 
 Neponset River, at Readville . 
 
 Neponset River, below Hyde Park. 
 
 1O4. Ratios of Standard Gallons. A portion of 
 above analyses were found with their quantities of im- 
 purities expressed in grains per imperial gallon, a British 
 standard measure containing 70,000 grains, and some of 
 them expressed in parts per 100,000 parts. They have all 
 been, as have those following, reduced to grains in a U. S. 
 standard gallon, containing 58372.175 grains. 
 
 The degrees of hardness are expressed by Clark's scale, 
 which refers to the imperial gallon. 
 
 * Selected from the Fifth Annual Report of the Mass. State Board of 
 Health. 
 
ANALYSES OF WELL WATERS. 
 
 121 
 
 The other quantities may be easily reduced to equiva- 
 lents for imperial gallons, by aid of logarithms of the quan- 
 tities or of the ratios : 
 
 Imperial gallon No. of grains 70000 Logarithm, 4.845098 
 
 U. S. gallon No. of grains 58372. 175 " 
 
 Ratio of imp. to U. S. gallon 1. 199201 " 
 
 " of U. S. to imperial gallon 833886 
 
 " of cubic foot to one imp. gallon. . . 6.23210 
 
 " " " " " " U. S. " . . 7-48052 
 
 " " one imp. gall, to one cu. ft 16046 " 
 
 " " " U.S. " " " " " 13368 
 
 The following analyses of various well waters are in a 
 more condensed form : 
 
 TABLE No. 33. 
 ANALYSES OF WATER SUPPLIES FROM DOMESTIC WELLS. 
 
 (Quantities in Grains per U. S. Gallons.) 
 
 4. 766206 
 0.078892 
 1.921108 
 0.794634 
 0.873932 
 1.205367 
 
 WELLS. 
 
 MINERAL 
 
 MATTERS. 
 
 ORGANIC 
 MATTERS. 
 
 j 
 
 <a 
 
 od 
 Hcfi 
 
 HARDNESS, 
 CLARK'S 
 SCALE. 
 
 
 
 
 65 20 
 
 
 Lydius Street 
 
 
 
 IQ 24 
 
 
 
 
 
 48.60 
 
 
 
 
 
 50.00 
 
 
 Tremont Street 
 
 
 
 26 60 
 
 
 
 
 
 56 80 
 
 
 average of three 
 
 
 
 44 46 
 
 
 Old Artesian 
 
 CA ae 
 
 I 8c 
 
 c e 20 
 
 
 Brookline Mass . . 
 
 Q 80 
 
 4 08 
 
 TT Q7 
 
 
 Brooklyn L I i . .. 
 
 
 
 AC AQ 
 
 
 " average of several 
 
 
 
 48.8^ 
 
 
 Cliarlestown Mass 
 
 
 
 26 4O 
 
 
 
 TO.OI 
 
 2.41 
 
 12 42 
 
 
 D p troit Mich 
 
 
 
 116 46 
 
 
 Dayton Ohio . 
 
 
 
 e6 co 
 
 
 Dedham Mass Driven Pipe 
 
 512 
 
 I 12 
 
 6 24 
 
 
 " " Artesian .... 
 
 4 08 
 
 I II 
 
 C IQ 
 
 
 Fall River, Mass., average of seventeen.. 
 
 25.16 
 
 7.00 
 
 32.16 
 
 IQ-33 
 
 12 17 
 
 8 30 
 
 No 2 
 
 
 
 ^2. l6 
 
 1*2 A A 
 
 No. 3 
 
 
 
 37. 10 
 
 
 No 4. . 
 
 
 
 4^.6o 
 
 IO ^^ 
 
 " " No. *.., 
 
 
 
 6q.oc 
 
 iq 22 
 
 
122 
 
 IMPURITIES OF WATER. 
 
 ANALYSES OF WATER SUPPLIES FROM DOMESTIC WELLS (Continued). 
 
 WELLS. 
 
 MINERAL 
 MATTERS. 
 
 ORGANIC 
 MATTERS. 
 
 P 
 II 
 
 HARDNESS, 
 
 CLARK'S 
 
 SCALE. 
 
 
 
 
 60 oo 
 
 
 
 
 
 
 3.Q. 3.-3 
 
 { 
 
 71 
 
 London Eng Leadenhall Street 
 
 QO.38 
 
 9CQ 
 
 QO O7 
 
 
 
 " " St. Paul's Churchyard 
 
 
 
 62 ^4. 
 
 
 
 Lambeth " 
 
 
 
 8-3 OQ 
 
 
 
 
 
 
 o^oy 
 
 74. 08 
 
 
 
 Manhattan, N. Y 
 
 
 
 104 oo 
 
 
 
 " average of several 
 
 
 
 4Q .OO 
 
 
 
 New Haven Conn average of five . 
 
 
 
 2O 32 
 
 
 
 New York west of Central Park. . . 
 
 38 QC 
 
 4 ^Q 
 
 AO. C.A 
 
 
 
 average of several 
 
 
 
 58 oo 
 
 
 
 Newark, N. J., average of several 
 
 
 
 IQ.^6 
 
 
 
 Providence R. I., average of twenty-four. 
 " " purest of " 
 " foulest of 
 Portland Me average of four 
 
 24.05 
 7.76 
 
 56.99 
 I" 7 , 3^ 
 
 8.82 
 
 3-35 
 24.12 
 5 IT 
 
 33.02 
 
 II. II 
 
 81.11 
 
 1 8 48 
 
 1C 
 ? 
 22 
 
 87 
 70 
 26 
 
 Pawtucket R I . 
 
 2Q l6 
 
 3.o / 3, 
 
 ^2 IQ 
 
 
 
 
 y* xw 
 
 25. 08 
 
 2.7-3 
 
 28 81 
 
 
 
 
 
 18 68 
 
 362 
 
 22 3O 
 
 
 
 Paris France Artesian 
 
 
 
 9 86 
 
 
 
 Rochester, N. Y., average of several 
 
 
 
 30 oo 
 
 
 
 Rye Beach, N. H 
 
 6.08 
 
 2.43 
 
 8.<u 
 
 
 
 Springfield Mass 
 
 7 82 
 
 2 O^ 
 
 o 8^ 
 
 
 
 
 8.81 
 
 2.OI 
 
 10 82 
 
 
 
 
 
 ii ^3 
 
 I.QI 
 
 13 44. 
 
 
 
 K 
 
 14 8l 
 
 3 08 
 
 17 QI 
 
 
 
 Schenectady N Y State Street .... 
 
 46 88 
 
 2. -3-3 
 
 4Q 21 
 
 
 
 Taunton Mass 
 
 2O 14, 
 
 2.Q8 
 
 23 12 
 
 
 
 
 
 20 86 
 
 4OQ 
 
 4."3. O 1 ^ 
 
 
 
 Wallham 
 
 7 68 
 
 4 08 
 
 II 76 
 
 
 
 Pump 
 
 17. 7Q 
 
 7 4.6 
 
 2C 2Z 
 
 
 
 Winchester, 
 
 4..OO 
 
 2.40 
 
 6. 40 
 
 
 
 M 
 
 8 OO 
 
 2 j.o 
 
 10 40 
 
 
 
 
 
 10 80 
 
 2.O4. 
 
 13 2O 
 
 
 
 
 ci C2 
 
 4.6o 
 
 c6. 12 
 
 
 
 
 
 
 
 
 
 1O5. Atmospheric Impurities. The constant disin- 
 tegration of mineral matters and the constant dissolutions 
 of organic matters, and their disseminations in the at- 
 mosphere, offer to falling rains ever-present sources of ad- 
 mixture, finely comminuted till just on the verge of trans- 
 formation into their original elements. The force of the 
 winds, the movements of animals, the actions of machines, 
 
SUB-SURFACE IMPURITIES. 
 
 are every moment producing friction and rubbing off minute 
 particles of rocks and woods and textile fabrics. Decaying 
 organisms, breaking into fibre, are caught "up and wafted 
 and distributed hither and thither. 
 
 The atmosphere is thus burdened with a mass of lifeless 
 particles pulverized to transparency. 
 
 A ray of strong light thrown through the atmosphere in 
 the night, or in a dark room, reveals by reflection this sea of 
 matter that vision passes through in the light of noon-day. 
 These matters the mists and the showers absorb, and dis- 
 solve in solution. 
 
 The respirations of all animate beings, the combustions 
 of all hearth-stones and furnaces, and the decaying dead 
 animals and vegetables, continually evolve acid and sul- 
 phurous gases into the atmosphere. Chief among the del- 
 eterious gases arising from decompositions are carbonic 
 acid, nitrous and nitric acids, chlorine, and ammonia. 
 These are all soluble in water, and the mists and showers 
 absorb them freely. Ehrenberg states that, exclusive of 
 inorganic substances, he has detected three hundred and 
 twenty species of organic forms in the dust of the winds. 
 Hence the so-called pure waters of heaven are fouled, before 
 they reach the earth, with the solids and gases of earth. 
 
 1O6. Sub-surface Impurities. The waters that flow 
 over or through the crevices of the granites, gneisses, ser- 
 pentines, trappeans, and mica slates, or the silicious sand- 
 stones, or over the earths resulting from their disintegrations, 
 are not usually impregnated with them to a harmful extent, 
 they being nearly insoluble in pure water. 
 
 The limestones and chalks often impart qualities objec- 
 tionable in potable waters, and troublesome in the house- 
 hold uses and in processes of art and manufacture. 
 
 The drift formation, wherever it extends, if unpolluted 
 
124 IMPURITIES OF WATER. 
 
 by organic remains upon or in its surface soil, usually sup- 
 plies a wholesome water. 
 
 The presence of carbonic acid in water adds materially 
 to its solvent power upon many ingredients of the soil that 
 are often present in the drift, such as sulphate of lime, 
 chloride of sodium, and magnesian salts, and upon organic 
 matters of the surface. 
 
 Carbonic acid in rain-water that soaks through foul sur- 
 face soils, gives the water power to carry down to the wells 
 a superabundance of impurities. 
 
 The presence of ammonia is a quite sure indication of 
 recent contamination with decaying organic matter capable 
 of yielding ammonia, whether in spring, stream, or well. 
 This readily oxidizes, and is thus converted into nitrous 
 acid and by longer exposure into nitric acid. 
 
 These acids combine freely with a lime base, as nitrate 
 and nitrite of lime. 
 
 Analysts attach great importance to the nature of the 
 nitrates and nitrites present, as indications of the nature of 
 the contaminations of the water. 
 
 Some of the subterranean waters penetrate occasional 
 strata that wholly unfit them for domestic use. A portion 
 of the carboniferous rocks are composed so largely of min- 
 eral salts that their waters partake of the nature of brine, as 
 in parts of Ohio ; in the Kanawha Valley, West Virginia ; 
 and in parts of New York State ; for instance, at Syracuse, 
 where the manufacture of salt from sub-surface water has 
 assumed great commercial importance. In other sections, 
 the bituminous limestones are saturated with coal-oils, as in 
 the famous oil regions of Pennsylvania. The dark waters 
 from the sulphurous strata of the Niagara group of the 
 Ontario geological division are frequently impregnated with 
 sulphuretted hydrogen. 
 
HARDENING IMPURITIES. 125 
 
 All along the western flank of the Appalachian chain, 
 from St. Albans and Saratoga on the north to the White 
 Sulphur Springs on the south, the frequent mineral springs 
 give evidence of the saline sub-structure of the lands, while 
 like evidences have recently become conspicuous in certain 
 portions of Kentucky, Arizona, New Mexico, Utah, Califor- 
 nia, and Oregon. 
 
 107. Deep-well Impurities. Deep well and spring 
 waters, except those from dipping sand or sandstone strata, 
 are especially liable to impregnations of mineral salts. 
 
 These impurities from deep and hidden sources, when 
 present in quantities that will be harmful to the animal 
 constitution, are almost invariably perceptible to the taste, 
 and are rejected instinctively. 
 
 108. Hardening Impurities. The solutions of salts 
 of lime and magnesia are among the chief causes of the 
 quality called hardness in water. Their carbonates are 
 broken up by boiling, for the heat dissipates the carbonic 
 acid, when the insoluble bases are deposited, and, with such 
 other insoluble matters as are present, form incrustations 
 such as are seen in tea-kettles and boilers where hard waters 
 have been heated. The carbonates, in moderate quantities, 
 are less troublesome to human constitutions than to steam 
 users. The effects of the carbonates are termed temporary 
 hardness. The sulphates, chlorides, and nitrates of lime 
 and magnesia are not dissipated by ordinary boiling. 
 Their effects are therefore termed permanent hardness. 
 
 An imperial gallon of pure water can take up but about 
 two grains of carbonate of lime, when it is said to have two 
 degrees of hardness ; but the presence of carbonic acid in 
 the water will enable the same 70,000 grains of water to dis- 
 solve twelve, sixteen, or even twenty grains of the carbonate, 
 when it will have twelve, sixteen, or twenty degrees of 
 
126 IMPURITIES OF WATER. 
 
 hardness, according to the number of grains taken into 
 solution. 
 
 These salts of lime and magnesia, and of iron, in water, 
 have the property of decomposing an equivalent quantity 
 of soap, rendering it useless as a detergent; thus, one 
 degree or grain of the carbonate neutralizes ten grains of 
 soap ; two degrees, twenty grains of soap ; three degrees, 
 thirty grains, etc. 
 
 This source of waste from foul hard waters, which extends 
 to the destruction of many valuable food properties, as well 
 as to destroying soap, is not sufficiently appreciated by the 
 general public. 
 
 It may be safely asserted that a foul hard well water 
 will destroy from the family that uses it, more value each 
 year than would be the cost in money of an abundant 
 supply of water for domestic purposes, from an accessible 
 public water supply ; and this refers to purchased articles 
 merely, and not to destruction of human health and energy, 
 which are beyond price. 
 
 1O9. Temperatures of Deep Sub-surface Waters. 
 Yery deep well and spring waters have, upon their first 
 issue, too high a temperature for drinking purposes, as from 
 the artesian wells of the Paris basin, which rise at a tem- 
 perature of 82 Fah., and as from hot springs, among which, 
 for illustration, may be mentioned the Sulphur Springs, 
 Florida, of 70 Fah., the Lebanon Springs, K Y., of 73 F. ; 
 and, as extremes of high temperature, the famous geysers 
 of the Yellowstone Valley, at a boiling temperature, and 
 the large hot spring near the eastern base of the Sierra 
 Nevadas and Pyramid Lake, whose broad pool has a tem- 
 perature of 206, and central issue 212. The springs at 
 Chaudes Aigues, in France, have a temperature of 176, 
 and the renowned geysers of Iceland, of 212. 
 
DECOMPOSING ORGANIC IMPURITIES. 
 
 127 
 
 Artesian wells have temperatures for given depths ap- 
 proximately as follows : 
 
 TABLE No. 36. 
 ARTESIAN WELL TEMPERATURES. 
 
 Depth in Feet .... 
 
 TOO 
 
 500 
 
 IOOO 
 
 1500 
 
 2OOO 
 
 2^OO 
 
 ^ooo 
 
 Temperature, deg. Fah 
 
 52 
 
 59 
 
 68 
 
 76 
 
 85 
 
 94 
 
 102 
 
 11O. Decomposing Organic Impurities. If we re- 
 solve, chemically, a piece of stone, ore, wood, fruit, a cup 
 of water, or an amputated animal limb, into their simple 
 elements within the limits of exact chemical investigation, 
 we shall find that their varied compositions and proper- 
 ties are results of combinations, substantially, of the same 
 few elements ; and that the organic substances that is, such 
 as are the result of growth under the influence of their own 
 vitality are composed chiefly of carbon, oxygen, hydrogen, 
 and nitrogen, with spare proportions of a few metalloids, 
 as above enumerated. The general order of predominance 
 of the gases and metalloids is not, however, quite the same 
 in mineral as in organic matters. But notwithstanding this 
 apparent similarity of chemical compositions, there is a 
 quality in organic substances accompanying the vital force, 
 that makes it as widely different in essential characteristics 
 from simple mineral compounds as life is from death. 
 
 The mysterious properties which accompany only the 
 vital force do not submit to analyses by human art. They 
 are known only by their results and their effects. 
 
 In the natural decomposition of animal matters, espe- 
 cially in their stage of putrefaction, their elements are often 
 in a condition of molecular activity that will not admit of 
 their being safely brought into contact with the human 
 
123 IMPURITIES OF WATER. 
 
 circulation, where they will be liable to induce similar con- 
 ditions. 
 
 Witness the extreme danger to a surgeon who receives 
 a minute quantity of animal fluid into a sore upon his hand, 
 when dissecting a dead body, even though the life has been 
 extinct but one or two days. 
 
 The excreta of living animals also passes through a 
 decomposing transformation, in which stage they cannot 
 safely be brought into contact with the human circulation, 
 however finely they may be dissolved in water, when re- 
 ceived. 
 
 The process of decay in dead animal bodies, and of de- 
 composition of vegetable substances, is quite rapid when 
 moisture and an abundance of atmospheric air, or available 
 oxygen in any form, are present, and a warm temperature 
 promotes the activity of the elements ; hence the same mat- 
 ter does not long remain in its most objectionable state, but 
 from the multiplicity of bodies on every hand, a constant 
 source of pollution may be maintained. 
 
 Potable waters, when exposed to those organic matters 
 in process of rapid decay, meet perhaps their most fatal 
 sources of natural contamination, that are not readily de- 
 tected ~by tlie eye and tongue. 
 
 111. Vegetable Organic Impurities. Nature around 
 us swarms with an abundance of both vegetable and ani- 
 mal Me, in air, in earth, in stream and sea, and therefore 
 death is constantly on every hand, and its dissolutions 
 meet the waters wherever they fall or flow. There are 
 numerous plants, trees, insects, and animals that we recog- 
 nize day by day, but there are undoubtedly species and 
 classes more innumerable above and below, that we can dis- 
 cover only when our vision is aided by magnifying lenses. 
 
 Upon the meadow pools and small ponds of the swamps, 
 
VEGETAL ORGANISMS IN WATER-PIPES. 129 
 
 species of microscopic fungi, not unlike the mould upon 
 decaying fruit, though, less luxuriant, are found in abun- 
 dance by searchers who suspect their presence. To the 
 general observer they appear as dust upon the water or 
 give to it a slight appearance of opaqueness. 
 
 There are species of fresh-water algse that thrive in 
 abundance, peculiar to all seasons, and they are said to have 
 been found in the heated waters of boiling spring basins, 
 and also in healthy life within an icicle, and they are the last 
 of life high up on the mountain slopes, near the borders of 
 eternal snows. Ditches, pools, springs, rivers, lakes, and 
 dripping grottoes have each their native class. In stagnant 
 waters abound the oscillatorise of dull-greenish or dark- 
 purplish or bluish color, forming dense slimy strata, and 
 the brighter green zygenemas which float or lie entangled 
 among the water plants. 
 
 The desmids abound in the early spring of the year, and 
 various algse flourish in the autumn. A thrifty fungus of 
 the genus Noctos frequents the quiet waters of lower New 
 England and the Middle States. 
 
 These plants at their dissolution often impart an oily 
 appearance, a greenish or brownish color, and a somewhat 
 offensive smell to the water. The noctos, while in active 
 growth, forms part of the green scum often seen upon the 
 surface* of still water. The fishy smell and the color which 
 they impart to the water in decomposing seems to be largely 
 due to an essential oil which they give out when breaking up. 
 
 113. Vegetal Organisms in Water-Pipes. A 
 species of confervso has been found growing and multiply- 
 ing rapidly within water-pipes, having taken root in the 
 le organic sediment deposited from feeble currents of 
 i/ter in the dead ends or in the large mains. These micro- 
 ;opic plants, after maturing in abundance, are detached 
 
130 IMPURITIES OF WATER. 
 
 by the current, decompose, and impart an appreciable 
 amount of odor and taste to the water, reduce its transpar- 
 ency and give a slight tinge of color. 
 
 113. Animate Organic Impurities. The waters are 
 not less pregnant with animate than vegetal life. The mi- 
 croscope has here extended our knowledge of varieties and 
 numbers of species also, especially in waters infused with 
 organic substances. 
 
 The tiny infusoria were first discovered in strong vegeta- 
 ble infusions, hence the name given to them ; but with the 
 extension of microscopical science, the class has been ex- 
 tended to include a variety of animate existences, from the 
 quiet fresh water sponge to the most energetic little creatures 
 that battle ferociously in a drop of water. 
 
 Dr. Grace Calvert has shown* that when albumen from 
 a new laid egg is introduced in pure distilled water and 
 exposed to the atmosphere, minute globular bodies soon 
 appear having independent motion. These he denominated 
 monads. 
 
 Their appearance was earlier in lake water than in dis- 
 tilled water, and earliest and most abundant in solutions 
 of largest exposure to the atmosphere. 
 
 These monads have diameters of about y^Wo f an 
 inch ; in their next successive stage, of about 2Tfihnr f an 
 inch ; and then of about ^TRT f an inch. He denominates 
 them vibrios in the two last stages. Then they change into 
 cells, having power to pass over the field of the microscope 
 rapidly. 
 
 The albuminous products of decaying leaves and plants 
 in water also promote the generation of aquatic life, and 
 dead animal substances are almost immediately inhabited 
 by a myriad of creatures. 
 
 * Papers read before the Royal Society, London. 
 
AQUATIC ORGANISMS. 131 
 
 The discussion upon the question of spontaneous gene- 
 ration in progress at the opening of our centennial year, is 
 adding many new and interesting experimental results to 
 the researches of Pasteur and Schroeder, relating to the 
 propagation of bacterial life from atmospheric mote germs, 
 and the agency of germs in the spread of epidemic cSntagia. 
 Prof. Tyndall and Dr. Bastian, the leading controversialists 
 in this discussion, are agreed that both vegetable and animal 
 infusions, if exposed to the summer atmosphere, will, ordi- 
 narily, abound in bacterial life in about three days. 
 
 There are also in the streams and lakes the larger 
 zoophytes, mollusca, articulata, and Crustacea, some of which 
 are familiar products of the waters, and also fish in great 
 variety. 
 
 But all of these do not pass through the objectionable 
 putrefactive stage described above. The weaker classes 
 are food for the stronger, and the smaller of some classes 
 food for the larger of the same class. Of the many that 
 come into being, comparatively few survive till a natural 
 death terminates their existence, but each devours others 
 for a substantial part of its own nourishment, and hides, 
 fights, or retreats to preserve its own existence. 
 
 114. Propagation of Aquatic Organisms. A warm 
 temperature of both air and water are requisite for the abun- 
 dant propagation of aquatic life. The presence of a consid- 
 erable amount of either vegetable or animal impurities in 
 the waters seems also a requisite for the lower grades of life. 
 
 How far certain electrical influences in the air and water 
 
 itrol the results are not yet determined. Certain it is, 
 lowever, that the microscopic creatures sometimes swarm 
 suddenly in abundance in quiet lakes and pools, in a seem- 
 ingly unaccountable manner, remain in abundance for a 
 few days, or possibly a few weeks in rare seasons, and then 
 
132 IMPURITIES OF WATER. 
 
 as mysteriously disappear. There is a similar appearance 
 of microscopic plants, when all the natural conditions favor- 
 able thereto occur simultaneously, but their coming cannot 
 always be predicted, neither can the time of their disap- 
 pearance be foretold. 
 
 A vf ry brief existence is allotted to a large share of the 
 minute vegetal and animate aquatic beings we have had in 
 consideration. Perhaps the greater share of the animate, 
 count scarce a single circuit of the sun in their whole term ; 
 others soon pass to a higher stage in their existence, and 
 are thereafter terrestrial in their habits. 
 
 115. Purifying Office of Aquatic Life. One of the 
 chief offices of the inferior inhabitants of the waters is to 
 aid in their purification by devouring and assimilating the 
 dead and decaying organic matters. 
 
 The infusorial animalculse are undoubtedly encouraged 
 in their propagation by the presence of impurities so far as 
 to be an unmistakable indication of such impurities ; and 
 they, on the other hand, attack and destroy such impurities 
 for their own nourishment, when they are devoured, and 
 their devourers devoured by higher existences, till the last 
 become food for fish that constitutes a food for man. 
 
 This, and this only, is the proper channel through which 
 the decomposing organic impurities in water should reach 
 the human stomach, having by Nature's wonderful pro- 
 cesses of assimilation been first converted into superior 
 living tissues. 
 
 A great variety of fish are daily consumed for our food, 
 also of mollusca from salt water, as clams, oysters, and mus- 
 sels, also of Crustacea, as lobsters, crabs, shrimp, etc. ; hence 
 we infer that the higher orders of fresh water inhabitants are 
 not harmful while living therein, and are nourishing as food, 
 if consumed while the influence of their vital force remains. 
 
ABRASION IMPURITIES. 133 
 
 The action of oxygen upon organic bodies tends always 
 powerfully to decomposition, but is counteracted by the 
 vital force. When the vital force ceases then decomposi- 
 tion soon begins, and then the body acted upon is unfitted 
 for the human digestive organs. 
 
 116. Intimate Relation between Grade of Organ- 
 isms and Quality of Water. The grade and character 
 of the growths in fresh water are almost invariably reliable 
 tests of the quality of the water, and if the plants be fine- 
 grained, firm, and delicate in outline, or the fish trim in 
 form, lithe in motion, and fine in flavor, the water is most 
 sure to be good. 
 
 117. Animate Organisms in Water-Pipes. Nearly 
 all of the animate aquatic existences must rise frequently 
 to the water surface to secure their necessary share of at- 
 mospheric oxygen. If any of them, not having tracheal 
 gills, or their equivalents, to enable them to breathe a long 
 time under water, are drawn into the pipes, and are thus 
 ut off from their supply of oxygen, they soon perish. 
 Then, if the water is not of low temperature, their decom- 
 position soon commences, and an offensive gas from their 
 bodies enters into solution with the water. 
 
 118. Abrasion Impurities in Water. The most 
 prominent sources of the frictional impurities are the banks 
 of clay and sand bordering upon the running streams, and 
 the plowed fields of the hillside farms. The movement 
 of these sedimentary matters in suspension is dependent 
 largely upon the force of storms and floods, and in the ma- 
 jority of streams their movement is rapid toward the sea, 
 where they are massed in foundations of lagoons and islands. 
 
 With them are swept away a great bulk of the matured 
 products of vegetation that annually ripen in the forest, the 
 field, and upon the banks of the streams. 
 
134 IMPURITIES OF WATER. 
 
 119. Agricultural Impurities. It remains now to re- 
 view in outline the artificial impurities, which are always 
 to be shunned if known to be present, and are to be sus- 
 piciously watched for, as secret poisons lurking in the clear 
 and sparkling water. 
 
 These are, it is true, compounds of mineral and organic 
 matters, similar in many respects to those already con- 
 sidered. 
 
 Nature provides prompt acting remedies for such nox- 
 ious impurities as she presents to the waters, and the 
 seasons of most rapid fouling have the most abundant 
 purifying resources. But when great bulks of decompos- 
 ing organic matters are massed and are permitted to foul 
 the streams with a blackening flow of disease-inducing 
 dregs, such as are washed from fertile gardens, or pour 
 from manufactories and sewers, no adequate, prompt, na- 
 tural remedy is at hand. 
 
 One of the first results of the massing of people together 
 is an increase in degree of fertilization of the land of their 
 neighborhood, and thus the lands over and through which 
 their waters flow are mixed with concentrated decomposing 
 vegetable and animal products. 
 
 2O. Manufacturing Impurities. Manufactories, 
 especially such as deal with organic products, are prolific 
 sources of contamination. Among their operations and 
 refuse may be enumerated as prominent polluters, washings 
 of wool and vegetable dyes of woollen mills, washing of old 
 rags and foul linens of paper-mills, the hair, scrapings, 
 bark, and liquors of tanneries, the refuse and liquors of 
 glue factories, bone-boiling and soap-works, pork render- 
 ing and packing establishments, slaughter-houses and gas- 
 works. 
 
 121. Sewage Impurities. Most foul and fearful of all 
 
IMPURE ICE IN DRINKING WATER. 135 
 
 the artificial pollutions which ignorant and careless human- 
 ity permits to reach the streams are the drainage of cesspools, 
 sewers, pig-styes, and stable-yards. 
 
 The man who permits his family to use waters impreg- 
 nated with fecal substances that the bodies of other persons 
 or animals have already excreted, and the authorities who 
 permit their citizens to use such waters, opens for them 
 freely the gates to aches and pains, weaknesses of body and 
 mind, injuries of tissues and blood, attacks of chronic dis- 
 eases and epidemics, and surely permits destruction of 
 their vigor, shortens their average life, and also degenerates 
 the entire existence of the generation they are rearing to 
 succeed them, whom it is their duty as well as pleasure to 
 cherish and protect. 
 
 There is no community, there are very few families, and 
 comparatively few animals without disease. In large com- 
 munities there is rarely a time when some virulent disease 
 does not exist. 
 
 The products of the humors and fevers of each individual 
 in large part escapes from the body in the feces and urine. 
 If drinking water is allowed to absorb these festering mat- 
 ters, either in the ground or in the stream, it transmits them 
 directly to the blood and tissues of other individuals, and a 
 hundred deaths may result from the evacuations of a single 
 diseased person. 
 
 122. Impure Ice in Drinking Water. Ice is now 
 so generally used in drinking-water in summer, to cool it 
 immediately before drinking, that the people should be 
 warned against such use of ice gathered from water that 
 would have been unfit for drinking before freezing. Chem- 
 istry has fully demonstrated that ice is not entirely purified 
 by the process of crystallization, as has been popularly 
 believed. 
 
136 
 
 IMPURITIES OF WATER. 
 
 The impurities that are in that portion of water that 
 freezes, some of which have just been brought from the 
 bottom by the vertical circulation that occurs when water 
 is chilled at the surface, are caught among the crystals and 
 preserved there, as even fresh meats, and fruits might be 
 preserved. The process of purification of the water that 
 would have gone on by the oxidation of the impurities, is 
 checked when they are surrounded by the ice crystals, and 
 proceeds again when the ice melts. 
 
 An instance, of much notoriety, of the effects of impure 
 ice, was that of the sickness among the numerous guests, 
 during the season of 1875, at one of the Rye Beach hotels, 
 a popular resort on the New Hampshire coast. 
 
 The sickness here, confined to one hotel in the early part 
 of the season, was, after much search by an expert physi- 
 cian, traced unmistakably to the ice, which was gathered 
 from a small stagnant pond, and all the peculiar unplea- 
 sant symptoms ceased when the source was located and a 
 purer supply of ice obtained. 
 
 An analysis of the impure ice in question, by Professor 
 W. R. Mchols, gave the following result, by the side of 
 which is placed a like analysis of water from Cochituate 
 Lake, for the purpose of comparison : 
 
 
 ICE FROM STAGNANT 
 POND. 
 
 WATER FROM 
 COCHITUATE 
 LAKE. 
 
 GRAINS PER U. S. GAL. 
 
 GRAINS PER 
 U. S. GAL. 
 
 Ammonia 
 
 Unfiltered. 
 O.OI2I 
 0.0410 
 4-55 
 3-33 
 
 Filtered. 
 O.OI24 
 .0096 
 4.01 
 1.66 
 
 0.0020 
 0.0068 
 
 1.61 
 
 1.22 
 
 
 
 
 Total solid residue at 212 Fahrenheit. . 
 Chlorine 
 
 7.88 
 
 5-67 
 1.88 
 
 0-495 
 
 2.8 3 
 .18 
 
 Oxygen required to oxidize organic matter. 
 
DEFINITION OF POLLUTED WATER. 137 
 
 123. A Scientific Definition of Polluted Water. 
 
 Subject, as the sensitive water is, to innumerable deteriora- 
 ting and purifying influences, in its transformations and 
 varied course from the atmosphere to the household foun- 
 tain, it becomes of the greatest sanitary importance to know 
 when the deteriorating influences still predominate, and when 
 further purification is essential for the well being of the 
 consumers. 
 
 Professor Frankland, an eminent English authority on 
 the quality of drinking water, has clearly defined a mini- 
 mum limit, when, in his opinion, water contains sufficient 
 mechanical or chemical impurities, in suspension or solu- 
 tion, to entitle it to be considered bad, or a polluted 
 liquid, viz. : 
 
 (a.) Every liquid which has not been submitted to pre- 
 cipitation produced by a perfect repose in reservoirs of suf- 
 ficient dimensions during a period of at least six hours ; or 
 which, having been submitted to precipitation, contains in 
 suspension more than one part by weight of dry organic 
 matter in 100,000 parts of liquid ; or which, not having been 
 submitted to precipitation, contains in suspension more 
 than 3 parts by weight of dry mineral matter, or 1 part by 
 weight of dry organic matter, in 100,000 parts of liquid. 
 
 (.) Every liquid containing in solution more than 2 
 parts by weight of organic carbon or 3 parts of organic 
 nitrogen in 100,000 parts of liquid. 
 
 (c.) Every liquid which, when placed in a white porce- 
 lain vessel to the depth of one inch, exhibits under daylight 
 a distinct color. 
 
 (d.) Every liquid which contains in solution, in every 
 100,000 parts by weight, more than 2> parts of any metal, 
 except calcium, magnesium, potassium, and sodium. 
 
 (e.) Every liquid which in every 100,000 parts by weight 
 
138 IMPURITIES OF WATER. 
 
 4 contains in solution, suspension, chemical combination, or 
 otherwise, more than 0.5 of metallic arsenic. 
 
 (/.) Every liquid which, after the addition of sulphuric 
 acid, contains in every 100,000 parts by weight more than 
 1 part of free chlorine. 
 
 (g.) Every liquid which, in every 100,000 parts by 
 weight, contains more than 1 part of sulphur, in the state 
 of sulphuretted hydrogen or of a soluble sulphuret. 
 
 (k.) Every liquid having an acidity superior to that pro- 
 duced by adding 2 parts by weight of hydrochloric acid to 
 1,000 parts of distilled water. 
 
 (i.) Every liquid having an alkalinity greater than that 
 produced by adding 1 part by weight of caustic soda to 
 1,000 parts of distilled water. 
 
 (/.). Every liquid exhibiting on its surface a film of 
 petroleum or hydrocarbon, or containing in suspension in 
 100,000 parts, more than 0.5 of such oils. 
 
PUMPING STATION, NEW BEDFORD. 
 
CHAPTER IX. 
 
 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 
 
 It remains now to add to these general theories respect- 
 ing the purity of water some special suggestions relating to 
 the selection of a potable water. 
 
 WELL WATER. 
 
 
 
 124. Location for Wells. We have seen that the 
 source of water supply to wells is, immediately, the rain, 
 and that in the vicinity of dense populations the rain reaches 
 the surface of the earth, already polluted by the impurities 
 of the town atmosphere. 
 
 In the open country, the water reaches the ground in a 
 tolerably pure condition, and by judicious selection of a 
 site for a well, its water may usually be procured of excel- 
 lent quality. Country wells must, however, be entirely 
 separated from the drainage of the stable yards, muck 
 heaps, and house sewerage, and from soakage through 
 highly fertilized gardens. 
 
 In towns, surface soils are continually recipients of 
 household refuse, manures, and sewer liquors, and of dead 
 and decaying animal matters. 
 
 These have, by abundant examples, been proved to be 
 the most dangerous of the ordinary contaminations of shal- 
 low wells. 
 
 The strictly mineral impurities, to which all wells are 
 to some extent subject, are not usually injurious to human 
 constitutions, though in districts where lime is present in 
 
140 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 
 
 the soil in considerable quantity, the resulting hardness is 
 inconvenient and indirectly expensive. 
 
 An intelligent examination of the positions, dip, and 
 porosity of the earth' s superstrata in the vicinity of a pro- 
 posed well will be a more infallible guide to its location 
 where it will yield an unfailing, abundant, and wholesome 
 supply, than will reliance upon "hazel forks" and " divin- 
 ing rods," in which the superstitious have evinced faith and 
 by which they have often been deceived. 
 
 125. Fouling of Old Wells. The table of analyses 
 of well-waters above presented (page 121, et seq.) indicates 
 that the old wells of towns are among the most impure 
 sources of domestic water supply. 
 
 The continued increase in the hardness of well-water as 
 the population about them becomes more dense, indicates 
 that this increase is due to the salts of the dissolved organic 
 refuse with which the ground in time becomes saturated. 
 
 Mr. F. Button, an English analyst, states, that "out of 
 four hundred and twenty-nine samples of water sent him 
 from wells in country towns, he was obliged to reject three 
 hundred and seven as unfit for drinking." Another Eng- 
 lish chemist states that " much of the well-water he is called 
 upon to examine proves to be more fit for fertilizing pur- 
 poses than for human consumption." 
 
 Prof. Chandler, President of the New York City Board 
 of Health, and Professor of Chemistry in the School of 
 Mines, Columbia College, remarked : "In many cases, from 
 the proximity of cesspools and privy vaults, the well-water 
 becomes contaminated with filtered sewage, matters which, 
 while they hardly affect the taste or smell of the water, 
 have nevertheless the power to create the niiost deadly dis- 
 turbances in the persons who use the waters." 
 
 Hall's "Journal of Health" remarked that, "in the 
 
HARMLESS IMPREGNATIONS. 141 
 
 autumn many wells, which supply families with drinking 
 and cooking water, get very low and their bottoms are cov- 
 ered with a iine mud, largely the result of organic decom- 
 positions, also containing poisonous matters of a very con- 
 centrated character. The very emanations from this well 
 mud are capable of causing malignant fevers in a few hours ; 
 hence many families dependent on well-waters are made 
 sick during the fall of the year by drinking these impreg- 
 nated poisons, and introducing them directly into the circu- 
 lation. Many obscure ailments and 'dumb agues' are 
 caused in this way." 
 
 SPRING WATERS. 
 
 126. Harmless Impregnations* The impurities of 
 spring water are chiefly mineral in character, derived from 
 the constituents of the earths through which their waters 
 percolate. Among the most soluble of the earths are mag- 
 nesium, calcium, potassium, and sodium, and these appear 
 in spring waters as carbonates, bicarbonates, chlorides, 
 sulphates, silicates, phosphates, and nitrates, and are usu- 
 ally accompanied by an oxide of iron and a minute quan- 
 tity of silica. 
 
 The above earths are harmless, and are, in fact, consid- 
 ered beneficial in drinking waters, when present in moderate 
 quantities, or not exceeding eight or ten grains per gallon. 
 Most persons are familiar with the medicinal properties of 
 the carbonate of magnesia, a mild cathartic, and of its sul- 
 phate (Epsom salts), a mild purgative, and with the carbon- 
 ate and nitrate of potassa (pearlash and saltpetre) in the 
 arts, and with the medicinal properties of the bromide of 
 potassium, a mild diuretic. 
 
 Sodium is more familiarly known as common sea-salt, 
 and calcium as common lime, of which it is the base, and 
 
142 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 
 
 silica as the base of quartz or common sand. Spring waters 
 are, by their passage through the earth, thoroughly filtered 
 and relieved of suspended impurities, and therefore appear 
 as the most clear and sparkling of all natural waters. 
 
 In the selection of a spring water, it is to be specially 
 observed that it is free from impregnation by decaying 
 organic matters. 
 
 127. Mineral Springs. In illustration of the facts 
 that clearness to the eye is not evidence of purity, or min- 
 eral impregnation of the most usual character immediately 
 dangerous to the constitution, we append a few analyses of 
 well-known mineral spring waters, with quantities of ingre- 
 dients expressed in grains per U. S. gallon. (See page 143.) 
 
 This formidable array of chemical ingredients indi- 
 cates that the waters have taken into solution the familiar 
 minerals, magnesia, common salt, lime, iron, potash, sul- 
 phur, quartz, and clay, and the gases, oxygen, hydrogen, 
 nitrogen, and carbonic acid. 
 
 It is much to be regretted that supplies from good springs 
 are usually so limited in quantity. 
 
 The water supply of Dubuque, Iowa, is obtained from 
 an adit pierced into the bluff near the city. The operations 
 of miners working in the bluff were seriously impeded by 
 water, and they relieved themselves by tunneling in from 
 the face of the bluff, and thus underdraining the mine. In 
 so doing, they intercepted numerous percolating streams of 
 water. This water is now utilized for the supply of the 
 city. 
 
 LAKE WATERS. 
 
 128. Favorite Supplies. Fresh water lakes and deep 
 ponds, whose watersheds have extents equal to at least ten 
 times their water surfaces, are ordinarily, of all ample 
 
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144 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 
 
 sources, least liable to objectionable impregnation in harm- 
 ful quantity. When such waters have been imprisoned in 
 their flow, by the uplifting of the rock foundations of the 
 hills across some resulting valley, or by more recent crowd- 
 ing by ice-fields of masses of rock and earth debris into a 
 moraine dam, they are bright and lovely features in their 
 landscapes, and favorite sources of water-supplies. 
 
 The accomplishments of scientific attainments are not 
 requisite to enable the intelligent populations to discover 
 in these waters wholesomeness for human draughts and 
 adaptability to quench thirsts. 
 
 When such waters are deep, and have a broad expanse 
 and bold shores, nature is ever at work with rain and wind 
 and sunshine, maintaining their natural purity and sparkle. 
 
 129. Chief Requisites. The prime requisites in lakes, 
 when to be used for domestic supplies, are abundant in- 
 flow and outflow, that will induce a general circulation ; 
 abundant depth, that will maintain the water cool through 
 the heats of summer and hinder organic growth ; and a 
 broad surface, which the wind can press upon, and roll, 
 and thus stir the water to its greatest depths. 
 
 These are features opposed to quietude, shallowness, 
 and warmth, which we have seen ( 114) to be promoters of 
 excesses of vegetal and animal life, accompanied by a very 
 objectionable mass of vegetable decay and animal decom- 
 position. Fortunately, the shallow waters are offcenest at 
 the upper ends, opposite to the usual points of draught from 
 the lake, or in indented bays along the sides, from whence 
 their vegetal products are least liable to reach the outflow 
 conduit. 
 
 130. Impounding. When supplying lakes have mod- 
 erate drainage areas in proportion to the total volume of 
 water required from them, it is then necessary to place the 
 
PLANT GROWTH. 145 
 
 draught conduit below their natural surface or to raise 
 their natural surface Iby a dam at their outlet, to avail of 
 their storage, thus in a degree changing their condition of 
 nature into the artificial condition of impounding reser- 
 voirs. 
 
 The theory of volume of supply from given drainage 
 areas ( 53), and the theory of making available a large 
 proportion of the rainfall by impounding ( 75), have 
 already been discussed in their appropriate sections. 
 
 Important results, affecting the purity of the water, may 
 follow from the disturbance of the long-maintained condi- 
 tions of the shores, analogous to those of the construction 
 of artificial impounding reservoirs in valleys, by embank- 
 ments across the outflow streams. 
 
 The waves, of natural broad lakes that have but little 
 rise and fall, have long since removed the soil from large 
 portions of their shores, leaving them paved with boulders 
 and pebbles, which the ice, if in northern latitudes, has 
 crowded into close rip-raps, and the removed soil has been 
 deposited in the quiet shallow bays. 
 
 Upon the paved shores the lack of vegetable mold and 
 the dash of the waters are obstacles to the growth of vege- 
 tation. 
 
 131. Plant Growth. If, under the new conditions, the 
 waters are drawn down in the summer, the wave power re- 
 duced, the shallow bottoms of the bays uncovered, and an 
 entire shore circuit of vegetable deposit exposed to the hot 
 sun, a mass of luxuriant vegetation at once springs into ex- 
 istence upon this uncovered bottom, and the greater its thrift 
 the more rapid its decay, and the more objectionable its 
 gaseous emanations that will enter into solution in the water. 
 
 Such growths and transformations may continue to re- 
 >eat themselves through several successive years, and to 
 
146 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 
 
 some extent continuously. Under the former conditions of 
 deeper water the plant life was of less abundance, of less 
 thrifty growth, and of less rapid decay, and the natural 
 processes of purification were adequate to maintain the 
 natural purity of the water. 
 
 Stimulated vegetable growths result in quick decay and 
 the production of vegetable muck, the foulest solid product 
 of vegetable decompositions in water. Slow decompositions 
 of vegetable matter in water rarely affect the water to a 
 noxious degree, and result in the production of a peat de- 
 posit almost entirely free from deleterious qualities in the 
 water. 
 
 The presence of the fishy or cucumber odor is evidence 
 that the water, or a considerable portion of it, has been too 
 warm for stored potable water ; and that there is too much 
 of shallow margin, or that the storage lake has received too 
 much of meadow drainage. It is not, as many have sup- 
 posed, an evidence of dead fish in the reservoir, but an effect 
 tending to drive the higher orders of the fish more closely 
 about the springs or inflowing streams. 
 
 132. Strata Conditions. The winds assist the ready 
 escape of the odorous gases when they have risen near to 
 the surface, and the stratum of water of greatest purity, in 
 summer, is usually a little below the surface, and would be 
 at the surface were it not for the microscopic organisms that 
 exist there, and the floating matters. 
 
 The change of density of water with change of tempera- 
 ture produces a remarkable effect in autumn. Water is at 
 its greatest density at the temperature just above freezing 
 (392 Fah.), and when the frosts of autumn chill the surfs 
 water it is then heavier than the water below, and sinks, 
 placing the bottom water ; and the vertical circulation, sti] 
 ring up the whole body, continues until the surface is seaJe< 
 
 - 
 
PLANT AND INSECT AGENCIES. 147 
 
 by ice, when quiet again reigns at the bottom. This action 
 stirs up the bottom impurities, and often makes them par- 
 ticularly offensive in autumn, even more than in mid- 
 summer. 
 
 In the case of new flowage of artificial reservoirs over a 
 meadow bottom, the live vegetable growth has all to go 
 through a certain chemical transformation, the influence of 
 which upon the water is often detectable, for a time, by the 
 sense of smell. This action in the water may be consider- 
 ably reduced by first burning thoroughly the whole surface, 
 and destroying the organic life and properties, leaving only 
 the mineral ash. 
 
 The breaking up of the vegetable fibres, if undestroyed 
 by fire, and their deposition in the quiet, shallow bays, 
 encourages the growth of aquatic plants, and, indirectly, 
 animal life there. 
 
 The protection of the shores by high water in winter, and 
 their exposure by drawing down the water in summer, is 
 favorable to aquatic growths upon them, as in the above- 
 mentioned lake examples. 
 
 133. Plant and Insect Agencies. In cases of ex- 
 cessive growths of either or both vegetal and animal life, 
 their products are liable to be drawn into the outflow con- 
 duit and the distribution pipes, where their presence becomes 
 disagreeably evident by the gaseous " fishy" or " cucum- 
 ber" odors liberated when the water is drawn from 
 faucets. 
 
 When conditions are favorable for the production of 
 either vegetal or animal life alone, in excessive abundance, 
 disagreeable effects, especially if the excess be animal, are 
 almost certain to follow, since both are among the active 
 agents employed by nature in the purification of water, and 
 natural laws tend to preserve the due balance in their 
 
148 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 
 
 growth, the one being producers of oxygen and the other 
 of carbon. 
 
 Newly flowed collecting or storage reservoirs should be 
 promptly stocked with a fine grade of fish, that will feed 
 upon and prevent the overabundance of the Crustacea, 
 which in turn will consume the organic decompositions, and 
 prevent their diffusion through the waters. 
 
 134. Preservation of Purity. General observation 
 teaches that neither vegetation or any species of the infu- 
 soria flourish to an objectionable extent in fresh waters in 
 the temperate zone where the depth exceeds about ten feet, 
 though it is true that insects are liable to swarm upon the 
 surface of all waters that arrive at a high temperature. 
 Stored waters, for domestic purposes, ought to have in our 
 American climate, depths of not less than twelve feet. 
 
 To insure purity of water, so far as protection from its 
 own products is concerned, it is necessary that the shallow 
 waters be cut off by embankments, or that they be deep- 
 ened, or that their place be supplied by clean sand or 
 gravel filling, raised to a level above high water. It is fre- 
 quently advisable, also, that the shores of artificial impound- 
 ing reservoirs of moderate extent be provided with an 
 equivalent for the natural rip-rap provided by nature 
 around natural lakes. 
 
 Each of the above expedients has been successfully 
 adopted by the writer in his own practice. 
 
 Fig. 7 is an illustration of the revetment of stone sur- 
 rounding the reservoir of the Norwich, Conn., water-works. 
 The reservoir in this case is two and one-half miles out 
 from the city, and fills the office of both a gathering and 
 distributing reservoir, for a gravitation supply. Its circum- 
 ference is two and one-quarter miles, and this revetment 
 protects the shore of the entire circuit. Its height above 
 
NATURAL CLARIFICATION. 
 
 149 
 
 FIG. 7. 
 
 high water, in the vicinity of the dam, is four feet, and in 
 the tipper part of the valley three feet. 
 
 If the supplying streams of a small lake bring with them 
 much vegetable matter in suspension, and the flow reaches 
 the conduit before complete clarification by natural pro- 
 cesses is effected, some method of artificial filtration of the 
 water will be necessary, the details of which will be dis- 
 cussed hereafter. 
 
 135. Natural Clarification. The various sources of 
 chemical impregnation to which waters reaching lakes, usu- 
 ally are subject, whether flowing over or through the earth, 
 have been already herein discussed ( 1O1, et seq.\ so that 
 persons of ordinary intelligence and information may detect 
 them, and form a tolerably accurate estimate of their harm- 
 fulness, and if they ought to be considered objectionable 
 when they are to be gathered in a lake and there subjected 
 to the processes in Nature's favorite laboratory of purifi- 
 cation. 
 
 Waters flowing in the brooks from the wooded hills and 
 ie swamps almost always come down to the lakes highly 
 charged with the coloring matter and substances of forest 
 leaves and grasses, and not unfrequently have a very per- 
 
150 WELL, SPRING, LAKE AND RIVER SUPPLIES. 
 
 ceptible reddish or chocolate hue. The waters are soon 
 relieved of these vegetable impurities by natural processes 
 in the lake, and their natural transparency and sparkle is 
 restored to them. Sunlight has been credited with a strong 
 influence in the removal of color from water. The chemical 
 transformation already begun upon the hills is continued in 
 the lake, and the atmospheric oxygen aids in releasing the 
 gases of the minutely subdivided vegetable products pro- 
 ducing the color, when the mineral residues have sufficient 
 specific gravity to take them speedily to the bottom. The 
 w T inds are the good physicians that bring the restoring 
 remedies. 
 
 Ponds and lakes often receive a considerable part of 
 their supply from springs along their borders, whose waters 
 have received the most perfect natural clarification. Such 
 springs, from quartzose earths, yield waters of the most 
 
 i/ ^ ** * ' "^} \$ ^Lt 
 
 desirable qualities. 
 
 136. Great Lakes. When lakes, on a scale of great 
 inland seas, like those lining our northern boundary, upon 
 which great marts of trade are developing, are at hand, 
 many of the above supposed conditions belonging to 
 smaller lakes and ponds, are entirely modified. 
 
 In such cases the cities become themselves the worst 
 polluters of the pure waters lying at their borders, and 
 they are obliged to push their draught tunnels or pipes 
 beneath the waters far out under the lakes to where the 
 water is undefiled. 
 
 This system was inaugurated on a great scale by Mr. 
 E. S. Cheesboro, C.E., for Chicago, and followed by the 
 cities of Cleveland, Buffalo, and with submerged pipe by 
 Milwaukee. 
 
 137. Dead Lakes. The waters of the Sinks, or Dead 
 Lakes of the Utah, Nevada, and southern California, Great 
 
METROPOLITAN SUPPLIES. 
 
 151 
 
 Desert, from which there are no visible outlets, are notable 
 exceptions to general conditions of lake waters. Here the 
 salts gathered by the inflowing waters, for centuries, which 
 evaporating vapors can not carry away, have been accu- 
 mulating, till the waters are nauseating and repugnant. 
 
 The skill of the well-borer must aid civilization when 
 these desert regions are to become generally inhabitable. 
 
 RIVER WATERS. 
 
 138. Metropolitan Supplies. Rivers are of necessity 
 the final resort of a majority of the principal cities of the 
 world for their public water supply. The volume of water 
 daily required in a great metropolis often exceeds the com- 
 bined capacity of all the springs, brooks, and ponds within 
 accessible limits, and supplies from wells become impos- 
 sible because of lack of capacity, excessive aggregate cost, 
 and the sickening character of their waters. 
 
 Since rivers occupy the lowest threads of the valleys in 
 which they flow, their surfaces are lower than the founda- 
 tions of the habitations and warehouses along their banks. 
 
 Their waters have therefore usually to be elevated by 
 power for delivery in the buildings, the expense of conduct- 
 ing their waters from their sufficiently elevated sources being 
 greater far than the capitalized cost of the artificial lift 
 nearer at hand. 
 
 The theories by which the minimum flow of the stream 
 ( 53), and the maximum demand for supply ( 19), are 
 determined and compared have been already herein dis- 
 cussed ; so we now assume that the supplies have, after 
 proper investigation, been determined ample, and also that 
 the geological structure ( 1O6) of the drainage area is found 
 to present no impregnating strata precluding the use of its 
 
152 WELL, SPRING, LAKE, AND EIVER SUPPLIES. 
 
 waters for domestic and commercial purposes, or in the 
 chemical arts. 
 
 139. Harmless and Beneficial Impregnations. 
 
 The natural organic impurities of rivers are seldom other 
 than dissolving vegetable fibres washed down from forests 
 and swamps, and these are rarely in objectionable amount ; 
 and the natural mineral impurities in solution are usually 
 magnesia, common salt, lime, and iron, and, in suspension, 
 sand and clay. The lime, sand, and clay are easily detect- 
 ible if in objectionable amount, and the remaining natural 
 mineral impregnation are quite likely to be beneficial 
 rather than otherwise, since they are required in drinking 
 water to a limited extent to render them palatable, and for 
 promotion of the healthy activity of the digestive organs, 
 and the building up of the bones and muscles of our bodies. 
 
 140. Pollutions. We reiterate that it is the artificial 
 impurities that are the bane of our river waters. Manufac- 
 tories, villages, towns, and cities spring up upon the river- 
 banks, and their refuse, dead animals, and sewage are 
 dumped into the running streams, making them foul potions 
 of putrefaction and destruction, when they should flow clear 
 and wholesome according to the natural laws of their crea- 
 tion and preservation. 
 
 141. Sanitary Discussions. The prolific discussion 
 upon the sanitary condition of the water of the river 
 Thames, England, since the report of the Royal Commis- 
 sion of 1850, has brought out a variety of conflicting opin- 
 ions in regard to the efficiency of natural causes to destroy 
 sewage impurities in water. 
 
 About one-half the population of London, or one-half 
 million persons, received their domestic water supply from 
 the Thames in 1875. The drainage area above the pump- 
 ing stations is about 3675 square miles, and the minimum 
 
SANITARY DISCUSSIONS. 153 
 
 summer flow is estimated to be about 350,000,000 imperial 
 gallons daily, and of this flow about 15,000,000 gallons is 
 pumped daily by the water companies. Upon the Thames 
 watershed above the pumping stations there resides a popu- 
 lation of about 1,000,000 persons, including three cities of 
 over 25,000 persons each, three cities of from 7000 to 10,000 
 persons each, and many smaller towns and villages. The 
 whole of the river and its principal tributaries are under 
 the strictest sanitary regulation which the government is 
 able to enforce, notwithstanding which a great mass of 
 sewage is poured into the stream. 
 
 Yet it is claimed by eminent authority that the Thames 
 water a short distance above London is wholesome, pala- 
 table, and agreeable, and safe for domestic use. 
 
 A remark by Dr. H. Letheby, medical officer of health 
 for the city of London until his decease in the spring of 
 1876, gives a comprehensive summary of the argument in 
 favor of the Thames water, viz. : "I have arrivec^at a very 
 decided conclusion that sewage, when it is mixed with 
 twenty times its volume of running water and has flowed a 
 distance of ten or twelve miles, is absolutely destroyed : 
 the agents of destruction being infusorial animals, aquatic 
 plants and fish, and chemical oxydation." 
 
 Several eminent chemists testify that analyses detect no 
 trace of the sewage in the Thames near London. Sir Benja- 
 min Broodie, Professor of Chemistry in the University of 
 Oxford, remarked in his testimony upon the London water 
 supply: "I should rely upon the dilution quite as much, 
 and more, than upon the destruction of the injurious 
 matter. 
 
 Dr. C. F. Chandler, President of the New York Board 
 of Health, and Professor of Chemistry in the School of 
 [ines, Columbia College^ has in his own writings quoted 
 
154 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 
 
 many eminent authorities,* with apparent indorsement of 
 their conclusions, supporting the theory of the wholesome- 
 ness and safety of the Thames water as a domestic supply 
 for the city of London. 
 
 142. Inadmissible Polluting Liquids. The Par- 
 liamentary Rivers Pollution Committee, when investigating 
 the subject of the discharge of manufacturing refuse and 
 sewage into the English rivers, Mersey and Bibble, and the 
 possibility of the deodorization and cleansing of the refuse 
 by methods then available, suggested f that liquids con- 
 taining impurities equal to or in excess of the limiting quan- 
 tity defined by Prof. Frankland (vide 123, p. 137), be 
 deemed polluting and inadmissible into any stream. 
 
 143. Precautionary Views. On the other hand, 
 many physicians, chemists, and engineers, whose scientific 
 attainments give to their opinions great weight, emphatically 
 protest against the adoption or use of a source of domestic 
 water supply that is at all subject to contamination by 
 sewage or putrefying organic matters of any kind. 
 
 There are certain laws of nature that have for their 
 object the preservation of human life to its appointed ma- 
 turity, which we term instinct, as, for instance, involuntary 
 grasping at a support to save from a threatened fall ; invol- 
 untary raising the arm to protect the eye or head from a 
 blow ; involuntary sudden withdrawal of the body from 
 contact with a hot substance that would burn. There is also 
 an instinctive repugnance to receiving any excrementitious 
 or putrefying animal substance, or anything that the eye or 
 sense of smell decides to be noxious, upon the tongue or 
 into the system. It is not safe to overlook or subdue the 
 natural instincts created within us for our preservation. 
 
 * Public Health Papers of American Public Health Association, vol. i. 
 f First Report. R. P. C., 1868, vol. i, p. 130. 
 
PRECAUTIONARY VIEWS. 155 
 
 Following are a few opinions supporting the cautionary 
 side of the question : 
 
 " Except* in rare cases, water which holds in solution a 
 perceptible proportion of organic matter becomes soon 
 putrid, and acquires qualities which are deleterious. It is 
 evident that diarrhoea, dysentery, and other acute or chronic 
 affections have been induced endemically by the continued 
 use of water holding organic matter in large proportions, 
 either in solution or in suspension. It is admitted, as the 
 result of universal observation, that the less the quantity of 
 organic matter held by the water we drink, the more whole- 
 some it is." 
 
 "Nof one has conclusively shown that it is safe to trust 
 to dilution, storage, agitation, filtration, or periods of time, 
 for the complete removal from water of disease-producing 
 elements, whatever these may be. Chemistry and micro- 
 scopy cannot and do not claim to prove the absence of these 
 elements in any specimen of drinking water." 
 
 "It:}: is a well- received fact, that decomposing animal 
 matter in drinking water is a fertile producer of intestinal 
 diseases." 
 
 Dr. Wolf (in Der Untergrund und das Frinkwasser der 
 Stadte, Erfurt, 1873) gives a large number of cases, which 
 prove conclusively that "bad water produces diarrhoea, 
 and can propagate dysentery, typhoid fever, and cholera, 
 and that such water is frequently clear, fresh, and very 
 agreeable to the taste." 
 
 Dr. Lyon Playfair, of London, remarks : "The effect of 
 
 * Boutron and Boudet. Annual of French Waters, 1851. 
 
 f Testimony of Dr. R. A. Smith before the Royal Commission of Water 
 ipply of London. 
 
 \ Report of Medical Commission on Additional Water Supply for Boston, 
 1874. 
 
156 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 
 
 organic matter in the water depends very much upon the 
 character of that organic matter. If it be a mere vegetable 
 matter, such as comes from a peaty district, even if the 
 water originally is of a pale sherry color, on being exposed 
 to the air in reservoirs, or in canals leading from one reser- 
 voir to another, the vegetable matter gets acted upon by the 
 air and becomes insoluble, and is chiefly deposited, and 
 what remains has no influence on health. But where the 
 organic matter comes from drainage, it is a most formid- 
 able ingredient in water, and is the one of all others that 
 ought to be looked upon with apprehension when it is from 
 the refuse of animal matter, the drainage of large towns, 
 the drainage of any animals, and especially of human 
 beings." 
 
 The Massachusetts State Board of Health, in their fifth 
 annual report, remarking upon the joint use of watercourses 
 for sewers and as sources of water supply for domestic use, 
 remarks: "We believe that all such joint use is to be 
 deprecated The importance of this matter is under- 
 rated for two reasons: first, because of the oft-repeated 
 assertion, made on the authority of Dr. Letheby, ' that if 
 sewage-matter be mixed with twenty times its bulk of ordi- 
 nary river water, and flow a dozen miles, there is not a 
 particle of that sewage to be discovered by chemical 
 means ;' secondly, because of the feeling that to be in any 
 way prejudicial to health, a water must contain enough 
 animal matter to be recognized readily by chemical tests 
 enough, in fact, to be expressed in figures." , 
 
 144, Speculative Condition of the Pollution 
 Question. Sanitary writings have abounded with dis- 
 cussions of this subject during the last decade ; still, look- 
 ing broadly over the field of discussion, it is evident that 
 the leading medical and chemical authorities have not 
 
SPONTANEOUS PURIFICATION. 157 
 
 agreed upon the limit for any case, or class of cases, when 
 water becomes noxious or harmful. 
 
 Some of the consumers of the waters of the Thames in 
 England and of the Mystic and Charles rivers in New Eng- 
 land, have evinced a remarkable faith in the toughness of 
 human constitutions. 
 
 The whole subject of water contamination remains as 
 yet rather physiologically speculative than chemically ex- 
 act. It is earnestly to be desired that the present experi- 
 mental practice upon human constitutions, so costly in 
 infantile life, may soon yield a sufficiency of conclusive 
 statistics, or that science shall soon unveil the subtle and 
 mysterious chemical properties of organic matters, at least 
 so far as they are now concealed behind recombinations, 
 reactions, and test solutions. 
 
 145. Spontaneous Purification. The river courses 
 are the natural drainage channels of the lands, and it can- 
 not but be expected that a considerable bulk of refuse, from 
 populous districts, will find its way to the sea by these 
 channels, however strict the sanitary regulations for the 
 preservation of the purity of the streams. Therefore it is a 
 matter of high scientific interest, and in most cases of great 
 hygienic and national importance, to determine what pro- 
 portion of the organic refuse is destroyed beyond the possi- 
 bility of harm to animals that drink the water, by spon- 
 taneous decomposition, and what proportion remains in 
 solution and suspension. 
 
 In ordinary culinary and chemical processes we find 
 that temperature has an important influence upon the dis- 
 solving property of water. Water of temperature below 
 60 Fah. dissolves meats, vegetables, herbs, sugar, or gum, 
 slowly, comparatively, and a cold atmosphere does not pro- 
 mote decomposition of organic matter. We therefore infer 
 
158 WELL, SPRING, LAKE, AND RIVER SUPPLIES. 
 
 that a temperature of both atmosphere and water as high, 
 or nearly as high, as 60 Fah. are required to promote 
 rapid oxydation of the organic impurities in water. In 
 winter the process must proceed slowly, and if the stream 
 is covered by ice, be almost suspended. Agitation of the 
 water is absolutely essential to the long-maintained pro- 
 cess of oxydation, in order that the water may continue 
 charged with the necessary bulk of oxygen in solution ; 
 therefore weirs across the stream, roughness of the bed and 
 banks of the stream, and rapidity of flow are essential ele- 
 ments in rapid oxydation. 
 
 Dr. Sheridan Murpratt remarks,* in respect to this spon- 
 taneous purification of river waters containing organic mat- 
 ters : "As a general rule, the carbon unites with oxygen to 
 form carbonic acid ; and with hydrogen to form marsh gas 
 or carbide of hydrogen ; hydrogen and oxygen unite to 
 form water ; nitrogen and oxygen with hydrogen to form 
 ammonia ; sulphur with hydrogen to form sulphide of hy- 
 drogen ; phosphorus with hydrogen to form phosphide of 
 hydrogen. 
 
 "The latter two are exceedingly o'ffensive to the sense of 
 smell, and are, moreover, highly poisonous. Thus in the 
 spontaneous decomposition of the organic matter contained 
 in water, there are produced carbonic acid, carbide of hy- 
 drogen, ammonia, sulphide of hydrogen, and phosphide of 
 hydrogen. These are the recognized compounds ;- but when 
 it is borne in mind that the gaseous emanations of decom- 
 posing animal matters are infinitely more offensive to the 
 sense of smell and injurious to health than any of the gases 
 above mentioned, or of any combination of them, it can 
 only be concluded that the effluvia of decaying organic 
 
 * Chemistry, Theoretical, Practical, and Analytical : Glasgow. 
 
A SUGAR TEST OF WATER. 
 
 159 
 
 matter contains other constituents, of which the true char- 
 
 tacter has not yet been determined." This chemical puri- 
 fication is assisted by vegetal absorption and animalculine 
 consumption. 
 
 146. Artificial Clarification. While water subjected 
 at all to organic, especially drainage or animal impurities, 
 should be avoided, if possible, for domestic consumption, 
 it should, on the .other hand, when necessarily submitted 
 to, be clarified before use, of its solids in suspension, by 
 precipitation, deposition in storage or settling basins, or by 
 one of the most thorough processes of filtration. 
 
 147. A Sugar Test of the Quality of Water. The 
 Pharmaceutical Journal quotes Heisch's simple sugar test 
 for water, as follows : 
 
 "Good water should be free from color, unpleasant 
 odor and taste, and should quickly afford a good lather 
 with a small proportion of soap. 
 
 " If half a pint of the water be placed in a clean; color- 
 less glass-stoppered bottle, a few grains of the best white 
 lump-sugar added, and the bottle freely exposed to the day- 
 light in the window of *a warm room, the liquid should not 
 become turbid, even after exposure for a week or ten days. 
 If the water becomes turbid, it is open to grave suspicion 
 of sewage contamination ; but if it remain clear, it is 
 almost certainly safe. 
 
STAND-PIPE, BOSTON. 
 

 SECTION II. 
 
 FLOW OF WATER THROUGH SLUICES, PIPES AND CHANNELS, 
 
 CHAPTER X. 
 
 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 148. Special Characteristics of Water. If we con- 
 sider those qualities of water that have reference to its 
 weight, its pressure, and its motion, we shall observe, espe- 
 cially : That the volume of the liquid is composed of an 
 immense number of minute particles ; that each particle 
 has weight individually ; that each particle can receive 
 and transmit the effect of weight, in the form of pressure, 
 in all directions ; and that the particles mow past and 
 upon each other with very slight resistance. 
 
 We are convinced by the sense of touch that the parti- 
 cles of a body of water are minute, and have very little 
 cohesion among themselves or friction upon each other, 
 when we put our hand into a clear pool and find that the 
 particles separate without appreciable resistance ; and also 
 by the sense of sight, when we see fishes and insects, and, 
 with the aid of the microscope, the tiny infusorise, moving 
 rapidly through the water, without apparent effort greater 
 than would be required to move in air. 
 11 
 
162 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 149. Atomic Theory. Ancient records of scientific 
 research inform us that the study of the divisibility and 
 nature of the particles of matter occupied, long ago, the 
 most vigorous minds. It is twenty-two centuries since 
 Democritus explained the atomic theory to his fellow- 
 citizens, and taught them that particles of matter are capa- 
 ble of subdivision again and again, many times beyond the 
 limit perceptible to human senses, but that finally the atom 
 will be reached, which is indivisible, the unit of matter. 
 Anaxagoras, the teacher of Socrates, maintained, on the 
 contrary, that matter is divisible to infinity, and that all 
 parts of an inorganic body, to infinite subdivision, are simi- 
 lar to the whole. This latter theory has not been generally 
 accepted. The whole subject of the nature of matter, in its 
 various conditions, forms, and stages of progress, has main- 
 tained its interest through the succeeding centuries, and is 
 to-day a favorite study of philosophers and theme of dis- 
 cussion in lecture halls. 
 
 150. Molecular Theory. Modern research has dem- 
 onstrated that the unit of water is composed of at least two 
 different substances, and therefore is not an atom. The 
 unit is termed a molecule, and, according to the received 
 doctrine, the foundation of each molecule of water is two 
 molecules of hydrogen and one molecule of oxygen. These 
 latter molecules may possibly be ultimate atoms. 
 
 The theory is advanced that each molecule of water is 
 surrounded by an elastic atmosphere, and by a few that it 
 is itself slightly elastic. 
 
 Sir William Thompson estimated that between five hun- 
 dred millions and five thousand millions of the molecules 
 of water may be placed side by side in the space of one 
 lineal inch. To enable us to detect the outline of one of 
 these molecules, our most powerful microscope must have 
 

 INFLUENCE OF CALORIC. 163 
 
 its magnifying power multiplied as many times again, or 
 squared. 
 
 A film of water flowing through an orifice one-hundredth 
 of an inch deep, or about the thickness of this leaf, would 
 be, according to the above estimate, from five to fifty mil- 
 lion molecule diameters in depth. It is impossible to com- 
 prehend so infinitesimal a magnitude as the diameter of one 
 of these molecules, so we shall be obliged to imagine them 
 so many times magnified as to resemble a mass of transpa- 
 rent balls, like billiard balls, for instance, or similar spheres, 
 and to consider them while so magnified. 
 
 151. Influence of Caloric. There is also a theory, 
 very generally accepted, that the molecules of water, more 
 especially their gaseous constituents, are constantly subject 
 to the influence of caloric, the cause of heat, and are in 
 consequence in incessant compound motion, both vibratory 
 and progressive, and that they are constantly moving past 
 each other, progressing with wavy motion, or are rebound- 
 ing against each other, and against their retaining vessel. 
 
 This motion may be partially illustrated by the motion 
 of a great number of smooth, transparent, elastic balls, in a 
 a vessel when the vessel is being shaken. It may be dem- 
 onstrated by placing a drop of any brilliant colored liquid, 
 for which water has an affinity, into a vessel of quiet water, 
 when the drop will be gradually diffused throughout the 
 whole mass, showing not only that among the molecules of 
 colored liquid there is activity, but that certain of the mole- 
 cules before in the vessel plunge into and through the drop 
 from all sides, dividing it into parts, and its parts again 
 into other parts, until the particles are distributed through- 
 out the mass. 
 
 While the molecules are arranged in crystalline form, 
 they require considerably more space than when in liquid 
 
164 
 
 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 form, and there are a less number of them in a cubic inch ; 
 therefore a cubic inch of ice weighs less than a cubic inch 
 of water. 
 
 152. Relative Densities and Volumes. The rela- 
 tive changes in weight and volume of water at different 
 temperatures are shown graphically in Fig. 8. When 
 
 FIG. 8. 
 
 weight is maintained constant and the temperature of the 
 water is increased or decreased, the volume will change as 
 indicated by the solid lines. When volume is maintained 
 constant and the temperature increased or decreased, the 
 weight will change as indicated by the dotted lines. 
 
 WEIGHT OF WATER. 
 
 153. Weight of Constituents of Water. Water is 
 substantially the result of the union ( 15O) of two volumes 
 of hydrogen, having a specific gravity equal to 0.0689, and 
 one volume of oxygen, having a specific gravity equal to 
 1.102 ; but various other gases that come in contact with 
 this combination are readily absorbed. 
 
 Bulk for bulk, the oxygen is sixteen times heavier than 
 the hydrogen. Water at its greatest density is about eight 
 hundred and fifteen times as heavy as atmospheric air. 
 
 The density of the vapor or gases enveloping the liquid 
 molecules is greatest at a temperature of about 39. 2 Fah. 
 At this temperature the greatest number of molecules is 
 
FORMULA FOR VOLUMES. 165 
 
 contained in one cubic inch, and the greatest weight for a 
 given volume obtains. 
 
 As the temperature of water rises from 39. 2, its gaseous 
 elements expand and are supposed to increase their activity ; 
 and a less number of molecules can be contained in a cubic 
 inch, or other given volume ; therefore the weight of water de- 
 creases as the temperature rises from 39. 2 Fall, (vide Fig. 8.) 
 
 154. Crystalline Forms of Water. As the temper- 
 ature falls below 39.2 Fah., the molecules, under one at- 
 mosphere of pressure, incline to arrange themselves in 
 crystalline form, their action is supposed to be more vibra- 
 tory and less progressive, and they become ice at a temper- 
 ature of about 32 Fah. 
 
 The relative weights and volumes of distilled water at 
 different temperatures on the Fahrenheit scale are shown 
 numerically in the table on the following page. 
 
 Although there is a slight difference in the results of 
 experiments of the best investigators in their attempts to 
 obtain the temperature of water at its maximum density, it 
 is commonly taken at 39.2 Fah., and the weight of a cubic 
 foot of water at this temperature as 62.425 pounds, and the 
 weight of a United States gallon of water at the same tem- 
 perature as 8.379927 pounds. 
 
 155. Formula for Volumes at Different Temper- 
 atures. The tables of weights and volumes of water is 
 extended, with intervals of ten degrees, to the extreme limits 
 within which hydraulic engineers have usually to experi- 
 ment. The intermediate weights and volumes for inter- 
 mediate temperatures, may be readily interpolated, or 
 reference may be had to the following formulas taken from 
 Watt's "Dictionary of Chemistry," combining the law of 
 expansion as determined by experiments of Matthiessen, 
 Sorby, Kopp, and Rossetti. 
 
166 
 
 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 TABLE No. 38. 
 
 WEIGHT AND VOLUME OF DISTILLED WATER AT DIFFERENT 
 TEMPERATURES. 
 
 Temperature 
 Fah. 
 
 Weight of a cu. 
 ft. in pounds. 
 
 Difference. 
 
 Ratio of volume to 
 volume of equal wt. 
 at max. density of 
 temperature, 
 39.2 Fah. 
 
 Difference. 
 
 Ice. 
 
 57.200 
 
 
 
 .916300 
 
 
 32 
 
 62.417 
 
 5- 2I 7 
 
 .000129 
 
 .083829 
 
 39-2 
 
 62.425 
 
 .008 
 
 .OOOOOO 
 
 .000129 
 
 40 
 
 62.423 
 
 .002 
 
 .000004 
 
 .000004 
 
 50 
 
 62.409 
 
 .014 
 
 .000253 
 
 .000249 
 
 60 
 
 62.367 
 
 .042 
 
 .000929 
 
 .000676 
 
 70 
 
 62.302 
 
 .065 
 
 .001981 
 
 .001052 
 
 80 
 
 62.218 
 
 .084 
 
 .00332 
 
 .001339 
 
 90 
 
 62. 119 
 
 .099 
 
 .00492 
 
 .OOl6o 
 
 100 
 
 62.OOO 
 
 .119 
 
 .00686 
 
 .00194 
 
 110 
 
 61.867 
 
 i33 
 
 .00902 
 
 .00216 
 
 120 
 
 61.720 
 
 .147 
 
 .01143 
 
 .00241 
 
 130 
 
 61.556 
 
 .164 
 
 .01411 
 
 .OO268 
 
 o 
 I4O 
 
 61.388 
 
 .168 
 
 .01690 
 
 .00279 
 
 15 
 
 6 i . 204 
 
 .184 
 
 .01995 
 
 .00305 
 
 160 
 
 6 i .007 
 
 .197 
 
 .02324 
 
 .00329 
 
 170 
 
 60.801 
 
 .206 
 
 .02671 
 
 .00347 
 
 1 80 
 
 60.587 
 
 .214 
 
 .03033 
 
 00362 
 
 o 
 
 IQO 
 
 60.366 
 
 .221 
 
 ,03411 
 
 .00378 
 
 o 
 200 
 
 60. 136 
 
 .230 
 
 .03807 
 
 .00396 
 
 210 
 
 59- 8 94 
 
 .242 
 
 .04226 
 
 .00419 
 
 212 
 
 59-707 
 
 .187 
 
 .04312 
 
 .00086 
 
 Let V= ratio of a given volume of distilled water, at the 
 temperature, T, on Fahrenheit's scale, to the volume of an 
 equal weight, at the temperature of maximum density. 
 
 W= weight of a cubic foot of distilled water, in pounds, 
 at any temperature, Fahrenheit. 
 
 For temperatures 32 to 70 Fah. 
 
 V= 1.00012 0.000033914 x (T 32) + 0.000023822 x 
 (T 32) 2 0.000000006403 (T 32) 3 . 
 
COMPRESSIBILITY AND ELASTICITY OF WATER. 167 
 For temperatures above 70. 
 
 Y = 0.99781 + 0.00006117 x (T - 32) + 0.000001059 x 
 (T - 32) 2 . 
 
 w= 62,425 
 
 156. Weight of Pond Water. Fresh pond and 
 brook waters are slightly heavier than distilled water, and 
 when not loaded with sediment have, for a given volume, 
 an increased weight equal to from 0.00005 to 0.0001 of an 
 equal volume of distilled water. 
 
 157. Compressibility and Elasticity of Water. 
 The compression of rain-water, according to experimental 
 results of Canton, is 0.000046 and of sea-water 0.000040 of 
 its volume under the pressure of one atmosphere. 
 
 According to experiments of Regnault, water suffers a 
 diminution of volume amounting to 48 parts in one million, 
 when submitted to the pressure of one atmosphere, equal to 
 14.75 pounds per square inch, and to 96 parts when sub- 
 mitted to twice that pressure. 
 
 Grassi found the compressibility of water to be 50 parts 
 at 37 Fah., and 44 parts at 127 Fah. in each million 
 parts, with one atmosphere pressure. 
 
 A column of water 100 feet high would, according to 
 these estimates, be compressed nearly one-sixteenth of an 
 inch. 
 
 The degree of elasticity of fluids was discovered by Can- 
 ton in 1762. He proved that the volume of liquids dimin- 
 ished slightly in bulk under pressure and proportionally 
 to the pressure, and recovered their original volume when 
 the pressure ceased. 
 
 This has been confirmed by experiments of Sturm, 
 (Ersted, Eegnault, and others. 
 
168 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 PRESSURE OF WATER. 
 
 158. Weights of Individual Molecules. If again 
 we consider the molecules of water magnified, as before ex- 
 plained, we can conceive that each molecule has its indi- 
 vidual weight, and is subject, independently, to the force 
 of gravity. Consider again the film of water of one-hun- 
 dredth of an inch in depth, flowing through the orifice of 
 same depth, and imagine the orifice to be magnified also in 
 the same proportion as the molecules have been imagined 
 to be magnified, that is, to five million molecule diameters ; 
 then the immense leverage that gravity has, proportionally, 
 upon each molecule to set it in motion and to press it out 
 of the orifice can be conceived, and the reason why there is 
 apparently so little frictional resistance to the passage of 
 the molecules over each other will be apparent. 
 
 159. Individual Molecular Actions. The magnified 
 molecule can also be conceived to be acting independently 
 upon any side of its retaining vessel, or upon any other 
 molecule, with which it is in contact, with the combined 
 weight or pressure of all the molecules acting upon it. 
 
 In a volume of fluid, each molecule presses in any 
 direction from which a sufficient resistance is opposed, 
 with a pressure due to the combined natural pressures of 
 all molecules acting upon it in that direction, and also 
 with the pressure transmitted through them from any 
 exterior force. 
 
 In treatises on hydrostatics, propositions relating to 
 pressures of fluids are commonly stated in some form sim- 
 ilar to the following :* " When a fluid is pressed by its own 
 weight, or by any other force, at any point it presses 
 equally in all directions." 
 
 * Vide Button's Mathematics, Hydrostatics, 310. 
 
INDIVIDUAL MOLECULAR REACTIONS. 
 
 169 
 
 16O. Pressure Proportional to Depth. The pres- 
 sure of a fluid at any point on an immersed surface, is in 
 proportion to the vertical depth of that point below the sur- 
 face of the fluid ; but not in proportion to variable breadths 
 of the fluid. 
 
 In vessels of shapes similar to Fig. 9 and Fig. 10, con- 
 taining equal vertical depths of water, the pressures on 
 equal areas of the horizontal bottoms are equal ; also the 
 pressures on equal and similar areas of their vertical sides, 
 having their centres of gravity at equal depths, are equal. 
 
 FIG. 9. 
 
 FIG. 10. 
 
 ej 
 
 a 
 
 CLJ 
 
 161. Individual Molecular Keactions. Any parti- 
 cle of fluid that receives a pressure reacts with a force equal 
 to tlie pressure, if its motion is resisted upon the opposite side. 
 
 Any point of a fixed surface pressed by a particle of 
 water reacts upon the particle with a force equal to the 
 pressure of the particle. 
 
 The large body of water in the section A of the tank, 
 Fig. 9, is perfectly counterbalanced by the slender body 
 in the section a". A pressure equal to that due to the 
 weight of all the particles above the horizontal bottom sur- 
 face, /, acts upon that surface, and the surface reacts with an 
 equal pressure and sustains all those particles. The effect 
 would be similar if the surface, or a portion of it, was in- 
 clined or curved ; therefore, only a pressure equal to the 
 
170 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 weight of those particles vertically over the opening in the 
 partition, /, acts upon the column below the partition /. 
 The right and left horizontal pressures of the individual 
 particles of A are transmitted to the particles on the right 
 and left, which, in turn, react with equal pressures, and sus- 
 tain them from motion sideways. The particles in contact 
 with the partitions a and 5 transmit their pressures horizon- 
 tally to the partition, which in turn react and sustain them, 
 and all the particles remain in equilibrium. 
 
 162. Equilibrium Destroyed by an Orifice. If an 
 orifice is made at the bottom of the side #, then the particles 
 at that point will be relieved of the reaction of the point, or 
 of its support, equilibrium will be destroyed, and motion 
 will ensue, and all the particles throughout A will begin to 
 move toward the orifice, though not with equal velocities. 
 
 163. Pressures from Vertical, Inclined and Bent 
 Columns of Water. In Fig 10 the particles in the body 
 of water, B, are pressed with a pressure due to the weight 
 of any one vertical column of particles or molecules in the 
 body of water above the opening in the partition #, conse- 
 quently the reaction horizontally from any point in the 
 partition c', or downward from any point in the covering 
 partition g, or upward from any point in the bottom d, is 
 equal to the weight of a column of molecules pressing upon 
 that point, of height equal to the depth of the given point 
 below the surface of the water a'U. The pressure due to 
 this vertical column of molecules would still remain the 
 same if the colnmn a'g was inclined or bent, so long as the 
 water surface remained in the level a' V, as is evident by 
 inspection of the column ~b." 
 
 Since the downward reaction from, any point in the sur- 
 face g is equal to the pressure of a column of molecules 
 equal in height to a' g, this reaction is added to the action 
 
PRESSURE UPON A UNIT OF SURFACE. 171 
 
 of gravity on all the molecules beneath the given point in g, 
 therefore the pressure on any point in d, beneath the given 
 point in g, is equal to the pressure of a column of molecules 
 of height a' d. 
 
 164. Artificial Pressure. If in the vessel illustrated 
 by Fig. 10, we close the openings 5' and 5" at the level of 
 the water surface, and fit a piston carrying a weight into 
 the opening a', then we will increase the pressure at points 
 d, g, <?', 5', &", etc., respectively, an amount equal to the 
 pressure received by a point in contact with the piston at a'. 
 This artificial pressure is equal in effect to a column of fluid 
 placed upon a' of weight equal to the weight of the loaded 
 piston. 
 
 165. Pressure upon a Unit of Surface. Since one 
 cubic foot of water, measuring 144 square inches on its 
 base and 12 inches in height weighs 62.425 pounds, there 
 must be a pressure exerted by its full bottom area of 62.425 
 pounds, and by each square inch of its bottom area of 
 
 32 425 Ibs \ V 
 
 v^tt 0.433472 pounds for each foot of vertical 
 144 sq. in. / j^> 
 
 depth of the water. 
 
 In ordinary engineering calculations 62.5 pounds is 
 taken as the weight of one cubic foot of water, and 0.434 
 pounds as the resulting pressure per square inch for each 
 vertical foot of depth below the surface of the water. These 
 weights used in the computation of the following table, give 
 closely approximate results, slightly in excess of the true 
 weights. 
 
 In nice calculations, as for instance, relating to tests of 
 turbines to determine their useful effect, or of pumping 
 engines to determine their duty, the weights due to the 
 measured temperatures of the water are to be taken. 
 
172 
 
 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 TABLE No. 39. 
 
 PRESSURES OF WATER AT STATED VERTICAL DEPTHS BELOW THE 
 SURFACE OF THE WATER, AT TEMP. 39.2 FAH. 
 
 DEPTH. 
 
 PRESSURE PER 
 SQ. INCH. 
 
 PRESSURE PER 
 SQ. FOOT. 
 
 DEPTH. 
 
 'RESSURE PER 
 SQ. INCH. 
 
 PRESSURE PER 
 SQ. FOOT. 
 
 Feet. 
 
 Pounds. 
 
 Pounds. 
 
 Feet. 
 
 Pounds. 
 
 Pounds. 
 
 I 
 
 4335 
 
 62.425 
 
 36 
 
 15.60 
 
 2247.30 
 
 2 
 
 .8670 
 
 124.85 
 
 37 
 
 16.04 
 
 2309.72 
 
 3 
 
 1.300 
 
 187.27 
 
 38 
 
 16.47 
 
 2372.15 
 
 4 
 
 1-734 
 
 248.70 
 
 39 
 
 16.91 
 
 2434-57 
 
 5 
 
 2.167 
 
 312.12 
 
 40 
 
 17-34 
 
 2497.00 
 
 6 
 
 2.601 
 
 374-55 
 
 4^ 
 
 17.77 
 
 255942 
 
 7 
 
 3-035 
 
 436.97 
 
 42 
 
 1 8.21 
 
 2621.85 
 
 8 
 
 3.468 
 
 499.40 
 
 43 
 
 18.64 
 
 2684.27 
 
 9 
 
 3.902 
 
 561.82 
 
 44 
 
 19.07 
 
 2746.70 
 
 10 
 
 4-335 
 
 624.25 
 
 45 
 
 I9-5 1 
 
 2809.12 
 
 ii 
 
 4.768 
 
 686.67 
 
 46 
 
 19.94 
 
 287L55 
 
 12 
 
 5.202 
 
 749.10 
 
 47 
 
 20.37 
 
 2933-97 
 
 13 
 
 5-636 
 
 811.52 
 
 48 
 
 20.81 
 
 2996.40 
 
 14 
 
 6.069 
 
 873-95 
 
 49 
 
 21.24 
 
 3058.82 
 
 15 
 
 6-503 
 
 936.37 
 
 5 
 
 21.67 
 
 3121.25 
 
 16 
 
 6.936 
 
 998.80 
 
 60 
 
 26.01 
 
 3745-5 
 
 i? 
 
 7-370 
 
 1061.23 
 
 70 
 
 30.35 
 
 437o 
 
 18 
 
 7.803 
 
 1123.65 
 
 80 
 
 34-68 
 
 4994 
 
 19 
 
 8.237 
 
 1186.07 
 
 90 
 
 39.01 
 
 5618 
 
 20 
 
 8.670 
 
 1248.50 
 
 IOO 
 
 43-35 
 
 6242.5 
 
 21 
 
 9.104 
 
 1310.92 
 
 no 
 
 47.68 
 
 6867 
 
 22 
 
 9-537 
 
 1373-35 
 
 120 
 
 52.02 
 
 7491 
 
 2 3 
 
 9.971 
 
 1435-77 
 
 130 
 
 56.36 
 
 8115 
 
 2 4 
 
 10.40 
 
 1498.20 
 
 I4O 
 
 60.69 
 
 8739 
 
 25 
 
 10.84 
 
 1560.62 
 
 !5 
 
 65-03 
 
 9364 
 
 26 
 
 11.27 
 
 1623.05 
 
 1 60 
 
 69.36 
 
 9988 
 
 27 
 
 11.70 
 
 1685.47 
 
 170 
 
 73-70 
 
 10612 
 
 28 
 
 12.14 
 
 1747.90 
 
 1 80 
 
 78.03 
 
 11237 
 
 29 
 
 I2 -57 
 
 1810.32 
 
 190 
 
 82.36 
 
 11861 
 
 30 
 
 13.00 
 
 1872.75 
 
 200 
 
 86.70 
 
 12485 
 
 3i 
 
 13-44 
 
 I935-I7 
 
 210 
 
 91.04 
 
 13109 
 
 3 2 
 
 13-87 
 
 1997.60 
 
 220 
 
 95-37 
 
 13733 
 
 33 
 
 I4-3 1 
 
 2060.02 
 
 230 
 
 99.71 
 
 14358 
 
 34 
 
 14.74 
 
 2122.45 
 
 240 
 
 104.04 
 
 14982 
 
 35 
 
 I5-I7 
 
 2184.87 
 
 2 5 
 
 108.37 
 
 15606 
 
 166. Equivalent Forces. In many computations in 
 elementary statics we are accustomed to consider the force 
 
A LINE A MEASURE OF WEIGHT. 
 
 173 
 
 acting from a weight as equivalent to the force of a pressure 
 and to place weights to represent statical forces. 
 
 On one square foot of the bottom of a vessel containing 
 one foot depth of water, a pressure is exerted by the water 
 that would tend to prevent any other force from lifting up 
 that bottom. We might remove that water and substitute 
 the pressure of a quantity of oil, or of stone, or of iron, as 
 an equivalent for the pressure of the water, but to be an 
 exact equivalent its weight must be exactly the same as the 
 weight of the water. In this case we should take for the 
 62.5 pounds pressure in the water, 62.5 pounds weight of 
 oil, or of stone, or of iron. 
 
 167. Weight a Measure of Pressure. Weight is, 
 then, a standard whose unit is one pound, by which pres- 
 sures may be compared and measured. 
 
 168. A Line a Measure of Weight In graphical 
 
 statics we are also accustomed to represent weights by lines 
 which are drawn to some scale. 
 
 If two forces act upon the centre of gravity of a body, 
 Fig. 11, one of which, a, is equal to 30 pounds, and the 
 other 5, to 40 pounds, we can, after adopting some scale, 
 
174 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 say one inch, to equal one pound, represent the force a by 
 a line 30 inches long, drawn from some given point, g, in its 
 direction of action, ga\ and the force b by a line 40 inches 
 long, drawn from the same point, in its direction, gb'. N"ow, 
 if we draw lines from the end of each line thus produced 
 parallel to the other line to r, completing the parallelogram, 
 and then draw the diagonal, gr, then the resultant of the 
 two forces will pass through the line gr, and the length of 
 gr will represent the combined effect of the two forces in 
 
 this direction. Its length will be 50 inches = V(gfff + (b'r) 2 , 
 and the combined effect of the two forces in this direction 
 will be 50 pounds. 
 
 169. A Line a Measure of Pressure upon a Sur- 
 face. Let the dimensions of the top surface of the body A, 
 be 10 feet long and 3 feet wide, and its area be 30 square 
 feet ; let the side dimensions, B, be 10 feet long and 4 feet 
 high, and its area be 40 square feet ; let the pressure upon 
 each surface be one pound per square foot, and the direc- 
 tion of the pressure be shown by the arrows a and 5. The 
 body being solid, the forces are to be considered as acting 
 through its centre of gravity. We can now plot the pres- 
 sure upon A of 30 pounds in its direction, and upon B of 
 40 pounds in its direction, and the diagonal of the parallel- 
 ogram gr will give the direction and ratio of the resultant, 
 as before. The forces being equal to those before considered 
 as acting upon a point, will again give a diagonal 50 inches 
 long and indicating an effect of 50 pounds. 
 
 It is plain, then, that we can take the line ga', or the 
 line &'r, which is equal to it, to represent the force or pres- 
 sure a acting upon the point g or upon the surface A ; and 
 we can take the line gb', or the line a'r, to represent the 
 force or pressure ~b acting upon the point g or the surface B, 
 and the line gr to represent the combined effect of the two 
 
ANGULAR RESULTANT 
 
 / 
 
 IF 
 
 ts 
 
 /y 
 
 , 
 
 RCE 
 
 4 
 
 p WF g> FORcsfcy , jt> ^ " 
 
 ;V ^ / ^> 
 
 it is cbn^BOTr.tp be4"ble 
 
 Xj^Vv **/ 
 
 forces. In various calculations 
 to do this. 
 
 170. Diagonal Force of Combined !*resstn:es 
 Graphically Represented. Again, if we know the mag- 
 nitude of the force r acting through the centre of the body, 
 and we desire to know the magnitude of the effects upon 
 the sides A and B, in directions at right angles to them, 
 that produced the force r, we draw the line r to a scale in 
 the direction the force acts, and from both of its ends draw 
 lines to the same scale in directions at right angles to the 
 sides A and B, and proportional to their areas, as^a' and gb', 
 and complete the parallelogram ; then will ga' measured to 
 scale indicate the effect of the force a upon A, and gb' 
 measured to scale indicate the force b upon B. If gr 
 measures 50 pounds, then will ga' measure 30 pounds and 
 gb' measure 40 pounds. 
 
 171. Angular Resultant of a Force Graphically 
 Represented. If a force represented by the line ag, 
 Fig. 12, acts upon and at right 
 
 angles to an inclined surface fe 
 at g, then its horizontal resultant 
 will be represented by the line 
 bg, and the end b will be perpen- 
 dicularly beneath a. The ratios 
 of the lengths of the lines ag and 
 ab and bg are the ratios of the 
 effects of the force in their three 
 directions respectively. 
 
 If a perpendicular line be let fall from / upon the hori- 
 zontal line ed, intersecting it in d, then the ratio of fe tofd 
 will be equal to the ratio of ag to bg ; consequently, the 
 horizontal pressure or effect of the force ag upon fe would 
 be to its direct effect as/<$ is tofe. Therefore, the ratio of 
 
 FIG. 12. 
 
176 
 
 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 the line fd to fe equals the ratio of the horizontal effect of 
 the direct force upon/b. 
 
 The ratio of the vertical downward effect of the force a 
 upon fe is to its direct effect as the length ab to the length 
 ag, and also as the length ed to the length ef. Therefore, 
 the ratio of the line or surface ed to the line fe represents 
 the ratio of the vertical downward effect of the direct force 
 uponfe. 
 
 172. Angular Effects of a Force Represented by 
 the Sine and Cosine of the Angle. Also, ab is the 
 sine, and bg the cosine of the angle agn, and we have seen 
 that their ratios are to radius ag as ed and fd are to fe; 
 therefore the vertical and horizontal effects of the force a 
 upon the inclined surface/*? are to its direct force as the sine 
 and cosine of the angle efd is to radius/e. 
 
 173. Total Pressure. To find the total pressure of 
 quiet water on any given surface : Multiply togetlier, its 
 area, in square feet; the vertical depth of its centre of 
 gravity, below the water surface, in feet; and the weight 
 
 of one cubic foot of water 
 c in pounds (= 62.5 Ibs.). 
 
 In the tank, Fig. 13, 
 filled with water, let the 
 depth ab be 9 feet ; then 
 the centre of gravity of 
 the surface ab will be at 
 a depth from a equal to 
 one-half ab = 4 J feet. If 
 the length of the side ab 
 is 1 foot, then the total pressure on ab will equal 
 
 9 ft. x 1 ft. x 4J ft. x 62.5 Ibs. = 2531.25 Ibs. 
 
 174. Direction of Maximum Effect. The direction 
 of the maximum effect of a pressure on a plane surface is 
 
 FIG. 13. 
 
CENTRES OF PRESSURE AND OF GRAVITY. 177 
 
 always at right angles to the surface. The maximum hori- 
 zontal effect of the pressure on the unit of length of ab 
 equals the product of ab, into the depth of its centre of 
 gravity, into the unit of pressure. The horizontal effect of 
 pressure on the unit of length of cd equals the product of 
 its vertical projection ce, into the depth of its centre of 
 gravity, into the unit of pressure ; and the vertical effect of 
 pressure on cd equals the product of its horizontal projec- 
 tion de, into the depth of its centre of gravity, into the unit 
 of pressure. 
 
 175. Horizontal and Vertical Effects. Assuming 
 the length of the side cd to be radius of the angle dee, then 
 the total pressure on cd is to its horizontal effect as radius 
 cd is to the cosine ce of the angle dee, or as the surface cd 
 is to its vertical projection ce; and the total pressure is to 
 its vertical effect as radius cd is to the sine de of the same 
 angle, or as cd to de. 
 
 The total pressure on dg is to its horizontal effect as dg 
 is to/*/, or to the cosine of the angle dgf; and to its vertical 
 effect as dg to df, or to the sine of the angle dgf. 
 
 176. Centers of Pressure and of Gravity. The 
 centre of hydrostatic pressure, which tends to overturn or 
 push horizontally the surface of equal width, ab, is not in 
 the center of gravity of that surface, but in a point at two- 
 thirds the depth from a at p = 6 feet. 
 
 The center of gravity of the surface cd is at one-half the 
 vertical depth ce, at h, or at one-half the length of the slope 
 cd, at h. The points h and h' are both in the same hori- 
 zontal plane. When the water surface is at ac, the center 
 of pressure of the surface cd is at two-thirds of the vertical 
 depth ce, at p', or at two-thirds the slope cd, at p. The 
 points p' and p are in the same horizontal plane. If ce 
 equals six feet, then the center of gravity of cd or ce will be 
 12 
 
178 
 
 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 at the vertical depth of three feet = ch', and the center of 
 pressure at the vertical depth of four feet = cp'. 
 
 The center of gravity of the surface dg is at a depth 
 from the water surface c, equal to the sum of one-half the 
 
 -, and the 
 
 vertical depth fg added to the depth ce = ce 
 center of pressure of dg is at a vertical depth equal to 
 = c <= 7.6 feet. 
 
 FIG. 14. 
 
 177. Pressure upon a Curved Surface and Effect 
 upon its Projected Plane. In a vessel, Fig. 14, filled 
 with water, one of whose ends, a5, is a segment of a cylin- 
 
 der, and opposite end in 
 part of the vertical plane 
 a"/b", and in part of a 
 hemisphere cd, the total 
 pressure on ab will he 
 as the total surface ab; 
 but its horizontal effect 
 will be as the area of its 
 vertical projection a'b'. The total pressure on the end a"b", 
 will be as the remaining surface of the vertical plane a"b" 
 increased by the concave surface of the hemisphere cM, but 
 its horizontal effect will be equal to its vertical projection 
 a"'V" or a'V. The vertical effect on 
 the plane a"b" is equal to zero, but 
 the vertical effect of the pressure in 
 the hemisphere is represented by 
 the plan of one -half a sphere of 
 diameter equal to cd. 
 
 In a hollow sphere, Fig. 15, filled 
 with water, the total pressure will 
 be as the total concave surface a'Tib'k", but the horizontal 
 
 FIG. 15. 
 
FLOATING AND SUBMERGED BODIES. 179 
 
 effect will be as its vertical projection at), which represents 
 a circular vertical plane of diameter equal to ab, and the 
 vertical effect will be as its horizontal projection bb", which 
 represents a horizontal circular area of diameter equal 
 to bb". 
 
 In a pipe, or cylinder, represented also in section by 
 Fig. 15, the total pressure within is as the inner circumfer- 
 ential area a'hb'h", and when the cylinder lies horizontally 
 the horizontal and vertical effects of its pressure in a unit 
 of length will be represented by its vertical and horizontal 
 projections ab and bb". 
 
 If the cylinder is inclined, the pressure at any point 
 upon its circumference is as the depth of that point below 
 the surface of the water, and the total pressure in pounds 
 upon any section of the cylinder will be found by multi- 
 plying its area in square feet into the depth of its center of 
 gravity, in feet, below the surface of the water and their 
 product into the weight, in pounds (62.5 Ibs.), of a cubic 
 foot of water. 
 
 178. Center of Pressure upon a Circular Area. 
 The center of pressure of a vertical circular area, repre- 
 sented also by Fig. 15, when its top a is in the water surface, 
 is at a depth below a equal to five-fourths the radius of the 
 circle. 
 
 179. Combined Pressures. The sum of pressures in 
 pounds, upon a number of adjacent surfaces, may be found 
 by multiplying the sum of their surfaces in square feet into 
 the depth of their common center of gravity, in feet, below 
 the surface of the water, and this product into the weight of 
 one cubic foot of water, in pounds (62.5 Ibs.). 
 
 ISO. Sustaining Pressure upon Floating and 
 Submerged Bodies. The pressure tending to sustain a 
 cylinder floating vertically in water c (Fig. 16) is equal to 
 
180 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 FIG. 16. FIG. 17. 
 
 fL 
 
 the vertical effect of the pressure on its bottom area. The 
 sustaining pressure may "be computed, in pounds, by mul- 
 tiplying the bottom area of the cylinder, in square feet, into 
 its depth, in feet (which gives the cubical contents of the 
 immersed portion of the cylinder), and this product into 
 the weight of a cubic foot of water. 
 
 The weight of water displaced may be computed also by 
 multiplying the cubic contents of the immersed portion of 
 the cylinder, in cubic feet, into the weight of a cubic foot 
 of water. The two results will be equal to each other ; 
 therefore the vertical effect tending to sustain the cylinder 
 is equal to the weight of water displaced. 
 
 To compute the pressure tending to sustain the trun- 
 cated cone, or pyramid, d, multiply the vertical projection 
 of the inclined surfaces (= top area bottom area), in feet, 
 into the depth of their common center of gravity, in feet, 
 and to this product add the product of its bottom area, in 
 feet, into its depth, in feet, and then multiply the sum of 
 the products into the weight of a cubic foot of water, in 
 pounds. 
 
 This sustaining pressure will also equal the weight of 
 the water displaced. 
 
 To compute the pressure tending to sustain the im- 
 mersed cube , multiply, in terms as before, the bottom 
 
UPWARD PRESSURE UPON A SUBMERGED LINTEL. 181 
 
 area into the depth, and into the weight of water, and from 
 the final product subtract the product of the top area into 
 its depth and into the weight of water. This sustaining 
 pressure also equals the weight of water displaced. 
 
 The downward pressure on the top of e tends to sink it, 
 and the upward pressure on its bottom to sustain it. The 
 difference of the two effects is the resultant. The resultant 
 will act vertically through the center of gravity of the body. 
 If e is of the same specific gravity as the water, then its 
 weight will just balance the resultant, and it will neither 
 rise or fall ; if of less specific gravity it will rise ; if of 
 greater, it will sink. The cylinder c is evidently of less 
 specific gravity than the water, and d of the same specific 
 gravity. 
 
 Let c be a hollow cylinder with a water-tight bottom, 
 then although it may be made of iron, and weights be 
 placed within it, it will still float if its total weight, includ- 
 ing its load, is less than the weight of the water it displaces. 
 On the same principle iron ships float and sustain heavy 
 cargoes. 
 
 181. Upward Pressure upon a Submerged Lin- 
 tel. If _, Fig. 17, be a horizontal lintel covering a sluice 
 between two reservoirs, the upward pressure of the water 
 upon ij, tending to lift it, will be equal to the product of 
 the rectangular area ij into its depth and into the weight 
 of a cubic foot of water ; that is, the upward pressure in 
 pounds will be equal to the weight in pounds of a prism 
 of water having the rectangular area ij for its base and the 
 depth of ij below the surface of the water for its height. 
 
 If the lintel is constructed of timber, at a considerable 
 depth, and is not equally as strong as the enclosing walls 
 of the reservoir at the same depth, it may be broken in or 
 thrust upward. 
 
182 
 
 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 FIG. 18. 
 
 182. Atmospheric Pressure. Upon the particles of 
 all bodies of water resting in open vessels or reservoirs, 
 
 there is a force constantly 
 acting, in addition to the 
 direct force of gravity, upon 
 the independent particles. 
 This force comes from the 
 effect of gravity upon the 
 atmosphere. The weight 
 of the atmosphere produces 
 a pressure upon the sur- 
 face of the water of about 
 14.75 pounds per square 
 
 inch, or about 2124 pounds per square foot. This is equiv- 
 alent to a column of water (0^0470 ff ) 34.028 feet high. 
 
 In the open vessel, Pig. 18, filled with water to the level 
 a, the effect of the pressure of the atmosphere is transmitted 
 through the particles, and acts on all the interior surface 
 below the water surface abb' a', with a force of 14.75 pounds 
 on every square inch, in addition to the pressure from the 
 weight of the water. There is also an equal atmospheric 
 pressure on the exterior of the vessel of 14.75 pounds per 
 square inch ; therefore the resultant is zero, and the weighl 
 of the atmosphere does not tend to move either side of the 
 vessel or to tear the vessel asunder. 
 
 183. Rise of Water into a Vacuum. -If the tube cd 
 be extended to a height of thirty -five or more feet above th( 
 surface of the water, and a piston, containing a proper valve, 
 be closely fitted in its upper end, then by means of the pistoi 
 the air may be pumped out of the tube, and the surface of 
 water in the tube relieved of atmospheric pressure. The 
 equilibrium of the particles within the tube will then be de- 
 
TRANSMISSION OF PRESSURE TO A DISTANCE. 183 
 
 stroyed, and the pressure of the atmosphere acting through 
 the particles in the lower end of the tube will press the 
 water up the tube to a height, according to the perfection 
 of the vacuum, of 34.028 feet approximately. It is atmos- 
 pheric pressure that causes pump cylinders to fill when they 
 are above the free surface of the water. 
 
 If the bottom of the immersed tube, cd, be closed by a 
 valve, and the tube filled with water, and the top then 
 sealed at a height of thirty-five or more feet above the sur- 
 face of the water aa', the valve at d may afterwards be 
 opened, and the pressure of the atmosphere acting through 
 the particles in the lower end of the tube will sustain the 
 column to a height of 34.028 feet approximately. 
 
 184. Siphon. If the bent tube or siphon, efg, Fig. 18, 
 having its leg/*? longer, vertically, than its leg ef, be filled 
 with water and its end e inserted in the water A, then the 
 action of gravity upon the water in the leg fg, will be 
 greater than upon the water in the leg ef, and the equi- 
 librium in the particles at / will be destroyed. The pres- 
 sure of the atmosphere on the surface aa', will constantly 
 press the water A up the leg ef, tending to restore the equi- 
 librium, and gravity acting in the leg fg will as constantly 
 
 md to destroy the equilibrium, consequently there will be 
 constant flow of the water A out of the end g, until the 
 rater surface falls nearly to the level e, or until the air can 
 iter at e. 
 
 185. Transmission of Pressure to a Distance. 
 The effect of pressure on a fluid is transmitted through Us 
 
 trticles to any distance, Tiowever indefinitely great, to the 
 imit of its volume. 
 
 If water is poured into the open top 5", Fig. 10, the divi- 
 sion b'c", will fill as fast as the division W, and the water 
 ill flow over Vg, and will reach the level a', at approxi- 
 
184 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 mately the same time as it reaches b" ; so in any inverted 
 siphon, or in a system of water pipes of a town, water will 
 in consequence of transmitted pressure, flow from an ele- 
 vated source down through a valley and up on an opposite 
 hill to the level of the source. If the syphon, or pipe, has 
 an indefinite number of branches with open tops as high as 
 the source, then the surface of the water at the source and 
 in each of the branches will rest in the same relative eleva- 
 tion of the earth's curvature. 
 
 186. Inverted Siphon. By transmission of pressure 
 through the particles, water in a pool or lake near the sum- 
 mit of one hill or mountain is sometimes, when the rock 
 strata have been bent into a favoring shape, forced through 
 a natural subterranean inverted siphon, and caused to flow 
 out as a spring on an opposite hill or mountain summit. 
 
 187. Pressure Convertible Into Motion. Thus we 
 see that the force of gravity in the form of weight is con- 
 vertible into pressure, and pressure into motion ; and that 
 motion may be converted into pressure, and pressure be 
 equivalent to weight. 
 
 Motion we are accustomed to measure by its rate, which 
 we term its velocity ; that is, the number of units of space 
 passed over by the moving body in a unit of time, as, feet 
 per second. 
 
 MOTION OF WATER. 
 
 188. Flow of Water. All forces tending to destroy 
 equilibrium among the particles of a ~body of water tend 
 to produce motion in that body. 
 
 We have above referred to the accepted theory of motion 
 due to the influence of caloric ; there is a motion of water 
 due to the winds, a motion due to the attraction of the 
 heavenly bodies, and an artificial motion, as, for instance, 
 
ACCELERATION OF MOTION. 185 
 
 that due to the pressure of a pump-piston. The motion 
 herein to be considered is that originated by the influence 
 of gravity and termed the flow of water. 
 
 189. Action of Gravity upon Individual Mole- 
 cules. All natural flow of water is due to the force of 
 gravity, acting upon and generating motion in its indi- 
 vidual molecules. 
 
 If in the side of a vessel filled with water there be made 
 an orifice ; if one end of a level pipe filled with water be 
 lowered ; or if a channel filled with water have its water 
 released at one end, then equilibrium among the particles 
 of the water will be destroyed, and motion of the water will 
 ensue. Gravity is the force producing motion in either case, 
 and it acts upon each individual molecule as it acts upon a 
 solid body, free to move, or devoid of friction. 
 
 190. Frictionless Movement of Molecules. The 
 molecules of water move over and past each other with such 
 remarkable ease that they have usually been considered as 
 devoid of friction. 
 
 The formulas in common use for computing the velocity 
 with which water flows from an orifice in the bottom or side 
 of a tank filled with water, assume that the individual 
 molecules, at the axis of the jet, will issue with a velocity 
 equal to that the same molecules would have acquired if 
 they had fallen freely, in vacuo, in obedience to gravity, from 
 a height above the orifice equal to the height of the surface 
 of the water. 
 
 191. Acceleration of Motion. The force of gravity 
 perpetually gives new impulse to a falling body and accel- 
 erates its motion, if unresisted, in regular mathematical 
 proportion. 
 
 Experiment has shown that a solid body falling freely 
 in vacuo, at the level of the sea, passes through a space or 
 
186 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 height of 16.1 feet nearly, during the first second of time ; 
 has a velocity at the end of the first second of 32.2 feet 
 nearly, and is accelerated in each succeeding second 32.2 
 feet nearly. The usual symbol of this rate of acceleration 
 is g, the initial of the word gravity r , and we shall have fre- 
 quent occasion for its use. 
 
 The latitude and altitude, or distance from the centre of 
 the earth, affects the rate of motion slightly, but does not 
 affect materially the results of ordinary hydrodynamic cal- 
 culations. 
 
 The resistance of the air affects slightly the motion of 
 dense bodies, and retards them more if they are just sepa- 
 rating, as water separates into spray. 
 
 192. Equations of Motion. The velocity, v 9 acquired 
 by a solid body at the end of any time, t, equals the prod- 
 uct of time into its acceleration by gravity, g, and is directly 
 proportional to the time : 
 
 v : g : : t : 1, or v = gt. 
 
 The height, 7i, through which the body falls in one 
 second of time equals ^7, and the heights in any given 
 times, t, are as the squares of those times : 
 
 Ji : \g :: t* : (I) 2 , or 
 and, by transposition, we have 
 
 g 
 
 This value of t in the equation of v gives 
 
 From these equations we deduce the following general 
 equations of time, t; height, h; velocity, v; and accelera- 
 tion, g : 
 
PARABOLIC PATH OF THE JET. 
 
 t = *- = M = J = .031063* 
 
 g v V ff 
 
 k = ^ = ^ = ~ = .015536* 2 
 
 187 
 (1) 
 
 = = =32.1908 
 
 (3) 
 
 (4) 
 
 The fo'me, space, and velocity are at the ends of the first 
 ten seconds as follows : 
 
 Time (zO 
 Space (A) 
 
 16.1 
 
 2 
 64.4 
 
 3 
 144.0 
 
 257.6 
 
 5 
 
 6 
 
 788 o 
 
 8 
 
 9 
 
 10 
 
 Velocity (z>) 
 
 
 644 
 
 06 6 
 
 1288 
 
 
 
 
 
 2898 
 
 
 Acceleration^) 
 
 ^2.2 
 
 72.2 
 
 02.2 
 
 02.2 
 
 72.2 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 193. Parabolic Path of the Jet. If we plot the 
 
 spaces of the column of 
 spaces or heights to a 
 scale on a vertical line, 
 beginning with zero at 
 the top, and then from 
 the space points plot 
 horizontally to scale the 
 velocities, as in Fig. 19, 
 and then from zero draw 
 a curved line <zc, cutting 
 the extremities of the 
 horizontal lines, the 
 curve ac will be a pa- 
 rabola, the vertical line 
 ab its abscissa, and the 
 horizontal lines its ordi- 
 nates. 
 
 ;S*j FIG. 19. 
 
 33 .fl Velocity in feet per second. 
 
188 
 
 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 194. Velocity of Efflux Proportional to the Head. 
 
 If in the several sides of a reservoir A, Fig. 19 a, kept 
 filled with water, orifices with thin edges are made at 
 depths of 20 feet, 25 feet, 50 feet, 75 feet, and 100 feet from 
 the surface of the water, then water will issue from each 
 
 FIG. 190. 
 
 orifice in a direction perpendicular to the side, with a veloc- 
 ity proportional to the square root of the head of water 
 above the centre of gravity of the orifice, and equal approx- 
 imately to the velocity one of its particles would have 
 acquired if it had fallen freely from the height of the head. 
 195. Conversion of the Force of Gravity from 
 Pressure into Motion. The accumulated vertical force 
 of gravity due to the head or " charge" will act upon the 
 
EQUAL PRESSURES GIVE EQUAL VELOCITIES. 189 
 
 particles as pressure before the orifice is opened, but in- 
 stantly upon an orifice being opened pressure will impel 
 the particles of water in the direction of the axis of the 
 orifice, and gravity will begin anew to act upon the parti- 
 cles in a vertical direction. If the axis of the orifice is not 
 vertical, gravity will deflect the particles through a curved 
 path. 
 
 196. Resultant Effects of Pressure and Gravity 
 upon the Motion of a Jet. If on a line at, drawn 
 through the center of an orifice, perpendicular to the plane 
 
 of the orifice, we plot to scale the products of any given 
 times into a given velocity, and from each of the points 
 thus indicated we plot vertically downward the distance, a 
 body will fall freely in those times, op, and then from the 
 orifice draw a line through the extremities of the vertical 
 lines, the curved line thus sketched will indicate the path 
 of the jet flowing from the orifice. The curved line is a 
 parabola, to which the axis of the orifice is tangent ; and 
 the distances ao upon the tangent are equal and parallel to 
 ordinates, and represent the force per unit of time given to 
 the particles of the jet by pressure, and the verticals from 
 the tangent are equal and parallel to abscisses, and repre- 
 sent by their increase the accelerating effect of gravity upon 
 the falling particles. The distances ao and op, ordinates op, 
 and abscisses aa', form a series of parallelograms, one angle 
 of which lies in the orifice and the opposite angles of which 
 lie in the curved path of the jet, and the diagonals of which 
 are equal to resultants of the effects of pressure and gravity. 
 
 197. Equal Pressures give Equal Velocities in all 
 Directions, The velocities of issues, downward from the 
 orifice d and upward from the orifice c, and horizontally 
 from the lower orifice b', will be equal, since they all are at 
 the same depth. 
 
190 
 
 WEIGHT, PRESSURE, AND MOTION OF WATER. 
 
 198. Resistance of the Air. Since the velocity of 
 upward issue from c is due to the gravity force of the head 
 dc, acting as pressure, the jet should theoretically reach the 
 level of the water surface d. The spreading of the particles 
 and consequent enhanced resistance of the air prevents such 
 result, and the resistance increases as the ratio of area of 
 orifice to height of head decreases. 
 
 199. Theoretical Velocities. The foUowing table of 
 theoretical velocities and times due to given heights or heads 
 has been prepared to facilitate calculation : 
 
 TABLE No. 4O. 
 
 CORRESPONDENT HEIGHTS, VELOCITIES, AND TIMES OF FALLING 
 
 BODIES. 
 
 H = ^ 
 
 2<r 
 
 v = Vzgn 
 
 t= ^?M 
 
 
 
 U=^ 
 
 2g 
 
 = V^H. 
 
 ,.5 
 
 s 
 
 Head in feet 
 
 Velocity in feet 
 per second. 
 
 Time 
 in seconds. 
 
 Head in feet. 
 
 Velocity in feel 
 per second. 
 
 Time 
 in seconds. 
 
 .010 
 
 .80 
 
 .0248 
 
 145 
 
 3.05 
 
 .0949 
 
 .015 
 
 .98 
 
 .0304 
 
 .150 
 
 3-n 
 
 .0964 
 
 .020 
 
 13 
 
 0350 
 
 155 
 
 3.16 
 
 .0980 
 
 .025 
 
 27 
 
 0394 
 
 .160 
 
 3-21 
 
 0995 
 
 .030 
 
 39 
 
 .0431 
 
 .165 
 
 3-26 
 
 .1011 
 
 035 
 
 50 
 
 .0465 
 
 .170 
 
 3-31 
 
 .1016 
 
 .040 
 
 .60 
 
 .0496 
 
 -175 
 
 3.36 
 
 .1042 
 
 045 
 
 .70 
 
 .0527 
 
 .180 
 
 3-40 
 
 .1054 
 
 .050 
 
 79 
 
 0555 
 
 .185 
 
 3-45 
 
 .1069 
 
 055 
 
 .88 
 
 0583 
 
 .190 
 
 3-50 
 
 .1085 
 
 .060 
 
 97 
 
 .0611 
 
 -195 
 
 3-55 
 
 .1100 
 
 .065 
 
 2.04 
 
 .0632 
 
 .20 
 
 3-59 
 
 .1113 
 
 .O7O 
 
 2.12 
 
 .0657 
 
 .21 
 
 3-68 
 
 .1141 
 
 .075 
 
 2.20 
 
 .0682 
 
 .22 
 
 3-76 
 
 .1166 
 
 .080 
 
 2.27 
 
 .0704 
 
 23 
 
 3-85 
 
 1193 
 
 .085 
 
 2-34 
 
 .0725 
 
 .24 
 
 3-93 
 
 .1221 
 
 .090 
 
 2.41 
 
 .0747 
 
 25 
 
 4.01 
 
 .1243 
 
 .095 
 
 2.47 
 
 .0766 
 
 .26 
 
 4-09 
 
 .1268 
 
 .100 
 
 2-54 
 
 .0787 
 
 .27 
 
 4.17 
 
 .1293 
 
 .105 
 
 2.60 
 
 .0806 
 
 .28 
 
 4-25 
 
 1317 
 
 .110 
 
 2.66 
 
 .0825 
 
 .29 
 
 4-32 
 
 1339 
 
 .115 
 
 2.72 
 
 .0843 
 
 30 
 
 4-39 
 
 .1361 
 
 .120 
 
 2.78 
 
 .0862 
 
 31 
 
 4-47 
 
 .1386 
 
 .125 
 
 2.84 
 
 .0880 
 
 32 
 
 4-54 
 
 .1407 
 
 .130 
 
 2.89 
 
 .0896 
 
 33 
 
 4.61 
 
 .1429 
 
 135 
 
 2-95 
 
 .0914 
 
 34 
 
 4.68 
 
 1451 
 
 .140 
 
 3.00 
 
 0930 
 
 35 
 
 4-75 
 
 .1472 
 
. 
 
 THEORETICAL VELOCITIES. 
 
 191 
 
 CORRESPONDENT HEIGHTS, VELOCITIES, AND TIMES OF FALLING 
 BODIES ( Continued. ) 
 
 -5 
 
 v = V 2 U 
 
 l= m 
 
 s 
 
 H=^ 
 
 2 
 
 v = y 2 n 
 
 f = ym 
 
 g 
 
 Head in feet. 
 
 Velocity in feet 
 per second. 
 
 Time 
 in seconds. 
 
 Head in feet. 
 
 Velocity in feet 
 per second. 
 
 Time 
 in seconds. 
 
 .36 
 
 4 .8l 
 
 .1491 
 
 83 
 
 7-31 
 
 .2266 
 
 37 
 
 4.87 
 
 .1510 
 
 .84 
 
 7-35 
 
 .2278 
 
 .38 
 
 4.94 
 
 1531 
 
 85 
 
 7.40 
 
 .2294 
 
 39 
 
 5-oi 
 
 1553 
 
 .86 
 
 7-44 
 
 .2306 
 
 .40 
 
 5-07 
 
 1572 
 
 87 
 
 7.48 
 
 .2319 
 
 .41 
 
 5-14 
 
 1593 
 
 .88 
 
 7-53 
 
 2334 
 
 .42 
 
 5-20 
 
 .1612 
 
 .89 
 
 7-57 
 
 2347 
 
 43 
 
 5.26 
 
 .1634 
 
 .90 
 
 7.61 
 
 2359 
 
 44 
 
 5-32 
 
 .1649 
 
 .91 
 
 7-65 
 
 2377 
 
 45 
 
 5.38 
 
 .1668 
 
 .92 
 
 7.70 
 
 .2387 
 
 .46 
 
 5-44 
 
 .1686 
 
 93 
 
 7-74 
 
 2399 
 
 47 
 
 5-50 
 
 1705 
 
 94 
 
 7-78 
 
 .2412 
 
 .48 
 
 5.56 
 
 .1724 
 
 95 
 
 7.82 
 
 .2424 
 
 49 
 
 5.62 
 
 .1742 
 
 .96 
 
 7.86 
 
 2437 
 
 50 
 
 5.67 
 
 1758 
 
 97 
 
 7.90 
 
 2449 
 
 5i 
 
 5-73 
 
 1779 
 
 .98 
 
 7-94 
 
 .2461 
 
 52 
 
 5-79 
 
 1795 
 
 99 
 
 7.98 
 
 .2474 
 
 53 
 
 5-85 
 
 .1813 
 
 
 8.03 
 
 .2491 
 
 54 
 
 5-90 
 
 .1829 
 
 .02 
 
 8.10 
 
 .2518 
 
 55 
 
 5-95 
 
 .1844 
 
 .04 
 
 8.18 
 
 2543 
 
 56 
 
 6.00 
 
 .i860 
 
 .06 
 
 8.26 
 
 .2567 
 
 57 
 
 6.06 
 
 .1879 
 
 .08 
 
 8-34 
 
 .2589 
 
 58 
 
 6. ii 
 
 .1894 
 
 .10 
 
 8.41 
 
 .2616 
 
 59 
 
 6.17 
 
 1913 
 
 .12 
 
 8.49 
 
 .2638 
 
 .60 
 
 6.22 
 
 .1928 
 
 .14 
 
 8-57 
 
 .2660 
 
 .61 
 
 6.28 
 
 1947 
 
 .16 
 
 8.64 
 
 .2685 
 
 .62 
 
 6. 3 2 
 
 .1959 
 
 .18 
 
 8.72 
 
 .2706 
 
 .63 
 
 6-37 
 
 1975 
 
 .20 
 
 8.79 
 
 .2730 
 
 .64 
 
 6.42 
 
 .1990 
 
 .22 
 
 8.87 
 
 2751 
 
 .65 
 
 6.47 
 
 .1999 
 
 .24 
 
 8.94 
 
 .2774 
 
 .66 
 
 6.52 
 
 .2O2I 
 
 .26 
 
 9.01 
 
 .2797 
 
 .67 
 
 6-57 
 
 2037 
 
 .28 
 
 9.08 
 
 .2819 
 
 .68 
 
 6.61 
 
 .2049 
 
 30 
 
 9- J 5 
 
 .2842 
 
 .69 
 
 6.66 
 
 .2065 
 
 32 
 
 9.21 
 
 .2866 
 
 70 
 
 6.71 
 
 .2080 
 
 34 
 
 9.29 
 
 .2885 
 
 7i 
 
 6.76 
 
 .2096 
 
 .36 
 
 9-36 
 
 .2906 
 
 72 
 
 6.81 
 
 .2111 
 
 38 
 
 9-43 
 
 .2927 
 
 73 
 
 6.86 
 
 .2127 
 
 .40 
 
 9-49 
 
 .2950 
 
 74 
 
 6.91 
 
 .2142 
 
 .42 
 
 9-57 
 
 .2968 
 
 75 
 
 6-95 
 
 .2154 
 
 44 
 
 9-63 
 
 .2991 
 
 .76 
 
 6.99 
 
 .2167 
 
 .46 
 
 9.70 
 
 .3010 
 
 77 
 
 7.04 
 
 .2182 
 
 .48 
 
 9-77 
 
 .3030 
 
 78 
 
 7.09 
 
 .2198 
 
 50 
 
 9-83 
 
 3052 
 
 79 
 
 7-13 
 
 .22IO 
 
 55 
 
 9.98 
 
 .3106 
 
 .80 
 
 7.18 
 
 .2226 
 
 .60 
 
 10.2 
 
 3137 
 
 .81 
 
 7.22 
 
 .2238 
 
 65 
 
 10.3 
 
 .3204 
 
 .82 
 
 7.26 
 
 .2251 
 
 .70 
 
 10.5 
 
 3238 
 
192 WEIGHT, PRESSURE, AND MOTION OF WATERS. 
 
 CORRESPONDENT HEIGHTS, VELOCITIES, AND TIMES OF FALLING 
 BODIES (Continued?) 
 
 H=^ 
 
 *g 
 
 v = VzgH 
 
 t= i/ 
 g 
 
 H=^ 
 
 2<r 
 
 v = V 2ig H 
 
 I= VM 
 
 g 
 
 Head in feet. 
 
 Velocity in feet 
 per second. 
 
 Time 
 in seconds. 
 
 Head in feet. 
 
 Velocity in feel 
 per second. 
 
 Time 
 in seconds. 
 
 1-75 
 
 10.6 
 
 .3302 
 
 8.4 
 
 23.3 
 
 .7210 
 
 i. 80 
 
 10.8 
 
 3333 
 
 8.6 
 
 23-5 
 
 .7319 
 
 1.85' 
 
 10.9 
 
 3394 
 
 8.8 
 
 23.8 
 
 7395 
 
 1.90 
 
 n. i 
 
 .3423 
 
 9 
 
 24.1 
 
 .7469 
 
 i-95 
 
 II. 2 
 
 .3482 
 
 9.2 
 
 24-3 
 
 .7572 
 
 2. 
 
 II.4 
 
 .3509 
 
 9.4 
 
 24.6 
 
 .7642 
 
 2.1 
 
 II.7 
 
 3590 
 
 9.6 
 
 24.8 
 
 .7742 
 
 2.2 
 
 II. 9 
 
 .3697 
 
 9.8 
 
 25.1 
 
 .7809 
 
 2-3 
 
 12.2 
 
 3770 
 
 10. 
 
 25.4 
 
 .7866 
 
 2. 4 
 
 12-4 
 
 .3871 
 
 10.5 
 
 26. 
 
 .8077 
 
 2-5 
 
 12.6 
 
 .3968 
 
 II. 
 
 26.6 
 
 .8277 
 
 2.6 
 
 I2. 9 
 
 .4031 
 
 II-5 
 
 27.2 
 
 .8456 
 
 2.7 
 
 13.2 
 
 .4091 
 
 12. 
 
 27.8 
 
 .8633 
 
 2.8 
 
 13.4 
 
 .4179 
 
 12.5 
 
 28.4 
 
 .8803 
 
 2.9 
 
 13.7 
 
 .4234 
 
 13- 
 
 28.9 
 
 .8997 
 
 3- 
 
 13-9 
 
 .4317 
 
 13.5 
 
 29-5 
 
 9*53 
 
 3-i 
 
 I4.I 
 
 -4397 
 
 14. 
 
 30. 
 
 9333 
 
 3-2 
 
 14-3 
 
 .4476 
 
 14-5 
 
 30-5 
 
 .9508 
 
 3-3 
 
 14.5 
 
 4552 
 
 IS- 
 
 3LI 
 
 .9646 
 
 3-4 
 
 14.8 
 
 4595 
 
 15.5 
 
 31-6 
 
 .9810 
 
 3-5 
 
 IS- 
 
 .4667 
 
 16. 
 
 32.1 
 
 .9969 
 
 3-6 
 
 15.2 
 
 4737 
 
 16.5 
 
 32.6 
 
 .0123 
 
 3-7 
 
 15.4 
 
 .4805 
 
 17- 
 
 33-1 
 
 .0272 
 
 3.8 
 
 I 5 .6 
 
 .4872 
 
 17.5 
 
 33-6 
 
 .0417 
 
 3-9 
 
 15.8 
 
 4937 
 
 18. 
 
 34- 
 
 .0588 
 
 4. 
 
 16. 
 
 .5000 
 
 18.5 
 
 34-5 
 
 .0725 
 
 4.2 
 
 16.4 
 
 5122 
 
 19. 
 
 35- 
 
 .0857 
 
 4-4 
 
 16.8 
 
 5238 
 
 19.5 
 
 35-4 
 
 .1017 
 
 4.6 
 
 17.2 
 
 5343 
 
 20. 
 
 35-9 
 
 .1142 
 
 4.8 
 
 17-6. 
 
 5454 
 
 20.5 
 
 36.3 
 
 .1295 
 
 5- 
 
 17.9 
 
 .5587 
 
 21. 
 
 36.8 
 
 1413 
 
 5-2 
 
 18.3 
 
 .5683 
 
 21.5 
 
 37-2 
 
 1559 
 
 5-4 
 
 18.7 
 
 5775 
 
 22. 
 
 37.6 
 
 .1702 
 
 5-6 
 
 19. 
 
 * .5895 
 
 22.5 
 
 38.1 
 
 .1811 
 
 5-8 
 
 19.3 
 
 .6010 
 
 23. 
 
 38.5 
 
 .1948 
 
 6. 
 
 19.7 
 
 .6091 
 
 23.5 
 
 38.9 
 
 .2082 
 
 6.2 
 
 20. 
 
 .6200 
 
 24. 
 
 39-3 
 
 .2214 
 
 6.4 
 
 20.3 
 
 6305 
 
 24.5 
 
 39-7 
 
 2343 
 
 6.6 
 
 20.6 
 
 .6408 
 
 25 
 
 40.1 
 
 .2469 
 
 6.8 
 
 20-9 
 
 .6507 
 
 26 
 
 40.9 
 
 .2714 
 
 7- 
 
 21.2 
 
 .6604 
 
 27 
 
 41.7 
 
 .2950 
 
 7.2 
 
 21.5 
 
 .6698 
 
 28 
 
 42-5 
 
 .3176 
 
 7-4 
 
 21.8 
 
 .6789 
 
 2 9 
 
 43-2 
 
 .3426 
 
 7.6 
 
 22.1 
 
 .6878 
 
 30 
 
 43-9 
 
 .3667 
 
 7-8 
 
 22.4 
 
 .6964 
 
 31 
 
 44.7 
 
 .3870 
 
 8. 
 
 22.7 
 
 .7048 
 
 32 
 
 45-4 
 
 .4097 
 
 8.2 
 
 23- 
 
 .7130 
 
 33 
 
 46.1 
 
 .4317 
 
THEORETICAL VELOCITIES. 
 
 193 
 
 CORRESPONDENT HEIGHTS, VELOCITIES, AND TIMES OF FALLING 
 BODIES ( Continued?) 
 
 H=^ 
 
 2- 
 
 v = VzgH. 
 
 ,= ^H 
 S 
 
 H=^! 
 2<r 
 
 v= VzgH 
 
 * m y* 
 
 s 
 
 
 
 Head in feet. 
 
 Velocity in feet 
 per second. 
 
 Time 
 in seconds. 
 
 Head in feet. 
 
 Velocity in feet 
 per second. 
 
 Time 
 in seconds. 
 
 34 
 
 46.7 
 
 .4561 
 
 77 
 
 70.4 
 
 2.1874 
 
 35 
 
 47-4 
 
 .4768 
 
 78 
 
 70.9 
 
 2.2003 
 
 36 
 
 48.1 
 
 .4968 
 
 79 
 
 71-3 
 
 2. 2160 
 
 37 
 
 48.8 
 
 .5164 
 
 80 
 
 71.8 
 
 2.2284 
 
 33 
 
 49-5 
 
 5354 
 
 81 
 
 72.2 
 
 2.2438 
 
 39 
 
 50.1 
 
 .5569 
 
 82 
 
 72.6 
 
 2.25 9 
 
 40 
 
 50-7 
 
 5779 
 
 83 
 
 73-1 
 
 2.2709 
 
 4i 
 
 51-3 
 
 .5984 
 
 84 
 
 73-5 
 
 2.285 7 
 
 42 
 
 52. 
 
 .6154 
 
 85 
 
 74-o 
 
 2.2973 
 
 43 
 
 52.6 
 
 6350 
 
 86 
 
 74-4 
 
 2.3II8 
 
 44 
 
 53-2 
 
 .6541 
 
 87 
 
 74-8 
 
 2 . 3262 
 
 45 
 
 53-8 
 
 .6729 
 
 88 
 
 75-3 
 
 2-3373 
 
 46 
 
 54-4 
 
 .6912 
 
 89 
 
 75-7 
 
 2.35H 
 
 47 
 
 55- 
 
 .7090 
 
 90 
 
 76.1 
 
 2.3653 
 
 48 
 
 55-6 
 
 .7266 
 
 9i 
 
 76.5 
 
 2.3791 
 
 49 
 
 56.2 
 
 .7438 
 
 92 
 
 76.9 
 
 2.3927 
 
 50 
 
 56.7 
 
 .7637 
 
 93 
 
 77-4 
 
 2.4031 
 
 51 
 
 57-3 
 
 .7801 
 
 94 
 
 77.8 
 
 2.4165 
 
 52 
 
 57-8 
 
 7993 
 
 95 
 
 78.2 
 
 2.4297 
 
 53 
 
 58.4 
 
 .8151 
 
 96 
 
 78.6 
 
 2.4427 
 
 54 
 
 59- 
 
 8305 
 
 97 
 
 79.0 
 
 2.4557 
 
 55 
 
 59-5 
 
 .8487 
 
 98 
 
 79-4 
 
 2.4685 
 
 56 
 
 60. 
 
 .8667 
 
 99 
 
 79-8 
 
 2.4812 
 
 57 
 
 60.6 
 
 .8812 
 
 100 
 
 80.3 
 
 2.4907 
 
 58 
 
 61.1 
 
 .8985 
 
 125 
 
 89.7 
 
 2.7871 
 
 59 
 
 61.6 
 
 .9156 
 
 150 
 
 98.3 
 
 3-0519 
 
 60 
 
 62.1 
 
 9324 
 
 175 
 
 106 
 
 3.3019 
 
 61 
 
 62.7 
 
 9458 
 
 200 
 
 114 
 
 3.5088 
 
 62 
 
 63.2 
 
 .9620 
 
 225 
 
 1 20 
 
 3.7500 
 
 63 
 
 63.7 
 
 .9780 
 
 250 
 
 126 
 
 3-9683 
 
 64 
 
 64.2 
 
 1.9938 
 
 275 
 
 133 
 
 4-1353 
 
 65 
 
 64.7 
 
 2.0093 
 
 300 
 
 139 
 
 4.3165 
 
 66 
 
 65.2 
 
 2.0245 
 
 350 
 
 150 
 
 4.6667 
 
 67 
 
 65.7 
 
 2.0396 
 
 400 
 
 160 
 
 5.0000 
 
 68 
 
 66.2 
 
 2.0544 
 
 450 
 
 170 
 
 5-2941 
 
 69 
 
 66.7 
 
 2.0690 
 
 500 
 
 179 
 
 5.5866 
 
 70 
 
 67.1 
 
 2.0864 
 
 550 
 
 188 
 
 5.85H 
 
 7i 
 
 67.6 
 
 2.1006 
 
 600 
 
 197 
 
 6.0914 
 
 72 
 
 68.1 
 
 2.1145 
 
 700 
 
 212 
 
 6.6038 
 
 73 
 
 68.5 
 
 2.1313 
 
 800 
 
 227 
 
 7.0485 
 
 74 
 
 69. 
 
 2.1449 
 
 9OO 
 
 241 
 
 7.4689 
 
 75 
 
 69.5 
 
 2.1583 
 
 1000 
 
 254 
 
 7.8740 
 
 76 
 
 69.9 
 
 2.1745 
 
 
 
 
CHAPTEE XI. 
 
 FLOW OF WATER THROUGH ORIFICES. 
 
 200. Motion of the Individual Particles. If an 
 
 aperture is made in the bottom or side of a tank, filled with 
 water, the particles of water will move from all portions of 
 the body toward the opening, and each particle flowing out 
 will arrive at the aperture with a velocity, T 7 , dependent 
 upon the pressure or head of water upon it, and, as we shall 
 see hereafter, upon its initial position. 
 
 201. Theoretical Volume of Efflux. If we assume 
 the fluid veins to pass out through the orifice parallel with 
 each other, and with a velocity due to the head upon each, 
 and the section of the jet to be equal to the area, &, of the 
 orifice, then the theoretical volume, or quantity, $, of dis- 
 charge will equal 8 x V= SV%gH; H being the head upon 
 the centre of the orifice, and g the acceleration of gravity 
 per second = 32.2 feet. We have then for the theoretical 
 volume 
 
 Q = 8 V2gH. 
 
 V 2O2. Converging Path of Particles. The particles 
 are observed to approach the orifice, not in parallel veins, 
 but by curved converging paths, and if the partition is 
 "thin" the convergence is continued slightly beyond the 
 partition, a distance dependent upon the velocity of the 
 particles. 
 
 2O3. Classes of Orifices. If the top of the orifice is 
 beneath the surface of the water, the orifice is termed a sub- 
 merged orifice, and if the surface of the water is below the 
 
RATIO OF MINIMUM SECTION OF JET. 
 
 195 
 
 top of the orifice, the notch is termed a "weir." We are 
 now to consider submerged orifices. 
 
 2O4. Form of Submerged Orifice-jet. In Fig. 20 
 is shown a submerged circular orifice in thin partition. 
 
 FIG. 21. 
 
 FIG. 20. 
 
 In Fig. 21 are delineated more clearly the proportions 
 of the issuing jet at the contracted vein, or vend conlractd, 
 as it was termed by Newton. The form of the contracted 
 vein has been the subject of numerous measurements, and 
 as the result of late experiments writers now usually assign 
 to the three dimensions FK^ fJc, and LI, the ratios 1.00, 
 0.7854, 0.498, as mean proportions of circular jets not ex- 
 ceeding one-half foot diameter. 
 
 2O5. Ratio of Minimum Section of Jet. The par- 
 ticles of the jet that arrive at the centre of the orifice have a 
 direction parallel with the axis of the orifice. The particles 
 that arrive near the perimeter have converging directions, 
 and since they have individually both weight and velocity, 
 they have also individual force or momentum in their direc- 
 tions. This force must be deflected into a new direction, 
 and as it can be most easily deflected through a curved 
 
196 FLOW OF WATER THROUGH ORIFICES. 
 
 path, the curve is continued until the particles have paral- 
 lelism. The point where the direction of the particles is 
 parallel is at a distance from the inside of a small square- 
 edged orifice, equal to about one-half the diameter of the 
 orifice, and the diameter of the jet at that point is equal 
 to about 0.7854 of the diameter of the orifice. The cross- 
 section of a circular jet at the same point has therefore a 
 mean ratio to the area of the orifice as (0.7854) 2 to (l.OO) 2 , 
 or as 0.617 to 1.00. 
 
 206. Volume of Efflux. If the velocity due to the 
 head upon the center of the orifice is the mean velocity of 
 all the particles of the jet, then we have for the volume of 
 discharge, 
 
 Q = 0.617# x V, or Q = 0.617 SVZgH. (2) 
 
 The real volume, Q, of the jet, and its ratios of velocity 
 and of contraction, have been the subjects of many obser- 
 vations, and have engaged the attention of the ablest ex- 
 perimentalists and hydraulicians, from time to time, during 
 many years. 
 
 207. Coefficient of Efflux. In every jet flowing 
 through a thin orifice there is a reduction of the diameter 
 of the jet immediately after it passes the orifice. Some 
 fractional value of the area S, or the velocity F, or the 
 the theoretical volume $, must therefore be taken that is, 
 they must be multiplied by some fraction coefficient to com- 
 pensate for the reduction of the theoretical volume of the 
 jet. This fractional coefficient is termed the coefficient of 
 discharge. Place the symbol c to represent this coefficient, 
 and the formula for volume of discharge becomes 
 
 Q = cSVZgH. (3) 
 
 2O8. Maximum Velocity of the Jet. The point 
 where the mean velocity of the particles is greatest is in the 
 
 
PRACTICAL USE OF A COEFFICIENT. 197 
 
 least section of the jet, and here only can it approximate to 
 V%gH. The mean velocity will be less at the entrance to 
 the orifice, and also after passing the contraction, than in 
 the contraction. When speaking of the velocity of the par- 
 ticles or of the jet hereafter, in connection with orifices, the 
 maximum velocity that is, the velocity in the contraction 
 is referred to, unless otherwise specially stated. 
 
 2O9. Factors of the Coefficient of Efflux. If the 
 edges of the orifice are square, the circumferential particles 
 of the jet receive some reaction from them ; therefore only 
 the axial particles can have a velocity equal to V%gH, and 
 the mean velocity is a small fraction less. 
 
 In such case the general coefficient of discharge (c) will 
 be the product of two factors, one representing the reduc- 
 tion of velocity, and the other the reduction of the sectional 
 area of the jet. 
 
 We shall have occasion to investigate these factors after 
 we have determined the value of the general coefficient. 
 
 21O. Practical Use of a Coefficient. The usefulness 
 of a coefficient, when it is to be applied to new computa- 
 tions, depends upon its accord with practical results. 
 
 All new and successful hydraulic constructions of orig- 
 inal design must have their proportions based upon com- 
 putations previously made. Those computations must be 
 founded upon hydrodynamic formulae in which the co- 
 efficient performs a most important office. In fact the 
 skillful application of formulae to hydraulic designs de- 
 pends upon the skillful adaptation of the one or more co- 
 efficients therein. 
 
 The coefficient product adopted must harmonize with 
 jsults before obtained, practically or experimentally, and 
 ie parallelism of all the conditions of the old or experi- 
 lental structure and the new design .cannot be too closely 
 
198 
 
 FLOW OF WATER THROUGH ORIFICES. 
 
 scrutinized when an experimental result is to control a new- 
 design for practical execution. 
 
 211. Experimental Coefficients. A few experimental 
 results are here submitted as worthy of careful study. 
 
 From Michelotti. The following table of experi- 
 ments with square and circular orifices, by Michelotti, we 
 find quoted by Neville.* They refer to a very carefully 
 made set of experiments, with an extensive apparatus 
 specially prepared, near Turin, where the apparatus was 
 supplied with the waters of the Doire by a canal. 
 
 The table is given by Neville in French measures, but 
 they are given here as we have reduced ' them to English 
 measures. 
 
 TABLE No. 41. 
 COEFFICIENTS FROM MICHELOTTI'S EXPERIMENTS. 
 
 DESCRIPTION, AND SIZE OF ORIFICE, 
 IN FEET. 
 
 Depth upon 
 the center of 
 the orifice 
 in feet. 
 
 Quantity 
 discharged in 
 cubic feet. 
 
 Time of 
 discharge in 
 seconds. 
 
 Resulting 
 coefficients 
 of discharge. 
 
 
 7.05 
 
 561.240 
 
 600 
 
 .619 
 
 
 7-30 
 
 685.762 
 
 720 
 
 .619 
 
 Square orifice, 3.197" x 3.197" 
 
 12.43 
 
 625.652 
 
 510 
 
 .610 
 
 = .071 square foot section. . .. 
 
 12.59 
 
 741-036 
 
 600 
 
 .611 
 
 
 23.13 
 
 502.931 
 
 300 
 
 .612 
 
 
 23.14 
 
 604.362 
 
 360 
 
 .613 
 
 Square orifice, 2. 13156" x 2.13156" 
 = .0315 square foot section . . 
 
 7.06 
 12.17 
 
 22.86 
 
 399-266 
 512.650 
 466. 500 
 
 900 
 900 
 600 
 
 .660 
 .645 
 .643 
 
 Sq. orifice, 1.06578" x 1.06578" 
 = .0079 square foot section. . 
 
 7.20 
 
 12.59 
 22.90 
 
 191.940 
 198.300 
 681.500 
 
 1800 
 1440 
 3600 
 
 .628 
 .612 
 .625 
 
 Circular orifice, 3.197" diameter 
 .05577 square foot section.. 
 
 7.13 
 12.31 
 23.03 
 
 657.130 
 691.200 
 631.090 
 
 900 
 720 
 480 
 
 .611 
 .610 
 .612 
 
 Circular orifice, 2.13156" diam. 
 = 0.2477 square foot section.. 
 
 7-23 
 11.71 
 23-44 
 
 591.610 
 713.700 
 
 696. 700 
 
 1800 
 1680 
 I2OO 
 
 .616 
 .605 
 .605 
 
 Circular orifice, 1.06578" diam. 
 = .0062 square foot section. . . 
 
 7-33 
 12.51 
 
 23-45 
 
 299.449 
 392.370 
 538.158 
 
 3600 
 3600 
 3600 
 
 .619 
 .620 
 .621 
 
 Circular orifice, 6.378" diameter. 
 
 6.92 
 
 12.01 
 
 
 :::: 
 
 .619 
 .619 
 
 Hydraulic Tables, by John Neville, C. E. ; M.R.I.A., London, 1853. 
 
EXPERIMENTAL COEFFICIENTS. 
 
 199 
 
 From Abbe Bossut. From experiments made by the 
 Abbe Bossut we have the following results, as reduced to 
 English measures : 
 
 T A BLE No. 42, 
 COEFFICIENTS FROM BOSSUT'S EXPERIMENTS. 
 
 DESCRIPTION, POSITION, AND SIZE OF ORIFICE, 
 
 Depth of the 
 centre of 
 
 Discharge, 
 in cubic 
 
 Resulting 
 
 IN INCHES. 
 
 the orifice, 
 
 feet per 
 
 coefficient. 
 
 
 in feet. 
 
 minute. 
 
 
 Lateral and circular, .53289" diameter 
 
 
 I 006 
 
 61 
 
 1.06578" 
 
 Q *\O 
 
 
 6l7 
 
 " .53289" " 
 
 4 273 
 
 72-1 
 
 616 
 
 1.06578" " 
 
 4 2T\ 
 
 j 952 
 
 619 
 
 1.06578" " 
 
 
 
 
 Horizontal and circular, .53289" diameter.. . 
 
 12 54 
 
 *2C5 
 
 
 " 1.06578" 
 
 12.54 
 
 5.040 
 
 .617 
 
 " 2.13156" 
 
 12.54 
 
 20. 201 
 
 .618 
 
 Horizontal and square, 1.06578" x 1.06578". . . 
 
 12-54 
 
 6.417 
 
 .617 
 
 " " 2.13156" x 2. 13156".. . 
 
 12.54 
 
 25.717 
 
 .618 
 
 Horizontal and rectangular, 1.06578" x .26644" 
 
 12.54 
 
 1-593 
 
 .613 
 
 From Rennie. We have also, from experiments of 
 Kennie with circular and square orifices, under low heads, 
 the following : 
 
 T A BLE No. 43. 
 COEFFICIENTS FOR CIRCULAR ORIFICES. 
 
 Heads at the centre 
 of the orifice, 
 in feet. 
 
 Jinch 
 diameter. 
 
 4 inch 
 diameter. 
 
 Jinch 
 diameter. 
 
 i inch 
 diameter. 
 
 Mean Values. 
 
 I 
 2 
 
 3 
 4 
 
 .6 7 I 
 .653 
 .660 
 .662 
 
 .634 
 .621 
 .636 
 .626 
 
 .644 
 .652 
 .632 
 .614 
 
 -633 
 .619 
 .628 
 
 584 
 
 645 
 .636 
 
 .639 
 .621 
 
 Means . 
 
 66 1 
 
 
 fiie 
 
 f\lf\ 
 
 f\ie. 
 
 
 
 
 35 
 
 
 .35 
 
200 
 
 FLOW OF WATER THROUGH ORIFICES. 
 
 COEFFICIENTS FOR RECTANGULAR ORIFICES. 
 
 Heads at the 
 
 centre of gravity, 
 
 in feet. 
 
 i inch x i inch. 
 
 2 inches wide 
 inch high. 
 
 i inches wide 
 x | inch high. 
 
 Equilateral 
 
 triangle of 
 
 i square inch, 
 
 base down. 
 
 Same triangle, 
 with base up. 
 
 .617 
 .635 
 .606 
 
 593 
 
 .617 
 635 
 .606 
 
 593 
 
 .663 
 .668 
 .606 
 593 
 
 593 
 
 .596 
 577 
 572 
 593 
 
 Means, 
 
 .632 
 
 593 
 
 From Castel. In 1836, M. Castel, the accomplished 
 hydraulic engineer of the city of Toulouse, made with care 
 certain experiments by request of D' Aubuisson, to determine 
 the volume of water discharged through apertures in thin 
 partitions. 
 
 He placed a dam of thin copper plate in a sluice which 
 was 2.428 feet broad, and in the plate opened three rectan- 
 gular apertures, each 3.94 inches wide and 2.36 inches high. 
 The distance between the orifices was 3.15 inches. The 
 flow took place under constant heads of 4.213 inches above 
 the centres of gravity of the orifices, with contractions as 
 follows : 
 
 {Coefficient for the middle 6198 
 " right ... .6192 
 " left 6194 
 
 {Coefficient for the two outsides 6205 
 " " middle and right 6205 
 " left 6207 
 
 Three orifices open, coefficient for all 6230 
 
 Subsequently, he experimented with two orifices, 1.97 
 inches wide and 1.18 inches high, with results as follows : 
 
 Head. No. of orifices open. Coefficient 
 
 3-379 \l Hi 
 
 ^3..... \l ? 
 
EXPERIMENTAL COEFFICIENTS. 
 
 201 
 
 When more than one aperture was open in these exper- 
 iments of Castel, the volume of water discharged induced 
 considerable velocity in each of the supplying sluices. 
 This actually increased the effective head. Its effect is here 
 recorded in the coefficient instead of in the head, conse- 
 quently an increased coefficient is given. 
 
 In such cases the real head is the observed head in- 
 creased by the head due to the velocity of approach = 
 
 F 2 
 64T 
 
 From Lespinasse. From among experiments on a 
 larger scale, the following by Lespinasse, with a sluice of 
 the canal of Languedoc, are of interest : 
 
 TABLE No. 44. 
 COEFFICIENTS OBTAINED BY LESPINASSE. 
 
 OPENINGS. 
 
 HEAD ON THE 
 
 DISCHARGE m 
 
 COEFFICIENT. 
 
 Breadth. 
 
 Height. 
 
 Area. 
 
 
 
 
 Feet. 
 
 Feet. 
 
 Sq.feet. 
 
 Feet. 
 
 Cubic feet. 
 
 
 4.265 
 
 1.805 
 
 7-745 
 
 14-554 
 
 145.292 
 
 .613 
 
 (i 
 
 1.640 
 
 6.992 
 
 6.631 
 
 92.635 
 
 .641 
 
 
 
 1.640 
 
 6.992 
 
 6.247 
 
 88.221 
 
 .629 
 
 H 
 
 1.509 
 
 6.466 
 
 12.878 
 
 138.937 
 
 .641 
 
 it 
 
 1-575 
 
 6.723 
 
 13.586 
 
 128.764 
 
 .647 
 
 (I 
 
 1-575 
 
 6.723 
 
 6-394 
 
 83.948 
 
 .616 
 
 " 
 
 1-575 
 
 6.723 
 
 6.217 
 
 79-857 
 
 594 
 
 <i 
 
 1-575 
 
 6.717 
 
 6.480 
 
 85-219 
 
 .621 
 
 From Gen. Ellis. Gen. Theo. G. EUis has reported 
 in a paper* presented to the American Society of Civil 
 Engineers, the results of some experiments very carefully 
 conducted by him at the Holyoke testing flume in the sum- 
 mer of 1874. 
 
 * Hydraulic Experiments with Large Apertures. Jour. Am. Soc. Civ. Eng., 
 1876, Vol. V, p. 19. 
 
202 FLOW OF WATER THROUGH ORIFICES. 
 
 The coefficients for the minimum, mean, and maximum 
 velocities are given to indicate generally the range, and the 
 results obtained by Gen. Ellis. 
 
 The volume of water discharged was determined by 
 weir measurement, and computed by Mr. James B. Fran- 
 cis' formula. 
 
 The edges of the orifices were plated with iron about 
 one-half inch thick, jointed square. 
 
 VERTICAL APERTURE, 2 ft. x 2 ft. 
 
 Minimum head, 2.061 feet. Coefficient, .60871 ) Centre of aperture, 1.90 feet 
 Mean " 3.037 " " .59676 > above top of weir. 
 
 Maximum " 3.538 " " .60325 ) Temp, of water, 73 Fah. 
 
 VERTICAL APERTURE, 2 ft. horizontal x i ft. vertical. 
 
 Minimum head, 1.7962 feet. Coefficient, .59748 } Centre of aperture, 2.40 feet 
 Mean " 5.7000 " " .59672 > above top of weir. 
 
 Maximum " 11.3150 " " .60572 ) Temp, of water, 76 Fah. 
 
 VERTICAL APERTURE, 2 feet horizontal x .5 feet vertical. 
 
 Minimum head, 1.4220 feet. Coefficient, .61165 J Centre of aperture, 2.15 feet 
 Mean " 8.5395 " " .60686 V above top of weir. 
 
 Maximum " 16.9657 " .60003 ) Temp, of water, 76 Fah. 
 
 VERTICAL APERTURE, i ft. x i ft. 
 
 Minimum head, 1.4796 feet. Coefficient, .58230 J 
 Mean " 9.8038 " " .59612 V 
 
 Maximum " 17.5647 " " .59687 ) 
 
 HORIZONTAL APERTURE, i ft. x i ft. AND SLIGHTLY SUBMERGED 
 
 ISSUE. 
 
 Minimum head, 2.3234 feet. Coefficient, .59871 ) 
 
 f Top surface of orifice .441 
 
 Mean 8.0926 " .60601 V 
 
 ., \ feet above crest of weir. 
 
 Maximum 18.4746 ' .60517 ; 
 
 HORIZONTAL APERTURE (IN PLANK) WITH CURVED ENTRANCE AND 
 SLIGHTLY SUBMERGED ISSUE. 
 
 Minimum head, 3.0416 feet. Coefficient, .95118 } 
 
 , f Issue about level with crest 
 Mean 10.5398 " .94246 > 
 
 r, r \ of weir. 
 
 Maximum ' 18.2180 ' -94364 ; 
 
COEFFICIENTS DIAGRAMMED. 
 
 203 
 
 The range, and results generally, of Gen. Ellis' experi- 
 ments with circular vertical orifices, are indicated by the 
 following extracts from his extended tables : 
 
 TABLE No. 45. 
 COEFFICIENTS FOR CIRCULAR ORIFICES, OBTAINED BY GEN. ELLIS. 
 
 DIAMETERS. 
 
 HEAD. 
 
 COEFFICIENTS. 
 
 2 feet. 
 
 it 11 
 11 
 
 1.7677 feet. 
 
 5.8269 " 
 9.6381 " 
 
 .58829 
 .60915 
 61530 
 
 i foot. 
 
 
 u 
 
 1.1470 feet. 
 10.8819 " 
 17.7400 " 
 
 57373 
 59431 
 59994 
 
 .5 foot. 
 
 u 
 u 
 
 2.1516 feet. 
 9.0600 " 
 17.2650 " 
 
 .60025 
 .60191 
 .59626 
 
 212. Coefficients Diagrammed. The coefficients, as 
 developed by the several experimenters, seem at first glance 
 to be very fitful, and without doubt the apparatus used 
 varied in character as much as the results obtained 
 
 To arrange all the series of coefficients that appeared to 
 have been obtained by a reliable method, in a systematic 
 manner, we have plotted all to a scale, taking the heads 
 for abscisses and the coefficients for ordinates. The curves 
 LUS developed were brought into their proper relations, 
 side by side, or interlacing each other. 
 
 Then we were able to plot in the midst of those curves 
 ie general curves due to each class of orifice under the 
 iveral heads, and those apparently due to the law govern- 
 
 the flow of water through submerged orifices. 
 
 From these curves we have prepared tables of coefficients 
 for various rectangular orifices, with greatest dimension. 
 
204 FLOW OF WATER THROUGH ORIFICES. 
 
 both horizontal and vertical, with ratios of sides varying 
 from 0.125 to 1, to 4 to 1, and for heads varying from 
 0.2 feet to 50 feet. 
 
 All of the curves increase from that for very low heads 
 rapidly as the head increases, until a maxima is reached, 
 and then to decrease gradually until a minima is reached, 
 and then again to increase very gradually, the head in- 
 creasing all the time. This increase, and decrease, and 
 increase again of the coefficients, arranges them, when thus 
 plotted, into two curves of opposite flexure, and with all 
 the curves tending to pass through one* intermediate point. 
 
 213. Effect of Varying the Head, or the Propor- 
 tions of the Orifice. The effect of increasing or decreas- 
 ing the head upon a given orifice is clearly shown by the 
 several columns of coefficients in Tables 46 and 47. 
 
 The effect of increasing or decreasing the ratio of the 
 base to the altitude of an orifice will be manifest by tracing 
 the lines of coefficients horizontally through the two tables, 
 for any given head. 
 
 These effects should be duly considered when a coef- 
 ficient is to be selected from the table for a special appli- 
 cation. 
 
 The coefficients apply strictly to orifices with sharp, 
 square edges, and with full contraction upon all sides. The 
 heads refer to the full head of the water surface, and not to 
 the depressed surface over or just in front of an orifice when 
 the head is small. 
 
 A very slight rounding of the edge would increase the 
 coefficient materially, as would the suppression of the con- 
 traction upon a portion of its border by interference with 
 the curve of approach of the particles. 
 
COEFFICIENTS DIAGRAMMED. 
 
 205 
 
 TABLE No. 46. 
 
 COEFFICIENTS FOR RECTANGULAR ORIFICES. 
 
 In thin vertical partition, with greatest dimension vertical. 
 
 BREADTH AND HEIGHT OF ORIFICE. 
 
 Head upon 
 centre of orifice. 
 
 4 feet high, 
 i foot wide. 
 
 2 feet high, 
 i foot wide. 
 
 ij feet high, 
 i foot wide. 
 
 i foot high, 
 i foot wide. 
 
 Feet. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 .6 
 
 .... 
 
 .... 
 
 
 .5984 
 
 7 
 
 .... 
 
 .... 
 
 ... 
 
 5994 
 
 .8 
 
 .... 
 
 .... 
 
 .6130 
 
 .6000 
 
 9 
 
 .... 
 
 .... 
 
 .6134 
 
 .6006 
 
 i 
 
 . . . 
 
 .... 
 
 .6135 
 
 .6010 
 
 1.25 
 
 .... 
 
 .6l88 
 
 .6140 
 
 .6018 
 
 1.50 
 
 .... 
 
 .6187 
 
 .6144 
 
 .6026 
 
 J -75 
 
 .... 
 
 .6186 
 
 .6145 
 
 6033 
 
 2 
 
 .... 
 
 6183 
 
 .6144 
 
 .6036 
 
 2.25 
 
 .... 
 
 .6l8o 
 
 .6143 
 
 .6039 
 
 2-5 
 
 .6290 
 
 .6176 
 
 .6139 
 
 .6043 
 
 2 -75 
 
 .6280 
 
 .6173 
 
 .6136 
 
 .6046 
 
 3 
 
 .6273 
 
 .6170 
 
 .6132 
 
 .6048 
 
 3-5 
 
 .6250 
 
 .6l6o 
 
 .6123 
 
 .6050 
 
 4 
 
 .6245 
 
 .6150 
 
 .6lIO 
 
 .6047 
 
 4-5 
 
 .6226 
 
 .6138 
 
 ,6lOO 
 
 .6044 
 
 5 
 
 .6208 
 
 .6124 
 
 .6088 
 
 .6038 
 
 6 
 
 .6158 
 
 .6094 
 
 .6063 
 
 .6020 
 
 7 
 
 .6124 
 
 .6064 
 
 .6038 
 
 .6011 
 
 8 
 
 .6090 
 
 .6036 
 
 .6022 
 
 .6010 
 
 9 
 
 .6060 
 
 .6O2O 
 
 .6014 
 
 .6010 
 
 10 
 
 6 35 
 
 .6015 
 
 .6OIO 
 
 .6010 
 
 15 
 
 .6040 
 
 .6oi8 
 
 .6OIO 
 
 .6011 
 
 20 
 
 .6045 
 
 .6024 
 
 .6OI2 
 
 .6012 
 
 25 
 
 .6048 
 
 .6028 
 
 .6014 
 
 .6012 
 
 3 
 
 .6054 
 
 .6034 
 
 .6017 
 
 .6013 
 
 35 
 
 .6060 
 
 .6039 
 
 .6021 
 
 .6014 
 
 40 
 
 .6066 
 
 .6045 
 
 .6025 
 
 .6015 
 
 45 
 
 .6054 
 
 .6052 
 
 .6029 
 
 .6016 
 
 5o 
 
 .6086 
 
 .6060 
 
 .6034 
 
 .6018 
 
206 
 
 FLOW OF WATER THROUGH ORIFICES. 
 
 TABLE No. 47. 
 
 COEFFICIENTS FOR RECTANGULAR ORIFICES. 
 
 In thin vertical partition, with greatest dimension horizontal. 
 
 BREADTH AND HEIGHT OF ORIFICE. 
 
 Head upon 
 centre of orifice. 
 
 0.75 feet high, 
 i foot wide. 
 
 0.50 feet high, 
 i foot wide. 
 
 0.25 feet high, 
 i foot wide. 
 
 0.125 feet high, 
 i foot wide. 
 
 Feet, 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 0.2 
 
 .... 
 
 .... 
 
 .... 
 
 6333 
 
 3 
 
 .... 
 
 .... 
 
 .6293 
 
 6 334 
 
 4 
 
 .... 
 
 .6140 
 
 .6306 
 
 6334* 
 
 '5 
 
 .6050 
 
 .6150 
 
 6313 
 
 6 333 
 
 .6 
 
 .6063 
 
 .6156 
 
 63*7 
 
 6332 
 
 7 
 
 .6074 
 
 .6l62 
 
 .6319 
 
 .6328 
 
 .8 
 
 .6082 
 
 .6165 
 
 .6322 
 
 .6326 
 
 9 
 
 .6086 
 
 .6l68 
 
 .6323* 
 
 .6324 
 
 i 
 
 .6090 
 
 .6172 
 
 .6320 
 
 .6320 
 
 !-25 
 
 .6095 
 
 .6l 73 * 
 
 .6317 
 
 .6312 
 
 1.50 
 
 .6lOO 
 
 .6172 
 
 6 3*3 
 
 6303 
 
 J -75 
 
 .6103 
 
 .6l68 
 
 .6307 
 
 .6296 
 
 2 
 
 .6104* 
 
 .6166 
 
 .6302 
 
 .6291 
 
 2.25 
 
 .6103 
 
 .6163 
 
 .6293 
 
 .6286 
 
 2. 5 
 
 .6102 
 
 .6157 
 
 .6282 
 
 .6278 
 
 2 -75 
 
 .6lOl 
 
 6155 
 
 .6274 
 
 .6273 
 
 3 
 
 .6100 
 
 6153 
 
 .6267 
 
 .6267 
 
 3-50 
 
 .6094 
 
 .6146 
 
 .6254 
 
 .6254 
 
 4 
 
 .6085 
 
 .6136 
 
 .6236 
 
 .6236 
 
 4-50 
 
 .6074 
 
 .6125 
 
 .6222 
 
 .6222 
 
 5 
 
 .6063 
 
 .6114 
 
 .6202 
 
 .6202 
 
 6 
 
 .6044 
 
 .6087 
 
 .6154 
 
 .6154 
 
 7 
 
 .6032 
 
 .6058 
 
 .6110 
 
 .6114 
 
 8 
 
 .6O22 
 
 6033 
 
 .6073 
 
 .6087 
 
 9 
 
 .6015 
 
 .6020 
 
 .6045 
 
 .6070 
 
 io 
 
 .6oiO 
 
 .6010 
 
 .6030 
 
 .6060 
 
 J 5 
 
 .6012 
 
 .6013 
 
 6033 
 
 .6066 
 
 20 
 
 .6014 
 
 .6018 
 
 .6036 
 
 .6074 
 
 2 5 
 
 .6016 
 
 .6022 
 
 .6040 
 
 .6083 
 
 30 
 
 .6018 
 
 .6027 
 
 .6044 
 
 .6092 
 
 35 
 
 .6022 * 
 
 .6032 
 
 .6049 
 
 .6103 
 
 40 
 
 .6026 
 
 .6037 
 
 6055 
 
 .6114 
 
 45 
 
 .6030 
 
 .6043 
 
 .6062 
 
 .6125 
 
 5 
 
 6035 
 
 .6050 
 
 .6070 
 
 .6140 
 
PECULIARITIES OF EFFLUX. 
 
 207 
 
 214. Peculiarities of Efflux from an Orifice. 
 
 In Fig. 22, containing a horizontal orifice, the horizontal 
 line cutting a has an altitude above the orifice equal to 3.5 
 diameters, and the horizontal line cutting e equal to 10 
 diameters of the orifice. As the altitude of the water sur- 
 
 FIG. 22. 
 
 
 < 
 
 a 
 
 
 
 K 
 
 i 
 
 * 
 
 
 V\" " 
 
 
 ^V?J^X-. 
 
 
 ; 
 "~ 
 
 ^Vx \\ 
 
 \\ 
 
 \ \ 
 
 
 \ X \ \ 
 
 \ \ 
 
 
 \ \ \ \ 
 \ \\ \ 
 
 \ \\ 
 
 1 \ 
 
 x ' \ 
 
 
 \ \ 
 
 \ \ 
 
 
 
 \ \ 
 
 
 N > 
 
 k \ \ 
 
 X 
 
 
 \ \ \ 
 
 
 
 \ \ i 
 
 
 
 \ ^ \ 
 
 
 
 \ \ \ 
 
 CL / 
 
 
 \\ \ 
 
 """^^"p 
 
 
 \ \ 
 
 // 'i^/fi< 
 
 
 \ \ ' 
 
 I i / / S/ \ 
 
 
 \\1 
 
 / //// .^\ 
 
 i',"// x 
 
 
 \\1 
 
 1 // / 
 
 
 
 / / / 
 
 / 
 
 Ml 
 
 |VJ 
 
 I/// 
 
 
 
 
 
 
 1 
 
 face above a square orifice increases from very low heads to 
 the level a, the particles continually find new advantage or 
 less hindrance in their tendency to flow out of the orifice, 
 possibly by decrease of the vortex effect accompanying 
 very low heads over orifices nearly square ; afterwards the 
 resistance increases up to the altitude e, possibly by more 
 effective reaction from the inner edges of the orifice, is, 
 until gravity is enabled to gather the jet well into a body 
 and establish firmly its path. For altitudes greater than 
 ten diameters the coefficients for square orifices remain 
 nearly constant. 
 
208 FLOW OF WATER THROUGH ORIFICES. 
 
 Similar effects are observed when the orifices are rectan- 
 gles, other than squares, though their first change occurs at 
 different depths. 
 
 These phenomena are not fully accounted for by ex- 
 periment. 
 
 215. Mean Velocity of the Issuing Particles. 
 We have heretofore assumed in our theoretic equations, 
 that all the particles of water bcdefg, Fig. 22, will arrive 
 at the point of greatest contraction of the issuing jet, with a 
 velocity equal to that which a solid body would have ac- 
 quired by falling freely from e to o, which, according to the 
 the theorem of Toricelli, and its demonstrations frequently 
 repeated by other eminent philosophers, would be equal to 
 
 V%gIL If being equal to the height e o. 
 
 The experiments of Mariotte, Bossut, Michelotti, Ponce- 
 let, Pousseile, and others, covering a large range of areas of 
 orifice, and of head, show that this is very nearly correct ; 
 and the velocity of issue of the axial particles has in some 
 of the experiments appeared to slightly exceed the value of 
 
 V2gH. An average of experiments gives the mean velocity 
 of the particles as a whole through the minimum section as 
 .974 VZgH. 
 
 Their dynamic effect if applied to work should have 
 .974 VZgH instead of V%gH as the factor of velocity. 
 
 216. Coefficients of Velocity and Contraction. 
 We have then, .974 for mean coefficient of velocity, indi- 
 cating a loss of .026 per cent, of theoretic volume or dis- 
 charge by reduction of velocity ; .637 for mean coefficient 
 of contraction, indicating a loss of 36.3 per cent, of theoretic 
 volume by contraction ; and .62 nearly for mean coefficient of 
 discharge, including all losses, a total of about 38 per cent. 
 
 The coefficient of velocity we will designate by <?<,, and 
 the coefficient of contraction by c c . 
 
VOLUME OF EFFLUX FROM A SUBMERGED ORIFICE. 209 
 
 Then c x c c = c = coefficient of discharge or volume. 
 
 217. Velocity of Particles Dependent upon their 
 Angular Position. Bayer assumed the hypothesis that, 
 the velocities of the particles approaching the orifice from 
 all sides are inversely as the squares of their distances from 
 its centre, but this should undoubtedly be applied only to 
 particles in some given angular position. 
 
 Gravity will not act with equal force in the direction of 
 the orifice, upon each of the particles e,f, g, and ^, Fig. 22, 
 though they are all equally distant from o, but more nearly 
 in the ratios of the cosines of the angles eoe, eof, eog, etc., 
 and it is not probable that the particle h will acquire a 
 velocity at its maximum through the contraction, quite 
 equal to that which e will acquire. If the velocity of e is 
 assumed equal to unity, and the mean velocity of all the 
 particles equal to .974, then, according to the hypothesis of 
 the angular distance, the mean velocity will be that due to- 
 particles having their cosines equal to .974, or an angular 
 distance of 13, as at b and/. 
 
 218. Equation of Volume of Efflux from a Sub- 
 merged Orifice. Neville suggests a formula* for the 
 discharge of water from rectangular orifices, more strictly 
 mathematical than the above simple formulas, as follows : 
 
 (4) 
 
 when D = volume of discharge, 
 A = area of orifice, 
 
 Ji = head upon the centre of the orifice, 
 d = depth of the orifice, or distance between its 
 
 bottom and top, 
 c = coefficient of discharge. 
 
 * Third Edition of Hydraulic Tables, page 48. London, 1875. Also vide 
 equation 3, page 283, ante. 
 
210 FLOW OF WATER THROUGH ORIFICES. 
 
 This formula can be advantageously applied when the 
 orifice is large and but slightly submerged, as is frequently 
 the case with sluice gates controlling the flow of water from 
 storage reservoirs or canals into flumes leading to water- 
 wheels, or with head-gates of races or canals. 
 
 Good judgment must, however, be exercised in each case 
 in the selection of the coefficient of velocity (c v ) and the co- 
 efficient of contraction (<? c ), the factors of c, especially the 
 coefficient of contraction ( 216), which is usually much the 
 most influential of the two. 
 
 219. Effect of Outline of Symmetrical Orifices 
 upon Efflux. According to the various series of experi- 
 ments, the coefficient for a circular orifice under any given 
 head is substantially the same as for a square orifice under 
 the same head, and it is probable that the coefficients for 
 elliptical orifices is substantially the same as that for their 
 circumscribing rectangles. 
 
 220. Variable Value of Coefficients. The coeffi- 
 cients obtained by careful experiment and recorded above, 
 as also tables of coefficients, indicate unmistakably that the 
 value of c in the equation 
 
 is a variable quantity, and that a general mean coefficient 
 cannot be used universally when close approximate results 
 are desired, but that, for a particular case, reference shoiald 
 always be made to a coefficient obtained under conditions 
 similar to that of the case in question. 
 
 221. Assumed Mean Volume of Efflux. In ordi- 
 nary approximate calculations, and in general discussions 
 of formulas for square and circular orifices, whether the jet 
 issues horizontally or vertically, it is customary to assume 
 0.62 as the ratio of the actual to the theoretical volume of 
 
CIRCULAR, AND OTHER FORMS OF JETS. 
 
 211 
 
 discharge. This makes the equation for ordinary calcu- 
 lations : 
 
 Q = 2SVZgH, or Q = .62SV. (5) 
 
 The expression for effect of acceleration of gravity 
 toeing a constant quantity, may be combined with the co- 
 efficient, when (.62 V2g = 4.9725) we have the equation 
 
 Q = 4.9725/S VTl, or approximately, Q = 5. 
 
 (6) 
 
 Q being the discharge in cubic feet in one second, it will be 
 multiplied by 60 to determine the discharge in one minute. 
 and by 3600 to determine the discharge in one hour. 
 
 222. Circular, and other Forms of Jets. A cir- 
 cular aperture, with full contraction, gives a jet always 
 circular in section, until it is broken up into globules by 
 the effects of the varying velocities of its molecules and the 
 resistance of the air. Through the vend conlractd its form 
 is that of a truncated conoid. 
 
 Polygonal and rectangular orifices give jets that continu- 
 ally change their sectional forms as they advance. 
 
 Fig. 22, from D'Aubuisson's Treatise on Hydraulics, 
 illustrates the transformations of 
 forms of a jet from a square orifice, 
 AC EG. The jet is square at the 
 itrance to the aperture, assumes 
 the form bcdefgha a short distance 
 
 front of it, and the form a'c'e'g' a 
 short distance further on, and con- 
 tinues to assume new forms until 
 its solidity is destroyed. Symmetrical orifices, without re- 
 entrant angles, give symmetrical jets that assume symmet- 
 rical, varying sections. 
 
 Star-shaped and irregular orifices, upon close observa- 
 
212 
 
 FLOW OF WATER THROUGH ORIFICES. 
 
 tion, are found to give very complex forms of jets. Their 
 coefficients of efflux have not been fully developed by ex- 
 periment. 
 
 223. Cylindrical and Divergent Orifices. In Fig. 
 23 and Figi 24 showing cylindrical and divergent orifices, 
 if the diameters, is, of the orifices, are greater than the 
 
 FIG. 23. 
 
 FIG. 24. 
 
 FIG. 25. 
 
 FIG. 26. 
 
 thickness of the partitions, the coefficients of discharge will 
 remain the same as in thin plate. In such cases the jets 
 will pass through the orifices without touching them, ex- 
 cept at the edges, is. Such orifices are also termed thin. 
 
 224:. Converging Orifices. -In Fig. 25 and Fig. 26, 
 showing converging orifices in thin partitions, if the diam- 
 eters, is, are taken, the coefficients will be reduced to .58, or 
 a little less ; bat if the diameters, ot, are taken, the co- 
 efficients will be increased nearly to .90, and will be greater, 
 for any given velocity, in proportion as the forms of the 
 orifices approach to the form of the perfect wnd contractd, 
 for that velocity. 
 
 When the converging sides of the orifice in Fig. 25, pro- 
 longed, include an angle of 16, the coefficient should be 
 about .93, and when in Fig. 26 the sides of the orifice are in 
 the form of the vend contractd, the coefficient should be 
 about .95.. 
 
V 
 
CHAPTEE XII. 
 
 FLOW OF WATER THROUGH SHORT TUBES. 
 
 225. An Ajutage. If a cylindrical orifice is in a parti- 
 tion whose thickness is equal to two-and-one-half or three 
 times the diameter of the orifice ; or if the orifice is a tube 
 of length equal to from two and one-half to three interior 
 diameters, then the orifice is termed a short tube, or ajutage. 
 The sides of short tubes may be parallel, divergent, or con- 
 vergent. 
 
 226. Increase of Coefficient. There is an influence 
 affecting the flow of water through short cylindrical tubes, 
 Fig. 28, sufficient to increase the coefficient materially, that 
 does not appear when the flow is through thin partition. 
 The contraction of the jet still occurs as in the flow through 
 thin partition, but after the direction of the particles has 
 become parallel in the vend contracta, a force acting from 
 the axis of the jet outward, together with the reaction from 
 the exterior air, begins to dilate the section of the jet and 
 to fill the tube again. The tube is in consequence again 
 filled at a distance, depending upon the ratio of the velocity 
 to the diameter, of about two and one-half diameters from 
 the inner edge of the orifice. The axial particles of the jet, 
 not receiving so great a proportion of the reaction from the 
 edges of the orifice as the exterior particles, obtain a greater 
 velocity. A portion of their force is transmitted to their 
 surrounding films through divergent lines, and the velocity 
 of the exterior particles within the tube is augmented, and 
 the section of the jet is also augmented, until its circumfer- 
 
214 FLOW OF WATER THROUGH CHORT TUBES. 
 
 ence touches the tube. At the same time, the transmission 
 of force from the axis toward the circumference tends to 
 equalize the velocity of the particles throughout the section, 
 and to materially reduce their mean velocity, and conse- 
 quently the coefficient of velocity, c v . 
 
 227. Ajutage Vacuum and its Effect. Immedi- 
 ately upon the issue of the jet, beyond the contraction, the 
 velocity of the particles tends to impel forward the impris- 
 oned air, and as soon as the tube fills to cause a vacuum* 
 about the contraction. The full force of gravity is here act- 
 ing upon the jet in the form of velocity ; the jet is therefore 
 without pressure in a transverse direction. 
 
 As soon as the exterior of the jet is relieved from the 
 pressure of the atmosphere about the contraction, its par- 
 ticles are deflected to parallelism with less force and in a 
 shorter distance from the entrance to the aperture, and the 
 contraction is consequently lessened ; also the pressure of 
 the atmosphere upon the reservoir surface tends to augment 
 the velocity of entry of the particles into the aperture 
 toward the vacuum, and atmospheric pressure equally 
 resists the issue of the jet, the combined effect resulting in 
 the expansion of the jet. 
 
 22S. Increased Volume of Efflux. If the cylin- 
 drical tube terminates at the point where the moving par- 
 ticles reach the circumference and fill the tube, and 
 before the reaction from the roughness of the interior of 
 the tube has begun sensibly to counteract the accelerating 
 force of gravity, the capacity of discharge is then found to 
 be increased about twenty-five per cent., and the mean co- 
 efficient becomes .815 approximately, or if the tube projects 
 
 * If the inside of a smooth divergent tube is greased, so as to repel the par- 
 ticles of water and prevent contact, the vacuum cannot take place. 
 
DIVERGENT TUBE. 
 
 215 
 
 into the reservoir, .72, instead of .62, as in the orifice in thin 
 plate. We have now for the volume of water discharged, 
 in cubic feet per second, 
 
 Q = .815 8 V2g&, orQ = .815 8 V, or Q = 6.54 8 VH. (1) 
 
 If the section of the tube is expressed in terms of the 
 diameter, in feet or fractional parts of feet, then since S = 
 .7854d 2 , the equation will become 
 
 Q = 6.54 (. 
 
 VH= 
 
 (2) 
 
 229. Imperfect Vacuum. If the tube is of less 
 length than above indicated, so that the vacuum is not 
 perfect, the conditions of flow and the coefficient will be 
 similar to that through thin plate ; and if the tube is length- 
 ened, the flow will be reduced by reaction from the interior 
 of the tube, in which case the tube will be termed a pipe. 
 
 FIG. 29. 
 
 FIG. 30. 
 
 23O. Divergent Tube. When a short divergent tube, 
 'ig. 29, is attached by its smaller base to the inside of a 
 plane partition, the phenomena of discharge will be similar 
 to that through an orifice in thin plate, unless a vacuum 
 shall be established about its contraction, as in the case of 
 
216 FLOW OF WATER THROUGH SHORT TUBES. 
 
 short cylindrical tubes. This can only occur when the 
 divergence is slight, or the velocity great. 
 
 For ordinary cases, the mean coefficient of discharge 
 through square-edged divergent tubes may be taken as .62, 
 but it is subject to considerable variation in tubes of small 
 divergence, as the divergences, the ratio of length to diam- 
 eter, and the velocity of flow or head varies. 
 
 When a vacuum takes place in a divergent tube, the 
 discharge exceeds that from a cylindrical tube with diam- 
 eter equal to the smaller diameter of the divergent tube, 
 and the coefficient of volume may then even become greater 
 than unity. 
 
 231. Convergent Tube. When a short, convergent 
 tube. Fig. 30, is attached by its larger base to the inside of 
 a plane partition, and its coefficient of flow with a perfect 
 vacuum is determined for its diameter of entrance, as above 
 in the cases of thin plate, cylindrical and divergent tubes, 
 then the coefficient of volume will be found to decrease as 
 the angle of convergence increases. 
 
 Contraction will take place as in thin plate, until the 
 angle of convergence, that is, the included angle between 
 the sides produced, exceeds 13, and a vacuum will also be 
 produced ; but the exterior of the jet will reach the inner 
 circumference and fill the tube at a shorter distance from 
 the point of least contraction, as the angle increases, and 
 the augmenting effect of the vacuum will be reduced. 
 
 232. Additional Contraction. There is always an 
 additional contraction just after the exit of the jet from 
 convergent tubes. 
 
 The coefficient of discharge will remain in excess of the 
 coefficient for thin plate until the second contraction equals 
 that in thin plate, after which the coefficient will be less 
 than for thin plate. 
 
COEFFICIENT OF SMALLER DIAMETER. 
 
 217 
 
 233. Coefficients of Convergent Tubes. In the 
 
 following table are given the coefficients of discharge for 
 the larger and the smaller diameters, also of the velocity, 
 for several angles of convergence. The table is based upon 
 careful experiments by Castel. The length of the tube was 
 2.6 diameters, and the smaller diameter and length of tube 
 remained constant. 
 
 TABLE No. 48. 
 
 CASTEL'S EXPERIMENTS WITH CONVERGENT TUBES. 
 Smallest diameter = .05085 feet. 
 
 Angle of convergence. 
 
 Larger diameter. 
 
 Smaller diameter. 
 
 Velocity. 
 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 0' 
 
 0.829 
 
 0.829 
 
 0.830 
 
 1 36' 
 
 .809 
 
 .866 
 
 .866 
 
 3 TO' 
 
 .786 
 
 .895 
 
 .894 
 
 4 10' 
 
 .771 
 
 .912 
 
 .910 
 
 5 26' 
 
 747 
 
 .924 
 
 .920 
 
 7 5* 
 
 .691 
 
 .929 
 
 -931 
 
 8 58' 
 
 .671 
 
 934 
 
 .942 
 
 10 20' 
 
 .647 
 
 .938 
 
 95 
 
 12 4 
 
 .611 
 
 .942 
 
 955 
 
 13 24' 
 
 597 
 
 .946 
 
 .962 
 
 14 28' 
 
 577 
 
 .941 
 
 .966 
 
 16 36' 
 
 -545 
 
 .938 
 
 .971 
 
 19 28' 
 
 .501 
 
 .924 
 
 .970 
 
 21 0' 
 
 .480 
 
 .918 
 
 .971 
 
 23 o' 
 
 457 
 
 .913 
 
 974 
 
 2 9 5 8' 
 
 59 
 
 .896 
 
 975 
 
 40 20' 
 
 3i9 
 
 .869 
 
 .980 
 
 48 50' 
 
 .276 
 
 .847 
 
 .984 
 
 The coefficients for the larger diameter have been com- 
 puted from the remaining data of the table for insertion 
 here. 
 
 234. Increase and Decrease of Coefficient of 
 Smaller Diameter. When the coefficient of volume is 
 
FIG. 31. 
 
 218 FLOW OF WATER THROUGH SHORT TUBES. 
 
 determined for the smaller diameter, or issue of a short, 
 convergent tube, the coefficient is found to increase from 
 that for cylindrical tubes at angle to an angle of about 
 13 30', when, under the conditions upon which Castel's 
 table was based, it has increased from .83 to .95. After- 
 wards, the coefficient gradually reduces, until at 180 it 
 becomes .62, as in thin plate. 
 
 235. Coefficient of Final Velocity The coefficient 
 of final velocity of issue gradually increases as the angle of 
 convergence increases, until it rises from .83* at angle to 
 nearly unity at angle 180 ; but that, for angles less than 
 
 13, is not the true coefficient of 
 velocity, since it refers to the ve- 
 locity of issue at the end of the 
 tube, instead of in the contrac- 
 tion. 
 
 236. Inward Projecting 
 Ajutage. When an orifice, or 
 the entrance of a short tube, is 
 projected into the interior of a 
 reservoir, as in Fig. 31, the angle 
 of approach of the particles be- 
 comes greater than when the orifice is in plane partition, 
 and the contraction becomes still more marked. Borda, 
 when experimenting with such a tube, in which the vacuum 
 was not perfected, found the coefficient to be .515. This 
 coefficient may be considered as an extreme minimum. 
 
 237. Compound Tube. When two or more of the 
 short tubes above described are joined together endwise 
 into one tube, as in Fig. 32, the new tube thus formed is 
 termed a compound tube. 
 
 * Its mean velocity, in a cylindrical tube, after the jet has expanded beyond 
 the contraction. 
 
COEFFICIENTS OF COMPOUND TUBES. 
 FIG. 32. 
 
 219 
 
 Venturi experimented with various forms and propor- 
 tions of compound tubes, and observed remarkable results 
 produced by certain of them, which apparently augmented 
 the force of gravity. 
 
 With a tube similar to Fig. 32, but with less perfect 
 contraction, having the included angle of the divergent tube 
 equal to 5 6', the smallest diameter equal to 0.1109 feet, 
 and the length equal to nine diameters, the coefficient, com- 
 puted for the smallest diameter, when flowing under a con- 
 stant head of 2.89 feet, was 1.46, or about 2.4 times that of 
 an equal orifice in thin plate. * 
 
 238. Coefficients of Compound Tubes. Other forms 
 of compound tubes, with conical diverging ajutages of dif- 
 ferent lengths and angles, gave results as follows : 
 
 TABLE No. 49. 
 EXPERIMENTS WITH DIVERGENT AJUTAGES. 
 
 AJUTAGE. 
 
 COEFFICIENT. 
 
 AJUTAGE. 
 
 COEFFICIENT. 
 
 Angle. 
 
 Length. 
 
 Angle. 
 
 Length. 
 
 3 30' 
 4 38' 
 4 38' 
 4 38' 
 5 44' 
 
 Feet. 
 0.364 
 1.095 
 1.508 
 1.508 
 0-577 
 
 0-93 
 I.2I 
 1. 21 
 
 1-34 
 1.02 
 
 5 44' 
 10 16' 
 10 16' 
 14 14' 
 
 Feet. 
 193 
 .865 
 .147 
 .147 
 
 .82 
 .91 
 .91 
 .61 
 
220 
 
 FLOW OF WATER THROUGH SHORT TUBES. 
 
 239. Experiments with Cylindrical and Coin- 
 pound Tubes. The following table gives interesting re- 
 sults of experiments by Eytelwein with both cylindrical 
 and compound tubes. 
 
 He first experimented with a series of cylindrical tubes 
 of different lengths, but of equal diameters ; he then placed 
 between the cylindrical tubes and the reservoir a conical 
 converging tube of the form of the verid contractd, and 
 repeated the experiments ; and afterwards added also to 
 the discharge end a conical diverging tube with 5 6' angle, 
 Fig. 33. 
 
 FIG. 33. 
 
 TAB LE No. 5O. 
 
 EXPERIMENTS WITH COMPOUND TUBES. 
 
 Length of tube P in 
 diameters. 
 
 Length of tube P 
 in feet. 
 
 Coefficient for 
 tube P. 
 
 Coefficient for 
 tube CP. 
 
 Coefficient for 
 tube CPD. 
 
 0.038 
 
 0.0033 
 
 O.62 
 
 
 
 I.OOO 
 
 0853 
 
 .62 
 
 .967 
 
 .... 
 
 3.000 
 
 2559 
 
 .82 
 
 943 
 
 I.I07 
 
 12.077 
 
 1.0302 
 
 77 
 
 .870 
 
 .978 
 
 24.156 
 
 2.0605 
 
 73 
 
 .803 
 
 905 
 
 36.233 
 
 3.0907 
 
 .68 
 
 .741 
 
 .836 
 
 48.272 
 
 4.1176 
 
 63 
 
 .687 
 
 .762 
 
 60.116 
 
 5- T 479 
 
 .60 
 
 .648 
 
 .702 
 
 The diameter of the tube P was 0.0853 feet, and the flow 
 took place under a computed average head of 2.3642 feet. 
 The mean head was computed by the formula, 
 
 
PERCUSSIVE FORCE OF PARTICLES. 
 
 
 (3) 
 
 in which ^T= maximum head, 7i = minimum head, H' 
 mean head. 
 
 24:0. Tendency to Vacuum. The effect of the per- 
 cussion of the axial particles, tending to produce a vacuum, 
 and of the enlargement of the circumference of the jet in Z>, 
 is apparent until the length reaches thirty-six diameters, 
 and is greatest at three diameters length, though still less 
 than with Fig. 28, because the surface of contact of the jet 
 against the tube is greater. 
 
 241. Percussive Force of Particles. The percus- 
 sive effect of particles of water in rapid motion is illustrated 
 by another experiment of Ventu- 
 ri's, with apparatus similar to 
 Fig. 34. 
 
 A is a high tank kept filled 
 with water, and C is a smaller 
 tank at its base, full of water at 
 the beginning of the experiment. 
 P is an open-topped pipe placed 
 in the small tank, and has holes 
 pierced around its base, so that 
 the water in C may enter it freely 
 and rise to the level c. From A a small tube, e, leads a jet 
 into P. 
 
 Upon the tube e being opened, the whole body of water 
 in P is set in motion and begins to flow over its top, and the 
 body of water in C is drawn into the pipe P through the 
 perforations, and the surface of C will be seen to fall grad- 
 ually from c to d, until air can enter through the perfora- 
 tions and destroy the partial vacuum in P. 
 
222 FLOW OF WATER THROUGH SHORT TUBES. 
 
 For a clear conception of the effect of the particles of the 
 jet upon the particles in P, imagine all the particles and 
 the apparatus to be greatly magnified, so that there will 
 appear to be a jet, e, of balls, like billiard balls, for illus- 
 tration, through a mass, P, of similar balls. 
 
 242. Range of a Set of Eytelwein's Experiments. 
 In the last table (No. 50), there appears the mean coef- 
 ficients due to several distinct classes of apertures, viz. : 
 0.62 due to a tube orifice or orifice in thin plate, with length 
 equal to 0.038 diameters ; 0.82 due to a sJiort cylindrical 
 tube, with length equal to 3 diameters ; 0.943 due to lessened 
 contraction by the convergent entrance, with length equal 
 to 3 diameters ; and 1.107 (which in more perfect form of 
 compound tube we have found to be 1.46) due to convergent 
 entrance and divergent exit, with length equal 3 diameters. 
 
 There also appears the increase of coefficient from orifice 
 to short tube, and then the gradual reduction of all the 
 coefficients by increase of length of tube (into pipe) from 3 
 to 60 diameters long. 
 
 These phenomena cannot fail to be of interest to students 
 in that branch of natural philosophy which relates to hydro- 
 dynamics, and the practical hydraulician cannot afford to 
 overlook their effects. 
 
 243. Cylindrical Tubes to be Preferred. There is 
 rarely occasion for the practical and honest use of the 
 divergent tube, when its object cannot better be accom- 
 plished by a slightly increased diameter of cylindrical tube. 
 The capability of the divergent ajutage to increase the dis- 
 charge from a given diameter of orifice, was known to the 
 ancient philosophers, and to some of the Roman citizens who 
 had grants of water from the public conduits, andD'Au- 
 buisson states that a Roman law prohibited their use within 
 52 J feet of the entrance of the tube. 
 

CHAPTER XIII. 
 
 FLOW OF WATER THROUGH PIPES, UNDER PRESSURE. 
 
 244. Pipe and Conduit. A cylindrical tube intended 
 to convey water under pressure is termed a pipe when its 
 length exceeds about three times its interior diameter ; or 
 immediately after its length has become sufficient for the 
 completion of the vacuum about the jet flowing into it. 
 
 A long pipe constructed of masonry is termed a conduit, 
 and when it is a continuous tube, or composed of sections 
 of tubes with their axes joined in one continuous line and 
 adapted to convey water under pressure, it is termed a main 
 pipe, sub-main, branch, waste, or service pipe, according 
 to its office. 
 
 245. Short Pipes give Greatest Discharge. The 
 greatest possible discharge through a cylindrical tube, due 
 to a given head, occurs when its length is just sufficient to 
 allow of the completion of the vacuum about the contrac- 
 tion of its jet at the influence, if its influent end is then 
 sufficiently submerged to maintain the pipe full at the 
 issue. 
 
 In the discussion of short tubes ( 228), we have seen 
 that their coefficient of discharge is increased from 0.62 
 (that for thin plate) to a mean of 0.815. There is still a loss 
 of eighteen per cent, of the theoretical volume, due chiefly 
 to the contraction of the vein at its entrance to the tube, 
 from which results a loss of velocity and a loss of energy as 
 the jet expands to fill the tube. 
 
224 FLOW OF WATER THROUGH PIPES, UNDER PRESSURE. 
 
 LOSS OF FORCE, OR EQUIVALENT HEAD, AT 
 THE ENTRANCE TO A PIPE. 
 
 246. Theoretical Volume from Pipes. Let J., Fig. 
 35, be a reservoir containing water one hundred feet deep =: 
 H, to the level of its horizontal effluent pipe, P. Let the 
 pipe P be one foot in diameter = d. 
 
 Then the theoretical volume of discharge will equal 
 V%gH x .7854^ 2 = 63.028 cubic feet per second ; but when 
 the pipe is three diameters long (= 3 feet), the real discharge 
 according to experiment, will be 
 
 Q = .815 VtySx .7854^ a , 
 
 (1) 
 
 = 51.40 cubic feet per second. 
 
 FIG. 35. 
 
 
 1000. feet* 
 
 Let V represent the theoretical velocity ; then will the 
 
 total head H = ^~ = 100 feet 
 
 <*9 
 Let v represent the measured velocity of discharge, and 
 
 h the head necessary to generate 0, then A = 
 

 MECHANICAL EFFECT OF THE 
 
 247. Mean Efflux from Pipes. The section of the jet, 
 having expanded beyond the contraction issues with a diain- r 
 eter equal to that of the tube, and the coefficient of velocity, 
 <?, is consequently equal to the coefficient of discharge, c, 
 which is, at a mean, .815 and the theoretical velocity V = 
 
 = 80.25 feet per second. 
 
 248. Subdivision of the Head. The total head ff y 
 acting upon a short cylindrical tube, consists of two por- 
 tions, one of which generates D = .815 V= 65.4 feet per 
 
 second. The other portion, capable of generating -r* 
 
 v 14.85 feet per second, acts in the form of pressure to 
 overcome the resistance of entry of the jet into the tube. 
 Let 7i' represent this force. 
 
 02 
 
 The head due to v is 7i = 5- , =66.5 feet in the above as- 
 sumed case. 
 
 The head due to - - ois *'= 
 
 (1 - l) | = 33.5 feet. ' . . .^ 
 
 The ratio of h' to 7i is therefore ( t l) = .5055 for this 
 
 \c ' 
 
 c v 
 case, and (7i + h') = (h + .5055 h) = H. 
 
 249. Mechanical Effect of the Efflux. Since the 
 
 dynamic force of the jet is as the effective head acting upon 
 it, the loss of .505 of Ti is a matter of importance, espe- 
 cially in cases of short pipes. 
 
 The theoretical velocity being = -^TK, the theoretical 
 
 energy of the jet, under the same assumed conditions, is -~-~- 3 
 
 2 
 
 x ^- x Q x w = 321250 foot pounds per second = 584.09 
 15 
 
226 FLOW OF WATER THROUGH PIPES, UNDER PRESSURE. 
 
 H.P. ; w representing the weight in pounds (= 62.34) per 
 cubic foot of the water, and Q the volume or quantity of 
 water in cubic feet per second. 
 
 The energy E, due to v, is expressed by the equation, 
 
 = 213631.2 foot pounds per second = 388.42 H.P. 
 
 The loss of energy from the quantity of water Q during 
 the efflux in one second, being proportionate to the loss of 
 head, is, 
 
 ' x |/) 4) X QW = (c* ~~ X )^ X W ' (3) 
 
 107618.75 foot pounds per second = 195.67 HP. 
 
 25O. Ratio of Resistance at Entrance to a Pipe. 
 
 The ratio, .505 of 7i' to h, is very nearly a mean for tubes 
 whose edges are square and flush in a plane partition. If 
 the entrance of the tube is well rounded in trumpet-mouth 
 form, corresponding to the form of the vend contractd, the 
 coefficient of velocity c v will be increased to about .98, and the 
 
 ratio of resistance will become f-^ l) = .0412, equal in 
 
 this case (Fig. 35) to about four feet head, and the head 
 that can be made available for work will equal ninety-six 
 feet. 
 
 The disadvantage of the square edges, as respects both 
 volume and dynamic force, is apparent. This resistance of 
 entry of the jet into a tube, whose ratio of head we have 
 determined, is force, or its equivalent head irrecoverably 
 lost. Its maximum for a given head occurs when the tube 
 is about three diameters long, the velocity being then at its 
 maximum, and thereafter its value is reduced as the pipe is 
 lengthened, and with the square of the velocity. 
 
COEFFICIENTS OF EFFLUX FROM PIPES. 
 
 227 
 
 RESISTANCE TO FLOW WITHIN A PIPE. 
 
 251. Resistance of Pipe-wall. We have heretofore 
 considered the whole head H as applied to and entirely 
 utilized in overcoming the resistance of entry of the jet into 
 the pipe, and in generating the velocity among the particles 
 of the jet. 
 
 We will now consider the resistances within the pipe and 
 its appendages, and the portion of the velocity that must be 
 converted into pressure or dynamic force to overcome them. 
 
 252. Conversion of Velocity into Pressure. If 
 the pipe P, Fig. 35, of three diameters length, "be extended 
 as at P', a new resistance arising within the added length 
 acts upon the jet and again reduces the volume of flow. A 
 portion of the velocity of the jet is converted into pressure 
 or dynamic force, and is applied to overcome the resistances 
 presented within the pipe, and the proportion of the velocity 
 thus consumed is almost directly proportional to the length 
 added of the pipe, of the given diameter. 
 
 253. Coefficients of Efflux from Pipes. The effects 
 upon the volume of discharge through a given pipe conse- 
 quent upon varying its length will be apparent upon inspec- 
 tion of a table of coefficients of efflux, c, due to its several 
 lengths respectively. 
 
 We will assume the pipe to be one foot diameter, of 
 clean cast iron, when the coefficients determined experi- 
 mentally have mean values about as follows : 
 
 ' TABLE No. 51. 
 COEFFICIENTS OF EFFLUX (c) FOR SHORT PIPES. 
 
 Lengths, in diameters . . 
 
 i 
 
 5 
 
 10 
 
 25 
 
 50 
 
 75 
 
 100 125 
 
 150 
 
 175 
 
 200 
 
 285 
 
 250 
 
 275 
 
 3 00 
 
 Coefficients (c) 
 
 .62 
 
 .792 
 
 .770 
 
 .714 
 
 .643 
 
 .588 
 
 .548 .5" 
 
 485 
 
 .462 
 
 .440 
 
 .420 
 
 405 
 
 .386 
 
 .378 
 
228 FLOW OF WATER THROUGH PIPES. 
 
 Plotted as ordinates, beginning with the theoretical 
 coefficient, unity, they range themselves as in Fig. 36. 
 
 013.5 10 25 5O 75 100 425 50 
 
 254:. Reactions from the Pipe-wall. A fair sam- 
 ple of ordinary pipe casting, a cement-lined, lead, or glazed 
 earthenware pipe are each termed smooth pipes, but a good 
 magnifying lens reveals upon their surfaces innumerable 
 cavities and projections. 
 
 The molecules of water are so minute that many thou- 
 sands of them might be projected against and react from a 
 single one of those innumerable projections, even though it 
 was inappreciable to the touch, or invisible to the naked 
 eye. 
 
 A series of continual reactions and deflections, originated 
 by the roughness of the pipe, act upon the individual 
 molecules as they are impelled forward by gravity, and 
 materially retard * their flow. 
 
 In a given pipe, having a uniform character of surface, 
 the sum of the reactions, for a given velocity, is directly as 
 
 * The resistance was, by the earlier philosophers, attributed chiefly to the 
 adhesion of the fluid particles to the sides of the pipe, and to the cohesion 
 among the particles. Vide Downing, who accepts the views of Du Buat, D'Au- 
 buisson, and other eminent authorities. Practical Hydraulics, p. 200. Lon- 
 don, 1875. 
 
FORMULA OF RESISTANCE TO FLOW. 229 
 
 its wall surface, or as the product of the inner circumfer- 
 ence into the length. Since in a pipe of uniform diameter 
 the circumference is constant, the sum of the reactions is 
 also directly as the length. 
 
 The impulse of the flowing particles, and therefore their 
 reactions and eddy influences, are theoretically proportional 
 to the head to which their velocity is due, which is propor- 
 tional to the square of the velocity, or, in general terms, the 
 effective reactions are proportional nearly to the square of 
 the velocity. 
 
 The resistances arising from the interior surface of the 
 pipe are, therefore, not only as the length, "but as the 
 square of the velocity, nearly. 
 
 The effect of the resistances is not equal upon all the 
 particles in a section of the column of water, but is greatest 
 at the exterior and least at the centre, or, in a given section, 
 approximately as its circumference divided ~by a function 
 of its area.* 
 
 255. Origin of Formulas of Flow. These simple 
 hypotheses constitute the foundation of all the expressions 
 of resistance to the flow of water in pipes, as they appear in 
 the varied, ingenious, and elegant formulas of those emi- 
 nent philosophers and hydraulicians who have investigated 
 the subject scientifically. 
 
 256. Formula of Resistance to Flow. Place R to 
 represent the sum of all the resistances arising from the 
 circumference of the pipe (excluding those due to the entry); 
 C for the contour or circumference of the pipe, in feet ; 8 for 
 the section of the interior of the pipe, in square feet ; I for 
 the length of the pipe, in feet ; and v for the mean velocity 
 
 * The law cf the effects of the resistances is believed to have been first for- 
 mulated in the simple algebraic expressions now in general use, by M. Chezy, 
 ^about the year 1775. 
 
230 FLOW OF WATER THROUGH PIPES. 
 
 of flow, in feet per second. Then the resistance to flow is 
 expressed by the equation 
 
 R = *JL x I x (m) &. (4) 
 
 257. Coefficient of Flow. In the equation a new 
 coefficient m appears, which also is to be determined by 
 experiment. It is not tb be confounded with the c hereto- 
 fore investigated, but will hereafter be investigated inde- 
 pendently. 
 
 258. Opposition of Gravity and Reaction. We 
 have seen that gravity ( 189) is the natural origin and the 
 accelerating force that produces motion of water in pipes. 
 
 Its effect, if no resistance was opposed, would be to con- 
 tinually accelerate the flow. On the other hand, if its effect 
 was removed, the resistances would bring the column to a 
 state of rest. 
 
 The two influences oppose each other continually, and 
 therefore tend to the production of a rate of motion in which 
 they balance eacji other. 
 
 259. Conversion of Pressure into Mechanical 
 Effect. When the motion has become sensibly constant, 
 a portion of the effect of gravity that appeared as velocity 
 in the cases of orifices and short tubes, or its equivalent in 
 the form of pressure or head, has been converted into 
 dynamic force and is acting to overcome the resistances, 
 and the remaining force due to gravity or head is producing 
 the velocity of flow then remaining. 
 
 260. Measure of Resistance to Flow. The effect 
 of the resistance along a main pipe, when discharging 
 water from a reservoir, as in Fig. 37, may be observed by 
 attaching a series of pressure gauges at intervals, or by at- 
 taching a series of open-topped pipes, as at p p l p^ etc. 
 
RESISTANCE INVERSELY. 
 
 231 
 
 If the end/ of the pipe is closed, water will stand in all 
 the vertical pipes at the same level, oik, as in the reservoir. 
 
 If the diameter of the pipe is uniform throughout its 
 length, and the flow, the full capacity of the pipe, then 
 water will stand in the several vertical pipes up to the in- 
 clined line a'f; provided that the top of p 2 be closed so that 
 there may be a tendency to vacuum at n, and provided also 
 that n is not more than thirty feet, or the height to which 
 the pressure of the atmosphere can maintain the pipe full, 
 above the line a'f, at n'. 
 
 When / is an open end discharging into air, and the 
 vacuum at n is not maintained, a'n will be the total effec- 
 tive head, and the portion of the pipe nf will be only parti- 
 ally filled. 
 
 261. Resistance Inversely as the Square of the 
 Velocity. If the discharge of the pipe is throttled at /, by 
 a partial closing of a valve, by a contraction of the issue, or 
 by diversion of the stream into other pipes of less capacity, 
 and a portion of the velocity is in consequence converted 
 into pressure equivalent to the head//, then the resistance 
 will be lessened as the square of the velocity decreases, and 
 water will stand in the vertical pipes, or the gauges will in- 
 dicate the inclined line a"f. This is the usual condition of 
 mains in public water supplies. 
 
232 
 
 FLOW OF WATER THROUGH PIPES. 
 
 262. Increase of Bursting Pressure. One effect of 
 throttling the discharge is seen to be an increase of bursting 
 pressure upon the pipes, which is greater when the exit is 
 entirely closed than when there is a constant flow, and which 
 decreases as the velocity increases, though a sudden clos- 
 ing of a valve against a rapid current will probably prove 
 disastrous to an ordinary pipe that is fully able to sustain 
 a legitimate pressure due to the head. 
 
 263. Acceleration and Resistance. Let db (Fig. 38) 
 be a vertical pipe discharging water from a reservoir A, 
 maintained always full. If, before the water entered the 
 
 FIG. 38. 
 
 
 pipe, a single particle had been dropped into its centre from 
 a, the velocity of movement of the particle would, in conse- 
 quence of the effect of gravity upon it, have been constantly 
 accelerated through its whole passage along the axis. 
 
DESIGNATION OF h" AND I. 233 
 
 Its velocity, when it had reached 6, would have been 
 equal to V%gH, when H represents the vertical height ab 
 in feet. 
 
 The greater the height ab the greater the sum of the ac- 
 celerations by gravity, and also, if the pipe is flowing full, 
 the greater the length a'b the greater the sum of the resist- 
 ances acting upon the column of water to retard it. 
 
 264. Equation of Head Required to Overcome 
 the Resistance. Let v be the velocity of the jet issuing 
 from b, li the head due to #, and h" the head acting upon 
 the resistance, R. 
 
 Then the amount of the force of gravity, or equivalent 
 head, ^", converted into dynamic force in each second to 
 overcome the resistances within the length of pipe traversed 
 
 by the jet in one second = ~- x I x ~-, and we have the 
 
 equation, 
 
 ,., mO 7 tf 
 
 A= ir xZx ^- < 5 > 
 
 representing the resistances overcome per second for the 
 given head and in the given length. 
 
 265. Designations of h" and I. In long pipes the 
 total head, H= h + h' + h". 
 
 The head, or charge of water h" acting upon the resist- 
 ances, is the vertical height of the surface of the reservoir, 
 less the height aa" = h (Fig. 38), necessary to generate the 
 velocity v, and also less the height a" a' = h' necessary to 
 overcome the resistance of entry, above the centre of the dis- 
 charging jet at the exit ; or if the discharge is into another 
 body of water, above the surface of the lower body. 
 
 The length I to be taken, is the actual length of the axis 
 of the pipe. 
 
 Then whatever the position or direction of the pipe a'b, 
 
234 FLOW OF WATER THROUGH PIPES. 
 
 or a'f, or if, or onf (abstracting for the present any resist- 
 ance of curvature), we have for its dynamic equation of re- 
 sistance to the force of gravity, 
 
 Clm tf Clm ., 
 71 ~S~ x 2g = ~S~ x ^ ^ ^ 
 
 unless, in the case of a pipe discharging near to its full capa- 
 city, an upward curve, n, shall rise more than thirty feet 
 above the line of hydraulic mean gradient a'f, when 7i" is 
 to be taken in two sections, first from a' to n vertically, and 
 second from n to f vertically reduced by the effect of the 
 vacuum, if any, or as a simple channel without pressure if 
 the length nf does not fill. 
 
 266. Variable Value of m. In the equation 
 
 ,. Cl tf 
 
 we have the coefficient m, whose several values are to be 
 deduced from actual measurements of the flow of water 
 through pipes, and whose governing conditions are to be 
 closely observed and studied. 
 
 The physical conditions of various pipes are so different 
 that special coefficients are required for each class of con- 
 ditions. 
 
 A slight increase in the roughness of the interior surface 
 of the pipe, occasional sudden enlargements or contractions 
 of the diameter of the pipe, and sudden bends in the direc- 
 tion of the pipe, may be instanced as sufficient departures 
 from the conditions of straight pipes with uniform diameters 
 and surfaces to materially modify the value of its coefficient 
 of flow. 
 
 267. Investigation of Values of m. For the de- 
 termination of a series or table of coefficients, m, for full 
 
DEFINITION OF SYMBOLS. 235 
 
 pipes, we will select data from published tables of* exper- 
 iments by Henry Darcy, made while he was director of the 
 public water service of the city of Paris ; fromf experiments 
 by Gfeo. S. Greene, made while chief engineer of the Croton 
 Aqueduct Department of New York city ; from experiments 
 by Geo. H. Bailey, Esq., made while chief engineer of the 
 Jersey City Water- works ; from some of the famous exper- 
 iments of Du Buat, Couplet, and Bossut, which furnished 
 the chief data for the elegant formulas of those eminent 
 philosophers, as well as those of PronyJ and Eytelwein, 
 and from several other sources. 
 
 68. Definition of Symbols. By transposition we 
 
 have 
 
 o $ h 1 /~\ 
 
 m = g x C x T x If W 
 
 The member -=- is the ratio of the height which the par- 
 (/ 
 
 tides fall through in the given length, equal = S__, or the 
 
 Jpngtn ^ , 
 
 sine of the angle of inclination Tea 1 /, Fig. 38. The inclina- 
 tion a'fis termed the "slope," or the hydraulic mean gra- 
 dient, and is usually designated by the letter i. The point 
 a 1 is always beneath the surface of the water a depth aa' 
 necessary to generate the velocity v in the pipe, and to 
 overcome the resistance of entry, whether the pipe be in the 
 position a'f, if, or onf. 
 
 The depth aa' varies as the velocity varies, and the 
 "slope" i corresponds to an imaginary right line connect- 
 ing the points a 1 and/. 
 
 * Recherches experimentales relatives au movement de 1'eau dans le 
 tuyaux. Paris, 1857. 
 
 f Descriptive Memoir of the Brooklyn Water-works, by James P. Kirk- 
 wood. Van Nostrand, N. Y., 1867. 
 
 \ Vide Recherches Physico-Mathematiques sur la Theorie du Mouvement 
 des Eaux Courantes, 1804. 
 
236 FLOW OF WATER THROUGH PIPES. 
 
 The member -^, as now inverted ( 256) refers to the 
 
 c 
 
 ratio of the section to the contour of the given pipe, or to the 
 
 sectional area T , . -, ,, ,. 
 
 - r It is termed the "mean radius*" or. in 
 wetted perimeter 
 
 the cases of pipes and channels partially filled, the hydrau- 
 lic mean depth, and is usually designated by the letter r. 
 The value of r for full pipes is always equal to one-fourth 
 
 of the diameter = , according to well-known properties of 
 the circle. 
 
 269. Experimental Values of the Coefficient of 
 Flow. We have then, as an equivalent for equation (7) : 
 
 (8) 
 
EXPERIMENTAL COEFFICIENTS. 
 
 237 
 
 TABLE No. 32. 
 EXPERIMENTAL COEFFICIENTS (m) OF FLOW OF WATER IN Clean 
 
 PIPES, UNDER PRESSURE, m ?j = -~* - 
 
 ir 
 
 EXPERIMENTS BY H. DARCY (Cast-iron Pipes). 
 
 Diameter = </, 
 infect. 
 
 Head = h, 
 in feet. 
 
 Length = /, 
 in feet. 
 
 Velocity = v , 
 in feet per sec. 
 
 Coefficient = m. 
 
 0.2687 
 
 O.O66 
 
 328.09 
 
 0.2885 
 
 .0104478 
 
 (t 
 
 1.742 
 
 tt 
 
 1.8399 
 
 .0067800 
 
 ct 
 
 3-347 
 
 (C 
 
 2.5946 
 
 .0065508 
 
 a 
 
 13.260 
 
 (t 
 
 5-i59 
 
 .0065850 
 
 u 
 
 39.299 
 
 tt 
 
 8.9242 
 
 .0065162 
 
 tt 
 
 56.011 
 
 tt 
 
 10.7115 
 
 .0064320 
 
 0.4501 
 
 0.079 
 
 328.09 
 
 0.4887 
 
 .0073054 
 
 a 
 
 .686 
 
 tt 
 
 i. 6021 
 
 .0059026 
 
 tt 
 
 1.558 
 
 tt 
 
 2.5021 
 
 .0054960 
 
 <( 
 
 54-975 
 
 tt 
 
 i5-39 2 9 
 
 .0051240 
 
 0.6151 
 
 0.089 
 
 328.09 
 
 0.6544 
 
 .0062884 
 
 u 
 
 1.207 
 
 tt 
 
 2.4991 
 
 .0058476 
 
 a 
 
 2.641 
 
 tt 
 
 3-7155 
 
 .0057898 
 
 a 
 
 4.369 
 
 tt 
 
 4.9045 
 
 .0055296 
 
 tt 
 
 12.500 
 
 tt 
 
 8.2564 
 
 .0055482 
 
 at 
 
 47.872 
 
 tt 
 
 16.2360 
 
 .0054948 
 
 0-975 1 
 
 0.092 
 
 328.09 
 
 0.7997 
 
 .0068802 
 
 tt 
 
 .883 
 
 tt 
 
 2.7134 
 
 .0057306 
 
 tt 
 
 1.762 
 
 tt 
 
 3-7863 
 
 .0058728 
 
 tt 
 
 3-625 
 
 tt 
 
 5.4039 
 
 .0059314 
 
 tt 
 
 7.562 
 
 tt 
 
 7.8330 
 
 .0058890 
 
 tt 
 
 13.473 
 
 tt 
 
 10-3575 
 
 .OO6OOIO 
 
 1.6427 
 
 0.148 
 
 328.09 
 
 1-3765 
 
 .0062950 
 
 tt 
 
 .148 
 
 tt 
 
 1.4685 
 
 0055310 
 
 tt 
 
 .197 
 
 tt 
 
 1-5549 
 
 .0065688 
 
 tt 
 
 394 
 
 tt 
 
 2-5954 
 
 .0047160 
 
 tt 
 
 .853 
 
 a 
 
 3.6637 
 
 .0051216 
 
 tt 
 
 .820 
 
 tt 
 
 3.6900 
 
 .0048536 
 
238 
 
 FLOW OF WATER THROUGH PIPES. 
 
 TABLE No. 53. 
 
 EXPERIMENTAL COEFFICIENTS (m) OF FLOW OF WATER IN Clean 
 
 2ghS 
 Civ* 
 
 PIPES, UNDER PRESSURE, m 
 
 EXPERIMENTS BY THE WRITER (Wrought-iron Cement-lined 
 
 Pipe). 
 
 Diameter = </, 
 in feet. 
 
 Head = h, 
 in feet. 
 
 Length = /, 
 in feet. 
 
 Velocity = v. 
 in feet per sec. 
 
 Coefficient = m. 
 
 1.6667 
 
 1.86 
 
 8171.0 
 
 0.949 
 
 .006360 
 
 ft 
 
 3.60 
 
 tt 
 
 1.488 
 
 005335 
 
 (( 
 
 5-93 
 
 ft 
 
 L9 2 5 
 
 .005251 
 
 
 
 8.48 
 
 (( 
 
 2.329 
 
 .005347 
 
 {( 
 
 10.93 
 
 (e 
 
 2.598 
 
 005313 
 
 (6 
 
 12.91 
 
 (( 
 
 2.867 
 
 005153 
 
 (( 
 
 16.28 
 
 (( 
 
 3.271 
 
 .004993 
 
 (( 
 
 18.60 
 
 (C 
 
 3-439 
 
 .005160 
 
 (( 
 
 22.22 
 
 tt 
 
 3-741 
 
 .005209 
 
 ft 
 
 24-54 
 
 (6 
 
 3.920 
 
 .005115 
 
 
 
 25.58 
 
 (( 
 
 4.OO 
 
 .005110 
 
 (t 
 
 26.16 
 
 
 
 4.04 
 
 .005100 
 
 TABLE No. 84. 
 EXPERIMENTS BY DU BUAT (Tin Pipes). 
 
 0.0889 
 
 973 
 
 10.401 
 
 5- T 79 
 
 .004992 
 
 (( 
 
 1.484 
 
 10.401 
 
 6-334 
 
 .005089 
 
 u 
 
 .0481 
 
 12.304 
 
 0.7717 
 
 .009393 
 
 (( 
 
 375 
 
 12.304 
 
 2.606 
 
 .006424 
 
 tt 
 
 i. 220 
 
 12.304 
 
 5.220 
 
 .005207 
 
 t( 
 
 .013 
 
 65.457 
 
 0.1411 
 
 .014276 
 
 tt 
 
 1.022 
 
 tt 
 
 1-775 
 
 .007091 
 
 u 
 
 I -954 i 
 
 2.546 
 
 .006585 
 
 TABLE No. 5S. 
 
 EXPERIMENTS BY BOSSUT (Tin Pipes). 
 
 0.0889 
 
 o.33i 
 
 53-284 
 
 1.085 
 
 .001698 
 
 et 
 
 .976 
 
 86.094 
 
 1.979 
 
 .004142 
 
 .11841 
 
 .864 
 
 3L956 
 
 2-945 
 
 005943 
 
 it 
 
 2.066 
 
 191.840 
 
 1.679 
 
 .007282 
 
 tt 
 
 1.699 
 
 3L956 
 
 4.308 
 
 .005461 
 
 .178 
 
 .765 
 
 3I-956 
 
 3-581 
 
 .005363 
 
 tt 
 
 2.019 
 
 191.840 
 
 2.196 
 
 .006270 
 
 tt 
 
 1.892 
 
 95-95 
 
 2.250 
 
 .011190 
 
 tt 
 
 1.491 
 
 31.956 
 
 5-230 
 
 .004901 
 
EXPERIMENTS COEFFICIENTS. 
 
 239 
 
 TABLE No. 56. 
 EXPERIMENTAL COEFFICIENTS (m) OF FLOW OF WATER IN Clean 
 
 2ghS 
 
 PIPES, UNDER PRESSURE, m = 
 
 Civ* 
 
 EXPERIMENTS BY COUPLET (Iron Pipes). 
 
 Diaameter = </, 
 in feet. 
 
 Head = k, 
 in feet. 
 
 Length = /, 
 in feet. 
 
 Velocity = , 
 in feet per sec. 
 
 Coefficient = m. 
 
 0.4439 
 
 0.492 
 
 7481.88 
 
 0.1785 
 
 .001475 
 
 tt 
 
 1.005 
 
 7481.88 
 
 .2802 
 
 .012230 
 
 4374 
 
 1.484 
 
 7481.88 
 
 .3665 
 
 .010390 
 
 ft 
 
 1.670 
 
 ft 
 
 .4258 
 
 .008667 
 
 a 
 
 2.130 
 
 tt 
 
 .4640 
 
 .009309 
 
 ft 
 
 2.215 
 
 tt 
 
 .4728 
 
 .009323 
 
 1.5988 
 
 12.629 
 
 3836.66 
 
 3-4779 
 
 .007004 
 
 TABLE No. 57. 
 EXPERIMENTS BY W. A. PROVIS. (Lead Pipes.) 
 
 0.125 
 
 2.91666 
 
 20.00 
 
 6.1495; 
 
 .006465 
 
 ft 
 
 " 
 
 40.00 
 
 4.7588 
 
 .005398 
 
 " 
 
 (( 
 
 60.00 
 
 3.9032 
 
 .005360 
 
 " 
 
 a 
 
 80.00 3-396I 
 
 .005287 
 
 (i 
 
 (( 
 
 100.00 
 
 3.0897 
 
 .005122 
 
 TABLE No. 58. 
 
 EXPERIMENTS BY RENNIE. 
 
 With glass pipes slightly rounded at the ends. 
 
 0.0020833 
 
 I.O 
 
 I.O 
 
 7.1627 
 
 .000653 
 
 tt 
 
 2 
 
 tt 
 
 10.4196 
 
 .000408 
 
 ff 
 
 3 
 
 " 
 
 12.9409 
 
 .000601 
 
 tt 
 
 4 
 
 ft 
 
 14.6240 
 
 .000627 
 
 .0041666 
 
 I.O 
 
 I.O 
 
 5-6450 
 
 .001672 
 
 tt 
 
 2 
 
 tt 
 
 8.3676 
 
 .001916 
 
 " 
 
 3 
 
 " 
 
 10.0497 
 
 .001992 
 
 tt 
 
 4 
 
 " 
 
 11.6000 
 
 .001994 
 
 .00625 
 
 1.0 
 
 I.O 
 
 5-5487 
 
 .004162 
 
 ft 
 
 2 
 
 tt 
 
 8.1852 
 
 .004814 
 
 tt 
 
 3 
 
 ft 
 
 9-855 I 
 
 .003956 
 
 tt 
 
 4 
 
 ft 
 
 10.8320 
 
 .004378 
 
 .00833 
 
 I.O 
 
 I.O 
 
 6.1028 
 
 .004584 
 
 tt 
 
 2 
 
 ft 
 
 8.5386 
 
 .004684 
 
 3 
 
 ft 
 
 10.8003 
 
 .004392 
 
 tt 
 
 L 
 
 4 
 
 ft 
 
 13.0400 
 
 .004016 
 
240 
 
 FLOW OF WATER THROUGH PIPES. 
 
 TABLE No. 59. 
 
 EXPERIMENTAL COEFFICIENTS (m) OF FLOW OF WATER IN Old 
 
 x i.r.no, UIN-U.EJK. JT KH/oa u K. n.. 7n ^, 
 EXPERIMENTS BY H. DARCY. (Foul Iron Pipes.) 
 
 Diameter = </, 
 in feet. 
 
 Head = h, 
 in feet. 
 
 Length = /, 
 in feet. 
 
 Velocity = , 
 in feet per sec. 
 
 Coefficient = m. 
 
 0.1194 
 
 0.223 
 
 328.09 
 
 0.2669 
 
 .018342 
 
 tt 
 
 .600 
 
 tt 
 
 .4273 
 
 .OI92IO 
 
 et 
 
 2.198 
 
 " 
 
 .8291 
 
 018735 
 
 ft 
 
 5-03 
 
 ee 
 
 1.2494 
 
 .018784 
 
 (( 
 
 10.630 
 
 ee 
 
 1.8079 
 
 .019055 
 
 te 
 
 13.632 
 
 ee 
 
 2.0772 
 
 .018511 
 
 0.2628 
 
 0.213 
 
 328.09 
 
 0.4040 
 
 .Ol68ll 
 
 " 
 
 .820 
 
 tt 
 
 .8242 
 
 .015551 
 
 " 
 
 2-379 
 
 ft 
 
 1.4645 
 
 .014288 
 
 (( 
 
 5.282 
 
 66 
 
 2.2226 
 
 .013774 
 
 te 
 
 10.171 
 
 ee 
 
 3-05I7 
 
 .014082 
 
 ft 
 
 14.879 
 
 ee 
 
 3-7434 
 
 .013679 
 
 0.8028 
 
 0.308 
 
 328.09 
 
 i. 0080 
 
 .011934 
 
 tt 
 
 .663 
 
 ft 
 
 1.4824 
 
 .011878 
 
 a 
 
 i-SS 2 
 
 tt 
 
 2.3218 
 
 OII334 
 
 " 
 
 3-773 
 
 tt 
 
 3.6283 
 
 .011285 
 
 tt 
 
 7-5 J 3 
 
 tt 
 
 5.0727 
 
 .011494 
 
 tt 
 
 10.499 
 
 tt 
 
 6.0169 
 
 .011417 
 
 " 
 
 13.468 
 
 tt 
 
 6.8037 
 
 .011454 
 
 .6 
 
 45.870 
 
 tt 
 
 12.5779 
 
 .011415 
 
 TABLE No. 60. 
 
 EXPERIMENT BY GEN. GEO. S. GREENE, C. E., 
 
 Upon a New York City cast-iron Main. (Tuberculated.) 
 3.0 | 20.215 | 11217.00 | 2.99967 .00966 
 
 1.6667 
 
 EXPERIMENT BY GEO. H. BAILEY, C. E., 
 Upon a Jersey City cast-iron Main. (Tuberculated.) 
 I 28.1285 I 29715.00 I 1-43795 I .01228 
 
EXPERIMENTAL COEFFICIENTS. 
 
 241 
 
 TABLE 6 O. (Continued.) 
 
 EXPERIMENTAL COEFFICIENTS (m) OF FLOW OF WATER IN Old 
 PIPES. UNDER PRESSURE, m 
 
 EXPERIMENT UPON THE COLINTON MAIN.* 
 Eight years in use. 
 
 Diameter = d, 
 in feet. 
 
 Head = h, 
 in feet. 
 
 Length = /, 
 in feet. 
 
 Velocity = z>, 
 in feet per sec. 
 
 Coefficient = m. 
 
 1-3334 
 tt 
 
 a 
 
 184 
 2 3 
 420 
 
 3815 
 25765 
 29580 
 
 14.500 
 5- 2 5 2 
 
 6.816 
 
 .004923 
 
 005556 
 .006559 
 
 LAMBETH WATER WORKS MAIN. 
 
 1.583 
 
 I 
 
 25 
 41 
 
 38 
 
 54120 
 
 2244O 
 
 52OO 
 
 1.772 
 2-734 
 4-353 
 
 .005918 
 .006229 
 .OO62O8 
 
 LIVERPOOL WATER WORKS MAIN. 
 I | 27 | 8140 | 2.644 | .007633 
 
 CARLISLE WATER WORKS MAIN. 
 I | 34.5 | 66OO | 3.568 .OO66lO 
 
 EXPERIMENTS BY THE WRITER. 
 
 With unlined wrought iron pipe (gas tubing), the jet entering through a stop- 
 cock and piston meter, with coefficient c = .58 when length = 0.25. The 
 pipe had been in use one week, but had rusted considerably. 
 
 0.08334 
 
 28.73 
 
 0.25 
 
 46.70 
 
 .... 
 
 85.57 
 
 9 
 
 18.964 
 
 035467 
 
 98.34 
 
 735 
 
 4.850 
 
 .007636 
 
 96.38 
 
 1337 
 
 3.538 
 
 .007722 
 
 87.33 
 
 2040 
 
 2.722 
 
 .007746 
 
 * Vide Proceedings of Inst. Civ. Engineers, p. 4, Feb. 6th, 1855, London. 
 
 16 
 
242 
 
 FLOW OF WATER THROUGH PIPES. 
 
 TABLE No. 6 1. 
 
 SERIES OF COEFFICIENTS OF FLOW (m) OF WATER IN CLEAN PIPES, 
 UNDER PRESSURE, AT DIFFERENT VELOCITIES, AND IN PIPES 
 
 OF DIFFERENT DIAMETERS, [m = -jrrr= -C-J. 
 
 \ Civ* v 2 I 
 
 VELOCITY. 
 
 DIAMETERS. 
 
 X inch. 
 
 .0417 /*. 
 
 K", 
 
 .0625'. 
 
 i" 
 .0834'- 
 
 i 1 //' 
 . 1250 . 
 
 *X" 
 
 .1458'. 
 
 2" 
 .1667'. 
 
 Feet per 
 Second. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 .1 
 
 O.OI5O 
 
 O.OI3O 
 
 O.OII9 
 
 O.OIO7 
 
 O.0097O 
 
 0.00870 
 
 .2 
 
 .0143 
 
 .0126 
 
 .0116 
 
 .OIO5 
 
 .00952 
 
 .00860 
 
 3 
 
 .0137 
 
 .0123 
 
 .0113 
 
 .0103 
 
 .00937 
 
 .00850 
 
 4 
 
 OI 33 
 
 .0119 
 
 .0110 
 
 .OIOO 
 
 .00920 
 
 .00840 
 
 5 
 
 .0128 
 
 .OIl6 
 
 .0107 
 
 .00984 
 
 .00904 
 
 .00830 
 
 .6 
 
 .0124 
 
 .0113 
 
 .OIO4 
 
 .00960 
 
 .00890 
 
 .00822 
 
 7 
 
 .0120 
 
 .0111 
 
 .0102 
 
 .00940 
 
 .00873 
 
 .00813 
 
 .8 
 
 .0116 
 
 .OI08 
 
 .0100 
 
 .00922 
 
 .OO860 
 
 .00804 
 
 9 
 
 .0113 
 
 .OI05 
 
 .00972 
 
 .00910 
 
 .00850 
 
 .00798 
 
 1.0 
 
 .0110 
 
 .OIO2 
 
 .00950 
 
 .00893 
 
 .00840 
 
 .00790 
 
 i.i 
 
 .0107 
 
 .00995 
 
 .00933 
 
 .00880 
 
 .00826 
 
 .00783 
 
 1.2 
 
 .0104 
 
 .00973 
 
 .00913 
 
 .00867 
 
 .00817 
 
 .00776 
 
 *-3 
 
 .OIOJ 
 
 .00952 .00898 
 
 .00854 
 
 .00809 
 
 .O077O 
 
 1.4 
 
 .00992 
 
 .00930 
 
 .00882 
 
 .00843 
 
 .00800 
 
 .00763 
 
 '5 
 
 .00959 
 
 .00910 
 
 .00868 
 
 .00832 
 
 .00793 -00757 
 
 1.6 
 
 .00942 
 
 .00890 
 
 .00854 
 
 .00823 
 
 .00786 
 
 .00750 
 
 J -7 
 
 .00920 
 
 .00872 
 
 .00840 
 
 .00814 
 
 .00777 
 
 .00746 
 
 1.8 
 
 .00900 
 
 .00856 
 
 .00830 
 
 .00806 
 
 .00769 
 
 .00741 
 
 1.9 
 
 .00880 
 
 .00842 
 
 .O0820 
 
 .0080O 
 
 .00763 
 
 .00736 
 
 2.0 
 
 .00862 
 
 .00830 
 
 .Oo8lO 
 
 .00790 
 
 .00757 
 
 .00731 
 
 2.25 
 
 .00840 
 
 .00804 
 
 .00785 
 
 .00770 
 
 .00742 
 
 .OO72I 
 
 2-5 
 
 .00795 
 
 .00780 
 
 .00768 
 
 .00752 
 
 .00730 
 
 .OO7IO 
 
 2.75 
 
 .00775 
 
 .00761 
 
 .0075O 
 
 .00736 
 
 .00716 
 
 .O07OO 
 
 3-0 
 
 00753 
 
 .00745 
 
 .00734 
 
 .00722 
 
 .00707 
 
 .00692 
 
 3-5 
 
 .00732 
 
 .O0722 
 
 .OO7I2 
 
 .OO7O2 
 
 .00692 
 
 .OO680 
 
 4 
 
 .00722 
 
 .007IO 
 
 .OO7O2 
 
 .00692 
 
 .00682 
 
 .00671 
 
 5 
 
 .00704 
 
 .00693 
 
 .00684 
 
 .00675 
 
 .00664 
 
 .00654 
 
 6 
 
 .00689 
 
 .00678 
 
 .00670 
 
 .O066O 
 
 .00650 
 
 .00640 
 
 7 
 
 .00675 
 
 .00664 
 
 .00657 
 
 .00648 
 
 .00639 
 
 .00629 
 
 8 
 
 .00663 
 
 .00652 
 
 .00646 
 
 .00638 
 
 .00627 
 
 .00618 
 
 9 
 
 .00652 
 
 .00643 
 
 .00636 
 
 .00628 
 
 .00618 
 
 .00609 
 
 10 
 
 .00644 
 
 .00634 
 
 .00628 
 
 .OO620 
 
 .OO6IO 
 
 .OO6OI 
 
 12 
 
 .00630 
 
 .0062O 
 
 .00614 
 
 .00607 
 
 .00599 
 
 .00590 
 
 14 
 
 .00622 
 
 .00613 
 
 .OO6o6 
 
 .O0600 
 
 .00592 
 
 .00584 
 
 16 
 
 .00618 
 
 .00608 
 
 .0060O 
 
 00595 
 
 .00589 
 
 .00581 
 
 18 
 
 .00616 
 
 .00606 
 
 .00599 
 
 .00594 
 
 .00588 
 
 .00580 
 
 20 
 
 .00615 
 
 .00605 
 
 .00598 
 
 00593 
 
 .00587 
 
 .00579 
 
COEFFICIENTS OF FLOW OF WATER. 
 
 243 
 
 TABLE No. 61 (Continued). 
 
 COEFFICIENTS OF FLOW (m) OF WATER IN CLEAN IRON PIPES 
 UNDER PRESSURE. 
 
 VELOCITY. 
 
 DIAMETERS. 
 
 3 inch 
 .250 feet. 
 
 4" 
 3333'- 
 
 6" 
 5'. 
 
 8" 
 .6667'. 
 
 10" 
 .8333'. 
 
 12" 
 
 !.</. 
 
 Feet per 
 Second. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient 
 
 Coefficient. 
 
 . I 
 
 O.OO80O 
 
 0.00763 
 
 0.00730 
 
 0.00704 
 
 0.00684 
 
 0.00669 
 
 .2 
 
 .00792 
 
 00755 
 
 .00724 
 
 .00698 
 
 .00678 
 
 .00662 
 
 3 
 
 .00784 
 
 .00750 
 
 .00720 
 
 .00693 
 
 .00673 
 
 .00657 
 
 4 
 
 .00780 
 
 .00742 
 
 .00713 
 
 .00688 
 
 .00668 
 
 .00652 
 
 5 
 
 .00774 
 
 .00737 
 
 .00708 
 
 .00682 
 
 .00663 
 
 .00648 
 
 .6 
 
 .00767 
 
 .00732 
 
 .00702 
 
 .00677 
 
 .00659 
 
 .00642 
 
 7 
 
 .00760 
 
 .00727 
 
 .00697 
 
 .00673 
 
 .00654 
 
 .00638 
 
 .8 
 
 .00754 
 
 .00722 
 
 .00693 
 
 .00668 
 
 .00651 
 
 00633 
 
 9 
 
 .00750 
 
 .00718 
 
 .00688 
 
 .00663 
 
 .00648 
 
 .00629 
 
 .0 
 
 .00743 
 
 .00712 
 
 .00684 
 
 .00659 
 
 .00643 
 
 .00624 
 
 . i 
 
 .00739 
 
 .00708 
 
 .00679 
 
 .00654 
 
 .00640 
 
 .0062O 
 
 .2 
 
 .00733 
 
 .00704 
 
 .00674 
 
 .00652 
 
 .00635 
 
 .00617 
 
 3 
 
 .00729 
 
 .00700 
 
 .00670 
 
 .00648 
 
 .00632 
 
 .00613 
 
 4 
 
 .00724 
 
 .00697 
 
 .00666 
 
 .00644 
 
 .00628 
 
 .Oo6lO 
 
 5 
 
 .00720 
 
 .00693 
 
 .00662 
 
 .00640 
 
 .00625 
 
 .00607 
 
 .6 
 
 .00716 
 
 .00690 
 
 .00658 
 
 .00637 
 
 .00622 
 
 .00603 
 
 7 
 
 .00712 
 
 .00687 
 
 .00655 
 
 .00633 
 
 .00618 
 
 .00601 
 
 .8 
 
 .00708 
 
 .00684 
 
 .00652 
 
 .00630 
 
 .00615 
 
 .00599 
 
 9 
 
 .00703 
 
 .00680 
 
 .00650 
 
 .00628 
 
 .00612 
 
 .00597* 
 
 2. 
 
 .00700 
 
 .00678 
 
 .00648 
 
 .00624 
 
 .00609 
 
 .00593 ' 
 
 2.25 
 
 .00690 
 
 .00670 
 
 .00640 
 
 .00617 
 
 .00603 
 
 .00588 
 
 .2.50 
 
 .00683 
 
 .00662 
 
 .00634 
 
 .Oo6ll 
 
 .00596 
 
 .00581 
 
 2-75 
 
 .00675 
 
 .00655 
 
 .00629 
 
 .00605 
 
 .00590 
 
 00575 
 
 3- 
 
 .00670 
 
 .00650 
 
 .00623 
 
 .OO60O 
 
 .00584 
 
 00570 
 
 3-5 
 
 .00660 
 
 .00640 
 
 .00614 
 
 00593 
 
 00574 
 
 .00561 
 
 4- 
 
 .00651 
 
 .00631 
 
 .00607 
 
 .00586 
 
 .00568 
 
 00553 
 
 5- 
 
 .00636 
 
 .00618 
 
 .00594 
 
 00573 
 
 .00558 
 
 00543 
 
 6. 
 
 .00622 
 
 .00605 
 
 .00582 
 
 .00562 
 
 .00548 
 
 00534 
 
 7- 
 
 .00610 
 
 00595 
 
 .00572 
 
 .00552 
 
 .00540 
 
 .00527 
 
 8. 
 
 .00600 
 
 .00587 
 
 .00562 
 
 .00544 
 
 .00532 
 
 .00520 
 
 9- 
 
 593 
 
 .00578 
 
 00555 
 
 .00538 
 
 .00525 
 
 .00512 
 
 10. 
 
 .00585 
 
 .00572 
 
 .00549 
 
 .00530 
 
 .00520 
 
 .00508 
 
 12. 
 
 .00582 
 
 .00560 
 
 .00540 
 
 .00522 
 
 .OO5I2 
 
 .00500 
 
 '4- 
 
 00573 
 
 00554 
 
 00533 
 
 .00516 
 
 .00507 
 
 .00494 
 
 16. 
 
 .00570 
 
 .00552 
 
 .00530 
 
 .00513 
 
 .005O2 
 
 .00491 
 
 18. 
 
 .00576 
 
 .00550 
 
 .00528 
 
 .005IO 
 
 .... 
 
 .... 
 
 20. 
 
 .00566 
 
 .00549 
 
 
 
 
 
 
 
 
 
244 
 
 FLOW OF WATER THROUGH PIPES. 
 
 TABLE No. 6 1 (Continued). 
 
 COEFFICIENTS OF FLOW (m) OF WATER IN CLEAN CAST-IRON 
 PIPES UNDER PRESSURE. 
 
 
 DIAMETERS. 
 
 VELOCITY. 
 
 14 inches 
 
 16" 
 
 18" 
 
 20" 
 
 24" 
 
 27" 
 
 
 1.1667 feet. 
 
 1-3333'- 
 
 i.5'. 
 
 1.6667'. 
 
 2.C/. 
 
 2.25'. 
 
 Feet per 
 Second. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 . I 
 
 0.00650 
 
 0.00623 
 
 .... 
 
 .... 
 
 .... 
 
 .... 
 
 .2 
 
 .00644 
 
 .00619 
 
 O.OO6OO 
 
 0.00583 
 
 .... 
 
 .... 
 
 3 
 
 .00640 
 
 .00614 
 
 .00597 
 
 .00578 0.00548 
 
 0.00530 
 
 -4 
 
 .00634 
 
 .Oo6ll 
 
 .00592 | .00574 .00544 
 
 .00526 
 
 5 
 
 .00630 
 
 .00607 
 
 .00588 .00570 .00540 
 
 .00523 
 
 .6 
 
 .00625 
 
 .00603 .00584 .00567 .00537 
 
 .00520 
 
 7 
 
 .OO62I 
 
 .OO600 .00580 ! .00563 
 
 00533 
 
 .00517 
 
 .8 
 
 .00617 
 
 .00597 .00577 
 
 .00561 
 
 .00531 
 
 00513 
 
 9 
 
 .Oo6l2 
 
 00593 : .00573 
 
 .00558 
 
 .00528 
 
 .00511 
 
 .0 
 
 .00609 
 
 .00588 .00570 
 
 00555 
 
 .00525 
 
 .00508 
 
 . i 
 
 .00605 
 
 .00584 
 
 .00568 
 
 .00552 
 
 .00522 
 
 .00505 
 
 .2 
 
 .OO6OI 
 
 .00581 
 
 .00564 
 
 .00550 
 
 .00520 
 
 .00503 
 
 3 
 
 .00598 
 
 .00578 
 
 .00561 
 
 .00548 
 
 .00517 
 
 .00500 
 
 4. 
 
 00593 
 
 .00575 
 
 00559 
 
 .00545 
 
 .00514 
 
 .00498 
 
 5 
 
 .00590 
 
 .00572 
 
 00556 
 
 .00542 
 
 .00512 
 
 .00495 
 
 .6 
 
 .00587 
 
 .00569 
 
 00553 
 
 .00539 
 
 .00510 
 
 .00493 
 
 7 
 
 .00584 
 
 .00566 
 
 00551 
 
 .00536 
 
 .00508 
 
 .00491 
 
 .8 
 
 .00582 
 
 .00563 
 
 00549 
 
 "00534 
 
 .00506 .00489 
 
 -9 
 
 .00579 
 
 .00561 
 
 .00546 
 
 .00532 
 
 .00503 
 
 .00487 
 
 2.0 
 
 .00576 
 
 .00559 
 
 00543 
 
 .00529 
 
 .00501 
 
 .00485, 
 
 2.25 
 
 .00570 
 
 .00553 
 
 00538 
 
 .00524 
 
 .00497 
 
 .00480 
 
 2.50 
 
 .00564 
 
 .00548 
 
 00533 
 
 .00518 
 
 .00492 
 
 .00475 
 
 2-75 
 
 00559 
 
 .00543 
 
 .00528 i .00513 
 
 .00488 
 
 .00472 
 
 3- 
 
 00554 
 
 .00538 
 
 00523 
 
 .00509 
 
 .00483 
 
 .00468 
 
 3-5 
 
 00547 
 
 .00529 
 
 .00516 
 
 .00502 
 
 .00478 
 
 .00462 
 
 4- 
 
 .00540 
 
 .00524 
 
 .00511 
 
 .00498 
 
 .00473 
 
 .00458 
 
 5- 
 
 .00530 
 
 00515 
 
 .00501 
 
 .00490 
 
 .00466 
 
 .00451 
 
 6. 
 
 .00520 
 
 .00507 
 
 .00495 
 
 .00482 
 
 .00460 
 
 .00446' 
 
 7- 
 
 .00512 
 
 .00500 
 
 .00489 
 
 .00476 
 
 00453 
 
 .00440 
 
 8. 
 
 .00503 
 
 . 0049 1 
 
 .00483 
 
 .00470 
 
 .00450 
 
 .00435. 
 
 9- 
 
 .00498 
 
 .00489 
 
 .00478 
 
 .00466 
 
 .00445 
 
 .00431 
 
 10. 
 
 00493 
 
 .00483 
 
 .00473 
 
 .00462 
 
 .00443 
 
 .00429 
 
 12. 
 
 .00487 
 
 .00478 
 
 .00468 
 
 .00457 
 
 .00440 
 
 .00429 
 
 14. 
 
 .00482 
 
 .00473 
 
 .00463 
 
 .00452 
 
 .00434 
 
 .00422 
 
 16. 
 
 .00480 
 
 .00470 ! .00460 
 
 .00450 
 
 .00432 
 
 .00420 
 
COEFFICIENTS OF FLOW OF WATER. 
 
 245 
 
 TABLE No. 61 (Continued). 
 
 COEFFICIENTS OF FLOW (m) OF WATER IN CLEAN CAST-IRON 
 PIPES, OR SMOOTH MASONRY, UNDER PRESSURE. 
 
 VELOCITY. 
 
 DIAMETERS. 
 
 30 inch 
 2.5' feet. 
 
 33" 
 2- 75'- 
 
 36'' 
 3.<S. 
 
 40" 
 3-3333- 
 
 44" 
 3.6667'. 
 
 48" 
 4.0'. 
 
 Feet per 
 Second, 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 4 
 
 O.OO5JO 
 
 O.OO497 
 
 0.00476 
 
 .... 
 
 .... 
 
 ... 
 
 5 
 
 .00507 
 
 .00492 
 
 .00473 
 
 0.00436 
 
 O.OO42O 
 
 O.OO4OO 
 
 .6 
 
 .00504 
 
 .00490 
 
 .00471 
 
 .00434 
 
 .00418 
 
 .00399 
 
 7 
 
 .O050I 
 
 .00488 
 
 .00469 
 
 .00432 
 
 .00416 
 
 .00398 
 
 .8 
 
 .00498 
 
 .00485 
 
 .00467 
 
 .00431 
 
 .00414 
 
 .00397 
 
 9 
 
 .00495 
 
 .00482 
 
 .00464 
 
 .00430 
 
 .00412 
 
 .00396 
 
 I.O 
 
 .00492 
 
 .00480 
 
 .00462 
 
 .00428 
 
 .OO4II 
 
 00395 
 
 i.i 
 
 .00490 
 
 .00478 
 
 .00459 
 
 .00426 
 
 .00410 
 
 .00394 
 
 1.2 
 
 .00488 
 
 .00475 
 
 .00457 
 
 .00424 
 
 .00409 
 
 .00393 
 
 i-3 
 
 .00486 
 
 .00472 
 
 00455 
 
 .00423 
 
 .00407 
 
 .00392 
 
 1.4 
 
 .00484 
 
 .00470 
 
 00453 
 
 .00422 
 
 .00406 
 
 .00391 
 
 i-5 
 
 .00482 
 
 .00468 
 
 .00451 
 
 .00421 
 
 .00404 
 
 .00390 
 
 1.6 
 
 .00480 
 
 .00466 
 
 .00450 
 
 .00400 
 
 .00403 
 
 .00388 
 
 i-7 
 
 .00477 
 
 .00464 
 
 .00448 
 
 .00419 
 
 .00402 
 
 .00387 
 
 1.8 
 
 .00475 
 
 .00462 
 
 .00446 
 
 .00418 
 
 .O04OI 
 
 .00386 
 
 1.9 
 
 .00473 
 
 .00460 
 
 .00444 
 
 .00417 
 
 .O04OO 
 
 .00385 
 
 2. 
 
 .00470 
 
 .00458 
 
 .00442 
 
 .00416 
 
 .00399 
 
 .00384 
 
 2.25 
 
 .00465 
 
 00453 
 
 .00437 
 
 .00413 
 
 .00397 
 
 .00382 
 
 2-5 
 
 .00460 
 
 .00449 
 
 .00432 
 
 .00410 
 
 .00394 
 
 .00380 
 
 2-75 
 
 .00456 
 
 .00444 
 
 .00428 
 
 .00408 
 
 .00391 
 
 .00378 
 
 3- 
 
 .00452 
 
 .00440 
 
 .00424 
 
 .00407 
 
 .00389 
 
 .00376 
 
 3 5 
 
 .00446 
 
 .00434 
 
 .00419 
 
 .00402 
 
 .00386 
 
 .00373 
 
 4 
 
 .00441 
 
 .00430 
 
 .00415 
 
 .00400 
 
 .00383 
 
 .00370 
 
 5- 
 
 .00436 
 
 .00423 
 
 .OO4IO 
 
 .00395 
 
 .00381 
 
 .00366 
 
 6. 
 
 .00430 
 
 .00418 
 
 .00405 
 
 .00391 
 
 .00377 
 
 .00363 
 
 7- 
 
 .00427 
 
 .00413 
 
 .OO4OI 
 
 .00388 
 
 .00373 
 
 .00361 
 
 8. 
 
 .00422 
 
 .00410 
 
 .00398 
 
 .00384 
 
 .00371 
 
 .00358 
 
 9- 
 
 .00418 
 
 .00407 
 
 00395 
 
 .00382 
 
 .00370 
 
 .00355 
 
 10. 
 
 .00415 
 
 .00404 
 
 .00392 
 
 .00380 
 
 .00367 
 
 -00353 
 
 12. 
 
 .00412 
 
 .00400 
 
 .00389 
 
 .00377 
 
 .00364 
 
 .00351 
 
 I 4 . 
 
 .00409 
 
 .00397 
 
 .00386 
 
 .00373 
 
 .00363 
 
 .00350 
 
 16. 
 
 .00406 
 
 00395 
 
 .... 
 
 
 
 .... 
 
246 
 
 FLOW OF WATER THROUGH PIPES. 
 
 TABLE No. 61 (Continued). 
 
 COEFFICIENTS OF FLOW (m) OF WATER IN CLEAN CAST-IRON PIPES, 
 OR SMOOTH MASONRY, UNDER PRESSURE. 
 
 
 
 
 DIAMETERS. 
 
 
 
 VELOCITY. 
 
 54 inches. 
 
 60" 
 
 72" 
 
 84" 
 
 9 6" 
 
 
 4.5 feet. 
 
 5.</. 
 
 6.0'. 
 
 7.0'. 
 
 8.c/. 
 
 Feet per second 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 Coefficient. 
 
 .4- 
 
 
 
 
 
 
 T" 
 
 5 
 
 0.00378 
 
 0.00358 
 
 0.00339 
 
 0.00318 
 
 O.0029O 
 
 .6 
 
 .00377 
 
 .00357 
 
 .00338 
 
 .00317 
 
 .00289 
 
 7 
 
 .00376 
 
 .00356 
 
 .00337 
 
 .00317 
 
 .00288 
 
 .8 
 
 -375 
 
 .00355 
 
 .00336 
 
 .003 i 6 
 
 .00287 
 
 9 
 
 .00374 
 
 .00354 
 
 00335 
 
 00315 
 
 .00286 
 
 I.O 
 
 .00373 
 
 00353 
 
 00334 
 
 .00314 
 
 .OO286 
 
 .1 
 
 .00372 
 
 .00352 
 
 00333 
 
 .00313 
 
 .00285 
 
 .2 
 
 .00371 
 
 .00351 
 
 .00332 
 
 .00313 
 
 .00285 
 
 3 
 
 .00370 
 
 .00350 
 
 .00332 
 
 .00312 
 
 .00285 
 
 4 
 
 .00369 
 
 .00350 
 
 .00331 
 
 .00312 
 
 .00284 
 
 5 
 
 .00368 
 
 .00349 
 
 .00331 
 
 .00311 
 
 .00284 
 
 .6 
 
 .00368 
 
 .00348 
 
 .00330 
 
 .00311 
 
 .00284 
 
 7 
 
 .00367 
 
 .00347 
 
 .00329 
 
 .00310 
 
 .00283 
 
 1.8 
 
 .00366 
 
 00347 
 
 .00329 
 
 .00309 
 
 .00283 
 
 1.9 
 
 .00365 
 
 .00346 
 
 .00328 
 
 .00309 
 
 .00283 
 
 2 
 
 .00364 
 
 .00346 
 
 .00328 
 
 .00308 
 
 .O0282 
 
 2.25 
 
 .00362 
 
 .00344 
 
 .00327 
 
 .00307 
 
 .O0282 
 
 2 -5 
 
 .00360 
 
 .00342 
 
 00325 
 
 .00306 
 
 .00281 
 
 2 -75 
 
 .00358 
 
 .00341 
 
 .00323 
 
 .00305 
 
 .0028O 
 
 3 
 
 00357 
 
 00339 
 
 .00321 
 
 .00302 
 
 .00278 
 
 3-5 
 
 oo353 
 
 .00337 
 
 .00320 
 
 .00300 
 
 .00276 
 
 4 
 
 .00350 
 
 00333 
 
 .00318 
 
 .00298 
 
 .00274 
 
 5 
 
 00345 
 
 .00329 
 
 00313 
 
 .00294 
 
 .00272 
 
 6 
 
 .00340 
 
 .00324 
 
 .OO3IO 
 
 .00292 
 
 .O0268 
 
 7 
 
 .00338 
 
 .00322 
 
 .00308 
 
 .00289 
 
 .O0266 
 
 8 
 
 .00335 
 
 .0032O 
 
 .00304 
 
 .00286 
 
 .00264 
 
 9 
 
 .00332 
 
 .00318 
 
 .OO3O2 
 
 .00283 
 
 .O0262 
 
 10 
 
 .00331 
 
 .00316 
 
 .O03OO 
 
 .00282 
 
 .O026l 
 
 12 
 
 .00330 
 
 00313 
 
 .00299 
 
 .00280 
 
 .O026O 
 
 14 
 
 .00329 
 
 .O03I2 
 
 .00298 
 
 .00279 
 
 .00259 
 
EFFECTS OF TUBERCLES. 247 
 
 270. Peculiarities of the Coefficient (HI) of Flow. 
 In the tables and diagram of coefficients (m) of flow in pipes, 
 as well as in those of coefficients of discharge (c) through 
 orifices, there is variation in value with each variation in 
 velocity of the jet. In the case of pipes, there is also a 
 variation with the variation of diameter of jet, that equally 
 demands attention. 
 
 It will be observed in the tables of experiment above 
 quoted that the coefficient decreases as the diameter or 
 hydraulic mean radius increases, and also that with a 
 given diameter the coefficient decreases as the velocity 
 increases; thus, with a given low velocity, we may trace 
 the decrease of the coefficient from 0.0128 for a half-inch 
 pipe to 0.0029 for a ninety-six inch pipe ; and with a given 
 diameter of one-half inch we may trace the decrease of the 
 coefficient from 0.0128 for .5 foot velocity per second to 
 0.00622 for 14 feet velocity per second, and with a given 
 diameter of 96 inches we may trace the decrease of the 
 coefficient from 0.0029 for a velocity of .5 foot per second to 
 0.00259 for a velocity of 14 feet per second. 
 
 We have then a large range of coefficients applicable to 
 clean, smooth, and straight bores. When the bores are of 
 coarse grain, or are slightly tuberculated, the range is still 
 greater, and the values of coefficients of the smaller diam- 
 eters quite sensibly affected ; and if the bores are very 
 mgh or tuberculated, the values of coefficient for small 
 Liameters and low velocities are very much augmented. 
 
 271. Effects of Tubercles. These effects, in tubercu- 
 ited pipes, as compared with clean pipes, are illustrated in 
 
 the following approximate table, which we have endeavored 
 adjust to a common velocity of three feet per second for 
 the diameters. The data for very foul pipes is however 
 scanty, though sufficient to show that the coefficients do in 
 
248 
 
 FLOW OF WATER THROUGH PIPES. 
 
 extreme cases exceed the limits given for the small diam- 
 eters ; and that conditions from clean to foul may occur, 
 with the several diameters, that shall cover the entire range 
 from minimum to maximum coefficients, and calling for a 
 careful exercise of judgment founded upon experience. 
 
 TABLE No. 62. 
 
 COEFFICIENTS FOR CLEAN, SLIGHTLY TUBERCULATED, AND FOUL PIPES, 
 OF GIVEN DIAMETERS, AND WITH A COMMON VELOCITY OF 3 FEET 
 
 / 2ghd * \2gri\*\ 
 
 PER SECOND. \v = \ . 6 N 7 \ = 4 - 
 
 \ Urn) / I m / 
 
 Hydraulic 
 Mean Radius, 
 S d 
 
 C ~ 4 
 
 Diameter. 
 
 Clean. 
 
 Slightly 
 tuberculated. 
 
 Foul. 
 
 
 Feet. 
 
 Inches. 
 
 Coef., m. 
 
 Coef., tn. 
 
 Coef., m. 
 
 .0104 
 
 .0417 
 
 1 
 
 0.00753 
 
 
 
 
 
 .0156 
 
 .0625 
 
 i 
 
 .00745 
 
 
 
 
 
 ,O2o8 
 
 o8^4 
 
 I 
 
 OO734. 
 
 0.00982 
 
 
 .0312 
 
 *-" J O'T 
 .1250 
 
 4 
 
 ^r/O*r 
 
 .00722 
 
 .00940 
 
 
 
 .0364 
 
 .1458 
 
 i* 
 
 .00707 
 
 .00925 
 
 
 
 .0417 
 
 .1667 
 
 2 
 
 .00692 
 
 .OO9IO 
 
 O.OI4OO 
 
 .0625 
 
 .2500 
 
 3 
 
 .00670 
 
 .00862 
 
 .01300 
 
 .0833 
 
 3334 
 
 4 
 
 .00650 
 
 .00825 
 
 .OI20O 
 
 .1250 
 
 .5000 
 
 6 
 
 .00623 
 
 .00772 
 
 .OIIOO 
 
 .1667 
 
 .6667 
 
 8 
 
 .006OO 
 
 00733 
 
 .00922 
 
 .2083 
 
 .8334 
 
 10 
 
 .00584 
 
 .00706 
 
 .00868 
 
 .2500 
 
 .0000 
 
 12 
 
 .00510 
 
 .0068O 
 
 .00828 
 
 .2917 
 
 .1667 
 
 H 
 
 00554 
 
 .00657 
 
 .00792 
 
 3333 
 
 3333 
 
 16 
 
 .00538 
 
 .00636 
 
 .00760 
 
 375 
 
 .5000 
 
 18 
 
 .00523 
 
 .00616 
 
 .00733 
 
 .4167 
 
 .6667 
 
 20 
 
 .00509 
 
 .00598 
 
 .00710 
 
 .5000 
 
 2.0OOO 
 
 24 
 
 .00483 
 
 .00567 
 
 .00664 
 
 5 62 5 
 
 2.25OO 
 
 27 
 
 .00468 
 
 .00544 
 
 .00635 
 
 .6250 
 
 2.5OOO 
 
 30 
 
 .00452 
 
 .00525 
 
 .00604 
 
 .6875 
 
 2.7500 
 
 33 
 
 .00440 
 
 .00507 
 
 .00578 
 
 .7500 
 
 3.OOOO 
 
 36 
 
 .00424 
 
 .00490 
 
 .00554 
 
 .8333 
 
 3-3333 
 
 40 
 
 .00407 
 
 .00466 
 
 .00524 
 
 .9167 
 
 3.6667 
 
 44 
 
 .00389 
 
 .00443 
 
 .00500 
 
 I.OOOO 
 
 4.0000 
 
 48 
 
 .00376 
 
 .00422 
 
 .00477 
 
EQUATION OF VELOCITY. 249 
 
 272. Classification of Pipes and their Mean Co- 
 efficients. In ordinary calculations, the mean coefficient 
 for medium diameters and velocities may be taken, for clean 
 pipes, as .00644 ; for rough or slightly tuberculated pipes, 
 as .0082 ; and for very rough or very foul pipes, as .012. 
 These coefficients apply approximately to pipes of about 
 five inches diameter, when the velocities are about three 
 feet per second, reference being made to the diameter of the 
 pipe itself when clean. 
 
 273. Equation of the Velocity Neutralized by Re- 
 sistance to Flow. Having now developed the several 
 values of m as applicable to the several conditions of pipes, 
 we will again transpose our equation and remove 0, the 
 member expressing velocity of flow, to one side by itself, 
 and we have the equation of velocity of flow : 
 
 or 
 
 ( m 
 or = or = 
 
 or = (8) 
 
 In which h = thr li 
 
 I = the length of the pipe, in feet. 
 d = the internal diameter of the pipe, in feet. 
 C the contour of the unit of length of pipe, in feet. 
 8 = the sectional area of the pipe, in square feet. 
 
 i = the sine of inclination = -=- 
 
 L 
 
 r = the hydraulic mean radius = ^ = -j- 
 g = 32.2. 
 
250 
 
 FLOW OF WATER THROUGH PIPES. 
 
 274. Equation of Resistance Head. By transposi- 
 tion again we have the equation for that portion, #', of the 
 total head ^included in the slope i : 
 
 Clmtf 
 
 or 
 
 or 7i" = m x 
 r 2 
 
 (9) 
 
 Let c r represent the ratio of 7i' to Ti, or coefficient of re- 
 sistance of entry of the jet = ( - 2 ij = (^ ~ l)* 
 
 . Equation of Total Head. Then 
 
 or* 
 
 and 
 
 ff = 
 
 g 
 
 (1 
 
 (10) 
 (11) 
 
 also, when c is the coefficient of discharge, 
 
 i 
 
 (12) 
 
 276. Equation of Volume. The velocity v having 
 been ascertained, we have, for volume of flow q per second, 
 
 and 
 
 * Compare Weisbach's Mechanics of Engineering, translated by E. B. 
 Coxe, A. M. N. T., 1870, p. 870. 
 
SUBDIVISIONS OF TOTAL HEAD. 
 
 251 
 
 also, we have 
 
 _ 
 
 .7854^ 
 
 q ^=V2gNx 
 
 4) 
 
 or 
 
 or 
 
 Hd? 
 
 (1 
 
 (13 s ) 
 
 . Equation of Diameter. By transposition again 
 for the value of d, we have 
 
 or 
 
 = .4788 
 
 c f ) d 
 
 JLZ 
 
 (14) 
 
 In this last equation of d, the assistance of the table of 
 velocities for given slopes and diameters (p. 259), and the 
 table of coefficients, m, for given velocities and diameters 
 ( 269, p. 242), will be required, since the unknown quan- 
 tities d and m appear in the equation. The approximate 
 values of d and m for the given velocity can be taken from 
 the tables and inserted in the right-hand side of the equa- 
 tion, and a close value of d worked out for a first approxi- 
 mation, and then the operation repeated for a closer value 
 of d, if necessary. 
 
 278. Kelative Values of Subdivisions of Total 
 Head. Referring again to the extended pipe, P', Fig. 35, 
 assume it to be 1000 feet long, horizontal, 1 foot diameter, 
 and under a constant head of 100 feet ; then the velocity of 
 discharge, according to equation (11) will be 
 
252 FLOW OF WATER THROUGH PIPES, 
 
 f 64.4 x 100 
 
 1+. 505 + . 00495 i feet per second; 
 
 [ = 17.; 
 
 and h = = 4.694 feet. 
 
 %9 
 
 = 2.370 " 
 
 h" = (. 00496^)^= 92.941 
 V .25/2^ 
 
 and H=7i + ?i' + n" = 100.0 feet. 
 
 . Many Popular Formulas Incomplete. The 
 
 fact that the majority of popular formulas for flow of water 
 in pipes, as usually quoted in cyclopedias and text-books, 
 refer to 7i' + h", or in some cases to h" only, and not to If, 
 has led us to treat the subdivisions of If more minutely in 
 detail than would otherwise have been necessary. 
 
 Serious errors are liable to result from the application 
 of such hydrodynamic formulae by persons not familiar 
 with their origin, especially when the problem includes a 
 high head of water and short length of pipe. 
 
 We believe that the coefficient of flow, m, has not here- 
 tofore been as fully developed as its importance has 
 demanded. 
 
 28O. Formula of M. Chezy. The formula of 
 M. Chezy, proposed a century ago, and into which nearly 
 all expressions for the same object, since introduced, can be 
 resolved, refers to h" only, or h + ?i", and not to If. When 
 stated in the symbols herein used, it becomes 
 
SUB-HEADS COMPARED. 
 
 253 
 
 As g is introduced in place of 2g in our equation, m' will 
 equal |- 
 
 281. Various Popular Formulas Compared. The 
 
 value of treating the question of flow of water in pipes in 
 detail may perhaps best be illustrated by computing the 
 velocity of flow from our pipe P , Fig. 35, as it is extended 
 to different lengths, from 5 feet to 10,000 feet, by a complete 
 formula, with m at its legitimate value, and then computing 
 the same by several prominent formulas, in the form in 
 which they are usually quoted. (See Table No. 63, p. 254.) 
 
 282. Sub-heads Compared. If we compute the total 
 head, to which the velocities, found by the first formula of 
 the table, are due, we shall have the sub-heads, as follows ; 
 when d = 1 foot. 
 
 LENGTHS IN FEET. 
 
 5- 
 
 5. 
 
 100. 
 
 1000. 
 
 10,000 
 
 VELOCITIES IN FT. 
 PER SECOND. 
 
 63.463- 
 
 51.111. 
 
 43i". 
 
 17-386. 
 
 5.392. 
 
 h 
 
 62.542 
 
 40.568 
 
 28.863 
 
 4.694 
 
 .451 
 
 h! 
 
 31-583 
 
 20.487 
 
 14-575 
 
 2.370 
 
 .228 
 
 h" 
 
 5.878 
 
 38.945 
 
 56.571 
 
 92.941 
 
 99-330 
 
 H 
 
 100. O 
 
 loo.o 
 
 IOO.O 
 
 IOO.O 
 
 IOO.O 
 
 It is here shown that the values of 7i and ~ti cannot be 
 neglected until the length of the pipe exceeds one thousand 
 diameters, under the ordinary conditions of public water 
 supplies. 
 
 In our first length of five feet, 7i is about ten and one- 
 half times 7i", and 7i' is about five and one-half times 7i". 
 
254 
 
 FLOW OF WATER THROUGH PIPES. 
 
 T A BLE No. 63. 
 
 RESULTS GIVEN BY VARIOUS FORMULAS FOR FLOW OF WATER IN 
 SMOOTH PIPES, UNDER PRESSURE, COMPARED. 
 
 DATA. To find the velocity, given : Head, H = 100 feet ; Diameter, d = i foot ; and Lengths, 
 /, respectively as follows : 
 
 AUTHORITY. 
 
 EQUATIONS. 
 
 LENGTHS. 
 
 fe 5 et 
 
 <& 
 
 100 
 
 feet. 
 
 IOOO 
 
 feet. 
 
 10,000 
 
 feet. 
 
 Equation (n) . . 
 Chezy 
 
 \ ^ /i* 
 
 Veloc. 
 63.463 
 
 223.607 
 
 216.94 
 223.214 
 241.778 
 67.40 
 246.171 
 218.758 
 213.761 
 62.540 
 294.650 
 214.267 
 244.120 
 223.607 
 223.607 
 62.555 
 
 Veloc. 
 
 51.111 
 
 70.710 
 
 102.918 
 
 68.54 
 70.480 
 76.367 
 50.00 
 73-682 
 69.114 
 67.589 
 47.080 
 90.263 
 67-715 
 77.133 
 70.710 
 70.710 
 47.084 
 
 Veloc. 
 43.111 
 
 50.000 
 81.510 
 
 48.446 
 49.792 
 53-96o 
 40.82 
 51-247 
 48.845 
 47.804 
 
 38-75 
 63.070 
 
 47-9I3 
 54-640 
 50.000 
 50.000 
 38.724 
 
 Veloc. 
 
 17-386 
 
 15.810 
 13.662 
 
 15-258 
 15-641 
 16.975 
 15-427 
 15-232 
 15-384 
 15.114 
 14.780 
 18.917 
 15.140 
 17.279 
 15.810 
 15.810 
 14-797 
 
 Veloc. 
 
 5-392 
 
 5.000 
 3-9781 
 
 4.770 
 4.842 
 5.280 
 4-985 
 4-592 
 4.800 
 4.780 
 4.780 
 5-507 
 4.791 
 5-464 
 5.000 
 5.000 
 4.804 
 
 { (i + <:,)*- J 
 v \** S \* 
 
 Du Buat 
 
 Prony (a) 
 
 " (6) 
 Eytelwein (a) . . 
 
 (*).- 
 Saint Vennant . . 
 D' Aubuisson (a) 
 * (*) 
 Neville (a) 
 " (*) 
 Blackwell 
 
 \lmlC\ 
 
 88. 5 r -.03 ,i } 
 
 //\A // \i ^ 3) 
 
 (D^Ms* 1 *) 
 
 
 v (11703 95?"* + .01698) .1308. 
 
 ( dk \\ 
 
 50 i /+ 5 orf \ 
 v 105.926 (rz)" 
 
 
 v 95.6 Vri 
 
 -- i Hr !* 
 
 ( .0234r + .oooioSs/ J 
 v 140 (rz)* ii (rz') ? 
 
 ( Arf) \ 
 
 V '7 QI^ < t .... 
 
 
 -,7.913 | ^ f 
 j "' fc ) * 
 
 D' Arcy 
 Leslie 
 
 v = -\ .00000162 > 
 
 1 .00007726 + j 
 
 w = 100 ^ri 
 z/-5o<:(^/)5 
 
 Hawksley 
 
 . , j dk j i 
 
 P 48 - 45 i/ + 54^1 
 
 In which C - contour of pipe, in feet ; / = length of pipe, in feet. 
 
 c = unity for smooth pipes, and m = coefficient of flow. 
 
 is reduced for rough pipes. r = hyd. mean radius, in feet, = 
 
 d diam. of pipe, in feet. S = sectional area of pipe, in square feet. 
 H = entire head, in feet. / = sine of inclination, in feet, = 
 
 k = resistance head, in feet. v = velocity of flow, in feet per sec. 
 
PEONY'S ANALYSIS. 255 
 
 In long pipes, sufficient velocity is converted into pres- 
 sure to reduce somewhat the contraction of the jet at its 
 entrance into the pipe. In very long pipes the effect of this 
 contraction becomes insignificant when compared with the 
 effect of reaction from the walls of the pipe. 
 
 283. Investigations by Du Buat, Coloumb, and 
 Prony. The investigations of Du Buat and Coloumb led 
 them to the conclusion that the velocity of the fluid occa- 
 sioned a resistance to flow, in addition to that arising from 
 the wet perimeter of a channel or pipe, which is propor- 
 tional to the simple velocity ; and afterwards Prony, coin- 
 ciding with this view, undertook the investigation of the two 
 coefficients thus introduced into the formula of resistance to 
 flow. 
 
 Since their new coefficient, 0, applied to the simple velo- 
 city and not to the square of the velocity, as does the co- 
 efficient m, their expression, in our symbols, became 
 
 - f g = (H- h) or K 
 
 284. Prony's Analysis. Prony analyzed the results 
 of fifty-one experiments to determine the values of m and 0, 
 including eighteen experiments by Du Buat with a tin 
 pipe of about one inch diameter and sixty -five feet long ; 
 twenty-six experiments by Bossut with pipes of about one, 
 one and one-quarter, and two-inch diameters, and varying 
 in length from thirty-two to one hundred and ninety -two 
 feet ; and seven experiments by Couplet. Six of these last 
 experiments were made with a five and one-quarter inch 
 pipe, under a head less than two and one-quarter feet, and 
 
256 FLOW OF WATER THKOUGH PIPES. 
 
 one with, a nineteen-inch pipe with a head of about twelve 
 and one-half feet. 
 
 We have quoted above ( 269) eight of the experiments 
 by Du Buat, nine of those by Bossut, and the full seven 
 by Couplet, and in the two first included the extremes so 
 as to cover their entire range. 
 
 This was a limited foundation upon which to build a 
 theory of the flow of water in pipes, nevertheless the attain- 
 ments of this eminent investigator enabled him to deduce 
 from the limited data hypotheses which were valuable con- 
 tributions to hydrodynamic science. 
 
 From these experiments Prony deduced the values, as 
 reduced to English measures, m = .0001061473 ; and ft = 
 .16327. 
 
 285. Eytelwein's Equation of Resistance to Flow. 
 Eytelwein, investigating the question anew, and believing 
 the contraction of the vein at the entrance to the pipe should 
 not be overlooked, soon afterward modified the equation to 
 the form, 
 
 9 f}~l 
 
 H-, = .000085434 (v a + .2756 v\ (16) 
 
 in which d refers to the effect of the contraction. 
 
 286. D'Aubuisson's Equation of Resistance to 
 
 Flow. D' Aubuisson, more than a half-century later, hav- 
 ing regard more particularly to the experiments of Couplet, 
 gave to m and ft values as follows : 
 
 v* n 
 
 E-^ = .000104392 ^ (V + .180449 ). (17) 
 
 287. Weisbach's Equation of Resistance to Flow. 
 
 Weisbach, availing himself of eleven experiments of his 
 own with high velocities, and one by M. Gueymard, in ad- 
 
UNINTELLIGENT USE OF PARTIAL FORMULAS. 257 
 
 dition to the fifty-one above referred to, proposed the fol- 
 lowing formula as coinciding better with the results of Ms 
 observations : 
 
 / m 
 
 This coefficient (a + p), which replaces 4m in our sym- 
 \ i/fl/ 
 
 bols, is founded upon the assumption that the resistance of 
 friction increases at the same time with the square and with 
 the square root of the cube of the velocity. 
 
 288. Transpositions of an Original Formula. 
 That Chezy's formula has been generally accepted as one 
 founded upon correct principles, we readily infer by its fre- 
 quent adoption, transposition and modification in the writ- 
 ings of many philosophers and hydraulicians. Note, for 
 instance, the second formulas (v) of Eytelwein and D'Au- 
 buisson in the above table (No. 63), and the formulas of 
 Beardmore, Blackwell, Downing, Hawksley, Jackson, Box, 
 Storrow, and others, which may be resolved into this orig- 
 inal form. 
 
 289. Unintelligent Use of Partial Formulas. 
 That serious errors may arise from an unintelligent and 
 improper use of these formulas is conspicuously apparent 
 in the above table of results, computed upon conditions in 
 the very midst of the range of conditions of ordinary muni- 
 cipal water supplies. A full knowledge of the origin of a 
 formula is essential for its safe practical application. 
 
 A solid body falling freely in a vacuum through a height 
 of 100 feet, acquires a rate of motion of only about 80.3 feet 
 per second, yet some of the formulas appear to indicate a 
 velocity of flow exceeding 200 feet per second, through five 
 feet of pipe, under 100 feet head pressure. 
 17 
 
258 FLOW OF WATER THROUGH PIPES. 
 
 29O. A Formula of more General Application. 
 
 Weisbach has suggested a more comprehensive form of 
 expression which includes the head generating the velocity 
 of flow and the head equivalent to the dynamic force lost at 
 the entry of the jet into the pipe, as well as the head balanc- 
 ing the resistance to flow in the pipe, and therefore his 
 equation presents the equality between the total head H, 
 and the sum of the velocity and resistance heads equal 
 to Ti + Ti'+Ti". 
 
 Weisbach has also developed a portion of the values 
 of m. 
 
 291. Value of v for Given Slopes. We have here- 
 tofore insisted that m, as introduced into the equation, shall 
 approximate near to its legitimate value for the given condi- 
 tions. Its value for each given diameter, or hydraulic mean 
 radius, r, depends upon the velocity of flow, and therefore 
 upon the slope, s, generating the velocity. 
 
 To aid in the selection of m from the tables of m, 
 page 242, we have plotted the several velocities as ordinates 
 with given sines of slopes, *', as abscissas for such experi- 
 mental data as was obtainable, and have taken the interme- 
 diate approximate values of v from their parabolic curves 
 thus determined from the experimental data, and have 
 arranged the following table of v ; which of course refers to 
 the head 7i", balancing the resistance in the slope s. 
 
VELOCITIES FOR GIVEN SLOPES ASD DIAMETERS. 
 
 TABLE No. 64. 
 
 VELOCITIES, v, FOR GIVEN SLOPES AND DIAMETERS. 
 FOR CLEAN IRON PIPES. 
 
 z; = 
 
 SLOPE. 
 
 in 250 
 
 " 200 
 
 " 167 
 
 " 143 
 
 ; ' 125 
 
 1 in 
 
 " loo 
 
 " 83>3 
 
 " 62^5 
 
 " 55-6 
 
 " 50.0 
 
 " 33-3 
 25.0 
 
 " 20. o 
 
 " 16.6 
 
 " 14.3 
 
 " 12.5 
 
 " n. i 
 
 " 10.0 
 
 " 8.33 
 
 " 7-14 
 
 " 6.25 
 
 " 5.55 
 5.oo 
 
 " 4.00 
 
 " 3-33 
 
 " 2.50 
 
 " 2.00 
 
 1.66 
 
 1.43 
 1.25 
 i. ii 
 
 
 
 
 DlAMI 
 
 DTERS. 
 
 
 
 SINE OF 
 SLOPE. 
 
 X inch. 
 
 %" 
 
 j// 
 
 I#" 
 
 ifc" 
 
 2" 
 
 
 .0417 ft. 
 
 .0625'. 
 
 .0834'- 
 
 .1250'. 
 
 .1458'. 
 
 .1667'. 
 
 . k 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 ~ T 
 
 Ft. per sec. 
 
 Ft. per sec. 
 
 Ft. per sec. 
 
 Ft. per sec. 
 
 Ft. per sec. 
 
 Ft. per sec. 
 
 OO4. 
 
 
 
 
 
 
 .184 
 
 .\J^JL^ 
 
 
 
 
 
 .206 
 
 340 
 
 !oo6 
 
 
 
 
 .190 
 
 .360 
 
 .500 
 
 .007 
 
 
 
 
 .290 
 
 453 
 
 .600 
 
 .008 
 
 
 
 .0^8 
 
 .391 
 
 .580 
 
 .730 
 
 .009 
 
 
 
 
 
 \J^^> 
 
 .130 
 
 * JV 
 .480 
 
 .700 
 
 .870 
 
 .010 
 
 
 mo 
 
 .240 
 
 .600 
 
 .790 
 
 .980 
 
 .012 
 
 0.892 
 
 .140 
 
 .430 
 
 730 
 
 / 7 
 
 953 
 
 2.219 
 
 .014 
 
 O.giO 
 
 .230 
 
 540 
 
 .860 
 
 2.130 
 
 2.360 
 
 .Ol6 
 
 0.990 
 
 .340 
 
 .640 
 
 2.010 
 
 2.220 
 
 2.500 
 
 .018 
 
 1.050 
 
 .450 
 
 . 7 60 
 
 2.100 
 
 2.350 
 
 2.630 
 
 .02 
 
 1. 100 
 
 .518 
 
 .813 
 
 2.276 
 
 2.530 
 
 2.800 
 
 .03 
 
 1.440 
 
 .920 
 
 2.280 
 
 2.810 
 
 3.100 
 
 3.390 
 
 .04 
 
 1.765 
 
 2.298 
 
 2.730 
 
 3.367 
 
 3.694 
 
 4.002 
 
 .05 
 
 2.O4O 
 
 2.600 
 
 i 3.050 
 
 3.730 
 
 4.280 
 
 5-020 
 
 .06 
 
 2.310 
 
 2.850 
 
 3-400 
 
 4.IIO 
 
 4-690 
 
 5.500 
 
 .07 
 
 2.490 
 
 3.100 
 
 3.640 
 
 4.420 
 
 5-020 
 
 5.900 
 
 .08 
 
 2.680 
 
 3.300 
 
 3.920 
 
 4.730 
 
 5.360 
 
 6.300 
 
 .09 
 
 2.850 
 
 3.540 
 
 4.180 
 
 5-045 
 
 5.630 
 
 6.610 
 
 .IO 
 
 3.040 
 
 3.730 
 
 4-437 
 
 5.480 
 
 6.009 
 
 6.979 
 
 .12 
 
 3.320 
 
 4.180 
 
 4.900 
 
 6.030 
 
 6.650 
 
 7.490 
 
 .14 
 
 3.460 
 
 4.500 
 
 5.290 
 
 6-535 
 
 7.190 
 
 8.010 
 
 .16 
 
 3.840 
 
 4-825 
 
 5.640 
 
 7.010 
 
 7.700 
 
 8.500 
 
 .18 
 
 4.090 
 
 5.108 
 
 5.998 
 
 7-500 
 
 8.221 
 
 8.960 
 
 .20 
 
 4.310 
 
 5.400 
 
 6.330 
 
 7.880 
 
 8.690 
 
 9.380 
 
 25 
 
 4.830 
 
 6.100 
 
 7.135 
 
 8.770 
 
 9.690 
 
 10.430 
 
 .30 
 .40 
 
 5-359 
 6.260 
 
 6.730 
 7.790 
 
 7.902 
 9.130 
 
 9.650 
 11.225 
 
 10.620 
 12.280 
 
 11.380 
 12.980 
 
 .50 
 
 7.070 
 
 8.818 
 
 10.339 
 
 12.600 
 
 
 
 
 
 .60 
 
 78OO 
 
 c\ *7r*/"\ 
 
 
 
 
 
 
 OvAJ 
 
 9.790 
 
 11.5 y o 
 
 
 
 
 *7O 
 
 8.470 
 
 m^jf\r\ 
 
 12 7IO 
 
 
 
 
 .80 
 
 9. 140 
 
 , ymj 
 1 1 7 2O 
 
 
 
 
 
 f\r\ 
 
 9800 
 
 
 
 
 
 
 .yu 
 
 . OCMJ 
 
 IO. 3QO 
 
 I2.OOO 
 
 
 
 
 
 
 
 
 
 
 
 
 
260 
 
 FLOW OF WATER THROUGH PIPES. 
 
 TABLE No. 64 (Continued). 
 
 VELOCITIES, v, FOR GIVEN SLOPES AND DIAMETERS. 
 FOR CLEAN IRON PIPES. 
 
 SLOPE. 
 
 SINE OF 
 SLOPE. 
 
 DIAMETERS. 
 
 3 inch. 
 .250 ft. 
 
 &. 
 
 6" 
 -5'. 
 
 8" 
 .6667'. 
 
 10" 
 .8333'- 
 
 12" 
 i.o'. 
 
 in mi 
 
 " 1000 
 
 " 909 
 
 " 833 
 " 769 
 " 714 
 " 667 
 " 625 
 " 588 
 
 " 556 
 " 526 
 
 " 5oo 
 " 455 
 " 417 
 " 385 
 ' 357 
 44 333 
 " 286 
 " 250 
 
 " 200 
 
 " I6 7 
 * 143 
 " I2 5 
 " III 
 " 100 
 
 " 83.3 
 71.4 
 " 62.5 
 
 " 55.6 
 " 50.0 
 33-3 
 25.0 
 
 " 2O.O 
 
 16.6 
 ' 14-3 
 1 12.5 
 1 1. 1 
 
 ' IO.O 
 
 ' 8.33 
 1 M4 
 6.25 
 
 5.55 
 5.00 
 * 4.00 
 3-33 
 
 h 
 
 ' = 7' 
 
 .0009 
 .0010 
 .001 1 
 
 .0012 
 .0013 
 .0014 
 .OOI5 
 .OOl6 
 .OOI7 
 .0018 
 .OOlg 
 .0020 
 .0022 
 .OO24 
 .0026 
 .0028 
 .0030 
 0035 
 .004 
 .005 
 
 .006 
 .007 
 .008 
 .009 
 .010 
 
 .012 
 .014 
 .016 
 .018 
 .02 
 
 03 
 
 .04 
 
 05 
 
 .06 
 07 
 .08 
 .09 
 .10 
 .12 
 .14 
 .16 
 .18 
 .20 
 25 
 30 
 
 Velocity. 
 
 Ft. per sec. 
 
 Velocity. 
 Ft. per sec. 
 
 Velocity. 
 Ft. per sec. 
 
 Velocity. 
 Ft. per sec. 
 
 Volocity. 
 Ft. per sec. 
 
 Velocity. 
 Ft. per sec* 
 
 540 
 .610 
 .680 
 
 .785 
 .880 
 .940 
 2.OIO 
 2.080 
 2.148 
 2.200 
 2.27O 
 
 2.325 
 2.470 
 
 2.58o 
 2.695 
 2.810 
 2.925 
 3.140 
 3-390 
 3.845 
 4-215 
 4.585 
 4.910 
 5-185 
 5480 
 
 6.020 
 
 6.485 
 6.980 
 
 7-435 
 7.842 
 9.715 
 11.280 
 12.689 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1.610 
 
 1.692 
 1.760 
 1.840 
 1.920 
 1.990 
 2.035 
 2.125 
 2.190 
 2.320 
 2.430 
 2.525 
 2.610 
 
 2.695 
 
 2.910 
 
 3-085 
 3-420 
 3.775 
 4.075 
 4.370 
 
 4.610 
 
 4.880 
 
 5-375 
 5.885 
 
 6.325 
 6.745 
 7.070 
 8.730 
 
 10.200 
 12.293 
 
 
 
 
 
 
 
 
 
 
 
 
 
 1.640 
 1.680 
 1.750 
 1.800 
 1.830 
 1.930 
 2.OI5 
 2. IIO 
 2.220 
 
 2.315 
 2.5IO 
 2.690 
 2-993 
 3-3I5 
 3.615 
 3.850 
 4.080 
 4.285 
 4.710 
 5-105 
 5-490 
 5.825 
 ' 6.175 
 7.640 
 9-OIO 
 10.062 
 11.020 
 12.020 
 
 
 
 
 .... 
 
 
 .... 
 
 1.284 
 I.4IO 
 
 1.525 
 I.7IO 
 1.863 
 2.O2O 
 2.160 
 2.280 
 2.425 
 2.675 
 2.880 
 3.070 
 3.240 
 3-498 
 4.240 
 5.030 
 
 5.674 
 6.213 
 
 6.785 
 7.250 
 
 7-775 
 8.238 
 
 9.045 
 
 9-773 
 10455 
 
 11.075 
 11.883 
 13.289 
 
 I.4I5 
 1.480 
 1-530 
 1.680 
 1.790 
 2.030 
 2.2O4 
 2.460 
 2.670 
 2.820, 
 2.960 
 2.230 
 2.480 
 2.710 
 
 3-9 1 
 4-134 
 
 5.160 
 6.110 
 6.825 
 7-324 
 7.985 
 8.604 
 
 9- I2 5 
 9-703 
 10.625 
 
 11-531 
 12.383 
 
 515 
 .600 
 .680 
 .760 
 .830 
 .920 
 2.IOO 
 2.26O 
 2.525 
 2.790 
 3.000 
 3-215 
 3425 
 3.670 
 3-992 
 4-370 
 4.695 
 4-965 
 5.206 
 6.430 
 7.560 
 
 8-479 
 9.828 
 10.062 
 10.920 
 H.583 
 I2.2O9 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
VELOCITIES FOR GIVEN SLOPES AND DIAMETERS. 261 
 
 TABLE No. 64 (Continued). 
 
 VELOCITIES, v, FOR GIVEN SLOPES AND DIAMETERS. 
 FOR CLEAN IRON PIPES. 
 
 
 SINE OF 
 
 
 
 DlAM 
 
 ETERS. 
 
 
 
 SLOPE. 
 
 SLOPE. 
 
 14 inch 
 
 16" 
 
 18" 
 
 30" 
 
 24" 
 
 27 // 
 
 
 
 1.1667 ft- 
 
 I.3333'. 
 
 1.5'. 
 
 I.666/. 
 
 2.0'. 
 
 a.2 5 '. 
 
 
 ,=* 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 
 / 
 
 Ft. per sec. 
 
 Ft. per sec. 
 
 Ft. per sec. 
 
 Ft. per sec. 
 
 Ft. per sec. 
 
 Ft. per. sec. 
 
 in 2500 
 
 .0004 
 
 
 
 
 
 
 
 2000 
 
 OOO5 
 
 
 
 
 
 
 2.O8O 
 
 1667 
 
 . \J\J*J$ 
 . 0006 
 
 
 
 
 i .6;5 
 
 I . Q-1O 
 
 2. IO5 
 
 1428 
 
 .0007 
 
 .... 
 
 1.610 
 
 1-755 
 
 * v 'DO 
 1.860 
 
 yt*' 
 2.115 
 
 2.285 
 
 1250 
 
 .0008 
 
 .610 
 
 1-738 
 
 1.850 
 
 1-995 
 
 2.265 
 
 2.385 
 
 mi 
 
 .0009 
 
 .710 
 
 1.855 
 
 1-975 
 
 2.145 
 
 2.405 
 
 2.580 
 
 1000 
 
 .0010 
 
 .800 
 
 1.950 
 
 2.070 
 
 2.255 
 
 2-530 
 
 2.700 
 
 909 
 
 .OOII 
 
 .895 
 
 2.065 
 
 2.195 
 
 2.360 
 
 2.655 
 
 2.880 
 
 833 
 
 .0012 
 
 975 
 
 2.I6O 
 
 2-295 
 
 2-475 
 
 2.785 
 
 3.000 
 
 769 
 
 .0013 
 
 2.040 
 
 2.275 
 
 2-395 
 
 2-575 
 
 2.910 
 
 3-155 
 
 714 
 
 .0014 
 
 2.130 
 
 2.350 
 
 2.400 
 
 2.675 
 
 3-015 
 
 3.260 
 
 667 
 
 .0015 
 
 2. 2OO 
 
 2.425 
 
 2.606 
 
 2-775 
 
 3.120 
 
 3-395 
 
 625 
 
 .0016 
 
 2.285 
 
 2.500 
 
 2.685 
 
 2.875 
 
 3-225 
 
 3.515 
 
 588 
 
 .0017 
 
 2-375 
 
 2.590 
 
 2-775 
 
 2.970 
 
 3.366 
 
 3.625 
 
 556 
 
 .0018 
 
 2.430 
 
 2.640 
 
 2.845 
 
 3-050 
 
 3-430 
 
 3-725 
 
 526 
 
 .0019 
 
 2.500 
 
 2.725 
 
 2.925 
 
 3.170 
 
 3-535 
 
 3.825 
 
 500 
 
 .0020 
 
 2-550 
 
 2.810 
 
 3.000 
 
 3-230 
 
 3.640 
 
 3-930 
 
 455 
 
 .0022 
 
 2.70O 
 
 2.950 
 
 3-187 
 
 3.400 
 
 3.835 
 
 4-135 
 
 417 
 
 .0024 
 
 2.825 
 
 3-095 
 
 3-320 
 
 3-570 
 
 4.015 
 
 4-335 
 
 385 
 
 .0026 
 
 2.950 
 
 3.230 
 
 3-495 
 
 3-730 
 
 4.210 
 
 4-530 
 
 357 
 
 .0028 
 
 3.080 
 
 3-355 
 
 3.610 
 
 3-885 
 
 4-388 
 
 4.715 
 
 333 
 
 .0030 
 
 3-200 
 
 3-490 
 
 3-755 
 
 4.020 
 
 4-535 
 
 4-905 
 
 286 
 
 0035 
 
 3-473 
 
 3.800 
 
 4.060 
 
 4-350 
 
 4-935 
 
 5.3I5 
 
 250 
 
 .OO4 
 
 3-735 
 
 4.060 
 
 4-330 
 
 4.655 
 
 5-290 
 
 5-690 
 
 200 
 
 .005 
 
 4.180 
 
 4-575 
 
 4.901 
 
 5.240 
 
 5-955 
 
 6-373 
 
 167 
 
 .006 
 
 4.602 
 
 5.025 
 
 5-400 
 
 5.770 
 
 6.502 
 
 6.975 
 
 143 
 
 .007 
 
 5-025 
 
 5.485 
 
 5-844 
 
 6.260 
 
 7.020 
 
 7.520 
 
 125 
 
 .008 
 
 5-400 
 
 5.845 
 
 6.275 
 
 6.718 
 
 7.515 
 
 8.045 
 
 in 
 
 .009 
 
 5-725 
 
 6.185 
 
 6.625 
 
 7.125 
 
 7.980 
 
 8-545 
 
 100 
 
 .OIO 
 
 6.030 
 
 6.515 
 
 7.000 
 
 7.550 
 
 8.410 
 
 9-025 
 
 83.3 
 
 .012 
 
 6-555 
 
 7.124 
 
 7.725 
 
 8.245 
 
 9.240 
 
 10.000 
 
 71.4 
 
 .014 
 
 7.120 
 
 7.785 
 
 8-345 
 
 8.935 
 
 10.025 
 
 10.870 
 
 62.5 
 
 .Ol6 
 
 7-655 
 
 8.330 
 
 8.965 
 
 9.640 
 
 10.790 
 
 11.715 
 
 55-6 
 
 .018 
 
 8.170 
 
 8.900 
 
 9-565 
 
 10.295 
 
 H.5I5 
 
 12.085 
 
 50 
 
 .02 
 
 8.667 
 
 9.409 
 
 10.104 
 
 10.801 
 
 12.238 
 
 .... 
 
 " 333 
 
 03 
 
 10.691 
 
 11-583 
 
 12.369 
 
 13.229 
 
 
 .... 
 
 I " 25 
 
 O4. 
 
 12.^8^ 
 
 flAAC 
 
 
 
 
 
 g 
 
 ut+ 
 
 j.^ j^fj 
 
 *O T"*TD 
 
 
 
 
 
262 
 
 FLOW OF WATER THROUGH PIPES. 
 
 TABLE No. 64 (Continued.) 
 
 VELOCITIES, v, FOR GIVEN SLOPES AND DIAMETERS. 
 FOR CLEAN IRON PIPES. 
 
 SLOPE. 
 
 SINE OF 
 SLOPE. 
 
 DIAMETERS. 
 
 30 inch 
 2.5 feet. 
 
 33" 
 3-75' 
 
 3 6" 
 
 3-0 7 
 
 4 o" 
 3-3333'- 
 
 \ 
 44" 48" 
 
 3.6667'. 4-c/. 
 
 
 . h 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 Velocity. 
 
 
 ~ I 
 
 Ft. per sec 
 
 Ft. per sec. 
 
 Ft. per sec 
 
 Ft. per sec 
 
 Ft. per sec. 
 
 Ft. per sec. 
 
 in 5000 
 
 .OO02 
 
 .... 
 
 .... 
 
 1-457 
 
 1.590 
 
 1.719 
 
 1.829 
 
 " 3333 
 
 .0003 
 
 1.586 
 
 I.68I 
 
 1-797 
 
 1.948 
 
 2.104 
 
 2.220 
 
 " 2500 
 
 .0004 
 
 1.831 
 
 1.962 
 
 2.O6O 
 
 2.255 
 
 2.420 
 
 2.620 
 
 " 2000 
 
 .0005 
 
 2.085 
 
 2.175 
 
 2.313 
 
 2.530 
 
 2-735 
 
 2-945 
 
 " 1667 
 
 .0006 
 
 2.235 
 
 2.355 
 
 2.550 
 
 2.800 
 
 2.980 
 
 3.200 
 
 " 1428 
 
 .0007 
 
 2.425 
 
 2.550 
 
 2.796 
 
 3.010 
 
 3.265 
 
 3-475 
 
 " 1250 
 
 .0008 
 
 2.617 
 
 2-755 
 
 2.950 
 
 3-225 
 
 3-510 
 
 3.725 
 
 " IIII 
 
 .OOOg 
 
 2-745 
 
 2.960 
 
 3.155 
 
 3.4I5 
 
 3-695 
 
 3-904 
 
 " 1000 
 
 .0010 
 
 2.895 
 
 3.156 
 
 3.320 
 
 3.605 
 
 3-890 
 
 4.150 
 
 " 909 
 
 .OOII 
 
 3.065 
 
 3.290 
 
 3.525 
 
 3.810 
 
 4.080 
 
 4-375 
 
 " 833 
 
 .0012 
 
 3.220 
 
 3.415 
 
 3.695 
 
 3-975 
 
 4.260 
 
 4-565 
 
 " 769 
 
 .OOI3 
 
 3-355 
 
 3.585 
 
 3.848 
 
 4.150 
 
 4-430 
 
 4.780 
 
 " 714 
 
 .OOI4 
 
 3-500 
 
 3.703 
 
 3-995 
 
 4-305 
 
 4.625 
 
 4.936 
 
 " 667 
 
 .0015 
 
 3-655 
 
 3-875 
 
 4.130 
 
 4.490 
 
 4-795 
 
 5-130 
 
 " 625 
 
 .0016 
 
 3.785 
 
 4.000 
 
 4.285 
 
 4.645 
 
 4.970 
 
 5-295 
 
 " 558 
 
 .OOI7 
 
 3.9I5 
 
 4.120 
 
 4-445 
 
 4.800 
 
 5.H9 
 
 5-450 
 
 " 556 
 
 .0018 
 
 4.006 
 
 4.245 
 
 4-595 
 
 4-935 
 
 5-255 
 
 5.620 
 
 " 526 
 
 .0019 
 
 4.140 
 
 4.400 
 
 4.725 
 
 5-075 
 
 5-400 
 
 5.790 
 
 ' 500 
 
 .0020 
 
 4-235 
 
 4-535 
 
 4.880 
 
 5.180 
 
 5.575 
 
 5-924 
 
 ' 455 
 
 .0022 
 
 4-445 
 
 4.759 
 
 5-II5 
 
 5.515 
 
 5.845 
 
 6.230 
 
 i ' 417 
 
 .OO24 
 
 4-650 
 
 5-000 
 
 5.340 
 
 5.785 
 
 6.095 
 
 6.500 
 
 i ' 385 
 
 .0026 
 
 4-875 
 
 5.230 
 
 5-575 
 
 6.035 
 
 6.335 
 
 6.780 
 
 i ' 357 
 
 .0028 
 
 5.065 
 
 5-435 
 
 5-780 
 
 6.307 
 
 6.590 
 
 7.040 
 
 ' 333 
 
 .0030 
 
 5.270 
 
 5.660 
 
 5.981 
 
 6-455 
 
 6.850 
 
 7.300 
 
 " 286 
 
 .0035 
 
 5-695 
 
 6.090 
 
 6.500 
 
 7.000 
 
 7.385 
 
 7.990 
 
 " 250 
 
 .OO4 
 
 6.080 
 
 6-493 
 
 6.907 
 
 7-495 
 
 7.920 
 
 8.425 
 
 " 200 
 
 005 
 
 6.835 
 
 7.260 
 
 7-765 
 
 8.375 
 
 8.845 
 
 9-497 
 
 " 167 
 
 .006 
 
 7-495 
 
 7.980 
 
 8.480 
 
 9-205 
 
 9.784 
 
 10.415 
 
 " 143 
 
 .007 
 
 8.080 
 
 8.645 
 
 9.220 
 
 9-935 
 
 10.585 
 
 11-307 
 
 " 125 
 
 .008 
 
 8.635 
 
 9-245 
 
 9.875 
 
 10.610 
 
 i i . 360 
 
 12.250 
 
 " in 
 
 .OOg 
 
 9.215 
 
 9.800 
 
 10.515 
 
 11.230 
 
 12.150 
 
 
 
 " 100 
 
 .OIO 
 
 9.720 
 
 10.375 
 
 II.IOO 
 
 11.919 
 
 .... 
 
 .... 
 
 " 8q ^ 
 
 .OI2 
 
 10.780 
 
 1 1 4J.O 
 
 u . 720 
 
 
 
 
 u J'O 
 
 u 71-4 
 
 .014 
 
 n-745 
 
 ** *t*ty 
 12.450 
 
 
 - 
 
 
 
 
 
 
 
VALUES OF h AND h' FOR GIVEN VELOCITIES. 263 
 
 TABLE No. 64 (Continued). 
 
 VELOCITIES, v 9 FOR GIVEN SLOPES AND DIAMETERS. 
 FOR CLEAN IRON PIPES. 
 
 
 
 
 
 
 DIAMETERS. 
 
 
 
 SLOPE. 
 
 SINE OF 
 SLOPE. 
 
 54 inch 
 
 60" 
 
 72" 
 
 8 4 " 
 
 96" 
 
 
 
 4*5 feet. 
 
 5 .c/. 
 
 e.o'. 
 
 7 .</. 
 
 8.0'. 
 
 
 <=/ 
 
 Velocity. 
 Ft. per sec. 
 
 Velocity. 
 Ft. per sec. 
 
 Velocity. 
 Ft. per sec. 
 
 Velocity. 
 Ft. per sec. 
 
 Velocity. 
 Ft. per sec. 
 
 in 10000 
 
 .0001 
 
 I.38I 
 
 I.5I6 
 
 I.66I 
 
 1.906 
 
 2.144 
 
 " 5000 
 
 .0002 
 
 1-993 
 
 1.945 
 
 2.039 
 
 2.719 
 
 3-033 
 
 " 3333 
 
 .0003 
 
 2.423 
 
 2.653 
 
 2.919 
 
 3-279 
 
 3-749 
 
 " 2500 
 
 .0004 
 
 2.837 
 
 3.007 
 
 3-395 
 
 3-779 
 
 4.352 
 
 " 2OOO 
 
 .0005 
 
 3.158 
 
 3-441 
 
 3.870 
 
 4.229 
 
 4.880 
 
 ' 1667 
 
 .0006 
 
 3-49 
 
 3.785 
 
 4-300 
 
 4.600 * 
 
 5.320 
 
 ' 1428 
 
 .0007 
 
 3.785 
 
 4-IOO 
 
 4.670 
 
 4.990 
 
 5.780 
 
 ' I25O 
 
 .0008 
 
 4.000 
 
 4-395 
 
 4-950 
 
 5.400 
 
 6.185 
 
 ' IIII 
 
 .0009 
 
 4-235 
 
 4.685 
 
 5.260 
 
 5.780 
 
 6.600 
 
 ' 1000 
 
 .0010 
 
 4-550 
 
 4-939 
 
 5 580 
 
 6.110 
 
 6.972 
 
 909 
 
 .0011 
 
 4.760 
 
 5.215 
 
 5.870 
 
 6-583 
 
 7.285 
 
 " 833 
 
 .0012 
 
 4-975 
 
 5-465 
 
 6. 1 20 
 
 6.880 
 
 7.600 
 
 " 769 
 
 .0013 
 
 5.190 
 
 5.680 
 
 6.340 
 
 7-150 
 
 7.915 
 
 ' 714 
 
 .0014 
 
 5-400 
 
 5-935 
 
 6.630 
 
 7-475 
 
 8.250 
 
 667 
 
 .0015 
 
 5-629 
 
 6.095 
 
 6.859 
 
 7.7oi 
 
 8.510 
 
 625 
 
 .0016 
 
 5.815 
 
 6.300 
 
 7.080 
 
 8.000 
 
 8.815 
 
 ' 588 
 
 .0017 
 
 5-995 
 
 6.500 
 
 7.300 
 
 8.215 
 
 9.100 
 
 1 556 
 
 .0018 
 
 6.140 
 
 6.685 
 
 7.500 
 
 8.490 
 
 9.360 
 
 ' 526 
 
 .0019 
 
 6.300 
 
 6.865 
 
 7.700 
 
 8.725 
 
 9.580 
 
 500 
 
 .0020 
 
 6.528 
 
 7.071 
 
 7-965 
 
 9.049 
 
 9.875 
 
 455 
 
 .0022 
 
 6.840 
 
 7-435 
 
 8.330 
 
 9.480 
 
 10.400 
 
 417 
 
 .0024 
 
 7-135 
 
 7.770 
 
 8.715 
 
 9.880 
 
 10.890 
 
 1 385 
 
 .0026 
 
 7-445 
 
 8.080 
 
 9.060 
 
 10.275 
 
 11.340 
 
 " 357 
 
 .0028 
 
 7-740 
 
 8.380 
 
 9-450 
 
 10.611 
 
 11.780 
 
 " 333 
 
 .0030 
 
 8.060 
 
 8.680 
 
 9.828 
 
 11.000 
 
 12.175 
 
 286 
 
 0035 
 
 8-735 
 
 9-370 
 
 10.615 
 
 12.550 
 
 
 " 250 
 
 .004 
 
 9.300 
 
 10.060 
 
 n-344 
 
 .... 
 
 
 I " 200 
 
 005 
 
 10.425 
 
 11.304 
 
 12.680 
 
 .... 
 
 
 I " 167 
 
 .006 
 
 11.470 
 
 12.440 
 
 
 
 
 
 
 I " 143 
 
 .007 
 
 12.450 
 
 .... 
 
 
 
 
 
 
 292. Values of h and h' for Given Velocities.-- 
 
 In Table 65 are given the values of Ji and 7i' for given 
 velocities, which are to be subtracted from H to ^compute 
 the height of the slope generating the velocity ?). 
 
 The velocity being known approximately, its correspond- 
 ing m for any given diameter may be taken from the table 
 of ra, page 242, and inserted in the formula : 
 
 (I + c r )+m - 
 
 1: 
 
264 
 
 FLOW OF WATER THROUGH PIPES. 
 
 TABLE No. 65. 
 TABLES OF h AND k' DUE TO GIVEN VELOCITIES, h AND h' BEING 
 
 IN FEET AND V IN FEET PER SECOND. 
 
 Velocity 
 
 h 
 
 h' 
 
 h + k f 
 
 Velocity 
 
 h 
 
 h' 
 
 h + h' 
 
 .80 
 
 .010 
 
 .0050 
 
 .OI5O 
 
 4-47 
 
 31 
 
 1565 
 
 4665 
 
 .98 
 
 .015 
 
 .0075 
 
 .0225 
 
 4-54 
 
 32 
 
 .1616 
 
 .4816 
 
 I.X3 
 
 .020 
 
 .OIOI 
 
 .0301 
 
 4.61 
 
 33 
 
 .1666 
 
 .4966 
 
 1.27 
 
 .025 
 
 .0126 
 
 .0376 
 
 4.68 
 
 34 
 
 .1717 
 
 5117 
 
 1-39 
 
 .030 
 
 .0151 
 
 .0451 
 
 4-75 
 
 35 
 
 .1767 
 
 .5267 
 
 1.50 
 
 .035 
 
 .0177 
 
 .0527 
 
 4.81 
 
 36 
 
 .1818 
 
 .5418 
 
 1.60 
 
 .040 
 
 .0202 
 
 .O6O2 
 
 4.87 
 
 37 
 
 .1868 
 
 5568 
 
 1.70 
 
 045 
 
 .0227 
 
 .0677 
 
 4-94 
 
 .38 
 
 .1919 
 
 57^9 
 
 1.79 
 
 .050 
 
 .0252 
 
 .0752 
 
 5.01 
 
 39 
 
 .1969 
 
 5869 
 
 1.88 
 
 055 
 
 .0278 
 
 .0828 
 
 5-07 
 
 .40 
 
 .2020 
 
 .6060 
 
 1.97 
 
 .060 
 
 .0303 
 
 .0903 
 
 5-14 
 
 .41 
 
 .2O7O 
 
 .6170 
 
 2.04 
 
 .065 
 
 .0328 
 
 .0978 
 
 5.20 
 
 .42 
 
 .2121 
 
 .6321 
 
 2.12 
 
 .070 
 
 0353 
 
 1053 
 
 5-26 
 
 43 
 
 .2172 
 
 .6472 
 
 2.2O 
 
 075 
 
 0379 
 
 .II2g 
 
 5-32 
 
 44 
 
 .2222 
 
 .6622 
 
 2.27 
 
 .080 
 
 .0404 
 
 .1204 
 
 5.38 
 
 45 
 
 .2272 
 
 .6772 
 
 2.34 
 
 .085 
 
 .0429 
 
 .1279 
 
 5-44 
 
 .46 
 
 .2323 
 
 .6923 
 
 2.41 
 
 .090 
 
 0454 
 
 1354 
 
 5-50 
 
 47 
 
 2373 
 
 7073 
 
 2.47 
 
 095 
 
 .0480 
 
 .1430 
 
 5.56 
 
 .48 
 
 .2424 
 
 .7224 
 
 2-54 
 
 .100 
 
 .0505 
 
 .1505 
 
 5.62 
 
 49 
 
 .2474 
 
 7374 
 
 2.60 
 
 .105 
 
 .0530 
 
 .1580 
 
 5-67 
 
 50 
 
 .2525 
 
 7525 
 
 2.66 
 
 .110 
 
 0555 
 
 .1655 
 
 5-73 
 
 5i 
 
 2575 
 
 7675 
 
 2.72 
 
 .115 
 
 .0580 
 
 .1730 
 
 5-79 
 
 52 
 
 .2626 
 
 .7826 
 
 2.78 
 
 .120 
 
 .0606 
 
 .1806 
 
 5.85 
 
 53 
 
 .2676 
 
 .7976 
 
 2.84 
 
 .125 
 
 .0631 
 
 .l88l 
 
 5-90 
 
 54 
 
 .2727 
 
 .8127 
 
 2.89 
 
 .130 
 
 .0656 
 
 .1956 
 
 5-95 
 
 55 
 
 .2777 
 
 .8277 
 
 2-95 
 
 .135 
 
 .0672 
 
 .2022 
 
 6.00 
 
 56 
 
 .2828 
 
 .8428 
 
 3.00 
 
 .140 
 
 .0707 
 
 .2107 
 
 6.06 
 
 57 
 
 .2878 
 
 .8578 
 
 3-05 
 
 .145 
 
 .0732 
 
 .2182 
 
 6.ii 
 
 58 
 
 .2929 
 
 .8729 
 
 3.H 
 
 .150 
 
 0757 
 
 .2257 
 
 6.17 
 
 59 
 
 .2979 
 
 .8879 
 
 3-i6 
 
 .155 
 
 .0772 
 
 .2322 
 
 6.22 
 
 .60 
 
 .3030 
 
 .9030 
 
 3.21 
 
 .160 
 
 .0808 
 
 .2408 
 
 6.28 
 
 .61 
 
 .3080 
 
 .9180 
 
 3.26 
 
 .165 
 
 0833 
 
 .2483 
 
 6.32 
 
 .62 
 
 .3131 
 
 9331 
 
 3-31 
 
 .170 
 
 .0858 
 
 .2558 
 
 6.37 
 
 63 
 
 .3l8l 
 
 .9481 
 
 3.36 
 
 .175 
 
 .0883 
 
 .2633 
 
 6.42 
 
 .64 
 
 .3232 
 
 .9632 
 
 340 
 
 .180 
 
 .0909 
 
 .2709 
 
 6.47 
 
 65 
 
 .3282 
 
 .9782 
 
 345 
 
 .185 
 
 .0934 
 
 .2784 
 
 6.52 
 
 .66 
 
 3333 
 
 9933 
 
 3.50 
 
 .190 
 
 .0959 
 
 .2859 
 
 6-57 
 
 .67 
 
 .3383 
 
 1.0083 
 
 3-55 
 
 .195 
 
 .0984 
 
 2934 
 
 6.61 
 
 .68 
 
 3434 
 
 ,0434 
 
 3-59 
 
 .200 
 
 .1010 
 
 .3010 
 
 6.66 
 
 .69 
 
 .3484 
 
 .0384 
 
 3.68 
 
 .21 
 
 .1060 
 
 .3160 
 
 6.71 
 
 70 
 
 3535 
 
 0535 
 
 3-76 
 
 .22 
 
 .1111 
 
 3311 
 
 6.76 
 
 .71 
 
 3585 
 
 .0685 
 
 3.85 
 
 23 
 
 .1161 
 
 .3461 
 
 6.81 
 
 .72 
 
 .3636 
 
 .0836 
 
 3-93 
 
 .24 
 
 .1212 
 
 .3612 
 
 6.86 
 
 73 
 
 .3686 
 
 .0986 
 
 4.01 
 
 25 
 
 .1262 
 
 .3762 
 
 6.91 
 
 74 
 
 .3737 
 
 II37 
 
 4.09 
 
 .26 
 
 .1313 
 
 39*3 
 
 6-95 
 
 75 
 
 .3787 
 
 .1287 
 
 4.17 
 
 .27 
 
 .1363 
 
 .4063 
 
 6-99 
 
 .76 
 
 .3838 
 
 .1438 
 
 4-25 
 
 .28 
 
 .1414 
 
 .4214 
 
 7.04 
 
 77 
 
 .3888 
 
 1.1588 
 
 4-32 
 
 29 
 
 .1464 
 
 .4364 
 
 7.09 
 
 .78 
 
 3939 
 
 i. 1739 
 
 4-39 
 
 30 
 
 .1515 
 
 .4515 
 
 
 
 
 
TABLES OF h AND h'. 
 
 265 
 
 TABLE No. 65 (Continued). 
 TABLES OF h AND h' DUE TO GIVEN VELOCITIES, h AND h' BEING 
 
 IN FEET AND V IN FEET PER SECOND. 
 
 Velocity. 
 
 h 
 
 h' 
 
 k + h' 
 
 , Velocity. 
 
 h 
 
 h' 
 
 h + &' 
 
 7-13 
 
 79 
 
 .3989 
 
 .1889 
 
 22.34 
 
 7-75 
 
 3.914 
 
 11.664 
 
 7 .I8 
 
 .80 
 
 .4040 
 
 .2040 
 
 22.70 
 
 8 
 
 4.040 
 
 12.040 
 
 7.22 
 
 .81 
 
 .4090 
 
 .2190 
 
 23.05 
 
 8.25 
 
 4.166 
 
 12.666 
 
 7.26 
 
 .82 
 
 .4141 
 
 2341 ' 
 
 23.40 
 
 8.50 
 
 4.292 
 
 12.792 
 
 7-31 
 
 .83 
 
 .4191 
 
 .2491 
 
 23-74 
 
 8.75 
 
 4.419 
 
 13-169 
 
 7-35 
 
 .84 
 
 .4242 
 
 .2642 
 
 24.07 
 
 9 
 
 4.545 
 
 13-545 
 
 7.40 
 
 .85 
 
 .4292 
 
 .2792 
 
 24.41 
 
 9-25 
 
 4.671 
 
 13.921 
 
 7.44 
 
 .86 
 
 4343 
 
 .2943 
 
 24-73 
 
 9-50 
 
 4-797 
 
 14.297 
 
 7.48 
 
 .87 
 
 4393 
 
 3093 
 
 25.06 
 
 9-75 
 
 4.924 
 
 14.674 
 
 7-53 
 
 .88 
 
 .4444 
 
 3244 
 
 25.38 
 
 10 
 
 5.050 
 
 15-050 
 
 7-57 
 
 .89 
 
 4494 
 
 3394 
 
 25.69 
 
 10.25 
 
 5.1/6 
 
 15-426 
 
 7.61 
 
 .90 
 
 4545 
 
 3545 
 
 26.00 
 
 10.50 
 
 5.302 
 
 15.802 
 
 7.65 
 
 .91 
 
 4595 
 
 .3695 
 
 26.32 
 
 10.75 
 
 5-492 
 
 16.242 
 
 7.70 
 
 .92 
 
 .4646 
 
 .3846 
 
 26.62 
 
 ii 
 
 5-555 
 
 16.555 
 
 7-74 
 
 93 
 
 .4696 
 
 .3996 , 
 
 26.91 
 
 ".25 
 
 5.681 
 
 16.931 
 
 7.78 
 
 .94 
 
 4747 
 
 .4147 ! 
 
 27.21 
 
 11.50 
 
 5-807 
 
 17.307 
 
 7.82 
 
 95 
 
 4797 
 
 4297 
 
 27.51 
 
 11-75 
 
 5-934 
 
 17.684 
 
 7.86 
 
 .96 
 
 .4848 
 
 4448 ! 
 
 2 7 .8 
 
 12 
 
 6.060 
 
 18.060 
 
 7.90 
 
 97 
 
 .4898 
 
 4598 1 
 
 28.4 
 
 12.5 
 
 6.186 
 
 18.686 
 
 7-94 
 
 .98 
 
 4949 
 
 .4749 
 
 28.9 
 
 13 
 
 6-565 
 
 19-565 
 
 7.98 
 
 99 
 
 4999 
 
 .4899 
 
 29.5 
 
 13.5 
 
 6.817 
 
 20.317 
 
 8.03 
 
 i 
 
 505 
 
 .505 
 
 30.0 
 
 14 
 
 7-070 
 
 21.070 
 
 8.97 
 
 1.25 
 
 .631 
 
 .881 
 
 30-5 
 
 14-5 
 
 7-322 
 
 21.822 
 
 9-83 
 
 1.50 
 
 757 
 
 2.257 
 
 3LI 
 
 15 
 
 7-575 
 
 22-575 
 
 10. 60 
 
 1-75 
 
 .884 
 
 2.634 
 
 31.6 
 
 15-5 
 
 7.827 
 
 23.327 
 
 zx .4 
 
 2 
 
 .010 
 
 3.010 
 
 32.1 
 
 16 
 
 8.080 
 
 24.080 
 
 11.35 
 
 2.25 
 
 .136 
 
 3.386 
 
 32.6 
 
 16.5 
 
 8-332 
 
 24.832 
 
 12.6 
 
 2.50 
 
 .362 
 
 3.862 
 
 33-1 
 
 17 
 
 8.585 
 
 25-585 
 
 13.30 
 
 2-75 
 
 389 
 
 4-139 
 
 33-6 
 
 17.5 
 
 8.837 
 
 26.337 
 
 13-9 
 
 3 
 
 SIS 
 
 4-515 
 
 34-0 
 
 18 
 
 9.000 
 
 27.090 
 
 14.47 
 
 3-25 
 
 .641 
 
 5.891 
 
 34.5 
 
 18.5 
 
 9-342 
 
 27.842 
 
 15-0 
 
 3-50 
 
 .767 
 
 5-267 
 
 35-0 
 
 19 
 
 9-595 
 
 28.595 
 
 15.54 
 
 3-75 
 
 1.894 
 
 5-644 
 
 35-4 
 
 19-5 
 
 9.847 
 
 29.347 
 
 16.05 
 
 4 
 
 2.020 
 
 6.020 
 
 35-9 
 
 20 
 
 10.100 
 
 30.100 
 
 16.54 
 
 4.25 
 
 2.146 
 
 6.396 
 
 36.8 
 
 21 
 
 10.352 
 
 3L352 
 
 I7.O2 
 
 4.50 
 
 2.272 
 
 6.772 
 
 37-6 
 
 22 
 
 II. IIO 
 
 33-110 
 
 17.49 
 
 4-75 
 
 2-399 
 
 7.149 
 
 38.5 
 
 23 
 
 11.615 
 
 34.615 
 
 17.94 
 
 5 
 
 2.525 
 
 7.525 
 
 39-3 
 
 24 
 
 I2.I2O 
 
 36.120 
 
 18.39 
 
 5.25 
 
 2.651 
 
 7.901 
 
 40.1 
 
 25 
 
 12.625 
 
 37 625 
 
 18.82 
 
 5-50 
 
 2.777 
 
 8.277 
 
 40.9 
 
 26 
 
 13.130 
 
 39.130 
 
 19.24 
 
 5-75 
 
 2.904 
 
 8.654 
 
 41.7 
 
 27 
 
 13.635 
 
 40-635 
 
 19.66 
 
 6 
 
 3-030 
 
 9.030 
 
 42.5 
 
 28 
 
 14.140 
 
 42.140 
 
 2O.O6 
 
 6.25 
 
 3-156 
 
 9.406 
 
 43-2 
 
 29 
 
 14.645 
 
 43.645 
 
 20.46 
 
 6.50 
 
 3.282 
 
 9.782 
 
 43-9 
 
 30 
 
 15.150 
 
 45.150 
 
 20.85 
 
 6.75 
 
 3-409 
 
 10.159 
 
 47-4 
 
 35 
 
 17.675 
 
 52.675 
 
 21.23 
 
 7 
 
 3-535 
 
 10.535 
 
 50.7 
 
 40 
 
 20.200 
 
 60.200 
 
 2I.6I 
 
 7-25 
 
 3.661 
 
 10.911 
 
 53.8 
 
 45 
 
 22.725 
 
 67.725 
 
 21.98 
 
 7-50 
 
 3.787 
 
 11.287 
 
 56.7 
 
 50 
 
 25.250 
 
 75-250 
 
 
266 FLOW OF WATER THROUGH PIPES. 
 
 293. Classified Equations for Velocity, Head, 
 Volume, and Diameter. The coefficients of flow for the 
 given slopes and diameters being determined, they, with 
 the coefficients of resistance of entry for different forms of 
 entrance, may be introduced into the classified equations 
 for velocity, and their resolutions for head, volume, and 
 diameter ; when the equations will become, 
 
 H 
 
 ^ ~ If I [ for pipes with well-rounded entrances. (n\ 
 
 1.054471- 
 
 4 r\ 
 
 _.j I } for pipes with square-edged flush entrances. (&} t (19^ 
 
 1.505m- 
 A r\ 
 
 2gN ] j 
 
 T^ J I for pipes with square-edged entrances pro- / \ 
 l.OSw?^ I jecting into the reservoir. 
 
 * r 
 
 H= J 
 
 - (20) 
 
 77/7 s 
 6 - 303 ^.054^ ^^' - - W 
 
 ? =^ 6 - 30 Ho05TO^P ' ' ' ^ (21 > 
 
 6 ' 803 |l956^ a 4mg[* . . .. (c) 
 
 .4788 -1 1.054^ + 4ml i* . . . (a) 
 
 .4788 1 1.505^ + 4mZ|i* . ... . (5) \- (22) 
 
COEFFICIENTS FOR PIPES. 
 
 267 
 
 294. Coefficients of Entrance of Jet. Other values 
 of c r , for other conditions of pipe entrance, or other coef- 
 ficients of velocity c p , may be taken from, or interpolated 
 in the following table, computed from the formulas, 
 
 and 
 
 , - ( * y 
 
 * ~ \c, + i> 
 
 TABLE No. 66. 
 VALUES OF e. AND c FOR TUBES. 
 
 c v or c. . 
 
 .980 
 
 974 
 
 950 
 
 .925 
 
 .900 
 
 .875 
 
 .850 
 
 .825 
 
 .'Sis 
 
 .800 
 
 750 
 
 715 
 
 .700 
 
 c r 
 
 .041 
 
 054 
 
 .109 
 
 .169 
 
 235 
 
 .306 
 
 .383 
 
 .469 
 
 SOS 
 
 .563 
 
 .778 
 
 .956 
 
 1.041 
 
 I**,.. 
 
 1.041 
 
 1.054 
 
 1.109 
 
 1.169 
 
 1.235 
 
 1.306 
 
 L383 
 
 1.469 
 
 1-505 
 
 1-563 
 
 1.778 
 
 1.956 
 
 2.041 
 
 295. Mean Coefficients for Smooth, Rough, and 
 Fonl Pipes. In ordinary approximate calculations for 
 long pipes, it is often convenient to select a mean coefficient 
 for medium diameters and velocities, and insert it in a fun- 
 damental formula as a constant. In such case we may 
 select, say, for clean and smooth iron pipes, .00644 ; for 
 rough or slightly tuberculated pipes, .0082 ; and for very 
 rough or very foul pipes, .012. 
 
 These coefficients are applicable more particularly (wit- 
 ness table No. 61) to pipes of about five inches diameter 
 with a velocity of flow of about three feet per second, and 
 to lengths exceeding one thousand diameters. 
 
 Since 
 
 1 h" 
 
 x -- x -7- x 
 m I 
 
 we have 
 
268 
 
 FLOW OF WATER THROUGH PIPES. 
 
 We may now unite the constant 2g = 64.4 and our 
 assumed constant coefficients, and substitute their algebraic 
 equivalents in the equations : 
 
 
 - 1341 - 6666 - 
 
 The equations will in this case become : 
 
 j 2500 j y= 50 ! j- y for clean pipes. (a) 
 
 J 1 no At AC* "* d \ A ^ ( II d \ i for slightly tuber- /7A 
 
 j 1963.4146 -j- j- : = 44.31 j -y- j- culated pipes. (&) 
 
 1341.6666 -y- |- = 36.63 | -p i forvery foul pipes, (d) 
 
 296. Mean Equations for Smooth, Rough, and 
 Foul Pipes. From these expressions of velocity, in long, 
 full pipes, the equations for head, length, and diameter 
 may be deduced, thus : 
 
 v = 
 
 Kn 
 
 OU 
 
 h"= 4 
 
 ( 7i' d I i / N 
 
 j j r for clean pipes . \O) 
 
 ( f)"(J } x 
 
 44 3^ J J. 3 for slightly rough pipes. () 
 
 ( Z ) 
 
 36.63 | -y- [ for very rough pipes . (c) 
 
 .0004 -g- . . ''; . (a) 
 
 .000508 ^ . ' - ( & ) 
 
 .000745 ^ : . . * .- ( c ) 
 
 (23) 
 
 " (24) 
 
I = 
 
 2500 
 
 1963.4146 
 
 MEAN COEFFICIENTS. 
 
 dh" 
 
 V 2 ... 
 
 dh" 
 
 269 
 
 (b) j. (25) 
 
 1341.6666^ 
 
 d= 4 
 
 ,0004 ^77 . 
 
 7^2 
 
 .000508-^77 - 
 .000745 ^r, 
 
 . (a) 
 
 (26) 
 
 In which, = velocity of flow, in feet, per second ; 
 
 h" = head in slope, or mean gradient, in feet ; 
 I = length of pipe, in feet ; 
 d internal diameter of pipe, in feet. 
 
 It is sometimes convenient to express the volume of flow 
 per second in a term of quantity, g, rather than in a term of 
 velocity. 
 
 Since v= Jf> therefore, 
 
 y (h"d[i ,(h"d 5 n 
 
 q = Sv 50 S j -j- j- 39.27 j ^ [ 
 
 The equations, in terms of quantity (q\ in cubic feet per 
 second, will then take the following forms : 
 
 q= . 
 
 39. 27 Yf't for clean pipes 
 
 34.80 j j- f for slightly rough pipes 
 
 28.77 j -y V for very rough pipes . 
 
 (27) 
 
270 
 
 FLOW OF WATER THROUGH PIPES. 
 
 1 = 
 
 d = 
 
 ,0006484 Jr 
 .0008257 | 
 ,001208 ^ 
 
 .00064845 
 
 .0008257 
 
 .001208 
 
 .23034 ]^r, 
 .24174 \ l f\ 
 
 (28) 
 
 7i"d 5 
 
 q* 
 h"d 5 
 
 <f 
 
 . . (a) 
 
 (29) 
 
 . . (a) 
 
 .2609 i *, 
 
 , (30) 
 
 In which, g = volume of flow, in cubic feet per second ; 
 7i" head in slope, or mean gradient, in feet ; 
 I length of pipe, in feet ; 
 d = internal diameter of pipe, in feet. 
 
 297. Modification of a Fundamental Equation 
 of Velocity. The following expressions for velocity, con- 
 taining the assumed constant coefficient of flow .00644, are 
 equivalent to each other : 
 
 They are sometimes modified "by another coefficient, 
 thus : 
 
 (31) 
 
VALUES OF c'. 
 
 271 
 
 to make them conform more nearly to experiment for cer- 
 tain classes of conditions. 
 
 This coefficient (c') equals unity (c' = 1) in cases when 
 .00644 is the proper coefficient of flow to embody in the 
 fundamental formula ; is greater than unity (c' > 1) when 
 the principal coefficient should be less than .00644, and 
 less than unity (c' < 1) when the principal coefficient should 
 exceed .00644. Generally, with medium velocities of say 
 two and one-half to three feet per second, this coefficient, c\ 
 will exceed unity for long clean pipes exceeding five inches 
 diameter, and be less than unity for pipes of less than five 
 inches diameter. 
 
 298. Values of c'. When the legitimate coefficient, m, 
 is replaced by the assumed constant coefficient .00644, then 
 approximately, 
 
 j %g I* j 2H . . ., . . 
 
 1 .00644 ( ( m ) 
 therefore, 
 
 C> '' \2g+ .00644) : tToOOOT/Tj 
 With a given velocity of flow of say three feet per second, 
 in pipes exceeding one thousand diameters in length, the 
 several values of c' for different diameters would be approx- 
 imately as follows : 
 
 TABLE No. 66a. 
 SUB-COEFFICIENTS OF FLOW (c') IN PIPES. 
 
 Diameter. 
 
 </. 
 
 Diameter. 
 
 c / . 
 
 Diameter. 
 
 c 1 . 
 
 ^ inch. 
 
 .930 
 
 6 inches. 
 
 I.OI5 
 
 24 inches. 
 
 .150 
 
 J " 
 
 936 
 
 8 " 
 
 .031 
 
 27 
 
 .170 
 
 I " 
 
 .942 
 
 10 " 
 
 .050 
 
 30 " 
 
 .195 
 
 4 " 
 
 95 
 
 12 " 
 
 .060 
 
 33 " 
 
 .207 
 
 ij " 
 
 .960 
 
 14 " 
 
 .080 
 
 36 " 
 
 .225 
 
 2 " 
 
 .970 
 
 16 
 
 095 
 
 40 " 
 
 .245 
 
 3 " 
 
 .980 
 
 18 " 
 
 .110 
 
 44 " 
 
 .287 
 
 4 " 
 
 995 
 
 20 " 
 
 125 
 
 48 
 
 .308 
 
272 
 
 FLOW OF WATER THROUGH PIPES. 
 
 These values of c' decrease as the velocity of flow de- 
 creases from three feet per second, and are approximately 
 correct for higher velocities up to ten feet per second. 
 
 BENDS AND BRANCHES 
 
 299. Bends. The experiments with "bends, angles, and 
 contractions in pipes, so far as recorded, have been with 
 very small pipes, and the deductions therefrom are of 
 uncertain value when applied to the ordinary mains and 
 distribution pipes of public water supplies. 
 
 Our pipes should be so proportioned that the velocity 
 of flow, at an extreme, need not exceed ten feet per second. 
 Our bends should have a radius^ at axis, equal at least to 
 four diameters. 
 
 Under such conditions, the loss of head at a single bend 
 will not exceed about one-tenth the height to which the 
 velocity is due (not including height balancing resistance 
 of pipe- wall). 
 
 In such case, we may for an approximation take,* 
 
 = /(l + Cf ) + 4m4\ (33) 
 
 (34) 
 
 According to this equation, if a pipe is 1 foot diameter, 
 1000 feet long, and flowing with free end under 100 feet 
 head, the loss at one 90 bend, whose axial radius of curva- 
 ture equals 4 diameters, will be .47 feet of head. If there 
 are two bends, the total head remaining constant, the loss 
 
 * The mean value of (1 + c r ) for short pipes is 1.505. 
 
BENDS. 
 
 273 
 
 at both, will not be double this amount, for the velocity 
 through the first will be reduced by the resistance in the 
 second, and therefore the resistance in the first will be 
 reduced proportionally with the square of the reduction of 
 the velocity ; and a similar proportional reduction of resist- 
 ance will take place in the first and second bends when a 
 third is added. 
 
 Let v be the velocity due to the given head and length 
 of pipe without a bend, and Vi the velocity after the bend is 
 inserted, then the height of head lost, ^ 6 , in consequence of 
 the bend, is 
 
 and II 7i b is the effective remaining head. 
 
 After computing the new value of H beyond tne 
 bend, we may substitute that in the equationffiyimuf 
 ouMiyiaoi 1 .0^ and proceed to deduce the value of H beyond 
 the second bend, etc. 
 
 For larger pipes, or for larger radius of curvature, or 
 reduced velocity, the value of the subdivisor may ris3 to .94 
 or .96, or even near to w#or <M/l/K/wj^ 
 
 When pipes exceed one thousand diameters in length, 
 the term (1 + c r ) may be neglected, and the equations 
 assume the more simple forms, 
 
 HfSS 
 
 <> 
 
 In which v = the rate of flow, in feet per second. 
 
 Ji = the head balancing frictional resistance of 
 
 pipe-wall, in feet. 
 i = the sine of inclination = 
 
 18 
 
 == '??- 
 length 
 
 i 
 
274 
 
 FLOW OF WATER THROUGH PIPES. 
 
 r = the hydraulic mean radius = ^-i^. 
 
 contour 
 
 m = a coefficient (vide table of m, page 242). 
 %g = 64.4. 
 
 The experiments by Du Buat, Venturi, and other of the 
 early experimentalists, with pipes varying from one-half to 
 two inches diameter, and more recent experiments by Weis- 
 bach, have been fully and ably discussed by the latter, in 
 " Mechanics of Engineering" and elsewhere. 
 
 Weisbach's formula for additional height of head, Ji^ 
 necessary to overcome the resistance of one bend, is 
 
 = z 
 
 180 
 
 (37) 
 
 in which z is a coefficient of resistance, the arc of the bend 
 in degrees, and h b the additional head required. 
 
 The value of z he deduces by an empirical formula : 
 
 z = .131 + 1.847 (j, 
 
 in which r is the radius or semi-diameter of the pipe, and R, 
 the axial radius of curvature of the bend. 
 
 For given ratios of r to R, z has the following values, 
 for pipes with circular cross- sections. 
 
 TABLE No. 67. 
 COEFFICIENTS OF RESISTANCE IN BENDS. 
 
 r 
 ~R 
 
 z 
 
 .1 
 
 '5 
 
 .2 
 
 2 5 
 
 3 
 
 35 
 .178 
 
 4 
 
 45 
 
 5 
 
 55 
 
 131 
 
 133 
 
 .138 
 
 145 
 
 .158 
 
 .206 
 
 .244 
 
 .294 
 
 35 
 
 r 
 ~R 
 
 z 
 
 .6 
 
 65 
 
 7 
 
 75 
 
 .8 
 
 85 
 
 9 
 
 95 
 
 i 
 
 
 
 .440 
 
 540 
 
 .661 
 
 .806 
 
 977 
 
 1.177 
 
 1.408 
 
 1.674 
 
 1.978 
 
 
 
BRANCHES. 275 
 
 3OO. Branches. In branches, the sums of the resist- 
 ances due to the deflections of the moving particles, the 
 contractions of sections by centrifugal force, and the con- 
 tractions near square edges, if there are such, will for each 
 given velocity vary inversely as the diameters of the 
 branches. 
 
 Until reliable data for other than small pipe branches is 
 supplied, we may assume in approximate preliminary 
 estimates of head required, when the velocity of flow, under 
 pressure, is ten feet per second, a reduction of that portion 
 
 (tf\ 
 = ) at a right- 
 angled branch, equal to about fifty per cent, in branches of 
 three to six inches diameter and thirty to forty per cent, in 
 larger branches. 
 
 The equations then take the following form : 
 
 a 
 .60 
 
 (1 + c r ) - 
 
 < *= _^/ x . (39 > 
 
 The value of the subdivisor will be changed according 
 to the special conditions of the given case, and the effects 
 of a series of branches will be similar to those above 
 ^described for a series of bends, but enhanced in degree. 
 
 For long pipes, equivalent equations will be, 
 
 (40) 
 (41) 
 
276 FLOW OF WATER THROUGH PIPES. 
 
 3O1. How to Economize Head. The losses of head 
 and of energy due to frictions of pipe- wall and to resistances 
 of angles, contractions, etc., increase with the square of the 
 velocity, and they occasionally consume so much of the 
 head that a very small fraction of the entire head only 
 remains to generate the final velocity of flow. 
 
 The losses, other than those due to the walls of the pipes, 
 originate chiefly about the square edges of the pipes, 
 orifices, and valves, where contractions and their resulting 
 eddies are produced, or are due to the centrifugal force of 
 the particles in angles and bends. 
 
 These losses about the edges may be modified materially, 
 even near to zero, by rounding all entrances to the form of 
 their vend contracta, and by joining all pipes of lesser 
 diameter to the greater by acutely converging or gently 
 curved reducers (Fig. 102), so that tJie solidity and sym- 
 metrical section of the column of water shall not be dis- 
 turbed, and so that all changes of velocity shall be gradual 
 and without agitation among the fluid particles. 
 
 It is of the utmost importance, when head and energy 
 are to be economized, that the general onward motion of 
 the particles of the jet be maintained, since wherever a 
 sudden contraction occurs an eddy is produced, and 
 wherever currents of different velocities and directions 
 intermingle an agitation results, both of which divert a 
 portion of the forward energy of the particles to the right 
 and left, and convert it into pressure against the walls of 
 the pipe, from whence so much reaction as is across the 
 pipe is void of useful effect, and the energy of the jet to a 
 like extent neutralized, and so much as is back into the 
 approaching column is a twofold consumption of dynamic 
 force. 
 
CHAPTER XIV. 
 
 MEASURING WEIRS, AND WEIR GAUGING. 
 
 302. Gauged Volumes of Flow. A partially sub- 
 merged measuring orifice or notch in one of the upright 
 sides of a water tank, or a horizontal measuring crest with 
 vertical shoulders, in a barrier across a stream, equivalent 
 to a notch, is termed a weir. 
 
 Weirs, as well as submerged orifices ( 2O6) are used 
 for gauging the flow of water, and in their approved forms 
 give opportunity to apply the constant force and accelera- 
 tion of gravity, acting upon the water that falls over the 
 weir, to aid in determining the volume of its flow. 
 
 The volume of flow, Q, equals the product of the section 
 of the jet upon the weir, S, into its mean velocity, V. 
 
 Q = 8V. (1) 
 
 303. Form of Weir. For convenience in practical 
 construction and use, hydraulicians usually form their 
 measuring weirs with horizontal crests, (7Z>, and vertical 
 ends J.(7and BD^ Fig. 41. 
 
 FIG. 40. FIG. 41. 
 
 ^ ~- 
 
 
 \ 
 
 
 $ 
 
 B 
 
 IB 
 
 
 rr- - '-ill 
 
 
 7'. ro^l 
 
 J 
 
 
 ^ 
 
 
 w///////. 
 
 ^^^^^^^"^^^^^^w 
 
 '//''. . 
 
278 
 
 MEASURING WEIRS, AND WEIR GAUGING. 
 
 FIG. 42. 
 
 The theory of flow over weirs of this description is more 
 accurately established by numerous experimental and posi- 
 tive measurements, than for any other form of notch. 
 
 The head of water upon rectangular weirs is measured 
 from the crest CD of the weir to the surface of still water, a 
 short distance above the weir, instead of from the centre of 
 pressure or centre of gravity ( 2O6) of the aperture, as in 
 the case of submerged orifices. 
 
 The weir is placed at right angles to the stream, with its 
 upstream face in a vertical plane. 
 
 The crest and vertical shoulders of the weir are cham- 
 fered so as to flare outward on the discharge side at an 
 angle not less than thirty degrees. The thin crest and 
 ends receiving the current must be truly horizontal and 
 vertical, and truly at right angles to the upper plane of the 
 
 weir, and sharp-edged, so 
 as to give a contracted jet 
 analogous to that flowing 
 through thin, square-edged 
 plate. 
 
 The edges are common- 
 ly formed of a jointed and 
 chamfered casting, or of a 
 jointed plate not exceeding 
 one-tenth inch thickness, as shown in Fig. 42. 
 
 3O4. Dimensions. The dimensions of the notch 
 should be ample to carry the entire stream, and yet not so 
 long that the depth of water upon a sharp crest shall be less 
 than five inches, and if contraction is obtained at the up- 
 right ends, the section of the jet in the notch should not 
 exceed one- fifth the section of the approaching stream, lest 
 the stream approach the weir with an acquired velocity that 
 will appreciate the natural volume of flow through the notch. 
 
END CONTRACTIONS. 
 
 279 
 
 305. Stability. Care is to be taken to make the foun- 
 dation of the weir firm, the bracing substantial, and the 
 planking rigid, so there shall be no vibration of the frame- 
 work or crest, and its sheet piling is to go deep, and well 
 into the banks on each side, when set in a stream, so that 
 there shall be no escape of water under or around it, and a 
 firm apron is to be provided to receive the falling water and 
 to prevent undermining. 
 
 306. Varying Length. Upon mountain streams, it is 
 frequently necessary to provide for increasing or shortening 
 the length of the weir, so that due proportions of notch to 
 volume may be maintained. This may be accomplished by 
 the use of vertical stop-planks with flared edges, placed at 
 one or both ends of the weir, as at^, Fig. 41. 
 
 Sometimes it is necessary to make the notch of the entire 
 width of the stream, when there will be crest contraction 
 only, and no end contractions, in which case partitions E 
 (Fig. 44) should be placed against the upper side of the 
 
 FIG. 43. FIG. 44. 
 
 weir flush with its shoulders and at right angles to its 
 plane. On other occasions the weir may be so long as to 
 require intermediate posts, F (Fig. 44), in its frame- work, 
 when intermediate contractions, one to each side of a post, 
 will be obtained, in additions to the crest and end contrac- 
 
280 MEASURING WEIRS, AND WEIR GAUGING. 
 
 tions ; each of which exerttan important diminishing influ- 
 ence upon the volume of flow. 
 
 307. End. Contractions. A short weir may be de- 
 fined, one which is appreciably affected by end contractions 
 throughout its entire length ; practically, when the length 
 of unbroken opening is less than about four times the 
 depth of water flowing over. 
 
 The end contractions affect a nearly constant length at 
 each end, for each given depth, on long weirs, and such 
 length increases with the depth of water upon the weir. 
 
 To obtain perfect end contractions, the distance from 
 the vertical shoulder to the side of the channel should 
 not be less than double the depth of the water upon the 
 weir. 
 
 If there is no end contraction, the volume for any given 
 depth is proportional to the entire length of the weir. 
 
 The flow, for a given length, on long weirs, or on weirs 
 without end contractions, is proportional to a power of the 
 depth on the weir. 
 
 308. Crest Contractions. To obtain perfect crest 
 contractions, the depth of water above the weir should not 
 be less than about double the depth upon the weir, especi- 
 ally when the depth flowing over is less than one foot j and 
 the clear fall below the crest to the surface of tail water 
 should be sufficient to maintain a perfect circulation of air 
 in the crest contraction, d (Fig. 42), under the jet, all along 
 the crest. Such supplies of air are to be provided for at 
 ends, and at central posts, F (Fig. 44), since a vacuum 
 under the jet would defeat the application of the ordinary 
 formula. 
 
 309. Theory of Flow over a Weir. To illustrate 
 the deduced theory of flow through rectangular notches, we 
 will first consider a case independent of contraction : 
 
THEORY OF FLOW OVER A WEIR. 
 
 281 
 
 FIG. 45. 
 
 \ 
 
 V 
 
 
 
 
 II^s: 
 
 
 \n 
 
 
 -x 
 
 
 
 Let #, 5, c, d, 6, /, etc. (Fig. 45), be orifices in the side 
 of a reservoir, at depths below the water surface, respec- 
 tively of 1, 2, 3, 4, 5, 6, etc., feet. 
 
 Then the velocity of issue of jet from each orifice will be 
 
 V= VfyH, 
 
 according to its depth, H, below the surface, viz. : 
 
 For orifice b, V = V2gi = 8.03 feet per second. 
 
 c, V= 
 
 d, V = 
 e,V = 
 
 /, T= 
 i, V= 
 *, V = 
 
 = 11.40 " 
 
 = 13.90 " 
 
 = 16.00 " 
 
 = 17.90 " 
 
 = 19.70 " 
 
 = 21.20 " 
 
 = 22.70 u 
 
 o,V=\ / 2g9 =24.10 " 
 
 p, V = 
 
 = 25.40 
 
 
 Plot each of these depth, a, >, c, etc., to scale upon the 
 same vertical line as abscisses and their corresponding 
 velocities of issue, W, cc\ dd\ etc., horizontally to the same 
 
282 MEASURING WEIRS, AND WEIR GAUGING. 
 
 scale as ordinates ; then the extremities of the horizontal 
 lines will touch a parabolic line, a, &', d, p\ whose vertex 
 is at a, abscissa is ap, ordinates are bb', cc f , pp\ etc., and 
 whose parameter equals 2g. 
 
 Suppose now the lintels separating the orifices are in- 
 finitely thin, then the volume issuing per second from each 
 orifice will equal a prism, whose length and height equals 
 that of the orifice, and whose mean projection is equal to 
 its ordinate, bb', cc', dd, etc., or equals in feet, the feet per 
 second of velocity of issue from the orifice. 
 
 Again, suppose the partitions to be entirely removed 
 and the fluid veins to be infinitely thin and infinite in num- 
 ber as respects height, then the velocities of the veins plot- 
 ted to scale, will touch, as before, the parabolic line ab'd'p', 
 and the volume of issue per second will equal a prism whose 
 end area equals the notch ap, and whose area of projection 
 equals the area of the parabolic segment, app'd'a. 
 
 According to well known properties of the parabola, the 
 segment app'd'a is equal to two-thirds its circumscribing 
 parallelogram Aapp'. 
 
 Let I be the length of the notch, H the height = ap, and 
 VSglfihe length of the segment =pp ; then the area of the 
 circumscribing parallelogram equals II x V%gH and the 
 area of the segment equals H x f V2gH and the volume of 
 issue Q = I x H x f VfyH. (2) 
 
 Let V be the velocity of the film of mean velocity. 
 Since the volume of the segmental prism app'd'a equals 
 two thirds of the parallelepiped Ap of equal height, length, 
 and projection, it follows that the volume of the segment 
 equals the volume of a parallelepiped of equal height and 
 length and of f the projection = pp", and the mean velocity 
 of issue, V = pp" = I V2gff. 
 
 The volume Q = I x H x V= I x H x | 
 
FLOW WITHOUT AND WITH CONTRACTIONS. 
 
 If the crest of the weir is raised to/, then let the height 
 of be ^, and the velocity of issue of the film at the crest f 
 will be ^2gkj and the volume of issue q from the notch of 
 will be, q = %l x h x Vk x V%g. 
 
 If the volume q of this segmental prism aff'b'a, be sub- 
 tracted from the volume Q of the segmental prism app'd'a, 
 the remainder will equal the volume of the prism fpp'f = 
 Q - q^(%lx H xVHx V2g) - (f I x h x Vh x V2g) = 
 
 (3) 
 
 31O. Formulas for Flow without and with Con- 
 tractions. The formula (2), Q = I x II x | Vty x t 7 ^ 
 may take the form Q = VZg x I x \H*. (4) 
 
 Taking into consideration the complete contraction in a 
 rectangular weir, we observe first, that in addition to the 
 crest and end contractions, the surface of the stream, Fig. 42, 
 begins to lower at a short distance above the weir, and the 
 jet assumes a downward curve over the weir. 
 
 Experiments demonstrate that the measurements are 
 facilitated, both in accuracy of observations and in ease of 
 calculations, by taking the height of water upon the weir 
 to the true surface level a short distance above the weir, 
 instead of to the actual surface immediately over the crest. 
 In such case the top contraction has no separate coefficient 
 in the formula of volume. 
 
 Experiments demonstrate also, that a perfect end con- 
 traction, when depths upon the weir are between three and 
 twenty-four inches, and length not less than three times the 
 given depth, will reduce the effective length of the weir a 
 mean amount, approximately equal to one-tenth of the 
 depth from still water surface to crest. 
 
 If H is this depth from surface to crest, and I the full 
 length of the weir, and I the effective length of the weir, 
 then one end contraction makes l'= (I 0.1 H) ; and two 
 
284 MEASURING WEIRS, AND WEIR GAUGING. 
 
 end contractions make l'= (I 0.2H) ; and any number, 
 n, of end contractions make l'= (I Q.lnH). 
 
 The reduction of volume by the crest contraction is com- 
 pensated for by a coefficient m introduced in the formula 
 for theoretical volume, as above deduced. This coefficient 
 (m) is to be determined for the several relative depths and 
 lengths by experiment. 
 
 If we insert the factors relating to end and crest contrac- 
 tions, the formula for volume becomes : 
 
 Q = lm x V2g x (I - O.lnlf)!?^ (5) 
 
 The factors f and V2g are constants, and for approximate 
 calculations within limits of 3 to 24 inches depths upon the 
 weir, m may be taken as constant. 
 
 Let O represent the product of these three factors, then 
 C=%m x Vfy. 
 
 The admirable experiments with weirs* upon a great 
 scale, which were conducted by James B. Francis, C. E., 
 with the aid of the most perfect mechanical appliances, in a 
 most thorough and careful manner, give to C a mean value 
 of 3.33, and we have 3.33 = \m x Vty. 
 
 Transposing and assigning to V%g its numerical value, 
 we have, 
 
 O OO O OO 
 
 m = 2 "g7)25 ^35 = -622 as a mean coefficient. 
 
 The formula for volume of flow may take the following 
 forms : 
 
 Q=l VZg x m(l - Q.lnB)IT* = 5.35m(Z - 0.1nH)H^ (6) 
 or for approximate results, 
 
 Q = O(l 0.lnff)IT* = 3.33(Z - O.lnffjNl (7) 
 
 This last formula, suggested by Mr. Francis, assumes 
 
 * Lowell Hydraulic Experiments ; Van Nostrand, New York, 1868. 
 
INCREASE OF VOLUME DUE TO INITIAL VELOCITY. 285 
 
 that the discharge is from a reservoir infinitely large, so that 
 the water approaching has received no initial velocity. 
 
 311. Increase of Volume due to Initial Velocity 
 of Water. When there is appreciable velocity of approach, 
 let $ be the section of stream in the channel of approach, 
 and Fthe mean velocity of flow in the section ', and h the 
 height to which the velocity V is due, and Q' the volume 
 enhanced by the initial velocity. Then 
 
 Q 
 
 SV= Q, and V= ^, and h = ^-. 
 
 If the mean velocity, F, is to be determined from the 
 surface motion of the water in the channel of approach, let 
 V be the surface motion ; then, as will be shown in the 
 consideration of flow of water in channels ( 332), the mean 
 velocity is, approximately, eight-tenths of the surface ve- 
 
 ( 8 F'Y 8 
 locity, and V= .8V, and 7i = % 
 
 Referring again to a parabolic segment of length equal 
 to the unit of length of weir, 
 Fig. 46, and let If = ap, and FIG. 4r>. 
 
 Ji sa, and V%gH = pp and 
 Tfc) = pt. 
 
 The ordinate pp' of the seg- 
 ment app' is the projection of a 
 parabolic segment whose volume 
 equals the volume of flow when 
 the depth upon the weir equals 
 ap. 
 
 When the flow has no initial 
 velocity the ordinate at a = 0, 
 
 but when the flow has an initial velocity due to the height 
 sa = Ti, the ordinate at a equals V2gk = aa\ and the ordi- 
 nate at p = V%g(H + 7i) =pt, and any ordinate /, at a 
 
286 - MEASURING WEIRS, AND WEIR GAUGING. 
 
 depth 7i' = sf, equals V2gh'=ff", therefore the increase 
 of volume of flow due to initial velocity is represented by 
 the volume aa'tp'f, and the whole volume of flow by the 
 volume apta'. 
 
 This last volume is the volume spt less the volume sad, 
 and equals, for unit of length, 
 
 .... (8) 
 
 Let Q' be the enhanced volume, and let H' be some 
 depth, yp, upon the weir, that substituted for H in the 
 ordinary formula for Q would give the value of Q'. 
 
 The formula then, if there are no end contractions, is 
 
 q = \ml^gH\ (9) 
 
 or, for approximate measures, including end contractions, 
 
 if any, 
 
 Q = 3.33 (I - O.lnlT) H\ (10) 
 
 To determine the value of H' from (H -f h\ substitute 
 the value of Q' in the equation (8) of volume for one unit of 
 length, and we have 
 
 and reducing, we have 
 
 If the volume of flow (Q = $ml V2g IT*) is known, and it 
 is desired to find the depth If upon a weir of given length, 
 then by transposition we have, 
 
 H= j ; (12) 
 
 \ 
 
 * 
 lrnl 
 
COEFFICIENTS FOR WEIR FORMULAS. 287 
 
 or, in case of initial velocity in the approaching water, 
 
 H = j 2 ^-J + *4 * - * ( 13 ) 
 
 
 The first of these two values of H will give results suf- 
 ficiently near for all ordinary practice, if the initial velocity 
 does not exceed one-half foot per second. 
 
 In the above formulas of volume the symbols represent 
 values as follows : 
 
 Q = volume due to natural flow, in cubic feet per second. 
 I length of weir, in feet. 
 I = effective length of weir, in feet. 
 
 m = coefficient of crest contraction, determined by exper- 
 iment. 
 
 H= observed depth of water upon the weir, in feet. 
 S = section of channel leading to the weir, in square feet. 
 V = mean velocity of water approaching the weir, in feet 
 
 per second. 
 
 7i = head to which this velocity is due, in feet. 
 2# = 64.3896, or 64.4 for ordinary calculations. 
 H' = head upon the weir, when corrected to include effect 
 
 of initial velocity of approaching water. 
 Q' = volume of flow, including effect due to initial velocity 
 of approaching water. 
 
 312. Coefficients for Weir Formulas. The con- 
 trolling influence of the contractions entitle them to a 
 detailed study. 
 
 In Mr. Francis' formula for volume, quoted above, the 
 end contraction is assumed to be a function of the depth, 
 and the crest contraction to be compensated for by the 
 coefficient C, of which m is the variable factor dependent 
 upon the depth. 
 
288 
 
 MEASURING WEIRS, AND WEIR GAUGING. 
 
 In the following table the quantities in columns A, B, 
 D, E, F have been selected from Mr. Francis' table, the 
 column C reduced from its corresponding column, and the 
 column G computed. Each of the columns are means of a 
 number of nearly parallel experiments, and they are here 
 arranged according to depth upon the weir. 
 
 TABLE No. 68. 
 EXPERIMENTAL WEIR COEFFICIENTS. 
 
 A. 
 
 B. 
 
 c. 
 
 D. 
 
 E. 
 
 F. 
 
 0. 
 
 II 
 
 & 
 
 i>.b. 
 
 if! 
 
 CL 5^ en 
 
 a T 
 w So 
 
 I Is 
 
 S V 
 
 s 
 
 || 
 
 g ^j 
 
 jte 
 
 H W S II 
 
 .b^ I <s 
 
 8 >, 3 s, 
 
 ni 
 
 1 7 
 
 o 
 
 0) 
 
 a 
 
 I" 
 
 g.jg 
 
 r; O.O N 
 
 5 
 
 ^ l' s 
 
 s S a 
 
 a - 
 
 
 
 9-997 
 
 .62 
 
 16.2148 
 
 16.0382 
 
 16.0502 
 
 3.3275 
 
 .622 
 
 9-997 
 
 65 
 
 17.3401 
 
 17.1990 
 
 17.2187 
 
 3.3262 
 
 .622 
 
 9-995 
 
 .80 
 
 23-7905 
 
 23.8821 
 
 23.8156 
 
 3.3393 
 
 .624 
 
 9-997 
 
 .80 
 
 23.4304 
 
 23.4011 
 
 23.439! 
 
 3.3246 
 
 .621 
 
 9-997 
 
 83 
 
 25.0410 
 
 24.8313 
 
 24.7548 
 
 3.3403 
 
 .624 
 
 9-995 
 
 .98 
 
 32.5630 
 
 32.3956 
 
 32.2899 
 
 3-3409 
 
 .624 
 
 9-995 
 
 .00 
 
 33.4946 
 
 33.2534 
 
 33.2833 
 
 3.3270 
 
 .622 
 
 9-997 
 
 .00 
 
 32.5754 
 
 32.5486 
 
 32.6240 
 
 3-3223 
 
 .621 
 
 9-997 
 
 .06 
 
 36.0017 
 
 35.8026 
 
 35-5602 
 
 3-3527 
 
 .627 
 
 9-997 
 
 25 
 
 45-5654 
 
 45-4125 
 
 45.3608 
 
 3-3338 
 
 .623 
 
 9-997 
 
 -56 
 
 62.6019 
 
 62.6147 
 
 62.8392 
 
 3.3181 
 
 .620 
 
 7-997 
 
 .68 
 
 14.5478 
 
 14.4581 
 
 14.4247 
 
 3.3368 
 
 .624 
 
 7-997 
 
 i. 02 
 
 26.2756 
 
 26.2686 
 
 26.0333 
 
 3.3601 
 
 .628 
 
 
 
 
 
 1 
 
 Mean, 
 
 .623 
 
 Mr. Francis points out the necessity of caution in apply- 
 ing the above formula for Q' beyond the limit covered by 
 the experiments, but it occasionally becomes necessary to 
 use some formula for depths both less and greater than is 
 included in the above table. 
 
 After plotting with care the results obtained in various 
 
DISCHARGES FOR GIVEN DEPTHS. 
 
 289 
 
 experiments by different experimentalists, we suggest the 
 following coefficients for the respective given depths, until a 
 series of equal range shall be established by experiments 
 with a standard weir gauge. At the same time, we advise 
 that weirs be so proportioned that the depths upon them 
 shall conform to the limits already covered by experiment, 
 or at least between 4 and 24 inches depths, and with length 
 equal to four times the depth. 
 
 TAB L E No. 69. 
 
 COEFFICIENTS FOR GIVEN DEPTHS UPON WEIRS (in thin vertical 
 
 plate). 
 
 Denths J 
 
 
 i in. 
 
 i* in. 
 
 2 in. 
 
 3 in. 
 
 4 in. 
 
 6 in. 
 
 Sin. 
 
 10 in. 
 
 
 
 
 .083 ft. 
 
 .124 ft. 
 
 .167 ft. 
 
 25ft. 
 
 333 ft- 
 
 .500 ft. 
 
 .667 ft. 
 
 .833 ft- 
 
 Value of nt ... 
 
 
 .6100 
 
 .6120 
 
 .6140 
 
 .6170 
 
 .6195 
 
 .6223 
 
 .6235 
 
 .6240 
 
 Value of C 
 
 
 
 
 3.285 
 
 
 o.oi4 
 
 3.329 
 
 3-336 
 
 3.338 
 
 
 
 
 
 
 
 
 
 
 
 Depths -j 
 
 12 in. 
 ift. 
 
 14 in. 
 1.167 ft* 
 
 i6iri. 
 1-333 ft- 
 
 i8in. 
 1.500 ft. 
 
 20 in. 
 1.667 ft 
 
 24 in. 
 2.oooft. 
 
 30 in. 
 2.500 ft. 
 
 40 in. 
 3-333 ft- 
 
 48 in. 
 4.000 ft. 
 
 Value of m... 
 
 .6241 
 
 .6242 
 
 .6243 
 
 .6242 
 
 .6241 
 
 .6240 
 
 .6232 
 
 .6226 
 
 .6200 
 
 Value of C 
 
 3-339 
 
 3-339 
 
 3-340 
 
 3-339 
 
 3-339 
 
 3.338 
 
 3-334 
 
 3-33i 
 
 3-317 
 
 313. Discharges for Given Depths. The following 
 table of approximate flow over each foot in length of a 
 sharp-crested rectangular weir has been prepared to aid in 
 adjusting the proportions of weirs for given streams. End 
 contractions are not here allowed for.* The coefficients C 
 (in CIH%) are taken from table above, and I equals unity. 
 
 The proportions of weir and its ratio to section of chan- 
 nel are here supposed to conform to the general suggestions 
 given above. 
 
 * To compensate for a single end contraction, on a weir of any length, 
 deductyOBe-tofitk the Tolmno duc-.to one foot length of th 
 
290 
 
 MEASURING WEIRS, AND WEIR GAUGING. 
 
 TABLE No. 7O. 
 DISCHARGES, FOR GIVEN DEPTHS OVER EACH LINEAL FOOT OF WEIR. 
 
 Head from 
 still water 
 in ft,=H. 
 
 ff*. 
 
 11 
 
 31* " 
 
 1 
 
 *. 
 
 Cubic feet. 
 
 i 
 
 P5 
 
 **. 
 
 Cubic feet. 
 
 .04 
 
 .0080 
 
 .0261 
 
 .46 
 
 .3120 
 
 .0386 
 
 1.2 
 
 I.3I45 
 
 4.3904 
 
 05 
 
 .0112 
 
 .0365 
 
 .48 
 
 .3326 
 
 . 1072 i 
 
 i-3 
 
 1.4822 
 
 4.9506 
 
 .06 
 
 .0147 
 
 .0480 
 
 So 
 
 3536 
 
 .1771 
 
 1.4 
 
 1.6565 
 
 5-53H 
 
 .07 
 
 .0185 
 
 .0604 
 
 52 
 
 3750 
 
 .2483 i 
 
 i-5 
 
 1.8371 
 
 6.1341 
 
 .08 
 
 .0226 
 
 0737 
 
 54 
 
 .3968 
 
 .3209 
 
 1.6 
 
 2.0239 
 
 6-7558 
 
 .09 
 
 .0270 
 
 .0881 
 
 .56 
 
 .4191 
 
 3951 
 
 1-7 
 
 2.2165 
 
 7o987 
 
 .10 
 
 .0316 
 
 1035 
 
 .58 
 
 .4417 
 
 4724 i 
 
 1.8 
 
 2.4150 
 
 8.0516 
 
 .11 
 
 .0365 
 
 1195 
 
 .60 
 
 .4648 
 
 .5506 j 
 
 1.9 
 
 2 6190 
 
 8.7317 
 
 .12 
 
 .0416 
 
 .1369 
 
 .62 
 
 .4882 
 
 .6286 
 
 2.O 
 
 2.8284 
 
 9.4299 
 
 13 
 
 .0469 
 
 .1536 
 
 .64 
 
 .5120 
 
 .7080 
 
 2.1 
 
 3-0432 
 
 10.1460 
 
 .14 
 
 0524 
 
 .1718 
 
 .66 
 
 .5362 
 
 .7888 
 
 2.2 
 
 3.2631 
 
 10.8694 
 
 -15 
 
 .0581 
 
 .1906 
 
 .68 
 
 .5607 
 
 .8705 
 
 2-3 
 
 3.4881 
 
 11.6189 
 
 .16 
 
 .0640 
 
 .2102 
 
 .70 
 
 .5875 
 
 9599 
 
 2.4 
 
 3.7I8I 
 
 12.3850 
 
 17 
 
 .O7OI 
 
 .2303 
 
 .72 
 
 .6109 
 
 2.0380 
 
 2-5 
 
 3-9528 
 
 13.1668 
 
 .18 
 
 .0764 
 
 .2512 
 
 74 
 
 .6366 
 
 2.1237 
 
 2.6 
 
 4.1924 
 
 13.9649 
 
 .19 
 
 .0828 
 
 .2726 
 
 .76 
 
 .6626 
 
 2.2118 
 
 2-7 
 
 4.4366 
 
 14.7783 
 
 .20 
 
 .0894 
 
 .2951 
 
 .78 
 
 .6889 
 
 2.2996 
 
 2.8 
 
 4-6853 
 
 15.6067 
 
 .22 
 
 .1032 
 
 .3407 
 
 .80 
 
 .7155 
 
 2.3883 
 
 2.9 
 
 4.9385 
 
 16.4501 
 
 .24 
 
 .1176 
 
 .3882 
 
 .82 
 
 .7426 
 
 2.4788 
 
 3.0 
 
 5.I962 
 
 17.3086 
 
 .26 
 
 .1326 
 
 4377 
 
 .84 
 
 .7699 
 
 2.5699 
 
 3-i 
 
 5.4581 
 
 18.1809 
 
 .28 
 
 .1482 
 
 .4892 
 
 .86 
 
 7975 
 
 2 . 6620 
 
 3-2 
 
 5.7243 
 
 19.0676 
 
 -30 
 
 .1643 
 
 5445 
 
 .88 
 
 .8255 
 
 2-7557 
 
 3-3 
 
 -9948 
 
 19.9687 
 
 -32 
 
 .1790 
 
 5932 
 
 .90 
 
 -8538 
 
 2.8500 
 
 3-4 
 
 6.2693 
 
 20-7953 
 
 -34 
 
 .1983 
 
 .6572 
 
 .92 
 
 .8824 
 
 2.9463 
 
 3-5 
 
 6-5479 
 
 21.7194 
 
 .36 
 
 .2160 
 
 .7158 
 
 .94 
 
 .9114 
 
 3.0432 
 
 3-6 
 
 6.8305 
 
 22.6568 
 
 .38 
 
 .2342 
 
 .7761 
 
 .96 
 
 .9406 
 
 3.1407 
 
 3-7 
 
 7.II7I 
 
 23.6074 
 
 .40 
 
 .2530 
 
 .8384 
 
 .98 
 
 .9702 
 
 3-2395 
 
 3-8 
 
 7.4076 
 
 24.5710 
 
 .42 
 
 .2722 
 
 .9020 
 
 1. 00 
 
 I. 0000 
 
 3-339 
 
 3-9 
 
 7.7019 
 
 25.5472 
 
 44 
 
 .2919 
 
 .9717 
 
 i.i 
 
 1-1537 
 
 3.8522 
 
 4.0 
 
 8.0000 
 
 26.5360 
 
 The coefficients derived from the experiments of Castel 
 and D' Aubuisson, Du Buat, Poncelet and Lebros, Smeaton 
 and Brindley, and Simpson and Blackwell, have been 
 deduced by those eminent experimentalists to compensate 
 for all contractions. In such cases, the ratio of length of 
 weir to depth, especially where depth exceeds one-fourth 
 the length, and the ratio of length to breadth of channel by 
 which water approaches, exert controlling influences upon 
 the coefficient. 
 
WEIR COEFFICIENTS. 
 
 291 
 
 The following table of coefficients, deduced "by Castel, 
 show the influence of depth and length. 
 
 In these experiments, Castel used for channel a wooden 
 trough 2 feet 5| inches wide, and the weir placed upon its 
 discharging end was in each case of thin copper plate. 
 
 TABLE No. 71. 
 WEIR COEFFICIENTS, BY CASTEL. 
 
 ** 
 
 P.C 
 
 o| 8 
 
 CANAL, 2.427 feet wide. COEFFICIENTS, the lengths of the overfall being respectively 
 
 Ft. 
 2.42 
 
 Ft. 
 2.23 
 
 Ft. 
 1.96 
 
 Ft. 
 1.64 
 
 Ft. 
 1.31 
 
 Ft. 
 
 0.98 
 
 Ft. 
 
 0.65 
 
 Ft. 
 
 0.32 
 
 Ft. 
 0.16 
 
 Ft. \ Ft. 
 0.09 0.06 
 
 Ft. 
 0.03 
 
 Ft. 
 
 0.78 
 
 % 
 
 50 
 52 
 45 
 39 
 
 3 
 
 :S 
 
 13 
 .09 
 
 
 
 
 
 
 
 
 0.595 
 
 0.615 
 
 . '0.639 
 
 
 
 
 
 
 
 
 
 594 
 
 6x4 
 
 6?n 
 
 
 
 
 
 
 
 
 0.596 
 595 
 595 
 593 
 592 
 593 
 595 
 .604 
 .611 
 .619 
 .624 
 
 594 
 594 
 592 
 592 
 591 
 591 
 592 
 595 
 
 .618 
 
 .614 
 .6,3 
 .613 
 .612 
 .612 
 .612 
 .612 
 .612 
 .613 
 .614 
 
 0.629 
 .628 
 .628 
 .628 
 .628 
 .627 
 .627 
 .628 
 .629 
 
 A 
 
 .641 
 .642 
 .643 
 645 
 .648 
 .652 
 .658 
 66 3 
 .669 
 
 0.670 
 .672 
 .674 
 
 7i3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 0.603 
 .604 
 .604 
 .606 
 .610 
 .616 
 .623 
 .631 
 
 
 
 
 
 0.621 
 .621 
 .620 
 .622 
 
 .626 
 .632 
 .636 
 
 0.662 
 .662 
 .662 
 .662 
 .663 
 
 -657 
 .656 
 .656 
 .656 
 656 
 .660 
 
 0.644 
 .644 
 .645 
 .644 
 .645 
 .651 
 
 0.631 
 .632 
 .632 
 
 633 
 .636 
 .642 
 
 If we plot certain series of experiments "by Smeaton and 
 Brindley, Poncelet and Lesbro, Du Buat, and Simpson and 
 Blackwell, and take the corresponding series of coefficients 
 from the resulting curves, we have the following results for 
 the given depths and lengths. 
 
 TABLE No. 72. 
 SERIES OF WEIR COEFFICIENTS. 
 
 EXPERIMENTERS. 
 
 !A& 
 
 fc 
 j-T 
 
 DEPTHS UPON WEIR, IN FEET. 
 
 Ft. 
 0.075 
 
 .682 
 .625 
 673 
 .740 
 .615 
 
 Ft. 
 
 O.I 
 
 .667 
 .618 
 .662 
 
 T 3 l 
 
 Ft. 
 
 015 
 
 .640 
 .608 
 6 45 
 
 Ft. 
 
 0.2 
 
 .623 
 .600 
 635 
 .678 
 .700 
 
 Ft. 
 0.25 
 
 613 
 
 597 
 .629 
 
 657 
 .718 
 
 Ft. 
 0-3 
 
 .605 
 
 .624 
 .638 
 735 
 
 Ft. 
 0.4 
 
 .596 
 
 '.608 
 754 
 
 Ft. 
 
 Ft. 
 0.6 
 
 '635 
 577 
 .780 
 
 Ft. 
 0.7 
 
 Ft. 
 
 0.8 
 
 .480 
 
 Ft. 
 
 0.9 
 
 478 
 
 Smeaton and Brindley 
 Poncelet and Lesbros 
 Du Buat 
 
 1-533 
 
 10.0 
 
 .482 
 
 .560 
 
 793 
 
 Simpson and Blackwell 
 
292 MEASURING WEIRS, AND WEIR GAUGING. 
 
 Within the limits of depths covered by the above experi- 
 ments the coefficients all increase as the depths decrease, 
 except in the last series belonging to the 10 foot weir. The 
 curves in each instance begin to bend rapidly at depths of 
 about three-tenths feet. In the two last series above, the 
 convexities of the curves are opposed to each other, and the 
 curves cross at a depth of .275 feet. 
 
 314. Vacuum under the Crest. If the partitions E 
 (Fig. 44) are prolonged below the weir so as to close the 
 ends of the crest contraction, and the fall is slight to surface 
 of tail water, the moving current will withdraw sufficient 
 air from under the fall to produce a vacuum in the crest 
 contraction, from which will result an increased flow over 
 the weir. Such vacuum will take place if the surface of 
 the tail water rises to the level of the crest when there is 
 two and one-half or more inches depth flowing over the weir. 
 
 The tail water may rise near to the crest of the weir, if 
 no vacuum is produced, without materially affecting the 
 volume of flow. 
 
 315. Examples of Initial Velocity. Mr. Francis 
 found that with a half foot depth upon the weir, a half foot 
 per second initial velocity of approach increased the dis- 
 charge about one per cent., and with one foot upon the 
 weir, one foot per second initial velocity increased the dis- 
 charge about two per cent. 
 
 When initial velocity exists in the approaching water, 
 and the flow is irregular, with eddies, results of submerged 
 obstructions or irregular channel, the channel should be 
 corrected, and, if necessary, a grating placed in the stream 
 some distance above the weir, so that the water will ap- 
 proach with steady and even flow upon each side of the 
 channel's axis, so that correct measurements may be taken 
 of the height of the surface of the stream above the weir. 
 
WIDE-CRESTED WEIRS. 293 
 
 316. Wide-Crested Weirs. If the crest of the weir is 
 thickened, as in the case of an unchamfered plank, the jet 
 tends to cross in contact with its full crest breadth, and the 
 contraction is distorted. This is especially the case when 
 the depth upon the weir is less than three inches. 
 
 If the edge receiving the current is not a perfect angle 
 not greater than a right-angle, that is, if it is worn or 
 rounded, the jet tends to follow the crest surface and dis* 
 tort the contraction. 
 
 In such cases the ordinary formula are not applicable, 
 'and the safest remedy is to correct the weir. 
 
 When the weir crest is about three feet wide, and level, 
 with a rising incline to its receiving edge, as in Fig. 47, Mr. 
 Francis suggests a formula for approximate measurements, 
 when end contractions are suppressed, for depths between 
 six and eighteen inches, as follows : 
 
 Q = 3.01208 IH* (12) 
 
 The coefficient m is here .563 approximately. 
 
 FIG. 47. 
 
 < 3-d' 
 
 In Mr. BlackwelTs experiments on weirs three feet wide, 
 both level and inclined downward from the receiving edge 
 to the discharge, coefficients m were obtained, as follows, 
 applicable to the formula 
 
 (13) 
 
294 
 
 MEASURING WEIRS, AND WEIR GAUGING 
 
 TABLE No. 73. 
 COEFFICIENTS FOR WEIR CRESTS THREE FEET WIDE. 
 
 Depths from 
 still water 
 upon the 
 the weir. 
 
 3 feet long, 
 level. 
 
 3 feet long, 
 inclined, 
 i in 18. 
 
 3 feet long, 
 inclined, 
 i in 12. 
 
 6 feet long, 
 level. 
 
 10 feet long, 
 level. 
 
 10 feet long, 
 inclined, 
 i in 18. 
 
 Feet. 
 
 m. 
 
 m. 
 
 m. 
 
 m. 
 
 m. 
 
 in. 
 
 .083 
 
 452 
 
 545 
 
 .467 
 
 .... 
 
 .381 
 
 .467 
 
 .167 
 
 .482 
 
 546 
 
 533 
 
 .... 
 
 479 
 
 495 
 
 .250 
 
 .441 
 
 537 
 
 539 
 
 .492 
 
 .... 
 
 .... 
 
 333 
 
 .419 
 
 431 
 
 455 
 
 497 
 
 .... 
 
 515 
 
 .417 
 
 479 
 
 .516 
 
 
 
 
 
 .518 
 
 .... s 
 
 .500 
 
 .501 
 
 .... 
 
 531 
 
 507 
 
 513 
 
 543 
 
 .583 
 
 .488 
 
 .513 
 
 527 
 
 497 
 
 
 
 .667 
 
 .470 
 
 .491 
 
 .... 
 
 .... 
 
 '.468 
 
 507 
 
 750 
 
 .476 
 
 .492 
 
 .498 
 
 .480 
 
 .486 
 
 
 833 
 
 
 .... 
 
 .... 
 
 465 
 
 455 
 
 
 .917 
 
 .... 
 
 .... 
 
 .... 
 
 .467 
 
 
 
 
 1. 000 
 
 .... 
 
 .... 
 
 .... 
 
 .... 
 
 . . . 
 
 .... 
 
 317. Triangular Notches. Prof. James Thomson, of 
 the University of Glasgow, proposed, in a paper read before 
 the British Association at Leeds, in 1858, a triangular form 
 of measuring weir. In his experiments with such weir, the 
 depths of water varied from 2 to 4 inches, and the volumes 
 from .033 to .6 cubic feet per second. From his experi- 
 ments he derived the formula 
 
 Q = 0.317 
 
 (14) 
 
 The flow for all depths would be through similar tri- 
 angles, therefore an empirical formula applies with greater 
 reliability to varying depths. 
 
 Prof. Thomson claimed that "in the proposed system 
 the quantity flowing comes to be a function of only one 
 variable namely, the measured head of water while in 
 the rectangular notches it is a function of at least two vari- 
 ables, namely, the head of water, and the horizontal width 
 
 
OBSTACLES TO ACCURATE MEASURES 295 
 
 of the notch ; and is commonly also a function of a third 
 variable, namely, the depth from the crest of the notch 
 down to the bottom of the channel of approach." 
 
 When the stream is of such magnitude as to require a 
 considerable number of triangular notches (say of 90 
 angles, or isosceles right-angled triangles) for a single gauge, 
 the greatest nicety will be required to place the inverted 
 apices all in the same exact level, so one measurement of 
 depth only may suffice for all the notches. 
 
 The angles of the notches in each weir must conform 
 exactly to the angles of the notch from which the empirical 
 formula, or series of coefficients for given depths, was de- 
 duced. 
 
 For large volumes of water, the great length required 
 for a sufficient number of notches, as well as depth required 
 in each notch, are often obstacles not easily overcome, and 
 the mechanical refinement necessary to ensure accuracy of 
 measurement is often difficult of attainment. 
 
 318. Obstacles to Accurate Measures. A correct 
 measurement of the depth of water upon a weir is not so 
 easily obtained as might be supposed by those unpractised 
 in hydraulic experiments. 
 
 If the weir is truly level and the shoulders truly vertical, 
 which are results only of good workmanship, and the 
 length intended to be some given number of even feet, the 
 chances are that only a skilled workman will have brought 
 the length within one, two, or even three-thousandths of a 
 foot of the desired length. Again, when the weir is truly 
 adjusted and its length accurately ascertained, it is not 
 easy to measure the depth upon the crest within one or two 
 thousandths of a foot, without excellent mechanical devices 
 for the purpose. 
 
 The errors due to agitation or ripple upon the water and 
 
296 MEASURING WEIRS, AND WEIR GAUGING. 
 
 the capillary attraction of the measuring-rod have to "be 
 eliminated. 
 
 If the graduated measuring-rod is of clean wood, glass, 
 steel, copper, or any metal for which water has an affin- 
 ity, and its surface is moist, or is wetted Iby ripple, the 
 water will, in consequence of capillarity, rise upon it above 
 the true water level ; or if, on the other hand, the rod is 
 greasy, the water may, in consequence of molecular repul- 
 sion, not rise upon it to the true surface level. 
 
 These sources of error may not be of much consequence 
 in gaugings of mountain streams, when the only object is 
 to ascertain approximately the flow from a given watershed ; 
 but in measurements of power, and in tests of motors, tur- 
 bines, and pumps, they are of consequence. 
 
 Upon a weir ten feet long, with one foot depth of water 
 flowing over, an error of one-thousandth of a foot in meas- 
 urement of depth will affect the computation of flow about 
 two cubic feet per minute, and an error of one-thousandth 
 of a foot (about -^ of an inch) in length will affect the com- 
 putation about two-tenths of a cubic foot per minute. 
 
 These amounts of water upon a twenty-five or thirty foot 
 fall would have quite appreciable effects and value. 
 
 319. Hook Gauge. A very ingenious and valuable 
 instrument for accurately ascertaining the true level of the 
 water surface, and depth upon a weir to still water, was 
 invented by Uriah Boy den, C.E., of Boston, and used by 
 him in hydraulic experiments as early as the year 1840. 
 
 This, shown in one of its forms, in Fig. 48, is commonly 
 termed a hook gauge. 
 
 This gauge renders capillary attraction a useful aid to 
 detect error, instead of being a troublesome source of error. 
 
 The instrument is firmly secured to solid substantial 
 beams or a masonry abutment, so that it will be suspended 
 
HOOK GAUGE. 
 
 297 
 
 FIG. 48. 
 
 HOOK GAUGE. 
 
 over the water channel a few feet up- 
 stream from the weir, and where the 
 water surface is protected, naturally 
 or artificially, from the influence of 
 wind and eddies. The gauge is here 
 adjusted at such a height that when it 
 reads zero the point of the hook shall 
 accurately conform to the level of the 
 crest of the weir ; or the vernier reading 
 is to be taken, with the hook at the 
 exact weir level, for a correction of 
 future readings. 
 
 This correction is to be verified as 
 occasion requires between successive ex- 
 periments. 
 
 When the full flow of water over the 
 weir has become uniform, the hook is 
 to be carefully raised by the screw mo- 
 tion, until the point just reaches the 
 surface of the water. If the point is 
 lifted at all above the water surface, the 
 water is lifted with it by capillary at- 
 traction, and the reflection of light from 
 the water surface is distorted and reveals 
 the fact. The screw is then to be re- 
 versed and the point slightly lowered 
 to the true surface. 
 
 In ordinary lights, differences of 
 0.001 of a foot in level of the water are 
 easily detected by aid of the hook, 
 and even 0.0001 of a foot by an expe- 
 rienced observer in a favorable light. 
 Such gauges are ordinarily gradu- 
 
298 MEASURING WEIRS, AND WEIR GAUGES. 
 
 ated to hundredths of a foot and are provided with a ver- 
 nier indicating thousandths of a foot, and fractions of this 
 last measure may be estimated with reliability. 
 
 320. Rule Gauge. For rougher and approximate 
 measures a post is set at an accessible point on one side of 
 the channel, above the weir, and its top cut off level at the 
 exact level of the weir crest. 
 
 The depth of the water is measured by a rule placed 
 vertically on the top of this post and observed with care. 
 
 321. Tube and Scale Gauge. For summer meas- 
 ures, a pipe, say three-fourth inch lead, is passed from the 
 dead water a little above the weir, through or around the 
 weir, and connected to a vertical glass water tube set below 
 the weir at a convenient point of observation. In such case 
 a scale with fine graduations is fastened against the glass 
 with its zero level with the weir. With such an arrange- 
 ment quite accurate observations can be taken, as the 
 water in a three-quarter inch tube will rise to the level of 
 the water above the weir over the open mouth of the tube, 
 due precautions being taken to keep sediment out of the 
 tube. 
 
CHAPTER XV. 
 
 FLOW OF WATER IN OPEN CHANNELS. 
 
 322. Gravity the Origin of Flow. Gravity tends to 
 cause motion in all bodies of water. Its effects upon the 
 flow of water under pressure have been already discussed 
 (Chap. XIII), as have also the effects of the reactions and 
 cohesive attractions that retard its flow. 
 
 The same influences control the flow of water in open 
 channels. 
 
 The fluid particles are attracted toward the earth's 
 centre along that path where the least resistance is op- 
 posed. 
 
 An inclination of water surface of one-thousandth of a 
 foot in one foot distance leaves many thousand molecules 
 of water, but partially supported upon the lower side, and 
 they fall freely in that direction, and by virtue of their 
 weight press forward the advanced particles in lower planes. 
 
 FIG. 49. 
 
 If water is admitted from the reservoir -4, into the open 
 canal B (Fig. 49), until it rises to the level W, it will there 
 stand at rest, although the bottom of the channel is in- 
 clined, for its surface will be in a horizontal plane. The 
 
300 FLOW OF WATER IN OPEN CHANNELS. 
 
 resistances to motion upon opposite inclosing sides, and 
 also upon opposite ends, balance each other. The alge- 
 braic sum of horizontal reactions from the vertical end bd, 
 is exactly equal to the sum of the horizontal reactions from 
 the inclined bottom db', for the vertical projection, or trace 
 of the inclined area, db', exactly equals the vertical area bd. 
 
 The same equilibrium would have resulted if the bot- 
 tom had been horizontal or inclined downward from d to/, 
 and a vertical weir placed at fb', for the horizontal reaction 
 from/ b' would have been balanced by the sum of the hori- 
 zontal reactions from bd and df. 
 
 A destruction of equilibrium permits gravity to generate 
 motion. 
 
 If a constant volume of water is permitted to flow from 
 the reservoir A into the channel B, the water surface will 
 rise above the level bb', when there will be less resistance at 
 the end b' than at &, and the fluid particles, impelled by the 
 force of gravity, will flow toward b'. When motion of the 
 water is fully established, and the flow past b' has become 
 uniform, there will result an inclination of the surface from 
 a toward a'. This inclination, being a resultant of a con- 
 stant force, gravity may be used as a measure of the por- 
 tion of that force that is consumed in maintaining the 
 velocity of flow. 
 
 323. Resistances to Flow. Let the channel be ex- 
 tended from b' (Fig. 49) indefinitely, and with uniform in- 
 clination, as from a' to 7c (Fig. 50). Some resistance to flow 
 will be presented by the roughness and attraction of the 
 sides and bottom of the channel. 
 
 If the sides and bottom are of uniform quality, as re- 
 spects smoothness or roughness, the amount of their resist- 
 ance in each unit of length will be proportional to the sum 
 of their areas, plus the water surface in contact with the 
 

 EQUATIONS OF RESISTANCE AND vLCKY. /01 
 
 / ' j 
 
 air reduced by an experimental fractional coefficient jr,nd } 
 to the square of the velocity of flow past them ; and' iji| - 
 versely to the section of the stream flowing past them. ' </ 
 
 The exact resistance due to the air perimeter, has yet to 
 be separated and classified by a series of careful experi- 
 ments, but we may assume that the resistance of calm air 
 for each unit of free surface will not exceed ten per cent, of 
 that for like units of the bottom and sides of smooth chan- 
 nels, and will bear a less ratio for rough channels. 
 
 The air perimeter resistance will be increased by oppos- 
 ing and lessened by following winds. 
 
 Let H be the sum of resistances from the sides, bottom, 
 and surface, in foot pounds per second ; C, the contour, or 
 wetted area of sides and bottom, and c, the width, or sur- 
 face perimeter, in square feet ; &, the sectional area of the 
 stream, in square feet ; and v, the mean velocity of flow of 
 the stream, in feet per second ; then we have for equation 
 of resistance to flow, from sides, bottom, and surface, for 
 one unit of length : 
 
 and for any length, Z, in lineal feet, 
 
 E = + s ' lC ' x I x mtf. (2) 
 
 324:. Equations of Resistance and Velocity. 
 
 When the surface of the water is level the entire force of 
 gravity acts through it as pressure, but when the surface is 
 inclined, a portion of the pressure is converted into motion. 
 Motion is measured by its rate or distance passed through 
 in the given unit of time, and the rate is expressed by the 
 term velocity. 
 
302 
 
 FLOW OF WATER IN OPEN CHANNELS. 
 
 In Fig. 50, let a'Jc be the inclination of the water surface 
 in a unit of length of the stream, then a"Jc will be its ver- 
 tical distance and Jc'Jc its horizontal distance. 
 
 The effective action of gravity g to maintain motion, or 
 velocity of the water, is dependent on this slope, and the 
 slope is usually indicated by a ratio of the vertical distance 
 to the horizontal distance. 
 
 FIG. 50. 
 
 Let 7i" be the vertical distance, a"Jc and I be the hori- 
 zontal distance Jc'Jc, and i the slope, or sine of the inclina- 
 tion, then the ratio of slope is i = -y-. 
 
 If the sides and bottom of the channel opposed no resist- 
 ance to flow, then the velocity v should be accelerated in 
 the length Jc'Jc an amount equal to the V%gh"-, but the flow 
 being uniform, the sum of the resistances in I just balance 
 the accelerating force of gravity <?, and the velocity v con- 
 tinues from a' to Jc at the same rate that had already been 
 established when the stream reached a', which was due to 
 
 some height aa' = Ji = ~ . 
 
 By transposition, we have v = V2gh. 
 
 If the sum of the resistances in the length Jc'Jc balance 
 the accelerating force due to the head a"Jc = Ji", then we 
 have 
 
 h , l= tf_ x a + .ic, x M . 
 
 m 
 
 (4) 
 
EQUATIONS OF RESISTANCE AND VELOCITY. 303 
 
 8 Section 
 
 The inverted fractional term eT^. = C5ntou^ ls 
 
 termed in open channels the hydraulic mean deptJi^ and 
 the letter r is used to express it. Since i expresses the 
 
 h" 
 value of the sine of tJie slope = -=-, we have 
 
 *. (5) 
 
 h" = . (6) 
 
 The total head H equals the heights aa' + a"Tc = 7i + h", 
 and 
 
 " 2# 2gr " ( r ) * 2^" 
 
 f_?fflH 
 
 V:t 1+I 4j' (8) 
 
 In long canals and rivers, with slopes not exceeding 
 three feet per mile, the velocity head 7i is usually insig- 
 nificant compared with the frictional head 7^", and may be 
 neglected in the equation. 
 
 When the rate of flow is uniform, 7i is a constant quan- 
 tity, independent of the length, and when the mean velocity 
 is known may be taken, by inspection, from the table of 
 " Heads (h) due to given Velocities," page 264. 
 
 The frictional head h" increases with the length, hence 
 the term I in the equation of h". 
 
 nr 
 
 * In full pipes equals the sectional area divided by the full circumfer- 
 L/ 
 
 ence, and is termed the hydraulic mean radius ( 268), but in open channels 
 the contour is the wetted perimeter ; that is, the sum of the sides and bottom 
 and air surface in contact with the water. 
 
304 FLOW OF WATER IN OPEN CHANNELS. 
 
 The mean velocity, which multiplied into the sectional 
 area of the stream will give the volume of discharge, is a 
 quantity often sought. 
 
 v 2 
 Neglecting the value of 7i = , which has given the 
 
 *9 
 
 stream its resultant motion, and taking the formula for A", 
 the head balancing the resistance to flow, 
 
 7 _ Imv* 
 
 : 
 
 and we have by transposition, 
 
 (9) 
 
 in which v = mean velocity of all the films, in feet per sec. 
 
 8f 
 r = hydraulic mean depth = Y in feet. 
 
 O ~f~ (J'iCg 
 
 i = sine of inclination = -j- in feet. 
 
 L 
 
 g = 32.2. 
 
 m a comprehensive variable coefficient. 
 C = wetted earth perimeter. 
 
 c s = surface (air) perimeter, taken at O.lc s for 
 smooth channels, or 0.05c s for rough channels. 
 I = length, referred to a horizontal plane. 
 7i = vertical fall in the given length. 
 
 325. Equation of Inclination. If the flow is to be 
 at some predetermined rate, and it is .desired to find the 
 inclination, or slope to which the given velocity, for the 
 given hydraulic mean radius, is due, then we have, by 
 transposing again, 
 
COEFFICIENTS OF FLOW IN CHANNELS. 305 
 
 The member v, refers to the mean motion of all the fluid 
 threads, or the rate which, multiplied into the section of the 
 stream, gives the volume of flow. 
 
 326. Coefficients of Flow for Channels, The value 
 of the coefficient of flow m, is very variable under the influ- 
 ences of 
 
 (a.) Velocity of flow, or inclination of water surface ; 
 
 (b.) Hydraulic mean depth ; 
 
 (c.) Mean depth ; 
 
 (d.) Smoothness or roughness of the solid perimeter; 
 
 (e.) Direction and force of wind upon the water surface. 
 
 A complete theoretical formula for flow in a straight, 
 smooth, symmetrical channel should have an independent 
 coefficient for each of these influences, and other coefficients 
 for influences of bends, convergence or divergence of banks, 
 and eddy influences ; but such mathematical refinement 
 belongs oftener to the recitation room than to expert field 
 practice. 
 
 The comprehensive coefficient m, for open channels, 
 which includes all these minor modifiers, is inconstant in a 
 degree even greater than the coefficient m for full pipes, 
 which we have already discussed ( 27O. Peculiarities of 
 the Coefficient of Flow), to which the reader is here referred. 
 
 Experience teaches that m is less for large or deep, than 
 for small or shallow streams ; for high velocities, than for 
 low velocities ; and for smooth, than for rough channels. 
 
 Kutter adopted,* for open channels, the simple formula 
 r> = c Vfi, and divided the values of c into twelve classes, 
 to meet the varying conditions, from small to great velocities 
 and sections of streams, and from smooth to rough sides 
 
 * Vide " Hydraulic Tables," trans, by L. D. A. Jackson. London, 1876. 
 
306 
 
 FLOW OF WATER IN OPEN CHANNELS. 
 
 and beds of channels. His c corresponds to y -^, as herein 
 employed, and a portion of its values are : 
 
 r. 
 
 I. 
 
 II. 
 
 III. 
 
 IV. 
 
 V. 
 
 VI. 
 
 VII. 
 
 VIII. 
 
 IX. 
 
 X. 
 
 XI. 
 
 XII. 
 
 5 
 
 S3 
 
 82.5 
 8^.8 
 
 77-9 
 79-5 
 
 72.4 
 74.2 
 
 66.9 
 68.9 
 
 61.1 
 
 63.3 
 
 55,8 
 
 49-5 
 51.8 
 
 43-2 
 45.5 
 
 36.7 
 38.9 
 
 29.7 
 
 22.5 
 24.1 
 
 ;| 
 
 & 
 
 84.8 
 8 S .6 
 
 80.7 
 81.7 
 
 Jlis 
 
 70-5 
 71.9 
 
 65.1 
 66.5 
 
 59-9 
 61.5 
 
 53-8 
 55-4 
 
 47-4 
 49.0 
 
 40.7 
 42.3 
 
 33-4 
 34-9 
 
 25-5 
 26.8 
 
 9 
 
 88.8 
 
 86.4 
 
 82.6 
 
 77-9 
 
 73-o 
 
 
 62.9 
 
 56.9 
 
 5'5 
 
 43-8 
 
 36.2 
 
 28.0 
 
 
 89-3 
 
 87.0 
 
 83-3 
 
 78.7 
 
 74.0 
 
 69.0 
 
 64.1 
 
 58.2 
 
 57-8 
 60 i 
 
 
 37-5 
 
 29.1 
 
 
 
 
 
 
 
 
 
 
 J 
 
 58 7 
 
 
 
 
 
 
 
 
 
 
 
 
 68 3 
 
 62 I 
 
 
 
 
 
 
 
 
 
 
 
 
 
 64 8 
 
 
 45-o 
 
 f 
 
 
 
 
 
 
 
 
 
 
 66*8 
 
 
 
 
 
 
 
 
 
 
 
 
 
 68 K 
 
 I?'"* 
 
 
 I 
 
 
 
 
 
 
 
 
 
 
 
 f '3 
 
 
 
 
 
 
 
 
 
 
 
 2 
 
 
 2.9 
 
 
 9 
 
 
 
 
 
 
 
 
 
 
 
 
 55- 1 
 
 co 
 
 IOO 
 
 IOO 
 
 IOO 
 
 IOO 
 
 IOO 
 
 IOO 
 
 IOO 
 
 IOO 
 
 IOO 
 
 IOO 
 
 IOO 
 
 IOO 
 
 327. Observed Data of Flow in Channels. Let us 
 
 deduce the several values of m from various actual meas- 
 urements of streams, and seek its curve of mean values, so 
 that when it is a divisor of the simple fundamental equation 
 = V2gri y we shall have some degree of confidence in the 
 use of this simple equation for channels and small streams. 
 For this purpose we will select at random from data given 
 by Messrs. Humphreys and Abbott, 1861 ; M.M. Darcy 
 and Bazin, 1865 ; M. Heinr Gerbenau, 1867 ; and sundry 
 reports of U. S. Engineer Corps, and compute the experi- 
 mental value of m for each case.* 
 
 It will be observed that the data cover ranges as follows : 
 Of sectional area, from 9.5 to 15911 sq. feet ; of hydraulic 
 mean depth, from .96 to 15.9 feet; and of velocity, from 
 .817 to 4.689 feet per second, or from three-quarters to about 
 three and one-quarter miles per hour. 
 
 * The same, with additional data for large rivers, has been used by General 
 H. L. Abbott, in a paper upon Gauging of Rivers, for the purpose of testing 
 the new (Humphreys and Abbott) formula for flow of rivers, vide Jour. Frank- 
 lin Institute, May, 1873. 
 
TABLE OF COEFFICIENTS FOR CHANNELS. 
 
 307 
 
 TABLE No. 74. 
 
 OBSERVED AND COMPUTED FLOWS IN CANALS AND RIVERS, 
 ( 2 gri 
 
 AND m = 
 
 
 A. 
 
 B. 
 
 C. 
 
 D. 
 
 E. 
 
 F. 
 
 G. 
 
 NAME OF STREAM. 
 
 t*j 
 
 II 
 
 8 
 
 53 
 
 Wetted 
 Perimeter 
 = C. 
 
 in 
 
 s-a 
 *f 
 
 EQ 
 
 Inclination 
 = /. 
 
 Observed 
 Velocity 
 
 Value of 
 Coefficient 
 = tn. 
 
 Computed 
 Velocity 
 
 = V. 
 
 Feeder Chazilly 
 
 Sq.ft. 
 
 9-5 
 
 Feet. 
 
 O.Q 
 
 Feet. 
 0.96 
 
 Feet. 
 
 0.000792 
 
 Feet. 
 1.234 
 
 .03215 
 
 Feet. 
 
 
 
 10.8 
 
 1.04 
 
 
 0.962 
 
 .03227 
 
 o 966 
 
 tt <t 
 
 14.0 
 
 12.3 
 
 1. 21 
 
 .000808 
 
 1.667 
 
 .02265 
 
 
 it u 
 
 18.1 
 
 13-1 
 
 1.38 
 
 .000450 
 
 1.296 
 
 .02381 
 
 1.275 
 
 a it 
 
 18.8 
 
 13.3 
 
 I.4I 
 
 
 1.798 
 
 .02789 
 
 1.926 
 
 44 14 
 
 
 13.8 
 
 I.4I 
 
 0008 58 
 
 1.815 
 
 .02363 
 
 
 U It 
 
 
 
 
 000086 
 
 
 
 
 11 il 
 
 22.9 
 
 14.7 
 
 IJ6 
 
 000842 
 
 1.998 
 
 .02118 
 
 
 a n 
 
 
 15.9 
 
 I 71 
 
 
 
 
 
 Feeder Grobois . . 
 
 
 IO.2 
 
 0.98 
 
 .000555 
 
 0.984 
 
 .03617 
 
 
 
 n.8 
 
 xi. 3 
 
 1.05 
 
 .000310 
 
 0.817 
 
 .03155 
 
 0.852 
 
 U it 
 
 17.2 
 
 12.5 
 
 1.38 
 
 .000450 
 
 1.326 
 
 .02274 
 
 I 278 
 
 it 41 
 
 
 14.1 
 
 1.63 
 
 
 
 
 
 It U 
 
 25.0 
 
 14.1 
 
 1.71 
 
 .000515 
 
 1.746 
 
 .01860 
 
 1.617 
 
 it it 
 
 26.8 
 30.8 
 
 15.7 
 17.3 
 
 ?* 
 
 .000493 
 .000275 
 
 1.683 
 
 1.467 
 
 .01917 
 
 1.585 
 
 1.231 
 
 It tt 
 
 02 ,O 
 
 17.3 
 
 is 
 
 
 
 
 I 781 
 
 Speyerbach . . .... 
 
 3O.2 
 
 19.7 
 
 1.54 
 
 .000467 
 
 1.814 
 
 .01408 
 
 I 422 
 
 Canal 
 
 
 20. 6 
 
 2.40 
 
 
 
 
 
 Lauter Canal 
 
 56.4 
 
 31.0 
 
 1.82 
 
 .000664 
 
 2.^06 
 
 .01754 
 
 
 Saalach 
 
 86.9 
 
 61.2 
 
 1.38 
 
 
 
 01082 
 
 
 
 96.7 
 
 71.8 
 
 1.34 
 
 .001136 
 
 1.970 
 
 .02585 
 
 ligio 
 
 1C 
 
 119 O 
 
 32.5 
 
 3-7 
 
 .000698 
 
 
 
 
 C. and O C. Feeder 
 
 121. 
 
 32.7 
 
 3-7 
 
 .000699 
 
 3.032 
 
 .01811 
 
 0. C27 
 
 River Haine 
 
 248.5 
 
 50.5 
 
 4.90 
 
 
 
 00836 
 
 
 Isaa 
 
 3OO.I 
 
 161.6 
 
 1.85 
 
 .002500 
 
 
 .01864 
 
 7.8l2 
 
 
 006.4 
 
 53-4 
 
 5 7 
 
 
 2 s<;8 
 
 00869 
 
 2 328 
 
 Seine . . . 
 
 1978 
 
 
 
 
 
 
 
 B. La Fourche 
 
 2868 
 
 230 
 
 
 
 2* C 8o 
 
 
 
 
 
 
 
 
 Z 
 
 
 
 tt 
 
 3708 
 
 238 
 
 
 
 
 
 3 145 
 
 Seine 
 
 
 
 
 
 
 
 3 8lO 
 
 
 
 
 
 * 
 
 
 .007 
 
 
 tt 
 
 8O34 
 
 
 
 
 4.232 
 
 4 682 
 
 
 6 126 
 
 (i 
 
 
 cxo 
 
 18 40 
 
 
 A 680 
 
 
 
 Rhine ... 
 
 
 I45 8 
 
 
 
 
 00828 
 
 
 Upper Mississippi 
 
 icgll 
 
 1612 
 
 9.87 
 
 .000074 
 
 
 
 2.554 
 
 
 
 
 
 
 
 
 
 328. Table of Coefficients for Channels. From 
 the experimental results we deduce the following values of 
 m for the given hydraulic mean depths. Since 2g is a con- 
 stant, we have also the corresponding values A /%?. 
 
 V m 
 
308 
 
 FLOW OF WATER IN OPEN CHANNELS. 
 
 TABLE No. 75. 
 
 VALUES OF m FOR OPEN CHANNELS, AND VALUES OF A / M. 
 FOR GIVEN HYDRAULIC MEAN DEPTHS. 
 
 .9 
 
 = c. 
 
 T. 
 
 4/^ 
 
 r 
 
 r-- 9 - 
 C 
 
 m. 
 
 4/. 
 
 V m 
 
 25 
 
 .0500 
 
 35-89 
 
 7 
 
 .0096 
 
 81.90 
 
 3 
 
 .0478 
 
 36.70 
 
 7-5 
 
 .0092 
 
 83.66 
 
 4 
 
 .0440 
 
 38.25 
 
 8 
 
 .0088 
 
 85-54 
 
 5 
 
 .0408 
 
 39-73 
 
 8-5 
 
 .0085 
 
 87.04 
 
 .6 
 
 .0378 
 
 41.27 
 
 9 
 
 .008I 
 
 89.16 
 
 7 
 
 353 
 
 42.71 
 
 9-5 
 
 .0077 
 
 9J-45 
 
 .8 
 
 0332 
 
 44.04 
 
 10 
 
 .0074 
 
 93-28 
 
 -9 
 
 .0312 
 
 45-43 
 
 ii 
 
 .0068 
 
 97.3i 
 
 1.0 
 
 .0298 
 
 46.49 
 
 12 
 
 .0064 
 
 100.30 
 
 1.25 
 
 .0260 
 
 49-77 
 
 13 
 
 .0058 
 
 105.36 
 
 i-5 
 
 .0234 
 
 52.46 
 
 14 
 
 .0054 
 
 109.21 
 
 2 
 
 .0197 
 
 57-17 
 
 15 
 
 .0049 
 
 . 114.65 
 
 2-5 
 
 .0172 
 
 61 . 19 
 
 16 
 
 .0043 
 
 122.37 
 
 3 
 
 OI 53 
 
 64.87 
 
 17 
 
 .0040 
 
 126.88 
 
 3-5 
 
 .0137 
 
 68.56 
 
 18 
 
 .0036 
 
 133.77 
 
 4 
 
 .0127 
 
 71.21 
 
 J 9 
 
 .0033 
 
 139.69 
 
 4-5 
 
 .0118 
 
 73-87 
 
 20 
 
 .0030 
 
 146.53 
 
 5 
 
 .0112 
 
 75-83 
 
 21 
 
 .OO29 
 
 149.04 
 
 5-5 
 
 .0107 
 
 77.58 
 
 22 
 
 .OO27 
 
 154-44 
 
 6 
 
 .0102 
 
 79.46 
 
 23 
 
 .OO25 
 
 160.49 
 
 6.5 
 
 .0099 
 
 80.65 
 
 25 
 
 .O02O 
 
 179.44 
 
 These values of m and of 
 
 were inserted in the 
 m 
 
 were used for a 
 
 simple formula, v = \\/ -2 Vri[ , and 
 
 test to compute the velocities in the column G, of the above 
 table of experimental data. The computed velocities may 
 there be compared with the observed velocities. The results 
 are satisfactory, if the exceeding difficulty of securing an 
 accurate measurement of mean velocity of the stream and. 
 the probability of small errors are considered. 
 
VARIOUS FORMULAS OF FLOW COMPARED. 309 
 
 The velocities in the experimental table albove, cover the 
 range in ordinary practice, excepting the extremes of floods 
 and droughts. The values of m are for the mean range of 
 velocities there given. A considerable increase of velocity 
 would reduce, or of roughness of channel would increase, 
 the value of m for its given hydraulic mean depth. The 
 influences of bends and eddies are to be eliminated from the 
 formula, since the formula applies to a straight, smooth, 
 symmetrical channel. 
 
 Jackson gives,* from Darcy, Bazin, Gauguillet, and 
 Kutter, variable coefficients for the channel surfaces named, 
 as follows. (These appear to be applicable to a constant 
 value of v, equal to about 2.5.) : 
 
 .018, Well-planed plank. 
 
 .020, Glazed pipes, or smooth cement lining. 
 
 .022, Smooth cement and sand mortar lining. 
 
 .024, Unplaned plank. 
 
 .026, Brickwork and cut-stone lining. 
 
 .034, Rubble masonry lining. 
 
 .040, Canals, in very firm gravel. 
 
 .050, Rivers in earth, free from stones and weeds. 
 
 .070,, " with stones and weeds in great quantities. 
 
 329. Various Formulas of Flow Compared. To 
 compare this simple formula, having its variable w, with 
 some of the more complex formulas, in the forms in which 
 they are generally quoted in text-books and cyclopedias, 
 four experiments are taken from the table, having their 
 hydraulic mean depths and sectional areas of mean, mini- 
 mum, and maximum values, and their velocities are com- 
 puted by it. The velocities are then computed by well- 
 known formulas upon the same data. The results are given 
 in the following table : 
 
 * Hydraulic Manual. London, 1875. 
 
310 
 
 FLOW OF WATER IN OPEN CHANNELS. 
 
 TABLE No. 76. 
 FORMULAS FOR FLOW OF WATER IN CHANNELS, TO FIND THE VELOCITY. 
 
 Comparing results given by the several formulas. 
 
 AUTHORITY. 
 
 FORMULAS. 
 
 FEEDER 
 CHAZILLY.* 
 
 LAUTER 
 CANAL.! 
 
 1 
 
 i 
 
 Cfl 
 
 4 
 
 "I 
 
 Eq. (9), 324 
 Du Buat 
 
 Eytelwein . . . 
 Girard 
 
 ..JJt.rfU... 
 
 Com- 
 puted 
 veloc. 
 in ft. 
 Per 
 sec. 
 
 0.966 
 1.929 
 
 1.932 
 1.109 
 1.962 
 1.932 
 2.161 
 2.151 
 
 2.151 
 
 Com- 
 puted 
 veloc. 
 in ft. 
 Per 
 sec. 
 
 1-934 
 3.627 
 
 3.184 
 2.289 
 3-352 
 3.184 
 S'fyS 
 3.338 
 
 3-438 
 3.438 
 2.086 
 
 1-747 
 2.078 
 
 Com- 
 puted 
 veloc. 
 in ft. 
 Per 
 sec. 
 
 2.107 
 2.411 
 
 2.442 
 1-572 
 2-545 
 2-435 
 2.778 
 2.691 
 
 2.691 
 2.691 
 2.166 
 2.350 
 2.642 
 
 Com- 
 puted 
 veloc. 
 in ft. 
 per 
 sec. 
 
 3-145 
 2.143 
 
 2.382 
 1-517 
 2.479. 
 2418 
 2.706 
 2.627; 
 
 2.627 
 2.627 
 2.582; 
 3.268 
 4-582 
 
 ( m ) 
 88.51 (r*-. 03) _ ^ Q3) 
 
 (_L)i_hyp.log. Q-+X.6)* 
 
 v = (10567.8?? + 2.67)^ 1.64 
 
 D'Aubuisson. 
 Neville 
 
 T f c i:/ 
 
 
 
 ioo 4/r" 
 
 Pole 
 
 */? 
 
 ( AS) i 
 
 Beardmore. . . 
 
 Darcy and I 
 Bazin. f 
 
 M. Hagen.... 
 
 Humphreys ) 
 and Abbott, f 
 
 r ** ic \ 
 
 \ IOOOZ J 1. 
 
 1.047 
 1.237 
 1.372 
 
 { .o8 534 r + .35 J 
 w = 4-39^(0* 
 
 i./ - /-^fTV .^-1* 2-4^ 
 
 ^ ~\ \/ .0081^+1 5 ' I .09 \b r ,. 
 
 (r W+w^/ ) 1+ ^ 
 
 * FEEDER CHAZILLY. Area, 11.3 sq. ft. Hydraulic mean depth, 1.04 ft Inclination, .000445. 
 Observed velocity, 0.962 ft. 
 
 t LAUTER CANAL. Area, 564 sq.ft. Hydraulic mean depth, 1.82 ft. Inclination, 000664. 
 Observed velocity, 2.106 ft. 
 
 $ SEINE. Area, 1978 sq. ft. Hydraulic mean depth, 5. 70 ft. Inclination, .000127. Ob- 
 served velocity, 2.094 ft. , 
 
 B. LA FOURCHE. Area, 3738 sq. ft. Hydraulic mean depth, 15.7 ft. Inclination, .000044- 
 Observed velocity, 3.076 It. 
 
VELOCITIES OF GIVEN FILMS. 311 
 
 In the preceding table, the symbols in the formulas have 
 values as follows : 
 
 r = hydraulic mean depth, in feet. 
 i = inclination of surface in straight channel, in feet. 
 I = length, in feet. 
 
 7i = head, or fall in the given length, in feet. 
 S = sectional area of stream, in square feet. 
 O = wetted solid perimeter, in feet. 
 v = mean velocity of stream, in feet per second. 
 
 In the Humphreys and Abbotts' formula, the symbols 
 have values as follows : 
 
 a = sectional area of stream, in square feet. 
 
 1 69 
 5 = a function of depth = 
 
 Vr + 1.5 
 p = wetted perimeter. 
 
 r = mean hydraulic depth. 
 
 i inclination of surface of stream, corrected for bends. 
 W = width of stream. 
 
 v' = value of first term in the expression for v. 
 v = mean velocity of stream. 
 
 33O. Velocities of Given Films. Since the chief 
 source of resistance to flow arises from the reactions at the 
 perimeter of the stream, along the bottom and sides, A, B, 
 B', A', Fig. 51, and in a small degree along the surface 
 A, A, in contact with the air, it is evident that the points 
 of minimum velocity will be along the solid perimeter, and 
 the point of maximum velocity will be that least influenced 
 by the resultant of all retarding influences. In a channel 
 of symmetrical section, the point of maximum velocity 
 should be, according to the above hypothesis, on a vertical 
 line passing through the centre of the section and a little 
 below the water surface, provided the surface was unin- 
 
312 
 
 FLOW OF WATER IN OPEN CHANNELS. 
 
 fluenced "by wind. The velocity measurements of Darcy 
 and Bazin*with an improved "Pitot" Tube, locate the 
 thread of maximum velocity in a trapezoidal channel, at a, 
 Fig. 51 ; a nearly concentric film of lesser velocity at &, and 
 other films, decreasing regularly in velocity, at c, d, e, f, 
 and g. 
 
 If the velocities, at the depths at which the given films 
 cross a vertical centre line, are plotted as ordinates from a 
 vertical line, as at a, &, c, etc., Fig. 52, their extremities will 
 lie in a parabolic curve, and the degree of curvature will be 
 less or greater as the velocity is less or greater, and as the 
 bottom is smoother or rougher, for the given section. 
 Velocity ordinates, plotted in the same manner for any 
 horizontal section, as in the surface, or through , a, &, c, 
 etc., Fig. 51, will also have their extremities from shore 
 
 FIG. 51. 
 
 FIG. 52. 
 
 nearly to the centre in parabolic curves, the longest ordi- 
 nate being near the centre of breadth of the canal, and the 
 two side parabolas being connected by a curve more or less 
 flat, according to breadth of canal. In Fig. 51, d indicates 
 the film of mean velocity, and it cuts the central vertical line 
 at nearly three-fourths the depth from the surface. In 
 deep streams, or channels in earth, it is usually a little 
 below the centre of depth. 
 
 * Tome XIX des Memoires presentes par divers Savants a 1'Institut Impe- 
 rial de France, Planche 4. 
 
SURFACE VELOCITIES. 313 
 
 331. Surface Velocities. The velocity of the centre 
 of the surface, in symmetrical channels, or of the mid- 
 channel in unsymmetrical sections, is that most readily 
 obtainable by simple experiment. 
 
 For such velocity observations a given length, say one 
 hundred feet of the smoothest and most symmetrical 
 straight channel accessible is marked off by stations on 
 both banks, and a wire stretched across at each end at 
 right angles to the axis of the channel. Thin cylindrical 
 floats are then put in the centre of the stream a short dis- 
 tance above the upper wire, by an assistant, and the time 
 of their passing each wire accurately noted. 
 
 A transit instrument at each end station is requisite for 
 very close observations. A small gong-bell, on a stand or 
 post beside the transit, is to be struck by the observer the 
 instant the centre of the float passes the cross-hair, or a 
 signal is to be transmitted by an electric current, and the 
 time, noted to the nearest quarter-second by a skillful 
 assistant, is to be recorded. 
 
 The floats are sometimes of wax, weighted until its 
 specific gravity is near unity ; sometimes a short, thick vial, 
 corked, and containing a few shot or pebbles ; and some- 
 times a thin slice of wood cut from a turned cylinder, which 
 for small channels may be two inches diameter. For large 
 rivers, the float may be a short keg, with both heads in 
 place, and weighted with gravel stones. The float is to be 
 loaded so its top end will be just above the surface of the 
 water. In broad streams, a small flag may be placed in the 
 centre of the float. 
 
 If a number of floats are started simultaneously at 
 known distances on each side of the axis of the channel, 
 they should have each a special color-mark or conspicuous 
 flag number, so that the time and distance from axis, at 
 
314 FLOW OF WATER IN OPEN CHANNELS. 
 
 each station, may be correctly noted for each individual 
 float. 
 
 Du Buat made experiments with small rectangular and 
 trapezoidal channels of plank, 141 feet long and about 
 18 inches wide, with depths from .17 to .895 feet, and veloc- 
 ities from .524 to 4.26 feet, to determine the ratio of the 
 mean velocity v of the channel section to its central surface 
 velocity, V. From the mean results he deduced the empi- 
 rical formula, 
 
 v = (A/T .15) 2 + .02233. (11) 
 
 This gives, when Fis taken as unity, 
 v = .545 V. 
 
 Prony afterwards, reviewing the same experimental re- 
 sults, proposed the formula, 
 
 _ F /F+ 7.782\ . 
 \ V + 10.345/ " 
 
 Ximenes' experiments upon the River Arno, Raucort's 
 upon the Neva, Funk's upon the Wesser, Defontaines and 
 Brunning's upon the Rhine, on larger scales, gave mean 
 velocities in a vertical line at the centre equal to .915 F, 
 which being the maximum velocity in its horizontal plane, 
 indicates, if the reduction of velocity toward the shore is 
 considered, an approximate mean velocity, 
 
 v = .915 (.915 F) = .837 F. (13) 
 
 Mr. Francis' experiments in a smooth, rectangular chan- 
 nel, with section about 10 feet broad and 8 feet deep, and 
 velocity of 4 feet per second, indicates 
 
 <y = .911F. (14) 
 
 In the Mississippi River, with depths exceeding one 
 
RATIOS OF SURFACE TO MEAN VELOCITIES. 315 
 
 hundred feet, Messrs. Humphreys and Abbott occasionally 
 found v greater than V. 
 
 The Ganges Canal experiments at Roorkee, in 1875, by 
 Capt. Cunningham, R. E., in a rectangular section 9 feet 
 deep and 85 feet wide, gave the mean surface velocity 
 equal to. 927 V. 
 
 In any series of rectangular channels of like constant 
 sectional areas or of like constant borders, it is seen, by 
 simple mathematical demonstrations, that the hydraulic 
 
 Sf 
 mean depth = -~, is at its maximum when the breadth 
 
 
 
 equals twice the depth.* Since the velocity of flow in a 
 series of rectangular channels is nearly proportional to the 
 square roots of their hydraulic mean depths, it follows that 
 the proportions of such channels most favorable for high 
 velocities is breadth equal twice depth. 
 
 These proportions of breadth to depth being adopted 
 again for another series of rectangular channels of varying 
 section, the velocities will again be sensibly proportional to 
 the square roots of their hydraulic mean depths. 
 
 The ratio of v to V should be at its maximum when 
 breadth equals twice the depth, and when the section is the 
 maximum of the given series. . 
 
 332. Ratios of Surface to Mean Velocities. Let 
 d depth and b = breadth of rectangular channels, then 
 letting depth be unity for a depth of 8 feet and approxi- 
 mately between 6 and 12 feet, and we shall have, according 
 to the various recorded experiments, approximate values 
 of the mean velocity v of flow in the channel, as compared 
 with the central surface velocity V, as follows, for smooth 
 channels : 
 
 * The influence of sectional profile upon flow is elaborately discussed by 
 Downing, in Elements of Practical Hydraulics, p. 204, et seq. (London, 1875.) 
 
316 
 
 FLOW OF WATER IN OPEN CHANNELS. 
 
 When 
 
 b = 2d 
 
 b = 3d 
 
 b = 4d 
 
 b = 5d 
 
 b = 6d 
 
 b = 7d 
 
 b = 8d 
 
 b = 9d 
 b = lOd 
 
 then 
 
 V = 
 
 V 
 
 V = 
 
 V = 
 
 V = 
 
 = .920F 
 = .910 F 
 = .896F 
 
 = .882F 
 = .864F 
 = .847F 
 .826F 
 .804F 
 .780F 
 
 (15) 
 
 The values of v should be slightly less for trapezoidal 
 canals of equal sections, decreasing as the side slopes are 
 flattened. The values of v will decrease also as the bottom 
 and sides increase in roughness. The wind may enhance 
 or retard the surface motion, and thus affect the mean 
 velocity. 
 
 Since inclination of water surface, section of stream, 
 hydraulic mean depth, and roughness of bottom and side, 
 all affect the final result of flow, it is evident that experi- 
 ence and good judgment will aid materially in the selection 
 of the proper ratio of v to F. A misapplication of formulae 
 that are valuable when judiciously used, may lead to gross 
 errors; as, for instance, Prony's formula, deduced from 
 experiments with Du Buat's small canal, gave result fifteen 
 per cent, too small when tested by the flow in the Lowell 
 flume, 10 feet wide and 8 feet deep, where the volume was 
 proved by tube floats and weir measurements at the same 
 time. 
 
 333. Hydrometer Gaugings. When opportunity 
 offers, the mean velocity for the whole depth should be 
 measured, and thus some of the uncertainties accompany- 
 ing surface measures be eliminated. Among the most 
 reliable hydrometers that have been used for this purpose 
 
TUBE GAUGE. 317 
 
 in canals and the smaller rivers may be mentioned, tin tubes 
 of length nearly equal to the depth of the stream ; improved 
 " Pitot tubes ; " and " Woltmann tachometers" 
 
 334. Tube Gauge. When the velocity measurements 
 are to be taken with Francis' tubes or Krayenhoff poles, 
 Fig. 53, a straight section of the stream is chosen, with 
 smooth symmetrical channel, clear of weeds and obstruc- 
 tions. A length of one hundred or more feet, according to 
 circumstances, is marked off by stations at each end on 
 each bank, located so as to mark lines at right angles to the 
 axis of the stream. A steel measuring chain, or wire with 
 marks at equal intervals, is then to be stretched across at 
 each end. The depths are then to be taken across the stream 
 at each end, and at the centre if the banks are warped, at 
 known intervals of a few feet, accord- 
 ing to the formation of the banks and 
 bottom of the stream, so that the sec- 
 tional area of the stream shall be 
 accurately known, and may be plot- 
 ted. The soundings are all to refer 
 to the same datum previously estab- 
 lished, and referred to a permanent 
 bench mark on the shore, which will greatly facilitate 
 future observations or verifications at the same point. 
 
 The requisite number of tight tin tubes, of say two 
 inches diameter,* are then to be prepared, one for the axis 
 of the stream, and others for short successive intervals on 
 each side of the axis, all to be duly numbered for their 
 respective positions. The length of each is to be such that 
 it will float just clear of the bottom, and extend to a little 
 above the water surface. The tube is to be loaded at one 
 
 './, /. ,-... ,/,,/ .,/, , 
 
 * Tubes 40 feet long, 3 inches diameter, made up in sections, have been, 
 used by the United States Coast Survey Staff. 
 
318 FLOW OF WATER IN OPEN CHANNELS. 
 
 end with fine shot or sand, until it has the proper sub- 
 mergence in a vertical position. 
 
 The several tubes are to be started by signal, simultane- 
 ously if possible, from a short distance above the upper end 
 station, so that they may cross the upper station as nearly 
 as possible at the same instant. Their arrivals at the lower 
 stations are to be carefully noted, and the time of transit of 
 
 each recorded. 
 
 When the experiment has been several times repeated, 
 the central and other tubes may be passed down singly, if 
 the volume of the stream still remains constant, to verify the 
 first observations. In the last observations, transits may 
 conveniently be used to observe the passage by the stations, 
 as suggested above for observing surface floats. 
 
 Suppose the stream to be divided transversely into seven 
 sections, as in Fig. 54, then tubes 1, 2, 3, etc., may be started 
 
 FIG. 54. 
 
 in the centres of their respective sections. The degree of 
 accuracy with which they will move along their intended 
 courses will depend upon the symmetrical regularity of 
 flow, and very much upon the regularity of the side banks, 
 and several trials may be necessary to get satisfactory 
 side and even central measurements, since a slight obstruc- 
 iion, or a stray boulder upon the bottom, may distort the 
 Huid threads in an unaccountable manner. The side floats 
 have also a tendency away from shore. 
 
 The mean area of each of the sub-sections being known, 
 ,and the mean velocity through each being ascertained, 
 
GAUGE FOKMULAS. 319 
 
 their product gives the volume flowing through, and the 
 sum of volumes of the sub-section gives the volume for the 
 whole section. 
 
 When streams are in the least liable to fluctuations from 
 the opening or closing of sluices above, or the opening or 
 closing of turbine gates when the stream is used for hy- 
 draulic power, a hook-gauge (Fig. 48), should be placed 
 over the axis of the stream where the usual vibration of 
 surface is least, to watch for such fluctuations, since a vari- 
 ation in the mean level of the water surface one-hundredth 
 of a foot will appreciably affect the velocity and volume of 
 flow. If the tubes have much clearance they will not be 
 influenced by the films of slowest velocity next the bottom. 
 A clearance of six inches in a rectangular flume eight feet 
 deep, may give an excess of three per cent, of velocity. 
 The cross-section depths, in canals and shallow streams, 
 may be taken with a graduated sounding-rod having a flat 
 disk of three or four inches diameter at its foot, and in deep 
 streams by a measuring-chain with a sufficient weight upon 
 its foot to maintain it straight and vertical in the current. 
 A good level instrument and level staff are requisite, how- 
 ever, for accurate work. 
 
 In broad streams the transverse stations may be located 
 trigonometrically by two transits placed at the extremities 
 of a carefully measured base line upon the shore. 
 
 335. Gauge Formulas. The volume of flow through 
 the mean transverse section (Fig. 64) is required. 
 
 Let s be the established length, or distance between the 
 longitudinal end stations, and A 4 4 4 the times occu- 
 pied by the several tubes in passing along their respective 
 courses between end stations ; then the mean velocities in 
 the respective sub-sections will be 
 
 s s s s 
 
320 
 
 FLOW OF WATER IN OPEN CHANNELS. 
 
 Let the transverse breadths of the sub-sections be, a l a z a 3 . . . . a,^ 
 " " mean depths " " " d t d a d 3 . . . . d n . 
 
 " " mean velocities in " " " v t a v 3 . . . . v n . 
 
 " " " volumes of flow in " q 1 q 2 q 3 . . . . q n . 
 
 Then the whole sectional area in square feet, $, of the 
 stream is, 
 
 8 = i . d l + a 2 . d 2 + a 3 . d B + . . . . a n . d n ; (16) 
 and the whole volume in cubic feet, <2, is 
 Q = fa. d { ) Vt + (a 2 . d 2 ) v 2 + ( 3 .^3)^3 + ... (a n d,>) v n ; (17) 
 and the mean velocity in feet per second, v, of the whole 
 section is, 
 
 |- . (18) 
 
 The summary of field notes, beginning at a on the left 
 shore, is : 
 
 Breadths of sub-sections 
 Mean depths of 
 Mean velocities in the I 
 sub-sections f 
 
 Feet, 
 a ! 16.45 
 </i 4-85 
 
 Z>! 2.25 
 
 Cu. //. 
 
 fi J 79-5 
 
 Feet. 
 
 a, 2 20,00 
 d* 9.74 
 
 v z 3.80 
 
 Cu.ft. 
 q* 740.2 
 
 Feet. 
 
 a 3 24.85 
 d a 12.37 
 
 v 3 4.62 
 
 Cu.ft. 
 q 3 1420.2 
 
 Feet. 
 
 a 32.00 
 di 15.68 
 
 v* 5-oo 
 Cu.ft. 
 ? 4 2508.8 
 
 Feet. 
 
 a* 29.50 
 d 6 12.52 
 
 v s 4-65 
 Cu.ft. 
 g s 1717-4 
 
 Feet. 
 
 a 26.80 
 d 9.71 
 
 3'7S 
 Cu.ft. 
 fo 975-8 
 
 Feet. 
 a 7 18.24 
 ^7 4-79 
 
 t/ 7 2.00 
 
 Cu.ft. 
 
 q-, 174.7 
 
 f.* 
 
 [ = c. 
 
 Volume in the sub-sec- j 
 
 
 The sum of the several products of breadth into depth is 
 S = 1800.675 square feet. 
 
 The sum of the several volumes is Q = 7716.73 
 
 Q 7716 73 
 
 The mean velocity for the whole section is ^ ^ Q( ^^ a ^ K 
 
 o loOU.bTo 
 
 = v = 4.285 feet per second. 
 
 If the tubes have several inches clearance at the bot- 
 tom, a slight reduction, say two and a half per cent., from 
 the computed velocity and volume are to be made, to com- 
 pensate therefor. 
 
 336. Pitot Tube Gauge. The Pitot tube has been 
 used with a tolerable degree of success in many experi- 
 ments upon a small scale. In its best simple form it has 
 
PITOT'S TUBE. 
 
 321 
 
 FIG. 55. 
 
 been constructed of glass tubing swelled into a bulb near 
 one end, and with tube of smaller diameter below the bulb 
 bent at a right angle, and terminated with an expanded 
 trumpet-mouth, as in Fig. 55. 
 
 For deep measures the mouth and bulb and a con- 
 venient part of the tube may be of copper, that part which 
 is to project above the surface 
 of the water being of glass, and 
 the whole instrument may be at- 
 tached to a vertical rod, which 
 rests on the bottom, so as to be 
 slid up and down on the rod to 
 the heights of the several films 
 whose velocities are required. 
 
 When in use, the bulb and 
 tube are to be held vertically, ^^ 
 and the small trumpet-mouthed 
 section exposed horizontally to the current so as to receive 
 its maximum force into the mouth. 
 
 The object of the expanded bulb and contraction below 
 the bulb is to reduce oscillation of the water within the tube 
 to a minimum. 
 
 Theoretically the impulse of the current, acting as pres- 
 sure on the water within the tube, should raise the surface 
 
 v 2 
 of the water within, a height, 7i = ~-, above the normal 
 
 f *9 
 
 surface. 
 
 But owing to reactions from several parts of the tube, 
 the entire force of the current does not act upon the column 
 of water in the vertical section of the tube, hence the eleva- 
 tion of the water in the tube is cji and 
 
 PITOT S TUBE. 
 
 - = cji and v = 
 
 (19) 
 
 21 
 
322 FLOW OF WATER IN OPEN CHANNELS. 
 
 The coefficient c , for the given tube and the different 
 velocities, must be determined by experiment before it can 
 be used for practical measures. 
 
 The stream is cross-sectioned, as before described for 
 the leading station when long tin tubes are used, and 
 the mean velocity is ascertained from the mean velocity of 
 the various superposed films taken in a vertical line at the 
 centre of each sub-section. 
 
 The computations of volume are made in a manner sim- 
 ilar to those when tubes are used. 
 
 Pitot introduced a plain tube bent at right angles as 
 early as 1730, and by his measurements with it in the Seine 
 and other streams, overthrew some of the hypotheses of the 
 older hydraulicians. 
 
 It has since received a variety of forms and entered into 
 a variety of combinations, among which may be mentioned 
 the " Darcy-Pitot " tube, which, after an instantaneous 
 closing of a stop-cock, can be lifted up for an observation, 
 and the Darcy double tube, but there is still difficulty in 
 reading by its graduations measures of small velocities, with 
 sufficient accuracy, and the capillarity may be a source of 
 error in un skillful hands. 
 
 The almost exclusive use of this instrument in improved 
 forms by Darcy and Bazin in their valuable series of ex- 
 perimental observations, has given to it prominent rank 
 among hydrometers. 
 
 337. Woltmann's Tachometer. The most success- 
 ful of all the simple mechanical hydrometers, not requiring 
 the assistance of an electric battery, has been the revolving 
 mill introduced by Woltmann in 1790, and known as 
 " Woltmanrts Tachometer" or moulinet. This current 
 meter has from two to five blades, either flat or like marine 
 propeller blades, set upon a horizontal shaft as shown in 
 
WOLTMANN'S TACHOMETER. 
 
 323 
 
 Fig. 56, which represents the entire instrument * in its actual 
 magnitude, for small canal and flume measures. 
 
 Upon the main axle, which carries the propeller, is a 
 worm-screw, G. A series of toothed wheels and pinions, 
 with pointers and dials similar to the registering apparatus 
 
 FIG. 56. 
 
 WOLTMANN'S TACHOMETER. 
 
 of a water or gas meter, are hung in a light frame, (?, imme- 
 diately beneath the main axle. One end of the frame is 
 movable upward and downward, but when out of use is 
 held down by a spring, F. 
 
 The whole instrument is secured by a set-screw upon an 
 Iron rod, Z>, on which it may be set at any desired height. 
 
 * Another form with two blades is illustrated in Stevenson's Canal and 
 River Engineering. Edinburgh, 1872, p. 101. 
 
324 FLOW OF WATEE IN OPEN CHANNELS. 
 
 When brought into practical use, the instrument is 
 adjusted upon the rod,* so that when the staff rests upon 
 the bottom, the main axle will be at the height of the film 
 to be first measured. It is then placed in position with the 
 propeller toward the approaching current and the main axle 
 parallel \frith the direction of the current. The propeller 
 will soon acquire its due velocity of revolution from the 
 moving current, when the movable end of the frame carry- 
 ing the recording train is lifted by the wire E, and the first 
 toothed wheel brought into mesh with the worm-screw. If 
 the train does not stand at zero, its reading is to be taken 
 before the instrument is brought into position. The times 
 when the train is brought into mesh with the worm-screw, 
 and when disengaged, are both to be accurately noted and 
 recorded. 
 
 Upon the slackening of the wire E, the spring F, in- 
 stantly throws the train out of mesh, and it is held fast by 
 the stud A^ which engages between two teeth of the wheel. 
 The instrument may then be raised and the revolutipns in 
 the observed time read off. In waters exceeding a few feet 
 in depth there are usually pulsations of about one minute, 
 more or less, intervals, and the instrument should be held 
 in position until several of these have passed. 
 
 The velocities are thus measured at several heights on 
 vertical centre lines in the several sub-sections, and the com- 
 putations for mean velocity and volume completed as in the 
 above described case when long tin tubes are used. 
 
 The blades of the propeller are usually set at an angle 
 of about 70, or with an equivalent pitch if warped as a pro- 
 peller blade. 
 
 * Several moulinets upon the same staff, at known heights between bottom- 
 and surface, expedite the work and tend to greater accuracy. 
 
HYDROMETER COEFFICIENTS. 325 
 
 338. Hydrometer Coefficients. The number of revo- 
 lutions of the main axle is nearly proportional to the velocity 
 of the impinging current ; but there is some frictional resist- 
 ance offered by the mechanism, hence it is necessary that 
 the coefficients for the given instrument and for given veloci- 
 ties be established by experiment, and tabled for convenient 
 reference before it is put to practical use. These coefficients, 
 which decrease in value as the velocity increases, may be 
 ascertained, or verified, by placing the instrument sub- 
 merged in currents of known velocity, or by causing it to 
 move, submerged, through still water at known velocities. 
 
 An apparatus adapted to the last purpose is described 
 by L' Abbe Bossut, and illustrated in Plates I and II, in 
 " Experts * De Bossut," 
 
 If the instrument is to be tested in a reservoir of still 
 water, by moving it with different known velocities through 
 a given distance, let s be that distance, t the time consumed 
 in passing the instrument from end to end stations, n the 
 number of revolutions of the main axle in the given time , 
 c the coefficient of revolutions for the given velocity, and v 
 the given velocity. 
 
 Then -^ = v ; and = c ; and c n = s ; and ~ = v. 
 
 v 7b t 
 
 Now if the instrument is placed in a current, and n is 
 the observed number of revolutions in the given time, c may 
 be taken from the table, or an approximate value of c as- 
 sumed and nearer values determined by the formula 
 
 = c, when the velocity will be, v = . (20) 
 
 * Nouvelles Experiences sur la Resistance des Fluids ; M. 1'Abbe Bossut, 
 Rapporteur. Paris. ' 
 
 Vide, also, Annales des Fonts et Chaussees, Nov. et Dec., 1847, and Journal 
 of Franklin Institute, May, 1869, and Beaufoy's Hydraulic Experiments. 
 
326 FLOW OF WATER IN OPEN CHANNELS. 
 
 339. Henry's Telegraphic Moulinet. An ingenious 
 indicating current meter * has been invented by D. Farrand 
 Henry, C. E., late assistant of the U. S. Lake Survey, and 
 was tested by him with very satisfactory results in the sur-' 
 veys of the large streams joining and flowing from the great 
 lakes of North America. The recording apparatus of this 
 meter may be retained above the water surface in a position 
 convenient for observation, while the revolving propeller is 
 submerged at any desired depth. The two portions of the 
 instrument are connected by flexible wires with an electric 
 battery so that the circuit passes through the axle of the 
 propeller. The electric circuit is closed for an instant during 
 each revolution, when the lever of the register moves the 
 first of the train of registering wheels forward one cog. 
 
 This meter gives promise of especial value for gaugings 
 of deep waters and tidal estuaries. 
 
 340. Earlier Hydrometers. Castelli's quadrant, or 
 hydrometric pendulum, Boileau's horizontal gauge glass, 
 Gauthey's and Brunning's pressure plates, Brewster's long 
 screw-meter, and Lapointe's beveled gear-meter, have now 
 all been superseded by the more perfect modern current 
 meters. 
 
 341. Double Floats. Various double-float combina- 
 tions, having one float at the surface and a second near the 
 bottom, connected with the first by a cord or fine wire rope, 
 have been used both in Europe and America. The liability 
 of erroneous deductions from the movements of such com- 
 binations has been ably discussed f by Prof. S. W. Rob- 
 inson. 
 
 342. Mid-depth Floats. The mid-depth float proves 
 
 * This meter is illustrated in the Jour, of the Franklin Inst., May, 
 and Sept. 1871. 
 
 f Vide Van Nostrand's Eclectic Engineering Magazine, Aug., 1875. 
 
MID-DEPTH FLOATS. 327 
 
 most generally satisfactory of all float apparatus, excepting 
 full-depth tubes, for gauging artificial channels and the 
 smaller rivers. 
 
 This may consist of a hollow metal globe of say six 
 inches diameter, with a cork-stopper or pet-cock at its 
 lower vertical pole, which permits the partial filling of the 
 globe with water until its specific gravity, submerged, is 
 slightly in excess of unity. This globe is connected by a 
 fine flexible wire with the smallest and lightest circular 
 disk-float upon the surface that can retain the globe in its 
 proper mid-depth position. 
 
 It is desirable that the float be controlled as fully as 
 possible by the mid-depth velocity, where, in artificial 
 channels and deep streams, the film of most constant 
 velocity is found. The reactions and eddies that continually 
 agitate all the particles that flow near the bottom and sides 
 of the stream, and the wind pressure and motion along the 
 surface, make the motions of all perimeter (so called) films 
 very complex, and continually cause the parabolic velocity 
 values in the central vertical plane to change between 
 flatter and sharper curves, or to straighten out and double 
 up, hinged, as it were, upon a mid-depth point ; hence the 
 bottom, side, and surface velocities are liable to great irreg- 
 ularities, and these irregularities are projected to some 
 extent through the whole body of the water. These effects 
 may be readily observed in a stream carrying fine quartz 
 sand, upon a sunshiny day, if a position is taken so that 
 the sunlight is reflected from the sand-grains to the eye. If 
 in such case the eye and body is moved along with the cur- 
 rent, the whole mass of water appears in violent agitation 
 and the particles appear to move upward, downward, back- 
 ward, forward, and across, with writhing motions, illus- 
 trating the method by which the water tosses up and bears 
 
328 FLOW OF WATER IN OPEN CHANNELS. 
 
 forward its load of sediment. In the midst of this agitation, 
 the film having a velocity nearest to the mean resultant of 
 onward progress is usually over the mid-channel of a 
 straight course, and near to, or a little below, the centre of 
 depth. The suspended float that takes this mean velocity 
 is more certain to give a reliable velocity measure than that 
 controlled by any other point of the stream section. 
 
 343. Maximum Velocity Floats. If it is desired to 
 place the submerged float in the film of maximum velocity 
 in artificial channels, then this may be sought over the 
 mid-channel, and between the surface and one-third the 
 depth, according to the cross-section of the stream and 
 velocity of flow. In a smooth rectangular section with 
 depth equal to width, or with depth one-half width, it will 
 probably be near one-third the depth, and higher as the 
 depth of stream is proportionately less, until depth is only 
 one-fourth breadth, when it will have quite, or nearly, 
 reached the surface. 
 
 The film of maximum velocity may reacn the surface in 
 trapezoidal canals when depth of stream is only one- third 
 mean breadth. It is at one-fourth depth in the trapezoidal 
 channel, Fig. 51 , in which bottom breadth equals twice depth. 
 
 In shallow streams, the maximum velocity is at or near 
 the surface. 
 
 344. Relative Velocities and Volumes due to 
 Different Depths. When the mean velocity has been 
 reliably determined in a channel, or small stream, at some 
 given section, and for some particular depth, it is often 
 desirable to construct a table of velocities and volumes of 
 flow, for other depths in the same section, so that, if a read- 
 ing of depth is taken at any time from a gauge established 
 at that section, the velocity and volume due to the observed 
 depth at that time may be read off from the table. 
 
RELATIVE VELOCITIES AND VOLUMES. 329 
 
 The inclination, or surface slope, i = ~ , and the value 
 
 of the coefficient of friction, m -~ , may be observed 
 
 within the ordinary extremes of depth at the time of the 
 experimental measurement, if opportunity offers, or other- 
 wise for the given experimental depth, and computed for 
 the remaining depths. 
 
 Theory indicates that the variation of velocity , with 
 varying depth, is nearly as the variation of the square root 
 
 /a 
 
 o*f the hydraulic mean radius, = y -^, and the variation of 
 
 G 
 
 volume of flow is nearly as the variation of the product of 
 sectional area into the square root of hydraulic mean radius, 
 
 These terms are readily obtained for the several depths, 
 from measurement of the channel. 
 
 To compare new depths, velocities, and volumes, with 
 the depth, velocity, and volume accurately measured by 
 experiment, as unity, 
 
 let the 
 
 imental depth be 
 
 d, and the 
 
 new depth b 
 
 e d,; 
 
 hy. mean rad. " 
 
 r, " " 
 
 " hy. mean rad. ' 
 
 ?i 
 
 slope " 
 
 i, " 
 
 " slope 
 
 h 
 
 coef. of friction " 
 
 m, " " 
 
 " coef. of friction 
 
 m l 
 
 sectional area " 
 
 8, " " 
 
 " sectional area 
 
 &i 
 
 velocity " 
 
 v, " " 
 
 " velocity ' 
 
 i 
 
 volume " 
 
 q. " " 
 
 " volume 
 
 <?! 
 
 The relative values of new depths, velocities, volumes, 
 etc., will be 
 
 * ^- gi etc 
 d ' v 9 q' 
 
 and v : Vi :: 1 : : 
 
330 FLOW OF WATER IN OPEN CHANNELS. 
 
 q : q, : : 1 : ^ ; etc. 
 The ratio of Vi to v is 
 
 _^i^ J2gyA|>_._ J2grt(i = (Wftli 
 -0 " " I /#! f I w I ' ~ ( Ti?^ ) ' 
 
 * 
 
 *>,. (22) 
 
 In long straight .channels of uniform section, ^ will be 
 less than for increased depths, and greater than i for 
 reduced depths ; but ordinarily (except with great velocities) 
 their values will be so nearly equal to each other that they 
 may be omitted from the equation without serious error, 
 when the equation of velocity will become, 
 
 The variations in m cannot be neglected in relatively 
 shallow channels. 
 
 For illustration of the equations, let Fig. 57 be a smooth 
 
 FIG. 57. 
 
 s/^X^sjjiUsE 
 
 /reet. > 
 
 trapezoidal channel, 6 feet broad at the bottom, = e, and 
 with side slopes inclined thirty degrees from the horizon, 
 
RELATIVE VELOCITIES AND VOLUMES. 
 
 331 
 
 During the experimental measurement, let the depth be 
 4 feet ; the slope, one foot in one mile = i = .000189 ; the 
 experimental velocity, 1.201 feet per second ; and the ex- 
 perimental volume, 62.128 cubic feet per second. 
 
 The velocities and volumes are to be computed when the 
 depths are 2 feet and 6 feet, respectively. 
 
 Let d be any given depth; 
 
 e " the bottom breadth, = 6 feet ; 
 
 5 " the mean breadth ; 
 
 </> " the slope of the sides, = 30 ; 
 
 6 " the sectional area ; 
 
 C " the wetted earth perimeter. 
 Then we have for the given values of d: 
 
 ASSUMED VALUES OF d. 
 
 2 FEET. 
 
 4 FEET. 
 
 6 FEET. 
 
 tan ' 
 
 S = -\- de . . = 
 tan !> 
 
 2d sec 
 
 r / 4 
 
 12.93 
 18.93 
 14.00 
 
 .OOO2 
 .02396 
 
 19.86 
 
 22.00 
 
 .OOOlSg 
 .0187 
 
 26.79 
 
 98.35 
 30.00 
 3.28 
 .000185 
 .0146 
 
 tan</> 
 S 
 
 C" 
 i 
 
 w .>........... 
 
 
 7;. . . 
 
 .836 
 
 I.2OI 
 62.128 
 
 1. 606 
 
 <7i . 
 
 
 With increase of depth, there is also increase of velocity ; 
 hence there are two factors to increase of volume. 
 
 Some practical considerations relating to open canals 
 are given in Chap. XVII, following. 
 
SECTION III. 
 
 PRACTICAL CONSTRUCTION OF WATERWORKS, 
 
 CHAPTER XYI. 
 
 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 345. Ultimate Economy of Skillful Construction. 
 
 An earthwork embankment appears to the uninitiated 
 the most simple of all engineering constructions, the one 
 feature that demands least of educated judgment an A expe- 
 rience. Possibly from such delusion has, in part, resulted 
 the fact, which is patent and undeniable, that failures of 
 reservoir embankments have exacted more terrible and 
 appalling penalties of human sacrifice, and sacrifice of cap- 
 ital, than the weaknesses of all other hydraulic works 
 together. 
 
 Each generation in succession has had its notable flood 
 catastrophes, when its broken dams have poured deluges 
 into the valleys, which have swept away houses and mills 
 and bridges and crops, and too often twenty, fifty, or a 
 hundred human beings at once. 
 
 Such devastations are scarcely paralleled by, though 
 more easily averted by forethought, than those historical 
 inundations when the sea has broken over the embanked 
 shores of Holland and England, and when great rivers 
 
334 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 have poured over their populous leveed plains, yet they 
 seem to be quickly forgotten, except by the immediate 
 sufferers who survived them. 
 
 The earliest authenticated historical records of the East- 
 ern tropical nations describe existing storage reservoirs and 
 embankments, and more than fifty thousand such reser- 
 voirs have been built in the Indian Madras Presidency 
 Districts alone. Arthur Jacobs, B. A., says* of these 
 Madras embankments, that they will average a half mile in 
 length each, and the longest has a length of not less than 
 thirty miles. 
 
 Two thousand years of practice seems to have developed 
 but a slight advance of skill in the construction of earth- 
 works, while their apparent simplicity seems to have dis- 
 tracted modern attention from their minute details, and to 
 have led builders to the practice of false economy in some in- 
 stances, and to the neglect of necessary precautions in others. 
 
 Among the recent disastrous failures may be mentioned 
 the Bradfield or Dale Dyke embankment of the Sheffield, 
 England, water- works, in 1864 ; the Danbury, Conn., water, 
 works embankment, in 1866 ; the Hartford, Conn., water- 
 works embankment, in 1867 ; the New Bedford, Mass., 
 water-works embankment, in 1868; the Mill Eiver, or 
 Williamsburgh, Mass., embankment, in 1875 ; and Worces- 
 ter, Mass., water-works embankment, in 1876. More than 
 one hundred other breakages of dams are upon record for 
 New England alone for the same short period. 
 
 The practical utility of streams is dependent largely 
 upon the storage of their surplus waters in the seasons of 
 their abundant flow, that they may be used when droughts 
 would otherwise reduce their volume. 
 
 * Vide Paper read before the Society of Engineers, London. 
 
EMBANKMENT FOUNDATIONS. 335 
 
 Their waters are usually stored in elevated basins, 
 whether stored for power, for domestic consumption, for 
 compensation, or to regulate floods ; and frequently single 
 embankments toward the head-waters of streams suspends 
 millions of tons of water above the villages and towns of 
 the lower valleys. In other instances, embanked distrib- 
 uting reservoirs crown high summits in the midst of popu- 
 lous cities. These are good angels of health, comfort, and 
 protection, when performing their appointed duties, but 
 very demons of destruction when their waters break loose 
 upon the hillsides. 
 
 Every consideration demands that a storage reservoir 
 embankment shall be as durable as the hills upon which it 
 rests. To this end, no water is to be permitted to percolate 
 and gather in a rill beneath the embankment ; its core must 
 be so solid, heavy and impervious that no water shall push 
 it aside, lift it up or flow through it, or follow along its dis- 
 charge pipes or waste culvert ; its core must be protected 
 from abrasions and disintegrations ; and its waste overfall 
 must be ample in length and strength to pass the most 
 extraordinary flood without the embankment being over- 
 topped. 
 
 346. Embankment Foundations. The foundation 
 upon which the structure rests is the first vital point requir- 
 ing attention, and may contain an element of weakness that 
 shall ultimately lead to the destruction of the structure 
 placed upon it. 
 
 The superposed drift strata beneath the surface layer of 
 muck or vegetable soil may consist of various combinations 
 of loam, gravel, sand, quicksand, clay, shale and demoral- 
 ized rock, resting upon the solid impervious rock, or above 
 an impervious stratum of sufficient thickness to resist the 
 penetration of water under pressure. If the water is raised 
 
336 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 fifty feet above the surface and there are thirty feet of per- 
 vious earth in the bed of the valley, then the pressure upon 
 the bed stratum will be five thousand pounds, or two and 
 one-half tons per square foot, which will tend to force the 
 water toward an outlet in the valley below. That much of 
 the natural earth is porous is well demonstrated by the 
 freedom with which water enters on the plains and courses 
 through the strata to the springs in the valleys, even with- 
 out a head of water to force its entrance. Such porous 
 strata must be cut off or sealed over, or the permanency and 
 efficiency of the structure, however well executed above, 
 cannot be assured. 
 
 If the valley across which the embankment is thrown is 
 a valley of denudation, or if the embankment stretches 
 across one or more ridges to cover several minor valleys 
 with a broad lake, the waters in rising may cover the 
 outcropping edges of coarse porous strata that shall lead 
 the flowage by subterranean paths to distant springs where 
 water had not flowed before. Hence the necessity of a 
 thorough examination of the geological substructure of 
 the valley, and of tests by trial shafts, supplemented by 
 deep borings, of the site of the embankment and the hill- 
 sides upon which it abuts. The test borings should cover 
 some distance above and below the site of the embankment, 
 lest a mere pocket filled with impervious soil be mistaken 
 for a thick strata supposed to underlie the whole vicinity. 
 
 The trial shafts only, permit a proper examination of the 
 covered rock, which may be so shattered, or fissured, as to 
 be able to conduct away a considerable quantity of water, 
 or to lead water from the adjoining hills to form springs 
 under the foundations. 
 
 Several deep reservoirs constructed within a few years 
 past have demanded excavations for cut-off walls, to a 
 
SURFACE SOILS. 337 
 
 depth of a hundred feet at certain points along their lines, 
 but the porosity and the firmness of the strata in such cases 
 are points demanding the exercise of the most mature judg- 
 ment, that the work may be made sure, and at the same 
 time labor be not wasted by unnecessarily deep cutting. 
 
 Thoroughness in the preliminary examination of the 
 substrata of a proposed site may frequently result in the 
 avoidance of a great deal of vexatious labor and enhanced 
 cost that would otherwise follow from the location of an 
 embankment over a treacherous sub-foundation. 
 
 347. Springs under Foundations. If the excava- 
 tion shall cut off or expose a spring that, when confined, 
 will produce an hydrostatic pressure liable to endanger the 
 outside slope of the embankment, it must be followed back 
 by a drift or open cutting to a point from whence it may 
 be safely led out in a small pipe below the site of the 
 embankment. 
 
 348. Surface Soils. Dependence cannot be placed 
 upon the vegetable soil lying upon the site of an embank- 
 ment to hold water under pressure, for it is always porous 
 in a state of nature, as is also the subsoil to the depth pene- 
 trated by frost. The vegetable soil should be cleared from 
 beneath the core of the embankment, and the subsoil rolled 
 and compacted. 
 
 The vegetable soil will be valuable for covering the top 
 and outside slope of the embankment. 
 
 If good hard-pan underlies the surface soil to a depth 
 sufficient to make a strong foundation for the embankment, 
 then its surface should be broken up to the depth it has 
 been made porous by frost expansion, and the material 
 rolled down anew in thin layers with a grooved roller of 
 not less than two tons gross weight, or of one-half ton per 
 lineal foot. 
 
 22 
 
338 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 If next to the surface soil there is a layer of hard-pan 
 within the basin to be flowed, and this hard-pan covers open 
 and porous strata that extend below the dam, caution 
 should be used in disturbing the hard-pan, lest the water 
 be admitted freely to the porous strata, when it will escape, 
 perhaps by long detour around the dam. 
 
 349. Concrete Cut-off Walls. If the trench for the 
 cut-off wall is deep and very irregular, it is well to level up 
 in the cuts with a water-proof concrete well settled in place, 
 and this may prove more economical than to cut the deep 
 trench of sufficient width to receive a reliable puddle wall ; 
 also, the greater reliability of the concrete under great pres- 
 sure should not be overlooked. 
 
 350. Treacherous Strata. In one instance the writer 
 had occasion to construct a low embankment, not exceed- 
 ing twenty feet height at the centre, across an abraided cut 
 through a plain. The embankment was to retain a storage 
 of water for a city water supply, and the enclosed lake was 
 to have an area of 200 acres. 
 
 The test pits and soundings developed the fact that the 
 abraided valley and adjacent plains were underlaid with a 
 stratum of fine sand twelve feet in thickness, which, when 
 disturbed, became a quicksand, and if water was admitted 
 to it, would flow almost as freely as water. 
 
 The sand lay in a compact mass, and would not pass 
 water freely until disturbed. Above the sand was a layer 
 of about three feet of fine hard-pan, and above this about 
 three feet of good meadow soil had formed. 
 
 For this case the decision was, not to uncover the quick- 
 sand, but to seal it over in the vicinity of the embankment. 
 The foundation of the embankment, and of the waste over- 
 fall which necessarily came in the centre of length of the 
 embankment, was made of concrete of such thickness as to 
 
EMBANKMENT CORE MATERIALS. 339 
 
 properly distribute the weight of the earthwork and over- 
 fall masonry. Above the embankment, after a careful 
 cleaning of the soil to the depth penetrated by the grass 
 roots, the valley was covered with a layer of gravel and 
 clay puddle for a distance of one hundred feet. 
 
 Beneath the toe of the inside slope, where the bottom 
 puddle joined the concrete foundation, a trench was cut 
 across the valley into the quicksand, as deep as could be 
 excavated in sections, with the aid of the light pumping 
 power on hand, and sheet piling placed therein and driven 
 through the quicksand, and then the trench was filled 
 around the piling with puddle, thus forming a puddle and 
 plank curtain under the inside edge of the embankment. 
 
 Such expedients are never entirely free from risks, 
 especially if a faithful and competent inspector is not re- 
 tained constantly on the work to observe that orders are 
 obeyed in the minutest detail. 
 
 In the case in question many thousands of dollars were 
 saved, and the work has at present writing successfully 
 stood the test of seven years use, during which time the 
 most fearful flood storm recorded in the present century has 
 swept over the section of Connecticut where the storage lake 
 is situated. 
 
 351. Embankment Core Materials. Rarely are 
 good materials found ready mixed and close at hand for 
 the construction of the core of the embankment. It is 
 essential that this portion be so compounded as to be im- 
 pervious. 
 
 If we fill a box of known cubical capacity, say one cubic 
 yard, with shingle or screened coarse gravel, we shall then 
 find that we can pour into the full box with the gravel a 
 volume of water equal to twenty-eight or thirty per cent, 
 of the capacity of the box, according to the volume of voids ; 
 
340 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 or if we attempt to stop water with the same thickness (one 
 yard) of gravel, we shall find that water will flow through 
 it very freely. Then let the same gravel be dumped out 
 upon a platform and twenty-eight per cent, nearly of fine 
 gravel "be mixed with it, so as to fill the voids equally, and 
 the whole be put into the measuring-box. We now find 
 that we can again pour in water equal to about thirty per 
 cent, of the cubical measure of the fine gravel. Then let fine 
 sand, equal to this last volume of water, be mixed with the 
 coarse and fine gravel, and the whole returned to the meas- 
 ure. We now find that we can pour in water, though not 
 so rapidly as before, equal to thirty-three per cent, approx- 
 imately of the cubical measure of the sand, and we resort 
 to fine clay equal to the last volume of the water to again 
 fill the voids. The voids are now reduced to microscopic 
 dimensions. 
 
 If we could in practice secure this strict theoretical pro- 
 portion and thorough admixture of the material, we should 
 introduce into one yard volume quantities as follows : Coarse 
 gravel, 1 cubic yard ; fine gravel, 0.28 cubic yard ; sand, 
 0.08 cubic yard ; and clay, 0.03 cubic yard, or a total of 
 the separate materials of 1.39 cubic yards. 
 
 In practice, with a reasonable amount of labor applied 
 to thoroughly mix the materials so as to fill the voids, we 
 shall use, approximately, the following proportion of ma- 
 terials : 
 
 Coarse gravel 1.00 cubic yard. 
 
 Finegravel 0.35 " 
 
 Sand 0.15 " 
 
 Clay 0.20 " 
 
 Total 1.70 " 
 
 which, when mixed loosely or spread in thin layers, will 
 make about one and three-tenths yards bulk, and when. 
 
WEIGHT OF EMBANKMENT MATERIALS. 
 
 341 
 
 thoroughly compacted in the embankment, will make about 
 one and one quarter cubic yards bulk. 
 
 The voids now remaining in the mass may each be a 
 thousand times broader than a molecule of water, yet they 
 are sufficiently minute, so that molecular attraction exerts 
 a strong force in each and resists flow of the molecules, 
 even under considerable head pressure of water. 
 
 It will be interesting here to compare the weights of a 
 solid block of granite with its disintegrated products of 
 gravel and sand, taking for illustration a cubic foot volume. 
 
 TABLE No. 77. 
 WEIGHTS OF EMBANKMENT MATERIALS. 
 
 MATERIAL. 
 
 Av. WEIGHT. 
 
 SPECIFIC GRAVITY. 
 
 Av. VOIDS. 
 
 Granite 
 
 166 
 
 I2O 
 
 116 
 no 
 
 I2 5 
 62.1 
 
 Ibs. 
 
 
 
 u 
 
 tt 
 
 u 
 
 , tt 
 > 
 
 2662 
 I 925 
 
 i. 86 1 
 1.440 
 
 I.OOO 
 
 .28 per cent. 
 
 .30 " " 
 ,, 
 
 .12 " " 
 
 Coarse Gravel 
 
 Gravel . 
 
 Sharp Sand 
 
 Clay 
 
 Water. . 
 
 
 If the shingle is omitted and common gravel is the bulk 
 to receive the finer materials, then the proportions in prac- 
 tice may be : 
 
 Common gravel 1 .00 cubic yard. 
 
 Sand 0.36 " 
 
 Clay 0.25 " 
 
 1.61 
 
 which, when loosely spread, will make about one and one- 
 sixth yards bulk ; and compacted, some less than one and 
 one-tenth yards bulk. 
 
 Gravel is usually found with portions of sand, or sand 
 and clay, already mixed with it, though rarely with a suf- 
 
342 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 ficiency of fine material to fill the voids. The lacking ma- 
 terial should be supplied in its due proportion, whether it 
 be fine gravel sand, fine sand, or clay. The voids must be 
 filled, at all events, with some durable fine material, to 
 ensure imperviousness. 
 
 It is sometimes found expedient to substitute for a por- 
 tion of the fine sand or clay, portions of loam or selected 
 soil from old ground, and on rare occasions peat, but 
 neither peat nor loam should be introduced in bulk into 
 the core of an embankment. 
 
 There is a general prejudice against the use of peat or 
 surface soils in embankments, and the objections hold good 
 when they are exposed to atmospheric influences. Mr. 
 Wiggin remarks,* howeve.r, that a peat sea-bank which was 
 opened after being built for seventeen years, exhibited the 
 material as fibrous and undecayed as when first deposited. 
 
 Weight is a valuable property in embankment material, 
 when placed upon a firm foundation, since, for a given bulk, 
 the heavier material is able to resist the greater pressure. 
 
 Peat and loam are very deficient in the weight property, 
 and therefore need the support of heavier materials. Clay 
 is heavier than sand or fine gravel ; shingle is heavier than 
 clay ; but the compound of shingle, gravel, sand, and clay, 
 above described, is heavier than either alone, and weighs 
 when compacted, for a given volume, nearly as much as 
 solid granite. 
 
 CoTiesiveness and stability are valuable properties in 
 embankment materials, but sand and gravel lack perma- 
 nent cohesiveness, and clay alone, though quite cohesive, 
 is liable to slips and dangerous fissures, if unsupported ; 
 but a proper combination of gravel, sharp sand, and clay, 
 
 * Embanking Lands from the Sea, p. 20. London, 1852. 
 
PECULIAR PRESSURES. 343 
 
 gives all the valuable properties of weight, cohesiveness, 
 stability, and iraperviousness. 
 
 352. Peculiar Pressures. There are peculiar pres- 
 sure influences in an earthwork structure that are not 
 identical with the theoretical hydrostatic pressures upon a 
 tight masonry, or fully impervious structure of the same 
 form. The hydrostatic pressure upon an impervious face, 
 whatever its inclination, might be resolved into its hori- 
 zontal resultant (171), and that resultant would be the 
 theoretical force tending to push the structure down the 
 valley, and would be equal to the pressure of the same 
 depth of water acting upon a vertical face. The pressure 
 would be, upon a vertical face, per square foot, at the given 
 depths, as follows : 
 
 Depth, in feet 
 Pressure, in Ibs 
 
 5 
 3".i 
 
 10 
 
 624.3 
 
 15 
 936.4 
 
 20 
 1249 
 
 25 
 1561 
 
 3 
 
 1873 
 
 35 
 2185 
 
 40 
 2497 
 
 2809 
 
 50 60 
 3121(3746 
 
 I 
 
 437 
 
 80 
 4994 
 
 90 
 
 5618 
 
 100 
 
 6243 
 
 The effective action of the theoretical horizontal resultant 
 is neutralized somewhat upon an impervious slope by the 
 weight of water upon the slope. 
 
 But all embankments are pervious to some extent. If 
 with the assistance of the pressure, the water penetrates to 
 the centre of the embankment, it presses there in all direc- 
 tions, upward, downward, forward and backward, and at a 
 depth of fifty feet the pressure will be a ton and a half per 
 square foot. Such pressure tends to lift the embankment, 
 and to soften its substance, as well as to press it forward, 
 and if in course of time the water penetrates past the centre 
 it may reach a point where the weight or the imperviousness 
 of the outside slope is not sufficient to resist the pressure, 
 when the embankment will crack open and be speedily 
 breached. 
 
 That portion of the embankment that is penetrated by 
 
344 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 the water has its weight neutralized to the extent of the 
 weight of the water, or at any depth, a total equal to the 
 water pressure at that depth ; thus, at fifty feet depth, that 
 portion penetrated is reduced in its total weight a total of 
 one and one-half tons per square foot. 
 
 Hence the value of imperviousness at the front as well 
 as in the centre of the embankment, so that the maximum 
 amount of its weight may be effective. 
 
 If water penetrates the subsoil beneath the embarikment, 
 as is frequently the case, it there exerts a lifting pressure 
 according to its depth. 
 
 353. Earthwork Slopes. If earth embankments of 
 the forms usually given to them, and their subsoils also, 
 were quite impervious, as a wall of good concrete would be, 
 the embankments would have a large surplus of weight, 
 and might be cut down vertically at the centre of their 
 breadth, and either half would sustain the pressure and 
 impact of waves with safety, but the vertical wall of earth 
 would not stand against the erosive actions of the waves 
 and storms. Surface slopes of earthwork are controlling 
 elements in their design, and govern their transverse profiles. 
 
 Different earths have different degrees of permanent 
 stability or of friction of their particles upon each other, 
 that enable them to maintain their respective natural sur- 
 face slopes, or angles of repose, against the effects of gravity, 
 ordinary storms, and alternate freezings and thawings, until 
 nature binds their surfaces together with the roots of weeds, 
 grasses and shrubs. The coefficient of friction of earth 
 equals the tangent of its angle of repose, or natural slope. 
 The amount or value of the slope is usually described by 
 stating the ratio of the horizontal base of the angle to its 
 vertical height, which is the reciprocal of the tangent of the 
 inclination. 
 
EARTHWORK SLOPES. 
 
 345 
 
 The following data relating to these values are selected * 
 in part from Rankine, and to them are added the angles at 
 which certain earths sustain by friction other materials laid 
 upon their inclined surfaces. 
 
 TABLE No. 78. 
 ANGLES OF REPOSE, AND FRICTION OF EMBANKMENT MATERIALS. 
 
 MATERIAL. 
 
 ANGLE OF 
 REPOSE. 
 
 COEFFICIENT OF 
 FRICTION. 
 
 RATIO OF SLOPE. 
 
 Dry sand fine 
 
 28 
 
 c 22 
 
 f/ari. Vert. 
 1.88 tO 
 
 " " coarse 
 
 10 
 
 jo* 
 
 .C77 
 
 1.71 " 
 
 Damp clay 
 
 i! 
 
 'Oil 
 
 I OOO 
 
 I 00 " 
 
 Wet clay . 
 
 iS 
 
 268 
 
 171 " 
 
 Clayey gravel 
 
 
 
 I OOO 
 
 O" 1 O 
 1.00 " 
 
 Shingle 
 
 4* 
 
 .000 
 
 I. II " 
 
 Gravel 
 
 38 
 
 7 ^ 
 
 .781 
 
 1.28 " 
 
 Firm loam 
 
 ^6 
 
 727 
 
 i *8 " 
 
 Vegetable soil . 
 
 3S 
 
 / */ 
 
 7OO 
 
 *o** 
 
 1.41 " 
 
 Peat 
 
 35 o 
 20 
 
 / ww 
 .^64. 
 
 A *tO 
 
 2.7C " 
 
 Masonry, on clayey gravel. . 
 " dry clay 
 " " moist clay. . . 
 Earth on moist clay ...... 
 " " wet clay 
 
 1 
 
 18 
 
 
 
 577 
 .510 
 
 325 
 
 I. OOO 
 
 .106 
 
 *"/ J 
 
 1.73 " 
 
 1.96 " 
 3.08 " 
 
 1. 00 " 
 
 1.26 " 
 
 
 x / 
 
 
 
 Inclined earth surfaces are most frequently dressed to 
 the slopes, having ratios of bases to verticals, respectively 
 1 J to 1 ; 2 to 1 ; 2J to 1 ; and 3 to 1 ; corresponding respect- 
 ively to the coefficients of friction 0.67, 0.50, 0.40, and 0.33, 
 and to the angles of repose 33J, 26^, 21|, and 18J, 
 nearly. 
 
 Gravel, and mixtures of clay and gravel, will stand 
 ordinarily, and resist ordinary storms at an angle of 1 J to 1, 
 but the angle must be reduced if the slope is exposed to 
 accumulations of storm waters or to wave actions, and upon 
 
 * Civil Engineering, p. 316. London, 1872. 
 
346 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 broad lake shores the waves will reduce coarse gravel, if 
 unprotected, to a slope of 5 to 1, and finer materials to 
 lesser slopes. Complete saturation of clay, loam, and vege- 
 table soil, destroys the considerable cohesion they have 
 when merely moistened, and they become mud, and assume 
 slopes nearly horizontal ; hence the conditions to which the 
 above table refers may be entirely destroyed and the angles 
 be much flattened, unless the slopes are properly protected. 
 On the other hand, the table does not refer to the temporary 
 stability which some moist earths have in mass, for com- 
 pact clay, gravel, and even coarse sand may, when their 
 adhesion is at its maximum, or when their pores are par- 
 tially and nearly filled with water, be trenched through, 
 and the sides of the trench stand for a time, nearly vertical, 
 at heights of from 6 to 15 feet. In such cases, loss or 
 increase of moisture destroys the adhesion, and the sides of 
 the trench soon begin to crumble or cave, unless supported. 
 354. Reconiioissance for Site. Let us assume, for 
 illustration, that a storage reservoir is to be formed in an 
 elevated valley. The minimum allowable altitude being 
 fixed upon, and designated by reference to a permanent 
 bench mark in the outfall of the valley, the valley is then 
 explored from the given altitude upward for the most favor- 
 able site for the storage basin, and for the site for an 
 embankment, or dam, as the circumstances may require. 
 We may expect to find a good site for the storage at some 
 point where a broad meadow is flanked upon each side by 
 abrupt slopes, and where those slopes draw near to each 
 other at the outlet of the meadow, as is frequently the case. 
 Having found a site that appears favorable, a preliminary 
 reconnoissance with instruments is made to determine if the 
 basin has the required amount of watershed and storage 
 capacity, previously fixed upon ( 59), and to determine 
 
DETAILED SURVEYS. 347 
 
 approximately the height the embankment or masonry 
 dam must have. If the preliminary reconnoissance gives 
 satisfactory results, then the site where the embankment 
 can be built most economically and substantially is care- 
 fully sought, and test pits and borings put down at the 
 point giving most promise upon the surface. It is import- 
 ant to know at the outset that the subsoil is firm enough to 
 carry the weight of the embankment without yielding, and if 
 there is an impervious substratum that will retain the pond- 
 ed water under pressure. It is important also to know that 
 suitable materials are obtainable in the immediate vicinity. 
 
 355. Detailed Surveys. The preliminary surveys all 
 giving satisfactory indications as respects extent of flowage, 
 volume of storage, depth of water, inclination and material 
 of shore slopes, soils of flowed basin, and the detailed sur- 
 veys confirming the first indications, and also establishing 
 that the drainage area and rainfall supplying the basin is 
 of ample extent and quantity to supply the required amount 
 of water ( 24) of suitable quality ( 1OO et seq.) ; then let 
 us suppose that the conditions governing the retaining em- 
 bankment may best be met by a construction similar to 
 that shown in Fig. 59, based upon actual practice. 
 
 356. Illustrative Case. Here the water was raised 
 fifty feet above the thread of the valley. The surface of the 
 impervious clay stratum, containing a small portion of fine 
 gravel, was at its lowest dip, thirty feet below the surface 
 of the valley, and was overlaid at this point, in the following 
 order of superposition, with stratas of sandy clay, coarse 
 sand, quicksand, sandy marl, gravel and sand, gravelly loam, 
 and vegetable surface soil, each of thickness as figured. 
 
 Gravel and sand and loam were obtainable readily in 
 the immediate vicinity, but clay was not so readily pro- 
 cured, and must therefore needs be economized. 
 
348 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 FIG. 59. 
 
 STORAGE RESERVOIR EMBANKMENT. 
 
 357. Cut-off Wall. A broad trench was cut, after the 
 clearing of the surface soil, down to the sandy marl, and 
 then a narrow trench cut down to eighteen inches depth in 
 the thick clay strata, finishing four feet wide at the bottom. 
 
 A wall of concrete, four feet thick, composed of machine- 
 broken stone, four parts ; coarse sand, one part ; fine sand, 
 one part ; and good hydraulic cement, one part, was built 
 up to eighteen inches above the top of the marl stratum. 
 
 The concrete was mixed with great care, and the materials 
 rammed into the interstices of the bank, to insure imper- 
 viousness in the wall, and to prevent water being forced 
 down its side and under its bottom. Puddle, of one part 
 mixed coarse and fine sharp gravel, one part fine sand, and 
 one part good clay then filled the broad trench up to the 
 surface of the embankment foundation. 
 
 358. Embankment Core. The core of the embank- 
 ment was composed of carefully mixed coarse and fine 
 gravel, sand, and clay, in the proportions given above 
 
EMBANKMENT CORE. 349 
 
 (p. 340), requiring for one cubic yard of core in place, ap- 
 proximately : 
 
 Coarse gravel 74 cubic yard. 
 
 Fiife " 26 " 
 
 Sand II 
 
 Clay : ^15 " 
 
 L26 " 
 
 When measured by cart-loads, these quantities became 
 eight loads* of mixed gravels, one load of sand, and two 
 loads of clay, the cubic measure of each load of clay being 
 slightly less than that of the dry materials. The gravel 
 was spread in layers of two inches thickness, loose, the clay 
 evenly spread upon the gravel and lumps broken, and the 
 sand spread upon the clay. When the triple layer was 
 spread, a harrow was passed over it until it was thoroughly 
 mixed, and then it was thoroughly rolled with a two-ton 
 grooved roller, made up in sections, the layer having been 
 first moistened to just that consistency that would cause it 
 to knead like dough under the roller, and become a com- 
 pact solid mass. 
 
 Such a core packs down as solid, resists the penetration 
 or abrasion of water, nearly as well, and is nearly as diffi- 
 cult to cut through as ordinary concrete, while rats and eels 
 are unable to enter and tunnel it. 
 
 The proportions adopted for the core was a thickness 
 of five feet at the top at a level three feet above high-water 
 mark, and approximate slopes of 1 to 1 on each side. 
 
 For the maximum height of fifty-four feet this gave a 
 breadth of 113 feet base. 
 
 This core was abundantly able to resist the percolation 
 of the water through itself, and to resist the greatest pres- 
 
 * Seven loads of coarse and three loads of fine gravel make, when mixed, 
 about eight loads bulk. 
 
350 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 sure of the water, and had these been the only matters to 
 provide for, the embankment core would have been the 
 complete embankment. 
 
 359. Frost Covering. Frost would gradually pene- 
 trate deeper and deeper into that part of the work above 
 water and into the outside slope, and by expansions make 
 it porous and loose to a depth, at its given latitude, of from 
 four to five feet. A frost covering was therefore placed 
 upon it, and carried to a height on the inside of five feet 
 above high-water line, and of just sufficient thickness at 
 high- water line to protect it from frost. 
 
 The frost-covering was composed of such materials as 
 could be readily obtained in the vicinity of the embank- 
 ment. It was built up at the same time, in thin layers, with 
 the core, and the whole was moistened and rolled alike, 
 making the whole so compact as to allow no apparent 
 "after settlement." The wave slope was built eighteen 
 inches full, and then dressed back to insure solidity be- 
 neath the pavement. 
 
 The core of an embankment should be built up at least 
 to the highest flood level, which is dependent upon length 
 of overfall as well as height of its crest, and the frost-cover- 
 ing should be built of good materials to at least three feet 
 above maximum flood level. 
 
 360. Slope Paving. The exterior slope, when soiled, 
 was dressed to an inclination of 1 J to 1 ; the interior slope 
 was made 2 to 1 from one foot above high water down to a 
 level, three feet below proposed minimum low water, where 
 there was a berm five feet wide, and the remainder of the 
 slope to the bottom was made 1J to 1. The lower interior 
 slope was paved with large cobbles driven tightly, the berm 
 with a double layer of flat quarried stone, and the upper 
 slope, which was to be exposed to wave action, was covered 
 
PUDDLE WALL. 351 
 
 with one foot thickness of machine-broken stone, like " road 
 metal" and then paved with split granite paving-blocks of 
 dimensions as follows : Thickness, 10 to 14 inches ; widths, 
 12, 14. or 16 inches ; and lengths, 24 to 48 inches. 
 
 A granite ledge, in sheets favorable for the splitting of 
 the above blocks, was near at hand, and supplied the most 
 economical slope paving, when labor of placing and future 
 maintenance was considered. From one foot above high 
 water to the underside of the coping, the paving had a slope 
 of 1 to 1 , and the face of the coping was vertical. 
 
 361. Puddle Wall. The policy might be considered 
 questionable of using clay in so large a section of the 
 embankment, when the haulage of the clay was greater 
 than of any of the other materials, and when the clay might 
 be confined to the lesser section of the usual form of puddle 
 wall. These methods of disposing the clay were compared 
 in a preliminary calculation, both upon the given basis, and 
 that of a puddle wall of minimum allowable dimensions, 
 viz., five feet thick at the top and increasing in thickness 
 on each side one foot in eight of height, which gave a maxi- 
 mum thickness of 18.6 feet at base with 54 feet height. (See 
 dotted lines in Fig. 59.) 
 
 The estimate of loose materials for each cubic yard of 
 complete core was coarse gravel, .74 cu. yard ; fine gravel, 
 .26 cu. yd. ; sand, .07 cu. yd. ; and clay, .15 cu. yd. ; and 
 for puddle wall of equal parts of gravel and clay gravel 
 .59 cu. yd., and clay .59 cu. yd. 
 
 This calculation gave the excess of clay in the maximum 
 depth of embankment, less than 4 cubic yards per lineal 
 foot of embankment, and the excess at the mean depth of 
 thirty feet, about three-fourths yard per lineal foot of 
 embankment. 
 
 The difference in estimated first cost was slightly against 
 
352 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 the mixed core, but in that particular case this was consid- 
 ered to be decidedly overbalanced by more certainly in- 
 sured stability, more probable freedom from slips and 
 cracks in a vital part of the work, and by the additional 
 safety with which the waste and draught pipes could be 
 passed through the core. 
 
 The value of puddle in competent hands has, however, 
 been demonstrated in many noble embankments. It is 
 usually placed in the centre of the embankment, as in 
 Fig. 61, and occasionally near the slope paving, as in 
 Fig. 62, from a design by Moses Lane, C. E. 
 
 363. Kubble Priming Wall. The drift formation 
 presents a great variety of materials ; but not always such 
 as are desired for a storage embankment, in the immediate 
 vicinity of its site. The selection of proper materials often 
 demands the best judgment and continued attention of the 
 engineer. Clay, which is often considered indispensable in 
 an embankment, may not be found within many miles. 
 
 Fig. 60 (p. 84) gives a section of an embankment con- 
 structed where the best materials were a sandy gravel and 
 a moderate amount of loam, but abundance of gneiss rock 
 and boulders were obtainable close at hand. 
 
 Here a priming wall of thin split stone was carried up 
 in the heart of the embankment from the bed-rock, which 
 was reached by trenching. Each stone was first dashed 
 clean with water, and then carefully floated to place in good 
 cement mortar, and pains taken to fill the end and side 
 joints, and exceeding care was taken not to move or in any 
 way disturb a stone about which the mortar had begun to 
 set. No stones were allowed to be broken, spalted, or 
 hammered upon the wall, neither were swing chains drawn 
 out through the bed mortar. The construction of a water- 
 tight wall of rubble-stone is a work of skill that can be 
 
APPLICATION OF FINE SAND. 353 
 
 performed, but the ordinary layer of foundation masonry 
 in cement mortar seems no more to comprehend it than 
 would a fiddler at a country dance the enchanting strains 
 of a Vieuxtemps or Paganini. 
 
 Grouting such rubble-stone walls, according to the usual 
 method, will not accomplish the desired result, and is 
 destructive of the most valuable properties of the cement. 
 
 363. A Light Embankment. In this embankment 
 (Fig. 60), selected loam and gravel were mixed in due pro- 
 portions on the upper side of the priming wall, so as to 
 insure, as nearly as possible, imperviousness in the earth- 
 work. The entire embankment was built up in layers, 
 spread to not exceeding four or five inches thickness, and 
 moistened and rolled with a heavy grooved roller. 
 
 The cross-section of this work is much lighter than that 
 advised by several standard authorities, both slopes being 
 1-J to 1, but great bulk was modified by the application of 
 excellent and faithful workmanship. This embankment 
 retains a storage lake of sixty-six acres and thirty feet 
 maximum depth. It was completed in 1868, and has 
 proved a perfect success in all respects. This work fills the 
 offices of both an impounding and distributing reservoir, in 
 a gravitation water supply to a New England city. 
 
 364. Distribution Reservoirs. Distributing reser- 
 voirs are frequently located over porous sub-soils and 
 require puddling over their entire bottoms and beneath 
 considerable portions of their embankments, and puddle 
 walls are usually carried up in the centres of their embank- 
 ments or near their inner slopes. . 
 
 The same general principles are applicable to distrib- 
 uting as to storage reservoir embankments. 
 
 365. Application of Fine Sand. Fig. 58 (p. 333) illus- 
 trates a case where the bottom was puddled with clay, but a 
 
354 
 
 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 sufficiency of clay to puddle the embankments was not ob- 
 tainable. The embankment is here constructed of gravel, 
 coarse sand, very fine sand, and a moderate amount of 
 loam. The materials were selected and mixed so as to 
 secure imperviousness to the greatest possible extent, and 
 were put together in the most compact manner possible, and 
 have proved successful. This has demonstrated to the sat- 
 isfaction of the writer that very fine sand may replace to a 
 considerable extent the clay that is usually demanded, and 
 his experience includes several examples, among which, on 
 a single work, is more than three-fourths of a mile of suc- 
 cessful embankment entirely destitute of clay, but sand 
 was used with the gravel, of all grades, from microscopic 
 grains to coarse mortar sand, and a sufficiency of loam was 
 used to give the required adhesion. The outside slopes 
 were heavily soiled and grassed as soon as possible. 
 
 FIG. 61. 
 
 REVETTED RESERVOIR EMBANKMENT. 
 
 366. Masonry-faced Embankment. When there 
 is a necessity for economizing space, one or both sides of an 
 embankment may be faced with masonry. 
 
 An example of such construction is selected from the 
 practice of a successful engineer in one of the Atlantic 
 
EMBANKMENT SLUICES AND PIPES. 355 
 
 States, and is shown in Fig. 61. A method of introducing 
 clay puddle into a central wall in the embankment, beneath 
 the embankment, and on the reservoir bottom, is also here 
 shown. The puddle of the reservoir bottom is usually 
 covered with a layer of sand. 
 
 367. Concrete Paving. The lower section of the 
 slope paving of the distributing reservoir, Fig. 58, was built 
 up of concrete, composed of broken stone 4 parts ; coarse 
 sand 1 part ; fine sand I part ; and hydraulic cement 1 part. 
 The cement and sand were measured and mixed dry, then 
 moistened, and then the stone added and the whole thor- 
 oughly worked together. The concrete was then deposited 
 and rammed in place, building up from the base to the top, 
 in sections of about forty feet length. A very small quan- 
 tity of water sufficed to give the concrete the proper con- 
 sistency, and if more was added the concrete inclined to 
 quake under the rammer, which was an indication of too 
 much water. 
 
 The general thickness of the concrete sheet is ten inches, 
 and there is in addition four ribs upon the back side to give 
 it bond with the embankment, and to give it stiffness, and 
 also to check the liability of the sheet being lifted or cracked 
 by back pressure from water in the embankment, when the 
 water in the reservoir may be suddenly drawn down. 
 
 The upper part of the slope that is exposed to frost is 
 of granite blocks laid upon broken stone. The layer of 
 broken stone at the wave line is fifteen inches thick, which 
 is none too great a thickness to prevent the waves from 
 sucking out earth and allowing the paving to settle. 
 
 368. Embankment Sluices and Pipes. Arched 
 sluices have been in many cases built through the founda- 
 tion of the embankment and the discharge pipes laid therein, 
 and then a masonry stop-wall built around the pipes near 
 
356 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 the upper end of the sluice. By this plan the pipes are 
 open for inspection from the outside of the embankment up 
 to the stop wall. If the sluice is not circular or elliptical, 
 its floor should be counter-arched, and its sides made strong, 
 to resist the great pressure of the water that may saturate 
 the earth foundation. 
 
 FIG. 62. 
 
 SLOPE PUDDLED RESERVOIR EMBANKMENT. 
 
 Such a sluice is sometimes built in a tunnel through the 
 hillside at one end of the embankment. The latter plan, 
 when the upper end of the tunnel is through rock, is the 
 safer of the two, otherwise there is no place where it can be 
 more safely founded, constructed, and puddled around, 
 than when it is built upon the uncovered foundation of the 
 embankment, either at the lowest point in, or upon, one 
 side of the valley, since every facility is then offered for 
 thorough work, which cannot so easily be attained in an 
 earth tunnel obstructed by timber supports. 
 
 A circular or rectangular well rising above the water 
 surface, is usually built over the upper end of the sluice, 
 and contains the valves of the discharge pipes, and inlet 
 sluices at different heights, admitting water to the pipes 
 from different points below the surface of the reservoir. 
 
 When the sluice is used for a waste-sluice, also, the 
 stop-wall is omitted, and the sluice well rises only to the 
 weir crest level, or has openings at that level and an addi- 
 tional opening at a lower level controlled by a valve. 
 
GATE CHAMBERS. 357 
 
 Sometimes heavy cast-iron pipes, for both delivery and 
 waste purposes, are laid in the earthwork instead of in 
 sluices, in which case the puddle should be rammed around 
 them with thoroughness. In this latter case they should be 
 tested, in place, under water pressure before being covered. 
 A "suitable hand force-pump may be used to give the 
 requisite pressure if not otherwise obtainable. Bell and 
 socket pipes with driven lead joints are used in such 
 cases, and projecting flanges are cast around the pipes at 
 intervals. 
 
 The method of laying and protecting discharge pipes, as 
 shown in Fig. 60 (p. 84), has been adopted by the writer in sev- 
 eral instances with very sati sfactory results. A foundation of 
 masonry is built up from a firm earth stratum to receive the 
 pipes, and then when the pipes have been laid and tested, 
 they are covered with masonry or concrete. In such case 
 the sides of the masonry are not faced, and pointed, or plas- 
 tered, but the stones are purposely left projecting and 
 recessed, and the covering stones are of unequal heights, 
 making irregular surfaces. This method is more economi- 
 cal in construction, and attains its object more successfully 
 than the faced break-walls sometimes projected from the 
 sides of gate-chambers and sluices. 
 
 The puddle or core material is rammed against the ma- 
 sonry in all cases, so as to fill all interstices solid. This 
 portion of the work demands the utmost thoroughness and 
 faithfulness ; and with such, the structure will be so far 
 reliable, and otherwise may be uncertain. 
 
 369. Gate Chambers. When an impounding reser- 
 Toir is deep, requiring a high embankment, it is advisable 
 to place the effluent chamber upon one side of the valley 
 toward the end of the embankment, with the effluent pipes 
 for ordinary use only as low as may be necessary to draw 
 
358 
 
 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 the lake down to the assumed low water level, as in Fig. 63 r 
 showing the inside slope of an embankment. 
 
 A waste-pipe for drawing off the lowest water is, in such 
 case, extended from the front of the effluent chamber, side- 
 ways down the slope and side of the valley to the bed of 
 its old channel, and is fitted with all details necessary for it 
 
 FIG. 63. 
 
 EFFLUENT CHAMBER AND SIPHON WASTE. 
 
 to perform the office of a siphon when there shall be occa- 
 sion to draw the reservoir lower than the level of the gate 
 chamber floor. By such arrangement the pipes may pass 
 through the embankment, or through a sluice or tunnel in 
 the side of a hill at a level twenty or twenty-five feet above 
 the bed of the valley. 
 
 When a valve-chamber is built up from the inner toe of 
 the embankment, so that the water surrounds it at a higher 
 level, provision must be made for the ice-thrust, lest it crowd 
 back toward the embankment the upper portion sufficiently 
 to make a crack in the wall ; and precaution must also be 
 taken to prevent the ice lifting bodily the whole top of the 
 
GATE CHAMBERS. 359 
 
 chamber when the water rises in winter, as it usually does 
 in large storage reservoirs. 
 
 The writer has usually connected the gate-house with 
 the embankment by a solid pier, when there would other- 
 wise be opportunity for the ice to yield behind the chamber 
 by slipping up the paving, as it expanded, and thus en- 
 danger the gate-chamber masonry. 
 
 There are inlets through the front of the effluent chamber 
 shown in Fig. 63, at different depths, permitting the water 
 to be drawn at different levels. 
 
 These, when the volume of water to be delivered is small, 
 may be pieces of flanged cast-iron pipe built into the 
 masonry, with stop-valves bolted thereon, but usually are 
 rectangular openings with cast-iron sluice - valves and 
 frames (Fig. 64) secured at their inside ends. The seat and 
 bearing of the valves are faced with a bronze composition, 
 which is planed and scraped so as to make water-tight 
 joints. The screw-stem of the valve is also of composition, 
 or aluminum or manganese bronze. 
 
 If such a valve exceeds 2'-3" x 2'-9" in area, or is 
 under a pressure of more than twenty feet head, some form 
 of geared motion is usually necessary to enable a single 
 man to start it with ease. 
 
 It is usually advisable to increase the number of valves 
 rather than to make any one so large as to be unwieldy in 
 the hands of a single attendant, even at the expense of some 
 frictional head. 
 
 The stem of the small valves usually passes up through 
 a pedestal resting on the floor of the chamber, and through 
 a nut in the centre of a hand- wheel that revolves upon the 
 pedestal. 
 
 The outside edge of each valve-frame should be so formed 
 that a temporary wood stop-gate might be easily fitted 
 
360 
 
 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 FIG. 64. 
 
 against it by a diver, in case accident required the removal 
 of the valve for repairs. The chamber might then be readily 
 emptied and the valve removed, without drawing down the 
 lake. 
 
 Upon the back of the valve (Fig. 64) are lugs faced with 
 bronze, and upon the frame corresponding lugs, both being 
 arranged as inclined planes, and their office is to confine the 
 valve snug to its seat when closed. 
 
 If the valve is secured to the side of the opening opposite 
 to that which the current approaches, or to the pressure, its 
 bolts must enter deep into or pass 
 through the masonry. 
 
 A slight flare is usually given to the 
 sluice-jambs, from the sluice-frame out- 
 ward. 
 
 370. Sluice-Valve Areas. When 
 the head is to be rigidly economized, 
 the submerged sluice-valve area must 
 be sufficient to pass the required vol- 
 ume of water at a velocity not exceeding 
 about five lineal feet per second; when 
 the loss of head due to passage of the 
 valve will not exceed about one-half 
 foot. 
 
 If Q is the maximum volume, in cu. 
 ft. per second ; S, the area of the sluice 
 in square feet ; , the assumed maxi- 
 mum velocity ; then 
 
 (1) 
 
 IRON SLUICE-VALVE. 
 
 in which c is a coefficient of contraction, 
 that may be taken, for a mean, as equal 
 to .70 for ordinary chamber-sluices. 
 
STOP-VALVE INDICATOR. 361 
 
 From this equation of Q, we derive that of area, 
 
 CD 
 
 (2) 
 
 Let Q = 70 cubic feet per second ; v = 5 lineal feet 
 per second ; then we have - L = 20 square feet area, and we 
 
 (?D 
 
 may make the valve opening, say 4' x 5'. 
 
 If there are a number of valves, whose respective areas 
 are ^, s 2 s s . . . . s then 
 
 i- = 
 Cc/ 
 
 (3) 
 
 advisedly we should give a slight excess to the sum of 
 
 . Q 
 
 or 
 
 areas and make 
 
 + s 2 + 
 
 FIG. 65. 
 
 371. Stop-Valve Indicator. When a stop-valve is 
 used, instead of a sluice-valve whose screw rises through 
 the hand- wheel, it is usually desir- 
 able to have some kind of an indi- 
 cator to show how nearly the stop- 
 valve is to full open. 
 
 Fig. 65 illustrates such an indi- 
 cator attached to. the hand -wheel 
 standard, as manufactured by the 
 Ludlow Valve Co., at Troy, N. Y. 
 A worm-screw upon the valve-stem 
 revolves the indicator-wheel at the 
 side of the standard, and indicates 
 the various lifts of the valve between 
 shut and full open. 
 
 372. Power Required to Open 
 a Valve. The theoretical computa- 
 tion of the power required to start a 
 
362 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 closed valve, when it is pressed to its seat by a head of water 
 upon one side and subject only to atmospheric pressure on 
 the other side, is 'attended with some uncertainties ; neverthe- 
 less this computation, subject to such coefficients as experi- 
 ence suggests, is a valuable aid when proportioning the parts 
 of new designs. 
 
 Take the case of the metal sluice-valve, Fig. 64, raised 
 by a screw, with its nut placed between collars in the top 
 of a pedestal, and revolved by a hand-wheel, and let the 
 centre of water pressure upon the valve be at a depth of 
 30 feet. Let the size of valve-opening be 2-6" x 2-9", the 
 pitch of the screw .75 inch, and the diameter of the hand- 
 wheel 30 inches. 
 
 The weight has to slide along the spiral inclined plane 
 of the screw, but its actual advance is in a vertical line, the 
 pitch distance, for each revolution of the screw. 
 
 The power is applied to the hand-wheel, which is equiva- 
 lent to a lever of length equal to its radius, moving through 
 
 a horizontal distance equal 
 FlG - 66. to the circumference of its 
 
 circle (= radius x 6.283*) 
 and a vertical distance 
 equal to the pitch of the 
 screw. 
 
 The distance d, moved through by the power in each 
 
 revolution, is the hypothenuse be, Fig. 66, of an angle 
 
 whose base, a&, equals the circumference of its circle, and 
 
 whose perpendicular, ac, equals the pitch of the screw = 
 
 '/circumference 2 + pitch 2 = d. 
 
 Let w be the weight in Ibs.; p the pitch, in inches ; d the 
 distance moved by the power per revolution, in inches, and 
 P, the power, in foot-pounds.. 
 
 According to a theory of mechanics, the 
 
POWER REQUIRED TO OPEN A VALVE. 363 
 
 Vel. of Power : Yel. of Weight :: Weight : Power; or, 
 d : p :: w : P. 
 
 The weight, in this case, includes the actual weight of 
 the iron valve and its stem ; its friction upon its seat due to 
 the pressure of water upon it ; the friction of the screw upon 
 its nut, and the friction of the nut upon its collar. These 
 we compute as follows : 
 
 Weight of valve, assumed = 300 Ibs. 
 
 Friction of valve (15469 Ibs. pres. x coef..20) = 3094 " 
 
 Friction of screw (300 + 3094) x coef. 20 = 679 " 
 
 Friction of nut (300 + 3094) x coef. 15 = 501 " 
 
 Total equivalent weight, w = 4574 " 
 
 Distance of power, d = \ circum. 2 -- pitch 8 fi = 94.25 inches. 
 
 Pitch = .75 " 
 
 In the form of equation, 
 
 Theoretically, this power applied at the circumference 
 of the hand- wheel would be just upon the point of inducing 
 motion, or if this power was in uniform motion around the 
 screw, it would just maintain motion of the weight. The 
 theory here admits that the screw and nut are cut truly to 
 their incline, and that there is no binding between them due 
 to mechanical imperfection. 
 
 When two metal faces remain pressed together an ap- 
 preciable length of time, the projections of each enter into 
 the opposite recesses of the other, to a certain extent. These 
 projections of the moving weight must be lifted out of lock, 
 and the inertia of the weight must be overcome before it 
 can proceed. Metal valves usually drop against an inclined 
 wedge at their back that presses them to their seat, and 
 there is also a fibre lock with this wedge, or "stick," as it 
 
364 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 is commonly called, according to the force with which the 
 valve is screwed home. 
 
 Hence, the power required to start A val^e is often double 
 
 i/( fasL-frC^ 
 
 or treble, or even quadruple that Q&B& would theoretically 
 be required to maintain it in motion the instant after start- 
 ing. The equation for starting the valve in such case may 
 become, 
 
 The computed distance which the power moves per revo- 
 lution (94.25 inches) equals 7.854 feet, and the computed 
 power 36.4 Ibs. If twenty revolutions of the hand- wheel are 
 made per minute, then the power exerted is theoretically 
 7.854 ft. x 20 rev. x 36.4 Ib. = 5717.7 foot-pounds per minute. 
 This is a little more than one-sixth of a theoretical horse- 
 power. 
 
 If, for the hand- wheel, which revolves the nut, there is 
 substituted a spur-gear of equal pitch diameter, and into 
 this meshes a pinion of one-third this diameter, and the 
 same hand- wheel is placed upon the axle of the pinion, then 
 the new power required will be reduced proportionally, as 
 the square of diameter of the pinion is reduced from the 
 square of diameter of the spur, or in this case, one-ninth. 
 
 373. Adjustable Effluent Pipe. An adjustable 
 effluent pipe, capable of revolving in a vertical plane, and 
 connected directly to the main supply pipe,* is shown in 
 Fig. 60 (p. 84). 
 
 This adjustable pipe is constructed of heavy sheet cop- 
 per, and is sixteen inches in diameter. Upon its end is a 
 
 * Tliis ingenious form of flexible joint was suggested to the writer by Hon. 
 Alba F. Smith, one of our most able American mechanical engineers. Mr. 
 Smith designed this joint many years ago, and used it at watering stations 
 upon the Hudson River, and other railroads under his charge. 
 
FISH SCREENS. 365 
 
 perforated bulb, through which the water enters the pipe. 
 The movable section of the pipe is counter- weighted within 
 the chamber, so the bulb can be set at any desired depth 
 in the water, or raised out of water to the platform upon the 
 chamber, for cleaning, expeditiously and easily by a single 
 attendant. This arrangement has operated most satisfac- 
 torily during the eight years since its completion, and de- 
 livers the water supply for about 18,000 inhabitants. 
 
 Equivalent devices have been adopted in several in- 
 stances in Europe and in India, and they are especially 
 applicable to cases where the impounding reservoirs are 
 also the distributing reservoirs, without the intervention of 
 filtering basins, and to cases where the surface fluctuates 
 frequently, rapidly, or to a considerable extent. 
 
 When a sudden or considerable decrease of the tem- 
 perature of the air chills the quiet reservoir water surface, 
 and thus induces a vertical motion in, or shifting of position 
 of the whole mass of water, the bulb may be made to fol- 
 low the most wholesome stratum. 
 
 If the impounded water is to be led to filter-beds or to 
 one or more distributing reservoirs, then the discharge- 
 pipes lead directly from the effluent chamber. 
 
 374. Fish Screens. In the chamber, Fig. 67, is shown 
 a set of fish-screens, arranged in panels so as to slide out 
 readily for cleaning. The finer ones of the double set are 
 of No. 15 copper wire, six meshes to the inch, and the 
 coarser ones of No. 12 copper wire, woven as closely as 
 possible. 
 
 Figs. 67 and 68 show a plan of and a vertical section 
 through an influent chamber of a distributing reservoir. 
 
 The pipes d d deliver water from the impounding reser- 
 voir, or may be force mains, leading from pumping engines 
 to the chamber A. The main chamber is divided in two 
 
366 RESERtOIR EMBANKMENTS AND CHAMBERS. 
 
 FIG. 67. 
 
 PLAN OF INFLUENT CHAMBER. 
 
 parts, for convenience in management when there are sev- 
 eral delivery pipes. There are sluices 7c Tc, controlled by 
 valves, through which the water may be admitted to the 
 reservoir O. There is also a weir, i, over which water may 
 be passed, instead of through the sluices. 
 
 FIG. 68. 
 
 SECTION THROUGH INFLUENT CHAMBER. 
 
 Grooves are prepared in each section of the main cham- 
 ber for a double set of screens, ss. 
 
V ^> * x '\ < bN 
 
 FOUNDATION^,/ 'V', 367 >T 
 
 </,^ ^ /';. \ 
 
 >, a waste Dme. and ^a wast&^^ r 
 
 GATE-CHAMBER 
 
 B is a waste chamber, and e a waste pipe, an 
 overflow weir. C^ 
 
 A frost curtain, w, is placed in front of the inflow weir/ 
 to prevent the water surface in the chamber from freezing, 
 if the pumps are not in operation during winter nights. 
 
 There are drain pipes, p, leading from the sections of 
 the main chamber to the waste well. 
 
 In the dividing partition is a sluice, with valve so that 
 the whole chamber may be connected as occasion requires. 
 A distributing reservoir effluent chamber might be simi- 
 lar to the above, omitting the waste chamber, weirs, and 
 frost curtain ; the direction of the current would in this case 
 be reversed, of course. 
 
 In the effluent chamber of the reservoir shown in Fig. 58, 
 a check-valve is placed in the effluent pipe, so that when 
 the pumps are forcing water into the distribution pipes 
 around the reservoir, with direct pressure, the water will 
 not return into the reservoir by the supply main. 
 
 375. Gate-Chamber Foundations. Gate-chambers 
 built into the inner slope of an earthwork embankment will 
 introduce an element of weakness at that point, unless 
 intelligent care is exercised to prevent it. 
 
 Any after settlement along t]je sides of the foundation 
 or walls of the chamber separates the earth from the 
 masonry, leaving a void or loose materials along the side 
 of the masonry, which permits the water of the reservoir to 
 percolate along the side to the back of the chamber, under 
 the full head pressure. 
 
 The stratum of earth on which the foundation rests 
 should be not only impervious, but so firm,- or made so 
 firm, that no settlement of the foundation can take place. 
 If the chamber is high and heavy, the footing courses 
 should be extended on each side so as to distribute the 
 
368 RESERVOIR EMBANKMENTS AND CHAMBERS. 
 
 weight on an area of earth larger than the section of the 
 chamber. 
 
 The foundation of the chamber is to be water-tight, and 
 capable of resisting successfully the upward pressure upon 
 its bottom due to the head of water in the reservoir, when 
 the chamber is empty. 
 
 376. Foundation Concrete. The use of belon, or 
 hydraulic concrete, is often advisable for the bed-course of 
 a valve-chamber foundation, to aid in distributing the 
 weight of the structure and in securing a water-tight floor. 
 The composition of the concrete is to be proportioned for 
 these especial objects. Concrete for a revetment, demands 
 weight as a special element ; for a lintel, tensile strength ; 
 for an arch, compressile strength ; but for the submerged 
 foundation of a gate-chamber, impermousness, which will 
 ensure sufficient strength. 
 
 The volume of cement should equal one and one-third 
 times the volume of voids in the sand. The volume of mor- 
 tar should equal one and one-third times the volume of 
 voids in the coarse gravel or broken stone. The cement 
 and sand should be first thoroughly mixed, then tempered 
 with the proper quantity of water equally worked in, and 
 then the mortar should be thoroughly mixed with the 
 coarse gravel or broken stone, which should be clean, and 
 evenly moistened or sprinkled before the mortar is intro- 
 duced. None of the inferior cement so often appearing in 
 the market should be admitted in this class of work. Good 
 hydraulic lime may in some cases be substituted for a 
 small portion of the cement, say one-third. 
 
 The concrete should be rammed in place, but never by 
 a process that will disturb or move concrete previously 
 rammed and partially set. A very moderate amount of 
 water in the concrete suffices when it is to be rammed. 
 
CHAMBER WALLS. 369 
 
 377. Chamber Walls. Fine -cut beds and builds, 
 hammered end joints, and coursed work, in chamber ma- 
 sonry, make expensive structures, but even such work is 
 hardly made water-tight by a poor or careless mechanic. 
 A great deal of skill and care must be brought into requi- 
 sition to make a rubble wall water-tight. 
 
 Imperviousness is here, again, a special object sought. 
 That a wall may be impervious, its mortar must be imper- 
 vious ; its voids must be compactly tilled, every one ; its 
 stones must be cleaned of dust, moistened, laid with close 
 x joints, and well bedded and bonded ; and no stone must 
 be shaken or disturbed in the least after the mortar has 
 begun to set around it. 
 
 Stone must not be broken or hammered upon the laid 
 wall, or other stones will be loosened. Stones should be so 
 lewised or swung that the bed or joint mortar shall not be 
 disturbed when the stone is floated into place. 
 
 The plan occasionally adopted of grouting several courses 
 at the same time with thin liquid grout, might answer in a 
 cellar wall when the object was to prevent rats from peram- 
 bulating through its centre, but it is unreliable in a cham- 
 ber or tank-wall intended to resist percolation under pres- 
 sure. Skillful workmanship, in hydraulic masonry, is 
 cheaper than expensive stock. 
 24 
 
CHAPTER XVII. 
 
 OPEN CANALS. 
 
 378. Canal Banks. The stored waters of an impound- 
 ing reservoir are sometimes conveyed in an open canal 
 toward the distributing reservoir, or the city where they are 
 to be consumed, or for the purposes of irrigation. "The 
 theory of flow in such cases has been already discussed 
 (Chap. XY). 
 
 The subsoils over which the canal leads require careful 
 examination, and if they are at any point so open and 
 porous as to conduct away water from the bed of the canal, 
 the bed and sides must be lined with a layer of puddle 
 protected from frost, as in Fig. 69, showing a section of a 
 puddled channel in a side-hill cut. 
 
 FIG. 69. 
 
 The retaining channel bank on the down-hill side is con- 
 structed upon the same principles as a reservoir embank- 
 ment ( 351), the chief objects being to secure solidity,, 
 imperviousness, and permanence. 
 
INCLINATIONS AND VELOCITIES. 
 
 371 
 
 A longitudinal drain along the upper slope of side-hill 
 sections will prevent the washing of soil into the canal. 
 The water slopes will require revetments or paving from 
 three feet below low-water to two feet above high-water 
 line, and paving or rubbling down the entire slope at their 
 concave curves. 
 
 Substantial revetments or pavings of sound stone are the 
 most economical in the end. 
 
 Kevetments, built up of bundles of fascines laid with 
 ends to the water and each layer in height falling back 
 with the slope line, have been used to some extent on the 
 banks of canals of transport, and on dykes.* 
 
 If the slopes are rip-rapped, or pitched with loose stone, 
 the slopes must be sufficiently flat, so the waves and the 
 frost will not work the stones down into the water, and de- 
 mand constant repairs. 
 
 The retaining canal banks of the head races of water- 
 powers have sometimes 
 a longitudinal row of 
 jointed-edged sheet-piles 
 through their centre. The 
 selected mixed earth is 
 compactly settled on both 
 sides of this piling, as 
 shown in Fig. 70. Such 
 piling tends to insure im- 
 perviousness, prevent vermin from burrowing through the 
 bank, and lasts a long time in compact earth. 
 
 379. Inclinations and Velocities in Practice. 
 The unrevetted trapezoidal canals in earthwork, for water- 
 
 * Vide illustration of Foss Dyke in Stevenson's Canal and River Engineer- 
 ing, p. 18, Edinburgh, 1872 ; and Mississippi River Dyke at Sawyer's Bend. 
 Report Chief of U. S. Engineers, June 30, 1873. 
 
 FIG. 70. 
 
 SHEET-PILED CHANNEL BANK. 
 
372 OPEN CANALS. 
 
 supplies, irrigation, and for hydraulic power, except in 
 water -powers of great magnitude, have sectional areas, 
 respectively, between 500 and 50 square feet limits, and 
 hydraulic mean radii between 7 and 2.5. 
 
 In such canals the surface velocities range between 
 5 feet and 2 feet per second, and the inclinations of surface 
 between .75 feet (= .000104) and 3.5 feet (= .000663) per 
 mile. 
 
 Practice indicates that the favorite surface velocity of 
 flow, in such straight canals, is about 2.5 feet per second, 
 in canals of ^about five feet depth, being less in shallower 
 canals, and increased to 3.5 feet per second in canals of 
 nine feet depth. 
 
 Only very firm earths, if unprotected by paving or rub- 
 ble, will bear greater velocities without such considerable 
 erosions as to demand frequent repairs. 
 
 Burnell states* that the inclinations given to the re- 
 cently constructed irrigation canals in Piedmont and Lom- 
 bardy, varies from y^ (= .000625) to ^^ (= .000278) ; 
 but that inclinations frequently given to main conductors 
 in the mountainous districts of the Alps, Tyrol, Savoy, 
 Dauphine, and Pyrenees, is ^ (= .002). 
 
 380. Ice Coverings. The maximum winter flow hav- 
 ing been determined upon, the sectional area, beneath the 
 thickest formation of ice at the lowest winter stage of water, 
 must be made ample to deliver this maximum quantity of 
 water, and the influence of the increase of friction on the ice 
 perimeter over that on the equal air perimeter must be duly 
 considered. 
 
 381. Table of Dimensions of Supply Canals. 
 The dimensions and inclinations of a few well-known canals 
 
 * Rudiments of Hydraulic Engineering, p. 127. London, 1858. 
 
CAN'AL GATES. 
 
 373 
 
 are given as illustrative of the general practice in various 
 parts of the world, relating especially to water supply and 
 irrigation. 
 
 TABLE No. 79. 
 DIMENSIONS OF WATER SUPPLY AND IRRIGATION CANALS. 
 
 
 ij 
 
 "I 
 
 1 
 
 & 
 
 | 
 
 ITIO OF 
 -INATION. 
 
 EAN 
 OCITY. 
 
 
 
 
 1$ 
 
 Q 
 
 c/5 
 
 
 | 
 
 "J 
 
 s 
 
 Henares Canal, Spain 
 
 Trapezoidal. 
 
 8.27 
 
 1 5 tO 
 
 4.02 
 
 i in 3067 
 
 .000326 
 
 2 2Q6 
 
 Roqueiavour Canal, France . . . 
 
 
 9.84 
 
 
 4-9* 
 
 n 3333 
 
 .0003 
 
 
 Marseilles 
 
 
 Q.8 4 
 
 i to 
 
 5.58 
 
 in 3000 
 
 .000333 
 
 2.72 
 
 Ourcq " 
 Montreal W. W. (old), Canada. 
 
 
 11.48 
 
 20 
 
 Jto 
 
 itO 
 
 4.92 
 
 in 9470 
 in 25000 
 
 .0001056 
 .00004 
 
 
 " (new), " 
 
 
 78 
 
 to 
 
 M 
 
 in 25000 
 
 .00004 
 
 .... 
 
 Manchester, N.H., W.W., U.S. 
 
 
 6 
 
 to 
 
 14 
 
 in 5280 
 
 .000189 
 
 
 Ganges Canal, India -< 
 
 and part 
 Twin Rect. 
 
 8= 
 
 ... . . 
 
 9 
 
 
 ::::::l 
 
 3-7 
 
 Glasgow W. W., Scotland 
 
 Rectangular. 
 
 8 
 
 
 8 
 
 i in 6325 
 
 .000158 
 
 1.478 
 
 Cavour Canal, Italy 
 
 " \ 
 
 131 
 
 
 
 6.1 
 
 i in 2800 
 
 .000357 i 
 
 2.6 
 
 
 } 
 
 
 
 11.15 
 
 
 .00025 j 
 
 
 In the numerous shallow irrigation canals of Spain, 
 Italy, and northern India, a mean velocity as great as three 
 feet per second is necessary to prevent a luxuriant growth 
 of weeds on the bottoms and side slopes, which reduce the 
 effective sectional area of the canal, and consequently the 
 volume of water delivered. 
 
 382. Canal Gates. Fig. 71 is a half elevation of the 
 gates in the Manchester, N. H., water- works canal, showing 
 also a profile of the canal beyond the wing walls of the 
 gate abutments. 
 
 This canal leads the water from Lake Massabesic to the 
 turbines and pumps at the pumping station. 
 
 The water surface rises and falls with the lake, which 
 has a maximum range of five feet, so that the turbines are 
 constantly under the full head of the lake. The canal is 
 sixteen hundred feet long, and has similar gates at its 
 
374 
 
 OPEN CANALS. 
 
 entrance and at the head of the turbine penstock. The 
 entrance gates are provided witli a set of iron racks to inter- 
 cept floating matters that might approach from the lake, 
 and the penstock gates are provided with a set of fine mesh 
 copper- wire fish-screens. 
 
 There are four gates in each set, each 3 feet wide and 
 5 feet high. On the top of each gate is secured a cast-iron 
 
 FIG. 71. 
 
 CANAL SLUICE-GATES. 
 
 tube containing a nut at its top. Over each tube is fastened, 
 to a lintel, a composition screw, working in its nut, which 
 raises or lowers its gate. 
 
 Two gates in each set have their screws provided with 
 gears and pinions. The pinions, or screws, are turned by a 
 ratchet wrench, so the operator may turn them either way, 
 to raise or lower the gate, by walking around the screw, or 
 by a forward and backward motion of the arms. 
 
 The floor covering the gate-chamber is of tar-concrete 
 resting upon brick arches. 
 
MINERS' CANALS. 375 
 
 When large sluices are necessary, a system of worm 
 gearing is usually applied for hoisting and lowering the 
 gates. These gears may be operated by hand-power, or 
 may be driven by the belts or gears upon a counter-shaft, 
 which is driven by a turbine or an engine. 
 
 Canals leading from ponds subject to floods or sudden, 
 rise above normal level, are to be provided with waste- weirs 
 near their head gates, and with waste-gates, so their banks 
 will not be overtopped or their waters rise above the pre- 
 determined height. 
 
 Stop-gates are placed at intervals in long water-supply 
 and irrigation canals, with waste-gates immediately above 
 them for drawing off their waters, to permit repairs, or for 
 flushing, if the waters deposit sediment. 
 
 Culverts are sometimes required to pass the drainage of 
 the upper adjoining lands beneath the canal, and these may 
 be classed among the treacherous details that require ex- 
 ceeding care in their construction to guard against settle- 
 ments, and leakage of the canal about them. 
 
 383. Miners' Canals. The sharp necessities of the 
 gold-mining regions of California and Nevada have led to 
 some of the most brilliant hydraulic achievements of the 
 present generation. The miners intercept the torrents of 
 the Sierras where occasion demands, and contour them in 
 open canals, along the rugged slopes, hang them in flumes 
 along the steep rock faces, syphon them across deep can- 
 yons, and tunnel them through great ridges, in bold defi- 
 ance of natural obstacles, though constant always to laws 
 of gravity and equilibrium. 
 
 The force of water is an indispensable auxiliary in sur- 
 face mining, and capital hesitates not at thirty, fifty, or a 
 hundred miles distance, or almost impassable routes, when 
 the torrent's power can be brought into requisition. A 
 
376 OPEN CANALS. 
 
 hundred ditches, as the miners term them, now skirt the 
 mountains, where but a few years ago there was no evi- 
 dence that the civilization or energy of man had ever been 
 present. 
 
 The Big Canyon Ditch, near North Bloomfield, Nevada, 
 for instance, is forty miles long and delivers 54,000,000 
 gallons of water per day. The sectional area of the stream 
 is about 33 square feet, and the inclination 16 feet to the 
 mile. Its flumes are 6 feet wide with grade of one-half 
 inch in twelve feet, or about 18 feet to the mile. The con- 
 tour line of the canal is from 200 to 270 feet above the 
 diggings, to which its waters are led down in wrought- 
 iron pipes. 
 
 With a terrible power, fascinating to observe, its jets 
 dash into the high banks of gravel, rapidly under-cutting 
 their bases, and razing them in huge slides that flow down 
 the sluice-boxes with the stream. 
 
 Thus, in a single mine, 30,000 cubic yards of gravel melt 
 away in a single day, under the mighty hydraulic influence 
 that has been gathered in the torrent and canaled along the 
 eternal hills. 
 
 The Eureka Ditch, in El Dorado County, is forty miles 
 long, and there are many others of great length, whose 
 magnitude and mechanical effect entitle them to considera- 
 tion, as valuable hydraulic works, and monuments of 
 hardy enterprise. 
 
 The Eureka embankment is seventy feet in height, flows 
 two hundred and ninety-six acres, and is located six thou- 
 sand five hundred and sixty feet above the level of the sea. 
 
CHAPTER XVIII. 
 
 WASTE-WEIRS. 
 
 384. The Office and Influence of a Waste- Weir. 
 
 An ample waste-weir is the safety-valve of a reservoir 
 embankment. 
 
 The outside slope of an earth embankment is its weakest 
 part, and if a flood overtops the embankment and reaches 
 the outer slope, it will be cut away like a bank of snow 
 before a jet of steam. 
 
 The overfall should be maintained always open and 
 ready for use, independent of all waste sluices that are 
 closed by valves to be opened mechanically, for a furious 
 storm may rage at midnight, or a waterspout burst in the 
 valley when the gate-keeper is asleep. 
 
 Data relating to the maximum flood flow is to be dili- 
 gently sought for in the valley, and the freshet marks 
 along the watercourse to be studied. The overfall is to be 
 proportioned, in both dimensions and strength, for the 
 extraordinary freshets, which double the volume of ordi- 
 nary floods, and if there are existing or there is a proba- 
 bility of other reservoirs being built in the valley above, it 
 may be wise to anticipate the event of their bursting, espe- 
 cially if an existing reservoir dam is of doubtful stability. 
 
 A short overfall may increase or affect the damage by 
 flood flowage to an important extent, and makes necessary 
 the building of the embankment to a considerable height 
 above its crest level ; while, on the other hand, a long over- 
 fall, if exposed to the direct action of the wind, may permit 
 
378 WASTE-WEIRS. 
 
 too great a volume of water to be rolled over its crest in 
 waves just at the commencement of a drought, when it is 
 important to save, to the uttermost gallon. Such wave 
 action, under strong winds, might draw down a small reser- 
 voir several inches, or even a foot below its crest, unless 
 such contingency is anticipated and guarded against. 
 Strong winds blowing down a lake often heap up its waters 
 materially at the outlet, and increase the volume of waste 
 flowing over its weir or outfall. 
 
 An injudicious use of flash-boards upon waste- weirs has 
 in many instances led to disastrous results. In all cases, a 
 maximum flood height of water should be determined upon, 
 and then the weir dimensions be so proportioned that no 
 contingency possible to provide for shall raise the water 
 above the predetermined height. The length of the overfall 
 and volume of maximum flood-flow govern the distance 
 the highest crest-level must be placed below the maximum 
 flood-level. Flash-boards may in certain cases, and in cer- 
 tain seasons, be serviceable in governing the level of water 
 below or just at the crest line, especially when there are low 
 lands, or lands awash, as they are termed, bordering upon 
 the reservoir, with their surfaces not exceeding three feet 
 above the crest line. 
 
 Several English writers mention that a general rule for 
 length of waste-weir, accepted in English practice, is to 
 make the waste-weir three feet long for every 100 acres of 
 watershed. This rule will apply for watersheds not exceed- 
 ing three square miles area, but for larger areas gives an 
 inconvenient length. 
 
 385. Discharges over Waste-Weirs. Having de- 
 termined, or assumed from the best data available, the 
 maximum flood-flow which the overfall may have to dis- 
 charge, if a very heavy storm takes place when the reservoir 
 
DISCHARGES OVER WASTE- WEIRS. 379 
 
 is full, the overfall is then to be proportioned upon the 
 basis of this flow. 
 
 For the calculation of discharge, the overfall may be 
 considered to be a species of measuring- weir ( 3O3), and 
 subject to certain weir formulas. 
 
 If there are flash-boards, with square edges, forming the 
 crest, then, for depths of from nine inches to three feet, Mr. 
 Francis' formula may be applied with approximate results, 
 and we have the discharge : 
 
 Q = 3.33 (I - O.lTi/7) H^ (I) 
 
 in which Q is the volume of discharge, in cubic feet per 
 second ; ZT, the depth of water upon the crest, measured to 
 the lake surface level ; Z, the clear length of overfall ; and 
 n the number of end contractions. 
 
 We have seen ( 3O9) that the velocities of the parti- 
 cles flowing over the crest are proportionate to the ordinates 
 of a parabola, and that the mean velocity is equal to two- 
 thirds the velocity of the lowest particles ; hence we have 
 the mean velocity, v, of flow over the crest, 
 
 = 5.35V Tl. (2) 
 
 Multiplying the depth of water H upon the weir, into 
 the length I of the weir, and into the mean velocity 0, we 
 have the volume of discharge, when there are no interme- 
 diate flash-board posts : 
 
 Q = mlH x l^ZgH= 6.96ml ff* 9 (3) 
 
 in which m is a coefficient of contraction ( 312), with 
 mean value about .622 for sharp-edged thin crests. 
 By transposition, we have : 
 
 If the overfall has a wide crest similar to that usually 
 given to masonry dams, Fig. 47, then we may apply more 
 
380 
 
 WASTE-WEIRS. 
 
 accurately the formula suggested by Mr. Francis for such 
 cases, viz. : * 
 
 Q = 3.0121H 1SB . (5) 
 
 If we desire to know the depth of discharge for a given 
 volume and weir length, then, by a transposition of this 
 last formula, we have : 
 
 ff- 
 - 
 
 -- 
 3M2l 
 
 L.M 
 
 (6) 
 
 A few approximate values of Q, for given values of H, 
 are given in the following table, to facilitate preliminary 
 calculations. 
 
 TABLE No. SO. 
 
 WASTE-WEIR VOLUMES PER LINEAL FOOT FOR GIVEI 
 
 DEPTHS. 
 
 H. 
 
 6=5.35^. 
 
 C =30i^>-. ^ 
 
 In feet. 
 
 In cu. ft. per sec. 
 
 In cu. ft. per sec.* 
 
 5 
 
 1.043 
 
 I.I77 
 
 75 
 
 J-939 
 
 2.167 
 
 1. 00 
 
 3.012 
 
 3-339 
 
 1.25 
 
 4.238 
 
 4.670 
 
 1.50 
 
 5.602 
 
 6.134 
 
 1.75 
 
 7-93 
 
 7.625 
 
 2.OO 
 
 8.699 
 
 9.430 
 
 2.25 
 
 10.415 
 
 11.244 
 
 2.50 
 
 12.238 
 
 13.167 
 
 2-75 
 
 14-159 
 
 I 5- I 93 
 
 3.00 
 
 16.171 
 
 17.309 
 
 3 CO 
 
 
 21.2 
 
 "0 
 
 
 
 4 .OO 
 ,\j\j 
 
 
 26 c. 
 
 
 
 w *o 
 
 4.50 
 
 
 T.2.7, 
 
 5 .OO 
 
 
 O 'O 
 
 38.6 
 
 
 
 O ' 
 
 C.CQ 
 
 
 45.0 
 
 00 
 
 6.00 
 
 
 C2.O 
 
 6. co 
 
 
 O 
 
 60.0 
 
 ^'O 
 
 7.00 
 
 
 68.3 
 
 / * w 
 
 
 w O 
 
 
 
 78.0 
 
 8.00 
 
 
 / 
 
 87.0 
 
 * In this column m increases from .563 for 1 foot depth to .670 for 8 feet 
 depth, but the values of m for depths exceeding 3 feet have not been de- 
 termined by experiment, and their results are subject to some uncertainty. 
 
REQUIRED LENGTH OF WASTE -WEIRS. 
 
 381 
 
 386. Required Length of Waste- Weirs. The fol- 
 lowing table, prepared to facilitate preliminary calculations, 
 gives estimated flood volumes of waste from small impound- 
 ing reservoirs, in ordinary Atlantic slope basins, for water- 
 sheds of given areas ; also the length of waste- weir required, 
 and approximate depth of water on the crest of the given 
 length : 
 
 TA BLE No. 81. 
 LENGTHS AND DISCHARGES OF WASTE-WEIRS. 
 
 Area of Water- 
 shed. 
 
 Required length 
 of overfall tor 
 given watershed. 
 
 Approx. depth of 
 water on overfall 
 of given length. 
 
 Approx. discharge 
 per lin. ft. of given 
 overfall, for given 
 depth. 
 
 Flood volume from 
 whole area, 
 Q=*<x>(M)$. 
 
 Square miles. 
 
 Feet. 
 
 Feet. 
 
 Cubicfeet. 
 
 Cubic feet per sec. 
 
 I 
 
 2 5 
 
 1.89 
 
 8 00 
 
 2OO 
 
 2 
 
 3 2 
 
 2-35 
 
 11.13 
 
 356 
 
 3 
 
 39 
 
 2. 5 6 
 
 12.82 
 
 500 
 
 4 
 
 44 
 
 2. 7 6 
 
 14-43 
 
 635 
 
 6 
 
 54 
 
 3.01 
 
 16.56 
 
 890 
 
 8 
 
 61 
 
 3.22 
 
 18-54 
 
 II 3 I 
 
 10 
 
 68 
 
 3-46 
 
 2O.O4 
 
 T363 
 
 15 
 
 83 
 
 3-70 
 
 23.01 
 
 1910 
 
 20 
 
 95 
 
 3-90 
 
 25-5 6 
 
 2428 
 
 2 5 
 
 !5 
 
 4.14 
 
 27.85 
 
 2925 
 
 30 
 
 116 
 
 4.28 
 
 29-35 
 
 3404 
 
 40 
 
 133 
 
 4-58 
 
 32.53 
 
 4326 
 
 50 
 
 149 
 
 4.71 
 
 34.95 
 
 5208 
 
 75 
 
 183 
 
 5-14 
 
 39-92 
 
 7304 
 
 100 
 
 212 
 
 5-34 
 
 43.78 
 
 9282 
 
 20O 
 
 2 95 
 
 6.28 
 
 56.08 
 
 16542 
 
 300 
 
 360 
 
 6.65 
 
 64.42 
 
 23190 
 
 40O 
 
 40O 
 
 7.36 
 
 73-70 
 
 29480 
 
 500 
 
 440 
 
 7.81 
 
 80.70 
 
 35500 
 
 6OO 
 
 480 
 
 7.98 
 
 86.08 
 
 41320 
 
 800 
 
 530 
 
 8.86 
 
 99.09 
 
 52520 
 
 IOOO 
 
 580 
 
 9-32 
 
 109.07 
 
 63260 
 
 The maximum flood, and consequently the required 
 length of overfall, or depth upon it, varies with the maxi- 
 mum periodic rainfall ; the inclination and porosity of 
 
382 
 
 WASTE -WEIRS. 
 
 soils; the sum of pondage surfaces; and to some extent 
 with temperatures. 
 
 The above estimated flood volumes refer to ordinary 
 American Atlantic slopes, and forty to fifty inch mean an- 
 nual rainfalls, and to streams with comparatively small 
 pondage areas. 
 
 The above tabled lengths of overfalls or range of depths 
 upon crests of waste-weirs, are to be increased for flashy 
 streams, and may be reduced for steady streams with large 
 or many small ponds. 
 
 The increase of pressure upon all portions of the em- 
 bankment and foundation, and upon the waste-weir, by the 
 flood rise, must be fully anticipated in the original design 
 of the structure. 
 
 387. Forms of Wastfe-Weirs. Fig. 72 illustrates a 
 waste-weir placed in the centre of length of an earthwork 
 embankment, retaining a storage lake of twenty-four hun- 
 dred acres, and the drainage of forty square miles of water- 
 shed. 
 
 FIG. 72. 
 
 n 
 
 The down-stream face of the weir is constructed in a 
 series of steps of decreasing height and increasing projec- 
 tion, from the crest downward, so that the edges of the steps 
 nearly touch an inverted parabolic curve. 
 
ISOLATED WEIRS. 383 
 
 The apron receiving the fall of waste water from the 
 crest of the weir is of rubble masonry, and contains two 
 upright courses intended to check any scour from the 
 "undertoe" during freshets, and also to lock the founda- 
 tion courses that receive the heaviest shocks of the falling 
 water. 
 
 The projection of the steps was arranged to break up 
 the force of the falling water as much as possible. 
 
 The fall from crest to apron is twenty-five feet, and the 
 flood depth upon the weir twenty inches ; yet the force of 
 the falling water is so thoroughly destroyed that it has not 
 been sufficient to remove, in three years service, the coarser 
 stones of some gravel carted upon the apron during con- 
 struction of the upper courses of the weir. 
 
 There is a 3 by 5 feet waste-sluice through the weir at 
 one end, discharging upon the apron. In front of the sluice 
 the apron consists of two eighteen-inch courses of jointed 
 granite upon a rubble foundation, doweled and clamped 
 together in a thorough manner. 
 
 A carriage-bridge spans the weir, and rests upon the 
 wing walls and three intermediate piers built upon the weir. 
 
 388. Isolated Weirs. Where the topography of the 
 valley admits of the waste- weir being separated from the 
 embankment, it should be so placed at a distance, and it 
 is often conveniently made to discharge into a side valley 
 where the flowage nearly, or quite, reaches a depression in 
 the dividing ridge. 
 
 But it is not always admissible to so divert the water, as 
 riparian rights may be affected, or flood damages be created 
 on the side stream. 
 
 When possible, it is advisable to locate the waste-weir 
 upon a ledge at one end of the embankment, so that the 
 fall from the crest will not exceed three or four feet. 
 
384 
 
 WASTE -WEIRS. 
 
 There should be a fall of at least three feet from the crest, 
 as in such case a less length of weir will be required than if 
 it slopes gently away as a channel. 
 
 FIG. 73 
 
 TIMBER CRIB-WEIR. 
 
 389. Timber Weirs. In those localities where sound 
 and durable building-stones are scarce, and timber is plenty 
 and cheap, the waste- weir may be substantially constructed 
 of timber in crib form. Fig. 73 represents such a weir 
 placed upon a gravel foundation. The fall is twenty feet, 
 and the face of the weir is divided into three benches so as 
 to neutralize the force of the fell that in freshets, if vertical, 
 would tend to excavate a hole in the gravel in front of the 
 dam at least two-thirds as deep below the lower water sur- 
 face as the height of the fall. 
 
 The timbers are faced upon two sides to twelve inches 
 thickness and entirely divested of bark. The bed-sills are 
 
TIMBER WEIRS. 385 
 
 sunk in trenches in the firm earth, and two rows of jointed 
 sheet-piling are sunk, as shown, to a depth that will prevent 
 the possibility of water working under them. Upon the 
 bed-sills longitudinal timbers are laid five feet apart, then 
 cross timbers as shown, and so alternately to the top. As 
 each tier is put upon another it is thoroughly fastened to 
 the lower tier by trenails or f -inch round iron bolts. The 
 bolts should pass entirely through two timbers depth and 
 one-half the depth of the next tier, requiring for twelve-inch 
 timbers 30-inch bolts. 
 
 As each tier is laid it should be filled with stone ballast 
 and sufficient coarse and fine gravel puddled in to make the 
 work solid, leaving no interstices by the side of or under 
 timbers. The gravel should be rammed under the timbers 
 so as to give them all a solid bearing. 
 
 A tier of plank is placed under each bench capping, and 
 a tier of close-laid timbers is placed under the crest capping. 
 The bench and crest cappings are of timbers jointed upon 
 their sides and laid close. The upper and lower faces are 
 planked tight with jointed plank. 
 
 A weir thus solidly and tiglitly constructed will prove 
 nearly as durable as the best masonry structures. The 
 capping and face plankings will be the only parts requiring 
 renewal, and these only at intervals of a number of years 
 if they are at first of proper thickness. 
 
 Similar forms of crib-work have been used with com- 
 plete success on rock bottoms, on impetuous mountain 
 streams, where they were subject to the shocks of ice at the 
 breaking up of winter, and to great runs of logs in the 
 spring. In such cases the bed-sills are bolted to the rocks. 
 
 Similar crib foundations may be used to carry masonry 
 weirs upon gravel bottoms, but the crib-work should in 
 such case be placed so low as to be always submerged. 
 25 
 
386 WASTE-WEIRS. 
 
 Fig. 73 was designed for a case where the watershed is 
 of about one hundred square miles area. Its crest-length is 
 two hundred feet, and six feet is the estimated maximum 
 flood-depth upon its crest. 
 
 390. Ice-thrust upon Storage Reservoir Weirs. 
 Those weirs that are located in Northern climates upon 
 storage ponds, such as are drawn down in summer and do 
 not rise to the crest-level until past mid-winter, should be 
 backed with gravel to the level of the backs of their caps, 
 and the gravel should be substantially paved, as in Fig. 72. 
 Otherwise the expansion of the thick ice against the verti- 
 cal backs of the weirs may act with such powerful thrust as 
 to displace or seriously injure its upper portion. 
 
 391. Breadth of Weir- Caps. The cap-stones of weirs 
 in running streams should incline downward toward the 
 pond side at least two inches for each foot of breadth, so 
 that the floating ice and logs will not strike against their 
 back ends when the water is flowing rapidly. 
 
 There is a lack of uniformity, in practice, in breadths of 
 tops of waste-weirs, and the unsatisfactory working of the 
 quarry from which the caps are supplied often controls 
 this dimension so far as to reduce it to an unsubstantial 
 measure. 
 
 The breadth of cap required depends somewhat on the 
 pond behind the weir. If the pond is relatively broad and 
 deep, water and whatever floating debris it carries, will 
 approach the weir with a relatively low velocity. If the 
 pond is small and the stream torrential, with liability of 
 great depth upon the weir, then the cap-stones must have 
 length and weight to resist the force of the current and im- 
 pact of the floating bodies. Overfalls upon logging streams 
 rising in the lumber regions, require particularly heavy 
 caps, and the force of the logs or ice upon the caps will 
 
THICKNESS OF WASTE -WEIRS AND DAMS. 
 
 387 
 
 usually be greater when the depth upon the weir is from 
 one and one-half to two feet, than when deeper. 
 
 392. Thickness of Waste-Weirs and Dams. If 
 
 the back, or pond side of the dam, is vertical, and the thick- 
 ness at cap constant, then the thicknesses at given depths 
 may be found, for plotting a trial section, by the following 
 equation : 
 
 Let b be the assumed top breadth, and t the thickness 
 at any given depth, d, then 
 
 t = b + .ld*. (7) 
 
 For illustration, let the assumed cap breadth, or length 
 of cap stones, for a long straight dam, be eight feet, then 
 for the following given depths, the ordinates or thicknesses 
 are as follows : 
 
 TABLE No. 82. 
 THICKNESS FOR MASONRY WEIRS AND DAMS. 
 
 DEPTHS FROM TOP 
 
 OF CAP. 
 
 
 THICKNESS. 
 
 Feet. 
 
 (6.) 
 
 (.*!.) 
 
 Feet. 
 
 O 
 
 8 + 
 
 o.o == 
 
 8.00 
 
 4 
 
 8 + 
 
 .8 = 
 
 8.80 
 
 6 
 
 8 + 
 
 1.47 = 
 
 9-47 
 
 8 
 
 8 + 
 
 2.26 = 
 
 10.26 
 
 10 
 
 8 + 
 
 3.16 = 
 
 ii. 16 
 
 12 
 
 8 + 
 
 4. 16 = 
 
 12. l6 
 
 15 
 
 x 8 + 
 
 5-81 = 
 
 13.81 
 
 20 
 
 8 + 
 
 8.94 = 
 
 16.94 
 
 25 
 
 8 + 
 
 12.50 = 
 
 20.50 
 
 30 
 
 8 + 
 
 16.43 = 
 
 24.43 
 
 35 
 
 8 + 
 
 20.71 = 
 
 28.71 
 
 40 
 
 8 + 
 
 25-30 = 
 
 33.30 
 
 45 
 
 8 + 
 
 30.19 = 
 
 38 19 
 
 50 
 
 8 + 
 
 35-36 = 
 
 43.36 
 
 If the face curve is resolved into steps, as is advisable 
 over gravel bottoms or tertiary rock, then the masonry of 
 
388 WASTE-WEIRS. 
 
 the steps must be very heavy and substantial, in the high 
 dams, to withstand for a long term of years the shock of the 
 falling water. 
 
 393. Force of the Overflowing Water. It is of 
 the utmost importance that the water passing over the lip 
 of a high dam shall reach the bed of the stream below the 
 dam with the least possible shock to the foundation, even 
 though it is of a tolerably hard rock, and especially if the 
 apron be of concrete or crib- work. 
 
 The "life" of numerous upright -face dams has been 
 materially shortened by the tremor due to the flood falls 
 upon their foundations. 
 
 In the case of an overfall twenty-five feet high, with six 
 feet depth of water above the crest, for instance, there is a 
 force of nearly 80,000 pounds per second pounding upon 
 each lineal foot of its apron, tending to shake the structure 
 into granular disintegration, and making the earth tremble 
 under the shock. 
 
 394, Heights of Waves. Stevenson gives, in his 
 treatise on Harbors, the following formula for computing 
 the height of waves coming from a given exposure, or 
 " fetch" of clear deep water : 
 
 H = 1.6 *SD + (2.5 - tfU), (8) 
 
 in which His, the height of waves in feet, and D is the length 
 of exposure or fetch in miles. 
 
 The numerical values of height of wave, according to 
 this formula, for given exposures, are as follows : 
 
 TABLE No. 83. 
 HEIGHTS OF RESERVOIR AND LAKE WAVES. 
 
 Exposure in miles . . . 
 
 25 
 
 .50 
 
 75 
 
 i 
 
 T5 
 
 g 
 
 3 
 
 5 
 
 10. 
 
 Height of wave, in feet.. 
 
 2-543 
 
 2.756 
 
 2.868 
 
 3 
 
 3-031 
 
 3.332 
 
 3.782 
 
 4.437 
 
 5.466 
 
HEIGHTS OF WAVES. 389 
 
 When waves meet a paved slope their vertical longi- 
 tudinal section is suddenly reduced and their velocity en- 
 hanced in inverse proportion. They will therefore rise up 
 the slope to a vertical height much greater than the height 
 of the approaching wave, which height will depend on both 
 the initial velocity of the wave and the suddenness with 
 which its sectional area is reduced. 
 
CHAPTER XIX. 
 
 PARTITIONS, AND RETAINING WALLS. 
 
 395. Design. The hydraulic engineer finds necessary- 
 exercise for his skill on every hand to adapt a variety of 
 constructions in masonry to their several ends, in methods 
 at once substantial and economical. 
 
 Designs are required for reservoir partitions and gate 
 chambers that are to sustain pressures of water upon both 
 sides, and either side alone ; revetments for reservoirs, 
 canals, and lake and river fronts that are to sustain pres- 
 sures of water and earth upon opposite sides, and earth 
 alone upon one side; coal-shed walls that are to sustain 
 the pressure of coal, whose horizontal thrust nearly equals 
 that of a liquid of equal specific gravity ; conduit and filter 
 gallery walls, that are to sustain pressures of earth and 
 water and thrusts of loaded arches ; basement walls and 
 bridge abutments that are to sustain thrusts of earth and 
 carry weight ; wing walls of triangular elevations and vary- 
 ing heights, that are to sustain varying thrusts ; and waste- 
 weirs, that are to sustain pressures of water higher than 
 their summits and moving with velocity. 
 
 Rule of thumb practice in such structures has led to 
 many failures, when the amounts and directions of thrusts 
 were not understood ; and such failures have, on the other 
 hand, led to the piling up of superfluous quantities of 
 masonry, often in those parts of section where it did not 
 increase the stability of position, but did endanger the 
 stability of the foundations. 
 
THEORY OF WATER PRESSURE. 391 
 
 * 
 
 Good design only, unites economy with stability in 
 masonry subjected to lateral thrusts. 
 
 396. Theory of Water Pressure upon a Vertical 
 Surface. The theory of pressure of water upon a plane 
 surface, and of the stability of a vertical rectangular retain- 
 ing wall, is quite simple, and is easily exemplified by 
 graphic illustration, and by simple algebraic equations. 
 
 Let BD, Fig. 74, be a vertical plane, receiving the 
 pressure of water. 
 
 The pressure, p, at any depth is proportional to that 
 depth into the density of the fluid. 
 
 Let w l be the weight of one cubic foot of waters 
 62.5 Ibs. ; then the pressure upon any square foot of the 
 vertical plane, whose depth of centre of gravity is represent- 
 ed by d, is p dwi. 
 
 Let the depth of the water B 2 D be 12 feet = h. Plot in 
 horizontal lines from B 2 D, at several given depths, the 
 magnitudes of the pressures at those depths = dw, as at ssi ; 
 then the extremities of those lines will lie in a straight line 
 passing through B, and cutting the horizontal line CDf, in 
 /, Df being equal to the magnitude of the pressure at D. 
 
 The total pressure upon the plane B 2 D, and its horizon- 
 tal effects at all depths are graphically represented by the 
 area and ordinates of the figure BJD. 
 
 In theoretical statics, the effect of a pressure upon a 
 solid body is treated as a force acting through the centre of 
 gravity of the body. 
 
 Consider the pressure of BfD to be gathered into its 
 resultant, passing through its centre of gravity,* g. The 
 
 * To find the centre of gravity of a triangle BfD, draw a broken line from 
 D, bisecting the opposite side in *,, and from/, bisecting the opposite side in 
 8 : the centre of gravity will then lie in the intersection of those lines. Or, 
 draw a line from any angle B 2 , bisecting the opposite side, and the centre of 
 
392 PARTITIONS, AND RETAINING WALLS. 
 
 FIG. 74 
 
 horizontal resultant through g will meet B 2 D in N, at two- 
 thirds the depth 2 D. 
 
 Let DCB be a section of wall one foot long. Let BJ) 
 
 gravity will lie in this line, at one-third the height from the side bisected. 
 The centre of gravity is at two-thirds the vertical depth B 2 D = f A from B z . 
 
WATER PRESSURE UPON AN INCLINED SURFACE. 393 
 
 = n = 12 ft. The centre of gravity of the submerged wall 
 surface BzD is at one-half its height, = - The total 
 
 <e 
 
 pressure of water p upon the wall-surface B 2 D equals the 
 product of the surface area, B 2 D = A^ into the weight of 
 one cubic foot of water, w^ into one-half the height, = 
 
 j> = 4n-} = k- (i) 
 
 19 
 = (12 x 1) x 62.5 x ~ 
 
 = 4500 pounds = 2.25 tons. 
 
 Draw this total pressure to scale, in the resultant gN, 
 meeting B 2 D in N. 
 
 The effect of a pressure, when applied to a solid body, 
 is the same at whatever point in the line of its direction it 
 is applied ; so we may consider gN as acting upon the wall 
 either at N or at x, in the vertical through the centre of 
 gravity of the wall. 
 
 The force tending to push the wall along horizontally 
 isgN. 
 
 397. Water Pressure upon an Inclined Surface. 
 The maximum resultant of pressure of water upon the 
 inclined plane JO has a direction perpendicular to the 
 plane, and meets the plane in P l9 at two-thirds the vertical 
 depth of the water. 
 
 The entire weight of the triangular body of water CiJ is 
 supported by the masonry surface JO. Its vertical pressure 
 resultant upon JC passes through its centre of gravity in g^ 
 and meets JC in P 1? at two-thirds the vertical depth iC or 
 JC. Its horizontal pressure resultant also meets JC in PI. 
 
 Let #q be the symbol of its horizontal resultant. 
 " e " " " vertical " 
 
 " y " " " maximum " 
 
394 PARTITIONS, AND RETAINING WALLS. 
 
 The horizontal effect of the pressure, a? l5 may be com- 
 puted as acting upon the plane of its vertical projection or 
 trace, iC, and will equal, 
 
 = 2.25 tons, when 7i = 12 ft. 
 
 Draw x l 2.25 tons to scale in XiP^ . Let fall a perpen- 
 dicular upon JC, meeting it in P l ; then will the angle 
 equal the angle JCi = 0, and yP t will equal * 
 
 ( 7i 2 ) 
 y = <zv sec = j w i -Q- r sec angle x^P^y (3) 
 
 = 2.515 tons ; 
 
 and ePi will equal 
 
 i ft?) 
 e x^ tan = \ w l \ - tan angle XiP^ (4) 
 
 ( * ) 
 
 = 1.125 tons. 
 
 The horizontal force tends to displace the wall horizon- 
 tally. The vertical downward force tends to hold the wall 
 in place, by friction due to its equivalent weight. 
 
 If water penetrates under the base of the wall, it -will 
 there exert an upward pressure upon the base, opposed to 
 the downward pressure upon JC, and to the weight of the 
 wall, with maximum theoretical effect equal to area CD 
 into depth of its centre of gravity into the weight of one 
 cubical foot of water. 
 
 Let ^be the symbol of the maximum upward pressure, 
 and let GI be the ratio of the effective upward pressure in 
 any case to the maximum. 
 
 Draw ctfi in the vertical line through the centre of gravity 
 of the masonry, in Gzi. 
 
 When computing the resultant weight of the masonry, 
 
 * Vide trigonometrical diagram and table in the Appendix. 
 
FRICTIONAL STABILITY 
 
 opposed to the horizontal water pressure, deduct from'th^ 
 weight of wall the excess of upward, c^, over downward 
 pressure, e, G& e. 
 
 398. Frictional Stability of Masonry. The weight, 
 W, in pounds, of the wall (of one foot length) equals its 
 sectional area DCB = A, in square feet, into the weight of 
 one cubical foot w of its material : 
 
 W = Aw. (5) 
 
 The downward resultant of weight is 
 
 W r = (Aw) + e- (c&). (6) 
 
 The upward pressure of the water upon the base will rare- 
 ly exceed .50 per cent, of the theoretical maximum, even 
 though the wall is founded upon a coarse porous gravel, or 
 upon rip-rap, without a like upward relief of backfilling. 
 
 The frictional stability, S, of the wall, equals its result- 
 ant weight into its coefficient, c, of friction, 
 
 8 = \W+e-(c^\ x c. (7) 
 
 Foundations of masonry upon earth are usually placed 
 in a trench, by which means the frictional stability upon 
 the foundation is aided by the resistance of the earth side 
 of the trench, and the coefficient thus made at least equal to 
 unity. In such case the measure of resistance to horizontal 
 displacement is the friction of some horizontal or inclined 
 joint. 
 
 The value of the adhesion of the mortar in bed-joints is 
 usually neglected in computations of horizontal stability, 
 and sufficient frictional stability should in all cases be given 
 by weight, so that the resistance of the mortar may be 
 neglected in the theoretical investigation. 
 
 If, however, the mortar is worthless, or its adhesion is 
 
396 
 
 PARTITIONS AND RETAINING WALLS. 
 
 destroyed by frost or careless workmanship, or otherwise, 
 then the mortar becomes equivalent to a layer of sand as a 
 lubricant, and the coefficient of friction may thus be reduced 
 very low. 
 
 399. Coefficients of Masonry Friction. The fol- 
 lowing table of coefficients of masonry frictions will be found 
 useful.* They are selected from several authorities, and 
 have been generally accepted as mean values. 
 
 TAB L E No. 84. 
 COEFFICIENTS OF MASONRY FRICTIONS (DRY). 
 
 
 
 COEF. 
 
 ANGLE 
 
 OF 
 
 REPOSE. 
 
 Point dressed granite 
 
 (medium) on dry clay . . 
 
 
 27 O 
 
 
 
 .3-3 
 
 
 
 
 .58 
 
 ^O 
 
 
 " ' like granite . . . 
 
 7O 
 
 qe 
 
 
 " ' common brickwork ...... 
 
 6-J 
 
 32 2 
 
 Fine cut granite 
 
 " ' smooth concrete 
 
 .62 
 
 "3,0 
 
 Very fine cut granite 
 
 
 .61 
 
 
 ( U 
 
 ' pressed Beton Coignet. . . 
 (medium) ' like limestone 
 
 .61 
 
 18 
 
 30.30 
 2O 48 
 
 11 
 
 " * brickwork 
 
 60 
 
 31 
 
 Beton blocks 
 
 (pressed) ' like Beton blocks 
 
 66 
 
 3 -3. 1C 
 
 Polished marble 
 
 
 .44 
 
 2-3.41; 
 
 1C (( 
 
 ' fine cut granite . . . 
 
 6l 
 
 3O.3O 
 
 
 " common bricks 
 
 64 
 
 
 
 " dressed hard limestone.. . 
 
 .60 
 
 31 
 
 When S and x^ are equal to each other, the wall is just 
 upon the point of motion, and x l must be increased ; that 
 is, more weight must be given to the wall to ensure frictional 
 stability. 
 
 Let the water be withdrawn from the side B D, Fig. 74, 
 and let the upward pressure attain to one-half the maxi- 
 mum, and the coefficient be that of a horizontal bed-joint 
 upon a concrete foundation, assumed to be .62, then S = 
 
 * Vide 353, pp. 344, 345. 
 
LEVERAGE STABILITY OF MASONRY. 397 
 
 (w + e .50^) x c = 2.79 tons, and x l 2.25 tons, and the 
 wall has a \ small margin of frictional stability. 
 
 The weight of the wall should be increased until it is 
 able to resist a horizontal thrust of at least 1.5^, or until 
 S= 1.5#i, when the equation of frictional stability becomes 
 
 S = (w 4- e C&) x c = 1.5#i, (8) 
 
 in which 
 
 w is the weight of masonry above any given plane. 
 e " vertical downward water pressure resultant. 
 2\ " maximum upward water pressure resultant. 
 d " ratio of effective upward water pressure to the 
 
 maximum. 
 c " coefficient of friction of the given section upon 
 
 its bed. 
 
 fy " horizontal water pressure resultant. 
 8 " symbol of frictional stability. 
 
 4OO. Pressure Leverage of Water. Since the hori- 
 zontal resultant of the water-pressure has its point of appli- 
 cation above the level of Z>, in N, its moment of pressure 
 leverage, L, has a magnitude equal to DN^ or Kx = \7i, 
 into the horizontal resultant. 
 
 (9) 
 
 4O1. Leverage Stability of Masonry. The moment 
 of pressure-leverage of the water tends to overturn the wall 
 about its toe, D or C, Fig. 74, opposite to the side receiving 
 the pressure alone, or the maximum pressure. 
 
 Let the weight of DCB, per cubical foot, be assumed 
 140 pounds, an approximate weight for a mortared rubble 
 wall of gneiss, or mica-slate ; then the total weight above 
 the bed-joint CD, is 140A = 5.25 tons, which we may con- 
 
398 PARTITIONS, AND RETAINING WALLS. 
 
 sider as acting vertically downward through (7, the centre 
 of gravity of DOR 
 
 Plot to scale this vertical resultant of weight in xe 2 = 
 5.25 tons (neglecting for the present the upward and down- 
 ward pressures of the water), and the horizontal resultant 
 of water pressure in xN z = 2.25 tons, and complete the 
 parallelogram xJV 2 Me 2 ; then the diagonal xM, is in mag- 
 nitude and direction the final resultant of the two forces. 
 The resultant arising from the horizontal pressure on 
 JC, and weight of the masonry, is in magnitude and direc- 
 tion xO. 
 
 If the directions of xM and xO cut the base DC, then the 
 wall has, theoretically, leverage stability, but if the direc- 
 tions of these diagonals are outside of DC, then the wall 
 lacks leverage stability and will be overturned. 
 
 For safety, the direction of xM should cut the base at a 
 distance from K not exceeding one-half KC, and the direc- 
 tion of xO cut the base at a distance from K not exceeding 
 one-half KD. 
 
 4O2. Moment of Weight Leverage of Masonry. 
 Since the vertical resultant of weight of masonry takes its 
 direction through 6r, and cuts DC at a distance from (7, 
 the point or fulcrum over or around which the weight must 
 revolve, the moment of weight leverage of the wall has a 
 magnitude, when resisting revolution to the right, equal to 
 the distance KD into the vertical weight resultant ; and 
 when resisting revolution to the left, equal to the distance 
 KC into the vertical weight resultant. 
 
 Let the symbol of distance of K from the fulcrum, on 
 either side, be d, and its value be computed or taken by 
 scale, at will ; and let the symbol of moment of weight 
 leverage be JS 9 then 
 
 M= Awd. (10) 
 
MOMENTS OF SECTIONS. 399 
 
 For double stability, or a coefficient of safety equal to 2, 
 A.wd 
 
 must, at least, be equal to A^ , or 
 
 D 
 
 4O3. Thickness of a Vertical Rectangular Wall 
 for Water Pressure. 
 
 Let 7i be the height of the wall and of the water. 
 " w " weight of a cubic foot of the masonry. 
 " M! " " " " " water. 
 
 " z " required thickness of the wall. 
 
 Then h x z x - t '- x w = leverage moment of weight of 
 
 T, T -, Ti 7i , 
 
 wall, = s - ; and 7ix^xWiX- = leverage moment of 
 ^ o 
 
 pressure of water = for double effect, ^ 
 
 The equation for a vertical rectangular wall, Fig. 75, 
 that is to sustain quiet water level with its top, and that 
 just balances a double effect of the water is : 
 
 from which we deduce the equation of thickness, 
 
 3 7iw 
 
 4O4. Moments of Rectangular and Trapezoidal 
 Sections. Let DCEB, Fig. 75, be a vertical rectangular 
 wall of masonry, of sectional area exactly equal to the tri- 
 angular section of wall in Fig. 74, viz., 15 feet in height and 
 6 feet in breadth, and weighing, also, 140 pounds per 
 cubical foot. Let the depth of water which it is to sustain 
 upon either side, at will, be 12 feet. 
 
400 PARTITIONS, AND RETAINING WALLS. 
 
 The horizontal resultant of water pressure is 
 w -|- = 2.25 tons, 
 
 and the vertical resultant of weight of wall into the coef- 
 ficient (.62) of friction is 
 
 [ w (.25s,)] x c = 2.96 tons. 
 
 This leaves a small margin of Motional stability. 
 The vertical weight resultant is 
 
 (Aw) - (.26s,) = 4.78 tons, 
 or, if there is no upward pressure, 
 
 Aw = 5.25 tons. 
 
 Plot to scale the horizontal and vertical resultants from 
 their intersection in x, and complete the parallelogram 
 
 xPMe 2 ; then will the diagonal 
 xM be the final resultant of the 
 two forces. 
 
 The direction of the diagonal 
 now cuts the base very near 
 the toe (7, and the given wall 
 with vertical rectangular sec- 
 tion lacks the usual coefficient 
 of leverage stability, though it 
 was found to have ample lever- 
 age stability in the equal tri- 
 angular section. 
 
 If we now give to this same 
 wall a slight batter upon each 
 side, as indicated by the dotted lines, its final resultant, 
 arising from the horizontal water pressure, will lie in x0 2y 
 
 FIG. 75. 
 
MOMENTS OF SECTIONS. 
 
 401 
 
 and its direction will cut the base farther from the toe, and 
 the leverage stability of the wall will be increased. 
 
 Let DCEB, Fig. 76, be a section of a partition wall in a 
 reservoir, subject to a pressure of water whose surface coin- 
 cides with its top, on either side, at will. Let the height be 
 12 feet, and the thickness at top 4 feet. 
 
 The side EC is vertical and the side BD has a batter of 
 three inches to the foot. 
 
 The maximum pressure resultants meet the respective 
 sides in P and PI, in directions perpendicular to their sides, 
 and at depths equal to two-thirds the vertical depth EC. 
 26 
 
402 PARTITIONS, AND RETAINING WALLS. 
 
 Plot to scale the horizontal pressure resultants in their 
 respective directions through P and P 15 and the weight 
 resultant in its vertical direction through the centre of grav- 
 ity,* (7, and complete the parallelograms. The diagonals 
 then give the directions and magnitudes of the maximum 
 leverage effects. 
 
 The diagonal xO cuts the base CD at a distance from K 
 less than half KD ; the diagonal xM cuts the base at a 
 distance from ./f more than half the distance KG. 
 
 The leverage stability of the wall is therefore satisfactory 
 to resist pressure from the left, but has not the desired 
 factor of safety to resist pressure from the right. 
 
 405. Graphical Method of Finding the Leverage 
 Resistance. The ratio of leverage resistance may be 
 obtained from the sketch by scale, as follows : Extend the 
 base, JO, of the parallelogram upon the right, indefinitely ; 
 draw a broken line from x through Z>, cutting J0r l in r x ; 
 then the ratio of leverage stability against the waiter pressure 
 upon EC is to unity as Jr^ is to JO. 
 
 Also extend K0 2 indefinitely ; draw a broken line from 
 y 2 through the toe C, cutting K0 2 r 2 in r 2 ; then the ratio of 
 leverage stability against the maximum water pressure 
 upon BD is to unity as Kr 2 is to K0 2 . 
 
 The ratio of r 2 2 to r 2 K exceeds .5, but the ratio of r M 
 to rJ is less than .5 ; therefore the effect of the horizontal 
 pressure xP to overturn the wall exceeds the effect of the 
 maximum pressure yP to overturn the wall. 
 
 406. Granular Stability. We have found the maxi- 
 
 * The centre of gravity of a rectangular symmetrical plane, Fig. 75, lies in 
 the intersection of its diagonals. 
 
 The centre of gravity of a trapezoidal plane DCEB, Fig. 76, may be found 
 graphically, thus : Prolong CD to t, and make Ci EB. Also prolong EB to 
 &, and make Bk = CD. Join ki. Bisect CD and EB, in d and b, and join db. 
 The centre of gravity G lies in the intersection of the lines db and ik. 
 
COMPUTED PRESSURE IN MASONRY. 
 
 403 
 
 mum water pressure resultant upon the inclined side, JO 
 {Fig. 74), to Ibe yP l = y 2.515 tons ; its direction to be 
 perpendicular to JC, and its point of application to Ibe at 
 two-thirds the vertical depth JO, or iC. 
 
 Plot this inclined resultant, in the prolongation of the 
 line yP^ from a vertical through G, in y 2 P 2 = 2.515 tons ; 
 and plot the vertical weight resultant of the wall from the 
 intersection y in y 2 K 2 = 5.25 tons ; complete the parallelo- 
 gram y 2 P 2 2 K 2 , then the diagonal y 2 2 is in magnitude 
 and direction the maximum pressure resultant of the two 
 forces tending to crush the granular structure of the wall 
 and its foundation. 
 
 The following table of data relating to computed pres- 
 sures in masonries of existing structures, is condensed and 
 tabulated from memoranda* given by Stoney and from 
 other sources : 
 
 TABLE No. 85. 
 COMPUTED PRESSURES IN MASONRY. 
 
 KIND OF MASONRY. 
 
 LOCATION. 
 
 MATERIAL. 
 
 PRESSURE 
 IN LBS. PER 
 
 SQ. FOOT. 
 
 Piers, All Saints Church . . 
 
 Angers 
 
 Forneaux stone 
 
 86 016 
 
 Pillar, Chapter House 
 
 
 
 
 Pillars, dome St. Paul's Church 
 " St. Peter's Church 
 Aqueduct, pier 
 
 London. 
 Rome. 
 Marseilles. 
 
 Portland limestone. 
 Calcareous tufa. 
 Stone 
 
 40,096 
 39424 
 33,376 
 
 Arch bricks, bridge, Charing ) 
 Cross . I 
 
 London. 
 
 London paviors. 
 
 26,880 
 
 Pier bricks, Suspension Bridge. 
 Bridge pier 
 
 Clifton. 
 Saltash 
 
 Staffordshire blue bricks. 
 Granite 
 
 22,400 
 
 21 280 
 
 Arch concrete, bridge, Char-) 
 ing Cross. y 
 
 London. 
 
 Port. Cement, i ; gravel, 7. 
 
 17,920 
 
 Arch bricks, viaduct 
 
 Birmingham 
 
 Red bricks 
 
 15 68O 
 
 Brick chimney 
 
 Glasgow 
 
 Rrirt 
 
 2O 1 60 
 
 Bricks, estimated pressure on ) 
 leeward side in a gale f 
 
 
 
 33,600 
 
 Long span bridges have sometimes pressures at their springing exceeding 
 125,000 pounds per square foot. 
 
 * The Theory of Strains in Girders and Similar Structures. New York, 1873. 
 
404 
 
 PARTITIONS, AND RETAINING WALLS. 
 
 Experimental data of the ultimate strength of masonry 
 in large masses has not been obtained in a sufficient number 
 of instances to determine a limit generally applicable for 
 safe practice. 
 
 Failure first shows itself by the spalting off of the angles 
 or edges of the stones, or by the breaking across of stones 
 subjected to a transverse strain, and next by the crushing 
 of the mortar. 
 
 4O7. Limiting Pressures. From experiments of sev- 
 eral engineers upon the ultimate crushing strength of small 
 cubes of dressed stones (1 inch and 1J inch square), and 
 from computations of pressures upon the lower courses of 
 tall stacks and spires, the data of the following table has 
 been prepared : 
 
 TABLE No. 86. 
 APPROXIMATE LIMITING PPESSURES UPON MASONRY. 
 
 
 Av. weight laid 
 in mortar, per 
 cubic foot. 
 
 Approx. ulti- 
 mate resistance 
 of dry, dressed, 
 one-inch cubes. 
 
 Est. safe static 
 pressure per 
 sq. ft. on thick 
 blocks, unlaid. 
 
 Est. safe pres- 
 sure per sq. ft. 
 in coursed rub- 
 ble masonry, at 
 2 ft. from edge, 
 when laid in 
 strong mortar. 
 
 Limestone 
 
 152 Ibs. 
 
 4,000 Ibs. 
 
 115,000 Ibs. 
 
 50,000 Ibs. 
 
 
 1*2 " 
 
 6,000 " 
 
 I7O,OOO " 
 
 <O OOO " 
 
 Granite 
 
 i"U " 
 
 10,000 " 
 
 280 ooo ft 
 
 6o,OOO " 
 
 Brick 
 
 120 " 
 
 2,^00 " 
 
 72,000 " 
 
 3^,000 " 
 
 
 
 
 
 
 McMaster mentions* that in Spain, and in some instances 
 in France, the limit of pressure in stone masonry has been 
 taken in practice as high as 14 kilogrammes per square 
 centimeter (= 28678 Ibs. per square foot) ; but in the ma- 
 jority of cases the limit is taken at from 6 kilometers to 8.50 
 kilometers per square centimeter. 
 
 * Profiles of High Masonry Dams. New York, 1876. 
 
WALLS FOR QUIET WATER. 405 
 
 The ultimate granular resistance of the masonry is 
 largely dependent upon the strength of the mortar, and 
 upon the skill applied to the dressing and laying of the 
 stones. * 
 
 It is not advisable to allow either a direct or resultant 
 pressure exceeding 140 pounds per square inch within one 
 foot of the face of rubble masonry, or 225 pounds per square 
 inch in the heart of the work ; and these limits should be 
 approached only when both materials and workmanship 
 are of a superior class. 
 
 The resultant of the horizontal pressure is seen to cut 
 the base-line nearer to the toe, or fulcrum, over which the 
 resultant tends to revolve the wall, than does the resultant 
 of maximum pressure ; the crushing strain is therefore 
 greater near the face of the masonry from the horizontal 
 than the maximum resultant. 
 
 Care must be exercised, in high structures, that the safe 
 pressure limit near the edge is not exceeded, lest the edge 
 spalt off, and the fulcrum be changed to a position nearer 
 the centre of the wall, and the leverage stability thus re- 
 duced. 
 
 4O8. Table of Walls for Quiet Water The fol- 
 lowing table gives dimensions for walls to sustain quiet 
 water on either side, and also on the back only, with a 
 limiting face batter of two inches per foot rise : 
 
406 
 
 PARTITIONS, AND RETAINING WALLS. 
 
 TABLE No. 87. 
 APPROXIMATE DIMENSIONS OF WALLS TO RETAIN WATER. 
 
 For granite rubble walls, in mortar, of specific gravity 2.25, ovyiveight, 140 pounds 
 per cubic foot ; to retain quiet water level with the top of the wall. 
 
 
 VERTICAL 
 RECTANGULAR 
 WALL. 
 
 PRESSURE ON EITHER SIDE. 
 SYMMETRICAL PARTITIONS. 
 
 PRESSURE ON BACK ONLY. 
 
 Height of 
 
 
 
 
 water and 
 wall, in feet. 
 
 Breadth in 
 
 Top 
 breadth in 
 
 Bottom 
 breadth in 
 
 Top 
 breadth in 
 
 Face batter 
 in inches 
 
 Bottom 
 breadth in 
 
 
 feet. 
 
 feet. 
 
 feet. 
 
 feet. 
 
 per ft. rise. 
 
 feet. 
 
 4 
 
 3-5 
 
 3-5 
 
 3-5 
 
 3-5 
 
 
 
 3-5 
 
 5 
 
 3-5 
 
 3-5 
 
 3-5 
 
 3-5 
 
 
 
 3-5 
 
 6 
 
 3-5 
 
 3-5 
 
 3-5 
 
 3-5 
 
 O 
 
 3-5 
 
 7 
 
 4.0 
 
 3-5 
 
 4.25 
 
 3-5 
 
 ^ 
 
 4.0 
 
 8 
 
 4-5 
 
 3-5 
 
 5-25 
 
 3-5 
 
 *i 
 
 5-o 
 
 9 
 
 S-o 
 
 3-5 
 
 6.00 
 
 3-5 
 
 2 
 
 5-75 
 
 10 
 
 5-5 
 
 3-5 
 
 6.50 
 
 3-5 
 
 2 
 
 6.75 
 
 ii 
 
 6.0 
 
 3-5 
 
 7-25 
 
 3-5 
 
 2 
 
 7-25 
 
 12 
 
 6-75 
 
 4.0 
 
 7-75 
 
 4.0 
 
 2 
 
 7-83 
 
 13 
 
 7-25 
 
 4.0 
 
 8.50 
 
 4.0 
 
 2 
 
 8.67 
 
 14 
 
 7-75 
 
 4.0 
 
 9-25 
 
 4.0 
 
 2 
 
 9-5o 
 
 15 
 
 8.25 
 
 4.0 
 
 10.00 
 
 4.0 
 
 2 
 
 10.50 
 
 16 
 
 9.00 
 
 4.0 
 
 10.75 
 
 4.0 
 
 2 
 
 11.50 
 
 17 
 
 9-So 
 
 4.0 
 
 11.67 
 
 4.0 
 
 2 
 
 12. OO 
 
 18 
 
 10.00 
 
 5-o 
 
 11.75 
 
 5-0 
 
 2 
 
 I2.5O 
 
 19 
 
 10.50 
 
 5-0 
 
 12.67 
 
 5-0 
 
 2 
 
 13.67 
 
 20 
 
 II.OO 
 
 5-0 
 
 13-33 
 
 5- 
 
 2 
 
 14.50 
 
 21 
 
 11.50 
 
 5-o 
 
 14.00 
 
 5-o 
 
 2 
 
 15.25 
 
 22 
 
 12.25 
 
 5-o 
 
 14.83 
 
 5-0 
 
 2 
 
 16.25 
 
 2 3 
 
 12.75 
 
 S-o 
 
 15-75 
 
 5-o 
 
 2 
 
 I7.25 
 
 24 
 
 13-25 
 
 5- 
 
 16.50 
 
 5-o 
 
 2 
 
 18.25 
 
 The top thickness is to "be increased if the top of the 
 wall is exposed to ice-thrust ; and the whole thickness 
 must be increased if water is to flow over the crest, accord- 
 ing to the depth of the crest, and its initial velocity of ap- 
 proach. 
 
 Unless partition- walls rest on solid rock, or on impervi- 
 ous strata of earth, as they should, percolation under the 
 
ECONOMIC PROFILES. 407 
 
 wall must be prevented by a concrete or puddle stop- wall, 
 or by sheet- piling ; or the previous strata must be effectu- 
 ally sealed over. 
 
 4O9. Economic Profiles. It is evident, from the 
 above investigations, that the profile has an important influ- 
 ence upon the leverage stability of a wall of given weight 
 of material, and therefore, for a given stability, upon econ- 
 omy of material. 
 
 The leverage stability against pressures of water upon 
 the vertical sides of triangular or trapezoidal sections of 
 masonry is greater than the leverage resistances to pressures 
 upon their inclined sides, as is graphically illustrated in the 
 above sketches ; hence there is an advantage in giving all 
 the batter to the side opposite to the pressure. 
 
 The vertical rectangular sections are least economic, and 
 the triangular sections most economic of material. 
 
 When some given thickness is assumed for the top of a 
 retaining wall, to give it stability against frost, or displace- 
 ment from any cause, then theory makes both sides vertical 
 from the top downward until the limiting ratio of leverage 
 stability is reached, and then gives to the side opposite to 
 the pressure a parabolic concave curve. 
 
 It may be necessary to widen the base of high walls 
 upon both sides beyond the breadth required for leverage 
 stability, to distribute the weight sufficiently upon a weak 
 foundation. Practical considerations, in opposition to 
 theory, tend to rectangular vertical sections. 
 
 The engineer who is familiar with both theory and prac- 
 tice, adjusts the profile for each given case, so as to attain 
 the requisite frictional, leverage, and granular stabilities, in 
 the most substantial and economical manner, having due 
 regard to the quality and cost of materials, and the skill 
 and cost of the required labor. 
 
408 PARTITIONS, AND RETAINING WALLS. 
 
 41O. Theory of Earth Pressures. Earth filling of 
 the different varieties behind retaining walls, is met in all 
 conditions of cohesiveness between that of a fluid and that 
 of a solid. 
 
 The same filling, in place, is subject to constant changes 
 in its degree of cohesion, as its moisture is increased or 
 diminished, or as its pressure and condensation is increased, 
 or as it is subjected to the tremulous action of traffic over it. 
 The theory of earth pressure, therefore, leads to less certain 
 results than does the theory of water pressure. 
 
 We have seen ( 353) that different earths have dif- 
 ferent natural angles of repose when exposed to atmos- 
 pheric influences, and they also tend to assume their natural 
 frictional angle when deposited in a bank. If we make a 
 broad fill with earth, behind a vertical wall and then sud- 
 denly remove the wall, a portion of the earth, of triangular 
 section, will at once fall, and the slope will assume its natu- 
 ral frictional angle. If we make such a fill even with the 
 top of a vertical rectangular wall, whose thickness is only 
 equal to one-fourth of its height, then the earth will over- 
 turn the wall. This is evidence that a portion of the earth 
 produces a lateral pressure. If the earth is fully saturated 
 with water, its lateral pressure may be nearly like that of a 
 fluid of equal specific gravity. If the earth is compact like 
 a solid, its thrust may be nearly like that of a rigid wedge. 
 
 Let LDBJ, Fig. 77, be an earth-fill behind a vertical 
 retaining wall DB. Let LDVi be the natural frictional 
 angle = </>, of that earth filling. It is evident that the por- 
 tion of earth LD 7i will produce no thrust upon the ma- 
 sonry, because it would remain at rest if the wall was 
 removed. Suppose all the filling above D Vi to be divided 
 into an infinite number of laminae whose planes of cleavage 
 all meet at one edge in D, and radiate from D. Then the 
 
THEORY OF EARTH PRESSURES. 
 
 409 
 
 thin lamina adjoining D V l will exert the minimum thrust 
 against the masonry and the maximum weight-pressure 
 upon D Vi. The thin lamina adjoining BD will exert the 
 
 FIG. 77. 
 
 maximum wedge-thrust against -the masonry and minimum 
 weight-pressure upon D Vi. 
 
 Suppose the mass ViDBJio be divided into two parts 
 
410 PARTITIONS, AND RETAINING WALLS. 
 
 by the plane DJ, which bisects the angle BD V v . Let the 
 wedge BDJ, then be increased in dimensions by revolving 
 the side JD to the right, around D ; then its weight, as a 
 solid, will rest more upon FjZ>, and its lateral thrust will 
 not be increased. Let the wedge BDJ, then be reduced in 
 dimensions by revolving the side JD to the left ; then its 
 total weight and its ability to produce lateral thrust upon 
 the masonry will be reduced. We may therefore assume 
 that that portion of the mass ViDBJ, included in the upper 
 wedge formed by bisecting the angle V^DB will be the 
 maximum portion of the earth that will first fall if the wall 
 is suddenly removed, and that the thrust of the wedge BDJ, 
 if considered alone, and as devoid of friction upon the plane 
 7Z>, will give a safe theoretical maximum effect upon the 
 masonry of the whole mass V^DBJ. 
 
 The practical value of such assumption has been ably 
 demonstrated by Coloumb, Prony, Canon Moseley, Ean- 
 kine, Neville, and others. 
 
 411. Equation of Weight of Earth-Wedge. The 
 weight W 2 of the wedge of earth (considered as one foot 
 in length), in pounds, equals its surface area DBJ, in square 
 feet, AS, into the weight of one cubical foot of the mate- 
 
 rial = w 2 . 
 
 W 2 = A 2 w 2 . (12) 
 
 Let the symbol of the frictional angle LDV of the 
 earth filling be </> ; then will the angle 
 
 Let the height BD equal 12 feet, = h ; then the area of 
 DBJ will equal DB into one-half BJ 
 
 A 2 = 7i x \ tan 6 = ^ cotan (<j> + 0). (13) 
 
PRESSURE OF EARTH-WEDGE. 411 
 
 Equation of Pressure of Earth-Wedge. 
 
 Assume the weight of the wedge DBJ= A 2 w 2 = W 2 to be 
 gathered into its vertical resultant passing through its cen- 
 tre of gravity, g ; then the thrust P of the wedge equals 
 its weight into its horizontal breadth BJ, divided by its 
 vertical height BD = 
 
 P = A 2 w 2 tan = W 2 cotan (<f> + 0). (14) 
 
 Draw the vertical resultant W 2 to scale in eP, meeting 
 the inclined plane JD, in P. 
 
 The thrust effect of W* will have its maximum action in 
 a line parallel to the line D Vi , since the mass V^DBJ, as 
 a whole, tends to move down the plane ViD. 
 
 The theoretical reaction from the wall, necessary to sus- 
 tain W 2 , will then be in a direction parallel to D V\ , cutting 
 the vertical resultant in P. Draw the reaction of the wall 
 to scale in nP. The reaction of the plane JD is in direc- 
 tion and magnitude equal to the diagonal Py, of the paral- 
 lelogram of which W 2 and P form two sides. Draw the 
 reaction of JD to scale in VP. Then, will the three result- 
 ants eP> nP y and VP be in equilibrium about the point P. 
 
 Let = 30. 
 
 Assume the filling to be of gravel, weighing 125 pounds 
 per cubic foot, and that after a storm, its drains being 
 obstructed, its voids are filled with water, increasing the 
 weight to 140 pounds per cubic foot, = w 2 ; then 
 
 7,2 
 
 
 = 12 feet x y feet x .57735 x 140 pounds 
 = 5,820 pounds = 2.91 tons. 
 
 The reaction from the wall necessary to sustain the 
 weight of the wedge JBD = 
 
412 PARTITIONS, AND RETAINING WALLS. 
 
 P = W 2 tan e = ^ cotan 2 (0 + 6) w, (15) 
 
 4> 
 
 = 2.91 tons x .57735 
 = 1.68 tons. 
 
 The horizontal effect of P = 
 
 x = P cos = A 2 w 2 tan 6 cos (16) 
 
 = 1.68 tons x .86602 = 1.45 tons. 
 
 The thrust of the wedge tending to push away and to 
 overturn the wall is equal to the reaction from the wall 
 necessary to sustain the wedge in position. We find its 
 horizontal effect in this case to be 1.45 tons, and this is the 
 maximum effect, = #, tending to displace the wall hori- 
 zontally. 
 
 413. Equation of Moment of Pressure Leverage. 
 The maximum moment of pressure leverage, Z>, tending 
 to overturn the wall around its toe, equals x into the height, 
 in feet, above D at which x meets the wall. 
 
 When the wall is vertical and the surface of filling hori- 
 zontal, x always meets BD at one-third Ti from Z>, = ~ ; 
 
 therefore the equation of moment of pressure leverage 
 becomes 
 
 L, = x^ = (A 2 w 2 tan e cos 0) | (17) 
 
 -10 ff 
 
 = 1.45 tons x =^p = 5.80 tons. 
 
 o 
 
 414. Thickness of a Vertical Rectangular Wall 
 for Earth Pressure. The moment of weight leverage of 
 
 a vertical rectangular wall is 5, in which z is the thick- 
 
 tt 
 
 ness of the wall. 
 
SURCHARGED EARTH-WEDGE. 413 
 
 The double moment of pressure leverage of earth level 
 with the top of the wall is 
 
 h h 3 
 (h 2 w* tan 2 d cos 0) x = w 2 tan 2 6 cos 0. 
 
 o o 
 
 When the wall just balances the theoretical double 
 pressure of the earth level with its top, 
 
 = w 2 tan 2 6 cos 0, 
 
 o 
 
 from which is deduced the equation of thickness for a ver- 
 tical rectangular wall, 
 
 ( 2h 3 w 2 tan 2 e cos ) 1 _ ( h 2 w 2 tan 2 6 cos 1 i 
 
 B r ~sM^ "f B r "TM~ -j 
 
 415. Surcharged Earth-Wedge. When the earth- 
 fill behind a wall is carried up above the top level BJ of 
 the wall, and is sloped down against the top angle B, or 
 upon the top of the wall, the fill DBF is then termed a 
 surcharged fill. 
 
 Its weight W 2 is, as in the case of the level fill, per lineal 
 
 foot, 
 
 W 2 = A 2 w 2 . (19) 
 
 To compute the pressure of the surcharged fill, we may 
 divide the mass ViDBF into two wedges by a plane DF, 
 bisecting the angle V V DB^ and take the action of the wedge 
 FDE as equivalent to the effective action of the whole mass 
 VDBF. 
 
 Let the natural Motional angle of the earth-fill be 
 
 = 30. 
 
 The area A 2 of the wedge FDB may be computed by 
 any method of ascertaining the area of a triangular super- 
 
414 PARTITIONS, AND RETAINING WALLS. 
 
 fices. If, with a given slope BF, the fill does not rise as 
 high as F, and its surface level cuts FB and FJ between 
 the levels of F and B, then its area is ascertained by any 
 method of ascertaining the superfices of a trapezium. 
 
 Let fall upon DF a perpendicular from B, meeting DF 
 in i ; then the distances Di and IF are equal, each, to the 
 
 QO <t\ 
 
 cosine of the angle BDF = cos. ^?- = cos and the 
 
 tO 
 
 distance iB is equal to sin 5 ? = sin 6. 
 
 & 
 
 Let the height DB = 7i = l2 feet. 
 
 The area BDF equals the length DF into one-half IB = 
 
 A 2 = Ji x 2 cos x Ji \ sin 6 = 7i cos x h sin (20) 
 = (12 x .866) x (12 x .5) = 62.53 sq. ft. 
 
 Let the mean weight of the fill, which is quite sure to be 
 drained above the level BJ, be assumed 130 pounds per 
 cubical foot. 
 
 416. Pressure of a Surcharged Earth- Wedge. 
 
 Suppose the weight to be gathered into its vertical resultant 
 passing through the centre of gravity g^ of the mass DFB. 
 This vertical resultant will meet the plane FD in P l at a 
 level higher than P. 
 
 The wedge-thrust P 15 due to the weight W 2 , equals the 
 weight into the horizontal breadth BJ, divided by the 
 height DB = 
 
 P! = TF 2 tan = A 2 w 2 cotan (< + 0) = (21) 
 
 62.53 sq. ft. x 130 Ibs. x .577 = 4690.38 Ibs. = 2.345 tons. 
 
 The. maximum pressure-action of the weight upon the 
 wall is in a direction parallel to ViD, the natural fractional 
 angle 0, of the filling material. Its horizontal pressure 
 effect, #1, is therefore : 
 
PRESSURE OF AN INFINITE SURCHARGE. 415 
 
 x l = PI x cos = A 2 w 2 tan cos = (22) 
 
 2.345 tons x .866 = 2.03 tons. 
 
 The maximum horizontal pressure resultant takes its 
 direction through P l and meets the wall at the altitude of 
 
 P,, which is greater than -^. 
 
 o 
 
 We may here observe that, even though the fill DBF 
 is of lighter material than the fill DBJ, so that the total 
 weight of one is exactly equal to the total weight of the 
 other, the pressure leverage effect from the surcharged fill 
 will exceed the pressure leverage effect from the level fill, 
 "because its centre of gravity g 2 will be higher than g, its 
 vertical resultant W 2 will meet the plane JD in PI at a point 
 higher than P, and its horizontal resultant x l will meet the 
 wall at a greater altitude from D than will the resultant x. 
 
 Let r h be the symbol of the ratio of *^ at which x l meets 
 the wall from D ; then if x l meets DB at J^, r h = .3333 ; 
 and if x { meet DB at &, r h = .5, etc. 
 
 417. Moment of a Surcharge Pressure Leverage. 
 The maximum moment of pressure leverage L^ of a sur- 
 charged fill, tending to overturn the wall around its toe, 
 equals x l into the height, in feet = (rji) above Z>, at which 
 XL meets the wall. 
 
 LI = X I x (rji) = A 2 w 2 tan cos </> (r h h) = (23) 
 2.03 tons x 5.98 = 12.14 tons. 
 
 418. Pressure of an Infinite Surcharge. Let 
 
 Fig. 78, be the natural slope of the filling material, and 
 parallel with DI, which makes with DL the natural fric- 
 tional angle LDI </>. Let BF extend indefinitely. 
 
 If IDBF is a perfect solid it will be just upon the point 
 of motion down the slope ID ; on the other hand, if IDBF 
 
416 PARTITIONS, AND RETAINING WALLS. 
 
 is liquid, of specific gravity equal to the specific gravity of 
 the filling material, it will then exert its maximum pressure 
 upon the wall-face DB. 
 
 Let the filling be considered liquid, resting upon the 
 equivalent horizontal "base DI, and having the equivalent 
 horizontal surface BF. 
 
 Let fall upon DI a perpendicular from B, meeting DI 
 iuj ; then will Bj be an equivalent vertical projection, or 
 trace, of BD. The angle DBj equals the angle LDI = 0. 
 The distance Bj = Ti^ equals the distance BD (=h) into the 
 cosine of the angle DBJ = 7i cos <f>. 
 
 7i 2 
 The direct liquid pressure P 1 upon Bj equals -~- w 2 = 
 
 , (24) 
 
 and the pressure upon BD in the same direction is 
 
 and its maximum resultant has a direction parallel with 
 ID, and meets Bj at one-third the height jB, in m, and BD 
 at one-third the height DB, in P^ 
 
 The horizontal pressure effect x l upon the wall BD, is 
 
 h 2 
 
 Xi = P l cos </> = w 2 -^ cos 3 = (25) 
 
 & 
 
 19 2 
 
 130 Ibs. x - x .6495 = 6079.32 Ibs. = 3.036 tons. 
 
 <e 
 
 The maximum moment of liquid pressure leverage LI 
 of the infinite surcharged fill tending to overturn the wall 
 around its toe, equals x l into one-third the height BD. 
 
 L, = x^= (w 2 | cos 3 0) x A = (26) 
 
 jo -Ft- 
 
 3.036 tons x ^^ = 12.14 tons. 
 
RESISTANCE OF MASONRY REVETMENTS. 417 
 
 419. Resistance of Masonry Revetments. The 
 
 elements of stability of a revetment that enables it to sus- 
 tain the thrust of an earth-filling behind it, are identical 
 with those we have already examined ( 4O1), that enable 
 it to sustain a pressure of water. 
 
 There must be sufficient weight, W, to give it fractional 
 stability, S, and the profile must be adjusted so that with 
 the given weight the mass shall have the requisite moment 
 M of weight leverage, with an ample coefficienty of safety, 
 to resist the thrust of the earth-filling, at its maximum. 
 
 The weight of wall above any given horizontal plane 
 between B and D (Fig. 77) equals the area of the section 
 above that plane in square feet, into the weight of a cubical 
 foot of the materials of the wall ( 398), 
 
 = W= Aw. 
 
 Thefrictional stability, S, of the wall at the given hori- 
 zontal plane, that has to resist the horizontal pressure of 
 the earth filling, equals the weight of masonry above that 
 plane, plus the vertical downward pressure of any water 
 that may rest upon its front batter (EC, Fig. 80), less the 
 vertical resultant of upward pressure beneath the plane or 
 in the bed-joints, and into the coefficient of friction of the 
 given section upon its bed ( 398), 
 
 S = (W+e - &).. 
 
 The moment of weight leverage of the wall that has to 
 resist the overturning tendency of the earth-thrust, equals 
 the weight of the masonry above the given plane into the 
 horizontal distance of the centre of gravity of the masonry 
 from the toe, or fulcrum, over which the thrust tends to 
 revolve it ( 4O2), 
 
 M Awd. 
 27 
 
418 PARTITIONS, AND RETAINING WALLS. 
 
 In these equations : 
 
 TFis the weight above the given plane. 
 S " " frictional stability of the given section. 
 M " " moment of weight leverage of the given section. 
 e " " vertical downward water pressure resultant. 
 Zi " " vertical upward water pressure resultant. 
 GI " " ratio of effective vertical upward water pressure. 
 c " " coefficient of friction of the given section upon 
 
 its bed. 
 
 The moment of weight leverage of the wall must, for a 
 safe coefficient of stability, be equal to double the moment 
 of pressure leverage of the earth fill ; that is, for a level fill 
 we must at least make 
 
 Awd , Ji 
 
 ^- = A 2 w 2 tan. 6 cos. -, 
 
 & d 
 
 and for a surcharged fill, 
 
 -^- = A 2 w 2 tan. cos. (/*), 
 
 40 
 
 and a like margin of frictional stability should be secured. 
 
 43O. Final Resultants in Revetments. The height 
 of the wall (Fig. 79) is the same, by scale, as the wall in 
 Fig. 77, whose reactions to sustain the level and surcharged 
 fills we have investigated. 
 
 The back of the wall (Fig. 79) is vertical, and the hori- 
 zontal earth-thrusts against it are as before computed viz., 
 1.45 tons for the level fill, and 2.03 tons for the surcharged 
 fill. Draw these horizontal earth-thrust resultants to the 
 left from a vertical line passing through the centre of gravity 
 of the masonry, in their respective directions and at their 
 respective altitudes. Draw in the vertical line the vertical 
 weight resultant of the masonry in PK; complete the paral- 
 lelogram PKQ& ; then will the diagonal P0 2 represent, in 
 
TRAPEZOIDAL REVETMENTS. 
 
 419 
 
 magnitude and direction, the resultant effect of the level fill 
 LDBJ. 
 
 Draw the vertical weight resultant of masonry, also, in 
 P 3 e. 2 , and complete the parallelogram P^Mx-^ ; then will the 
 diagonal PJtt represent, in magnitude and direction, the 
 resultant effect of the surcharged fill LDBF. 
 
 The comparative thrust effects of the level and sur- 
 charged fills upon the masonry are shown by the positions 
 of the respective final resultants, and the comparative re- 
 sistances of the wall against each, by the distances from 
 O, at which their directions cut the plane CD. 
 
 FIG. 79. 
 
 E 
 
 421. Table of Trapezoidal Revetments. The fol- 
 lowing table of dimensions of walls, to sustain earth, in 
 which the sections are trapezoidal, and face batters limited 
 to two inches per foot rise, is adapted for walls to sustain 
 gradings about pump-houses, reservoir-grounds, etc., and 
 will give approximate dimensions for plotting trial sections 
 when it is desired to resolve the profile into other forms. 
 
420 
 
 PARTITIONS, AND RETAINING WALLS. 
 
 TABLE No. 88. 
 APPROXIMATE DIMENSIONS OF WALLS TO SUSTAIN EARTH. 
 
 For granite rubble walls, in mortar, of specific gravity 2.25, or weight 140 pounds 
 per cubic foot, to retain earth level with the top of the wall. 
 
 Height of wall, 
 in feet. 
 
 Top breadth of 
 wall, in feet. 
 
 Face batter of 
 wall, in inches 
 per foot rise. 
 
 Base breadth of 
 wall at lower earth 
 surface, in feet. 
 
 Thickness of a 
 vertical rectangular 
 wall, in feet. 
 
 4 
 
 3-0 
 
 O 
 
 3.0 
 
 3.0 
 
 5 
 
 3.0 
 
 O 
 
 3.0 
 
 3.0 
 
 6 
 
 3.0 
 
 
 
 3.0 
 
 3.0 
 
 7 
 
 3.0 
 
 
 
 3-25 
 
 3-5 
 
 8 
 
 3- 
 
 
 3.83 
 
 4.00 
 
 9 
 
 3-33 
 
 I 
 
 4-83 
 
 4-25 
 
 10 
 
 3-33 
 
 I 
 
 5.00 
 
 4-5 
 
 ii 
 
 3-5 
 
 I- 
 
 5-25 
 
 5.00 
 
 12 
 
 3-5 
 
 2 
 
 5.67 
 
 5-5 
 
 13 
 
 3-5 
 
 2 
 
 6-33 
 
 5-83 
 
 14 
 
 3-5 
 
 2 
 
 7.0O 
 
 6.25 
 
 15 
 
 3-5 
 
 2 
 
 7-50 
 
 6.75 
 
 16 
 
 4.0 
 
 2 
 
 8.00 
 
 7-25 
 
 17 
 
 4.0 
 
 2 
 
 8.67 
 
 7-75 
 
 18 
 
 5.0 
 
 2 
 
 9.00 
 
 8.25 
 
 19 
 
 5.0 
 
 2 
 
 9-5 
 
 8-75 
 
 20 
 
 5-o 
 
 2 
 
 9.87 
 
 9.00 
 
 21 
 
 5.0 
 
 2 
 
 10.50 
 
 9.50 
 
 22 
 
 5* 
 
 2 
 
 ii .00 
 
 10.25 
 
 23 
 
 5 - 
 
 2 
 
 u-33 
 
 10.50 
 
 24 
 
 5- 
 
 2 
 
 11.78 
 
 10.75 
 
 It will rarely be advisable to reduce the top thicknesses 
 given in the table, with a view only to economizing ma- 
 terial lest the top courses be too light to withstand the 
 variety of shocks to which they will be liable, and which 
 are not recognized in the common formulas. 
 
 Several eminent professors who have written upon the 
 theory of retaining walls, give formulas for determining their 
 proportions ; but such formulas usually give too small top 
 breadths, for practical adoption, for low walls, and objec- 
 tionably great top breadths for high walls. 
 
CURVED FACE BATTER EQUATION. 421 
 
 Each class of wall has its own most convenient top 
 breadth, which remains nearly constant through a large 
 range of height. 
 
 Common uncoursed rubble walls of granite, laid dry, 
 should be increased from the above dimensions six inches 
 in the top breadth and thirty -three per cent, in the bottom 
 breadth. If the level earth-filling behind the wall is to be 
 loaded, or subject to traflic, the weight and leverage resist- 
 ance of the wall are to be increased accordingly. 
 
 The thrust of the filling material behind a retaining wall, 
 upon the wall, will be lessened if the filling next the wall 
 is spread in thin horizontal layers and well settled, instead 
 of being allowed to slope against it, as it falls at the head 
 of a dump. 
 
 422. Curved Face Batter Equation. When it is 
 desired to give to the face a curve, the back being perpen- 
 dicular, and the top breadth constant, the following equa- 
 tion will assist in determining ordinates at any given depths 
 for plotting a trial section. 
 
 Let 5 be the assumed top breadth, and t the thickness 
 at any given depth d, then 0?)r 
 
 t=b+-ttV&. (27) 
 
 For illustration, assume the top breadth not less than 
 3.5 feet ; then for several given depths, from 0.0 to 30 feet, 
 we have ordinates, or thicknesses, as given in Table No. 89. 
 
 Upon the curve thus^ obtained, steps may be laid off with 
 either vertical or battered risers. 
 
 Tests with the equation for moment of leverage stability, 
 will determine whether the risers may cut the curve, or if 
 the inner angle of tread and riser shall lie in the curve. 
 
 A slight increase or reduction of the top breadth, or of 
 the fractional multiplier, will increase or reduce the wall- 
 section, as desired. 
 
422 
 
 PARTITIONS, AND RETAINING WALLS. 
 
 TABLE No. 89. 
 THICKNESS AT GIVEN DEPTHS OF A CURVED FACE WALL. 
 
 DEPTHS. 
 
 
 THICKNESS. 
 
 Feet. 
 
 (*.) 
 
 
 75 t'^ 
 
 Feet. 
 
 O 
 
 3-5 
 
 H- 
 
 .O = 
 
 3-5 
 
 4 
 
 3-5 
 
 + 
 
 .6 = 
 
 4.10 
 
 6 
 
 3-5 
 
 + 
 
 1. 10 = 
 
 4.60 
 
 8 
 
 3-5 
 
 + 
 
 1.69 = 
 
 5.19 
 
 10 
 
 3-5 
 
 + 
 
 2-37 = 
 
 5^7 
 
 12 
 
 3-5 
 
 + 
 
 3.12 = 
 
 6.62 
 
 IS 
 
 3-5 
 
 + 
 
 4.36 = 
 
 7.86 
 
 2O 
 
 3-5 
 
 + 
 
 6.71 = 
 
 10.21 
 
 25 
 
 3-5 
 
 + 
 
 9.38 = 
 
 12.88 
 
 30 
 
 3-5 
 
 + 
 
 12.32 
 
 15.82 
 
 423. Back Batters, and their Equations. When 
 for practical or other reasons there is objection to giving all 
 the batter to the front of the wall, and a portion of it is 
 placed upon the back, then it is usually arranged in a 
 series of offsets or steps D l , Fig. 80. 
 
 In such case, the weight of the triangle of earth BJ)^E. 
 may be assumed to be supported entirely by the wall, and 
 as producing no lateral thrust upon the wall. This triangle 
 increases the weight leverage of the wall, and moves its 
 weight resultant farther back from the toe C. 
 
 Find the centre of gravity of the masonry, in g, and find 
 the centre of gravity of the triangle of earth, in g 2 ; then will 
 the centre of gravity of the two united bodies be in G. 
 
 Let Z>!/be the natural fractional angle of the material. 
 Bisect the angle IDiS 2 by the plane D^F ; then we may 
 assume the trapezium D<J$J?-J? to be that portion of the 
 earth-filling that, considered alone, will produce the maxi- 
 mum thrust effect upon the wall, and its horizontal and 
 leverage effects may be computed by equations 21 and 23. 
 
INCLINATION OF FOUNDATION. 
 
 423 
 
 
 Prof. Moseley's equation* for the maximum pressure of 
 a surcharge similar to^this is 
 
 P l = %w 2 Jsec </> (hi 2 tan 2 </> + c 2 2 )^ 2 , (28) 
 
 In which c 2 is the height B 2 c 2 . 
 
 P L " maximum pressure of the earth. 
 W 2 " weight of one cubic foot of earth. 
 hi c vertical distance DiC 2 . 
 " frictional angle of the earth. 
 
 424. Inclination of Foundation. The frictional 
 stability of a wall upon its foundation is materially in- 
 
 Mechanics of Engineering, p. 426. Van Nostrand, New York, 1860. 
 
 ? 
 
4:24 PARTITIONS, AND RETAINING WALLS. 
 
 
 
 creased, and its pressure is more evenly distributed upon 
 the foundation stratum, if an inclination is given to the bed 
 nearly at right angles to the final thrust resultant, as in 
 Fig. 80. Bed-joints may often be similarly inclined with 
 advantage. 
 
 A sliding motion in such case involves the additional 
 work of lifting the whole weight up the inclined plane. 
 
 425. Front Batters and Steps. Masons experience 
 a very considerable difficulty in laying the face of rubble 
 walls with batters exceeding two inches to the foot, and 
 often with batters exceeding one and one-half inches to the 
 foot, unless with stones from a quarry where the transverse 
 cleavage varies several degrees from a perpendicular to 
 the rift. 
 
 The difficulty is increased when the bed-joints of the 
 work are level from front to rear, as the workmen prefer to 
 make them. 
 
 It is especially troublesome to the workmen, and expen- 
 sive as well, to make face-batters of high walls conform to 
 the theoretical curved batters deduced from the logarithmic 
 equations. 
 
 It is better, therefore, to transpose the curve into a series 
 of steps when its tangent inclination exceeds two inches to 
 the foot, in which case the steps may have equal heights 
 and varying projections, as in Fig. 81, which is a revetment 
 ujKm a navigable river, or may have both varying rise and 
 projection, with batter upon the rise, as in the weir, Fig. 72. 
 
 426. Top Breadths, The thickness at the top of a 
 revetment should in all cases be sufficient, so that its weight 
 will be able to resist the frost expansion thrust of the sur- 
 face layers of the earth. Sometimes a batter is given to the 
 back of the wall, three or four feet down from the top, to 
 enable the earth to expand readily in a vertical direction, 
 
TOP BREADTHS. 
 
 425 
 
 and thus act with less force horizontally against the backs 
 of the cap-stones. 
 
 An increased thickness at the top of the wall, and at all 
 points of depth, is also necessary when the filling is liable 
 to be loaded with construction materials, fuel, merchandise, 
 
 FIG. 81. 
 
 or other weights, or if it is to sustain traffic of any kind. 
 The additional weight may in such case be considered 
 equivalent to a surcharge weight, and the centre of gravity 
 of the filling and of the additional weight will be resolved 
 into their united centre of gravity and the vertical resultant 
 
426 
 
 PARTITIONS, AND RETAINING WALLS. 
 
 be considered as passing through this new centre of gravity. 
 The new horizontal thrust resultant will then act upon the 
 wall at a greater altitude, and with greater leverage than 
 the horizontal resultant of filling alone ( 416), as has 
 been already demonstrated. 
 
 In the cases of discharge weirs the floods are considered 
 as surcharge weights, and not only the depth of water 
 behind the weir and upon its crest is to be considered, but 
 
 FIG. 82. 
 
 the additional height to which the velocity of approach of 
 the water is due. 
 
 If there is but one or two feet depth of water flowing 
 over, then the cap-stones may be subject to the blows of 
 logs, cakes of ice, and such debris as the floods gather. 
 
 427. Wharf Walls. When a wall is to be generally 
 
ELEMENTS OF FAILURE. 427 
 
 used for wharf purposes, its face should be protected by 
 fender piles, both for its own advantage and that of the 
 vessels that lie alongside. 
 
 Fig. 82 illustrates the method of piling and capping, 
 adopted by the writer, in an extensive wharf -pier of one- 
 half mile frontage in one of the deep harbors upon the New 
 England coast. The caps are, in this case, dressed dimen- 
 sion stones, three and one-half feet wide and one foot thick. 
 The wharf log is made up of 12" x 10" and 12" x 8" hard 
 pitch pine, placed one upon the other so as to break joints, 
 and tre-nailed together. The anchors of the pile-heads pass 
 through the cap-log, and their bolts pass through the cap- 
 stones into headers specially placed to receive them. The 
 piles are placed eight feet between centres, and each fourth 
 pile extends above the log for a belay pile. Waling 
 pieces of 6" x 12" hard pine are fitted between the pile-heads, 
 and spiked to the face of the cap-log to confine the pile- 
 heads rigidly in place. Midway between the belay piles 
 are belay rings, whose bolts pass through the cap-logs into 
 headers, and are also anchored by straps to cap-stones. 
 
 428. Counter-forted Walls. There is so rarely an 
 economic advantage in counter-forting a wall, except in 
 those cases of brick walls where the counter-fort may take 
 the form of a buttress upon the exterior face, that we shall 
 not here devote space to their special theoretical investiga- 
 tion, which, by graphical analysis, is a simple reapplication 
 of the principles already laid down. 
 
 429. Elements of Failure. In our theoretical inves- 
 tigation of the resistances of masonry to sliding or overturn- 
 ing we have supposed the walls to be laid in mortar and 
 solid, and well bonded, so that the mass was practically 
 one solid piece, considered as one foot long. 
 
 If any given foot of length, considered alone as a unit 
 
428 PAKTITIONS, AND KETAINING WALLS. 
 
 of length, is found stable, and each other foot is equal to it, 
 then evidently the whole length will be stable. 
 
 The joints from front to rear in cut and first-class rubble 
 walls are usually laid level, and the workmen intend to give 
 a good bond of one course upon another. When consider- 
 ing the leverage stability of a high wall, at the respective 
 joints, working from top downward, we usually treat the 
 joints as horizontal planes. Let us turn again to the sketch 
 of the partition wall, Fig. 76, which has joints laid off upon 
 it showing an average class of rubble work. Suppose the 
 water to be drawn off from the side EC, and the full water 
 upon the opposite side to be freezing, and the ice exerting a 
 thrust upon the upper courses of the wall. We investigate 
 the leverage stabilty at the joint jj\, and find that it will 
 resist a considerable leverage strain, which for further illus- 
 tration we assume to be ample. Examining critically the 
 building of the wall, we find that jj\ is not the real joint, 
 and,/! the fulcrum to be considered in connection with 
 pressure upon Bj\ but in consequence of faulty workman- 
 ship, jjzjz is the zigzag joint and / 3 the fulcrum, and that 
 the joint, instead of being horizontal, is an equivalent in- 
 clined plane on which the wall is quite likely to yield by 
 slipping slightly with each extra lateral strain "put upon it. 
 
 If in a high and long wall such weaknesses are repeated 
 several times, the result will be a bulge upon the face of 
 the wall, ordinarily reaching its maximum at about one- 
 third the height of the wall, the portion above that level 
 appearing to have been moved bodily forward, and retain- 
 ing nearly its true batter. 
 
 When walls are so high as to require a thickness in a 
 considerable portion of their height exceeding seven or 
 eight feet, careless wall-layers, who are not entitled to the 
 honorable name mechanic, often pile up an outside and 
 
f " ! 
 
 FACED, AND CONCRETE REVETMENTS. 429 
 
 inside course, and fill in the middle with their refuse stone, 
 thus producing a miserable structure, especially if it is dry 
 rubble, that is almost destitute of leverage stability, unless 
 a great surplus of stone is put into the wall sufficient to 
 resist the thrust of an earth-backing by compounded weight 
 alone. 
 
 Short walls supported at each end may by such trans- 
 verse motion be brought into an arched form, concave to 
 the pressure, but at the same time into a state of longitudi- 
 nal tension that will assist in preventing further motion. 
 
 If there is the least transverse motion in a mortared wall 
 sustaining water, the masonry ceases from that instant to 
 be water-tight, and if the stones are in the least disturbed 
 on their bed after their mortar has begun to set, the wall 
 will never be tight. 
 
 430. End Supports. Well constructed short walls, 
 supported at each end, such as gate-chamber and wheel-pit 
 walls, have an appreciable amount of that transverse resist- 
 ance prominently recognized in a beam, which permits 
 their sections to be reduced, an amount dependent on the 
 effective value of such transverse support. The supported 
 ends of long walls transmit the influence of the support in a 
 decreasing ratio, out to some distance from the supports, 
 and walls whose ends abut upon inclines, as in the case of 
 stone weirs across valleys, may be reduced in thickness, 
 ordinarily, at the top and through their whole height, as 
 the height reduces. 
 
 431. Faced, and Concrete Revetments. Walls on 
 deep water-fronts, as in Fig. 81, for instance, when laid 
 within coffer-dams, are often faced with coursed ashler 
 having dressed beds and builds, and backed up with either 
 rubble- work laid in mortar, or with concrete, the headers of 
 the ashler being intended to give the requisite bond between 
 
430 PARTITIONS, AND RETAINING] WALLS. 
 
 the two classes of work. Much care must be exercised in 
 such composite work, lest the unequal settlement of the 
 different classes of work entirely destroy the effective bond 
 between them and thus lead to failure. 
 
 Such walls have been constructed with perfect success 
 without coffer-dams, of heavy blocks of moulded beton, and 
 also successfully by depositing concrete in place in the wall, 
 under water, with the assistance of a caisson mould, or 
 sheet-pile mould, thus forming a monolithic revetment. 
 
 Foundations under water to receive masonry structures 
 have also been successfully placed by the last-mentioned 
 system. 
 
 Concrete structures under water laid without coffers, 
 however, demand the exercise of a great deal of good judg- 
 ment, educated both in theory and by practice, and admit 
 only of the most faithful workmanship. 
 
FIG. 83. 
 
 FIG. 84. 
 
 FIG. 88. 
 
 FIG. 87. 
 
 FIG. 89. 
 
 n I 2 3 4- 5 6 7 Sf 9 10 II 12. 
 CONDUIT SECTIONS. 
 
OHAPTEE XX. 
 
 MASONRY CONDUITS. 
 
 432. Protection of Channels for Domestic Water 
 Supplies. The observations, sound reasonings, and good 
 judgments that influence municipalities to seek and secure 
 the most wholesome and coolest waters for their domestic 
 uses, compel them also to guard the purity and maintain 
 the equable temperature of the waters as they flow to the 
 point of distribution. 
 
 The larger cities, with few exceptions, must lead their 
 waters in artificial conduits, from sources in distant hills, 
 where neither the soils nor atmosphere are tainted by 
 decompositions such as are always in progress in the midst 
 of large concourses of human beings and animals. 
 
 Such long water-courses ought to be paved or revetted, 
 or their currents will be impregnated with the minerals 
 over which they flow, and will cut away their banks where 
 the channels wind out and in among the hills. An arch of 
 masonry spanning from wall to wall is then the most sure 
 >rotection from inflowing drainage, the approach of cattle 
 id vermin, the heating action of the summer sun, and the 
 i-owth of aquatic plants in too luxuriant abundance. 
 
 433. Examples of Conduits. When proper grades 
 ire attainable to permit the waters to flow with free sur- 
 faces, such conduits, requiring more than six or eight square 
 feet sectional area are usually, and most economically, con- 
 structed of hydraulic masonry. 
 
432 MASONRY CONDUITS. 
 
 Figures 83 to 89 illustrate some of the forms adopted in 
 American masonry conduits. 
 
 Fig. 87 is a section of the Croton conduit, at a point 
 where it is raised upon embankment. This conduit is 7'-5" 
 wide and 8-5J" high, and conveys from Croton River to the 
 distributing reservoir in Central Park, New York city, 
 about one hundred million gallons of water daily. The 
 combined length of conduit and of siphons between Croton 
 Dam and Central Park is about thirty-eight miles, and they 
 were completed in 1842. 
 
 Fig. 88 is a section of the Washington conduit, which is 
 circular, of 9 feet internal diameter. This leads water from 
 a point in the Potomac River about sixteen miles from the 
 capital, to a distributing reservoir in Georgetown, from 
 whence the water is led to the Government buildings and 
 grounds, and throughout the City of Washington, in iron 
 pipes. This conduit was constructed in 1859. 
 
 Fig. 84 is a section of the Brooklyn, L. I., conduit lead- 
 ing the waters of Jamaica and other ponds to the basin ad- 
 joining the well of the Ridge wood pumping-engines. This 
 conduit increases in dimensions at points where its volume 
 of flow is augmented from 8'-2" wide to lO'-O" wide, and to 
 a maximum height of 8'-8". It was constructed in 1859. 
 
 Fig. 86 is a section of the Charlestown, Mass., conduit, 
 leading the water of Mystic Lake to the well of the Mystic 
 pum ping-station. This conduit is 5-0" wide and 5-8" high, 
 and was constructed in 1864. 
 
 Fig. 85 is a section of the Lowell, Mass., conduit, of 
 4-3" diameter. This leads water from a subterranean 
 infiltration gallery along the margin of the Merrimack 
 River, a short distance above Lowell, a portion of the dis- 
 tance to the pumping-station. It was constructed in 1872. 
 
 Fig. 89 is a section of the second Chicago tunnel, extend- 
 
 
FOUNDATIONS OF CONDUITS. 433 
 
 ing under Lake Michigan two miles from the shore to the 
 lake crib, and underneath the city to the side opposite to 
 the shore of the lake. It is 7'-0" wide and 7-2" high in the 
 clear. The masonry of this tunnel consists of three rings of 
 brickwork, the two inner of which have the sides of their 
 bricks in radial lines, and the outer having its sides of 
 brick at right angles to radial lines. This tunnel was com- 
 pleted in 1874. 
 
 Fig. 83 is a section of the Boston conduit, commenced in 
 1875, to lead an additional supply from Sudbury Eiver to 
 the Chestnut Hill reservoir. Its length is sixteen and one- 
 half miles, its width 9-0", and height 7-8". 
 
 The new Baltimore conduit, as in progress in 1876, is to 
 be 36,495 feet in length, entirely in tunnel, extending from 
 Gunpowder River to the receiving reservoir. The portions 
 lined with masonry are circular in section, of 12 feet clear 
 diameter. The inclination is 1 in 5000, and the anticipated 
 capacity about 170,000,000 gallons per 24 hours. 
 
 The Cochituate conduit of the Boston water supply is 
 5 feet wide, 6'-4" high, of oviform section, and has an incli- 
 nation of 3 inches to the mile. Its capacity is 16,500,000 
 gallons per 24 hours. 
 
 434i Foundations of Conduits. The foundations of 
 masonry conduits must be positively rigid, since the super- 
 structures are practically inelastic, and any movement is 
 certain to produce rupture. A crack below the water-line 
 admits water into the foundation, and tends to soften or 
 undermine the foundation, and to further settlement, and 
 to additional leakage. So long as the foundation yields, 
 the conduit cannot be maintained water-tight, for the set- 
 tling away of the support at any point results in an undue 
 transverse strain upon the shell, and the adhesion of the 
 mortar to the masonry is overcome and the work cracks. 
 28 
 
434 
 
 MASONRY CONDUITS. 
 
 435. Conduit Shells. A perfect shell should have 
 considerable tensile strength in the direction of its circum- 
 ference ; but when a longitudinal crack is produced its 
 tensile strength is destroyed at that point, and cannot again 
 be fully restored except by rebuilding. 
 
 When the side walls are of rubble masonry they are 
 usually lined with a course of brick-work laid in mortar, or 
 with a smooth coat of hydraulic cement mortar. The bot- 
 toms are frequently lined with a nearly flat invert arch of 
 brick. 
 
 All the materials and workmanship entering into this 
 class of structures should be of superior quality. 
 
 436. Ventilation of Conduits. Conduits of form and 
 construction similar to those above illustrated are usually 
 proportioned so that they are capable of delivering the max- 
 imum volume of water required when flowing about two- 
 thirds lull. Provision is then made for the free circulation 
 of a stratum of air over the water surface and beneath the 
 covering arch. 
 
 FIG 90. 
 
 FIG. 91. 
 
 Figs. 90 and 91 illustrate the form of ventilating shaft 
 and cover used upon the New Bedford, Mass., conduit. 
 
CONDUITS UNDER PRESSURE 
 
 435 
 
 These shafts may be used also for man-hole shafts, which 
 are required at frequent intervals for inspection and care of 
 the conduit. 
 
 FIG. 92. 
 
 437. Conduits under Pressure. Fig. 92 illustrates a 
 <5onduit of locked bricks, designed by the writer to convey 
 water under pressure. The specially moulded bricks are 
 eight inches long and eight inches wide and two and one- 
 half inches thick. They have upon one side a mortise six 
 inches long, four and one-quarter inches wide, and one-half 
 inch deep, and upon the opposite side two tenons, each 
 matching in form a half mortise. When the bricks are laid 
 
436 MASONRY CONDUITS. 
 
 in the shell the tenons at the adjoining ends of two bricks 
 fill the mortise in the brick over which the joint breaks. 
 
 In brick conduits as usually constructed the bricks have 
 their greatest length in a longitudinal direction, but here the 
 length is in circumferential direction. The object here is to 
 utilize to the fullest extent the tensile bonding strength of 
 the masonry, and then to reinforce this strength by inter- 
 locking the bricks themselves. The conduit cannot be rup- 
 tured by pressure of water without shearing off numerous 
 tenons in addition to overcoming the cohesive strength of 
 the masonry. 
 
 This system permits of vertical undulations in the grade 
 of the conduit within moderate limits, and reduces mate- 
 rially the amount of lift of the conduit required upon em- 
 bankments. 
 
 Upon long conduits it permits the insertion of stop-gates 
 and the examination and repair of any one section while 
 the other sections remain full of water. Also when of 
 a given sectional area and flowing full, and delivering 
 to a pump- well or directly into distribution-pipes a given 
 volume of water, it transfers more of the pressure due 
 to the head than the usual form of construction of like 
 sectional area, and thus reduces the lift of the pump or 
 increases the head upon the distribution. This is more 
 especially the case when the consumption is less than the 
 maximum. 
 
 438. Protection from Frost. The masonry of con- 
 duits must be fully protected from frost, or its cement 
 mortar will be seriously disintegrated by the freezing and 
 expansion of the water filling its pores. The frost coverings 
 are usually earthen embankments, of height above the top 
 of the masonry equal to the greatest depth to which frost 
 penetrates in the given locality. The level breadth of the 
 
MASOXRY TO BE SELF-SUSTAINING. 437 
 
 top of the embankment should equal the breadth of the 
 conduit, and the side slopes be not less than i J to 1. 
 
 439. Masonry to be Self- sustaining. When the 
 conduit is in part or wholly above ground surface, its ma- 
 sonry should be self-sustaining under the maximum pres- 
 sure, independent of any support that may be expected / 
 from the embanked earth. The winds of winter generally { 
 clear the embankments very effectually of their snow cover- 
 ings, and leave them exposed to the most intense action 
 of frost. 
 
 In periods of most excessive cold weather the entire em- 
 bankment may be frozen into a solid arch, and by expan- 
 sion rise appreciably clear of the masonry, and possibly 
 exert some adhesive pull upon the hances of the arch. If 
 the conduit is then under full pressure, and not wholly 
 independent of earth support, a rupture at the crown of the 
 arch may result. 
 
 Each quadrant of the covering arch, above its springing 
 line, exerts a horizontal thrust at the springing line as indi- 
 cated in Fig. 92 by the shorter arrow, and the water pres- 
 sure exerts an additional horizontal thrust, as indicated by 
 the lower arrow in Fig. 92. When the conduit is just even 
 full, the point of mean intensity of this latter pressure is at 
 one-third the height from the bottom of the conduit. 
 
 The amount of horizontal pressure upon each side in 
 ach unit of length is equal to the vertical projection of the 
 submerged portion of that side, per unit of length into 
 the vertical depth from free water surface, of the centre of 
 gravity of the submerged surface, into the weight of one 
 cubic foot of water ; the depths being in feet, and weight 
 and pressure in pounds. 
 
 The product of weight of backing masonry at any given 
 depth below the crown of the arch into its coefficient of 
 
438 
 
 MASONRY CONDUITS. 
 
 FIG. 93. 
 
 friction, should be greater than the sum of thrusts at that 
 depth, and for a safe margin to insure frictional stability 
 should be equal to double the sum of thrusts. 
 
 The backing masonry is liable to receive some pull from 
 
 the embankment, if one 
 side of the embankment 
 settles or slides, but if the 
 foundations of the sides of 
 the embankments are rea- 
 sonably firm, the earth at 
 the sides of the backings 
 may be assumed capable 
 of neutralizing the thrusts 
 due to the weight of cover- 
 ing earth upon the hances 
 of the arch. 
 
 44O. A Concrete Conduit. The use of hydraulic 
 concrete, or beton, is at present being more generally intro- 
 duced" into American hydraulic constructions, in those 
 localities where good quarried stones are not readily and 
 cheaply accessible, than has been practiced in years past. 
 
 Fig. 93 is introduced here as a matter of especial interest, 
 since it illustrates the form of a conduit constructed entirely 
 of beton, in the new Vanne water supply for the city of 
 Paris. This conduit is two meters (6.56 feet) in diameter. 
 
 The beton agglomere of this conduit is a very superior 
 quality of hydraulic concrete, which has resulted from the 
 experiments and researches of M. Francois Coignet, of Paris. 
 Gen. Q. A. Gillmore has described* in Professional 
 Papers, Corps of Engineers, U. S. Army, No. 19, the mate- 
 rials, compositions, manipulations, and properties of this 
 
 * Report on Beton Agglomere, or Coignet Beton. Washington, 1871. 
 
 
EXAMPLE OF CONDUIT UNDER HEAVY PRESSURE. 439 
 
 "beton in a masterly manner, and has given several plates 
 illustrating some of the magnificent monolithic aqueducts 
 of concrete, spanning valleys and quicksands, in the great 
 forest of Fontainebleau, on the line of the Vanne conduit, 
 between La Vanne River and the city of Paris. 
 
 441. Example of Conduit under Heavy Pressure. 
 The details of the Penstock, leading water from the canal 
 above referred to ( 382), to the Manchester, N. H., -turbines 
 and pumps, are shown in Fig. 94. 
 
 This penstock is six hundred feet long, and six feet clear 
 internal diameter. Its axis at the upper end is under 
 twelve feet head of water, and at the lower end under thirty- 
 eight feet head of water. It was constructed, in place, in a 
 trench averaging thirteen feet deep. The staves, which are 
 of southern pitch-pine, 4 inches thick, were machine-dressed 
 to radial lines, and laid so that each stave breaks joint at its 
 end at a distance from the ends of the adjoining staves, after 
 the usual manner of laying long floors. The end-joints 
 where each two staves abut are closed by a plate of flat 
 iron, one inch wide, let into saw-kerfs cut in the ends of the 
 staves at right angles to radius. Thus a continuous cylin- 
 der is formed, except at the two points where changes of 
 grade occur. The hoops are of 2| x ^-inch rolled iron, each 
 made in two sections with clamping bolts, and they are 
 placed at average distances of eighteen inches between 
 centres. 
 
 Its capacity of delivery is sixty-five million gallons in 
 twenty-four hours, with velocity of flow not exceeding four 
 feet per second.* It was completed in the spring of 1874, 
 and has since been in successful use, requiring no repairs. 
 It lies in a ground naturally moist, and sufficiently satu- 
 
 * This penstock is more fully described in a paper read before the Ameri- 
 can Society of Civil Engineers in January, 1877. Vide Trans., March, 1877. 
 
MEAN RADII OF CONDUITS. 441 
 
 rated to fully protect the wood-work from the atmospheric 
 gases. 
 
 The city of Toronto, Canada, has just completed a con- 
 duit of wood, which conveys water under pressure from the 
 filtering gallery on an island in Lake Ontario, opposite to 
 the city, about 7,000 feet, to the pumping-station on the 
 main land. The internal diameter of this conduit is 4 feet. 
 
 442. Mean Radii of Conduits. In the formula of 
 flow for open canals (323), the influence of the air pe- 
 rimeter is taken into consideration in establishing the value 
 
 , , -, -, sectional area, S 
 
 of the hydraulic mean depth, r = - ^ , and a 
 
 contour, o 
 
 fractional portion of the air perimeter, equal to its propor- 
 tional resistance, is added to the solid wet perimeter. 
 
 It is more especially necessary that the resistance of the 
 air perimeter be recognized in conduits partially full. As 
 the depth of water increases above half-depth, the influence 
 of the confined air section is, apparently, inversely as the 
 mean hydraulic radius of the stream. 
 
 If we compute, for circular conduits, values of r, as equal 
 
 to -r TT-j : T , we have at o depth, r = Od ; at one- 
 wet solid perimeter 
 
 fourth depth, r = .14734^ ; at one-half depth, r = .25d ; at 
 three-fourths depth, r = .30133d ; and at full depth, r = 25d. 
 This series gives a maximum value of r at about eight-tenths 
 depth and a decrease in its value from thence to full. 
 
 The relative discharging powers, in volume, of a circular 
 conduit, with different depths of water, are as the product 
 
 \/ > when S is the sectional area of the stream ; r, the 
 
 V 772' 
 
 mean hydraulic radius ; and m, a coefficient. 
 
 If for a given series of depths, in the same conduit, we 
 compute its series of volumes of discharge, neglecting the 
 
442 MASONRY CONDUITS. 
 
 influence of the air perimeter, we arrive at the paradoxical 
 result that when the depth is eighty-eight hundredths of 
 full the volume flowing is ten per cent, greater than when 
 the conduit is full. This theoretical result has misled sev- 
 eral hydraulicians who have written upon the subject. 
 
 With a true value of r, the discharge has some ratio of 
 increase so long as sectional area of column of water in a 
 circular conduit increases ; but the maximum capacity of 
 discharge of a conduit is very nearly reached when it is 
 seven-eighths full. 
 
 TAB LE No. 9O. 
 HYDRAULIC MEAN RADII FOR CIRCULAR CONDUITS, PART FULL. 
 
 (Expressed in decimal parts of the diameter?) 
 
 RATIO OF FULL DEPTH. 
 o | .1 | .2 I .25 | .3 I -4 I -5 I -55 I -6 | .65 | .7 | .75 | .8 | .85 | .875 | .9 I -95 1 Full. 
 
 HYDRAULIC MEAN RADII, IN RATIO OF DIAMETER. 
 o | .058] .no| .136! .157! .200! .235 | .250! .263) .272] .275.1.278! .277] .273! .270! .265! .260] .250 
 
 443. Formulas of Flow, for Conduits. Rankine's 
 formula* for loss of head in an open conduit is, 
 
 A"- . v * m 
 
 r *f 
 
 from which, by transposition, we have the equation of 
 velocity, 
 
 ,= ]?*= ]??(*. (2) 
 
 ( ml \ ( m } 
 
 For value of the coefficient m he adopts Weisbach's for- 
 mula, viz. : 
 
 .00023 
 m = .0074 + 
 
 * Civi] Engineering, p. 678. London, 1872. 
 
FORMULAS OF FLOW, FOR CONDUITS. 443 
 
 This formula for m gives a constant value to m, while v 
 remains constant, even though r varies. Experiment shows 
 that the variable r exerts a very appreciable influence upon 
 the value of the coefficient m, when 
 
 It is unfortunate that data for the construction of a table 
 of m for conduits, not under pressure, is so scanty. Their 
 values for brick conduits, or brick linings for a given series 
 of r, evidemy lie somewhere between the values of m for 
 smooth pipes under pressure, and the values of m for 
 straight open channels in earth. 
 
 The following column of values for the given series of r 
 are suggested merely as approximate mean values for 
 smooth conduits three-quarters full, and are placed between 
 columns of values of m for smooth pipes under pressure, 
 and for straight open channels in earth for convenience of 
 ready comparison. 
 
 They are applicable to the formulas, for conduits : 
 
 in 
 ml 
 
 mtf ,, 
 
 , 
 
 *= 
 
 in which 
 
 v velocity of flow, in feet per second. 
 
 T = hydraulic mean radius. 
 
 i = sine of inclination of water surface. 
 
 Ji vertical head lost in given length, in feet 
 
 I = given length, in feet. 
 
444 
 
 MASONRY CONDUITS. 
 
 TABLE No. 9O. 
 COEFFICIENTS FOR SMOOTH CONDUITS, THREE-QUARTERS FULL. 
 
 (For a mean velocity of about 2.5 feet per second?) 
 
 Hydraulic mean radii 
 r in feet. 
 
 Coefficient w for 
 smooth pipes, under 
 pressure. 
 
 Coefficient m for 
 smooth conduits, 
 9gri 
 
 ~ v* ' 
 
 Coefficient m for open 
 channels in earth. 
 
 I 
 
 .00380 
 
 .OIOO 
 
 .0298 
 
 1-25 
 
 .00342 
 
 .0084 
 
 .0260 
 
 1.50 
 
 .00325 
 
 .0071 
 
 .0234 
 
 i-75 
 
 .00300 
 
 .0063 
 
 .O2I2 
 
 2 
 
 .OO28l 
 
 .0057 
 
 .0197 
 
 2.25 
 
 .0027 
 
 53 
 
 .0183 
 
 2.50 
 
 .OO26 
 
 .0050 
 
 .0172 
 
 2.75 
 
 
 .0048 
 
 .Ol6l 
 
 3 
 
 
 .0046 
 
 I53 
 
 3-25 
 
 
 .0045 
 
 .0143 
 
 3-5 
 
 
 .0044 
 
 .0131 
 
 3-75 
 
 
 .0042 
 
 .0137 
 
 4 
 
 
 .0040 
 
 .0127 
 
 A mean velocity of flow of about two and one-half_iket 
 per second is usually preferred in smooth conduits and 
 supply mains, when local circumstances permit the inclina- 
 tion and sectional area to be adapted to this end. Less 
 velocities, in conduits of three feet or more diameter, per- 
 mits the waters to deposit the sediments they have in sus- 
 pension. 
 
 444. Table of Conduit Data. The following table 
 gives such data as is at present obtainable respecting some 
 of the well-known conduits of masonry : 
 
CONDUIT DATA. 
 
 445 
 
 TABLE No. 91. 
 CONDUIT DATA. 
 
 LOCALITY. 
 
 | 
 
 j 
 
 1 
 
 "3 5; 
 
 I 5 
 . ^ 
 
 Q 
 
 r. 
 
 i. 
 
 v 
 per 
 sec. 
 
 in. 
 
 Daily de- 
 livery at 
 given 
 depth. 
 
 Total 
 daily 
 capacity. 
 
 Cochituate, Boston 
 Croton, New York 
 Washington Aq., D.C 
 
 Feet. 
 
 5 
 7-4I7 
 9 
 
 10 
 
 9 
 7.0522 
 
 c 66? 
 
 Feet. 
 
 6-333 
 8.458 
 
 8.667 
 7.667 
 
 I 
 
 ^ 
 
 Feet. 
 
 6.333 
 6.083 
 3-465 
 5-00 
 5-3 
 
 1.417 
 
 2.3415 
 I.8735 
 2.5241 
 
 .0000496 
 
 .00021 
 .00015 
 .0001 
 
 Feet. 
 
 i .0 
 2.218 
 1.893 
 
 .00452 
 .006435 
 00505 
 
 U.S.gal. 
 
 16,398,980 
 59,340,243 
 27i559i364 
 
 U.S. gal. 
 16,500,000 
 
 100,000,000 
 100,000,000 
 
 70,000,000 
 70.000,000 
 170,000,000 
 60,000,000 
 52,000,000 
 
 23,500,000 
 
 5,500,000 
 
 Sudbury, Boston. . . . 
 
 
 
 
 Baltimore 
 Loch Katrine, Glasgow.. 
 Canal of Isabel II, Madrid 
 Vienna 
 
 
 
 
 6.85 
 
 2-5253 
 
 .0001578 
 
 1.7126 
 
 .00876 
 
 60,000,000 
 
 
 .000435 
 
 .0001 
 
 .... 
 
 
 
 
 
 6.6' 
 
 6.6 
 
 5.00 
 
 .... 
 
 Dhuis " .... 
 
 Pont du Gard, Nimes.... 
 Pont Pyla, Lyons 
 Metz 
 
 4.OO 
 
 1.833 
 3-167 
 
 
 3-333 
 1-833 
 2.167 
 
 
 .0004 
 
 .00166 
 
 .001 
 
 .0004 
 .0003 
 
 .0002 
 .0003 
 
 2 
 
 2-95 
 2.783 
 
 
 ... 
 
 
 
 Arcueil 
 
 Roquencourt, Versailles. . 
 
 3-925 
 
 2-583 
 
 
 
 
 
 1.333 
 .716 
 
 
 
 
 Montpellier. 
 
 X 
 
 o.S 
 
 .... 
 
 
 
 
 
CHAPTEE XXI. 
 
 MAINS AND DISTRIBUTION PIPES. 
 
 445. Static Pressures in Pipes. Passing from the 
 consideration of masonry conduits to that of pipes with 
 tough metal shells, the pressure strains and the capabilities 
 of resistance of the pipe metals to these strains, first de- 
 mand^ our attention. 
 
 The theoretical relations of thickness to pressure are so 
 
 simple that we may easily adapt any tough metal pipe to 
 
 withstand any practical static head pressure, however great. 
 
 By the term static pressure, we indicate the full pressure 
 
 due to the head of water, while standing at rest. 
 
 The unit of pressure area is commonly taken as one 
 square inch, and this is the area used 
 herein for the unit. 
 
 The pressure p upon the unit of 
 area a of a conduit or water-pipe, is 
 equal to the product of the given area 
 into the vertical height h of the surface 
 of water above the centre of gravity of 
 the given area, into the weight w of 
 one cubic foot of water (= 62.5 Ibs.) 
 divided by 144. 
 
 FIG. 95. 
 
 *1 
 
 a, x 7i x w 
 
 144 
 
 = .434^. 
 
 (1) 
 
 Let dbcef, Fig. 95, be the internal circumference of a 
 
NEW-YORK 
 
 SCALE, 
 
 FORMS OF PIPE SOCKETS. 
 
THICKNESS OF SHELL. 447 
 
 water-pipe, of diameter d, in inches ; then the total pressure 
 P of water upon the circumference is 
 
 P = S.UlQd x .434^. (2) 
 
 The maximum pressure acts upon each point of the cir- 
 cumference radially outward, tending to tear the shell 
 asunder. 
 
 The resultant of the maximum pressure upon any given 
 portion of the circumference a&, acts in a radial direction 
 ox, through the centre of gravity 6f the surface a&, and is 
 equal to the product of pressure into the projection or trace 
 of the surface ij, at right-angles to radius, 
 
 ) x p\. 
 
 Also the resultant of the maximum pressure upon the 
 semi-circumference cbaf is equal to the product of pressure 
 into its trace gk^ at right-angles to the radial line cutting its 
 
 centre of gravity, 
 
 = f(area #&) x p\. 
 
 The trace of the semi-circumference is also equal to the 
 diameter d, and its resultant equals the product dp. 
 
 Opposed to the resultant ox is an equal resultant of the 
 pressure upon the semi-circumference fee. 
 
 These two resultants exert their maximum tensile strain 
 upon the pipe-shell at the points c and/. 
 
 446. Thickness of Shell resisting Static Pressure. 
 Let 8 be the cohesive strength or ultimate tenacity per 
 sq. in. of the metal of the shell, and t be the thickness cc^ and 
 ffi in inches of the shell, then we have for equation of resist- 
 ance of shell that will just balance the steady static pressure, 
 
 2tS=dp. (3) 
 
 from which we deduce the required thickness of shell : 
 
448 MAINS AND DISTRIBUTION PIPES. 
 
 t _dp_ rp 
 
 '2S"~S 9 
 
 in which r equals radius in inches, = 
 
 
 
 It is not enough that the shell be able to just sustain the 
 steady static pressure, since this pressure may be increased 
 by " water -rams " incident to ordinary or extraordinary 
 use of the pipe, or the metal may have unseen weaknesses, 
 or deteriorate by use. 
 
 The thickness t should therefore be multiplied by a 
 coefficient, for safety, equal to 4, 6, 8, or 10 ; or the pressure 
 be assumed to be increased 4, 6, 8, or 10 times, or the 
 tenacity of the metal be taken at .1, .2, .3, or .4 of its test 
 value ; in which case the equation of t may take the form, 
 
 pr 
 = --., or t=2g. (5) 
 
 The pressure due to a given head H of water is greater 
 within a pipe when the water is at rest, than when the cur- 
 rent is flowing through the pipe at a steady rate, for when 
 the current is moving, a portion of the force of gravity is 
 consumed in producing that motion, and in balancing fric- 
 tions ; hence the effective head H v remaining at a given 
 point is less than the static head by an amount equal to the 
 
 (V 2 \ 
 = Jl = ] T 
 
 and the head overcoming the Mctional resistances between 
 the reservoir and the given point in the length of the pipe 
 
 , ml 
 Ti - - x 
 r 
 
 , = H-(7i + h"). ( Vide 265.) 
 
 When a pipe has a stop-valve at its outflow, or in its 
 line, the pressure p, used in its formula of thickness , for 
 
WATER-RAM. 449 
 
 any point above the valve, should be the static presssure of 
 the water at rest. 
 
 447. Water-ram. If any valve in a line or system of 
 water-pipes can be suddenly closed while the water is flow- 
 ing freely under pressure, such sudden closing of the valve 
 will produce a strain upon the pipes far greater than that 
 due to the static head of water. 
 
 For illustration, let any delivery-pipe, having a stop- 
 valve at its outflow end, be 1 ft. diameter = d\ , and 5280 ft. 
 long = Z, and the current of water filling it be flowing at a 
 uniform rate v of 5 feet per second. Then the momentum 
 M of this column of water, due to its weight and velocity, is 
 
 M = .785M 2 x w x I x jf (6) 
 
 = .7854 x 62.5 x 5280 x .3882 
 = 100,614.45 Ibs. 
 
 If the valve is closed and the flow checked instantaneous- 
 ly, this great force will act upon the valve and upon the 
 shell of the pipe. If the given length of column of water in 
 motion is doubled or quadrupled, the force of the ram will 
 be doubled or quadrupled. If the valve is one second or 
 one minute in closing, then the force will be distributed 
 through one second or one minute in time, and its intensity 
 will be correspondingly reduced. Also, if there are any 
 accumulations of air in the pipe at summits, they will help 
 to prolong the time of action and to modify the force be- 
 hind them. 
 
 No system of distribution-pipes should be fitted with 
 stop-valves of instantaneous action, lest the pipes be con- 
 
 itly in danger of destruction by "water rams." 
 
 Genieys made allowance, in the old water-pipes of Paris, 
 >r water-rams, of force equal to static heads of 500 feet, 
 29 
 
450 MAINS AND DISTRIBUTION-PIPES. 
 
 but he used on his smaller mains plug- valves that might be 
 very rapidly closed. 
 
 With proper stop and hydrant valves, it is not probable 
 that the momentum strain will exceed that due to a steady 
 static head of 200 or 225 feet, but it is liable to be great in 
 pipes under low static heads as well as in pipes under great 
 heads, and it is in either case in addition to the static head. 
 The momentum strain must be fully allowed for, whether 
 the head be ten feet or three hundred feet. 
 
 448. Formulas of Thickness for Ductile Pipes. 
 Ordinarily, for ductile pipes, such as lead, brass, welded 
 iron, etc., an allowance of from 200 to 300 feet head is made 
 for the momentum strain, and the tenacity of the material 
 is taken at .25 or .3 of its ultimate resistance 8, in which 
 case the formula for thickness o ductile pipes, subject to, 
 water-ram,, may take the forai, ft ~^-z 
 
 , _ (7i + 230 ft.) rw _ (7i + 230)dw _ (7i + 230)^ 
 (.258) x 144 " (.68) x 144 " 728) 
 
 in which 7i is the head of water, in feet. 
 
 w " " weight of one cubic foot of water, in Ibs. 
 r " " radius of the pipe, in inches. 
 d" " diameter of the pipe, in inches. 
 t " " thickness of the pipe-shell, in inches. 
 8 " " tenacity of the metal, per square inch. 
 
 If we substitute a term of pressure per square inch, p 
 (= .434^), for -T-7J- in the equation for thickness of ductile 
 
 pipes, it becomes 
 
 , _ (p + 100 pounds) r _ (p + 100) d fff . 
 
 .258 .68 
 
 If the pipes have merely a steady static pressure to sus- 
 
MOULDING OF PIPES. 
 
 451 
 
 tain, then the term + 100 may be omitted, and the equation, 
 with factor of safety equal to 4, takes the simple form, 
 
 pr 
 
 '.258 
 
 pd 
 
 or with factor of safety equal to 6, 
 
 pd 
 
 .16667#~ .33333#' 
 
 (9) 
 
 (10) 
 
 449. Strengths of Wrought Pipe Metals. The fol- 
 lowing values of S give the tenacities of the respective ma- 
 terials named, in pounds per square inch of section of 
 metal, when the metal is of good quality for pipes : 
 
 TAB LE No. 92. 
 TENACITIES OF WROUGHT PIPE METALS. 
 
 
 WEIGHT 
 PER CU- 
 BIC INCH. 
 
 
 COEF. 
 
 6(/r). 
 
 COEF. 
 4 Or)- 
 
 COEF. 
 6 (pd). 
 
 COEF. 
 4 (Pd\ 
 
 
 Pounds. 
 
 S. in Ibs. 
 
 .16667^. 
 
 .255". 
 
 33333S. 
 
 . 5 s. 
 
 Lead 
 
 
 2 -*86 
 
 .jo- 66 
 
 
 
 
 Block tin 
 
 
 
 
 
 
 H93 
 
 Glass 
 
 
 4i 
 
 766 66 
 1566 66 
 
 1150 
 
 J 533-33 
 
 
 Brass 
 
 
 
 4666 66 
 
 
 
 
 Copper .... 
 
 .3000 
 
 2 ,000 
 
 
 
 
 
 Wrought-iron, single riveted 
 " u double " 
 
 ' 6 * 
 .2607 
 
 35ioo 
 
 liirii 
 
 8750 
 
 11666.66 
 
 17500 
 
 
 
 
 
 
 
 
 CAST-IRON PIPES. 
 
 45O. Moulding of Pipes. The successful founding 
 of good cast-iron pipes requires no inconsiderable amount 
 of skill, such as is acquired only by long practical experi- 
 ence, and keen, watchful observation. 
 
 The loam and sand of the moulds and cores must be 
 carefully selected for the best characteristics of grain, and 
 
452 MAINS AND DISTRIBUTION-PIPES. 
 
 proportioned, combined, and moistened, so that the mix- 
 ture shall be of the right consistency to form smooth and 
 substantial moulds and cores, and be at the same time suf- 
 ficiently porous to permit the free exit of moisture and 
 steam during the process of drying. The moulds must be 
 filled and rammed with a care that insures ttteir stability 
 during the inflow of the molten metal, and must be dried 
 so there will be no further generation of steam during the 
 inflow ; and yet not be overdried so as to destroy the ad- 
 hesion among their particles, lest the grains of sand be 
 detached and scattered through the casting. The core rop- 
 ing of straw must be judiciously proportioned in thickness 
 for the respective diameters of their finished cores, and must 
 be twisted to a firmness that will resist the pressure of the 
 molten metal, so that the pipe will be free from swells and 
 the proper and uniform thickness of metal will be secured. 
 The mixture of the metals and fuel in the cupola must 
 be guided by that experience by which is acquired a fore- 
 knowledge of the degree of tenacity, elasticity, and general 
 characteristics of the finished castings. A superior class of 
 pipe is produced only when excellent materials are used, 
 and when superior workmanship and mechanical appli- 
 ances give to them accuracy of form and excellence of 
 texture. 
 
 451. Casting of Pipes. A certain thickness of shell, 
 of twelve-foot pipes, cast vertically, is required for each 
 diameter of pipe, to insure a perfect filling of the mould 
 before the metal chills, or cools, and also to enable the 
 pipes to be safely handled, transported, laid, and tapped. 
 
 In the smaller pipes this thickness is greater than that 
 ordinarily required to sustain the static pressure of the 
 water. 
 
 The necessary additional thickness, beyond that re- 
 
THICKNESS OF CAST-IRON PIPES. 453 
 
 quired to resist the water pressure, decreases as the diam- 
 eter of the pipe increases. 
 
 There must, therefore, be affixed to the formula of thick- 
 ness of cast-iron pipes, a term expressing the additional 
 thickness required to be given to the pipes beyond that re- 
 quired to resist the pressure of the water, and this term 
 must decrease in value as the diameter increases in value. 
 
 452. Formulas of Thickness of Cast-iron Pipes. 
 The ultimate tenacity of good iron-pipe castings ranges 
 from 16,000 to 29,000 pounds per square inch of section of 
 metal. Their value of 8, the symbol of tensile strength 
 per square inch, is usually taken at 18,000 pounds, and the 
 coefficient of safety equal to 10, or the term of tensile resist- 
 ance is taken equal to .1$, or if an independent term is 
 introduced in the formula for the effect of water-ram, the 
 coefficient of S may be increased to, say .2. 
 
 Assuming that the probable or possible water-ram will 
 not produce an additional effect greater than that due to a 
 static pressure of 100 pounds per square inch, or head of 
 230 feet, then the formula for thickness of cast-iron pipes 
 may take the form, 
 
 ,_ 
 
 " 
 
 Oqq/1 & \ _ (& + 230>&0 , 
 
 100/ " .48 x 144 " 
 
 (.28) x 144 100/ " (.48 )x 144 
 
 in which Ji is the head of water, in feet. 
 
 w " weight of one cubic foot of water, in Ibs. 
 r " internal radius of the pipe, in inches. 
 d " internal diameter of the pipe, in inches. 
 t " thickness of the pipe shell, in inches. 
 8 " tenacity of the metal, in pounds per sq. in. 
 
 If we substitute a term of pressure per square inch, 
 
454 MAINS AND DISTRIBUTION PIPES 
 
 p ( .434A) for - -j, in the above equations for thickness 
 
 of cast-iron pipes, they become, 
 
 _ (p + 100)7- / eZ \ _ (p + IQOyZ 
 
 Tag" H 1 'loo/ -^r~ 
 
 . . .333(1 -A). (12) 
 
 453. Thicknesses found Graphically. Since with a 
 constant head, pressure, or assumed static strain, the in- 
 crease of tensile strain upon the shell is proportional with 
 the increase of diameter, and also since the decrease of 
 additional thickness is proportional with the increase of 
 diameter, it is evident that if we compute the thickness of a 
 series of pipes, say from 4-inch to 48-inch diameters, for a 
 given pressure, by a theoretically correct formula, and then 
 plot to scale the results, with diameters as abscissas and 
 thicknesses as ordinates, the extremes of all the ordinates 
 will lie in one straight line ; and also, that if the thicknesses 
 for the minimum and maximum diameters of the series be 
 computed and plotted as ordinates, in the same manner, 
 and their extremities be connected by a straight line, the 
 intermediate ordinates, or thicknesses for given diameters 
 as abscissas, will be given to scale. This method greatly 
 facilitates the calculation of thicknesses of a series of 
 " classes" of pipes, and if the ordinates are plotted to large 
 scale, gives a close approximation to accuracy. 
 
 454. Table of Thicknesses of Cast-iron Pipes. 
 The following table gives thicknesses of good, tough, and 
 elastic cast-iron, with 8= 18,000 Ibs., for three classes of 
 cast-iron pipes, covering the ordinary range of static pres- 
 sures of public water supplies. 
 
 The thicknesses in the table are based upon the formula, 
 
 d 
 
 d\ 
 -ioo/ 
 
THICKNESSES OF CAST-IRON PIPES. 
 
 455 
 
 TABLE No. 93, 
 THICKNESSES OF CAST-I'RON PIPES. 
 
 (When S = 18000 Ibs.) 
 
 
 CLASS A. 
 
 CLASS B. 
 
 CLASS C. 
 
 DIAMETER. 
 
 Pressure, 50 Ibs. per 
 square inch, or less. 
 Head, 116 feet. 
 
 Pressure, 100 Ibs. per 
 square inch. 
 Head, 230 feet. 
 
 Pressure, 130 Ibs. per 
 square inch. 
 Head, 300 feet. 
 
 THICKNESSES. 
 
 THICKNESSES. 
 
 THICKNESSES. 
 
 Inches, 
 
 3 
 
 Inches. 
 .3858 
 
 AP- 
 
 prox. 
 in. 
 
 H 
 
 Inches. 
 .4066 
 
 AP- 
 
 prox. 
 in. 
 
 H 
 
 Inches. 
 
 .4191 
 
 Ap- 
 prox. 
 in. 
 
 TV 
 
 4 
 
 4033 
 
 tt 
 
 43 ii 
 
 A 
 
 4477 
 
 TV 
 
 6 
 
 .4383 
 
 A 
 
 .4800 
 
 * 
 
 5050 
 
 \ 
 
 8 
 
 4734 
 
 i 
 
 .5289 
 
 tt 
 
 .5622 
 
 TV 
 
 10 
 
 5083 
 
 * 
 
 5777 
 
 H 
 
 .6194 
 
 1 
 
 12 
 
 5433 
 
 A 
 
 .6266 
 
 1 
 
 .6766 
 
 
 
 14 
 
 .5783 
 
 if 
 
 6 755 
 
 
 
 7338 
 
 i 
 
 16 
 
 .6166 
 
 1 
 
 .7277 
 
 i 
 
 7944 
 
 
 
 18 
 
 .6483 
 
 
 
 7733 
 
 H 
 
 .8483 
 
 H 
 
 20 
 
 6833 
 
 tt 
 
 .8222 
 
 11 
 
 9055 
 
 B 
 
 22 
 
 7183 
 
 H 
 
 .8711 
 
 1 
 
 .9628 
 
 H 
 
 24 
 
 7533 
 
 | 
 
 .9200 
 
 
 
 I.02OO 
 
 I 
 
 27 
 
 .8058 
 
 
 
 9933 
 
 I 
 
 1.1058 
 
 'A 
 
 30 
 
 8583 
 
 1 
 
 i. 0666 
 
 'A 
 
 I.I9l6 
 
 i* 
 
 33 
 
 .9108 
 
 
 
 1.1400 
 
 i/ 2 
 
 1-2775 
 
 iA 
 
 36 
 
 9 6 33 
 
 H 
 
 1.2133 
 
 'A 
 
 L3633 
 
 4 
 
 40 
 
 1-0333 
 
 A 
 
 1.3111 
 
 '* 
 
 1.4778 
 
 'H 
 
 44 
 
 1.1033 
 
 i 
 
 1.4088 
 
 i 
 
 I.592I 
 
 i 
 
 48 
 
 i.i733 
 
 i* 
 
 1.5066 
 
 4 
 
 1.7066 
 
 i 
 
 In the following table are given the thicknesses of cast- 
 iron pipes, as used by various water departments. 
 
456 
 
 MAINS AND DISTRIBUTION PIPES. 
 
 TABLE No, 93a. 
 THICKNESSES OF CAST-IRON PIPES, AS USED IN SEVERAL CITIES. 
 
 \ 
 
 Q 
 
 PHILADELPHIA. 
 
 1 
 
 BALTIMORE. 
 
 BROOKLYN. 
 
 { 
 
 CHICAGO. 
 
 p 
 
 u 
 
 PROVIDENCE. 
 
 i 
 
 ROCHESTER. 
 
 I 
 
 ALLEGHENY. 
 
 DETROIT. 
 
 ALBANY. 
 
 MILWAUKEE. 
 
 DIAMETER, INCHES. 
 
 250 
 
 He 
 IOO 
 
 ad P 
 
 218 
 
 ress 
 
 1 2O 
 170 
 198 
 
 ures 
 
 130 
 170 
 
 for 
 125 
 
 whic 
 150 
 
 ;h P 
 
 TOO 
 140 
 1 80 
 
 ipes 
 
 130 
 170 
 
 200 
 
 are 
 
 150 
 2OO 
 
 Clas 
 
 80 
 140 
 260 
 
 sed, 
 162 
 
 in fe 
 IOO 
 
 et. 
 144 
 2OO 
 
 JI50 
 200 
 
 
 
 
 
 
 
 4 
 6 
 6 
 
 8 
 8 
 
 10 
 12 
 12 
 
 16 
 16 
 
 20 
 
 20 
 2 4 
 24 
 30 
 30 
 30 
 36 
 
 4 8 
 
 f 
 
 TV 
 
 'V 
 
 TV 
 TV 
 
 Thic 
 A 
 
 H 
 
 A 
 
 1 
 
 if 
 
 kne 
 
 A 
 A 
 
 f- 
 
 tt 
 
 ft 
 
 sses 
 
 of P 
 
 ipe Shells, in 
 
 ... .1 . i 
 
 incl 
 
 f 
 
 T 
 
 H 
 
 
 
 les. 
 
 TV 
 TV 
 
 I 
 
 I 
 f 
 f 
 1 
 
 1 
 
 7 
 
 if 
 
 A 
 
 'f 
 H 
 
 4 
 6 
 6 
 
 8 
 8 
 
 12 
 12 
 
 16 
 16 
 
 20 
 20 
 24 
 24 
 
 30 
 
 30 
 30 
 36 
 36 
 
 48 
 
 i 
 i 
 \ 
 
 A 
 H 
 H 
 
 f 
 If 
 II 
 \l 
 if 
 ft 
 
 TV 
 
 A 
 
 11 
 f+ 
 tt- 
 I 
 
 f 
 1 
 
 1 
 
 A+ 
 
 
 
 * 
 
 ^ 
 
 * 
 
 f 
 
 
 
 i 
 
 f 
 
 tt 
 
 1 
 1 
 
 f 
 f 
 
 1 
 
 f 
 
 I 
 
 f 
 
 I 
 
 f 
 
 I 
 
 f 
 if 
 t 
 
 1 
 TnV 
 
 f 
 
 A 
 
 t 
 
 1 
 
 if 
 
 1 
 
 1 + 
 
 1 
 
 f 
 
 
 
 tt 
 
 f 
 
 if 
 
 1 
 
 I 
 
 if 
 
 .... 
 
 7 
 
 f 
 
 I 
 
 1 
 
 
 f 
 
 1 
 
 if 
 
 i 
 i 
 
 
 
 1 
 
 
 
 1 + 
 
 it* 
 
 t 
 
 I 
 
 1 
 
 f 
 
 I 
 
 I 
 
 
 
 
 
 
 
 
 
 H 
 
 I 
 
 4 
 
 If 
 
 J 
 
 
 
 4 
 
 4 
 
 .... 
 
 .... 
 
 
 
 
 
 
 
 'A 
 
 4 
 
 
 
 
 
 4 
 
 I 
 
 
 
 4 
 
 4+ 
 
 .... 
 
 "A 
 
 
 jj 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 Ti 
 
 
 T-i 5 ,- 
 
 
 
 4 
 
 
 
 
 
 
 
 
 
 
 
 
 8 
 
 
 
 
 
 
 
 
 
 
 
 455. Table of Equivalent Fractional Expressions. 
 
 The following tables of equivalent expressions for fractions 
 of an inch and of a foot, may facilitate pipe calculations : 
 
CAST-IRON PIPE JOINTS. 
 
 457 
 
 TABLE No. 94. 
 PARTS OF AN INCH AND A FOOT, EXPRESSED DECIMALLY. 
 
 Equivalent 
 INCHES. Dec. part of 
 
 Equivalent 
 Dec. part of 
 
 
 
 an inch. 
 
 a foot. 
 
 
 1-32 .03125 
 
 . 002604 
 
 
 1-16 
 
 .06250 
 
 .005208 
 
 
 3-32 
 
 09375 
 
 .007812 
 
 
 1-8 
 
 .12500 
 
 .010416 
 
 
 5-32 
 
 .15625 
 
 .010420 
 
 
 
 
 
 3-i6 
 7-32 
 1-4 
 
 .18750 
 .21875 
 .25000 
 
 .015625 
 .018229 
 .020833 
 
 INCHES. 
 
 Equivalent 
 Dec. parts of 
 a loot. 
 
 Dec. parts 
 of a foot. 
 
 Equiv. inches 
 and 32cl pts., 
 nearly. 
 
 9-32 
 
 .28125 
 
 023437 
 
 
 
 
 
 
 
 
 
 5-16 
 n-32 
 3-8 
 13-32 
 , 7-16 
 15-32 
 
 1-2 
 17-32 
 9~l6 
 IQ-32 
 
 5-8 
 21-32 
 11-16 
 
 .31250 
 
 34375 
 37500 
 .40625 
 43750 
 .46875 
 .50000 
 
 .53125 
 56250 
 
 59375 
 .62500 
 .65625 
 .68750 
 
 .026041 
 .028645 
 .031250 
 .033854 
 036458 
 .039062 
 .041666 
 .044270 
 .046875 
 .049479 
 .052083 
 .054607 
 057291 
 
 I 
 2 
 
 3 
 4 
 
 6 
 
 8 
 9 
 
 10 
 
 ii 
 
 12 
 
 0833 
 .1667 
 .2500 
 3333 
 4167 
 .5000 
 
 .5833 
 .6667 
 7500 
 
 .8333 
 .9167 
 
 I.OOOO 
 
 .1 
 
 .2 
 
 3 
 4 
 
 '.6 
 
 7 
 .8 
 
 9 
 
 I.O 
 
 'f* 
 
 2* 
 
 3il 
 
 F 
 If 
 
 12 
 
 27 -72 
 
 .71875 
 
 .0^080^ 
 
 
 
 
 
 **j j** 
 
 3-4 
 
 / x u / O 
 
 .75000 
 
 v oy > -'yj 
 .062500 
 
 
 25-32 
 
 .78125 
 
 .065104 
 
 
 13-16 
 
 .81250 
 
 .067708 
 
 
 27-32 
 
 .84375 
 
 .070312 
 
 
 7-8 
 
 .87500 
 
 .072916 
 
 
 29-32 
 
 .90625 
 
 .075520 
 
 
 15-16 
 
 .93750 
 
 .078125 
 
 
 31-32 
 
 .96875 
 
 .080729 
 
 
 i 
 
 I. 
 
 083333 
 
 
 456. Cast-iron Pipe Joints. According to Crecy,* 
 cast-iron pipes were first generally adopted in London very 
 near the close of the last century. The great fire destroyed 
 many of the lead mains in that city. These were in part 
 replaced by wood pipes, but when water-closets were intro- 
 duced and more pressure was demanded, the renewals were 
 afterward wholly of iron. 
 
 * Encyclopedia of Civil Engineering, p. 549. London, 1865. 
 
458 MAINS AND DISTRIBUTION-PIPES. 
 
 The earliest pipes had flanged joints with a packing ring 
 of leather, and were bolted together. These were two and 
 one-half feet in length. Those first generally used by the 
 New River Company were somewhat longer, and were 
 screwed rigidly together at the joints. This prevented 
 their free expansion * and contraction, with varying temper- 
 atures of water and earth, rendering them troublesome in 
 winter, when they were frequently ruptured. Cylindrical 
 socket-joints were then substituted. These were accurately 
 turned in a lathe, to a slightly conical form, and, being 
 luted with a little whiting and tallow, were driven together. 
 
 The length of the pipes was subsequently increased to 
 nine feet, and a hub and spigot-joint formed, adapted first 
 to a joint packing of deal wedges, and afterward to a pack- 
 ing of lead. 
 
 The hub and spigot-joint, with various slight modifica- 
 tions, has been generally adopted in the British and con- 
 tinental pipe systems, for both water and gas pipes ; but 
 the turned joint has by no means been entirely superseded 
 in European practice. 
 
 A variety of the forms given to the turned joint are illus- 
 trated and commented upon in a paper f recently read by 
 Mr. Downie in Edinburgh. The illustrations include turned 
 joints used in Glasgow, Launceston, Dundee, Flyde, Liver- 
 pool, Trieste, Sydney, Hobart Town, and Hamilton (Canada) 
 water- works, and in the Buenos Ayres gas-works. These 
 joints were also used by Mr. George H. Norman, the well- 
 known American contractor for water and gas works, in 
 gas works constructed by him in Cuba. 
 
 * M. Girard found that the lineal expansion of cast-iron pipes, when free 
 and in the open air was .C00036 of an inch for each additional degree of Fah- 
 renheit. 
 
 f Proceedings Inst. E. S., vol. vii, p. 16. 
 
 
DIMENSIONS OF PIPE-JOINTS. 
 
 459 
 
 The turned joint has not as yet been adopted in the 
 pipe systems in the United States ; but in the new water- 
 work of Ottawa, Canada, completed in 1875 under the direc- 
 tion of Thos. C. Keefer, C.E., they were very generally used. 
 
 The depths of hub and of lead packing in the early Eng- 
 lish and Scotch pipes, and in fact in the first pipes used in 
 connection with the Fainnount, Croton, and Washington 
 aqueducts, exceeded greatly the depths at present used. 
 
 The pine-log water-pipes of Philadelphia had been gen- 
 erally replaced by cast-iron pipes as early as about 1819. 
 The forms of hubs and spigots then used, as designed by 
 Mr. Graffe, Sr., were very similar to those now used, ex- 
 cept that the hubs had somewhat greater depth. The 
 lengths of the pipes were nine feet, and other dimensions as 
 in the following table, from data in the "Journal of the 
 Franklin Institute" : 
 
 Diameter of pipe, in inches. 
 
 Thickness of shell 
 
 Depth of hub 
 
 3 
 
 f 
 31 
 
 10 
 I 
 
 5 
 
 12 
 
 [6 
 
 6 
 
 20 
 
 ! 
 
 It is observed that the set, by which the lead is com- 
 pacted in the joint, acts upon the lead, ordinarily only to a 
 depth of from one to one and one-quarter inches. The lead 
 beyond the action of the set is of but little practical value, 
 and there is no advantage in giving the hemp packing an 
 excessive depth. 
 
 Deep joints run solid with lead often give to the line of 
 pipes such rigidity that it cannot accommodate itself to the 
 levenness of its bearings and weight of backfilling, espe- 
 Lly in ledge cuttings, and rupture results. 
 When trenches are too wet to admit of pouring the lead 
 Lccessfully, small, soft lead pipe may be pressed into the 
 >int and faithfully set up with good effect. 
 457. Dimensions of Pipe -joints. Fig. 96 is a re- 
 
460 
 
 MAINS AND DISTRIBUTION-PIPES. 
 
 FIG. 96. 
 
 duced section of a bell and spigot of a 12-inch diameter 
 pipe. Dimensions of cast-iron pipe socket-joints for diam- 
 eters from 4-inch to 48-inch, corresponding to the letters in 
 the sketch, are given in the following table (No. 95), and 
 like data are given for flange-joints in the next succeeding 
 table, No. 96. 
 
 The weight of flanged pipes, per lineal foot, exclusive of 
 weight of flanges, which is given in Table No. 96, may be 
 computed by the following formula (vide 461) : 
 
 w = 9.817 (d + t) 1. 
 
 (13) 
 
 458. Templets for Bolt Holes. A sheet-metal tem- 
 plet for marking centres of bolt holes on flanges should be 
 laid out and pricked with the nicest accuracy, and have its 
 face side and one hole conspicuously marked. 
 
 On special castings intended for fixed positions the tem- 
 plet should be placed upon the flange so that the centre of 
 the marked hole shall fix the position of one bolt hole ex- 
 actly over the centre of the bore of the pipe when the pipe 
 shall be placed in position, then the bolt holes of abutting 
 flanges will match with uniformity. 
 
DIMENSIONS OF PIPES. 
 
 461 
 
 TABLE No. 95. 
 DIMENSIONS OF CAST-IRON WATER-PIPES. (Fig. 96.) 
 
 (Thickness of shell is herein proportioned for 100 Ibs. static pressure.) 
 
 Diameter. I 
 
 'a 
 
 )-4 
 
 O 
 
 > 
 
 o 
 
 JS 
 
 ! 
 
 a Thickness 
 S- of shell. 
 
 <0 
 
 ^' 
 
 as 
 -_ 
 
 * 
 
 lq 
 
 ^ Joint room. 
 
 * 
 
 ^ 
 
 ce 
 
 W 
 
 ef 
 
 fP 
 
 kl 
 
 &m 
 
 7W71 
 
 to 
 
 <?j 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 in. 
 
 4 
 
 12-3 
 
 TV 
 
 3 
 
 TV 
 
 I* 
 
 i] 
 
 il 
 
 i 
 
 TV 
 
 f 
 
 i 
 
 A 
 
 t 
 
 1 
 
 2 
 
 . 6 
 
 12-3 
 
 i 
 
 3 
 
 I 5 * 
 
 If 
 
 il 
 
 it 
 
 i 
 
 TV 
 
 f 
 
 i 
 
 A 
 
 1 
 
 i 
 
 2 
 
 8 
 
 12-3 
 
 H 
 
 3 
 
 A 
 
 If 
 
 ii 
 
 4 
 
 -1 
 
 TV 
 
 f 
 
 i 
 
 TV 
 
 I 
 
 4 
 
 2i 
 
 10 
 
 12-3 
 
 it 
 
 3 
 
 A 
 
 If 
 
 i| 
 
 4 
 
 i 
 
 T 8 * 
 
 f 
 
 i 
 
 A 
 
 1 
 
 it 
 
 21 
 
 12 
 
 12-3^ 
 
 I 
 
 3i 
 
 A 
 
 2 
 
 i| 
 
 ii 
 
 i 
 
 TV 
 
 1 
 
 i 
 
 A 
 
 1 
 
 ii 
 
 2i 
 
 14 
 
 12-31 
 
 H 
 
 3i 
 
 TV 
 
 2j 
 
 if 
 
 4 
 
 i 
 
 TV 
 
 1 
 
 i 
 
 T^ 
 
 1 
 
 4 
 
 2* 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 16 
 
 I2-3| 
 
 I 
 
 3i 
 
 t 
 
 *i 
 
 if 
 
 if\ 
 
 f 
 
 i 
 
 1 
 
 A 
 
 I 
 
 i 
 
 4 
 
 2f 
 
 18 
 
 12-3? 
 
 If 
 
 3i 
 
 f 
 
 2* 
 
 if 
 
 iA 
 
 f 
 
 i 
 
 1 
 
 TV 
 
 t 
 
 i 
 
 4 
 
 2f 
 
 20 
 
 i2-3i 
 
 II 
 
 3i 
 
 I 
 
 2l 
 
 if 
 
 iA 
 
 f 
 
 i 
 
 1 
 
 TV 
 
 I 
 
 1 
 
 4 
 
 2f 
 
 22 
 
 I2-3| 
 
 1 
 
 3f 
 
 t 
 
 2i 
 
 if 
 
 iA 
 
 f 
 
 i 
 
 I 
 
 A 
 
 t 
 
 I 
 
 if 
 
 3 
 
 24 
 
 I2-3| 
 
 ft 
 
 3f 
 
 t 
 
 2i 
 
 if 
 
 iA 
 
 f 
 
 i 
 
 I 
 
 A 
 
 1 
 
 I 
 
 if 
 
 3 
 
 27 
 
 12-4 
 
 I 
 
 4 
 
 TV 
 
 2f 
 
 il 
 
 ii 
 
 f 
 
 i 
 
 li 
 
 t 
 
 TV 
 
 I* 
 
 if 
 
 3i 
 
 30 
 
 12-4 
 
 'A 
 
 4 
 
 TV 
 
 2f 
 
 i| 
 
 ii 
 
 f 
 
 i 
 
 I* 
 
 t 
 
 TV 
 
 I* 
 
 if 
 
 3i 
 
 33 
 
 12-41 
 
 iA 
 
 4i 
 
 TV 
 
 2f 
 
 2 
 
 4 
 
 f 
 
 i 
 
 M 
 
 f 
 
 TV 
 
 I* 
 
 if 
 
 3i 
 
 30 
 
 i2-4i 
 
 iA 
 
 4j 
 
 t 
 
 2f 
 
 2 
 
 ii 
 
 f 
 
 i 
 
 4 
 
 TV 
 
 * 
 
 4 
 
 if 
 
 3i 
 
 40 
 
 12-41 
 
 IA 
 
 4i 
 
 i 
 
 2f 
 
 H 
 
 il 
 
 f 
 
 i 
 
 Ii 
 
 iV 
 
 * 
 
 H 
 
 2 
 
 3! 
 
 
 
 I2-4| 
 
 iM 
 
 4| 
 
 i 
 
 2| 
 
 2i 
 
 ii 
 
 f 
 
 i 
 
 M 
 
 TV 
 
 i 
 
 x* 
 
 2 
 
 3f 
 
 , 
 
 T2-4f 
 
 Ii 
 
 4f 
 
 i 
 
 3 
 
 2i 
 
 ii 
 
 f 
 
 i 
 
 If 
 
 TV 
 
 i 
 
 if 
 
 2 
 
 4 
 
462 
 
 MAINS AND DISTRIBUTION-PIPES. 
 
 TAB LE No. 96. 
 FLANGE DATA OF FLANGED CAST-IRON PIPES. 
 
 Diam. 
 of 
 bore 
 of 
 pipe. 
 
 Diameter 
 of 
 flange. 
 
 Thick- 
 ness of 
 flange. 
 
 Approx. 
 weight 
 of one 
 flange. 
 
 No. of 
 bolts.* 
 
 Diam. 
 of 
 bolts. 
 
 Diameter 
 of circle of 
 bolts. 
 
 Distance 
 between 
 centres of 
 bolts. 
 
 Com- 
 mon 
 diam. 
 of valve 
 flanges. 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 Pounds. 
 
 
 Inches. 
 
 Decimal 
 
 inches. 
 
 Decimal 
 inches. 
 
 Inches. 
 
 3 
 
 6i 
 
 
 
 3-45 
 
 8 
 
 & 
 
 5-6 
 
 2.19 9 
 
 8 
 
 4 
 
 7i 
 
 1 
 
 6.64 
 
 IO 
 
 i 
 
 6.7 
 
 2.105 
 
 9 
 
 6 
 
 10 
 
 
 
 8.56 
 
 10 
 
 A 
 
 8.9 
 
 2.796 
 
 1 1 
 
 8 
 
 I*i 
 
 tt 
 
 11.98 
 
 12 
 
 1 
 
 II. I 
 
 2.906 
 
 i3 
 
 10 
 
 Hi 
 
 7 
 ^ 
 
 16.5 
 
 14 
 
 I 
 
 13-3 
 
 2.985 
 
 16 
 
 12 
 
 17 
 
 tf 
 
 22.3 
 
 14 
 
 i 
 
 IS-S 
 
 3.478 
 
 18 
 
 14 
 
 19* 
 
 I 
 
 28.6 
 
 16 
 
 i 
 
 J 7-75 
 
 3.485 
 
 20 
 
 16 
 
 2lf 
 
 'A 
 
 36.8 
 
 18 
 
 f 
 
 20.0 
 
 3-49 1 
 
 22 
 
 18 
 
 *3j 
 
 4 
 
 45-5 
 
 20 
 
 i 
 
 22.2 
 
 3-487 
 
 24 
 
 20 
 
 26J 
 
 i* 
 
 56-9 
 
 20 
 
 i 
 
 24.4 
 
 3.833 
 
 26J 
 
 22 
 
 28J 
 
 4 
 
 62.8 
 
 22 
 
 1 
 
 26.5 
 
 3-784 
 
 28i 
 
 2 4 
 
 3J 
 
 4 
 
 65-4 
 
 24 
 
 1 
 
 28.6 
 
 3-744 
 
 3| 
 
 27 
 
 33l 
 
 '* 
 
 80.8 
 
 26 
 
 7 
 ? 
 
 31.8 
 
 3.842 
 
 33l 
 
 30 
 
 36* 
 
 it 
 
 95-9 
 
 28 
 
 1 
 
 35- 
 
 3-927 
 
 36J 
 
 33 
 
 40 
 
 4 
 
 117 
 
 30 
 
 i 
 
 38-1 
 
 3-99 
 
 40 
 
 36 
 
 43i 
 
 -A 
 
 J 43 
 
 3 2 
 
 7 
 ? 
 
 41.6 
 
 4.084 43$ 
 
 40 
 
 471 
 
 'I 
 
 160 
 
 34 
 
 1 
 
 45-75 
 
 4.227 
 
 47l 
 
 44 
 
 54 
 
 4 
 
 197 
 
 36 
 
 1 
 
 50.0 
 
 4-363 
 
 54 
 
 48 
 
 56 
 
 4 
 
 224 
 
 40 
 
 1 
 
 54-1 
 
 4.249 
 
 56 
 
 * The number of bolts given in the table may be decreased when the 
 water pressures aiid transverse strains upon the bolts are light. 
 
FLEXIBLE PIPE-JOINT. 
 
 463 
 
 If an even number of bolts are used, then there will be 
 a bolt vertically over and under the centre of the bore of 
 the pipe. 
 
 If the templet is not very exactly spaced the face side 
 should be placed against one flange with the marked hole 
 at top, and the back against the other abutting flange with 
 same hole at top ; otherwise the bolt holes may not exactly 
 match. 
 
 459. Flexible Pipe- Joint. It is sometimes necessary 
 to take a main or sub-main across a broad, deep stream or 
 
 FIG. 97. 
 
 estuary, or arm of a lake, where it is both difficult and 
 expensive to coffer a pipe course so as to make the usual 
 form of rigid joint. Different forms of ball and socket 
 
464 
 
 MAINS AND DISTRIBUTION-PIPES. 
 
 flexible joints have been adopted for such cases, which 
 allow the pipes to be joined and the joints completed above 
 the water surface, and the pipe then to be lowered into 
 its bed. 
 
 Fig. 97 illustrates the form of joint designed by the 
 writer for a twenty-four inch pipe, which is especially 
 adapted to large-size pipe-joints. It is a modification of the 
 Glasgow " universal joint." 
 
 The difficulty of making the back part of the lead-pack- 
 ing of the joint firm and solid, which difficulty has here- 
 tofore interfered with the complete success of the larger 
 flexible pipes, is here overcome by separating the bell into 
 two parts, so as to permit both the front and rear parts of 
 the packing to be driven. 
 
 In putting together this joint, the loose ring is passed 
 over the ball-spigot and slipped some distance toward the 
 
 FIG. 98. 
 
 centre of the pipe ; the ball-socket is then entered into the 
 solid part of the bell and its lead joint packing poured and 
 snugly driven ; the loose ring is then bolted in position, and 
 its lead joint packing is poured and firmly driven, also. 
 This secures a solid packing at both front and rear of the 
 
WEIGHTS OF CAST-IRON PIPES. 465 
 
 joint, capable of withstanding the strain that comes upon it 
 as the pipe is lowered into position, and ensures a tight 
 joint. The ball-spigot is turned smooth in a lathe to true 
 spherical form. 
 
 Fig. 98 illustrates J. B. Ward's patent flexible joint. 
 
 460. Thickness Formulas Compared. The results 
 given by some of the well-known formulas for thicknesses 
 of cast-iron pipes, may be compared in Table No. 97. 
 
 461. Formulas for Weights of Cast-iron Pipes. 
 The mean weight of cast-iron is about 450 pounds per cubic 
 foot, or .2604 pounds per cubic inch. 
 
 Let d be the diameter of a cast-iron pipe, in inches ; 
 , the thickness of the pipe-shell, in inches ; and n the ratio 
 of circumference to diameter (= 3.1416) ; then the cubical 
 volume V l , in inches, of a pipe-shell (neglecting the weight 
 of hub), is, for each foot in length, 
 
 V l = (d + ) x t x TT x 12. (14) 
 
 When the length of a pipe is mentioned, it is commonly 
 the length between the bottom of the hub and the end of 
 the spigot that is referred to ; that is, the net length of the 
 pipe laid, or which it will lay. 
 
 The average weight of a pipe per foot includes the 
 weight of the hub, which, as thus spoken of, is assumed to 
 be distributed along the pipe. 
 
 The weights of the hubs, of general form shown in 
 Fig. 96, and whose dimensions are given in Table No. 95 
 (p. 461), increase the average weight per foot of the twelve- 
 foot light pipes, approximately, eight per cent. ; of the 
 medium pipes, seven and one-half per cent. ; and of heavier 
 pipes, seven per cent. 
 
 The equation for cubical volume of pipe-metal, includ- 
 ing hub, is 
 30 
 
466 
 
 M\INS AND DISTRIBUTION-PIPES. 
 
 T A B I E No. 9*7. 
 FORMULAS FOR THICKNESS OF CAST-IRON PIPES COMPARED. 
 
 Assumed static pressure, 75 Ibs. per square inch. Assumed tenacity of metal, 18,000 Ibs. per 
 
 square inch. 
 
 AUTHORITY. 
 
 EQUATIONS. 
 
 DIAMETERS. 
 
 48 in. 
 
 4 in. 
 
 12 in. 
 
 24 in. 
 
 Equation (12), 452. . 
 M Dupuit . . 
 
 (/ + ioo)</ / d\ 
 
 Thick- 
 ness. 
 
 Inches. 
 .4172 
 
 455 
 4550 
 .3899 
 4534 
 
 3776 
 .4074 
 .2887 
 
 4175 
 .3600 
 
 3334 
 .4129 
 .4900 
 3542 
 4554 
 4384 
 .4496 
 
 Thick- 
 ness. 
 
 Inches. 
 .5850 
 
 .5766 
 
 5750 
 .4897 
 .6002 
 
 5794 
 .6121 
 
 .5000 
 
 .6126 
 6235 
 .5002 
 .6148 
 .6699 
 5625 
 .6461 
 7152 
 .6488 
 
 Thick- 
 ness. 
 
 Inches. 
 .8367 
 
 .8333 
 7550 
 6394 
 .8204 
 
 .8069 
 .7242 
 .7071 
 
 953 
 .8818 
 7504 
 .9176 
 
 9397 
 .8750 
 9322 
 1.1304 
 .9476 
 
 Thick- 
 ness. 
 
 Inches. 
 1.3400 
 
 1.3466 
 1.1150 
 
 9389 
 1.2608 
 
 1.1750 
 1.0684 
 
 I.OOOO 
 
 1.4902 
 1.2470 
 1.2508 
 1.5232 
 
 1-4795 
 1.5000 
 1.5000 
 1.9608 
 1-5452 
 
 .*S h ' 333 l 1 IO oJ 
 t = (.coi6nd) + .013^ + .32 
 
 t= (.015^) +.395.. 
 / ( aoz'&nd) +34 
 
 J. F. D'Aubuisson... 
 Julius Weisbach 
 Dionysius Lardner. . 
 
 Thomas Box 
 
 t ( ooTfir) + 78 
 
 t - ji^ + . I5 l + _M_ 
 
 G. L. Molesworth... 
 
 Wm. J. M. Rankine. 
 John Neville 
 
 ( 10 ) 25000 
 {.37 for 4" to 12" ) 
 .50 U 12 " 30 > 
 .62 " 3 " 50 ) 
 
 ,-./Z 
 
 V 48 
 
 Thos. Hawksley 
 Baldwin Latham 
 
 t = .rtVd 
 
 whd 
 t + .2"; 
 
 James B. Francis. . . 
 Thos. J. Whitman... 
 M. C. Meigs 
 J H Shedd 
 
 28.85 1 5 " 
 t = (.000058^^9 + .0152^ + .312 
 
 t = (.oo45</) + .4 .oo-Lid 
 t ( 0260416^) +25 
 
 J? ~~ ( oooo8A</) + old + .36 
 
 J F Ward 
 
 
 Jos. P. Davis 
 
 t = (.oo475rf) + .35 
 
 In which / = thickness of pipe wall, in inches. 
 
 d = interior diameter of pipe, in inches. 
 h head of water, in feet 
 w = weight of a cubic foot of water, = 62.5 Ibs. 
 = number of atmospheres of pressure, at 33 feet each. 
 / = pressure of water, in pounds per square inch. 
 .S 1 = ultimate tenacity of cast-iron, in pounds per square inch. 
 
WEIGHTS OF CAST-IRON PIPES. 467 
 
 V=(d + 1.08Q x t x TT x 12. (15) 
 
 Let Wi be the weight per cubic inch of the metal 
 (= .2604 Ibs.), and w the average weight per foot of the pipe, 
 then we have for equation of average weight per foot, of 
 twelve-foot pipes, 
 
 w = 12 (d + 1.08Q t n w,. (16) 
 
 t 
 To compute the average weight per lineal foot of an 
 
 18-inch diameter pipe, twelve feet long, and f J inch thick in 
 the shell, assign the numerical value to the symbols, and 
 the equation is : 
 
 w = 12 [18 + (1.08 x .65625)] x .65625 x 3.1416 x .2604 
 = 120.58 pounds. 
 
 In the equation, 12, TT, and Wi are constants, and may be 
 united, and their product (= 9.81687) supply their place in 
 the equation, when the equation for average weight per 
 foot is, 
 
 w = 9.82 (d + 1.08Q ' * ; (17) 
 
 and for the total weight of a 12-foot pipe : 
 
 W = 117.8 (d + 1.08Q t. (18) 
 
 462. Table of Weights of Cast-iron Pipes, The 
 following table gives minimum weights of three classes of 
 cast-iron pipes, of good, tough, and elastic cast-iron (with 
 8 = 18,000 Ibs.), for heads up to 300 ft. ; also, approximate 
 weights of lead required per joint for the respective diam- 
 eters, from 4 to 48 inches, inclusive. 
 
468 
 
 MAINS AND DISTRIBUTION-PIPES. 
 
 TABLE No. 98. 
 MINIMUM WEIGHTS OF CAST-IRON PIPES. 
 
 
 CLASS A. 
 
 CLASS B. 
 
 CLASS C. 
 
 
 
 
 Head, n6feet. 
 
 Head, 230 feet. 
 
 Head, 300 feet. 
 
 
 
 
 Pressure, 50 Ibs. 
 
 Pressure, 100 Ibs. 
 
 Pressure, 130 Ibs. 
 
 . 
 
 c 
 
 
 
 
 
 1 
 
 > 
 
 1 
 
 
 % ^ 
 
 ej 
 
 
 , L 
 
 
 & > 
 
 Bl 
 
 
 I 
 
 B 
 
 
 *j < o 
 
 
 
 
 - 1 - 1 ^ PS 
 
 
 JL-f 
 
 
 .s 
 
 a 
 
 P 
 
 o 
 
 til 
 
 <u S x 
 
 II 
 
 '-> +J 
 
 1 
 
 f|| 
 
 ft 
 
 | 
 
 
 jj 5 
 
 If 
 
 o 
 
 
 en 
 
 
 c 
 * 
 
 hoc N 
 
 r* 
 
 || 
 
 I 
 
 |l| 
 
 3| 
 
 c 
 
 o 
 
 3 
 
 \*\ 
 
 I"! 
 
 1 
 
 1 
 
 
 
 > n 
 
 H 
 
 H 
 
 > if 
 ^ g 
 
 ^ 
 
 H 
 
 > n 
 
 H" 
 
 Q 
 
 
 
 in. 
 
 r*. 
 
 IBs. 
 
 /^. 
 
 in. 
 
 /&. 
 
 Ibs. 
 
 in. 
 
 Ibs. 
 
 Ibs. 
 
 in. 
 
 Ibs. 
 
 4 
 
 .4033 
 
 17.57 
 
 211 
 
 43" 
 
 18.94 
 
 227 
 
 4477 
 
 19.69 
 
 236 
 
 i| 
 
 4-25 
 
 6 
 8 
 
 4383 
 4734 
 
 27.87 
 39.67 
 
 Si 
 
 .4800 
 .5289 
 
 30.71 
 44.5 
 
 369 
 
 534 
 
 5050 
 .5622 
 
 32.43 
 47-49 
 
 570 
 
 if 
 
 6.25 
 8.25 
 
 10 
 
 5083 
 
 52.66 
 
 632 
 
 5777 
 
 60.25 
 
 7 2 3 
 
 .6194 
 
 64.85 
 
 778 
 
 T H 
 
 10.25 
 
 12 
 
 5433 
 
 67.12 
 
 805 
 
 .6266 
 
 76.20 
 
 914 
 
 .6766 
 
 84-53 
 
 1014 
 
 2 
 
 13.00 
 
 3 
 
 x! 
 
 83.04 
 
 100.90 
 
 996 
 
 I2II 
 
 6755 
 .7277 
 
 97.68 
 
 "9-93 
 
 1172 
 1439 
 
 7338 
 
 106.54 
 I3L45 
 
 1278 
 
 2 
 
 15.00 
 24.25 
 
 18 
 
 20 
 
 .6483 
 .6833 
 
 "9-35 
 
 1432 
 l6 7 
 
 7733 
 .8222 
 
 143.00 
 168.61 
 
 1716 
 2023 
 
 9055 
 
 1 57-5 I 
 186.45 
 
 ^890 
 2237 
 
 3 
 
 27.25 
 30-75 
 
 22 
 
 .7183 
 
 160.64 
 
 1928 
 
 .8711 
 
 196.00 
 
 2352 
 
 .9628 
 
 217.74 
 
 2613 
 
 2 i 
 
 35-25 
 
 24 
 2 7 
 
 
 183.55 
 220.53 
 
 2203 
 2646 
 
 .9200 
 9933 
 
 225.75 
 273.76 
 
 2709 
 3285 
 
 .0200 
 .1058 
 
 25L33 
 306.15 
 
 3016 
 3674 
 
 S 
 
 38.25 
 51-25 
 
 30 
 
 .9108 
 .9633 
 
 260.66 
 304.00 
 350.31 
 
 3128 
 3648! 
 4204 
 
 1.0666 
 1.1400 
 1.2183 
 
 326.01 
 
 383-13 
 444.48 
 
 3912 
 
 4598 
 5334 
 
 .1916 
 2775 
 3633 
 
 366.00 
 43 I - I 5 
 501.48 
 
 4392 
 5i74 
 6018 
 
 2 
 28 
 
 56.75 
 62.25 
 79-50 
 
 40 
 
 3 
 
 1.0333 
 1.1033 
 1.1733 
 
 417.20 
 
 489.50 
 567-63 
 
 5006 
 6812 
 
 1.3111 
 1.4088 
 1.5066 
 
 533-iS 
 629.70 
 734-iQ 
 
 6398 
 7556 
 8809 
 
 4778 
 5921 
 .7066 
 
 603.45 
 7I4-55 
 835.00 
 
 7241 
 8575 
 
 10020 
 
 5 
 
 88.75 
 107.75 
 
 III.OO 
 
 The following table gives the weights of pipes that have 
 "been used by various water departments for their maximum 
 pressures : 
 
 * Vide thicknesses of pipes in Table No. 93, p. 455. 
 
INTERCHANGEABLE JOINTS. 
 
 469 
 
 TABLE No. 
 
 WEIGHTS OF CAST-IRON PIPES, AS USED IN SEVERAL CITIES FOR 
 THEIR MAXIMUM PRESSURES. 
 
 
 DELPHIA. 
 
 o 
 
 S5 
 
 w 
 
 K 
 O 
 3 
 
 t 
 
 S3 
 
 s 
 
 6 
 o 
 
 3ENCE. 
 
 J 
 
 p 
 
 H 
 
 (5 
 
 
 
 Id 
 
 S 
 
 < 
 
 Q 
 Z 
 
 O 
 
 \UKEE. 
 
 a 
 
 X 
 u 
 
 PH 
 
 & 
 
 I 
 
 1 
 
 CQ 
 
 S 
 
 u 
 
 X 
 
 O 
 
 i 
 
 OH 
 
 U 
 
 1 
 
 I 
 
 
 3 
 
 X 
 u 
 
 
 
 X 
 u 
 
 " 
 
 
 
 
 1 
 
 
 
 
 
 
 
 
 
 
 2 
 
 a 
 
 
 H 
 
 s 
 $ 
 
 Maximum Head, in feet 
 
 | 
 
 fi 
 
 
 Q 
 
 
 R. 
 
 R. 
 
 R. 
 
 R. 
 
 R. 
 
 R. 
 
 S.-P.I R. R. 
 
 S.-P. 
 
 S.-P. 
 
 R. & 
 D.-P. 
 
 D.-P. 
 
 R. 
 
 R. & 
 S.-P. 
 
 
 
 250 
 
 100 
 
 180 
 
 218 
 
 198 
 
 170 
 
 125 1 l8ol 200l 260 
 
 175 
 
 200 
 
 250 
 
 237 
 
 200 
 
 
 
 Average "Weights, per lineal foot, in pounds. 
 
 
 
 
 
 T? 1 
 
 
 
 
 
 
 
 
 
 
 
 14 
 
 
 
 000\*.<j 
 
 19 
 3 1 
 42 
 
 .?. 
 
 20 
 
 5 
 
 28 1 
 40 
 
 18 
 55 
 
 35 
 
 sef 
 50 
 
 '33J 
 
 49 
 
 34 
 49 
 
 24 
 
 ii 
 it 
 
 20 
 32 
 
 45 
 
 
 20 
 
 3 
 45 
 
 
 
 35 
 5 
 
 4 6 
 
 
 
 
 
 t-6 
 
 
 
 
 
 
 87 
 
 
 col 
 
 
 60 
 
 
 
 12 
 
 71 
 
 86 
 
 81 
 
 85 
 
 90 
 
 85 
 
 83! 
 
 85" 
 
 8.S 
 
 123 
 
 85 
 
 75 
 
 86 
 
 100 
 
 87 
 
 12 
 
 3 
 
 
 
 
 
 
 
 
 
 
 
 
 
 *I25 
 
 
 
 S 
 
 
 
 124 
 
 130 
 
 
 
 
 128 
 
 i 
 
 
 
 
 
 17O 
 
 I2Q 1 
 
 20 
 24 
 
 3 
 
 37 
 330 
 
 170 
 
 235 
 340 
 
 231 
 337 
 
 200 
 
 208 
 
 183 
 
 250 
 
 178! 
 2 39 
 
 2413 
 
 239 
 257 
 
 i 
 
 265 
 334 
 
 202 
 257 
 
 170 
 230 
 
 330 
 
 % 
 
 20 
 24 
 30 
 
 350 
 
 407 '- 
 
 325 
 
 06 
 
 
 -icH 
 
 
 400 
 
 13 
 
 45 
 
 472 
 
 412 
 
 
 
 
 
 
 
 ^6 
 
 
 585 696 
 
 606 
 
 
 (U 
 
 
 
 
 
 
 
 
 
 
 
 48 
 
 The initials in the horizontal column of heads indicate the systems of pressure, viz., R M res- 
 ervoir ; S.-P., stand-pipe ; and D.-P., direct pressure. 
 
 463. Interchangeable Joints. When several classes 
 of pipes, varying in weight for similar diameters, enter into 
 the same system of distribution, as, for instance, in an un- 
 dulating town, with considerable differences in levels, there 
 is an advantage in making the exterior diameters the con- 
 stants, instead of the interiors, for then the spigots and bells 
 of both plain and special castings, and of valves and 
 hydrants, have uniformity, and are interchangeable, as occa- 
 sion requires, and the different classes join each other with- 
 >ut special fittings. 
 
 ' The Ottawa pipe weights classed as of 4 and 14 inch diameters are in 
 5 and 15 inch diameters respectively. 
 
470 MAINS AND DISTRIBUTION-PIPES. 
 
 If it is objectionable to increase and decrease the interior 
 diameters of the light and heavy classes, then the object 
 may be attained by increasing the thickness of the ends of 
 the light and medium classes, so far as they enter the hubs. 
 
 464. Characteristics of Pipe-Metals. The metal 
 of pipes should be tough and elastic, and have great 
 tenacity. In proportion as these qualities are lacking, bulk 
 of metal, increased in a geometrical ratio, must be sub- 
 stituted to produce their equivalents. In our formula given 
 above ( 452) for thickness of cast-iron, it will be re- 
 membered that we were obliged to add a term of thickness 
 
 j .333(1 ;j--A I to enable the pipes to be safely handled. 
 
 If the metal is given great degrees of toughness and elas- 
 ticity, we may omit, for the larger pipes, this last member 
 of the formula ; but now we add to each twelve-foot piece 
 of pipe, of 20-inch diameter, five or six hundred pounds ; 
 36-inch diameter, six or eight hundred pounds, etc., that 
 would not be required with a superior metal. 
 
 It is expensive to freight this extra metal a hundred or 
 more miles, and then to haul it to the trenches and swing it 
 into place, and at the same time to submit to the breakage 
 of from three to five per cent, of the castings because of the 
 brittleness of the inferior metal. 
 
 It is well known that the same qualities of iron stone, and 
 of fuel, may produce from the same furnace very different 
 qualities of pigs, and it is the smelter's business to know, 
 and he generally does know, whether he has so proportioned 
 his materials and controlled his blast, as to produce pigs 
 that when remelted will flow freely into the mould, take 
 sharply its form, and become tough and elastic castings. 
 The founders will supply a refined and homogeneous iron, 
 if such quality is clearly specified, and it is well worthy of 
 
CHARACTERISTICS OF PIPE METALS. 471 
 
 consideration in the majority of cases whether such iron 
 will not be in fact the most economical, at its fair additional 
 cost, if extra weight, extra freight and haulage, and extra 
 breakage, are duly considered. 
 
 Expert inspectors cannot with confidence pronounce 
 upon the quality of the cast metal from an examination 
 of its exterior appearance, nor infallibly from the appear- 
 ance of its fracture. Wilkie says * of the fracture of good 
 No. 1 cast-iron, that it shows a dark gray color - nth high 
 metallic lustre ; the crystals are large, many of them shining 
 like particles of freshly-cut lead ; and that however thin 
 the metal may be cast, it retains its dark gray color. It 
 contains from three to five per cent, of carbon. This is 
 the most fusible pig iron and most fluid when melted, and 
 superior castings may be produced from it. 
 
 No. 3 has smaller and closer crystals, which diminish in 
 size and brightness from the centre of the casting toward 
 the edge. Its color is a lighter gray than No. 1, with less 
 lustre. No. 2 is intermediate in appearance and quality 
 between Nos. 1 and 3. 
 
 The "bright," "mottled," and "white" irons have still 
 lighter colored fractures, with a white "list" at the edges, 
 are less fusible, and are more crude, hard, and brittle. 
 
 The mottled and white irons are sometimes produced by 
 the furnace working badly, or result from using a minimum 
 of fuel with the ore and flux. 
 
 The crystals of the coarser kinds of cast-irons were found 
 by Dr. Schott, in his microscopical examinations of frac- 
 tures, to be nearly cubical, and to become flatter as the 
 proportion of carbon decreased and the grain became more 
 uniform. 
 
 * " The manufacture of Iron in Great Britain." London, 1857. 
 
472 MAINS AND DISTRIBUTION PIPES. 
 
 In wrought iron, the double pyramidal form of the cast 
 
 crystal is almost lost, and has become flattened down to 
 
 parallel leaves, forming what is termed the fibre of the iron. 
 
 In steel the crystals have become quite parallel and 
 
 fibrous. 
 
 465. Tests of Pipe Metals. The toughness and elas- 
 ticity of pipe metal may be tested by taking sample rings 
 of, say, 24-inch diameter, 1-inch width, and f -inch thickness, 
 hanging them upon a blunt knife-edge, and then suspending 
 weights from them, at -a point opposite to their support, 
 noting their deflections down to the breaking point ; also, by 
 letting similar rings fall from known heights upon solid an- 
 vils. The iron may also be submitted to what is termed the 
 "beam test," generally adopted to measure the transverse 
 strength and elasticity of castings for building purposes. 
 In such case the standard bar, Fig. 99, is 3 ft. 6 in. long, 
 
 2 in. deep, and 1 in. broad, and 
 FlG - " is placed on bearings 3 ft. apart, 
 
 and is loaded in the middle till 
 broken. 
 
 Iron that has been first skill- 
 fully made into pigs, from good 
 ore and with good fuel, and has 
 
 then been remelted, should sustain in the above described 
 beam test, from 4,000 to 4,500 pounds, and submit to a de- 
 flection of from ^ to J-inch. 
 
 The tenacity of the iron is usually measured by submit- 
 ting it to direct tensile strain in a testing machine, fitted for 
 the purpose. Its tenacity should reach an ultimate limit 
 of 25,000 pounds per square inch of breaking section, while 
 still remaining tough and elastic. Hard and brittle irons 
 may show a much greater tenacity, though making less 
 valuable pipes. 
 
THE PRESERVATION OF PIPE SURFACES. 473 
 
 466. The Preservation of Pipe Surfaces. The 
 
 uncoated iron mains first laid down in London, by the New 
 River Company, were supposed to impart a chalybeate 
 quality to the water, and a wash of lime-water was applied 
 to the interiors of the pipes before laying to remedy this evil. 
 
 Before iron pipes had been long in use, in the early part 
 of the present century, in those European towns and cities 
 supplied with soft water, it was discovered that tuberculous 
 accretions had formed so freely upon their interiors as to 
 seriously diminish the volume of flow through the pipes of 
 three, four, and six-inch diameters. 
 
 This difficulty, which was so serious as to necessitate the 
 laying of larger distribution pipes than would otherwise 
 have been necessary, engaged the attention of British and 
 continental engineers and chemists from time to time. Many 
 experimental coatings were applied, of silicates and oxides, 
 and the pipes were subjected to baths of hot oil under 
 pressure, with the hope of fully remedying the difficulty. 
 A committee of the British Association also inquired into 
 the matter in connection with the subject of the preservation 
 of iron ships, and instituted valuable experiments, which 
 are described in two reports of Robert Mallet to the Asso- 
 ciation. 
 
 A similar difficulty was experienced with the uncoated 
 iron pipes first laid in Philadelphia and New York. 
 
 In the report of the city engineer of Boston, January, 
 L852, mention is made of some pipes taken up at the South 
 Boston drawbridge, which had been exposed to the flow 
 of Cochituate water nine years. 
 
 He remarks that " some of the pipes were covered inter- 
 nally with tubercles which measured about two inches in 
 area on their surfaces, by about three-quarters of an inch 
 in height, while others had scarcely a lump raised in them. 
 
474 MAINS AND DISTHIBUTION-PIPES. 
 
 Those which were covered with the tubercles were corroded 
 to a depth of about one- sixteenth of an inch ; the iron to 
 that depth cutting with the knife very much like plumbago." 
 Mr. Slade, the engineer, expressed the opinion, after com- 
 paring the condition of these pipes with that of pipes exam- 
 ined in 1852, that the corrosion is very energetic at first, 
 but that it gradually decreases in energy year by year. 
 
 The process used by Mons. Le Beuffe, civil engineer of 
 Vesoul, France, for the defence of pipes, as communicated* 
 by him to Mr. Kirk wood, chief engineer of the Brooklyn 
 Water- works, " consists of a mixture of linseed oil and 
 beeswax, applied at a high temperature, the pipe being 
 heated and dipped into the hot mixture. 
 
 The varnish of M. Crouziere, tested on iron immersed in 
 sea-water at Toulon, by the French navy, consisted of a 
 mixture of sulphur, rosin, tar, gutta-percha, minum, blanch 
 de ceruse, and turpentine. This protected a plate of 
 wrought iron perfectly during the year it was immersed. 
 
 A process that has proved very successful for the preser- 
 vation of iron pipes used to convey acidulated waters from 
 German mines, is as follows :f "The pipes to be coated 
 are first exposed for three hours in a bath of diluted sul- 
 phuric or hydrochloric acid, and afterward brushed with 
 water ; they then receive an under-coating composed of 
 34 parts of silica, 15 of borax, and 2 of soda, and are ex- 
 posed for ten minutes in a retort to a dull red heat. After 
 that the upper coating, consisting of a mixture of 34 parts 
 of feldspar, 19 of silica, 24 of borax, 16 of oxide of tin, 4 of 
 fluorspar, 9 of soda, and 3 of saltpetre, is laid over the inte- 
 rior surface, and the pipes are exposed to a white heat for 
 twenty minutes in a retort, when the enamel perfectly unites 
 
 * Vide Descriptive Memoir of the Brooklyn Water- works, p. 43.' N. Y., 1867. 
 f Vide "Engineering." London, Jan., 1872, p. 45. 
 
**'>**<' 
 
 '*/,, *" ' 
 
 PRESERVATION OF PIPE SURFACES. w/ / y V ; 475 
 
 with the cast-iron. Before the pipes are quite cooled down, 
 their outside is painted with coal-tar. The above ingre- 
 dients of the upper coating are melted to a mass in a cru- 
 cible, and afterwards with little water ground to a fine 
 paste." 
 
 Prof. Barff, M.A., proposes to preserve iron (including 
 iron water-pipes) by converting its surfaces into the mag- 
 netic or black oxide of iron, which undergoes no change 
 whatever in the presence of moisture and atmospheric 
 oxygen. 
 
 He says, "The method which long experience has taught 
 us is the best for carrying out this process for the protection 
 of iron articles, of common use, is to raise the temperature 
 of those articles, in a suitable chamber, say to 500 F., and 
 then pass steam from a suitable generator into this cham- 
 ber, keeping these articles for five,- six, or seven hours, as 
 the case may be, at that temperature in an atmosphere of 
 superheated steam. 
 
 " At a temperature of 1200 F., and under an exposure 
 to superheated steam for six or seven hours, the iron surface 
 becomes so changed that it will stand the action of water 
 for any length of time, even if that water be impregnated 
 with the acid fumes of the laboratory." 
 
 The first coated pipes used in the United States, were 
 imported from a Glasgow foundry in 1858. These were 
 coated by Dr. Angus Smith's patent process, which had 
 been introduced in England about eight years earlier. 
 Dr. Smith's Coal Pitch Varnish is distilled from coal-tar 
 until the naphtha is entirely removed and the material 
 deodorized, and Dr. Smith recommends the addition of five 
 or six per cent, of linseed oil. 
 
 The pitch is carefully heated in a tank that is suitable 
 to receive the pipes to be coated, to a temperature of about 
 
476 MAINS AND DISTRIBUTION-PIPES. 
 
 300 degrees, when the pipes are immersed in it and allowed 
 to remain until they attain a temperature of 300 Fah. 
 
 A more satisfactory treatment is to heat the pipes in a 
 retort or oven to a temperature of about 310 Fah., and 
 then immerse them in the bath of pitch, whicli is maintained 
 at a temperature of not less than 210. 
 
 When linseed oil is mixed with the pitch, it has a ten- 
 dency at high temperature to separate and float upon the 
 pitch. An oil derived by distillation from coal-tar is more 
 frequently substituted for the linseed oil, in practice. 
 
 The pipes should be free from rust and strictly clean 
 when they are immersed in the pitch-bath. 
 
 467. Varnishes for Pipes and Iron-work. A good 
 tar varnish, for covering the exteriors of pipes where they 
 are exposed, as in pump and gate houses, and for exposed 
 iron work generally, is mentioned* by Ewing Matheson, 
 and is composed as follows : 30 gallons of coal-tar fresh, 
 with all its naphtha retained ; 6 Ibs. tallow ; 1 J Ibs. resin ; 
 3 Ibs. lampblack ; 30 Ibs. fresh slacked lime, finely sifted. 
 These ingredients are to be intimately mixed and applied 
 hot. This varnish may be covered with the ordinary lin- 
 seed-oil paints as occasion requires. 
 
 A Hack varnish, that has been recommended for out- 
 door iron work, is composed as follows : 20 Ibs. tar-oil ; 
 5 Ibs. asphaltum ; 5 Ibs. powdered rosin. These are to be 
 mixed hot in an iron kettle, with care to prevent ignition. 
 The varnish may be applied cold. 
 
 468. Hydraulic Proof of Pipes. When the cast- 
 iron pipes have received their preservative coating, they 
 should be placed in an hydraulic proving-press, and tested 
 by water pressure, to 300 Ibs. per sq. in. ; and while under 
 
 " Works in Iron," p. 281. London, 1873. 
 
HYDKAULIC PROOF OF PIPES. 
 
 477 
 
 the pressure be smartly rung with, a hammer, to test them 
 for minor defects in casting, and for undue internal strains. 
 Fig. 100 is one of the most simple forms of hydraulic 
 proving-presses. The cast-iron head upon the left is fixed 
 stationary, while toward the right is a strong head that is 
 movable, and that advances and retreats by the action of 
 
 FIG. 100. 
 
 the screw working in the nut of the fixed head at the right. 
 When the pipe is rolled into position for a test, suitable 
 gaskets are placed upon its ends, or against the two heads, 
 and then by a few turns of the hand- wheel of the screw, the 
 movable head is set up so as to press the pipe between the 
 two heads. Levers are then applied to the screw, and the 
 pressure increased till there will be no leakage of water at 
 the ends past the gaskets. The air-cock at the right is then 
 opened to permit escape of the air, and the water- valve at 
 the left opened to fill the pipe with water. The hydraulic 
 pump and the water-pressure gauge, which are attached at 
 the left, are not shown in the engraving. When the pipe is 
 filled with water, and the valves closed, the requisite pres- 
 sure is then applied by means of the pump. Care must be 
 taken that all the air is expelled, before pressure is applied, 
 lest in case of a split, the compressed air may scatter the 
 pieces of iron with disastrous results. 
 
FIG. 101. 
 
 W////////////////K ' '////MW/W//// 
 
 SINGLE BRANCH. 
 
 FIG. 102. 
 
 FIG. 103. 
 
CEMENT-LINED AND COATED PIPES. 
 
 479 
 
 469. Special Pipes. Fig. 101 is a section through a 
 single Branch, with side views of lugs for securing a cap or 
 hydrant branch. 
 
 Fig. 102 is a section through a Reducer. 
 
 Fig. 103 is a section through a Bend. 
 
 FIG. 104. 
 
 FIG. 105. 
 
 Fig. 104 is a section through a Sleeve, the upper half 
 being the form for covering cut ends of pipes, and the lower 
 half the form for uncut spigot ends. 
 
 Fig. 105 is a part section and plan of a clamp Sleeve. 
 
 WROUGHT-IRON PIPES 
 
 47O. Cement-Lined and Coated Pipes. Sheet-iron 
 water-pipes, lined and coated with hydraulic cement mor- 
 tar, by a process invented by Jonathan Ball, were laid in 
 Saratoga, N. Y., to conduct a supply of water for domestic 
 purposes to some of the citizens, as early as 1845. 
 
 The inventor, who was aware of the ready corrosion of 
 wrought-iron when exposed to a flow of water and to the 
 dampness and acids of the earth, had observed the pre- 
 servative influence of lime and cement when applied to iron, 
 and saw that with its aid, the high tensile strength of 
 
480 MAINS AND DISTRIBUTION-PIPES. 
 
 wrought or rolled iron, could be utilized in water-pipes to 
 sustain considerable pressures of water, and the weight of 
 the iron required, thus be materially reduced. 
 
 The reduction in the weight of the iron reduced also the 
 total cost of the complete pipe in the trench. 
 
 The favorable qualities of hydraulic cement as a conduc- 
 tor of potable waters had long been well-known, for the 
 Romans invariably lined their aqueducts and conduits 
 with it. 
 
 Twenty-five or thirty towns and villages, and a number 
 of corporate water companies had already adopted the 
 wrought-iron cement-lined water pipes in their systems, and 
 still others were experimenting with it at the breaking out 
 of the civil war in 1861. 
 
 As one result of the war, the price of iron* rose to more 
 than double its former value, and the difference in cost be- 
 tween cast and wrought iron pipes became conspicuous, and 
 the cost of all pipes rose to so great total sums that the pipe 
 of least first cost must of necessity be adopted in most 
 instances, almost regardless of comparative merits. So 
 long as the high prices of iron and of labor remained firm, 
 the contractors for the wrought-iron were enabled to lay it 
 at a reduction of forty per cent, from the cost of the cast- 
 iron pipe. 
 
 Increased attention to sanitary improvements led many 
 towns to complete their water supplies even at the high 
 rates, and many hundred miles of the cement-lined pipes 
 came into use. 
 
 471. Methods of Lining. Its manufacture is simple. 
 The sheet-iron is formed and closely riveted into cylinders 
 
 * New York and Philadelphia prices current record the nearly regular 
 average monthly increase in the price of Anthracite Pig Iron No. 1, from 18f 
 dollars per ton of 2240 pounds in August, 1861, to 73f dollars per ton in 
 August, 1864. 
 
COVERING. 481 
 
 of seven or eight feet in length, and of diameter from one 
 to one and one-half inches greater than the clear bore of the 
 lining is to be finished. The pipe is then set upright and a 
 short cylinder, of diameter equal to the desired bore of the 
 pipe, is lowered to the bottom of the pipe. Some freshly 
 mixed hydraulic cement mortar is then thrown into the pipe 
 and the cylinder, which has a cone-shaped front ; and guid- 
 ing spurs to maintain its central position in the shell, is 
 drawn up through the mortar. A uniform lining of the 
 mortar is thus compressed within the wrought-iron shell. 
 The ends are then dressed up with mortar by the aid of a 
 small trowel or spatula, and the pipes carefully placed upon 
 skids to remain until the cement is set. 
 
 The interiors of the pipe-linings are treated to a wash of 
 liquid cement while they are still fresh, so as to fill their pores. 
 
 In another process of lining, a smoothly-turned cylin- 
 drical mandril of iron, equal in length to the full length of 
 the pipe, and in diameter to the diameter of the finished 
 bore, is used to form the bore, and to compress the lining 
 within the shell. A fortnight or three weeks is required for 
 the cement to set so as safely to bear transportation or haul- 
 age to the trenches. In the meantime the iron is or should 
 be protected from storms and moisture, and also from the 
 direct rays of the sun, which unduly expands the iron, and 
 separates it from a portion of the cement lining. 
 
 472. Covering. When these pipes are laid in the 
 trench, a bed of cement mortar is prepared to receive them, 
 and they are entirely coated with about one inch thickness 
 of cement mortar, as is shown in the vertical section of a 
 six-inch pipe, Fig. 106. 
 
 The writer has used upwards of one hundred miles of 
 this kind of pipes, and the smaller sizes have proved uni- 
 formly successful. 
 31 
 
482 
 
 MAINS AND DISTRIBUTION-PIPES. 
 FIG. 106. 
 
 The iron is relied upon wholly to sustain the pressure 
 of the water and resist the effects of water-rams. The 
 cement is depended upon to preserve the iron, which object 
 it has accomplished during the term these pipes have been 
 in use, when the cement was good and workmanship faith- 
 ful, which, unfortunately for this class of pipe, has not 
 always been the case, and the reputation of the pipe has 
 suffered in consequence. 
 
 FIG. 107. 
 
 473. Cement- Joint. A sheet -iron sleeve, about eight 
 inches long, as shown in Fig. 107, is used in the common 
 form of joint to cover the abutting ends of the pipe as they 
 are laid in the trench. 
 
 The diameter of the sleeve is about one inch greater than 
 the diameter of the wrought-iron pipe shell, and the annular 
 space between the pipe and sleeve is filled with cement. The 
 sleeve and pipe are then covered with cement mortar. 
 
 In a more recently patented form of pipe, the shell has a 
 taper of about one inch in a seven-foot piece of pipe, and 
 
CAST HUB-JOINTS. 
 
 483 
 
 the small end of one piece of pipe enters about four inches 
 into the large end of the adjoining pipe, thus forming a 
 lap without a special sleeve. The thickness of lining in 
 these pipes varies, but the bore is made uniform. 
 
 474. Cast Hub- Joints. The writer having experienced 
 some difficulty with both the above forms of cement-joints, of 
 the larger diameters, and desiring to substitute lead pack- 
 ings for the cement, in a 20-inch force main, to be subjected 
 to great strains, devised the form of joint shown in Fig. 108. 
 
 FIG. 108. 
 
 In this case the wrought-iron shells were riveted up as 
 for the common 20-inch pipe, and then the pipe was set 
 upon end in a foundry near at hand, a form of bell moulded 
 about one end, and molten iron poured in, completing the 
 "bell in the usual form of cast-iron bell. A spigot is cast 
 upon the opposite end in a similar manner. The lead pack- 
 ig is then poured and driven up with a set, as the pipes 
 laid, as is usual with cast-iron pipes. The joint is as 
 Lccessfui in every respect as are the lead-joints of casiriron 
 ipes. 
 
 The force-main in question has been in use upwards of 
 years, and water was, during several months of its 
 
484 
 
 MAINS AND DISTRIBUTION-PIPES. 
 
 earliest use, pumped through it into the distribution pipes, 
 on the direct pumping system. 
 
 For lead joints on wrought-iron pipes from ten to sixteen 
 inches diameter inclusive, about four inches width of the 
 edge of the spigot end sheet may be rolled thicker, so as to 
 bear the strain of caulking the lead, as a substitute for the 
 cast spigot. 
 
 475. Composite Branches. The wrought - iron 
 branches were originally joined to their mains by the appli- 
 cation of solder, the iron being first tinned near and at the 
 junction. After the successful pouring of the bells, the 
 experiment was tried of uniting the parts by pouring molten 
 metal into a mould, formed about them, the metal being 
 
 FIG. 109. 
 
 cast partly outside and partly inside the pipes, as in the 
 case of the hub-joint. The parts were rigidly and very sub- 
 stantially united by the process, which is in practical effecl 
 equal to a weld. 
 
 Fig. 109 shows a section of a double six-inch branch o] 
 a twelve-inch sub-main. 
 
THICKNESS OF SHELLS FOR CEMENT LININGS. 
 
 485 
 
 Fig. 110 is a section of a wrouglit-iron angle with its 
 parts united by a cast union. 
 
 Several holes, similar to the rivet holes of the pipe, are 
 punched near the ends to be united at different points in 
 the circumference, so that the metal flows through them, 
 as shown in the sketches. 
 
 FIG. 110. 
 
 The writer has used these branches and angles exclu- 
 sively in several cities, in wrought-iron portions of the 
 distribution-pipes, without a single failure. 
 
 476. Thickness of Shells for Cement Linings. 
 
 When computing the thickness of sheets for the shells of 
 wrought-iron cement-lined pipes, the internal diameter of 
 the shell itself, and not of finished bore, is to be taken. 
 The longitudinal joints of the shells for pipes of 12-inch and 
 
 iter diameters, should be closely double riveted. 
 
 The tensile strength of the shells, when made of the best 
 Lates, may be assumed, if single riveted, 36,000 pounds 
 per square inch, and double riveted 40,000 pounds per 
 square inch. 
 
 A formula of thickness, given above, with factor of 
 safety = 4, in addition to allowance for water-ram, may be 
 used to compute the thickness of plates, viz.: 
 
 (19) 
 
486 
 
 MAINS AND DISTRIBUTION-PIPES. 
 
 in which t is the thickness of rolled plate, in inches. 
 d " diameter of the shell, in inches. 
 p " static pressure due to the head in Ibs. per 
 
 sq. in. = .434 7i. 
 S " tenacity of riveted shells, in Ibs. per. sq. in. 
 
 The following table gives the thickness of shells for 
 cement linings, and the nearest No. of Birmingham gauge 
 in excess, suitable for heads of from 100 to 300 feet, by 
 formula, 
 
 *-(p- 
 
 TABLE No. 99. 
 
 THICKNESS OF WROUGHT IRON PIPE SHELLS. 
 
 (Diameters 4" to 10" single riveted, S = s6,ooolbs. Diameters 12" and upward, double riveted, 
 
 S = 40,000 Ibs.) 
 
 
 
 HEAD 116 FEET. 
 
 HEAD 175 FEET. 
 
 HEAD 300 FEET. 
 
 DIAMETER 
 OF BORE. 
 
 DIAMETER 
 OF SHELL. 
 
 Thickness 
 by 
 Formula. 
 
 Nearest 
 No. Birm. 
 Gauge in 
 Excess. 
 
 Thickness 
 by 
 Formula. 
 
 Nearest 
 No. Birm. 
 Gauge in 
 Excess. 
 
 Thickness 
 by 
 Formula. 
 
 Nearest 
 No. Birm. 
 Gauge in 
 Excess. 
 
 Inches. 
 
 Inches. 
 
 Inches. 
 
 
 Inches. 
 
 
 Inches. 
 
 
 4 
 
 5 
 
 .0417 
 
 *9 
 
 .0486 
 
 18 
 
 .0639 
 
 16 
 
 6 
 
 7 
 
 .0528 
 
 17 
 
 .0681 
 
 15 
 
 .0894 
 
 13 
 
 8 
 
 9-25 
 
 .0771 
 
 15 
 
 .0899 
 
 13 
 
 .1182 
 
 ii 
 
 10 
 
 11.25 
 
 0937 
 
 13 
 
 .1094 
 
 12 
 
 1437 
 
 9 
 
 12 
 
 T 3-25 
 
 .0994 
 
 12 
 
 IT 59 
 
 II 
 
 .1524 
 
 8 
 
 14 
 
 15-25 
 
 .1144 
 
 12 
 
 1334 
 
 10 
 
 -1754 
 
 7 
 
 16 
 
 17-5 
 
 1313 
 
 10 
 
 1532 
 
 8 
 
 .2OI2 
 
 6 
 
 18 
 
 ip-5 
 
 .1463 
 
 9 
 
 .1706 
 
 7 
 
 .2242 
 
 5 
 
 20 
 
 21.5 
 
 .1613 
 
 8 
 
 .1881 
 
 6 
 
 .2472 
 
 3 
 
 22 
 
 23-5 
 
 .I76 3 
 
 7 
 
 .2056 
 
 5 
 
 .2702 
 
 2 
 
 24 
 
 2 5-5 
 
 .1913 
 
 6 
 
 .2236 
 
 4 
 
 .2932 
 
 I 
 
 Shells having less factors of safety than our formula 
 gives, have been used in many small works. A factor 
 equal to 6, to include effect of water-ram, should always 
 
LINING COVERING, AND JOINT MORTAR. 487 
 
 taken, and this may be found directly by a formula in the 
 following form : 
 
 477. Gauge Thickness and Weights of Rolled 
 Iron. The following table (No. 100) gives the thicknesses 
 and weights of sheet-iron, corresponding to Birmingham 
 gauge numbers ; also thicknesses and weights increasing 
 by sixteenths of an inch. 
 
 478. Lining, Covering, and Joint Mortar. The 
 lining mortar and covering mortar should have the volume 
 of cement somewhat in excess of the volume of voids in the 
 sand, or, for linings, equal parts of the best hydraulic 
 cement and fine-grained, sharp, silicious sand; and, for 
 coverings, two-fifths like cement and three-fifths like sand. 
 
 The joint mortar should be of clear cement, or may be 
 of four parts of good Portland cement, and one part of 
 hydraulic lime, with just enough water to reduce it to a 
 stiff paste. 
 
 This kind of pipe demands very good materials for all 
 its parts, and the most thorough and faithful workmanship. 
 
 A concrete foundation should be laid for it in quicksand, 
 or on a soft bottom, and a bed of gravel, well rammed, 
 should be laid for it in rock trench, and exceeding care 
 must be taken in replacing the trench back-fillings. Poor 
 materials or slighted workmanship will surely lead to after 
 annoyance. 
 
 Some of the cement-lined pipes are given a bath in hot 
 asphaltum before their linings are applied. In such case, a 
 sprinkling of clean, sharp sand over their surfaces imme- 
 diately after the bath, while the coating is tacky, assists in 
 forming bond between the cement and asphaltum. 
 
488 
 
 MAINS AND DISTRIBUTION-PIPES. 
 
 TABLE No. 1OO. 
 THICKNESSES AND WEIGHTS OF PLATE-IRON. 
 
 Birming- 
 ham 
 gauge 
 No. 
 
 Thickness. 
 
 Weight of a 
 square foot. 
 
 Thickness, 
 in 
 sixteenths 
 of an inch. 
 
 Thickness, 
 
 in decimals of 
 an inch. 
 
 Weight of 
 a square foot 
 
 
 Inches. 
 
 Pounds. 
 
 Inches. 
 
 Inches. 
 
 Pounds. 
 
 OOOO 
 
 -454 
 
 18.35 
 
 A 
 
 .03125 
 
 1.263 
 
 000 
 
 425 
 
 I7.I8 
 
 yV 
 
 .06250 
 
 2.526 
 
 00 
 
 .38 
 
 15.36 
 
 A 
 
 09375 
 
 3.789 
 
 
 
 34 
 
 x 3-74 
 
 k 
 
 .12500 
 
 5.052 
 
 I 
 
 3 
 
 12.13 
 
 A 
 
 .15625 
 
 6.315 
 
 2 
 
 .284 
 
 11.48 
 
 A 
 
 .18750 
 
 7.578 
 
 3 
 
 259 
 
 10.47 
 
 A 
 
 .21875 
 
 8.841 
 
 4 
 
 238 
 
 9.619 
 
 \ 
 
 .25OOO 
 
 IO.IO 
 
 5 
 
 .22 
 
 8.892 
 
 A 
 
 .28125 
 
 H-37 
 
 6 
 
 .203 
 
 8.205 
 
 ~TZ 
 
 ^SO 
 
 12.63 
 
 7 
 
 .18 
 
 7.275 
 
 ii 
 
 34375 
 
 13.89 
 
 8 
 
 I6 5 
 
 6.669 
 
 i 
 
 .37500 
 
 15.16 
 
 9 
 
 .148 
 
 5.981 
 
 H 
 
 .40625 
 
 16.42 
 
 10 
 
 .134 
 
 5.416 
 
 lV 
 
 43750 
 
 17.68 
 
 ii 
 
 .12 
 
 4.850 
 
 T 
 
 46875 
 
 18.95 
 
 12 
 13 
 
 .109 
 
 -95 
 
 4-405 
 3.840 
 
 A 
 
 .50000 
 56250 
 
 20.21 
 22.73 
 
 14 
 
 .083 
 
 3-355 
 
 1 
 
 .62500 
 
 25.26 
 
 15 
 
 .072 
 
 2.910 
 
 tt 
 
 .68750 
 
 27-79 
 
 16 
 
 .065 
 
 2.627 
 
 i 
 
 .75000 
 
 30.31 
 
 17 
 
 .058 
 
 2.344 
 
 Jt 
 
 .81250 
 
 32.84 
 
 18 
 
 .049 
 
 .980 
 
 7 
 "g" 
 
 .87500 
 
 35-37 
 
 19 
 
 .042 
 
 .697 
 
 tt 
 
 .93750 
 
 37.89 
 
 20 
 
 35 
 
 415 
 
 I 
 
 i 
 
 40.42 
 
 21 
 
 .032 
 
 293 
 
 T rV 
 
 1.06250 
 
 42.94 
 
 22 
 
 .028 
 
 .132 
 
 4 
 
 1.12500 
 
 4547 
 
 23 
 
 025 
 
 I.OIO 
 
 
 1.18750 
 
 48.00 
 
 24 
 
 .022 
 
 .8892 
 
 if 
 
 1.25000 
 
 50-5 2 
 
 25 
 
 .02 
 
 .8083 
 
 
 1.31250 
 
 53.05 
 
 26 
 
 .018 
 
 7225 
 
 if 
 
 L37500 
 
 55-57 
 
 27 
 
 .016 
 
 .6467 
 
 
 1.43750 
 
 58.10 
 
 28 
 
 .OI4 
 
 5658 
 
 ij 
 
 1.50000 
 
 60.63 
 
 29 
 
 .013 
 
 5254 
 
 T T% 
 
 1.56250 
 
 63-15 
 
 30 
 
 .012 
 
 .4850 
 
 14 
 
 1.62500 
 
 65.68 
 
 31 
 
 .010 
 
 .4042 
 
 I T6' 
 
 1.68750 
 
 68.20 
 
 32 
 
 .009 
 
 .3638 
 
 I t 
 
 1.75000 
 
 70.73 
 
 33 
 
 .008 
 
 3233 
 
 I T 
 
 1.81250 
 
 73.26 
 
 34 
 
 .007 
 
 .2829 
 
 4 
 
 1.87500 
 
 75.78 
 
 35 
 
 .005 
 
 .2021 
 
 'If 
 
 1-9375 
 
 78.31 
 
 36 
 
 .004 
 
 .1617 
 
 2 
 
 2 
 
 80.83 
 
ASPHALTUM-BATH FOR PIPES. 
 
 489 
 
 479. Asphaltum-coateil Wrought-iron Pipes. 
 
 Wrought-iron pipes, coated with asphaltum, have been 
 used almost exclusively in California, Nevada, and Oregon, 
 some of those of the San Francisco water supply being 
 thirty inches in diameter. 
 
 Some of these wrought-iron pipes, in siphons, are sub- 
 jected to great pressure, as, for instance, in the Virginia 
 City, Nevada, supply main, leading water from Marlette 
 Lake. 
 
 This main is 11| inches diameter, and 37,100 feet in 
 length, and crosses a deep valley between the lake, upon 
 one mountain and Virginia City upon another. The inlet, 
 where the pipe receives the water of the lake, is 2,098 feet 
 above the lowest depression of the pipe in the valley, where 
 it passes under the Virginia and Truckee Railroad, and the 
 delivery end is 1528 feet above the same depression. A 
 portion of the pipe is subjected to a steady static strain of 
 750 pounds per square inch. 
 
 The thickness of this pipe-shell varies, according to the 
 pressure upon it, as follows : 
 
 Head in feet < 
 
 200 
 or 
 
 200 
 
 to 
 
 33 
 
 to 
 
 430 
 to 
 
 570 
 
 to 
 
 7 00 
 
 to 
 
 95 
 to 
 
 1050 
 to 
 
 1250 
 
 to 
 
 1400 
 and 
 
 
 less. 
 
 33> 
 
 43 
 
 57 
 
 700 
 
 950 
 
 1050 
 
 1250 
 
 1400 
 
 over. 
 
 No. of iron, Birmingham gauge . . . 
 
 16 
 
 15 
 
 14 
 
 12 
 
 II 
 
 9 
 
 7 
 
 5 
 
 3 
 
 
 
 Thickness in inches 
 
 .06 5 
 
 
 087 
 
 .IOQ 
 
 .12 
 
 .148 
 
 .18 
 
 .22 
 
 250 
 
 
 
 
 
 
 
 
 
 
 
 
 
 The joints are covered with a sleeve, and the joint pack- 
 ing is of lead. 
 
 48O. Asphaltum -Bath for Pipes. A description of 
 the asphaltum coating, as prepared for these pipes by 
 Herman Schussler, C.E., under whose direction many pipes 
 have been laid, is given in the January, 1874, Report of 
 J. Nelson Tubbs, Esq., Chief Engineer of the Rochester 
 Water- works, as follows, in Mr. Schussler' s language : 
 
490 MAINS AND DISTRIBUTION-PIPES. 
 
 "The purest quality of asphaltum (we use the Santa 
 Barbara) is selected and broken into pieces of from the size 
 of a hen' s egg to that of a fist. With this, three or four 
 round kettles are filled full, then the interstices are filled 
 with the best quality of coal tar (free from oily substances), 
 and boiled from three to four hours, until the entire kettle 
 charge is one semi-fluid mass, it being frequently stirred up. 
 The best and most practical test then, as to the suitability 
 of the mixture, is to take a piece of sheet-iron of the thick- 
 ness the pipe is made of, say six inches square, it being 
 cold and freed from impurities, and dip it into the boiling 
 mass, and keep it there from five to seven minutes. Imme- 
 diately after taking it out, plunge it into cold water, if 
 possible near the freezing-point, and if, after removal from 
 the water, the coating don't become brittle, so as to jump 
 off the iron in chips, by knocking it with a hammer, but 
 firmly adheres (like the tin coating to galvanized iron), the 
 coat is good and will last for ages. If, on the other hand, 
 it is brittle, it shows that there is either too much oil in the 
 tar or asphaltum, or the mixture was boiled too hot, or 
 there was too much coal-tar in the mixture ; as adding coal- 
 tar makes the mixture brittle, while by adding asphaltum 
 it becomes tough and pliable. The pipes are immersed in 
 the bath as thus prepared." 
 
 Wrought-iron pipes of this description are extensively 
 used in France, in diameters up to 48 inches. 
 
 They are first subjected to a bath of hot asphaltum, and 
 then the exteriors are coated with an asphaltum concrete, 
 into which some sand is introduced, as into the cement- 
 covering above described. 
 
 481. Wrought Pipe Plates. The shells of wrought- 
 iron conduits and pipes should be of the best rolled plates, 
 of tough and ductile quality, of ultimate strength not less 
 
WYCKOFFS PATENT PIPE. 491 
 
 than 55,000 Ibs. per square inch, and that will elongate 
 fifteen per cent, and reduce in sectional area twenty -five per 
 cent, before fracture. 
 
 WOOD PIPES. 
 
 482. Bored Pipes. The wooden pipes used to replace 
 the leaden pipes, in London, that were destroyed by the 
 great fire, three-quarters of a century ago, reached a total 
 length exceeding four hundred miles. These pipes were 
 bored with a peculiar core-auger, that cut them out in 
 nests, so that small pipes were made from cores of larger 
 pipes. 
 
 The earliest water-mains laid in America were chiefly of 
 bored logs, and recent excavations in the older towns and 
 cities have often uncovered the old cedar, pitch-pine, or 
 chestnut pipe-logs that had many years before been laid by 
 a single, or a few associated citizens, for a neighborhood 
 supply of water. 
 
 Bored pine logs, with conical faucet and spigot ends, 
 and with faucet ends strengthened by wrought-iron bands, 
 were laid in Philadelphia as early as 1797. 
 
 Detroit had at one time one hundred and thirty miles of 
 small wood water-pipes in her streets. 
 
 483. Wyckoff's Patent Pipe. A patent wood pipe, 
 manufactured at Bay City, Michigan, has recently been 
 laid in several western towns and cities, and has developed 
 an unusual strength for wood pipes. Its chief peculiarities 
 are, a spiral banding of hoop-iron, to increase its resistance 
 to pressure and water-ram ; a coating of asphaltum, to 
 preserve the exterior of the shell ; and a special form of 
 thimble-joint. 
 
 Fig. Ill is a longitudinal section through a joint of this 
 wood pipe, showing the manner of inserting the thimble, 
 
492 MAINS AND DISTRIBUTION-PIPES. 
 
 FIG. 111. 
 
 and Fig. 112 is .an exterior view of the pipe, showing the 
 spiral banding of hoop-iron, and the asphaltum covering. 
 
 The manufacturer's circular, from which the illustra- 
 tions are copied, states that the pipes made under this 
 
 FIG. 112. 
 
 patent are from white pine logs, in sections eight feet long. 
 The size of the pipes is limited only by the size of the suit- 
 able logs procurable for their manufacture. 
 
 Judged by schedules of factory prices, these pipes do 
 not appear to be cheaper in first cost than wrought-iron 
 pipes. 
 
FIGS. 114, 115. 
 
 FLOWERS STOP-VALVE. (.blowers Brothers, Detroit.) 
 
 FIGS. 116, 117. 
 
 COFFIN'S STOP- VALVE. (Boston Machine Co., Boston.) 
 
CHAPTEE XXII. 
 
 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 484. Loss of Head by Friction. In the chapter 
 upon flow of water in pipes (XIII, ante), we have discussed 
 at length the question of the maximum discharging ca- 
 pacities of pipes. When planning a system of distribution 
 pipes for a domestic and fire service, it is quite as import- 
 ant to know how much of the available head will be con- 
 sumed by, or will remain after, the passage of a given 
 quantity of water through a given pipe. 
 
 For a really valuable fire service, the effective head 
 pressure remaining upon the pipes, with full draught, 
 should be, in commercial and manufacturing sections of a 
 town, not less than one hundred and fifty feet, and in 
 suburban sections, not less than one hundred feet. 
 
 Water at such elevations, near a town, has a large com- 
 mercial value, whether it has been lifted by the operations 
 of nature and retained by ingenuity of man, or has been 
 pumped up through costly engines and with great expend- 
 iture of fuel. 
 
 When such head pressures are secured at the expense 
 of pumps and fuel, they are too costly to be squandered in 
 friction in the pipes. Such frictional loss entails a corre- 
 sponding daily expense of fuel so long as the works exist. 
 In such case, the pipes may be economically increased in 
 size until the daily frictional expense capitalized, approxi- 
 mates to the additional capital required to increase the 
 given pipes to the next larger diameters. 
 
494 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 The frictional head h" in pipes under pressure, is found 
 by the formula, 
 
 . (1) 
 
 The frictional head for a given diameter is as the square 
 of the velocity, nearly (v 2 m) and, for different diameters, 
 inversely as the diameters. 
 
 The coefficient* m decreases in value as the velocity 
 increases, and for a given velocity decreases as the diameter 
 increases. 
 
 485. Table of Frictional Heads in Pipes. The 
 following table (No. 101, p. 493) we have prepared to facili- 
 tate frictional head calculations, and to show at a glance the 
 frictional effect of increase of velocity, in given pipes from 
 4 to 36 inch diameters. The second and last columns show 
 also the theoretical volume of delivery through clean, smooth 
 pipes at different given velocities. 
 
 The fourth column gives approximate values of the 
 coefficient m for given diameters and velocities, and for 
 clean smooth pipes under pressure. 
 
 * Vide Table No. 62, page 248, of coefficients (m) for clean, slightly tuber- 
 culated, and foul pipes ; also 274, page 250, for formula of frictional resist- 
 ance to flow. 
 
. ^RICTIONAL HEADS IN PIPES. 
 
 495 
 
 TABL E No. 1 Ol. 
 
 FRICTIONAL HEAD IN MAIN AND DISTRIBUTION PIPES (in each 
 1000 feet length). ti' = V 1 * (qm) -, 
 
 Diam. 
 of 
 pipe. 
 
 Volume of 
 water 
 delivered 
 
 Velocity 
 of 
 flow. 
 
 Coefficient 
 of 
 friction. 
 
 Frictional head 
 per 1000 feet. 
 
 U. S. gallons 
 in 24 hours. 
 
 Inches. 
 
 Cu.ft.per 
 inin. 
 
 Feet per 
 second. 
 
 
 Feet. 
 
 Gallons. 
 
 4 
 
 5 
 
 958 
 
 .00714 
 
 1.221 
 
 53,856 
 
 
 7-5 
 
 1-437 
 
 .00695 
 
 2.675 
 
 80,784 
 
 
 10 
 
 1.916 
 
 .00680 
 
 4.653 
 
 I07JI2 
 
 
 12.5 
 
 2.394 
 
 .00666 
 
 7.114 
 
 134,640 
 
 
 15 
 
 2.873 
 
 .00654 
 
 10.06 
 
 161,568 
 
 
 17-5 
 
 3-295 
 
 .00644 
 
 13.03 
 
 188,496 
 
 
 20 
 
 3-831 
 
 .00633 
 
 17.32 
 
 215,424 
 
 6 
 
 17-5 
 
 1.409 
 
 .00666 
 
 1.643 
 
 188,496 
 
 
 20 
 
 1.701 
 
 .00655 
 
 2.355 
 
 215,424 
 
 22.5 
 
 I.9I3 
 
 .00648 
 
 2.946 
 
 242,352 
 
 
 25 
 
 2.126 
 
 .00646 
 
 3.628 
 
 269,280 
 
 
 27-5 
 
 2-339 
 
 .00638 
 
 4.337 
 
 296,208 
 
 
 30 
 
 2-551 
 
 .00634 
 
 5.126 
 
 323.136 
 
 
 35 
 
 2.976 
 
 .00623 
 
 6.855 
 
 376,992 
 
 
 40 
 
 3.401 
 
 .00615 
 
 8.838 
 
 430,848 
 
 
 45 
 
 3.827 
 
 .00610 
 
 11.100 
 
 484,704 
 
 ,. 
 
 
 
 
 
 8 30 
 
 1.429 
 
 .00644 
 
 1.225 
 
 323,136 
 
 35 
 
 1.685 
 
 .00635 
 
 1.680 
 
 376,992 
 
 40 
 
 1.905 
 
 .00628 
 
 2.124 
 
 430,848 
 
 
 45 
 
 2.143 
 
 .00620 
 
 2.654 
 
 484,704 
 
 
 50 
 
 2.381 
 
 .00615 
 
 3.249 
 
 538,560 
 
 
 55 
 
 2.619 
 
 .00609 
 
 3.893 
 
 592,416 
 
 
 60 
 
 2.857 
 
 .00603 
 
 4.587 
 
 646,272 
 
 
 65 
 
 3-095 
 
 .00600 
 
 5.356 
 
 700,128 
 
 
 70 
 
 3-331 
 
 .00596 
 
 6.159 
 
 753,984 
 
 
 75 
 
 3-571 
 
 .00592 
 
 7.035 
 
 807,840 
 
 
 80 
 
 3-809 
 
 .00589 
 
 7.963 
 
 861,696 
 
 
 85 
 
 4.048 
 
 .00586 
 
 8.948 
 
 915,552 
 
 
 90 
 
 4.298 
 
 .00584 
 
 10.056 
 
 969,408 
 
 10 
 
 60 
 
 1.835 
 
 .00614 
 
 1.541 
 
 646,272 
 
 
 70 
 
 2.141 
 
 .00606 
 
 2.071 
 
 753,984 
 
 
 80 
 
 2-447 
 
 .00597 
 
 2.665 
 
 861,696 
 
 
 90 
 
 2.752 
 
 .00590 i 8.331 
 
 969,408 
 
 
 100 
 
 3-058 
 
 .00584 
 
 4.071 
 
 1,077,120 
 
 
 no 
 
 3.364 
 
 .00578 
 
 4.876 
 
 1,184,832 
 
 
 120 
 
 3.670 
 
 -00572 
 
 5.743 
 
 1,292,544 
 
 
 130 
 
 3-976 
 
 .00569 
 
 6.706 
 
 1,400,256 
 
 
 140 
 
 4.281 
 
 .00566 
 
 7.733 
 
 1,507,968 
 
 
 150 
 
 4-587 
 
 .00562 
 
 8.815' 
 
 1,615,680 
 
496 
 
 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 TABLE No. 1O1 (Continued). 
 
 FRICTIONAL HEAD IN MAIN AND DISTRIBUTION PIPES (in each 
 1000 feet length). 
 
 Diam. 
 of 
 pipe. 
 
 Volume of 
 water 
 delivered. 
 
 Velocity 
 of 
 flow. 
 
 Coefficient 
 of 
 friction. 
 
 Frictional head 
 per 1000 feet. 
 
 U. S. gallons 
 in 24 hours. 
 
 Inches. 
 
 Cu.ft.per 
 min. 
 
 Feet per 
 Second. 
 
 
 Feet. 
 
 Gallons. 
 
 12 
 
 1 2O 
 
 2.548 
 
 .00581 
 
 2.343 
 
 1,292,544 
 
 
 I 4 
 
 2.972 
 
 .00571 
 
 3.133 
 
 1,507,968 
 
 
 1 60 
 
 3-397 
 
 .00563 
 
 4.036 
 
 1,723,392 
 
 
 1 80 
 
 3.821 
 
 00555 
 
 5.033 
 
 1,938,816 
 
 
 200 
 
 4.246 
 
 .00551 
 
 6.171 
 
 2,154,240 
 
 
 22O 
 
 4.637 
 
 .00546 
 
 7.407 
 
 2,369,664 
 
 
 240 
 
 5-098 
 
 .00542 
 
 8.755 
 
 2,585,088 
 
 14 
 
 175 
 
 2.721 
 
 .00560 
 
 2. 207 
 
 1,884,960 
 
 
 200 
 
 3.109 
 
 00553 
 
 2.845 
 
 2,154,240 
 
 
 225 
 
 3-498 
 
 .00546 
 
 3.550 
 
 2,423,520 
 
 
 250 
 
 3.887 
 
 .00542 
 
 4.359 
 
 2,692,800 
 
 
 275 
 
 4-275 
 
 .00537 
 
 4.989 
 
 2,962,080 
 
 
 300 
 
 4-665 
 
 .00538 
 
 6.232 
 
 3,231,360 
 
 
 325 
 
 5-053 
 
 .00530 
 
 7.203 
 
 3,500,640 
 
 
 350 
 
 5-597 
 
 .00524 
 
 8.738 
 
 3,769,920 
 
 16 
 
 225 
 
 2.682 
 
 00554 
 
 1.857 
 
 2,423,520 
 
 
 250 
 
 3.099 
 
 .00538 
 
 2.408 
 
 2,692,800 
 
 
 275 
 
 3.226 
 
 .00536 
 
 2.599 
 
 2,962,080 
 
 
 300 
 
 3.576 
 
 .00530 
 
 3.158 
 
 3,231,360 
 
 
 325 
 
 3.874 
 
 .00526 
 
 3.679 
 
 3,500,640 
 
 
 350 
 
 4.172 
 
 .00523 
 
 4-242 
 
 3,769,920 
 
 
 375 
 
 4.471 
 
 .00520 
 
 4.844 
 
 4,039,200 
 
 
 400 
 
 4.768 
 
 .00518 
 
 5.488 
 
 4,308,480 
 
 
 425 
 
 5.066 
 
 .00515 
 
 6.159 
 
 4,577,760 
 
 
 450 
 
 5.368 
 
 .00508 
 
 6.848 
 
 4,847,040 
 
 
 475 
 
 5.676 
 
 .00510 
 
 7.657 
 
 5,116,320 
 
 
 500 
 
 5.961 
 
 .00507 
 
 8.395 
 
 5,385,600 
 
 IS 
 
 300 
 
 2.830 
 
 .00530 
 
 1.758 
 
 3,231,260 
 
 
 350 
 
 3-301 
 
 .00519 
 
 2.342 
 
 3,769,920 
 
 
 400 
 
 3-773 
 
 .00513 
 
 3.024 
 
 4,308,480 
 
 
 450 
 
 4-245 
 
 .00508 
 
 3.791 
 
 4,847,040 
 
 
 500 
 
 4.717 
 
 . 00504 
 
 4.644 
 
 5,385,600 
 
 
 550 
 
 5.188 
 
 .00499 
 
 5.562 
 
 5,924,160 
 
 
 600 
 
 5.660 
 
 .00497 
 
 6.594 
 
 6,462,720 
 
 
 650 
 
 6.132 
 
 .00495 
 
 7.708 
 
 7,OOI.28o 
 
 
 675 
 
 6.367 
 
 .00494 
 
 8.293 
 
 7,270,560 
 
FBICTIONAL HEADS IN PIPES. 
 
 497 
 
 TABLE 1 O 1 (Continued). 
 
 FRICTIONAL HEAD IN MAIN AND DISTRIBUTION PIPES (in each 
 1000 feet length). 
 
 Diam. 
 of 
 pipe. 
 
 Volume of 
 water 
 delivered. 
 
 Velocity 
 of 
 flow. 
 
 Coefficient 
 of 
 friction. 
 
 Frictional head 
 per looo feet. 
 
 U. S. gallons 
 in 24 hours. 
 
 Inches. 
 
 Cu.ft.per 
 mtn. 
 
 Feet per 
 second. 
 
 
 Feet. 
 
 Gallons. 
 
 20 
 
 350 
 
 2.674 
 
 .00516 
 
 1.375 
 
 3,769,920 
 
 
 4OO 
 
 3-056 
 
 .00509 
 
 1.731 
 
 4,308,480 
 
 
 450 
 
 3.438 
 
 .00503 
 
 2.215 
 
 4,847,040 
 
 
 500 
 
 3-821 
 
 .00500 
 
 2.720 
 
 5,385,600 
 
 
 550 
 
 4.2O2 
 
 .00496 
 
 3.264- 
 
 5,924,160 
 
 
 600 
 
 4.585 
 
 .00493 
 
 3.862 
 
 6,462,720 
 
 
 650 
 
 4.967 
 
 .00490 
 
 4.505 
 
 7,OOI,28o 
 
 
 700 
 
 5.341 
 
 .00487 
 
 5.177 
 
 7,539,840 
 
 
 750 
 
 5-731 
 
 .00484 
 
 5.924 
 
 8,078,400 
 
 
 800 
 
 6.II3 
 
 .00481 
 
 6.698 
 
 8,616,960 
 
 
 850 
 
 6.572 
 
 .00479 
 
 7.710 
 
 9,155,520 
 
 
 900 
 
 6.878 
 
 .00477 
 
 8.409 
 
 9,694,080 
 
 24 
 
 550- 
 
 2.918 
 
 .00484 
 
 1.280 
 
 5,924,160 
 
 
 600 
 
 3.183 
 
 .00482 
 
 1.517 
 
 6,462,720 
 
 
 650 
 
 3-449 
 
 .00477 
 
 1.762 
 
 7,OOI,28o 
 
 
 700 
 
 3.714 
 
 .00475 
 
 2.035 
 
 7,539,840 
 
 
 750 
 
 3-979 
 
 .00473 
 
 2.326 
 
 8,078,400 
 
 
 800 
 
 4.245 
 
 .00471 
 
 2.636 
 
 8,616,960 
 
 - 
 
 850 
 
 4.510 
 
 .00469 
 
 2.963 
 
 9^55,520 
 
 
 QOO 
 
 4-775 
 
 .00467 
 
 3.307 
 
 9,694,080 
 
 
 950 
 
 5.041 
 
 .00466 
 
 3.678 
 
 10,232,640 
 
 
 1000 
 
 5-306 
 
 .00464 
 
 4.057 
 
 10,771,200 
 
 
 1050 
 
 5-571 
 
 .00463 
 
 4.463 
 
 11,309,760 
 
 
 IIOO 
 
 5.826 
 
 .00462 
 
 4.871 
 
 11,848,320 
 
 
 1150 
 
 6.314 
 
 .00459 
 
 5.684 
 
 12,386,880 
 
 
 I2OO 
 
 9-367 
 
 .00457 
 
 5.754 
 
 12,925,440 
 
 
 1250 
 
 6.633 
 
 00455 
 
 6.218 
 
 13,464,000 
 
 27 
 
 800 
 
 3-353 
 
 .00465 
 
 1.410 
 
 8,616,960 
 
 
 900 
 
 3-772 
 
 .00461 
 
 1.811 
 
 9,694,080 
 
 
 1000 
 
 4.192 
 
 .00457 
 
 2.217 
 
 10,771,200 
 
 
 IIOO 
 
 4.611 
 
 .00453 
 
 2.659 
 
 11,848,320 
 
 
 I2OO 
 
 5-030 
 
 .00451 
 
 3.150 
 
 12,925,440 
 
 
 1300 
 
 5-454 
 
 .00449 
 
 3.687 
 
 14,002,560 
 
 
 I4OO 
 
 5.868 
 
 .00447 
 
 4.250 
 
 15,079,680 
 
 
 1500 
 
 6.287 
 
 .00445 
 
 4.856 
 
 16,156,800 
 
 
 1600 
 
 6.707 
 
 .00443 
 
 5.502 
 
 17,233,920 
 
 
 1700 
 
 7.126 
 
 .00439 
 
 6.155 
 
 18,311,040 
 
498 
 
 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 TABLE No. 1 Ol (Continued). 
 
 FRICTIONAL HEAD IN MAIN AND DISTRIBUTION PIPES (in each 
 1000 feet length). 
 
 Diam. 
 of 
 pipe. 
 
 Volume of 
 water 
 delivered. 
 
 Velocity 
 of 
 flow. 
 
 Coefficient 
 of 
 friction. 
 
 Frictional head 
 per looo feet. 
 
 U. S. gallons 
 in 24 hours. 
 
 Inches. 
 
 Cu.ft.per 
 tnin. 
 
 Feet per 
 second. 
 
 
 Feet. 
 
 Gallons. 
 
 30 
 
 IOOO 
 
 3-396 
 
 .00448 
 
 1.28Jp 
 
 10,771,200 
 
 
 1200 
 
 4-075 
 
 .00441 
 
 1.820 
 
 12,925,440 
 
 
 I4OO 
 
 4-754 
 
 .00438 
 
 2.460 
 
 15,079,680 
 
 
 1600 
 
 5-433 
 
 .00434 
 
 3.257 
 
 I7,233,9 2 
 
 
 I800 
 
 6. 112 
 
 .00429 
 
 4.009 
 
 19,388,160 
 
 
 2OOO 
 
 6.791 
 
 .00428 
 
 4.904 
 
 21,542,400 
 
 
 2200 
 
 7.471 
 
 .00425 
 
 5.894 
 
 23,696,640 
 
 
 24OO 
 
 8.149 
 
 .00421 
 
 6.947 
 
 25,850,880 
 
 36 
 
 1500 
 
 3.536 
 
 .00419 
 
 1.085 
 
 16,156,800 
 
 
 2OOO 
 
 4-708 
 
 .00412 
 
 1.891 
 
 21,542,400 
 
 
 2500 
 
 5.894 
 
 .00406 
 
 2.920 
 
 26,928,000 
 
 
 3000 
 
 7-073 
 
 .00401 
 
 4.154 
 
 32,313,600 
 
 
 3500 
 
 8.252 
 
 .00397 
 
 5.598 
 
 37,699,200 
 
 
 4OOO 
 
 9-431 
 
 .00394 
 
 7.257 
 
 43,084,800 
 
 486. Relative Discharging Capacities of Pipes. 
 
 The volume of water delivered, <?, by a pipe, is, as we have 
 seen ( 296), equal to the product of its section 8 9 into its 
 mean velocity of flow v, 
 
 The equation of velocity is, 
 
 I m ) 
 hence we have, for full pipes, 
 
 By uniting the two terms of d, within the vinculum, we 
 have the equation of volume, 
 
RELATIVE CAPACITIES OF PIPES. 499 
 
 For a given inclination, all the terms in the right-hand 
 member are constant, except d and m. We have then the 
 
 relative discharging powers of pipes, as the quotients, , or 
 
 772- 
 
 nearly as the square roots of the fifth powers of the diam- 
 eters. 
 
 By transposition of the equation for volume, q, we have 
 the equation for diameter, d, 
 
 _ , 
 
 ~ X ' X ' 
 
 .61685 
 
 By this we perceive that the relative diameters required 
 for equally effective deliveries are as the products (fm, or 
 nearly as the squares of the volumes. 
 
 487. Table of Relative Capacities of Pipes. The 
 following table (No. 102) of approximate relative discharg- 
 ing powers of pipes, will facilitate the proper proportioning 
 of systems of pipe distributions. It shows at a glance the 
 ratio of the square root of the fifth power of any diameter, 
 from 3 to 48 inches, to the square root of the fifth power of 
 any other diameter within the same limit. 
 
 In the second column of this table, the diameter 1 foot 
 is assumed as unit, and the ratios of the square roots of the 
 fifth powers of the other diameters, in feet, are given oppo- 
 site to the respective diameters in feet written in the first 
 column. Thus the approximate relative ratio of discharging 
 power of a 3-foot pipe to that of a 1-foot pipe is as 15.588 to 
 1 ; and of a .5 foot pipe to a 1-foot pipe as .1768 to 1 ; also 
 the relative discharging power of a 4-foot pipe (= 48-inch) 
 is to that of a 2-foot pipe (= 24-inch) as 32 to 5.657 ; and of 
 
500 
 
 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 
 
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DEPTHS OF PIPES. 501 
 
 a 2.5-foot pipe to the combined discharging powers of a 
 2-foot and 1.5-foot pipes as 9.859 to (5.657 + 2.756). 
 
 The last vertical column gives the diameters in inches, 
 as does also the horizontal column at the head of the right- 
 hand section of the table. 
 
 The numbers in the intersections of the horizontal and 
 vertical columns from the diameters in inches give also 
 approximate relative discharging capacities. For instance, 
 if we select in the vertical column of diameters that of the 
 48-inch pipe and desire to know how many smaller pipes it 
 is equal to in discharging capacity, we trace along the hori- 
 zontal column from it, and find that it is equal to 15.59, 
 sixteen -inch pipes, or 5.65 twenty-four-inch pipes, or 1.58 
 forty -inch pipes, etc. Also, for other diameters, we find 
 that a 24-inch pipe is equal to 32 six-inch pipes, or 2.05 
 eighteen-inch pipes, and a 12-inch pipe is equal to 5.65 six- 
 inch pipes. 
 
 488. Depths of Pipes. The depths at which pipes 
 are to be placed, so they shall not be injured by traffic or 
 frost, is a matter for special local study, general rules being 
 Ibut partially applicable. The depth is controlled in each 
 given latitude, or thermic belt, by first, the stability of the 
 earth, whether it be soft and quaky, or heavy clay, or close 
 sand, or rock ; second, whether the ground be saturated by 
 surface waters that remain and freeze and conduct down 
 frost, or by living springs flowing up and opposing deep 
 penetration of frost ; third, whether the ground be porous, 
 well underdrained to a level below the pipes, and the pores 
 filled with air, which is a good non-conductor ; and fourth, 
 whether the winds sweep the snows off from given localities 
 and leave them unprotected, or given localities are shaded 
 .and the severity of night is uncounteracted at noonday. 
 
 Along those thermic lines whose latitudes at the Atlan- 
 
502 
 
 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 tic coast are as given, the depths of the axes of the pipes, in 
 close gravelly soils, may be approximately as follows : 
 
 TA B L E No. 1O3. 
 APPROXIMATE DEPTHS FOR AXES OF WATER-PIPES. 
 
 DlAM. 
 
 LATITUDE 
 40 North. 
 
 LATITUDE 
 42 North. 
 
 LATITUDE 
 44 North. 
 
 DlAM. 
 
 LATITUDE 
 40 North. 
 
 LATITUDE 
 42 North. 
 
 LATITUDE 
 44 North. 
 
 
 Depth of 
 
 Depth of 
 
 Depth of 
 
 
 Depth of 
 
 Depth of 
 
 Depth of 
 
 
 axis. 
 
 axis. 
 
 axis. 
 
 
 axis. 
 
 axis. 
 
 axis. 
 
 II 
 
 i n 
 
 / it 
 
 t it 
 
 // 
 
 t n 
 
 i ff 
 
 i n 
 
 4 
 
 4-8 
 
 52 
 
 62 
 
 20 
 
 4 10 
 
 5 5 
 
 6-3 
 
 6 
 
 4-8 
 
 52 
 
 62 
 
 22 
 
 4 10 
 
 5 5 
 
 6-3 
 
 8 
 
 47 
 
 5i 
 
 62 
 
 24 
 
 4 ii 
 
 5 6 64 
 
 10 
 
 47 
 
 5i 
 
 62 
 
 27 
 
 4 ii 
 
 5 7 64 
 
 12 
 
 4-7 
 
 51 
 
 62 
 
 30 
 
 5 o 
 
 5-8 
 
 6-4 
 
 14 
 
 47 
 
 52 
 
 62 
 
 33 
 
 5 o 
 
 5-9 
 
 6-5 
 
 16 
 
 4-8 
 
 53 
 
 62 
 
 36 
 
 5 o 
 
 5io 
 
 66 
 
 18 
 
 49 
 
 54 
 
 6-3 
 
 40 
 
 5 i 
 
 5-i i 
 
 6-7 
 
 There is a general impression that the water passed into 
 pipes, will in a very short time take the temperature of the 
 ground in which the pipes are laid. Close observation does 
 not confirm this impression. 
 
 If water at a high temperature is admitted to a deep 
 pipe system, in the early summer, while the ground is yet 
 cool, the consumers will derive but little benefit from the 
 coolness of the earth, and this is especially the case when 
 the pipes are coated and lined with cement. 
 
 Frost also penetrates at various points as low as the 
 bottoms of sub-mains, without seriously interfering with 
 the flow, and water-pipes are often suspended beneath 
 bridges, where ice forms in the river near by, a foot or more 
 in thickness, without their flow being interfered with. An 
 eight or ten inch pipe will resist cold a long time before it 
 will freeze solid. 
 
 The hydrants, small dead ends, and service-pipes are 
 
RATES OF CONSUMPTION OF WATER. 503 
 
 most sensitive to cold, and their depths and coverings should 
 receive especial attention. 
 
 Dead ends should be avoided as much as possible, and 
 circulation maintained for the protection of the pipes against 
 frost, as well as to maintain the purity, or to prevent the 
 fermentation of the motionless water. 
 
 489. Elementary Dimensions of Pipes. A table 
 of the elementary dimensions of pipes facilitates so much, 
 pipe calculations, that we insert it here (p. 504). The last 
 column gives also the quantity of water required to fill each 
 lineal foot of the pipes, when laid complete, or the quan- 
 tities they contain. 
 
 490. Distribution Systems. We have now reduced 
 to tabular form the data that will assist in establishing the 
 proportions of the several parts of a system of distribution 
 pipes, for the domestic and fire supply of a town or city. 
 
 For illustration, let us assume a case of a thriving young 
 city of 25,000 inhabitants, situated on the bank of a naviga- 
 ble river, and that the contour of the land had permitted 
 its streets to be straight, and to intersect at right-angles. 
 In such case its system of distribution pipes will form a 
 series of parallelograms, inclosing one, two or more of the 
 city blocks, as circumstances require, substantially as is 
 shown in the plan of a system of pipes, Fig. 113. 
 
 491. Rates of Consumption of Water. The healthy 
 >wth of the city gives reason to anticipate an increase to 
 
 >,000 inhabitants within a decade, and this number at 
 should be provided for in the first supply main, the 
 reservoir, and such parts as are expensive to duplicate, 
 id a larger number should be provided for in the con- 
 Luit, and such parts as are very expensive and difficult to 
 luplicate. 
 
 The continued popularization of the use of water, and 
 
504 
 
 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 TABLE No. 1O4. 
 
 ELEMENTARY DIMENSIONS OF PIPES. 
 
 Diameter 
 
 Diameter. 
 
 Contour. 
 
 Sectional area. 
 
 Hydraulic 
 mean radius. 
 
 Cubical con- 
 tents per lineal 
 foot. 
 
 Inches. 
 
 Feet. 
 
 Feet. 
 
 Sq.feet. 
 
 
 Cubicfeet. 
 
 i 
 
 .0417 
 
 .1310 
 
 .001366 
 
 .0104 
 
 .001366 
 
 i 
 
 .0625 
 
 .1965 
 
 .003068 
 
 .0156 
 
 .003068 
 
 I 
 
 .083 
 
 .26l8 
 
 .005454 
 
 .0208 
 
 .005454 
 
 'I 
 
 .1250 
 
 39 2 7 
 
 .OI227 
 
 .0312 
 
 .OI227 
 
 ij 
 
 .1458 
 
 .4581 
 
 .01670 
 
 .0364 
 
 .01670 
 
 2 
 
 .1667 
 
 .5235 
 
 .02232 
 
 .0418 
 
 .02232 
 
 3 
 
 .250 
 
 .7854 
 
 .04909 
 
 .0625 
 
 .04909 
 
 4 
 
 3333 
 
 1.047 
 
 .08726 
 
 0833 
 
 .08726 
 
 6 
 
 .5000 
 
 I-57I 
 
 -19635 
 
 .1250 
 
 19635 
 
 8 
 
 .6667 
 
 2.094 
 
 3490 
 
 .1666 
 
 -3490 
 
 10 
 
 .8333 
 
 2.618 
 
 5454 
 
 .2083 
 
 5454 
 
 12 
 
 I.OOOO 
 
 3.142 
 
 .7854 
 
 .2500 
 
 7854 
 
 14 
 
 1.1667 
 
 3.66 5 
 
 1.069 
 
 .2916 
 
 1.069 
 
 16 
 
 t-3333 
 
 4.189 
 
 J -397 
 
 3333 
 
 r-397 
 
 18 
 
 1.5000 
 
 4-713 
 
 1.767 
 
 .3750 
 
 1.767 
 
 20 
 
 1.6667 
 
 5-235 
 
 2.181 
 
 .4166 
 
 2.181 
 
 24 
 
 2.00OO 
 
 6.283 
 
 3.142 
 
 .5000 
 
 3.142 
 
 27 
 
 2.250O 
 
 7.069 
 
 3.976 
 
 -56^5 
 
 3-976 
 
 30 
 
 2.5OOO 
 
 7.854 
 
 4.909 
 
 .6250 
 
 4.909 
 
 33 
 
 2.7500 
 
 8.639 
 
 5-940 
 
 .6875 
 
 5-940 
 
 36 
 
 3.OOOO 
 
 9.425 
 
 7.069 
 
 .7500 
 
 7.069 
 
 40 
 
 3-3333 
 
 10.47 
 
 8.726 
 
 .8333 
 
 8.726 
 
 44 
 
 3-6667 
 
 11.52 
 
 10.558 
 
 .9166 
 
 10.558 
 
 48 
 
 4.0000 
 
 12.56 
 
 12.567 
 
 .OOOO 
 
 12.567 
 
 54 
 
 4.5000 
 
 14.14 
 
 I5-905 
 
 . 1250 
 
 15-905 
 
 60 
 
 5.0000 
 
 15.71 
 
 J 9- 6 35 
 
 .2500 
 
 I9-635 
 
 72 
 
 6. oooo 
 
 19.29 
 
 29.607 
 
 .5000 
 
 29.607 
 
 84 
 
 7.0000 
 
 21.99 
 
 38.484 
 
 .7500 
 
 38.484 
 
 96 
 
 8. oooo 
 
 25.45 
 
 50.265 
 
 2. OOOO 
 
 50.265 
 
7 
 
 s-t- 
 
 * .1 
 
 fcl - 
 
 IT 
 
 7 i * : 
 
 G F E 
 
506 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 the increasing demand for it for domestic, irrigating, orna- 
 mental, and mechanical purposes, with the increasing waste 
 to which they all tend, requires that at least an annual 
 average of 75 gallons per capita daily must be provided for 
 the 35,000 persons. 
 
 In our discussion of the varying consumption of water 
 ( 19), it is shown that in certain seasons, days of the week, 
 and hours of the day, the rate of consumption, independent 
 of the fire supply, is seventy-five per cent, greater than the 
 average daily rate for the year. In anticipation of this 
 varying rate, we should proportion our main for not less 
 than fifty per cent, increase (= 75 x 1.50 = 112.5), or for a 
 rate of 112.5 gallons per capita daily, which for 35,000 per- 
 sons equals a rate of 365 cubic feet per minute. 
 
 492. Rates of Fire Supplies. For fire supply we 
 anticipate the possibility of two fires happening at the same 
 time requiring ten hose streams each. The minimum fire 
 supply estimate is, then, twenty hose streams of say 20 
 cubic feet per minute, or a total of 400 cubic feet per minute. 
 
 The combined rate of flow of fire and domestic supply is 
 (365 + 400) 765 cubic feet per minute. 
 
 493. Diameter of Supply Main. Turning now to the 
 table of Frictional Head in Distribution Pipes, and looking 
 for volume in the second column, we find that a 24-inch 
 pipe will deliver 765 cubic feet per minute, with a velocity 
 of flow of about 4 feet per second, and with a loss of head 
 of about 2.5 feet in each thousand feet length of main. A 
 20-inch pipe will deliver the same volume with a velocity 
 of flow of about 5.75 feet per second, and with a loss of 
 head of about 6 feet in each thousand feet length. Unless 
 the main is short, this velocity, and this loss of head, in- 
 creased by the loss at angles and valves, is too great. We 
 adopt, therefore, the 24-inch diameter for supply main. 
 

 
 MAXIMUM VELOCITIES OF FLOVT3 / ''<S' 
 
 ^ 
 
 <> *" /* 
 
 494. Diameters of Sub-Mains. We now compute Oj^ 
 the portions of the whole supply that will be required in / 
 each section of the city. If our plan of distribution i^J^/ 
 divided into twelve sections, then the average section sup- 
 
 ply is one-twelfth of the whole. We find, for instance, that 
 Sec. 1 requires 85 per cent, of the average ; Sec. 3, 125 per 
 cent, of the average ; Sec. 12, 100 per cent, of the average ; 
 Sec. 22, 95 per cent, of the average, etc. 
 
 Now, with the aid of the table of relative discharging 
 powers of pipes, and the table of frictional heads in pipes, 
 we can readily assign the diameters to the sub-mains that 
 are to distribute the waters to the several sections, adding 
 to the domestic and fire supply volumes for the nearest 
 sections the estimated volumes that are to pass beyond them 
 to remoter sections. 
 
 This done, we may sum up the frictional losses of head 
 along the several lines from the supply to any given point, 
 and deduct the sum from the static head, and see if the 
 required effective head remains. The volume and effective 
 head are matters of the utmost importance, when the pipes 
 are depended upon exclusively to supply the waters re- 
 quired for fire extinguishment. The lack of these has cost 
 several of our large cities a million dollars and more in a 
 single night. 
 
 An inspection of the table of Frictional Head shows how 
 rapidly the friction increases when velocity increases. The 
 increase of frictions are, in the same pipe, as the increase of 
 squares of velocities (tfm\ nearly. 
 
 495. Maximum Velocities of Flow. As a general 
 rule, the velocities in given pipes should not exceed, in feet 
 per second, the rates stated in the following table for the 
 respective diameters. 
 
508 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 TABLE No. 1 OB. 
 MAXIMUM VELOCITIES OF FLOW IN SUPPLY AND DISTRIBUTION PIPES. 
 
 
 
 
 
 
 
 
 
 
 
 Diameter, in inches 
 
 4 
 
 6 
 
 8 
 
 10 
 
 12 
 
 14 
 
 16 
 
 18 
 
 20 
 
 22 
 
 24 
 
 27 
 
 3 
 
 33 
 
 36 
 
 Velocity, in ft. per sec. . 
 
 2.5 
 
 2 .8 
 
 3 
 
 3-3 
 
 3-5 
 
 3.9 
 
 4.2 
 
 4-5 
 
 4-7 
 
 5 
 
 5-3 
 
 5.8 
 
 6.2 
 
 6.6! 7 
 
 496. Comparative Frictions. As regards friction 
 alone in any given pipe, it does not matter whether the 
 water is flowing up a hill or down a hill, or materially if 
 the pressure is great or little; or in long, conical, and 
 smooth pipes, whether the water is flowing toward the large 
 end or toward the small end. The total friction will be the 
 same in both directions in the first case, and will also be the 
 same in both directions in the last case. In the conical 
 pipe, however, the friction per unit of length, or per lineal 
 foot, will be less than the average at the large end, because 
 the velocity of flow will be less there, and more than the 
 average at the small end. The total frictional head will be 
 the same as though the whole pipe had a uniform diameter 
 just equal to the diameter in the conical pipe at the point 
 where the friction is equal to the average for the whole 
 length. 
 
 497. Relative Rates of Flow of Domestic and 
 Fire Supplies. The actual consumption of water by the 
 fire department for the extinguishment of fires, in any city, 
 per annum, is very insignificant when compared with either 
 the domestic, the irrigation and street sprinkling, or the 
 mechanical supply for the same limit of time, yet it has 
 appeared above that the pipe capacity required for the fire 
 service, in the general main of a small city, exceeds that 
 required for the whole remaining consumption. If we 
 examine this question still closer, taking a length of 1200 
 feet of distribution pipe in a closely built up section of the 
 
REQUIRED DIAMETERS FOR FIRE SUPPLIES. 509 
 
 city, we find on the 1200 feet length, say 40 domestic service 
 pipes, and consumption of say 750 gallons each per day, or 
 total of 15000 gallons per day. Making due allowance for 
 fifty per cent, increase of flow at certain hours, we have a 
 required delivery capacity of 1.5 cubic feet per minute to 
 cover this whole consumption. On the same 1200 feet of 
 pipe there are, say four fire-hydrants. If in case of fire we 
 take from these hydrants only four streams, in all, of 20 
 cubic feet per minute each, we require a delivery capacity 
 of 80 cubic feet per minute. In this case, which is not an 
 uncommon one, the required capacity for the fire service is 
 to that for the remaining service as 80 to 1.5. 
 
 If the given pipe, 1200 feet long, is a six-inch pipe, sup- 
 plied at both ends, then the delivery for fire at each end is 
 forty cubic feet per minute. Referring to the table of fric- 
 tional head, we find that this quantity requires a velocity of 
 flow of 3.401 feet per second, and consumed head, in fric- 
 tion, at the rate of 8.8 feet per thousand feet. 
 
 If the 80 cubic feet per minute must all come from one 
 end of the pipe, then the pipe should be eight inches diam- 
 eter, in which case the velocity will be nearly four feet per 
 second and the head consumed at the rate of about eight 
 feet per thousand feet length. 
 
 498. Required Diameters for Fire Supplies. 
 As a general rule, the minimum diameters of pipes for sup- 
 plying given numbers of hydrant streams, when the given 
 pipes are one thousand feet long, and static head of water 
 one hundred and fifty feet, are as follows : 
 
510 
 
 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 TABLE No. 1O6. 
 DIAMETERS OF PIPES FOR GIVEN NUMBERS OF HOSE STREAMS. 
 
 
 
 
 
 
 
 6 
 
 
 8 
 
 
 
 
 
 Approximate total quantity of water, 
 
 
 
 60 
 
 Rn 
 
 
 
 
 160 
 
 1 80 
 
 
 
 
 Required diameter of pipe, in inches. . 
 
 4 
 
 ? 
 
 8 
 
 8 
 
 10 
 
 10 
 
 10 
 
 12 
 
 12 
 
 12 
 
 12 
 
 14 
 
 Number of hose streams 
 
 
 
 
 rfi 
 
 
 18 
 
 
 
 
 
 
 
 Approximate total quantity of water, 
 in cubic feet per minute. 
 
 "fin 
 
 "Ro 
 
 
 
 
 060 
 
 080 
 
 
 
 
 4.60 
 
 .g 
 
 Required diameter of pipe, in inches. . 
 
 14 
 
 14 
 
 14 
 
 16 
 
 16 
 
 jw 
 16 
 
 JOU 
 
 16 
 
 16 
 
 16 
 
 18 
 
 4 i8 
 
 18 
 
 If the pipes are short, the velocities of flow may be 
 increased somewhat, for a greater ratio of loss of head per 
 unit of length is then permissible. 
 
 If the pipe is supplied from both ends, then the nnmber 
 of hose streams may be doubled without increase of the 
 frictional head ; hence the advantage of so distributing the 
 sub-mains as to deliver a double supply to as many points 
 as possible, for this is equivalent to doubling the capacity 
 of the minor pipes. If the pipes are several thousand feet 
 long, and have a large proportionate domestic draught, 
 then a due increase should be given to the diameters. 
 
 499. Duplication Arrangement of Sub -Mains. 
 When the sub-mains can be distributed in parallel lines, at 
 several squares distance, and "gridironed" across by the 
 smaller service mains, as in v the plan, Fig. 113, or arranged 
 in some equivalent manner, then a most excellent system 
 will be secured. In such case, if an accident happens to a 
 pipe, or valve, or hydrant, in any central location, there are 
 at least two lines of sub-mains around that point, and the 
 supply will with certainty be maintained at points beyond. 
 
 Pipes are always liable to accident in consequence of 
 building excavations, sewerage excavations, sewer over- 
 flows, quicksand or clay slides, floods, and various other 
 causes that cannot be foreseen when the pipes are laid ; and 
 
STOP-VALVE SYSTEM. 
 
 511 
 
 FIG. 118. 
 
 when new hydrants are to be attached, or large pipe con- 
 nections to be made, or repairs to be made, it is frequently 
 necessary to shut off the water. The advantage of dupli- 
 cate lines of supply to all points is apparent in such case. 
 When a city has become dependent on its pipes for its 
 water supply and protection from fire, it is absolutely neces- 
 sary that the supply be maintained, and the result may be 
 disastrous if it fails for an hour. 
 
 5OO. Stop-Valve System. It is equally advantage- 
 ous to have a sufficient number of stop-valves, or "gates," 
 as they are frequently 
 termed, upon the pipe, 
 so the water may be shut 
 off from any given point 
 without cutting off the 
 supply from both a long 
 and a broad territory, or 
 even a very long length 
 of pipe. The sub-main 
 parallelogram system 
 shown in the plan, Fig. 
 113, permits of such an ar- 
 rangement of stop-valves, 
 chiefly of small diameters 
 and inexpensive, that an 
 accident at any point will 
 not leave that point with- 
 out a tolerable fire pro- 
 tection from both sides. 
 For instance, if it is 
 necessary to shut off in EDDY'S STOP-VALVE. 
 
 , . ._ (R. D. Wood & Co., Philadelphia.) 
 
 Section 2 a part of East 
 
 Fourth Street between Avenues A and D, the hydrants at 
 
512 DISTRIBUTION SYSTEMS, AND APPENDAGES, 
 
 the corners of East Third and Fifth Streets will still be avail- 
 able. If the gates are placed at each branch from the sub- 
 mains, and at the intersections of the sub-mains, as they 
 should be, then an accident to a sub-main will not neces- 
 sitate the shutting off of any service-main joining it, for the 
 service-main supplies can be maintained from the opposite 
 ends. Wherever cross service-mains are required, as in 
 Avenues B and C, in Section 3 in the plan, they may pass 
 under the other service-mains whose lines they cross and 
 have gates at their end branches only, which admits of their 
 being readily isolated. 
 
 5O1. Stop-Valve Locations. A systematic disposi- 
 tion of the pipes generally should be adopted. If the pipes 
 are not placed in the centres of streets, they should be placed 
 with strict uniformity at some certain distance from the 
 centre of the street, and carefully aligned, and uniformly 
 upon the same geographical side, as, upon the northerly and 
 westerly side. The stop-valves should be disposed also, 
 with rigid system, as, always in the line of the street boun- 
 dary, the line of the curb, or some fixed distance from the 
 centre of the street. An accident may demand the prompt 
 shutting of any gate of the whole number, at any moment 
 of day or night ; and if, perchance, its curb-cover is hidden 
 by frozen earth or by snow, it is important to know exactly 
 where to strike without first journeying to the office and 
 searching for a memorandum of distances and bearings. 
 Searching for a gate-cover buried under frozen earth is a 
 tedious operation, and it is not always possible to uncover 
 every one of several hundred gates after every thaw and 
 every snow-storm in winter. 
 
 Strict adherence to a system in locating gates enables 
 new assistants to readily learn and to know the exact posi- 
 tion of them all. 
 
STOP-VALVE DETAILS. 513 
 
 Strict adherence to system in locating pipes is requisite 
 for the strict location of gates, and pipes should be cut, if 
 necessary, to bring the gates to their exact locations. If a 
 gate is a half-length of pipe out of position, it may cost 
 several hours delay in digging earth frozen hard as a sand- 
 stone rock, to find the gate-cover. 
 
 502. Blow-off, and Waste Valves. When pipes are 
 located upon undulating ground, blow-off valves and pipes 
 will be required in the principal depressions of the mains 
 and sub-mains, to flush out the sediment that is deposited 
 from unfiltered water. The diameters of the blow-off pipes 
 may be about half the diameters of the mains from which 
 they branch. Smaller wastes will answer for the drainage 
 of the service-main sections for repairs or connections, and 
 these may lead into sewers, or wherever the waste-water 
 may be disposed of. 
 
 503. Stop- Valve Details. A variety of styles of stop- 
 valves are now offered by different manufacturers, and a 
 special advantage is claimed for each, so that no little prac- 
 tical sagacity is required on the part of the engineer to pro- 
 tect his works from the introduction of weak and defective 
 novelties, that may prove very troublesome. 
 
 He must observe that the valve castings are so designed 
 as to be strong and rigid in all parts, that there are no thin 
 spots from careless centring of cores ; that flat parts, if any, 
 are thickened up, or ribbed, so they will not spring ; that 
 the valve-disks are so supported as not to spring under 
 great pressures, and that they and their seats are faced with 
 good qualities of bronze composition and smoothly scraped, 
 ground, or planed, and that they will not stick in their 
 seats ; that the valve-stems are particularly strong and stiff, 
 with strong square or half-V threads, and that they and 
 their nuts are of a tough bronze or aluminum composition. 
 33 
 
514 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 FIG. 119. FIG. 119a. 
 
 LUDLOW'S STOP-VALVE (Ludlow Manufacturing Co., Troy). 
 
 Figs. 114 to 119& illustrate the principal features of 
 valves that have been well introduced. 
 
 A majority of the good valves have double disks, that 
 are self-adjusting upon their seats, and their seats are 
 slightly divergent, so that the pressure of the screw can set 
 the valve-disks snug upon the seats. 
 
 The loose disks should have but a slight rocking move- 
 ment between their guides, and must not be permitted to 
 chatter when the valve is partially open. 
 
 The blow-off valves may be solid or single-disk valves, 
 but the valves in the distribution must be tight against 
 pressure from both and either sides, whether the difference 
 of pressure upon the two sides be much or little. 
 
 Valves exceeding twenty inches diameter are usually 
 placed upon their sides, except in chambers, and the disks 
 have lateral motions, or sometimes the valve-cases are so 
 
VALVE CURBS. 
 
 515 
 
 arranged that the disks have vertical downward motions. 
 Otherwise the water in the valve-domes would be too much 
 exposed to frost in winter, as it would rise nearly to the 
 ground surface. 
 
 5O4. Valve Curbs. The stop-valve curbs are some- 
 times of chestnut or pitch-pine plank, with strong cast-iron 
 covers, and sometimes of cast-iron, placed upon a founda- 
 tion of bricks laid in cement. 
 
 The plank curbs are about eighteen by twenty-four 
 inches dimensions at top, flaring downward according to 
 
 FIG. 120. 
 
 the size of the valve, and they are often of such dimensions 
 as to admit a man, with room to enable him conveniently to 
 renew the packing about the valve-stem. 
 
516 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 The cast-iron curbs are usually elliptical in section. 
 The writer has used in several cities, for the smaller gates, 
 up to twelve inches diameter, circular curbs (Fig. 120) of 
 beton coignet, with cast-iron necks and covers. The neck is 
 six inches clear diameter at the road surface, fifteen to 
 eighteen inches deep, according to the size of the valve, and 
 flares to the size of the cement curb, which is just large 
 enough to slip over the dome-flange of the valve-case. The 
 cement curb rests upon a foundation of brick or stone laid 
 in cement mortar. 
 
 When these are paved about, the whole surface exposed 
 is only seven and one-half inches diameter, and they are 
 not as objectionable in the streets as the larger covers. 
 
 All gate-curbs must be thoroughly drained, so that 
 water cannot stand in them, and freeze in winter. 
 
 5O5. Fire-Hydrants. The design of a fire-hydrant 
 that is a success in every particular is a great achievement. 
 It ranks very nearly with the design of a successful water- 
 meter. 
 
 Nearly every speculative mechanic, it would seem, who 
 has had employ in a machine-shop for a time, has felt it 
 his duty to design the much-needed successful hydrant ; as 
 so many doctors and lawyers have grappled with, and 
 believed for a time, that they had solved the great meter 
 problem. 
 
 Innumerable patterns of hydrants are urged upon water 
 companies and engineers, and are accompanied by an 
 abundance of certificates setting forth their excellence ; and 
 many of them have good points and will answer all practi- 
 cal purposes until an emergency comes, when they fail, and 
 the experiment winds up with a loss that would have paid 
 for a thousand reliable hydrants. 
 
 A considerable practical experience with hydrants, and 
 
HYDRANT DETAILS. 
 
 517 
 
 FIG. 121. 
 
 an expert knowledge of the qualities demanded in the 
 design and materials of a hydrant, are necessary to enable 
 one to judge at sight of the value of a new pattern. 
 
 506. Post-Hydrants. In the smaller 
 towns and in the suburbs of cities, post- 
 Jiydrants, of which Fig. 121 illustrates one 
 pattern, are more generally preferred, as 
 they are more readily found at night, and 
 are usually least expensive in first cost. 
 
 They are placed on the edge of the 
 sidewalk, and a branch pipe from the 
 service main furnishes them with their 
 water. If the service main is of sufficient 
 capacity, the post-hydrant may have one, 
 two, three, or four nozzles. In cities where 
 steam fire-engines are used, a large nozzle 
 is added for the steamer supply, and if 
 there is a good head pressure, two nozzles 
 are usually supplied for attaching leading 
 hose. 
 
 For the supply of two hose streams, or 
 a steamer throwing two or more streams, 
 the hydrant requires a six-inch branch 
 pipe from the service main, and a valve of 
 equal capacity. The supply to post-hy- 
 drants has too often been throttled down, 
 when there was no head pressure to 
 spare, and the effectiveness of the hy- 
 drant very much reduced thereby. 
 
 507. Hydrant Details. In New 
 England and the Northern States, a 
 
 frost-case is a necessary appendage to MATHEW'S HYDRANT- 
 
 J -^ (R. D. Wood & Co., 
 
 a post-hydrant, and it must be free to Philadelphia). 
 
518 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 move up and down with the expansion and contraction of 
 the earth, without straining upon the hydrant base. In 
 clayey soils, these frost cases are often lifted several inches 
 in one winter season, and if the post is not supplied with 
 the movable case in such instances, it is liable to be torn 
 asunder. 
 
 A waste-valve must be provided in every hydrant that 
 will with certainty drain the hydrant of any and all water 
 it contains as soon as the valve is closed, and the waste 
 must close automatically as soon as the valve begins to 
 open. 
 
 The main valve must be positively tight, or great trouble 
 will be experienced with the hydrant in severe winters. A 
 moderate leakage, as in some stop-valves, cannot be per- 
 mitted. A free drainage must be provided to pass away 
 the waste water from the hydrant, or, if the hydrant is fre- 
 quently opened, for testing or use, the ground will soon be- 
 come saturated and the hydrant cannot properly drain. 
 
 If the valve closes "with" the pressure there must be 
 no slack motion of its stem, or when the valve is being 
 closed and has nearly reached its seat, the force of the cur- 
 rent will throw it suddenly to its seat and cause a severe 
 water-ram. 
 
 The screw motion of hydrant valves must be such that 
 the hydrant cannot be suddenly closed, or with less than 
 ten complete revolutions of the screw. The valves should 
 move slowly to their seats in all cases, as, if several hydrants 
 happen to be closed simultaneously, the water-ram caused 
 thereby may exert a great strain upon the valves, and the 
 shock will be felt to some extent throughout the whole 
 system of pipes. The sudden closing of a hydrant may 
 make a gauge, attached to the pipes, that is more than a 
 mile distant, kick up fifty or sixty pounds. 
 
HYDRANT DETAILS. 
 
 519 
 
 FIG. 122. 
 
 
 If a hydrant branch is taken from a main-pipe or sub- 
 main, there should be a stop-valve between the main and 
 hydrant, so the hydrant may be repaired without shutting 
 off the flow through the main. 
 
 In 1874 the writer made some 
 measurements of the quantities of 
 water delivered, under different 
 heads, through Boston Machine 
 Co. Post Hydrants, which are sim- 
 ilar in form to the Mathews Hy- 
 drant (Fig. 121). The volume of 
 water was measured by passing it 
 through a 3-inch Union water-meter, 
 which was connected to each hy- 
 drant by a length of fire-hose. 
 
 The length of hose between the 
 hydrant and meter in each and 
 every experiment was 49 feet 10 
 inches. The bores of the hydrant 
 nozzles and of the hose and meter 
 couplings were two and one-quar- 
 ter inches diameter. The hydrant 
 branches were six inches in di- 
 ameter, and hydrant barrels four 
 and one-half inches diameter. The 
 lengths of hose given, following, 
 were in all cases beyond the meter, 
 and were attached to the meter. 
 
 The hydrant was filled with 
 
 water and pressure without flow, taken by a gauge just 
 previous to the beginning of each test. 
 
 The following tests, at different elevations, covers a range 
 of head pressures between 42 feet and 183 feet : 
 
 FLUSH HYDRANT. 
 
520 
 
 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 TABLE No.107. 
 EXPERIMENTAL VOLUMES OF HYDRANT STREAMS. 
 
 REMARKS. 
 
 Pressure 
 before 
 test. Ibs. 
 
 Delivery 
 cu. ft. 
 per minute. 
 
 A. 42 Feet Head. 
 
 18.21 
 
 20.^76 
 
 
 H 
 
 q.372 
 
 
 u 
 
 12. <^O 
 
 
 tt 
 
 I 2 . 096 
 
 li- " " " 108 " Ilij " " " 
 
 ts 
 
 11.382 
 
 Open butt of 108 " n " " " 
 
 tt 
 
 15.342 
 
 B. HO Feet Head. 
 Open nozzle of meter, 2.\ inch diameter 
 
 47.74 
 
 4O.OOO 
 
 l|- inch nozzle attached to meter 
 
 
 24.666 
 
 ig- " " on 53 feet n inches of hose 
 
 
 
 21 .276 
 
 I*. " " " 108 " n^ " " " 
 
 <( 
 
 2O . 408 
 
 C. 136. S Feet Head. 
 
 CQ 24 
 
 43 Q74 
 
 
 a 
 
 24 . 3QO 
 
 ji " " on 55 feet \ inch of hose 
 
 a 
 
 23 ^26 
 
 D. 183.18 Feet Head. 
 T-J- inch nozzle on 55 feet 10 inches of hose 
 
 7Q H. 
 
 27 648 
 
 i " " " 108 " 4| " " " 
 
 
 oe. Q7/1 
 
 i| " " " 162 " 7 " " " 
 
 ^l 
 
 24 648 
 
 Open butt of 162 " 7 " " " 
 
 
 
 37 672 
 
 
 
 
 5O8. Flush Hydrants. A style of flush hydrant, that 
 may be placed under a paved or flagged sidewalk, near the 
 edge, is shown in Fig. 122. This style may have one, two, 
 or three fixed nozzles. 
 
 Figs. 123 and 124 illustrate a style of hydrant with a 
 portable head. This style is manufactured under the 
 Lowry patent. It is designed to be placed at the intersec- 
 tions of mains, in the street, or in the line of a main, but 
 may be placed in the sidewalk. In either case it is placed 
 within an independent curb, and the cast-iron case rises 
 about to the surface. The portable head is of brass and 
 composition, nicely finished, as light as is consistent with 
 
FIG. 123. 
 
 FIG. 124. 
 
 
 
 LOWRY'S FLUSH HYDRANT. (Boston Machine Co., Boston.) 
 
522 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 strength, and is usually carried upon the steamer or the 
 hose carriage. It has any desired number of nozzles, from 
 one to eight, each of which has its independent supplemen- 
 tary valve. 
 
 In the centre of the portable head is a revolving key that 
 operates the main valve stem. 
 
 509. Gate Hydrants. A variety of metallic "gate" 
 hydrants have been introduced, from time to time, and had 
 a brief existence, but the majority of them have been soon 
 abandoned. The most minute particle of grit upon their 
 faces gives trouble, and they are much more likely to stick 
 than valves of good sole-leather or of rubber properly pre- 
 pared, and clamped between metallic plates. Gate hydrants 
 of good design and excellent workmanship, should be fully 
 successful with filtered water. 
 
 The rubber of valves requires to be very skillfully tem- 
 pered, or it will be too soft or too hard. It hardens, also, 
 as the temperature of the water lowers. 
 
 510. High Pressures. But a few years since the 
 maximum static strain upon hydrants, in public water 
 supplies, did not exceed that of a hundred and fifty feet 
 head, and the majority of the hydrants in each system had 
 not over one hundred feet pressures when the water was at 
 rest. Hand or steam fire-engines were necessities in such 
 cases, and the pipes were so small that often the engines 
 had to exert some suctions on the pipes to draw their full 
 supplies. Now the values of pressure that will permit six 
 or eight effective streams to be taken direct from the hy- 
 drants in any part of the system is more fully appreciated, 
 and direct pumping pressures equivalent to three or four 
 hundred feet head are not uncommon. The effect upon the 
 hydrants is, however, a greatly increased strain which they 
 must be able to meet. 
 

 AIR-VALVES. 523 
 
 511. Air- Valves. All water contains some atmos- 
 pheric air. When water has passed through a pumping- 
 engine into a force-main under great pressure, it absorbs 
 some of the air in the air-vessel. If, then, it is forced along 
 a pipe having vertical curves and summits at different 
 points, it parts with some of the air at those summits. In 
 time, sufficient air will accumulate at each summit to oc- 
 cupy a considerable part of the sectional area at that point, 
 and it will continue to accumulate until the velocity of the 
 water is sufficient to carry the air forward down the incline. 
 
 At such summits an air-valve is required to let off the 
 accumulated air, as occasion requires. Also, when the 
 water is drawn off from the pipes, as for repairs or any 
 other purpose, there is always a tendency to a vacuum at 
 the summits if no air is supplied there ; and if the pipes are 
 not thick and rigid, they may collapse in consequence of 
 the vacuum strain, or exterior pressure. 
 
 When pipes are being filled, there should always be 
 ample escape for the air at the summits, or the air contained 
 in the pipes will be compressed and recoil, again be still 
 more compressed and again recoil with greater force, shoot- 
 ing the column of water back and forth in the pipe with 
 enormous force, and straining every joint. 
 
 In the distribution, hydrants are usually located upon 
 summits, and in such case will perform the functions of 
 air-valves. 
 
 If a stop-valve is inserted in an inclined pipe, and is 
 closed during the filling of the section immediately below it, 
 it makes practically a summit at that point, and an air- 
 valve or vent will be required there. 
 
 An air and vacuum valve, for summits, may with advan- 
 tage be combined in the same fixture, the air-valve motion 
 being positive in action for the purpose of an air-valve, 
 
524 
 
 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 f 
 
 FIG. 125. 
 
 opening against the pressure, but automatic as a vacuum- 
 valve, opening freely to the pressure of the atmosphere. 
 
 Fig. 125 is a com- 
 bined air and vacuum 
 valve designed by the 
 writer, and used in sev- 
 eral cities with success. 
 A two-inch air- valve 
 answers tolerably for 
 four, six, eight, and 
 ten inch pipes, but for 
 large pipes a special 
 branch with stop-valve 
 may be used. 
 
 Great care should 
 be exercised in filling 
 pipes with water, and 
 the water should not 
 be admitted faster 
 than the air can give 
 place to it by issue at 
 the air-valves, or open 
 hydrant nozzles, with- 
 out reactionary con- 
 vulsions. 
 
 512. Union of High and Low Services. Many 
 cities have high lands within their built-up limits that are 
 so much elevated above the general level that it is a matter 
 of convenience to divide the distribution into "high" and 
 " low services," and to give to each its independent reservoir. 
 In such case the benefit of the pressure of the high reser- 
 voir may be secured in the low system in case of a large 
 fire, by simply opening a valve in a branch connecting the 
 
 AIR VALVE. 
 
COMBINED RESERVOIR AND DIRECT SYSTEMS. 
 
 525 
 
 two systems. A check-valve, Fig. 126, will be required in 
 the effluent pipe, or supply main from the lower reservoir 
 to prevent the flow back into the lower reservoir. 
 
 A weighted valve, automatic in action, may also be 
 placed in the branch connecting the two systems, and then 
 
 FIG. 126. 
 
 CHECK-VALVE. 
 
 in case of an accident to the supply pipe of the lower sys- 
 tem, or a malicious closing of its valve, the upper service 
 will maintain the supply at a few pounds diminished 
 pressure. 
 
 If the pumps are arranged so as to give a direct increased 
 pressure in the lower system for fire purposes, then a check- 
 valve in the branch connecting the two systems, opening 
 toward the high system, will be an excellent relief and pro- 
 tection against undue pressure. 
 
 513. Combined Reservoir and Direct Systems. 
 In the plan of a pipe system, Fig. 113, a pipe leads from the 
 pumps direct to the reservoir, and a second pipe leads direct 
 from the pumps into the distribution, so that water may be 
 sent either to the reservoir or to the distribution, at will. 
 
526 DISTRIBUTION SYSTEMS, AND APPENDAGES. 
 
 A branch pipe connects these two pipes so as to supply the 
 distribution from the force main. 
 
 A check-valve opening toward the distribution is placed 
 in this branch. If a fire-pressure is put upon the distribu- 
 tion through the direct pipe this valve prevents the flow 
 back toward the reservoir, but upon the reduction of the 
 fire-pressure it comes into action and maintains the supply 
 to the distribution from the reservoir. 
 
 For additional security against unforseen contingencies, 
 another pipe may lead from the reservoir to one of the prin- 
 cipal sub-mains, as shown in the plan, when the relative 
 positions of the reservoir and distribution permits, and this 
 pipe may contain in the effluent chamber a check-valve 
 against fire-pressure and a weighted relief- valve to prevent 
 undue pressure. 
 
 In the reservoir plan, Fig. 58 (page 333), the force and 
 supply mains are shown to be connected by a pipe passing 
 along the side of the reservoir, so that the water may be sent 
 from the pumps direct into the distribution. The supply- 
 main has a check-valve in the effluent chamber in this case. 
 
 A combined reservoir and direct pressure system, sub- 
 stantially like that of Fig. 113, including high and low ser- 
 vices, was designed by the writer for one of the large New 
 England cities in 1872, and the same was constructed with the 
 exception of the high service reservoir, in the two following 
 seasons. 
 
 514. Stand-Pipes. Several of the American cities, 
 whose reservoirs are distant from their pumping stations, 
 have placed a stand-pipe upon their force-main, to equalize 
 the resistance against the pumps, as in St. Louis, Louis- 
 ville, and Milwaukee. Other cities use tall open-topped 
 stand-pipes without reservoirs, when no proper site for a 
 reservoir is readily attainable, as at Chicago and Toledo. 
 
 All the American stand-pipes now in use are of the 
 
FRICTIONAL HEADS IN SERVICE PIPES. 527 
 
 single leg class. The city of Sandusky, Ohio, has now 
 (Nov. 1876) in process of construction a tank stand-pipe of 
 25 feet diameter and 208 feet height, surrounding a delivery 
 stand-pipe of 3 feet diameter and 225 feet height. This 
 tank is being built up of riveted metal plates, from designs 
 by J. D. Cook, Esq., chief engineer. In Europe, the stand- 
 pipes are more frequently double-legged, with connections 
 between the up and down legs at intervals of height. 
 
 The stand-pipes as generally used, serve as partial sub- 
 stitutes for relief- valves combined or acting in conjunction 
 with tall and capacious air-chambers. The surface of the 
 water in the stand-pipes vibrates up and down according to 
 the rate of delivery into them from the pumps, and the rate 
 of draught, if the main over which they are placed is con- 
 nected with the distribution. In northern cities it is neces- 
 sary that they be housed and protected from frost. 
 
 The Boston Highlands Stand-pipe (page 161) stands 
 upon an eminence 158 feet above tide, is of wrought-iron, 
 and is 80 feet high, and 5 feet interior diameter. It is 
 inclosed in a masonry tower. 
 
 The Milwaukee stand-pipe (page 25) rises to 210 feet 
 above Lake Michigan, and the Toledo stand-pipe (page 31) 
 to 260 feet above Maumee River. 
 
 515. Frictional Heads in Service-Pipes. The fol- 
 lowing shows the frictional head in clean, smooth service- 
 pipes, with given velocities, for each one-hundred feet length. 
 
 The numbers of the first column are the given velocities, 
 in feet per second. The second column gives the head, 
 which is necessary to generate the given velocities opposite. 
 
 In the first column, under each of the given diameters 
 from J inch to 4 inches, is the volume of flow, at its given 
 velocity ; in the next column the corresponding coefficient 
 of friction ; and in the next column the frictional head per 
 each one hundred feet length at its given velocity. 
 
528 
 
 DISTRIBUTION SYSTEMS, AND APPENDAGES, 
 
 TABLE No. 1O8. 
 FRICTIONAL HEAD IN SERVICE PIPES* (in each 100 feet length), 
 
 1 
 
 
 Y 2 IN. DIAMETER 
 
 % IN. DIAMETER. 
 
 I IN. DIAMETER. 
 
 lYz IN. DIAMETER. 
 
 ll 
 
 1. 
 SI 
 
 If 
 
 I 
 
 13 
 
 a > 
 
 11 
 
 "a 
 
 1. 
 
 If 
 
 g 
 
 1-d 
 
 || 
 
 1 
 
 1 . 
 
 'Is 
 
 |a 
 
 2l 
 
 i 
 
 2 12 
 
 ll 
 
 1 
 
 11 
 
 g! 
 
 | 
 
 
 |a 
 
 o 
 
 1 
 
 11 
 
 1* 
 
 > 
 
 31 
 
 j 
 
 
 
 h 
 
 o 
 
 O 
 
 gj 
 
 si 
 
 a 
 
 fa 
 
 si 
 
 I 
 
 E* 
 
 
 , 
 
 
 
 Feet. 
 
 r 
 
 
 Feet. 
 
 / 
 
 
 Feet. 
 
 / 
 
 
 Feet. 
 
 Xf 
 
 .030 
 .040 
 
 .0115 
 .01^0 
 
 .00992 
 .00942 
 
 2.899 
 3.502 
 
 .0257 
 .0294 
 
 .00930 
 .00890 
 
 1.812 
 
 2.265, 
 
 .0458 
 
 5 2 3 
 
 .00882 
 .00854 
 
 1.289, 
 1.636 
 
 .1030 
 .1178 
 
 .00843 
 .00823 
 
 .821 
 .955 
 
 1.8 
 
 .050 .0147 
 
 .00900 
 
 k.3kk 
 
 033 1 
 
 .00856 
 
 2.756 
 
 .0589 
 
 .00830 
 
 2.005 
 
 .1325 
 
 .00806 
 
 1.268 
 
 2.O 
 
 .062 
 
 .0164 
 
 .00862 
 
 8.136 
 
 .0368 
 
 .00830 
 
 3.m 
 
 .0654 
 
 .00810 
 
 2.kl6 
 
 .1472 
 
 .00790 
 
 1.570 
 
 2.2 
 
 .075 
 
 .0180 
 
 .00845 
 
 6.091 
 
 .0405 
 
 .00811 
 
 &.902 
 
 .0719 
 
 .00790 
 
 2.851 
 
 .1619 
 
 .00775 
 
 1.86k 
 
 2.4 
 
 .090 
 
 .0196 
 
 .00810 
 
 6.950 
 
 .0442 
 
 .00792 
 
 k.53k 
 
 .0785 
 
 .00773 
 
 3.320 
 
 .1766 
 
 .00760 
 
 2,175 
 
 2.6 
 
 .105 
 
 .0213 
 
 .00788 
 
 7.935 
 
 .0478 
 
 .00773 
 
 5.193 
 
 .0850 
 
 .00758 
 
 3.821 
 
 .1914 
 
 .00745 
 
 2.520 
 
 2.8 
 
 .122 
 
 .0229 
 
 .00770 
 
 8.993 
 
 0515 
 
 .00756 
 
 5.891 
 
 .0916 
 
 
 k.356 
 
 .2061 
 
 .00730 
 
 2.8kk 
 
 3 
 
 .140 
 
 .0246 
 
 .00753 
 
 10.07 
 
 055 2 
 
 00745 
 
 6.66k 
 
 .0981 
 
 .00734 
 
 k.926 
 
 .2209 
 
 .00722 
 
 3229 
 
 3- 2 
 
 ,l6o .0262 
 
 00745 
 
 11.36 
 
 .0589 
 
 00737 
 
 7.501 
 
 .1046 
 
 .00726 
 
 5.5kk 
 
 .2356 
 
 .00714 
 
 3.63k 
 
 3.4 
 
 .180 .0278 
 
 .00736 
 
 12.67 
 
 .0626 
 
 .00729 
 
 8.337 
 
 .1112 
 
 .00720 
 
 6.207 
 
 .2503 
 
 .00706 
 
 k.05t> 
 
 3-6 
 
 .202 
 
 .0295 
 
 .00729 
 
 lk.01 
 
 .0662 
 
 .00718 
 
 9.038 
 
 JI 77, 
 
 .00714 
 
 6.900 
 
 .2651 
 
 .00700 
 
 k.509 
 
 3-8 
 
 .225 
 
 .0311 
 
 .00726 
 
 15.62 
 
 .0699 
 
 .00714 
 
 10.25 
 
 I2 43 
 
 .00708 
 
 7.62k 
 
 .2 79 8 
 
 .00696 
 
 k.99k 
 
 4.0 
 4.2 
 
 .250 
 .275 
 
 .0328 
 344 
 
 .00722 
 .00719 
 
 17.21 
 18.89 
 
 .0736 
 0773 
 
 .00710 
 .00706 
 
 11.29 
 12.38 
 
 1309 
 
 .00702 
 .00698 
 
 8.376 
 9.182 
 
 2945 
 .3092 
 
 .00692 
 .00687 
 
 5.502 
 6.022 
 
 4.4 
 
 .302 
 
 .0360 
 
 .00715 
 
 20.62 
 
 .0810 
 
 .00702 
 
 13.51 
 
 1440 
 
 .00694 ! 10.02 
 
 3239 
 
 .00683 
 
 6.571 
 
 4.6 
 
 33 
 
 0377 
 
 .00711 
 
 22.kl 
 
 .0846 
 
 .00699 
 
 lk.70 
 
 1505 
 
 .00691 10.90 
 
 .3387 
 
 .00680 
 
 7.1k9 
 
 4.8 
 
 .360 
 
 0393 
 
 .00708 
 
 2k.30 
 
 .0883 
 
 .00696 
 
 15.9k 
 
 
 .00687 11.80 
 
 3534 
 
 .00677 
 
 7.751 
 
 5- 
 
 39 
 
 .0410 
 
 .00704 
 
 26.22 
 
 '.0920 
 
 .00693 
 
 17.22 
 
 1636 
 
 .00684 12.75 
 
 .3681 
 
 .00675 
 
 8.386 
 
 5-2 
 
 .422 
 
 .0426 
 
 .00701 
 
 28.2k 
 
 .0957 
 
 .00689 
 
 18.52 
 
 1701 
 
 .00681 13.73 
 
 .3828 
 
 .00671 
 
 9.017 
 
 5-4 
 
 455 
 
 .0442 
 
 .00698 
 
 30.32 , 
 
 0993 
 
 .00686 
 
 19.88 
 
 1767 
 
 00678 lk.7k 
 
 3975 
 
 .00668! 9.680 
 
 5-6 
 
 49 
 
 0459 
 
 .00695 
 
 32.k7 f 
 
 .1030 
 
 .00683 
 
 21.29 
 
 1832 
 
 .00675 15.79 
 
 .4123 
 
 .00665 
 
 10.37 
 
 5.8 
 
 
 0475 
 
 .00692 
 
 3k.76 
 
 .1067 
 
 .00680 
 
 22.7k 
 
 1898 
 
 .00672 16.86 
 
 .4270 
 
 .00662 
 
 11.07 
 
 6.0 
 
 '.562 
 
 .0492 
 
 .00689 
 
 36.315 
 
 .1104 
 
 .00678 
 
 2k.26 
 
 1963 
 
 .00670 
 
 17.99 
 
 .4417 
 
 .00660 
 
 11.81 
 
 6.2 
 
 .600 
 
 .0508 
 
 .00686 
 
 39.88 
 
 .1141 
 
 .00675 
 
 25.79 
 
 2028 
 
 .00667 
 
 19.12 
 
 .4564 
 
 .00657 
 
 12.55 
 
 6.4 
 
 .640 
 
 .0524 
 
 .00683 
 
 kli67 
 
 .1177 
 
 .00672 
 
 27.35 
 
 2094 
 
 .00664 20.28 
 
 47" 
 
 .00654 
 
 13.31 
 
 6.6 
 
 .680 
 
 .0541 
 
 .00681 
 
 U.09 
 
 .1214 
 
 .00669 
 
 28.96 
 
 2159 
 
 .00661 21.k7 
 
 4859 
 
 .00652; lk.ll 
 
 6.8 
 
 .722 
 
 0557 
 
 .00678 
 
 lfi.70 
 
 .1251 
 
 .00666 
 
 30.61 
 
 2225 
 
 .00659 2S-7* 
 
 .5006 
 
 .00650 
 
 lk.9k 
 
 7.0 
 
 765 
 
 0574 
 
 .00675 
 
 1,9.27 
 
 .1288 
 
 .00664 
 
 32.3k 
 
 2291 
 
 .00657 
 
 2k.01 
 
 5153 
 
 .00648 
 
 15.78 
 
 * This table does not include the resistances of the stop-cocks and short 
 bends in service pipes. Such resistances, as services are usually laid, reduce 
 the effective delivery of water fully fifty per cent. 
 
 jfli.. oc^-^- 7 
 
 X 
 
FRICTIONAL HEAD IN SERVICE PIPES. 
 
 529 
 
 TABLE No. 1 O 8 (Continued). 
 FRICTIONAL HEAD IN SERVICE PIPES (in each 100 feet length). 
 
 1 
 
 
 1% IN. DIAMETER. 
 
 2 IN. DIAMETER. 
 
 3 IN. DIAMETER. 
 
 4 IN. DIAMETER. 
 
 =_ 
 
 *o *- 
 
 2s. 
 
 |.a 
 
 bic feet 
 minute. 
 
 i 
 
 1l 
 
 11 
 
 .2 
 
 li 
 
 ibicfeet 
 minute. 
 
 "a 
 & 
 
 3 
 -I'S 
 
 tsj 
 
 ibic feet 
 minute. 
 
 9t 
 
 '5 
 
 1| 
 
 33 * 
 
 V 
 
 ul 
 
 1 
 
 ir 
 
 38 
 
 a 
 
 
 
 U 
 
 
 
 O 
 
 C*" 
 
 
 
 l 
 
 O 
 
 2T 
 
 
 
 
 
 Feet. 
 
 
 
 Feet. 
 
 
 
 Feet. 
 
 
 
 Feet. 
 
 1.4 
 
 .030 
 
 1.403 .00800 
 
 .668 
 
 1.875 
 
 .00763 
 
 .557 
 
 4- "3 
 
 .00724 
 
 .353 
 
 7.330 .00697 
 
 .255 
 
 1.6 
 1.8 
 
 .040 
 
 .050 
 
 1.603! .00786 
 1.804' -00769 
 
 .857 2.142 
 1.062 2.410 
 
 .00750 
 .00741 
 
 .715 
 .895 
 
 4.712 
 5-301 
 
 .00716 
 .00708 
 
 .456 
 .570 
 
 8-377 
 9-424 
 
 .00690 .SkSf 
 . 00684! .415 
 
 2.0 
 
 .062 
 
 2.004 -00757 
 
 1.290 2.678 
 
 .00731 
 
 1.090 
 
 5.891 
 
 .00700 
 
 .696 
 
 
 .00678 .505 
 
 2.2 
 
 .075 
 
 2.204 .00745 
 
 1.536 
 
 2.046 
 
 .00724 
 
 1.306 
 
 6.480 
 
 .00693 
 
 .833 
 
 11.52 
 
 .00672 
 
 .606 
 
 2.4 
 
 .090 
 
 2.405 .00733 
 
 1.799 3.214 
 
 .00717 
 
 1.539 
 
 7.069 
 
 .00687 
 
 .983 
 
 12.56 
 
 .00666 
 
 .715 
 
 2.6 
 
 .105 
 
 2.605 .00723 
 
 2.083 3.481 
 
 .00711 
 
 1.791 
 
 7.685 
 
 .00681 
 
 l.lkk 
 
 13.61 
 
 .00660 
 
 .839 
 
 2.8 
 
 3' 
 
 .122 
 .140 
 
 2.806 .00713 
 3.006 .00707 
 
 f Jftfj 3.794 
 2.711 4-018 
 
 .00704 
 .00692 
 
 2.057 
 I4WJ 
 
 8.247 
 8.846 
 
 .00675 
 .00670 
 
 1.315 
 1.498 
 
 14.66 
 15-71 
 
 .00655 
 .00650 
 
 .957 
 1.090 
 
 3-2 
 
 .l6o 
 
 3.206 .00700 
 
 3.05k 4.286 
 
 .00686 
 
 2.618 
 
 9-435 
 
 .00665 
 
 1.692 
 
 16.76 
 
 .00645 
 
 1.231 
 
 3.4 
 
 .ISO 
 
 3-407 
 
 .00604 
 
 3.418 4.554 
 
 .00681 
 
 2.934 
 
 10.02 
 
 .00661 
 
 1.899 
 
 17.80 
 
 .00641 
 
 1.381 
 
 3.6 
 
 .202 
 
 3.607 .00688 
 
 3.799 4.821 
 
 .00677 
 
 3.270 10.61 
 
 00657 
 
 .117 
 
 18.85 
 
 .00637 
 
 1.538 
 
 3.8 
 
 .225 
 
 3.808 .00685 
 
 4.215 5.089 
 
 .00674 
 
 3.628 
 
 IT. 20 
 
 .00654 
 
 2.347! 19.90 
 
 .00634 
 
 1.706 
 
 4.0 
 
 4-2 
 
 4-4 
 
 .250 
 275 
 .302 
 
 4.008 
 4.208 
 4.409 
 
 .00682 
 .00678 
 .00674 
 
 4.649 5.357 
 5.096 5.625 
 5.560 5.893 
 
 .00671 
 .00667 
 .00663 
 
 4.002 11.78 
 4.385: 12.37 
 4.784 12.96 
 
 .00651 
 .00647 
 .00644 
 
 2.588 
 2.836 
 3.098 
 
 20.94 
 21.99 
 23.03 
 
 .00631 
 .00628 
 .00625 
 
 1.889 
 2.065 
 2.255 
 
 4.6 
 
 33 
 
 ! 4.609 
 
 .00670 
 
 6.040J 6.160 
 
 .00660 
 
 5.205 13.55 
 
 .00641 
 
 3.370 
 
 24.08 
 
 .00623 
 
 2.457 
 
 4.8 
 5.0 
 
 .360 
 .39 
 
 4.810 
 5.010 
 
 .00667 
 .00664 
 
 6.5471 6.428 
 6.7391 6.696 
 
 .00657 
 .00654 
 
 5.643 14.14 
 6.0941 14.73 
 
 .00638 
 .00636 
 
 3.653 
 3.951 
 
 33 
 
 .00620 
 .00618 
 
 2.662 
 2.880 
 
 5.2 
 
 .422 
 
 5.210 
 
 .00661 
 
 7.615: 6.064 
 
 .00651 
 
 6.561 
 
 15-32 
 
 .00633 
 
 4.253 
 
 27.23 
 
 .00615 
 
 3.099 
 
 5-4 
 5-6 
 
 455 
 .490 
 
 525 
 
 5-4" 
 5.611 
 5.812 
 
 .00658 8.175 7.232 
 .00655! 8.751 7.499 
 .00652 9.345 7.767 
 
 .00648 
 .00645 
 .00642 
 
 7.059 
 7.527 
 8.049 
 
 15-9I 
 16.50 
 17.09 
 
 .00630 
 .00627 
 .00624 
 
 4.565 
 4:886 
 5.167 
 
 28.27 
 30.32 
 30-37 
 
 .00612 3.326 
 .00609' 3.559 
 .00607 3.816 
 
 6.0 
 
 .562 
 
 6.012 
 
 .00650 9.970 8.035 
 
 .00640 
 
 8.587! 17.67 
 
 .00622 
 
 5.56k 
 
 
 .00605 
 
 4.059 
 
 6.2 
 
 .600 
 
 6.212 
 
 .00647 10.59 
 
 8.303 
 
 .00637 
 
 9.126 18.25 
 
 .00619 
 
 5.912 32.46 
 
 .00603 
 
 4.320 
 
 6.4 
 
 .640 
 
 6.413 
 
 .00645! 11.26 
 
 8,571 
 
 .00635 
 
 9.694 18.85 
 
 .00616 
 
 ejn 
 
 33-50 
 
 .00601 
 
 4.588 
 
 6.6 
 6.8 
 
 .680 
 .722 
 
 6.613 
 6.8l4 
 
 .00643' 11-93 
 .00641 12.63 
 
 8.838 
 9.I06 
 
 .00633 
 .00631 
 
 10.28 
 10.88 
 
 19.44 
 20.03 
 
 .00614 
 .00612 
 
 6646 
 7.032 
 
 34-55 
 35-6o 
 
 .00599 4.863 
 .00597 5.145 
 
 7.0 
 
 .765 
 
 7.014 
 
 .00639 
 
 13.34 
 
 9-374 
 
 .00629 
 
 11.49 
 
 20.62 
 
 .00610 
 
 7.427 
 
 36-65 
 
 .00595 5.310 
 
 34 
 
CHAPTER XXIII. 
 
 CLARIFICATION OF WATER. 
 
 516. Rarity of Clear Waters. A small but favored 
 minority of the American cities have the good fortune to 
 find an abundant supply of water for their domestic pur- 
 poses, within their reach, that remains in a desirable state 
 of transparency and limpidity. 
 
 The origin and character of the impurities that are 
 almost universally found in ^suspension in large bodies of 
 water, have been already discussed in the chapters devoted 
 to " Impurities of Water" (Chap. VIII), and to " Supplies 
 from Lakes and Rivers" (Chap. IX) ; so there remains now 
 for investigation only the methods of separating the foreign 
 matters before pointed out. 
 
 517. Floating Debris, The running rivers, that are 
 subject to floods, bring down all manner of floating debris, 
 from the fine meadow grasses to huge tree-trunks, and 
 buildings entire. These are all visible matters, that remain 
 upon the surface of the water, and their separation is 
 accomplished by the most simple mechanical devices. 
 
 Coarse and fine racks of iron, and fine screens of woven 
 copper wire are effectual intercepters of such matters and 
 prevent their entrance into artificial water conduits. 
 
 518. Mineral Sediments. Next among the visible 
 sediments may be classed the gravelly pebbles, sand, disin- 
 tegrated rock, and loam, that the eddy motions continually 
 
ORGANIC SEDIMENTS. 531 
 
 toss up from the channel bottom, and the current bears 
 forward. 
 
 These are not intercepted by ordinary screens, but are 
 most easily separated from the water by allowing them 
 quickly to deposit themselves, in obedience to the law of 
 gravitation, in a basin where the waters can remain quietly 
 at rest for a time. 
 
 When the water is received into large storage reservoirs, 
 it is soon relieved of these heavy sedimentary matters, by 
 deposition ; and a season of quietude, even though but a few 
 hours in duration, is a valuable preparation for succeeding 
 stages of clarification. 
 
 Next are more subtle mineral impurities, consisting of 
 the most minute particles of sand and finely comminuted 
 clay, which consume a fortnight or more, while the water is 
 at rest, in a confining basin, in their leisurely meanderings 
 toward the bed of the basin. 
 
 If these mineral grains are to be removed by subsidence 
 for a public water supply, the subsidence basin must 
 usually be large enough to hold a three- weeks supply, and 
 must be narrow and deep, so the winds will stir up but a 
 comparatively thin surface stratum, and also so the exposed 
 water will not be heated unduly in midsummer. 
 
 519. Organic Sediments. Next are the organic frag- 
 ments, including the disintegrating seeds, leaves, and stalks 
 of plants, the legs and trunks of insects and Crustacea, and 
 the macerated refuse from the mills. 
 
 All these have so nearly the same specific gravity as the 
 water, that they remain in suspension until decomposition 
 has removed so much of their volatile natures that the 
 mineral residues can finally gravitate to the bottom. 
 
 If these are to be removed by subsidence, the basin must 
 hold several months supply, at least, and be so formed 
 
532 CLAKIFICATION OF WATER. 
 
 and protected as to neither generate or receive other im- 
 purities. 
 
 In addition, are the innumerable throngs of living 
 creatures that people the ponds and streams, and their 
 spawns. These cannot be removed by subsidence during 
 their active existence, and reproduction maintains always 
 their numbers good. 
 
 520. Organic Solutions. Still more subtle than all 
 the above impurities, that remain in suspension, are the 
 dissolved organic matters that the water takes into solution. 
 These include the dissolved remains of animate creatures, 
 dissolved fertilizers, and dissolved sewage. 
 
 All the former may be treated mechanically with toler- 
 able success, but the latter pass through the finest filters 
 and yield only to chemical transformations. 
 
 521. Natural Processes of Clarification. Nature's 
 process for removing all these impurities, to fit the water 
 for the use of animals, is to pass them through the pores of 
 the soil and fissures of the rocks. The soil at once removes 
 the matters in suspension, and they become food for the 
 plants that grow upon the soil, and are by the plants recon- 
 verted into their original elements. The minerals of the 
 soil reconvert the organic matters in solution into other 
 combinations and separate them from the water. 
 
 522. Chemical Processes of Clarification. Arti- 
 ficial chemical processes, more or less successful in their 
 action, have been employed from the remotest ages to sep- 
 arate quickly the fine earthy matters from the waters of 
 running streams. The dwellers on the banks of streams, 
 who had no other water supply, treated them, each for 
 themselves, and in like manner have others treated the rain 
 waters which they caught upon their roofs, when they had 
 no other domestic supplies. 
 
PROCESSES OF CLARIFICATION. 533 
 
 Many centuries ago the Egyptians and Indians had dis- 
 covered that certain bitter vegetable substances which grew 
 around them were capable of hastening the clarification of 
 the waters of the Nile, Ganges, Indus, and other sediment- 
 ary streams of their countries. 
 
 The Canadians have long been accustomed to purify 
 rain-water by introducing powdered alum and borax, in 
 the proportions of 3 ounces of each to one barrel (31 J- gals.) 
 of water ; and alum is used by dwellers on the banks of 
 the muddy Mississippi to precipitate its clay. Arago ob- 
 served also the prompt action of alum upon the muddy 
 water of the Seine. One part of a solution of alum in fifty 
 thousand parts of water results in the production of a floc- 
 culent precipitate, which carries down the clayey and 
 organic matters in suspension, leaving the water perfectly 
 -clear. 
 
 Dr. Gunning demonstrated by many experiments that 
 the impure waters of the river Mans, near Rotterdam, could 
 be fully clarified and rendered fit for the domestic supply 
 of the city, by the introduction of .032 gramme of per- 
 chloride of iron into one liter of the water. The waters of 
 the Maas are very turbid and contain large proportions of 
 organic matter, and they often produce in those visitors who 
 -are not accustomed to their use, diarrhoeas, with other un- 
 pleasant symptoms. 
 
 Dr. Bischoff, Jr., patented in England, in 1871, a process 
 of removing organic matter from water by using a filter of 
 spongy iron, prepared by heating hydrated oxide of iron 
 with carbon. The water is said to be quite perceptibly 
 impregnated with iron by this process, and a copious pre- 
 cipitate of the hydrated oxide of iron to be afterwards 
 separated. 
 
 Horsley's patent process for the purification of water 
 
534 CLARIFICATION OF WATER. 
 
 covers the use of oxalate of potassa, and Clark's the use of 
 caustic lime. 
 
 Mr. Spencer has used in England with great success, in 
 connection with sand filtration, the crushed grains of a car- 
 bide of iron, prepared by roasting red hematite ore, mixed 
 with an equal part of sawdust, in an iron retort. This he 
 mixes with one of the lower sand strata of a sand filter, and 
 its office is to decompose the organic matters in solution in 
 the water. The carbide is said to perform its office thor- 
 oughly several years in succession without renewal. Mr. 
 Spencer's process may be applied on a scale commensurate 
 with the wants of the largest cities, and has been adopted 
 in several of the cities of Great Britain. 
 
 Dr. Medlock was requested by the Water Company of 
 Amsterdam to examine the water gathered by them from 
 the Dunes near Haarlem, for delivery in the city. The 
 water had a peculiar " fish-like" odor, and after standing 
 awhile, deposited a reddish-brown sediment. 
 
 Under the microscope, the deposit was seen to consist of 
 the filaments of decaying algse, confervse, and other micro- 
 scopic plants, of various hues, from green through pale- 
 yellow, orange, red, brown, dark-brown, to black. 
 
 The Doctor found the open water channels lined with a 
 luxuriant growth of aquatic plants, and the channel-bed 
 covered with a deposit of black decaying vegetal matter. 
 He discovered also that the reddish-brown sediment was- 
 deposited in greatest abundance about the iron sluice-gates. 
 Copper, platinum, and lead, in finely-divided states, were 
 known by him to have the power of converting ammonia 
 into nitrous acid, and he was led to suspect that iron pos- 
 sessed the same power. Experiments with iron in various 
 states, and finally with sheet-iron, demonstrated that strips 
 of iron placed in water containing ammonia, or organic 
 
CHARCOAL PROCESS. 535 
 
 matter capable of yielding it, acted almost as energetically 
 as the pulverized metal. The organic matters of the Thames 
 water in London, and the Rivington Pike water in Liver- 
 pool, as well as the Dune water in Amsterdam, were found 
 to be completely decomposed or thrown down by contact 
 with iron, and the iron acted effectually when introduced 
 into the water in strips of the sheet metal or in coils of wire. 
 This simple and easy use of iron may be employed in sub- 
 sidence basins or reservoirs on the largest scale for towns, 
 as well as on a smaller scale for a single family. 
 
 The results of these experiments with iron were consid- 
 ered of such great hygienic and national importance by Dr. 
 Sheridan Muspratt that he has put an extended account of 
 them on record.* 
 
 523. Charcoal Process. The charcoal plate niters 
 prepared under the patent of Messrs. F. H. Atkins & Co., 
 of London, have not been introduced here as yet, so far as 
 the writer is informed. 
 
 The valuable chemical and mechanical properties of 
 animal charcoal for the purification of water have long been 
 recognized, and it was the practice in the construction of the 
 early English filter-beds, as prepared by Mr. Thorn, to mix 
 powdered charcoal with the fine sand. 
 
 If there is either lime or iron in the water, as there is in 
 most waters, the chemical action results in the formation of 
 an insoluble precipitate upon the grains of charcoal, when 
 they become of no more value than sand, and their action 
 is thenceforth only mechanical. Messrs. Atkins & Co. have 
 devised a method of overcoming this difficulty, in part at 
 least, by forming the charcoal into plates, usually one foot 
 square and three inches thick, and so firm that their coated 
 surfaces can be scraped clean. These plates may be set in 
 
 * Muspratt's Chemistry, p. 1085, Vol. II. 
 
536 
 
 CLARIFICATION OF WATER 
 FIG. 129. 
 
 CHARCOAL-PLATE FILTERS. 
 
 frames, Fig. 129, as lights of glass are set in a sash, and the 
 water be made to flow through them. They are compound- 
 ed for either slow or quick filtration ; the detise plates (a 
 square foot) passing 30 to 40 imperial gallons per diem, the 
 porous 80 to 100 gallons, and the very porous 250 to 300 
 gallons per diem, when clean. The water may be first 
 passed through sand, for the removal of the greater part of 
 the organic matters. 
 
 The use of charcoal has heretofore been confined almost 
 entirely to the laboratory, so far as relates to the purifica- 
 tion of water, and animal charcoal has been found very 
 much superior to wood and peat coals. Its success has 
 undoubtedly been due largely to its intermittent use and 
 frequent cleanings and opportunities for oxidation. Its 
 power of chemical action upon organic matter is very 
 quickly reduced, and it must be often cleaned to be 
 
INFILTRATION BASINS. 
 
 effectual. Some very interesting and valuable experiments 
 to test the purification powers of charcoal upon foul waters, 
 were described to the members of the Institution of Civil 
 Engineers, by Edward Byrne, in May, 1867. 
 
 524:. Infiltration. If any water intended for a do- 
 mestic supply is found to be charged with organic matter 
 in solution, the very best plan of treatment, relating to that 
 water, is to let it alone, and take the required supply from 
 a purer source. 
 
 The impurities in suspension in water may best be 
 treated on Nature's plan, by which she provides us with the 
 sparkling limpid waters of the springs that bubble at the 
 bases of the hills and from the fissures in the rocks. 
 
 525. Infiltration Basins. In the most simple natural 
 plan of clarification, a well, or basin, or gallery, is excavated 
 in the porous margin of a lake or stream, down to a level 
 below the water surface, where the water supply will be 
 maintained by infiltration. 
 
 All those streams that have their sources in the mount- 
 ains, and that flow through the drift formation, transport in 
 flood large quantities of coarse sand and the lesser gravel 
 pebbles. These are deposited in beds in the convex sides 
 of the river bends, and the finer sands are spread upon them 
 as the floods subside. From these beds may be obtained 
 supplies of water of remarkable clearness and transparency. 
 
 The volume of water to be obtained from such sources 
 depends, first, upon the porosity of the sand or gravel be- 
 tween the well, basin, or gallery, and the main body of 
 water, the distance of percolation required, the infiltration 
 area of the well or gallery, and the head of water under 
 which the infiltration is maintained. 
 
 A considerable number of American towns and cities 
 have already adopted the infiltration system of clarification 
 
538 CLARIFICATION OF WATER. 
 
 of their public water supplies, and although it is not one 
 that can be universally applied, it should and will meet 
 with favor wherever the local circumstances invite its use. 
 Attention has not as yet become fairly attracted in America 
 to the benefits and the necessities of filtration of domestic 
 water supplies, and many of the young cities have been 
 obliged to make an herculean effort to secure a public water 
 supply, having even the requisite of abundance, and they 
 have been obliged to defer to days of greater financial 
 strength the additional requisite of clarification. A knowl- 
 edge of the processes of clarification, which are simple for 
 most waters, is being gradually diffused, and this is a sure 
 precursor of the more general acceptance of its benefits. 
 
 In some of the small western and middle State towns, 
 the infiltration basins have heretofore taken the form of one 
 or more circular wells, each of as large magnitude as can 
 be economically roofed over, or of narrow open basins. In 
 the eastern States the form has usually been that of a cov- 
 ered gallery along the margin of the stream or lake, or of a 
 broad open basin. Some of these basins are intended quite 
 as much to intercept the flow of water from the land side 
 toward the river as to draw their supplies from the river, 
 and the prevailing temperatures and chemical analyses of 
 the waters, as compared with the temperatures and analyses 
 of the river waters, give evidence that their supplies are in 
 part from the land. 
 
 A thorough examination of the substrata, on the site of 
 and in the vicinity of the proposed infiltration basin, down 
 to a level eight or ten feet below the bottom of the basin, 
 will permit an intelligent opinion to be formed of its percola- 
 tion capacity. 
 
 526. Examples of Infiltration. Pig. 130 illustrates 
 a section of the infiltration gallery at Lowell, Mass. This 
 
EXAMPLES OF INFILTRATION. 
 
 539 
 
 gallery is a short distance above the city and above the 
 dam of the Locks and Canal Co. in the Merrimac River, 
 that supplies some 10,000 horse-power to the manufacturers 
 of the city. The gallery is on the northerly shore of the 
 stream, parallel with it, and lies about one hundred feet 
 from the shore. 
 
 Its length is 1300 feet, width 8 feet, and clear inside 
 height, 8 feet. Its floor is eight feet below the level of the 
 crest of the dam. The side walls have an average thickness 
 of two and three-fourths feet, and a height of five feet, and 
 are constructed of heavy rubble masonry, laid water-tight 
 in hydraulic mortar. 
 
 LOWELL INFILTRATION GALLERY. 
 
 The covering arch is semicircular, of brick, one foot 
 thick, and is laid water-tight in cement mortar. 
 
 Along the bottom, at distances of ten feet between 
 centres, stone braces one foot square and eight feet long, 
 are placed transversely between the side walls to resist the 
 exterior thrust of the earth and the hydrostatic pressure. 
 
540 CLARIFICATION OF WATER. 
 
 The bottom is covered with coarse screened gravel, one foot 
 thick, up to the level of the top of the brace stones. 
 
 The required depth of excavation from the surface of the 
 plain averaged about sixteen feet. 
 
 The Merrimac Kiver is tolerably clear of visible impuri- 
 ties during a large portion of the year, but during high- 
 water carries a large quantity of clay and of a silicious sand 
 of very minute, microscopic grains. 
 
 An inlet pipe, thirty inches in diameter, connects the 
 lower end of the gallery directly with the river, for use in 
 emergencies, and to supplement the supply temporarily at 
 low- water in the river, when it is usually clear. At the ter- 
 minal chamber of the gallery into which the inlet pipe leads, 
 and from which the conduit leads toward the pumps, are 
 the requisite regulating gates and screens. 
 
 This gallery was completed in 1871, and during the 
 drought and low water of the summer of 1873, a test devel- 
 oped the continuous infiltration capacity of the gallery to 
 be one and one-half million gallons per twenty-four hours, 
 or about one hundred and fifty gallons for each square foot 
 of bottom area per twenty-four hours. 
 
 At Lawrence, Mass., is a similar infiltration gallery along 
 the eastern shore of the Merrimac Kiver, from which the 
 city's supply is at present drawn. 
 
 The infiltration gallery for the supply of the town of 
 Brookline, Mass., completed in 1874, lies near the margin 
 of the Charles River. The bottom is six feet below the 
 lowest stage of water in the river, its breadth between walls 
 four feet, and length seven hundred and sixty-two feet. The 
 side walls are two feet high, laid without mortar, and the 
 covering arch is semicircular, two courses thick, and tight. 
 
 During a pump test of thirty-six hours duration, this 
 gallery supplied water at a rate of one and one-half million 
 
EXAMPLES OF INFILTRATION. 541 
 
 gallons in twenty-four hours, or four hundred and ninety 
 gallons per square foot of bottom area per twenty-four 
 hours. The ordinary draught up to the present writing is 
 about one-third this rate. 
 
 The pioneer American infiltration basins were constructed 
 for the city of Newark, N. J., under the direction of Mr. 
 Geo. H. Bailey, chief engineer of the Newark water-works. 
 These basins are somewhat more than a mile above the 
 city, on the bank of the Passaic River. There are two 
 basins, each 350 feet long and 150 feet wide, distant about 
 200 feet from the river. They are revetted with excellent 
 vertical-faced stone walls, and everything pertaining to 
 them is substantial and neat. An inlet pipe connects them 
 with the river for use as exigencies may require. 
 
 At Waltham, Mass., a basin was excavated from the 
 margin of the Charles Eiver back to some distance, and 
 then a bank of gravel constructed between it and the river, 
 intended to act as a filter. 
 
 The excavation developed a considerable number of 
 springs that flowed up through the bottom of the basin, 
 and these are supposed to furnish a large share of the 
 water supply. 
 
 At Providence, two basins have been excavated, one on 
 each side of the Pawtuxet River. These are near the mar- 
 gin of the River, and are partitioned from the floods by 
 artificial gravelly levees. 
 
 At Hamilton and Toronto, in Canada, basins have been 
 excavated on the border of Lake Ontario. The Hamilton 
 basin has, at the level of low-water in the lake, a water area 
 of little more than one acre. 
 
 At Toronto, the infiltration basin lies along the border 
 of an island in the lake, nearly opposite to the city. It is 
 excavated to a depth of thirteen and one-half feet below 
 
542 CLARIFICATION OF WATER. 
 
 low- water in the lake, has an average bottom width of 26J 
 feet, side slopes 2 to 1, and length, including an arm of 
 390 feet, of 3090 feet. This basin is distant about 150 feet 
 from the lake. 
 
 The top of the draught conduit, which is four feet diam- 
 eter, is placed at six and one-half feet below low-water, or 
 the zero datum of the lake ; and the water area in the basin, 
 if drawn so low as the top of the conduit, will then be 3.75 
 acres, and when full to zero line is 5.64 acres, the average 
 surface width being then eighty feet. 
 
 During a six days test this basin supplied about four 
 and one-quarter million imperial gallons per twenty -four 
 hours under an average head of five feet from the lake, or 
 at the rate of fifty-two imperial gallons per square foot of 
 bottom area per twenty-four hours. 
 
 At Binghamton, 1ST. Y., two wells of thirty feet diameter 
 each, were excavated about 150 feet from the margin of the 
 Susquehanna River, one on each side of the pump-house. 
 These wells are roofed in. 
 
 At Schenectady there is a small gallery along the margin 
 of the Mohawk River. 
 
 Columbus opened her works with a basin on the bank 
 of the Scioto, and has since added a basin with a process 
 of sand filtration. 
 
 Other towns and cities have formed their infiltration 
 basins according to their peculiar local circumstances. 
 
 These basins generally clarify the water in a most satis- 
 factory manner, and accomplish all that can be expected 
 of a mechanical process, but they have not always delivered 
 the expected volumes of water; but perhaps too much is 
 sometimes anticipated through ignorance of the true nature 
 of the soil. 
 
 527. Practical Considerations. The experience with 
 
PRACTICAL CONSIDERATIONS. 543 
 
 the American and European infiltration basins shows that 
 when judiciously located they should supply from 150 to 
 200 U. S. gallons per square foot of bottom area in each 
 twenty-four hours continuously. This requires a rate of 
 motion through the gallery inflow surface, of from twenty 
 to twenty-five lineal feet per twenty-four hours. 
 
 This inflow is dependent largely upon the area of shore 
 surface through which the water tends toward the basin, 
 and the cleanliness and porousness of that surface. 
 
 We have not here the aid of Nature's surface process, in 
 which the intercepted sediment is decomposed by plant 
 action, and the pores thrown open by frost expansions, but 
 are dependent upon floods and littoral currents to clean off 
 the sediment separated from the intiltering water. If the 
 infiltering surface is not so cleaned periodically by currents, 
 it becomes clogged with the sediment, and its capability of 
 passing water is greatly reduced. 
 
 A uniform sized grain of sand or gravel offers greater 
 percolating facilities than mixed coarse and fine grains. 
 The proportion of interstices in uniform grains is from thirty 
 to thirty- three per cent, of the bulk, and the larger the grains 
 the larger the interstices and the more free the flow. On 
 the other hand, the smaller the grains, or the more the ad- 
 mixture of smaller with predominating grains, the smaller 
 the interstices, and the less the flow, but the more thorough 
 the clarification and the sooner the pores are silted with 
 sediment. 
 
 If there is much fine material mixed with the gravel, 
 water will percolate very slowly, and a larger proportional 
 infiltration area will be required to deliver a given volume 
 of water. 
 
 It will be remembered that we found gravel ( 351) with 
 due admixtures of graded fine materials to make the very 
 
544 CLARIFICATION OF WATER. 
 
 "best embankment to retain water, even under fifty or more 
 feet head. 
 
 The best bank in which to locate an infiltration basin is 
 one which is made up of uniform silicious sand grains of 
 about the size used for hydraulic mortar, and which has a 
 thin covering of finer grains next the body of water to be 
 filtered. The silting will in such case be chiefly in the sur- 
 face layer, and the cleaning by flood current then be most 
 effectual. 
 
 The distance of the basin from the body of water is gov- 
 erned by the nature of the materials, being greater in coarse 
 gravel than in sand. It should be only just sufficient to 
 insure thorough clarification when the surface is cleanest. 
 A greater distance necessitates a greater expense for greater 
 basin area to accomplish a given duty, and a lesser distance 
 will not always give thorough clarification. 
 
 The distance should be graduated in a varying stratum, 
 so that the work per unit of area shall be as uniform as 
 possible. 
 
 528. Examples of European Infiltration. Mr. Jas. 
 P. Kirkwood, C.E., in his report* to the Board of Water 
 Commissioners of St. Louis, by whom he was commissioned 
 to examine the filtering processes practised in Europe, as 
 applied to public water supplies, has given most accurate 
 and valuable information, which those who are interested in 
 the subject of filtration will do well to consult. 
 
 From Mr. Kirkwood' s elaborate report we have con- 
 densed some data relating to European infiltration galleries. 
 
 Perth, in Scotland, has a covered gallery located in an 
 island in the River Tay. Its inside width is 4 feet, height 
 8 feet, and length 300 feet. Its floor is 2 j feet below low- 
 water surface in the river. Its capacity is 200,000 gallons 
 
 * Filtration of River Waters, Van Nostrand, New York, 1869. 
 
1 
 EUROPEAN INFILTRATION. 545 
 
 per diem, and rate of infiltration per square foot of bottom 
 area, 182 gallons per diem. 
 
 Angers, in France, has a covered gallery located in an 
 island in the River Loire. This gallery has two angles of 
 slight deflection, dividing it into three sections. The two 
 end sections are 3'-4" wide and the centre section 6-0" wide. 
 The floors of the two end sections are 7 below low- water in 
 the river, and of the central section 9J feet below. The 
 combined length of these galleries is 288 feet, and their de- 
 livery 187 gallons per diem per square foot of bottom area. 
 
 These were constructed in 1856, and rest on a clayey 
 substratum ; consequently the greater part of their inflow- 
 must be through the open side walls. 
 
 More recently, these have been reinforced by a new 
 gallery, with its floor 5J feet below low- water surface in the 
 river, and not extending down to the clay stratum. This is 
 5 feet wide and 8 feet high, and delivers 300 gallons per 
 diem per square foot of bottom area. 
 
 Lyons, in France, has two covered galleries along the 
 banks of the Rhone, the first 16-6" wide and 394 feet long. 
 The second is 33 feet wide, except at a short section in the 
 centre, where it is narrowed to 8 feet, and is 328 feet long. 
 There are also two rectangular covered basins. The com- 
 bined bottom areas of the two galleries is 17,200 square 
 feet, and of the two basins 40,506 square feet. The total 
 delivery at the lowest stage of the river is nearly six mil- 
 lion gallons per diem, or 100 gallons per square foot of 
 bottom area. The capacity of the 33-foot gallery alone is, 
 however, 147 gallons per square foot of bottom area. About 
 6J feet head is required for the delivery of the maximum 
 quantity. The average distance of the galleries from the 
 river is about 80 feet, and the two basins are behind one of 
 the galleries. 
 35 
 
546 CLARIFICATION OF WATER. 
 
 At Toulouse, France, three covered galleries extend 
 along the bank of the Garonne. The first two, after being 
 walled, were filled with small stones. 
 
 The new gallery has its side-walls laid in mortar, is cov- 
 ered with a semicircular arch, is 7-6" wide, 8-8" high, and 
 
 1180 feet long. Its floor is 8'-7" below low- water surface in 
 the river. Its total capacity is a little in excess of 2% mil- 
 lion gallons, or 228 gallons per diem, per square foot of 
 bottom area. 
 
 For the supply of Genoa, in Italy, which lies upon the 
 Mediterranean, a gallery has been constructed, in a valley 
 of a northern slope of the Maritime Alps, at an altitude of 
 
 1181 feet above the sea. This gallery extends in part 
 beneath the bed of the River Scrivia, transversely from side 
 to side, and in part along the banks of the stream. The 
 width is 5 feet, height 7 to 8 feet, and length 1780 feet. 
 
 The extraordinarily large delivery, per lineal foot, is 
 6412 gallons per diem. 
 
 The waters are conveyed down to Genoa in cast-iron 
 pipes, with relieving-tanks at intervals. 
 
 529. Example of Intercepting Well. The great 
 well in Prospect Park, Brooklyn, L. I., is a notable instance 
 of intercepting basin, such as is sometimes adopted to inter- 
 cept the flow of the land waters toward a great valley, or 
 the sea, or to gather the rainfall upon a great area of sandy 
 plain. 
 
 This portion of Long Island is a vast bed of sand, which 
 receives into its interstices a large percentage of the rainfall. 
 The rain-water then percolates through the sand in steady 
 flow toward the ocean. Although the surface of the land 
 has considerable undulation, the subterranean saturation is 
 found to take nearly a true plane of inclination toward the 
 sea, and this inclination is found by measurements in 
 
FILTER-BEDS. 547 
 
 numerous wells to be at the rate of about one foot in 770 ft., 
 or seven feet per mile. So if a well is to be dug at one-half 
 mile from the ocean beach, water is expected to be found 
 at a level about three and one-half feet above mean tide ; 
 or, if one mile from the beach, at seven feet above mean 
 tide, whatever may be the elevation of the land surface. 
 If in such subsoils a well is excavated, and a great draught 
 of water is pumped, the surface of saturation will take its 
 inclination toward the well, and the area of the watershed 
 of the well will extend as the water surface in the well is 
 lowered. If the well has its water surface lowered so as to 
 draw toward it say a share equal to twenty-four inches of 
 the annual rainfall on a circle around it of one-quarter mile 
 radius, then its yield should be at the rate of very nearly 
 one-half million gallons of water daily. 
 
 The Prospect Park well, Fig. 131 (p. 102), is 50 ft. in diam- 
 eter. A brick steen or curb of this diameter, resting upon 
 and bolted to a timber shoe, edged with iron, was sunk by 
 excavating within and beneath it, fifty-nine feet to the sat- 
 uration plane, and then a like curb of thirty -five feet diam- 
 eter was sunk to a further depth of ten feet. The top of the 
 inner curb was finished at the line of water surface. A 
 platform was then constructed a few feet above the water 
 surface, within the large curb, to receive the pumping 
 engine. The boilers were placed in an ornate boiler-house 
 near the well. 
 
 On test trial, the well was found to yield, after the water 
 surface in the well had been drawn down four and one-half 
 feet, at the rate of 850,000 gallons per twenty-four hours. 
 
 53O. Filter-beds. A method of filtration, more arti- 
 ficial than those above described, must in many cases be 
 resorted to for the clarification of public water supplies. 
 
 The most simple of the methods that has had thorough 
 
648 
 
 CLARIFICATION OF WATER. 
 FIG. 132. 
 
 trial, consists in passing the water downward, in an arti- 
 ficial basin specially constructed for the purpose, through 
 layers of fine sand, coarse sand, fine gravel, coarse gravel, 
 and broken stone, to collecting drains placed beneath the 
 whole, Fig. 132. 
 
FILTER-BEDS. 549 
 
 The basins in such cases are usually from 100 to 200 
 feet wide, and from 200 to 300 feet long, each. Each basin 
 is made quite water-tight, the horizontal bottom or floor 
 being puddled, if necessary, and sometimes also covered 
 with a paving of concrete, or layer of bricks in cement 
 mortar. The sides are revetted with masonry, or have 
 slopes paved with substantial stone in mortar, or with 
 concrete. 
 
 A main drain extends longitudinally through the centre 
 of the basin, rests upon the floor, and is about two feet 
 wide and three feet high. From the main drain, on each 
 side, at right-angles, and at distances of about six feet 
 between centres, branch the small drains. These are six or 
 eight inches in diameter, of porous, or, more generally, per- 
 forated clay tiles, resting upon the bottom or floor, and they 
 extend from the central drain to the side walls, where they 
 have vertical, open-topped, ventilating, or air-escape pipes, 
 rising to the top of the side walls. 
 
 These pipes and the central drain form an arterial sys- 
 tem by which water may be gathered uniformly from the 
 whole area of the basin. 
 
 This arterial system is then covered, in horizontal layers, 
 according to the suitable materials available, substantially 
 as follows, viz.: two feet of broken stone, like "road 
 metal ;" one foot of shingle or coarse-screened gravel ; one 
 foot of pea-sized screened gravel ; one foot of coarse sand ; 
 and a top covering of one and one-half to three feet of fine 
 sand. 
 
 This combination is termed a filter-bed, and over it is 
 flowed the water to be clarified. 
 
 Provision is made for flowing on the water so as not to 
 disturb the fine sand surface. This inflow duct is often 
 arranged in the form of a tight channel on the top of the 
 
550 CLARIFICATION OF WATER. 
 
 covering of the central gathering drain, and the water flows 
 over its side walls, during the filling of the "basin, to right 
 and left, with slow motion. 
 
 The depth of water maintained npon the filter-bed is 
 four feet or more, according to exposure and climatic effects 
 upon it. 
 
 At the outflow end of the central gathering drain is an 
 effluent chamber, with a regulating gate over which the 
 filtered water flows into the conduit leading to the clear- 
 water basin. The water in the effluent chamber is connected 
 with the water upon the filter-bed through the drains and 
 interstices of the bed ; consequently, if there is no draught, 
 its surface has the same level as that upon the bed, but if 
 there is draught, the surface in the chamber is lowest, and 
 the difference of level is the head under which water flows 
 through the filter-bed to the effluent chamber. 
 
 The regulating gate in the effluent chamber controls the 
 outflow there to the clarified water basin, and consequently 
 the head under which filtration takes place, and the rate of 
 flow through the filter-bed. 
 
 531. Settling and Clear- water Basins. When the 
 water is received from a river subject to the roil of floods, it 
 should be received first into a settling basin, where it will 
 be at rest forty-eight hours or more, so that as much as 
 possible of the sediment may be separated by the gravity 
 process, before alluded to. Its rest in large storage basins 
 prepares it very fully for introduction to the filter-bed, 
 which is to complete the separation of the microscopic 
 plants, vegetable fibres, and animate organisms, that can- 
 not be separated by precipitation. 
 
 Since the domestic consumption of the water at some 
 hours of the day is nearly or quite double the average con- 
 sumption per diem, the clarified water basin should be 
 
FILTER-BED SYSTEM. 551 
 
 large enough to supply the irregular draught and permit 
 the flow through the niter to be uniform. 
 
 This system of clarification in perfection includes three 
 divisions, viz. : the Settling Basin, the Filter-bed, and the 
 Clear-water Basin. 
 
 The settling and clear- water basins may be constructed 
 according to the methods and principles already discussed 
 for distributing reservoirs (Chap. XYI). The capacity of 
 each should be sufficient to hold not less than two days 
 supply, and the depth of water should be not less than 
 ten feet, so that the water may not be raised to too high 
 a temperature in summer, and that its temperature may 
 be raised somewhat in winter before it enters the distribu- 
 tion-pipes. 
 
 532. Introduction of Filter-bed System. Pough- 
 keepsie, on the Hudson, was the first American city to 
 adopt the filler-bed system of clarification of her public 
 water-supply. 
 
 The Poughkeepsie works were constructed in 1871, to 
 take water from the Hudson Eiver. During the spring 
 floods, the river is quite turbid. These filtering works con- 
 sist of a small settling basin and two filter-beds, each^73^ ft. 
 wide and 200 ft. long. Each bed is composed of 
 
 24 inches of fine sand. 
 
 6 " " -inch gravel. 
 
 6 " " |-inch gravel. 
 
 6 " " i-inch broken stone. 
 
 24 " " 4 to 8-inch spalls. 
 
 72 " total. 
 
 The floors on which the beds rest are of concrete, twelve 
 inches thick. 
 
 The clear- water basin is 28 by 88 feet in plan, and 17 ft. 
 deep. 
 
552 CLARIFICATION OF WATER. 
 
 Water is lifted from the river to the settling basin by a 
 pump, and it flows from the clear-water basin to the suction 
 chamber of the main pump, giving some back pressure. 
 From thence it is pumped to the distributing reservoir. 
 
 The filter-beds are at present used but a portion of the 
 year, subsidence in the main reservoir being sufficient to 
 render the water acceptable to the consumers. 
 
 In the recent construction of the new water supply for 
 the city of Toledo, 20,000 square feet of filter-bed was at 
 first prepared to test its efficiency in the clarification of the 
 turbid Maumee River water. The great demand for water 
 has, however, made the construction of additional filter area 
 and large subsidence basins a necessity, the consumption 
 having already (1876) reached nearly 3,000,000 gallons per 
 diem. Anticipating the necessity, Chief Engineer Cook has 
 devised and is experimenting with a series of chambers, to 
 contain filtering materials through which the water is to be 
 flowed with an upward current. 
 
 When our American water consumers are more familiar 
 with this filter-bed system of clarification, now in such gen- 
 eral use in England and Scotland and on the Continent, its 
 use will be oftener demanded. Subsidence, as we have 
 
 4 
 
 before remarked, does not completely clarify the water, 
 even in a fortnight's or three weeks' time, but a good sand 
 filter, if not overworked, intercepts not only the visible sedi- 
 ment and fine clay, but the most minute vegetable fibres 
 and organisms and the spawn of fish, and it is highly im- 
 portant that these should be separated before the water is 
 passed to the consumer. 
 
 533. Capacity of Filter-Beds. Experience indicates 
 that the flow through a filter-bed, such as we have above 
 described, should not exceed the rate of 17 feet lineal per 
 diem, or be reduced by silting of the sand layer to less than 
 
 i 
 
CLEANING OF FILTER-BEDS. 553 
 
 6.5 feet per diem. It must not be so rapid as to suck the 
 sand grains or clay particles or the intercepted fibres 
 through the bed, or its whole purpose will be entirely 
 defeated. 
 
 A rate of about one-half inch per hour, or twelve lineal 
 feet per diem, when the filter is tolerably clean, is generally 
 considered the best. This gives the filter-bed a capacity of 
 twelve cubic feet, or 89.76 gallons, per square foot of sur- 
 face per twenty-four hours, and requires, in work, about 
 12,000 square feet of filtering surface for each million gal- 
 lons of water to be filtered per diem. 
 
 534. Cleaning of FUter-Beds. The filter-beds upon 
 the English streams require cleaning about once a week, 
 when the rivers are in their most turbid condition, and 
 ordinarily once in three or four weeks. 
 
 The process of cleaning consists of removing a slice of 
 about one-half inch thickness from the surface of the fine 
 sand layer, and the stirring or loosening up of the sand that 
 is packed hard by the weight of the water, when the clog- 
 ging of the filter prevents or hinders greatly its flow. This 
 requires the water to be drawn off from the bed to be cleaned, 
 and of course puts the portion of filter area being cleaned 
 out of service. According to the usual practice, the water is 
 drawn down only about a foot below the sand surface for 
 the cleaning ; but there is a great advantage, though an in- 
 convenience, in drawing the water entirely out of the bed, 
 for this admits the air to oxidize the organic matters that 
 are drawn into the filter, which is of great importance. 
 
 To provide for cleaning, the required area for service 
 should be divided into two or more independent beds, and 
 then one additional bed should be provided also, so that 
 there shall always be one bed surplus that may be put out 
 of use for cleaning. 
 
554 
 
 CLARIFICATION OF WATER. 
 
 The greater the number of equal divisions the less will 
 be the surplus area to be provided, and on the other hand, 
 each division adds something to the cost, so that both con- 
 venience and finance are factors controlling the design as 
 well as the form and extent of lands available. 
 
 As a suggestion merely, it is remarked that the divisions 
 may be approximately as follows, for given volumes, de- 
 pendent on the turbidness of water and local circumstances : 
 
 3 ' 
 
 80 
 
 x 150 ' 
 
 3 " 
 
 100 
 
 X 1 80 ' 
 
 4 " 
 
 100 
 
 X 1 80 ' 
 
 4 " 
 
 100 
 
 x 240 ' 
 
 4 " 
 
 1 20 
 
 x 270 ' 
 
 5 " 
 
 1 20 
 
 x 270 ' 
 
 TABLE No. 1O9. 
 DIMENSIONS OF FILTER-BEDS FOR GIVEN VOLUMES. 
 
 For i million gallons per diem, 3 beds 60 feet x 100 feet. 
 2 
 3 
 
 4| 
 6 
 8 
 10 
 
 535. Renewal of Sand Surface. When the repeated 
 pairings from the surface have reduced the top fine-sand 
 layer to about twelve inches thickness, a new coat should 
 be put on restoring it to its original thickness. 
 
 If good fine sand is difficult of procurement, the pairings 
 may perhaps be washed for replacing with economical 
 result. 
 
 This is sometimes accomplished by letting water flow 
 over the sand in an inclined trough of plank, having cleats 
 across it to intercept the sand, or by letting water flow up 
 through it in a wood or iron tank. In the latter case water 
 is admitted under pressure through the bottom of the tank, 
 and the sand rests upon a grating covered with a fine wire 
 cloth, placed a short distance above the bottom of the tank. 
 The current is allowed to flow up through the sand and over 
 the top of the tank until it runs clear. 
 
BASIN COVERINGS. 555 
 
 536. Basin Coverings. The British and Continental 
 filter-beds are rarely roofed in, although the practice is 
 almost universal of vaulting over the distributing reservoirs 
 that are near the towns. 
 
 The intensity of our summer heat and intensity of winter 
 cold in our northern and eastern States, makes the roofing 
 in of our filter-beds almost a necessity, though we are not 
 aware that this has been done as yet in any instance. 
 I The use of the shallow depth of four feet of water, so 
 common in the English filters, would be most fatal to open 
 filters here, for the water would frequently be raised in 
 summer to temperatures above 80 Fah. and sent into the 
 pipes altogether too warm, with scarce any beneficial 
 change before it reached the consumer. Such tempera- 
 tures induce also a prolific growth of algcB upon the sides 
 of the basin, and upon the sand surface when it has become 
 partially clogged, and soon produce a vegetable scum upon 
 the water surface also. As these vegetations are rapidly 
 reproduced and are short-lived, their gases of decomposi- 
 tion permeate the whole flow, and render the water ob- 
 noxious. 
 
 Depth of water and protection from the direct heating 
 action of the sun are the remedies and preventatives for 
 such troubles. A free circulation of air and light must, 
 however, be provided, and also the most convenient facili- 
 ties for the cleansing and renewal of the bed. 
 
 In Fig. 132 is presented a suggestion for a roof-covering 
 that will give the necessary protection from sun and frost, and 
 the requisite light, ventilation, and convenience of access. 
 
 The side walls are here proposed to be of brick, and the 
 truss supporting the roof to be of the suspended trapezoidal 
 . class. The confined air in the hollow walls, and the saw- 
 dust or tan layer over the truss, are the non-conductors that 
 
556 CLARIFICATION OF WATER. 
 
 assist in maintaining an even temperature within the basin, 
 and resist the effects of intense heat and intense cold. 
 
 The Parisian reservoirs at Menilmontant, and the splen- 
 did new structure at Moutrouge, are covered with a system 
 of vaulting, after the manner practised by the Romans, and 
 this system is also followed by the British engineers in their 
 basin covers. 
 
 A substantial cover over a filter basin will reduce the 
 difficulties with ice to a minimum, and remove the risk of 
 the bed being frozen while the water is drawn off for clean- 
 ing in winter. In such case, if the water is drawn imme- 
 diately from a deep natural lake, or a large impounding 
 reservoir, the only ice formation will be a mere skimming 
 over of the surface in the severest weather, and the inflow 
 of water, at a temperature slightly above freezing, will tend 
 constantly to preserve the surface of the water uncongealed, 
 and the sand free from anchor ice. 
 
FIG. 133. 
 
 PUMPING ENGINE No. 3, BROOKLYN. 
 
CHAPTER XXIV. 
 
 PUMPING OF WATER. 
 
 537. Types of Pumps. The machines that have been 
 used for raising water for public water supplies in the United 
 States present a variety of combinations, but their water 
 ends may be classified and illustrated by a few type forms. 
 
 Our space will not permit a discussion of the theories 
 and details of their prime movers, nor more than a general 
 discussion of the details of the pumps, with their relations 
 to the flow of water in their force mains. 
 
 The horizontal double-acting piston pump of the type, 
 Fig. 134, is an ancient device, and in its present form re- 
 mains substantially as devised by La Hire, and described 
 in the Memoirs of the French Academy in 1716. This was 
 at one time a favorite type, and was adopted for the most 
 prominent of the early American pumping works, as at 
 Philadelphia, Eichmond, New Haven, Cincinnati, Mon- 
 treal, etc. 
 
 Several modifications of the vertical plunger pump, after 
 the modern Cornish pattern (Fig. 135), were later intro- 
 duced at Jersey City, Cleveland, Philadelphia, Louisville, 
 etc., and in 1875 at Providence. 
 
 The vertical bucket pump (Fig. 133), in various modifi- 
 cations (referring to the water end only), was introduced at 
 Hartford, Brooklyn, New Bedford, etc. 
 
 The bucket-plunger pump (Fig. 136, water end), has 
 been more recently introduced at Chicago, St. Louis, Mil- 
 waukee, Lowell, Lynn, Lawrence, Manchester, etc. 
 
558 
 
 PUMPS. 
 
 A vertical acting differential plunger pump, having one 
 set of suction and one set of delivery valves, each arranged 
 in an annular ring around the plunger chamber, has re- 
 cently been invented by at least two engineers, independ- 
 ently of each other, and with similar disposition of parts. 
 This, like the bucket and plunger pump, is single-acting in 
 suction and double-acting in delivery. This pump gives 
 promise of superior excellence 
 
 The double-acting horizontal plunger pump (page 223), 
 itself an ancient and admirable invention, was first intro- 
 duced in combination with the Worthington duplex engine 
 about the year 1860, and has since been adopted at Harris- 
 burg, Charlestown, Newark, Salem, Baltimore, Toledo, 
 
 Toronto, Montreal, etc. 
 
 FIG. 134. 
 
 HORIZONTAL DOUBLE-ACTING PISTON PUMP. 
 
 Kotary, and gangs of small piston pumps have been in- 
 troduced to some extent, in direct pressure systems, in some 
 of the small Western towns. 
 
EXPENSE OF VARIABLE DELIVERY of WATER. 559 
 
 538. Several of the earliest pumps * of magnitude worthy 
 of note were driven by overshot, or breast water-wheels, as 
 at Bethlehem, Pa., Fairmount Works, Philadelphia, New 
 Haven, Richmond, and Montreal. Turbines have, how- 
 ever, taken the places of the horizontal wheels at Phila- 
 delphia and Richmond, and in part at Montreal, and tur- 
 bines give the motion at Manchester, Lancaster, Bangor, 
 and at other cities. 
 
 Fig. 143 shows the latest improved form of the G-eyelin- 
 Jonval turbine, which has been used very successfully in 
 several of the large cities for driving pumps. 
 
 The greater number of the pumping machines now in 
 use are actuated by compound steam-engines. 
 
 A considerable number of the large pumping machines 
 have their pump cylinders in line with their steam cylin- 
 ders, and their pump rods in prolongation of their steam 
 piston rods. 
 
 539. Expense of Variable Delivery of Water. 
 It is important that the delivery of water into the force-main 
 from the pumping machinery be as uniform as possible, 
 and constant, 
 
 If the delivery of water is intermittent or variable, and 
 the flow in the main equally variable, then power is con- 
 sumed at each stroke in accelerating the flow from the 
 minimum to the maximum rate. 
 
 The ms viva^ of the column of water in the force-main, 
 surrendered during the retardation at each stroke, is neutral- 
 
 * Bethlehem, Pa., constructed in 1762 the first public water supply in the 
 United States in which the pumps were driven by water-power. Philadelphia 
 constructed, in 1797, on the Schuylkill River, a little below Fairmount, the 
 first public water- works in the United States driven by steam-power. In 1812 
 steam-pumps were started at Fairmount, and the old works abandoned. In 
 April, 1822, the hydraulic- power pumps were started at Fairmount. 
 
 f Vide " principle of ms viva," in Moseley's " Mechanics of Engineering," 
 p. 115, New York, 1860, and Poncelet's Mecanique Industrielle, Art. 135, 
 Paris, 1841. 
 
560 * PUMPS. 
 
 ized by gravity, and no useful effect or aid to the piston of 
 the pump is given back, as useful work is given during the 
 retardation of the fly-wheel of an engine. 
 
 If, as when the pump is single-acting, motion is gener- 
 ated during each forward stroke, and the column comes to 
 rest during the return stroke of the piston, or between 
 strokes of the piston, the power consumed (neglecting fric- 
 tion) to generate the maximum rate of motion, equals the 
 product of the weight of the column of water into the height 
 to which such maximum rate of motion would be due if the 
 column was falling freely, in vacuo, in obedience to the in- 
 fluence of gravity. 
 
 Let Q be the volume of water to be set in motion, in 
 cubic feet, w the weight of a cubic foot of water, in pounds 
 (= 62.5 Ibs), ^i the equivalent height, in feet, to which the 
 
 (t) 2 \ 
 = ^-), and PI the power required to 
 &g' 
 
 produce the acceleration ; then 
 
 p l Q x w x hi. (1) 
 
 If the velocity is checked and then accelerated during 
 each stroke, without coming to a rest, let v be the maximum 
 velocity, in feet per second, and Vi the minimum velocity ; 
 then the power consumed in or necessary to produce the 
 acceleration is 
 
 In illustration of this last equation, which represents a 
 smaller loss than the first, assume the force-main, with air- 
 vessel inoperative, to be 1000 feet long and 2 feet diameter, 
 and the maximum and minimum velocities of flow to be 
 5 feet and 4 feet per second respectively. 
 
 The weight of the contents of the main into its accelera- 
 
 tion will be (.7854d 2 x 1) x w x \- - -^ j- = 3142 cu. ft. x 
 
 * *) 
 
EXPENSE OF VARIABLE DELIVERY OF WATER. 561 
 
 62.5 Ibs. x .14 ft. = 27492.5 foot-lbs. If there are ten strokes 
 per minute, 274925 foot Ibs. = 8J HP will be thus con- 
 sumed. If the main is twice, or four times as long, the 
 power consumed will be doubled, or quadrupled. 
 
 The power required to accelerate the motion of the 
 column is in addition to the dynamic power P l in foot-lbs., 
 required to lift it through the height H, of actual lift. 
 
 For the equation of lifting power per second, when Q is 
 the volume per second (neglecting friction), we have 
 
 P, = Q x w x If, (3) 
 
 or for any time, 
 
 P l = QxtxwxH. (4) 
 
 The frictional resistance to flow in a straight main is 
 proportional, very nearly to the square of the velocity of 
 flow (to mv 2 ), and is computed by some formula for frictional 
 head 7i", among which for lengths exceeding 1000 feet is 
 
 in which 7i" is the vertical height, in feet, equivalent to the 
 
 frictional resistance. 
 I " length of main, in feet. 
 d " diameter of the main, in feet. 
 m is a coefficient, which may be selected from 
 Table 61, page 242, of values of m. 
 
 The equation of power p", to overcome the frictional 
 head, is 
 
 The equation of power required, expressed in horse- 
 powers \_H.P.} of 33,000 foot-pounds per minute, each, for 
 dynamic lift, and frictional resistance to flow combined, is 
 
 33,000 
 36 
 
562 
 
 PUMPS. 
 
 The several resistances above described are all loads 
 upon the pump-piston, and their sum, together with the 
 frictions at angles and contractions, is the load, from the 
 flow in the main which the prime mover has to overcome. 
 
 When the delivery of the water into the main is constant 
 and uniform, these resistances are at their minimum. 
 
 54O. Variable Motions of a Piston. If we analyze 
 the rates of motion during the forward stroke of a piston 
 moved by a revolving crank with uniform motion, whose 
 length or radius of circle is 1 foot, we find the spaces or dis- 
 tances moved through in equal times by the piston, while 
 the crank-pin passes through equal arcs, to be as in the fol- 
 lowing table. 
 
 TABLE No. HO. 
 PISTON SPACES, FOR EQUAL SUCCESSIVE ARCS OF CRANK MOTION, n^. 
 
 Arcs 
 
 
 
 "i 
 
 22* 
 
 33* 
 
 45 
 
 56* 
 
 67* 
 
 7 8| 
 
 90 
 
 Space, ft. . 
 
 
 
 .0223 
 
 .0648 
 
 .1034 
 
 1384 
 
 1655 
 
 .1849 
 
 .1946 
 
 .1981 
 
 Arcs 
 
 I0li 
 
 na| 
 
 4i 
 
 
 
 135 
 
 i 4 6i 
 
 iS7l 
 
 i68| 
 
 180 
 
 
 Space, ft. . 
 
 .1921 
 
 .1806 
 
 .1609 
 
 1375 
 
 .1104 
 
 .0814 
 
 .0488 
 
 .0163 
 
 
 The spaces are equal to the above, but in inverse order 
 during the return stroke. To compute spaces for other 
 lengths of crank, and the same arcs, multiply the given 
 lengths of crank in feet by the above spaces. 
 
 The sum of the motions of the piston while the pin moves 
 through the first 90 is 1.072 feet, and while through the 
 second 90 is .928 feet; therefore the motion of the piston 
 is faster during the first and fourth parts of the revolution 
 than during the second and third. 
 
 The motion of the piston is accelerated through .5218 of 
 its forward and .4782 of its return stroke, and is retarded 
 during the remaining parts of its forward and backward 
 
FIG. 135. 
 
 CORNISH PUMP, JERSEY CITY. 
 
564 
 
 PUMPS. 
 
 motions ; and with the usual length of connecting rod, it 
 attains a maximum velocity equal to about 1.625 times its 
 mean velocity. 
 
 If the pump is single acting, then no delivery of water 
 takes place during the return stroke, and this is the most dif- 
 ficult case of intermittent motion to provide for in the main. 
 
 541. Ratios of Variable Delivery of Water. If we 
 analyze the ratios of movement of a single, and the sums of 
 ratios of movement of two or three coupled double-acting 
 pump pistons, when the two crank-pins are 90 apart, and the 
 three pins 60, we find the ratios, during the forward motion 
 of piston No. 1, for given arcs, approximately as in the 
 following table : 
 
 TABLE No. 111. 
 
 RATIOS, AND SUMS OF RATIOS, OF PISTON MOTIONS FOR EQUAL 
 SUCCESSIVE ARCS OF CRANK MOTION, nj. 
 
 Arcs 
 
 
 
 
 
 Hi 
 
 22* 
 
 33f 
 
 
 
 45 
 
 5^ 
 
 67! 
 
 78| 
 
 90 
 
 i piston 
 2 pistons . 
 
 .0 
 
 .1620 
 
 .0423 
 
 .2293 
 
 .0840 
 
 .2550 
 
 .1180 
 
 .2607 
 
 .1490 
 
 .27S3 
 
 .1653 
 .2730 
 
 .1906 
 .2567 
 
 .1967 
 .2766 
 
 1953 
 .1960 
 
 3 pistons 
 
 .3426 
 
 .3700 
 
 .3866 
 
 .3896 
 
 3776 
 
 3577 
 
 .3640 
 
 3853 
 
 3930 
 
 Arcs 
 
 
 
 
 
 
 I2-* 3 
 
 
 
 
 
 id6 l 
 
 I c 7 1 
 
 
 
 168' 
 
 180 
 
 
 
 
 
 
 
 
 
 
 
 
 i piston 
 
 18^3 
 
 
 
 
 
 0660 
 
 
 
 
 2 pistons 
 
 .22Q3 
 
 */~* 
 
 .2680 
 
 
 
 
 
 .1960 
 
 
 3 pistons 
 
 .3810 
 
 3613 
 
 .3200 
 
 3777 
 
 3893 
 
 .3856 
 
 .3700 
 
 3740 
 
 .... 
 
 The variations of motion, and of delivery of water, on 
 each side of the mean rate of delivery is with one piston 
 about 10 per cent., with two pistons about 5\ per cent., and 
 with three pistons about 2J per cent., or in other words, the 
 ratios of excess of delivery are .10, .055, .025, and the ratios 
 of deficiency have like values. 
 
 542. Office of Staiid-Pipe and Air- Vessel. It is 
 the office of the stand-pipe and air-vessel to take up the 
 
CAPACITIES OF AIR-VESSELS. 565 
 
 excess, and to compensate for the deficiency of delivery by 
 the pump pistons, plungers, or buckets. These are most 
 effective when nearest to the pump cylinders. 
 
 The excess of delivery enters the open-topped stand-pipe 
 and raises its column of water, and the column is drawn 
 from and falls to supply the deficiency. Work is expended 
 to lift the column, and this work is given to the advancing 
 water in the main when the column falls again, but when 
 the piston is again accelerated it has the labor of checking 
 the motion of the falling column in the stand-pipe. 
 
 The air-vessel on the force main is practically a shorter, 
 closed-top stand-pipe containing an imprisoned body of 
 air. The excess of delivery of water from the pumps enters 
 the air-vessel and compresses the air, and the expansion of 
 the air forces out water to supply the deficiency. The reduc- 
 tion at each stroke of the mean volume of the air in the 
 vessel is directly proportioned to the excess of water deliv- 
 ered and received into the air-vessel, which is; for different 
 pumps, proportional to their variations, or if coupled or 
 working through the same air-vessel, to the algebraical 
 sums of their variations. 
 
 543. Capacities of Air- Vessels. The cubical capa- 
 city of an air-vessel for one pair of double-acting pumps is 
 usually about five or six times the combined cubical capa- 
 city of the water cylinders ; but we shall see that the capa- 
 city of the cylinders alone is not the full basis on which the 
 capacity of the vessel is to be proportioned. 
 
 If the air-vessel is filled with air under the pressure of 
 the atmosphere only, and then is subjected to a greater 
 pressure of water, it will not remain full of air, for the air 
 will be compressed, and, according to Mariotte's law,* its 
 
 * Vide Lardner's Hydrostatics and Pneumatics, p. 158. London, 1874. 
 
566 PUMPS. 
 
 volume will "be inversely proportional to the pressure under 
 which it exists, provided the temperature remains the same. 
 Thus, if the vessel was filled under a pressure of 15 Ibs. per 
 square inch, and the water pressure is six times greater or 
 90 Ibs. per square inch, and the temperature is unchanged, 
 then the air-vessel will be but one-sixth full. 
 
 It is the reduced volume of air in the vessel that is com- 
 pressed to take up the excess of water delivered by the 
 pumps ; therefore the degree of pressure should be a factor 
 in the equation of capacity of air-vessel, as well as the ratio 
 of excess of delivery during a half stroke. 
 
 Let q be the volume of delivery of a pump piston dur- 
 ing its forward stroke, r the ratio of excess ; or if two or 
 more pistons are coupled, the algebraic sum of ratios of 
 excess of delivery of water during the forward stroke of 
 No. 1 piston, n the maximum pressure of water in atmos- 
 pheres (= 14.7 Ibs. per square inch each), and /an experi- 
 ence coefficient whose value will ordinarily be about 15, 
 then the equation for cubical capacity, (?, in cubic feet, of 
 air-vessel is, 
 
 C = qxrxnxf, (8) 
 
 or if p is the maximum water pressure, in pounds per square 
 inch, then the equation, when/ = 15, may take the form 
 
 C = pqr. (9) 
 
 If the water is to be permitted to abstract an appreciable 
 portion of the air from the air-vessel, that is, if the air-vessel 
 is not to be frequently recharged, then the coefficient in the 
 above equation should be greater than 15. If the air-vessel 
 is to be recharged often, mechanically, with volumes of air 
 greater than the atmospheric pressure would supply, then 
 the coefficient may be some less than 15. 
 
FIG. 136. 
 
 LYNN PUMPING ENGINE. - (E. D. Leavitt, Jr.'s, Patent.) 
 
568 PUMPS. 
 
 The larger the water surface in contact with the air in 
 the air-vessel, the faster the air is absorbed by the water ; 
 therefore it is advisable to give considerable height in pro- 
 portion to diameter to the air-vessel, and a disk of wood or 
 other nearly or quite impervious material, one or two inches 
 less in diameter than the air-vessel, may be allowed to lie 
 on the water in the vessel, and thus still more reduce the 
 surfaces of contact of air and water. 
 
 544. Valves. Pumps that have to lift water to heights 
 greater than thirty feet, are usually of necessity, or for 
 convenience of access, placed between the water to be 
 raised and the point of delivery. When so situated they 
 perform two distinct operations, one of which is to draw the 
 water to them, and the other to force it up to the desired 
 elevation. When the pump piston or plunger advances, 
 
 FIG. 137. 
 
 the water in front of it is pressed forward, and at the same 
 time the pressure of the atmosphere forces in water to fill 
 the space or vacuum that it would otherwise leave behind 
 it. The return of the water must be prevented, or the work 
 done by lifting it will be wasted. Valves which open freely 
 to forward motion of the water and close against its return, 
 are, therefore, a necessity, both upon the suction and the 
 delivery sides of the pump. 
 
 All valves break up and distort, in some degree, the ad- 
 vancing column of water. Such distortions and divisions 
 
VALVES. 569 
 
 cause frictional resistance, which consumes power. The 
 valve that admits the passage of the column of water by or 
 through it with the least division or deflection from its direct 
 course, neutralizes least of the motive power. Short bends 
 and contractions in water passages, that consume a great 
 deal of power or equivalent head, often occur in their worst 
 degree in pump valves. 
 
 The piston valve which moves entirely out of the water- 
 passage, and permits the flow of water in a single cylindrical 
 column, such for instance as was used in the Darlington 
 and Junker water -engines,* is perhaps least objectionable 
 in the matter of frictional resistance to the moving water, 
 but is often inconvenient to use. The single flap- valve 
 (Fig. 137), with area at 30 lift exceeding the sectional area 
 of the pump cylinder, gives also a minimum amount of fric- 
 tional resistance. 
 
 The single annular form of column, while passing through 
 the valve, is less objectionable than any of the other divi- 
 sions of the water, and annular valve openings have been 
 the favorite forms in nearly all the large pumping ma- 
 chines. 
 
 In some of the earlier pumps the suction was through a 
 single valve with two annular openings, after the Harvey 
 and West model, or, as more familiarly known, the Cornish 
 double-beat valve, similar to Fig. 138, illustrating the valves 
 used in the Brooklyn engines. 
 
 When pumps began to be built of great magnitude, 
 requiring large capacities for flow, and the valves were 
 increased in size to two feet diameter and upward, the 
 valves were found to strike very powerful blows as they 
 
 * Vide illustration of a water-engine in Rankine's "Steam Engine," p. 140, 
 London, 1873, and Lardner's Hydrostatics and Pneumatics, p. 312. London, 
 1874. 
 
570 
 
 PUMPS. 
 FIG. 138. 
 
 came upon their seats, and to make the whole machine, the 
 "building, and the earth around the foundations tremble. 
 
 This annoyance led to dividing the valves into nests of 
 five or more valves of similar double-beat form. In London 
 and other large English cities the valves have of late been 
 of the four-beat class, or Husband's model. 
 
 In many pumps the valves have of late been divided into 
 nests of twelve or more rubber-disks (Fig. 139) in each set, 
 seating upon grated openings in a flat valve-plate. Each 
 subdivision increases the frictional resistance, but reduces 
 the force of the blow, or water-hammer., when the valve 
 strikes its seat. 
 
 The suction and delivery valves of the piston pumps 
 (Fig. 134) were usually of the flap or hinged pattern. These 
 piston-pumps had sometimes, though rarely, their cylinders 
 placed vertically, as at the Centre Square Works erected in 
 
MOTION OF WATER THROUGH PUMPS. 
 
 571 
 
 Philadelphia in 1801, and at the Schuylkill Works erected 
 in the same city in 1844. They were inclined ten or twelve 
 degrees from the horizontal at Montreal. 
 
 The horizontal plunger, 
 or " Worthington " pumps 
 (page 223), have uniformly 
 been fitted with nests of rub- 
 ber disk valves. 
 
 The best of the modern 
 steam fire-engines are fitted 
 with nests of rubber disk 
 valves, showing that this 
 class of valve is a favorite 
 when the pressure is great and the motion is rapid. 
 
 The rubber disk valve (Fig. 139) was sketched from an 
 Amoskeag fire-steamer valve. 
 
 545. Motion of Water Through Pumps. Water is 
 so heavy and inelastic that large columns of it cannot be 
 quickly started or stopped, without the exertion or opposi- 
 tion of great power to overcome its inertia, or vis viva. 
 There is therefore an advantage, as respects the even and 
 moderate consumption of power, when the piston or plunger 
 motion is reciprocal, in making the strokes long, and few 
 per minute. 
 
 The case is entirely different with an elastic fluid like 
 steam. The tendency of the most successful modern steam 
 engineering has been toward quick strokes and high steam 
 pressures, and with high degrees of expansion in the larger 
 engines. 
 
 The "indoor" ends of the beams of the best Cornish 
 pumping-engines are longer than the " outdoor" ends, and 
 it is claimed as one of their special advantages that the in- 
 door or steam stroke that lifts the plunger pole can be made 
 
572 PUMPS. 
 
 with rapidity, while the outdoor stroke, or fall of the 
 plunger by its own weight, can "be gradual, and thus the 
 water be pressed forward at a nearly steady and uniform 
 rate. The single-cylinder, single-acting, non-rotative Cor- 
 nish engine is admirably adapted to the work to which 
 it was early applied by Watt and Boulton namely, the 
 raising of water from the deep pits of mines by suc- 
 cessive lifts to the surface adits, where it flowed freely 
 away ; but when applied to long force-mains of water- 
 supplies, a stand-pipe near the pump becomes a necessity 
 to neutralize the straining and laborious effects of the inter- 
 mittent action. 
 
 546. Double- Acting Pumping-Engines. The de- 
 sire to overcome the objectionable intermittent delivery of 
 the single-acting pump, as well as the influence of the sharp 
 competition among engine-builders, that forced them to 
 study methods of economizing the first cost of the machines 
 while maintaining their capacity and economy of action, 
 led to the introduction, for water-supply pumping, of the 
 compound or double cylinder, double-acting, rotative or 
 fly-wheel engine. This last class of engines was brought to 
 a high state of perfection by Mr. Wicksted and Mr. Simp- 
 son at the London pumping stations. Some admirable 
 pumping machines of this class have been constructed for 
 American water-works from designs of Messrs. Wright, 
 Cregeir, Leavitt, and others. 
 
 547. Geared Pumping-Engines. Geared compound 
 pumping-engines, one style of which (the Nagle) is shown in 
 side and end elevations* in Figs. 140 (p. 377) and 141 (p. 573), 
 are well adapted both for direct pumping, and also where 
 the reservoir and direct systems are combined. Advantage 
 
 * From the design adopted for the Providence High Service, and working 
 with direct pressure. 
 
FIG. 141. 
 
 A. F. NAGIE. 
 
 CROSS SECTIONAL ELEVATION. 
 NAGLE'S GEARED PUMPING ENGINE. 
 
574 PUMPS. 
 
 may here be taken of high pressure of steam, rapid steam 
 piston stroke, and large degree of steam expansion, while 
 the water piston moves relatively slow with a minimum 
 number of reversals. 
 
 548. Costs of Pumping Water. The following table 
 (p. 575) gives the running expenses for pumping water in 
 various cities. 
 
 549. Duty of Pumping Engines. The duty or 
 effective work of a steam pumping-engine, as now usually 
 expressed, is the ratio of the product, in foot-pounds, of 
 the weight of water into the height it is lifted, to one hun- 
 dred pounds of the coal burned to lift the water. 
 
 This standard is an outgrowth from that established 
 by Watt, about the year 1780, for the purpose of compar- 
 ing the performances of pumping-engines in the Cornish 
 mines, when Messrs. Boulton and Watt first introduced 
 their improved pumping-engines upon condition that their 
 compensation was to be derived from a share of the saving 
 in fuel. Watt first used a bushel of coal as the unit of 
 measure of fuel, equal to about 94 pounds, and afterward 
 a cwt. of coal, equal to 112 pounds. More recently, in 
 European practice, and generally in American practice, 
 100 pounds of coal is the unit of measure of fuel. In some 
 recent refined experiments, the weight of ashes and clinkers 
 is deducted, and the unit of measure of fuel is the combus- 
 tible portion of 100 pounds of coal. The use of these sev- 
 eral units, differing but slightly from each other in value, 
 leads to confusion or apparent wide discrepancies in results, 
 when the performances of different pumping-engines are 
 compared, unless the results are all reduced to an uniform 
 standard. 
 
 To construct an equation in conformity with the more 
 generally accepted standard of duty, let Q be the volume 
 
r 
 
COSTS OF PUMPING WATER. 
 
 575 
 
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 ;33j ai yiq 
 
 1 
 
 :: 
 
 -gdddj/ 
 
 
 : 
 
 liifi 
 
 26 * ^sa 
 
 M' 4co 
 
 m . \o t*> 
 
 il 
 
 Philadelphia 
 New Haven 
 
 Montreal 
 
676 PUMPS. 
 
 of water delivered in any given time into the force-main, in 
 gallons ; w the weight * of a gallon of water in pounds 
 (= 8.34 Ibs. approximately) ; H the dynamic height of lift ; 
 Ti the height equivalent to the Motional resistance "between 
 pumps and reservoir, including resistances of flow, valves, 
 bends, etc., in the force-main, but not the work due to in- 
 termittent motion of pumps, or to bends and frictions within 
 the pump iiself ; W the weight, in pounds, of coal passed 
 into the furnace in the given time ; and D the duty per 100 
 pounds of coal ; then 
 
 D _Q x w x (H+ 7i) 
 
 :enr~ 
 
 Sometimes the value of Q is expressed in cubic feet, in 
 which case w is the weight in pounds of a cubic foot of 
 water (= 62.33 Ibs. approximately). 
 
 If it is preferred to use the area of plunger, its mean rate 
 of motion in the given time, and the pressure against which 
 it moves, as factors in the calculation, then the equivalent 
 equation of duty D, takes the form, 
 
 __cA xVx t x (P+p) 
 
 ~~~ 
 
 in which A is the area, in square feet, of the piston or 
 bucket, and c its coefficient of effective delivery, which 
 varies from .60 to .98, according to design or condition of 
 the valves and velocity of flow through them ; V the mean 
 rate of motion, in feet per minute, of the plunger or bucket ; 
 t the given time, in minutes ; P the pressure, in pounds, 
 due to the dynamic head ; p the pressure in pounds due to 
 the resistances in the force-main ; and W the weight of 
 
 * Vide Table 38 for weights of water per cubic foot, at different temperatures. 
 
DUTY OF PUMPING ENGINES. 577 
 
 coal, in pounds, passed into the furnace in the given 
 time. 
 
 If W is taken for denominator in the equation instead of 
 .01 TF, then the result gives the duty per pound of coal. 
 
 The numerator in each equation refers to the foot-pounds 
 of work done by the plunger or bucket of the pump in effec- 
 tive delivery of water into and efflux from the force-main, 
 and the denominator refers to the foot-pounds of work con- 
 verted from the heat in the coal, and effectively applied by 
 the combination of boiler and steam engine. 
 
 The coefficient c and the terms Ji and p in equations 10 
 and 11 are ordinarily appreciably variable with variable 
 rates of plunger or bucket motion. Preliminary to a general 
 duty test of a pump the values of c for different velocities 
 or rates of piston motion, from minimum to maximum, 
 should be determined by a reliable and accurate weight or 
 weir test, and the value of 7i or p be accurately determined 
 for similar conditions by an accurate gauge or pressure test, 
 and a scale, per unit of velocity prepared for each, so that 
 values may be read off for the actual rates of piston motion 
 during the general test. 
 
 The main parts or divisions which make up a steam 
 pumping engine, are : 
 
 1. Boilers (including grates, heating surfaces, steam and 
 water spaces, and flues). 
 
 2. Steam engine (including steam pipes, cylinders, valves, 
 pistons, and condensing apparatus). 
 
 3. Pump (including water passages, cylinders, plunger 
 bucket, and valves). 
 
 In comparisons of data, for the selection or design of the 
 of such a combination, the classes of each part should 
 considered in detail, independently, with prime costs, 
 37 
 
578 PUMPS. 
 
 since if either part gives a low duty alone, the duty of the 
 combination will suffer in consequence. 
 
 Attention will be given especially to the evaporative 
 power of the boiler and its duty, or ratio of effective to 
 theoretical pressure delivered into the steam pipe ; the effec- 
 tive piston pressure capabilities or duty of the steam cylin- 
 der, over and above its condensations, enhanced by slow 
 motion, leakages of steam, arid frictions ; and the fractional 
 resistances of the pump piston or plunger, and valves, and 
 reactions in the water passages. 
 
 Each pound of good coal, according to the dynamic 
 theory of heat, contains in its combustible part about 12,000 
 heat units, which are developed into a force by the burning 
 of the coal to produce steam, and this force is capable of 
 performing a definite amount of work. From sixteen to 
 twenty per cent, of these heat units are, ordinarily, lost by 
 escape up the chimney ; sixteen to twenty per cent addi- 
 tional are lost by condensation of the steam in the pipes 
 and cylinders, and by leakage past the piston or valves into 
 the condenser, and about fifty per cent, of their equivalents 
 escape with the exhaust steam into the condenser. Only 
 about ten or twelve per cent, of these heat units are ordi- 
 narily transformed into actual useful work done by the 
 steam. 
 
 If the engine has many rubbing surfaces, or binds at 
 any bearing, or if the pumps have crooked water passages, 
 many divisions of the jet in the valves, frequent and rapid 
 startings and checkings of the water column, or if its binds 
 at any bearing, then each of these resistances consume a 
 portion of the remaining ten or twelve per cent, of useful 
 work of the steam. 
 
 Stability and substantiality are matters of the utmost 
 importance to be considered in the selection of a class or 
 
ECONOMY OF A HIGH DUTY. 
 
 579 
 
 manufacture of pumping engines. By these terms, in this 
 connection, we mean the capability of endurance of contin- 
 uous action at the standard rate and work, without stoppage 
 for repairs, and with the minimum expenditure for repairs. 
 This power of continuous work at a maximum rate is of 
 far greater value, ordinarily, than an extremely high duty, 
 if stability is sacrificed in part for the attainment of a high 
 duty, for the comfort and safety of the city may be jeopard- 
 ized by a weakness in its pumping engine. Stability being 
 first attained, then duty becomes an element of excellence 
 and superiority. 
 
 FIG 142. 
 
 GEYELIN'S DUPLEX-JONVAL TURBINE (R. D. WOOD & co., PHILA.) 
 
 550. Special Trial Duties. The following table (page 
 580) gives the duty results obtained by special trials of 
 various engines, under the direction of experts.* 
 
 551. Economy of a High Duty. The financial value 
 of a high duty is too often overlooked. 
 
 * Vide report of Messrs. Low, Roberts and Bogart ; in Journal of American 
 Society of Civil Engineers. Vol. IV, p. 142. 
 
580 
 
 PUMPS. 
 
 }99J UI -QH OIUmiA'Q 
 
 I9VBM JO }U9tH 
 -9inSB9UI pUB 
 
 yi\ oiureuA'p Ag 
 
 vo H vo cr> 
 
 IO O N H 
 
 oo ^ tx 
 
 w ON -* 
 
 
 i 
 
 in 4 
 
 t^'OO *t^ 
 
 tx in H 
 
 drand 
 
 
 
 
 
 -^- IH 
 
 
 
 oo w ro i 
 VO t^ ^ < 
 
 ut aariss9Jd 
 
 ui 
 
 Ag 
 
 li 
 
 lBoojo*q^J9d'( 
 eiej09jn^BJ9dui91 
 PJBPUB^S o; pgonp 
 -9j 'jg^BM. jo spuno j 
 
 UB9A 
 
 " 
 
 Vertical bucket and 
 double-beat valves 
 
 It t( (( 
 
 Horizontal plunger, disk valves,. 
 
 Doub. act. piston, flap valves 
 " rubber bar val 
 Horizontal piston, disk valves 
 
 vert 
 ori 
 
 No. i, 
 No, i, 
 beam 
 No. 2, 
 No. 2, 
 No, 3, 
 
 No. 3, 
 Mt. Pr 
 
 Cornish 
 Leavitt, rotativ 
 Simpson, " 
 Leavitt, " 
 Compound beam 
 Worthington, ho 
 compound, dir 
 McAlpine, beam 
 Corliss, radial ho 
 Worthington, ho 
 compound 
 Nagle, geared 
 Worthingto 
 mpoun 
 
 Ph 
 

 a * 
 
 r 
 
 ESC 
 
COSTS OF PUMPING WATER. 
 
 581 
 
 Engines of substantial construction can now be readily 
 obtained, that, when working continuously at their stand- 
 ard capacities, will give duties of from 75 to 100 million 
 foot-pounds per 100 pounds of coal. When they are real- 
 izing less than their maximum duties, money, or its equiva- 
 lent, goes to waste. 
 
 We have just seen ( 549) that duty is a ratio of effec- 
 tive work. If we divide the dynamic work to be done by 
 this ratio, then we have the pounds of coal required to do 
 the work when the given duty is realized. 
 
 Let D be the given duty in foot-pounds per 100 pounds 
 of coal ; Q the volume of water delivered into the force-main 
 in gallons ; w the weight of a gallon of water, in pounds 
 (= 8.34 Ibs., approximately) ; If the actual height of lift ; 
 7i the height equivalent to the frictional resistances in the 
 main ; and TFthe weight of coal required, in pounds ; then 
 we have for equation of weight of coal, 
 
 W= IOOQ x w x (ff+7i) 
 
 D 
 
 (12) 
 
 When Q and D are in even millions, the computation 
 will be shortened by taking one million as the unit for those 
 quantities. 
 
 Let us assume that we have one million gallons of water 
 to lift 100 feet high in twenty -four hours, then the pounds 
 of coal required at various duties will be approximately 
 as follows : 
 
 TABLE No. 114. 
 COMPARATIVE CONSUMPTIONS OF COAL AT DIFFERENT DUTIES. 
 
 "Duty, in millions 
 
 105 
 
 too 
 
 ne 
 
 
 64 
 
 80 
 
 75 
 
 70 
 
 Pounds of coal 
 
 794 
 
 834 
 
 8?8 
 
 
 981 
 
 
 III2 
 
 IIQI 
 
 
 
 
 
 
 
 
 
 
 Duty, in millions 
 Pounds of coal .... 
 
 6 5 
 i 2 go 
 
 60 
 
 55 
 
 So 
 1668 
 
 45 
 
 4 
 
 3 
 2780 
 
 20 
 
 
 
 
 
 
 
 
 
 
582 
 
 PUMPS. 
 
 The relative costs per annum, in dollars, for lifting 
 various quantities of water daily 100 feet high, at different 
 duties, will be approximately as in the following table, 
 on the assumption that the coal costs $8 per ton of 2000 
 pounds, when delivered into the furnace. 
 
 TABLE No. 1 15. 
 FUEL EXPENSES FOR PUMPING, COMPARED ON DUTY BASES. 
 
 Duty in 
 
 Number of millions of gallons pumped daily, one hundred feet high. 
 (Coal in furnace at $8 per ton.) 
 
 millions of 
 
 
 foot-pounds. 
 
 
 
 
 
 
 
 
 
 1 
 
 2 
 
 3 
 
 4 
 
 6 
 
 8 
 
 10 
 
 
 Cost of coal per annum, in dollars. 
 
 100 
 
 $1277-86 
 
 $2556 
 
 $3834 
 
 $5111 
 
 $7667 
 
 $10223 
 
 $12779 
 
 90 
 
 1419.85 
 
 2840 
 
 4260 
 
 5679 
 
 8519 
 
 H359 
 
 14198 
 
 80 
 
 1597.32 
 
 3195 
 
 4792 
 
 6389 
 
 9584 
 
 12778 
 
 15973 
 
 70 
 
 1825.51 
 
 3651 
 
 5477 
 
 7302 
 
 10953 
 
 14604 
 
 18255 
 
 60 
 
 2129.76 
 
 4260 
 
 6389 
 
 8519 
 
 12779 
 
 17038 
 
 21298 
 
 50 
 
 2555.72 
 
 CHI 
 
 7667 
 
 10223 
 
 15334 
 
 20446 
 
 25557 
 
 40 
 
 3194.65 
 
 6389 
 
 9584 
 
 12769 
 
 19168 
 
 25537 
 
 31946 
 
 30 
 
 4259-53 
 
 8519 
 
 12779 
 
 17038 
 
 25557 
 
 34076 
 
 42595 
 
 20 
 
 6389.30 
 
 12768 
 
 19168 
 
 25537 
 
 39336 
 
 5H74 
 
 63893 
 
 If the lift is 150 feet, then the annual cost will be one 
 and one-half times the above amounts respectively, if 200 
 feet, twice the above amounts, etc. 
 
 If we have four million gallons per day to pump 100 feet 
 high, then the cost of coal per annum for a 100 million 
 duty engine will be about $5000, and with a 20 million duty 
 engine about $25000. If we have to pump the same water 
 200 feet, the coal for the first engine will cost about $10,200 
 and with the second engine $51,000. These sums capital- 
 ized represent the relative financial values of the engines, 
 so far as relates to cost of fuel. 
 
 If pumping-engines are sufficiently strong, of good me- 
 chanical workmanship, and simple in arrangement of parts, 
 then the cost of attendance, lubricants, and ordinary re- 
 pairs, while doing a given work, will be substantially the 
 
COSTS OF PUMPING WATER. 583 
 
 same for different makes or designs. Beyond this the rela- 
 tive merits of machines of equal stability, independent of 
 prime cost, are nearly in the inverse order of the amount of 
 fuel they require to do a given work. 
 
 But the first costs of the complete combination should 
 be made a factor in the comparison, including costs of foun- 
 dations and extra costs of buildings, standpipes, etc., if re- 
 quired, as in the case of Cornish engines. Then the relative 
 economic merits are inversely as the products of costs into 
 reciprocals of duties, or directly as duty divided by cost. 
 
 Let C d be the cost in dollars of the complete pumping- 
 engine, including foundations, pump- wells, etc., and D the 
 duty in millions, then the most economic engine, so far as 
 relates to cost of fuel, will be that which has the least 
 
 product of O d x JY or -^, and the relative result will be very 
 
 ) 
 
 nearly the same if the cost of engine is capitalized. 
 
 Let % be the per cent., or rate of interest at which the 
 cost is capitalized, then the most economic engine, as to 
 prime cost and duty, will be that which has the least pro- 
 
 (71 1 Q 
 duct of -~ x jy, or -, x ~. 
 
 Let us assume that we have five million gallons of water 
 to lift 100 feet high per day, and that a standard engine of 
 suitable capacity to do the work, realizing one hundred mil- 
 lion duty, will cost $65,000. 
 
 With this standard let us compare, financially, engines 
 of less first cost and giving less duties, as in the following 
 table, in which the ratio of the standard is taken equal 
 unity. 
 
584 
 
 PUMPS. 
 
 TABLE No. 11 6. 
 
 COMPARISON OF VALUES OF PUMPING-ENGINES OF VARIOUS PRIME 
 COSTS AND DUTIES ON FUEL BASES. 
 
 COST = Q. 
 
 DUTY = D. 
 
 C x X - Cd 
 
 RATIO. 
 
 $65,000 
 
 IOO M. 
 
 650.0 
 
 
 6o,OOO 
 
 9 o " 
 
 666.6 
 
 .025 
 
 5O,OOO 
 
 75 " 
 
 666.6 
 
 .025 
 
 45,000 
 
 60 " 
 
 750.0 
 
 153 
 
 35,000 
 
 5 " 
 
 700.0 
 
 .077 
 
 25,000 
 
 30 " 
 
 833.3 
 
 .282 
 
 By the column of ratios in the table we learn that the 
 $25,000 engine will really cost twenty-eight per cent, more 
 per annum than the $65,000 engine, for the same work, and 
 that the purchase of the assumed standard engine, if it has 
 stability equal to that of the lower-priced engine, will lead 
 to the most profitable results. 
 
 In the table, the $50,000 pumping-engine giving a seventy- 
 five million duty, is seen to have a financial value almost 
 identical with that of the assumed standard engine. If it 
 is also freer from liability to breakage or interruption, if it 
 requires less labor or less skill in attendance, if it is easier 
 in adjustment to varying work when variable work is to 
 be performed, or if it is better adapted mechanically to the 
 special work to be performed, then the practical over- 
 balances the financial advantages, and it is obviously en- 
 titled to preference in the selection, and good judgment will 
 lead to the purchase of this rather than of the assumed 
 standard engine. 
 
FIG. 143. 
 
 TURBINES AND PUMPS, MANCHESTER. 
 
OHAPTEE XXV. 
 
 SYSTEMS OF WATER SUPPLY. 
 
 552. Permanence of Supply Essential. Let the 
 
 projector of a public water supply first make himself famil- 
 iar with the possible scope and objects of a good and ample 
 system of water supply, and become fully conscious of how 
 intimately it is to be connected with the well-being of the 
 people and their active industries in all departments of their 
 arts, mechanics, trade, and commerce, as well as in their 
 culinary operations, and let him also appreciate the conse- 
 quences of its failure, or partial failure after a season of 
 success. 
 
 When the people have become accustomed to the ready 
 flow from the faucets, at the sinks and basins, and in the 
 shops and warehouses, then, if the pumps cease motion or 
 the valve is closed at the reservoir, the household oper- 
 ations, from laundry to nursery, are brought to a stand- 
 still engines in the shops cease motion, hydraulic hoists 
 and motors in the warehouses cease to handle goods, rail- 
 way trains, ocean steamers, and coasters delay for water, 
 and a general paralysis checks the busy activity of the 
 city. What a thrill is then given by an alarm of fire, be- 
 cause there is no pressure or flow at the hydrants ! 
 
 The precious waters of the reservoirs preside over cities 
 with protecting influences, enhancing prosperity, comfort, 
 safety and health, and are not myths, as were the goddesses 
 in ancient mythology, presiding over harvests, flowers, 
 fruits, health and happiness. 
 
586 SYSTEMS OF WATER SUPPLY. 
 
 Let the designer and builder of the public water system 
 feel that his work must be complete, durable, and unfail- 
 ing, and let this feeling guide his whole thought and 
 energy, then there is little danger of his going astray as to 
 system, whether it be called " gravitation," " reservoir/' 
 "stand-pipe," or "direct pressure," or of his being enam- 
 ored with lauded but suspicious mechanical pumping au- 
 tomatons, and uncertain valve and hydrant fixtures. 
 
 When the people have learned to depend, or must of 
 necessity depend, upon the public pipes for their indis- 
 pensable water, it must flow unceasingly as does the blood 
 in our veins. All elements of uncertainty must be over- 
 come, and the safest and most reliable structures and ma- 
 chines be provided. 
 
 Many times, in different cities, a neglect, apparently 
 slight, has cost, through failure, a fearful amount, when 
 sacrificed life and treasure and a broad smouldering swarth 
 across the city were the penalty. Having water- works is 
 not always having full protection, unless they are fully 
 adequate for the most trying hour. 
 
 553. Methods of Gathering and Delivering Water. 
 There is no mystery about "systems" of water supply, 
 as they have of late been often classified. The problem is 
 simply to search out the best method of gathering or secur- 
 ing an ample supply of wholesome water, and then to 
 devise the best method of delivering that supply to the 
 people. 
 
 Usually there is one source whose merits and demerits, 
 when intelligently examined, favorably outweighs the 
 merits and demerits of each and every other source, and 
 there is usually one method of delivery that is conspicu- 
 ously better than all others, when all the local exigencies 
 are seen and foreseen. 
 
CHOICE OF WATER. 587 
 
 The usual methods of gathering the required supply are, 
 to impound and store the rainfall or flow of streams among 
 the hills ; draw from a natural lake ; draw from a running 
 river ; or draw from an artesian well. 
 
 The usual methods of delivering water are, by gravita- 
 tion from an elevated impounding basin ; elevation by 
 steam or water power to a reservoir and from thence a flow 
 by gravity ; elevation to low and high service reservoirs, 
 and from thence flow by gravity to respective districts ; and 
 by forcing with pressure direct into the distribution-pipes, 
 and cushioning the motion by a stand-pipe, or ample air- 
 vessel and relief valve. 
 
 554. Choice of Water. The pumped supplies are 
 usually drawn from lake, river, or subterranean sources. 
 
 The selection of a lake or river water for domestic use is 
 to be governed by considerations of wholesome purity ; and 
 cautiousness of financial expenditure must not in this direc- 
 tion exert too strong an influence in opposition to inflexible 
 sanitary laws. 
 
 This selection involves an intelligent examination of the 
 origin and character of the impregnations and suspended 
 impurities of the water, and the possibility of their thorough 
 clarification. 
 
 None of the waters of Nature are strictly pure. Some 
 of the impurities are really beneficial, while others, which 
 are often present, are not to be accepted or tolerated. A 
 mere suspicion that a water supply is foul or unwholesome, 
 even though not based on substantial fact, is often a serious 
 financial disadvantage ; therefore earnest effort to maintain 
 the purity of the water must extend also to the removal of 
 causes of suspicion. 
 
 Chemical science and microscopy are valuable aids in 
 this portion of the investigation of the qualities of waters ; 
 
.588 SYSTEMS OF WATER SUPPLY. 
 
 but we have detailed in the first part of this treatise so 
 minutely the nature and source of the chief impurities, and 
 so -carefully pointed out those that are comparatively harm- 
 less and those that are deadly, that an intelligent opinion 
 can generally be readily formed of the comparative puri- 
 ties and values of different waters. We have also pointed 
 out how waters may be clarified and conducted in their best 
 condition to the point of delivery, and distributed in the 
 most efficient manner. 
 
 Predictions of any value as to quantity and quality of a 
 supply from a proposed artesian well, demand a knowledge 
 of the local geology and subterranean hydrology, which, is 
 rarely obtainable until the completion and test of the well ; 
 nevertheless we have shown the conditions under which a 
 good supply of water may be anticipated with reasonable 
 confidence. 
 
 555. Gravitation. When a good and abundant sup- 
 ply of water can be gathered at a sufficient elevation, and 
 within an accessible distance, the essential element of con- 
 tinuous full-pressure delivery can then most certainly be 
 secured, and in the matter of possible safety the gravitation 
 method will usually be superior to all others. 
 
 The quality of impounded water, when gathered in small 
 storage reservoirs and from relatively limited watersheds, is 
 subject to some of those unpleasant influences, heretofore 
 referred to, which are to be provided against ; and unless the 
 hydrology and substructure of the gathering basin is well 
 understood, the permanence of the supply may not fulfill 
 enthusiastic anticipations. 
 
 The value and importance of sufficient elevation of the 
 supplying reservoir, when the delivery is by gravity, to 
 meet the most pressing needs of the fire-service, ought not 
 to be overlooked, for an efficient fire-service is usually one 
 
PUMPING WITH RESERVOIR RESERVE. 589 
 
 of the chief objects to be attained in a complete water 
 supply. 
 
 A water pressure of sixty to eighty pounds per square 
 inch in the hydrants in the vicinity of an incipient fire, ha& 
 a value which cannot be wholly replaced by a brigade of 
 fire-steamers in commission, for with light-hose carriages 
 and trained hosemen, connection will usually be made 
 with the hydrants, streams be put in motion, and the fire 
 overpowered before pressure is raised in the steamer's boil- 
 ers ; and the fire will not be suffered to assume unconquer- 
 able headway during the delay. 
 
 Constant liberal pressures in the hydrants is the first 
 element of prompt and effective attack upon a fire immedi- 
 ately after an alarm is given. Each moment lost before the 
 beginning of an energetic attack increases greatly the diffi- 
 culty of subduing the fire, and the probability of a vast 
 conflagration. 
 
 The element of distance of a gravitation supply, as re- 
 gards cost of delivery, is an exacting one, and the lengths 
 of conduit and large main are surprisingly short, while the 
 balance of economy of delivery remains with the side of the 
 gravitation scheme ; for conduits and mains are expensive 
 constructions, and soon absorb more capital and interest 
 than would pay for pumps and fuel for lifting a nearer 
 supply ; still an element of safety is not to be sacrificed for 
 a moderate difference in first cost. 
 
 556. Pumping with Reservoir Reserve. As re- 
 gards safety and reliability of operation, we place second the 
 method of delivery when the supply is elevated by hydrau- 
 lic power, and third when it is elevated by steam power to 
 a liberal-sized reservoir holding in store from six to ten 
 days reserve of water, from whence the supply flows by 
 gravity into the distribution-pipes. If in such case there 
 
590 SYSTEMS OF WATER SUPPLY. 
 
 are duplicate first-class pumping-machines whose combined 
 capacity is equal to the delivery of the whole daily supply 
 in ten hours, or one-half equal to the delivery of the whole 
 daily supply in twenty hours, then this method is scarcely 
 inferior in safety to the gravitation method. 
 
 The elements of safety may Ibe equally secured in the 
 low and high service method, when the physical features of 
 the town or city make such division desirable. In a pre- 
 vious chapter we have shown how a union of the high and 
 low service may be made an especially valuable feature in 
 efficient fire service. 
 
 The records of nearly all the water departments of our 
 largest cities, having duplicate pumping machinery, show 
 how valuable and indispensable have been their reserve 
 stores of water, and refer to the risks that would have been 
 incurred had such reservoir storages been lacking. 
 
 557. Pumping with Direct Pressure. We place 
 fourth, as regards safety and reliability, the direct pressure 
 delivery by hydraulic power, and fifth, by steam power, 
 with either stand-pipe or air-vessel cushions and safety 
 relief-valves. 
 
 The mechanical arrangements that admit of this method 
 of delivery are simple, and several builders of pumping 
 machinery have adapted their manufactures to its special 
 requirements, but in point of continuous reliability the 
 method still remains inferior to gravity flow. 
 
 Even when the most substantial and most simple steam 
 pumping machinery is adopted, if not supplemented by an 
 elevated small reserve of water, this method of delivery is 
 accompanied with risks of hot bearings, sudden strains, 
 unexpected fracture of connection, shaft, cylinder, valve- 
 chest or pipe, and occasional necessary stoppages. 
 
 The best pumping combinations are so certainly liable 
 
PUMPING WITH DIRECT PRESSURE. 591 
 
 to such contingencies that cities may judiciously hesitate to 
 rely entirely upon the infallibility of their boilers, engines, 
 and pumps, even when so fortunate as to secure attendants 
 upon whom they can place implicit confidence. 
 
 The direct pressure method, alone, necessitates unceas- 
 ing firing of the boiler and motion of the pumping-engine, 
 and consequently double or triple sets of hands, to whose 
 integrity and faithfulness, night and day and at all times, 
 the works are committed. 
 
 Hydraulic power and machinery are far more reliable 
 than steam machinery, for direct pressure uses, and hy- 
 draulic power presents the great advantage of being able 
 to respond almost instantaneously to the extreme demand 
 for both water and pressure, while a dull fire under the 
 boiler may require many minutes for revival so as to raise 
 the steam to the effective emergency pressure. An example 
 of pumping machinery of five million gallons capacity per 
 diem, driven by hydraulic power, is shown in Fig. 143. 
 This set of pumping machinery was constructed for the city 
 of Manchester, N. H., by the Geyelin department of Messrs. 
 K. B. Wood & Co., Philadelphia, from general designs by 
 the writer, and has operated very satisfactorily since its 
 completion in 1874. This machinery is adapted in all re- 
 spects to direct pressure service, and was so used during a 
 full season while the reservoir was in process of construction, 
 and it is equally well adapted to its ordinary work of pump- 
 ing water to the distributing reservoir. 
 
 The direct forcing method does not provide for the de- 
 position or removal of impurities after they have passed the 
 engine, but the sediments that reach the pumps are passed 
 forward to the consumers in all sections of the pipe distri- 
 bution. 
 
 In combination with a reservoir sufficient for all the 
 
592 SYSTEMS OF WATER SUPPLY. 
 
 ordinary purposes, and equalizing the ordinary work and 
 the ordinary pressures at the taps, and also in combination 
 with a very small reservoir, the direct pressure facilities 
 may prove a most valuable auxiliary in times of emergency, 
 and they are then well worth the insignificant difference in 
 first cost of pumping machinery. 
 
 In the smaller works the entire machinery, and in larger 
 works one-half the machinery, may with advantage be 
 capable of and adapted for direct pressure action. 
 
 If, instead of substantial and simple machinery built 
 especially for long and reliable service, some one of the 
 intricate and fragile machines freely offered in the market 
 for direct pumping is substituted, and is not supplemented 
 by an ample reservoir reserve, then a risk is assumed which 
 no city can knowingly afford to suffer ; and if true prin- 
 ciples of economy of working are applied, it will generally 
 be found that no city can, upon well-established business 
 theories, afford to purchase and operate such machinery. ' 
 
 Well designed and substantially constructed pumping- 
 machines, such as are now offered by several reliable build- 
 ers, when contrasted with several of the low-priced and low- 
 duty contrivances, are most economical in operation, most 
 economical in maintenance, and infinitely superior in reli- 
 ability for long-continuous work. 
 
JONVAL TURBINE. 
 CONSTRUCTED BY R. D. WOOD & Co., PHILADELPHIA. 
 
APPENDIX. 
 
 THE METRIC SYSTEM OF WEIGHTS AND MEASURES. 
 
 The use of the metric system of measure and weights 
 was legalized in the United States in 1866 by the National 
 Government, and is used in the coast survey by the engineer 
 corps, and to considerable extent in the arts and trades. 
 
 Several of the best treatises on theoretical hydraulics 
 give their lengths and volumes in metric measures, and we 
 give their equivalents in United States measures in the 
 following tables. 
 
 The metre, which is the unit of length, area, and volume, 
 equals 39.37079 inches or 3.280899 feet in length lineal, and 
 along each edge of its cube. 
 
 This unit is, for measures of length, multiplied decimally 
 into the decametre, hectometre, 'kilometre, and myriametre, 
 and is subdivided decimally into the decimetre, centimetre, 
 and millimetre. 
 
 The affixes are derived from the Greek for multiplication 
 by ten, and from the Latin for division by ten. 
 
 The measures for surface and volume are similarly 
 divided. 
 
 The gramme is the unit of weight, and it is equal to the 
 weight of a cubic centimetre of water, at its maximum 
 density, in vacuo. = .0022046 Ibs. 
 
 A cubic metre of water, at its maximum density, weighs 
 2204.6 Ibs. avoir. 
 38 
 
694 
 
 APPENDIX. 
 
 TABLE OF FRENCH MEASURES AND UNITED STATES EQUIVALENTS. 
 
 Measures of Length. 
 
 
 No. of 
 Metres. 
 
 
 i Millimetre 
 
 .OOI 
 
 .0393708 inch .0032809 foot. 
 
 i Centimetre . 
 
 .OI 
 
 .393708 inch 032809 foot 
 
 i Decimetre 
 
 . i 
 
 ^.0^708 inches ^280800 ft. .100^6^^ vd. 
 
 
 T J 
 
 = 39.3708 inches = 3.2808992 ft. .198842 rod 
 
 i Decametre . 
 
 ( 
 IO 
 
 = .0006214 mile. 
 32 808902 ft i 08842 rods 0062138 mile 
 
 
 ICO 
 
 328.08992 ft. 19.88424 rods ,062138 mile. 
 
 i Kilometre ... . 
 
 IOOO 
 
 3280 8992 ft 198 8424 rods 621383 mile 
 
 i Myriametre 
 
 IOOOO 
 
 32808 992ft 1988.424 rods 6 21383 miles 
 
 
 
 
 Measures of Area. 
 
 
 No. of sq. 
 Metres. 
 
 
 
 
 J 
 
 = 10.7643 sq. ft. = 1.196033 sq. yds. = .039538 
 
 i Deciare 
 
 ( 
 
 IO 
 
 sq. rod. 
 107 643 sq. ft. 39538 sq. rd. .002471 acre. 
 
 
 IOO 
 
 = 1076.43 sq. ft. 3.95383 sq. rds. = .02471 acre. 
 
 i Decare (not used) 
 i Hectare 
 
 IOOO 
 IOOOO 
 
 = 10764.3 sq.ft. = 39.5383 sq. rds. = .2471 acre. 
 107643 sq. ft. 395.383 sq. rds. 2.471 acres. 
 
 
 
 
 Measures of Volume. 
 
 
 No. of cu. 
 Metres. 
 
 
 
 I Millilitre . 
 
 OOOOOI 
 
 ~ 0610279 cubic inch 
 
 
 i Centilitre 
 
 .00001 
 
 610279 cubic inch. 
 
 
 i Decilitre 
 
 .0001 
 
 6.10279 cu. ins. 'OO353 cu. 
 
 ft. .0264165 gal. 
 
 
 .OOI ] 
 
 = 61.0279 cu. ins. = .0353136 
 
 cu. ft. = .264165 
 
 
 .01 ] 
 
 gallon. 
 = 610.279 cu - ins - = 353 I 3 6 
 
 cu. ft. = .0130791 
 
 i Hectolitre 
 
 .1 
 
 cu. yard. 
 = 26.4165 gallons = 3-53I36 c 
 
 u. ft. = .130791 cu. 
 
 
 I 
 
 yard. 
 = 264.1651 gallons = 35.313 
 
 cu. ft. = 1.30791 
 
 
 
 cubic yards. 
 
 
APPENDIX. 
 
 595 
 
 TABLE OF FRENCH MEASURES AND UNITED STATES EQUIVALENTS 
 
 (Continued). 
 
 Measures of Solidity. 
 
 
 No. of cu. 
 Metres. 
 
 
 
 I Millistere 
 
 .OOI 
 
 61.0279 cubic inches 3532 cubic foot 
 
 
 .OI 
 
 = 610.279 cu. ins. = .353166 cu. ft. = .013079 cu. 
 
 i Decistere 
 
 I 
 
 yard. 
 6102.79 cu. ins. = 3.53166 cu. ft. = .130791 cubic 
 
 i Stere 
 
 I 
 
 yard. 
 = 61027.9 cu. ins. = 35.3166 cu. ft. = 1.30791 cu. 
 
 I Decastere . 
 
 IO 
 
 yards. 
 353 *66 cu. ft. 13 0791 cu yards. 
 
 i Hectostere 
 
 IOO 
 
 3531 66 cu. ft. 130.791 cu. yards. 
 
 I Kilostere 
 
 IOOO 
 
 35316.6 cu. ft. 1307.91 cu. yards. 
 
 
 
 
 Measures of Weight. 
 
 
 No. of 
 Grammes. 
 
 . 
 
 i Milligramme .... 
 i Centigramme. . . . 
 I Decigramme 
 
 .001 
 .01 
 
 .1 
 
 I 
 
 = .015432 grain. 
 = .15432 grain. 
 = 1.5432 grains = .0035274 oz. Avoir. 
 15.432 grs. = .035274 oz. Av. = 002205 Ib- Av. 
 
 i Decagramme 
 I Hectogramme . . . 
 I Kilogramme 
 
 IO 
 IOO 
 IOOO 
 
 = 154.32 grs. = .35274 oz. Av. = .02205 Ib. Av. 
 = 1543.2 grs. = 3.5274 oz. Av. = .2205 Ib Av. 
 = 15432 grs. = 35.274 oz. Av. = 2.205 Ibs. Av. 
 2204.737 Ibs. 
 
 
 
 
 A cubic inch is equal to 
 
 .004329 gallon; or .0005787 cu. ft; or 16.38901 millilitres ; or 1.638901 
 centilitres ; or .1638901 decilitre ; or .016389 litre ; or .016389 millistere ; or 
 0016389 centistere. 
 
 A gallon is equal to 
 
 231 cubic inches, .13368 cubic foot; or .031746 liquid barrel; or 3785.513 
 millilitres ; or 378.551 centilitres ; or 37.8551 decilitres ; or 3.785513 litres ; or 
 .3785513 decalitre ; or .037855 hectolitre ; or .0037855 kilolitre. 
 
 
 
 A cubic foot is equal to 
 
 1728 cubic inches; or 7.48052 liquid gallons; or 6.2321 imperial gallons ; 
 or 3.21426 U. S. pecks ; or .803564 U. S. struck bushel ; or .23748 liquid bar- 
 
696 APPENDIX. 
 
 rel of 31^ gallons ; or 2831.77 centilitres ; or 283.177 decilitres : or 28.3177 
 litres ; or 2.83177 decalitres ; or .283177 hectolitre ; or .0283177 kilolitre ; or 
 28.3177 millisteres; or 2.83177 centisteres ; or .283177 decistere ; or .0283177 
 stere. 
 
 The imperial gallon is equal to 
 
 .16046 cu. feet ; or 1.20032 U. S. liquid gallons. 
 
 A cubic yard is equal to 
 
 46656 cu. inches ; or 201.97404 liquid gallons ; or 27 cu. feet ; or 21.69623 
 struck bushels ; or 764.578 litres ; or 76.4578 decalitres ; or 7.64578 hectolitres ; 
 or .764578 kilolitre ; or 764.578 milisteres ; or 76.4578 centisteres ; or 7.64578 
 decisteres ; or .764578 stere ; or .0764578 decastere ; or .0076458 hectostere ; 
 or .00076458 kilostere. 
 
 TABLE OF UNITS OF HEADS AND PRESSURES OF WATER AND 
 EQUIVALENTS. 
 
 (RANKINE.) 
 
 One foot of water at 52. 3 Fah. = 62.4 Ibs. on the square foot- 
 
 " = .433 " inch. 
 
 " " " " = .0295 atmosphere. 
 
 " " " " = .8823 inch of mercury at 32. 
 
 One Ib, on the square foot = .016026 foot of water. 
 
 " " " inch = 2.308 feet of water. 
 
 One atmosphere ( 29.922 in. mercury) = 33.9 " 
 
 One inch of mercury, at 32 = 1.1334 " 
 
 One cubic foot of average sea-water = 1.026 cu. ft. of pure water in 
 
 weight. 
 
 One Fahrenheit degree = -55555 Centigrade degree. 
 
 One Centigrade degree = 1.8 Fahrenheit degrees. 
 
 Temperature of melting ice = 32 on Fahrenheit's scale, 
 
 " " = O " Centigrade scale. 
 
APPENDIX. 
 
 597 
 
 TABLE OF AVERAGE WEIGHTS, STRENGTHS, AND ELASTICITIES OF 
 MATERIALS. (From Trautwine, Neville, and Rankine.) 
 
 MATERIALS. 
 
 Weight 
 per 
 cu. in. 
 
 Weight 
 per 
 cu. ft. 
 
 Specific 
 Grav. 
 
 Tenacity 
 per 
 sq. in. 
 
 Resist- v 3 
 ance per >, 
 sq. in.to 1 
 crush- ^u 
 ing force. NX\ 
 
 JS 
 
 Woods (seasoned, and dry). 
 Ash 
 
 Lbs. 
 
 Lbs. 
 48.0 
 38 
 48 
 
 47 
 
 56.8 
 
 36.8 
 35 
 25 
 53 
 49 
 59-3 
 51-8 
 
 0-77 
 .61 
 
 77 
 75 
 
 
 
 59 
 56 
 .40 
 
 85 
 79 
 95 
 
 83 
 
 Lbs. 
 17000 
 
 16000 
 
 11400 
 12000 
 13500 
 
 13000 
 I6OOO 
 10250 
 
 i*. \^ 
 
 9000 *A\ 
 
 8500 N> 
 4900 A 
 5600 * Oj 
 
 10300 ^J 
 
 :::: x : 
 
 6400 oy ^ 
 6500 \3 
 6000 X^> 
 
 " American white 
 
 
 Beech , 
 
 
 
 
 
 
 
 
 Elm .. .. 
 
 
 
 
 Hemlock 
 
 
 Hickory 
 
 
 
 
 Oak, live 
 
 
 " white 
 
 
 red 
 
 
 
 
 
 
 
 
 34-3 
 45-0 
 25.0 
 38 
 
 < 
 
 162 
 
 525 
 524 
 
 533 
 529 
 
 538 
 
 549 
 560 
 
 153 
 441 
 
 440 
 485 
 474 
 717 
 713 
 
 846 
 644 
 
 49 
 456 
 
 437 
 
 Cu.yd. 
 2357 
 3375 
 2700 
 4050 
 1512 
 1339 
 
 55 
 .72 
 .40 
 .61 
 
 - 
 
 2.6 
 
 8.40 
 8.40 
 8-54 
 8.5 
 8.61 
 8.80 
 8.88 
 
 2-45 
 7.07 
 7.04 
 
 7-77 
 7.60 
 11.44 
 11.40 
 
 13-58 
 
 10.31 
 
 7.85 
 7-30 
 7.00 
 
 1.4 
 
 7800 
 12400 
 
 
 
 ISOOO 
 
 49000 
 36000 
 igOOO 
 30000 
 00000 
 
 9400 
 
 16700 
 
 13500 
 
 50000 
 48000 
 1800 
 
 3300 
 40900 
 
 120000 
 5300 
 7500 
 
 280 
 
 5400 /Jl 
 5500 1 
 
 7200 / 
 10300 
 
 33000 
 
 106000 
 108000 
 
 'Soo 
 
 " southern " 
 
 
 
 
 Walnut black 
 
 
 Metals. 
 
 .30972 
 
 Brass cast 
 
 " rolled 
 
 
 .03085 
 .03062 
 03113 
 
 
 
 " sheet 
 
 " wire drawn *... 
 
 -03241 
 .00885 
 .02552 
 
 Glass . . >. 
 
 
 " " hot blast 
 
 " " wrought sheet or plate 
 
 .02807 
 
 " " " large bars 
 
 
 .04152 
 
 " milled 
 
 Mercury (at 32 Fah., 849 Ibs.) (at 212, ) 
 836 Ibs.), at 60 o ) 
 
 .04896 
 
 0373 
 .02836 
 .02637 
 .02532 
 
 Cu. ft. 
 87.3 
 125 
 100 
 
 150 
 
 56 
 
 49.6 
 
 Silver .... 
 
 Steel 
 
 Tin cast 
 
 Zinc 
 
 Earth and Stones (dry). 
 
 Brick common hard 
 
 
 " best pressed . . . .... 
 
 
 
 
 Cement, American Rosendale, loose 
 
 
 
 
 
 
 
APPENDIX. 
 
 TABLE OF AVERAGE WEIGHTS, STRENGTHS, ETC. (Continued}. 
 
 MATERIALS. 
 
 Weight 
 per 
 cu.ft. 
 
 Weight 
 per 
 cu. yd. 
 
 Specific 
 Grav. 
 
 Tenacity 
 per 
 sq. in. 
 
 Resist- 
 ance per 
 sq. in. to 
 crush- 
 ng force. 
 
 Lbs. 
 
 
 Lbs. 
 
 go 
 80 
 119 
 63 
 
 Ll>s. 
 
 2430 
 2l6o 
 
 3213 
 I7OI 
 
 .... 
 
 Lbs. 
 280 
 
 
 
 1.9 
 
 .... 
 
 
 
 
 
 
 
 556- 
 
 Coal bituminous . 
 
 84 
 50 
 
 2268 
 1350 
 
 i-35 
 
 .... 
 
 " broken loose 
 
 
 
 
 
 
 75 
 95 
 no 
 168 
 96 
 168 
 
 IOO 
 
 187 
 107 
 
 IOO 
 120 
 130 
 
 168 
 53 
 165 
 165 
 154 
 138 
 125 
 144 
 no 
 125 
 
 IOO 
 
 140 
 no 
 103 
 25 
 
 IOO 
 
 no 
 125 
 150 
 86 
 1 80 
 170 
 
 58.7 
 
 2025 
 
 2565 
 2970 
 4536 
 2592 
 4 53 6 
 2700 
 
 5049 
 2889 
 2700 
 3240 
 3510 
 4536 
 1431 
 4455 
 4455 
 4158 
 3726 
 
 3375 
 3888 
 2970 
 
 3375 
 2700 
 3780 
 2970 
 2781 
 
 675 
 2700 
 2970 
 
 3375 
 4050 
 2322 
 4873 
 459 
 
 1585 
 
 
 
 
 " " moderately rammed . 
 
 
 
 
 " " as a mud . . 
 
 
 
 
 
 2.69 
 2.69 
 
 .... 
 
 1 0000 
 
 " Quarried in loose piles 
 
 
 
 
 
 
 
 " ouarried in loose piles 
 
 
 
 
 Gravel 
 
 
 
 
 
 1.90 
 
 .... 
 
 .... 
 
 " " " moist . . 
 
 
 2.7 
 
 
 
 8335 
 
 
 Marble 
 
 2.64 
 
 
 
 5500 
 
 Masonry, dressed granite, or limestone. . 
 " well-scabbled mortar rubble of do. 
 " " " dry " " do. 
 " roughly " " " " do. 
 " dressed sandstone . 
 
 
 
 
 
 
 
 
 
 
 " dry rubble " 
 
 
 
 
 
 
 
 .... 
 
 345 
 
 
 " " press'd bricks, close joints 
 Marl 
 
 
 
 
 1-75 
 1.65 
 
 50 
 
 .... 
 
 
 
 
 
 
 
 
 1.76 
 
 .... 
 
 
 
 
 
 .... 
 
 
 
 5000 
 
 
 glate 
 
 2.89 
 2-73 
 
 0.94 
 
 42OO 
 
 12000 
 2OO 
 
 
 Miscellaneous Materials. 
 Ice 
 
 
 Oil, linseed 
 Petroleum 
 Powder, slightly shaken 
 
 58.68 
 54.81 
 62.3 
 
 12 
 
 50 
 62.334 
 
 324 
 1350 
 1693 
 
 .94 
 
 .878 
 
 I.O 
 
 
 
 
 
 Water . 
 
 I.O 
 
 .... 
 
 
 
 
APPENDIX. 
 
 599 
 
 FORMULAS FOR SHAFTS. (Francis.) 
 Wrought-iron prime movers, with gears : 
 
 d = V)/ 100P , and P = 
 Wrought-iron transmitting shaft : 
 
 d = 
 
 -, and P = .02Nd?. 
 
 Steel prime mover, with gears : 
 3/62.5P 
 
 Steel transmitting shaft : 
 3/31.25P 
 
 d = 
 
 N 
 
 and P = .OHUKP. 
 
 and P = .03&ZVS 8 . 
 
 In which ^ = diameter of shaft in inches. 
 
 -ZV = number of revolutions per minute. 
 P = horse powers. 
 
 TRIGONOMETRICAL EXPRESSIONS. 
 
 COTANGENT 
 
 Radius = AC. 
 
 Sine = Cd. 
 
 Cosine = Ce. 
 
 Tangent = Bf. 
 
 Cotangent = hg. 
 
 Secant = Af. 
 
 Cosecant = Ag. 
 
 Versine = Bd. 
 
 Coversine = he. 
 
00 
 
 APPENDIX. 
 
 TRIGONOMETRICAL EQUIVALENTS, WHEN RADIUS = i. 
 
 Sine 
 
 = 
 
 1 -=- Cosec. 
 
 u 
 
 = 
 
 Cosin. -^ Cotan. 
 
 u 
 
 = ' 
 
 l/(l - Cosin 2 .) 
 
 Cosine 
 
 = 
 
 1 -- Sec. 
 
 
 
 =. 
 
 Sin. -^- Tan. 
 
 
 
 = 
 
 Sin. x Cotan. 
 
 a 
 
 = 
 
 VT^^Sin 2 ? 
 
 Tangent 
 
 =s 
 
 1 -f- Cotan. 
 
 " 
 
 = 
 
 Sin. -^- Cosin. 
 
 Cotangent 
 
 = 
 
 1 + Tan. 
 
 " 
 
 
 
 Cosin. -^- Sin. 
 
 Secant 
 
 = 
 
 1 -j- Cosin. 
 
 " 
 
 = 
 
 VT+ Tan 2 . 
 
 Cosecant 
 
 = 
 
 1 -T- Sin. 
 
 Yersine 
 Coversine 
 
 + Cotan 2 . 
 
 Rad. Cosin. 
 
 Rad. Sin. 
 Complement = 90 Angle. 
 Supplement = 180 Angle. 
 
 If radius of an arc of any angle is multiplied or divided 
 Tby any given number, then its several correspondent trigo- 
 nometrical functions are increased or diminished in like 
 
 ratio. 
 
 Diameter = Rad. x 2. 
 
 Circumference = Rad. x 6.2832. 
 
 " = Diam. x 3.1416. 
 
 Area of circle = Diam 2 . x .7854. 
 
 Surface of a sphere = Diam 2 . x 3.1416. 
 Volume of a sphere = Diam 3 . x .5236. 
 Length of one second of arc = Rad. x .0000048. 
 minute " " = Rad. x .0002909. 
 " degree " " = Rad. x .0174533. 
 
 " " 
 
APPENDIX. 
 
 601 
 
 VALUES* OF SINES, TANGENTS, ETC., WHEN RADIUS = i. 
 
 Deg. 
 
 Sine. 
 
 Cover. 
 
 Cosec. 
 
 Tang't. 
 
 Cotan. 
 
 Secant. 
 
 Versine. 
 
 Cosine. 
 
 Deg. 
 
 o 
 
 .00 
 
 I.OOOOO 
 
 Infinite. 
 
 .0 
 
 Infinite. 
 
 I.OOOOO 
 
 o. 
 
 I.OOOOO 
 
 90 
 
 I 
 
 2 
 
 01745 
 .03480 
 
 .98254 
 .96510 
 
 57.2986 
 28.6537 
 
 .oi745 
 .03492 
 
 57.2899 
 28.6362 
 
 1.00015 
 I 00060 
 
 .0001 
 
 .0006 
 
 99984 
 
 99939 
 
 88 
 
 3 
 
 05234 
 
 .94766 
 
 19.1073 
 
 .05241 j 19.0811 
 
 1.00137 
 
 .0013 
 
 .99863 
 
 87 
 
 4 
 
 .06976 
 
 .93024 
 
 14-3355 
 
 .06993 
 
 14.3007 
 
 1.00244 
 
 .0024 
 
 99756 
 
 86 
 
 5 
 6 
 
 .08716 
 
 .10453 
 
 .91284 
 89547 
 
 9.5667 
 
 .08749 
 .10510 
 
 ".4300 
 9-5144 
 
 I 00381 
 i 00550 
 
 .0038 
 
 .0054 
 
 .99619 
 .99452 
 
 85 
 84 
 
 7 
 
 .12187 .87813 
 
 8.2055 
 
 .12278 
 
 8.1443 
 
 1.00750 
 
 .0074 
 
 99255 
 
 83 
 
 8 
 
 13917 
 
 .86082 
 
 7.1852 
 
 14054 
 
 7-ii54 
 
 1.00982 
 
 .0097 
 
 .99027 
 
 82 
 
 9 
 
 15643 
 
 .34356 
 
 6.3924 
 
 15838 
 
 6-3137 
 
 1.01246 
 
 .0123 
 
 .98769 
 
 81 
 
 10 
 
 17365 
 
 .82035 
 
 5-7587 
 
 17633 
 
 5-6712 
 
 1.01542 
 
 .0151 
 
 .98481 
 
 80 
 
 ii 
 
 .19081 
 
 .80919 
 
 5-2408 
 
 .19438 
 
 5.1446 
 
 1.01871 
 
 .0183 
 
 98163 
 
 79 
 
 12 
 13 
 
 .20791 .79208 
 .22495 .77504 
 
 4.8097 
 4-4454 
 
 21255 
 .23087 
 
 4.7046 
 4-331? 
 
 1.02234 
 1.02630 
 
 .0218 
 .0256 
 
 978i5 
 97437 
 
 78 
 77 
 
 14 
 
 .24192 .75807 
 
 4-1335 
 
 24933 
 
 4.0108 
 
 1.03061 
 
 .0297 
 
 97030 i 76 
 
 11 
 
 .25882 
 
 .74118 
 .72436 
 
 3-8637 
 3-6^79 
 
 26795 
 .28674 
 
 3-7320 
 3-4874 
 
 1-03527 
 1.04029 
 
 .0340 
 
 .0387 
 
 96593 
 .96126 
 
 75 
 74 
 
 '7 
 
 .29237 
 
 .70762 
 
 3.4203 
 
 3573 
 
 3-2708 
 
 1.04569 
 
 .0436 
 
 95630 
 
 73 
 
 18 
 
 .30902 
 
 .69098 
 
 3-2360 
 
 32492 
 
 3-0777 
 
 1.05146 
 
 .0489 
 
 .95106 
 
 72 
 
 19 
 
 32557 1 -67443 
 
 3-07I5 
 
 34433 
 
 2.9042 
 
 1.05762 
 
 0544 
 
 .94552 
 
 71 
 
 20 .34202 
 21 .35337 
 
 .65797 
 .64163 
 
 2.9238 
 2.7904 
 
 36397 
 .38386 
 
 2-7475 
 2.6051 
 
 1.06417 
 1.07114 
 
 .0603 
 
 .0664 
 
 93969 
 93358 
 
 7 
 60 
 
 22 
 
 .37461 
 
 62539 
 
 2.6694 
 
 .40403 
 
 2.4751 
 
 1-07853 
 
 .0728 
 
 .92718 
 
 68 
 
 23 
 
 39 3 73 
 
 .60926 
 
 25593 
 
 42447 
 
 2.3558 
 
 1.08636 
 
 .0794 
 
 .92050 
 
 67 
 
 24 
 
 .40674 
 
 59326 
 
 24585 
 
 44523 
 
 2.2460 
 
 1.09463 
 
 .0864 
 
 91355 
 
 66 
 
 25 
 
 .42262 
 
 57738 
 
 
 .46631 
 
 2.1445 
 
 I - I0 337 
 
 .0936 
 
 .90630 
 
 65 
 
 26 
 
 43837 
 
 .56162 
 
 2.2811 
 
 .48773 
 
 2.0503 
 
 1.11260 
 
 .1012 
 
 .89879 
 
 64 
 
 27 
 
 45399 
 
 54600 
 
 2.2026 
 
 50952 
 
 1.9626 
 
 1.12232 
 
 .1089 
 
 
 6 3 
 
 28 
 
 46947 
 
 .53052 
 
 2.1300 
 
 .53171 1.8807 
 
 1-13257 
 
 .1170 
 
 .88295 
 
 62 
 
 29 
 
 .48481 
 
 51519 
 
 2.0626 
 
 55431 
 
 1.8040 
 
 1-14335 
 
 .1253 
 
 .87462 
 
 61 
 
 30 
 
 .50000 
 51504 
 
 .50000 
 
 .48496 
 
 2.0000 
 I.94I6 
 
 57735 
 .60086 
 
 as 
 
 1.15470 
 1.16663 
 
 .1339 
 .1428 
 
 .86603 
 
 60 
 
 32 
 
 .52992 
 
 .47008 
 
 1.88 7 
 
 .62487 
 
 1.6003 
 
 I-I7917 
 
 .1519 
 
 .84805 
 
 5 
 
 33 
 
 54464 
 
 45536 
 
 1.8360 
 
 .64941 
 
 1.5398 
 
 1.19236 
 
 1613 
 
 .83867 
 
 57 
 
 34 
 
 . 1:5919 
 
 .44080 
 
 1.7882 
 
 67451 
 
 1.4826 
 
 1.20621 
 
 1709 
 
 .82904 
 
 56 
 
 35 
 
 57358 
 
 .42642 
 
 1-7434 
 
 .70020 
 
 1.4281 
 
 1.22077 .1808 .81915 
 
 55 
 
 36 
 
 58778 
 
 41221 
 
 1.7013 
 
 .72654 
 
 1-3764 
 
 1.23606 .1909 .80902 
 
 54 
 
 37 
 
 .60181 
 
 .39818 
 
 i. 6616 
 
 75355 
 
 1.3270 
 
 1.25213 .2013 
 
 .79864 
 
 53 
 
 38 
 
 .61566 
 
 38433 
 
 1.6242 
 
 .78128 
 
 1.2799 
 
 1.26901 .2110 
 
 .78801 
 
 S 2 
 
 39 
 
 .62932 
 
 .37067 
 
 1.5890 
 
 .80978 
 
 1.2349 
 
 1.28675 
 
 .2228 
 
 77715 
 
 
 40 
 
 .64279 
 
 35721 
 
 1-5557 
 
 .83970 1.1918 
 
 1.30540 
 
 2339 
 
 .76604 
 
 50 
 
 41 
 
 .65606 
 
 34394 
 
 1.5242 
 
 .86929 i 1.1504 
 
 I.3250I 
 
 .2452 
 
 75471 
 
 49 
 
 42 
 
 66913 
 
 33086 
 
 1-4944 
 
 .90040 
 
 1.1106 
 
 1.34563 
 
 .2568 
 
 74314 
 
 48 
 
 43 
 
 .68200 
 
 .31800 
 
 1.4662 
 
 93251 
 
 1.0724 
 
 1-36732 
 
 .2686 
 
 
 47 
 
 44 
 
 .69465 
 
 30534 1-4395 
 
 .96569 
 
 i 355 
 
 I.390I6 
 
 .2808 
 
 71934 
 
 46 
 
 45 
 
 .70711 
 
 .29289 14142 
 
 i. 
 
 1- 
 
 I.4I42I 
 
 .2928 
 
 .70711 
 
 45 
 
 
 Cosine. 
 
 Versine. 
 
 Secant. 
 
 Cotan. 
 
 Tang't. 
 
 Cosec. 
 
 Cover. 
 
 Sine. 
 
 
 * When the angle exceeds 45, read upward ; the number of degrees will then be found in 
 the right-hand column, and the names of columns at the bottom. 
 
602 APPENDIX. 
 
 IN RIGHT-ANGLED TRIANGLES. 
 
 Base = VRyp\ -- Perp*. 
 
 = '/(Hyp. + Perp.) x (Hyp. - Perp.) 
 
 Perpendicular = 4/Hyp. 2 Base 2 . 
 
 = '/(Hyp. + Base) x (Hyp. - Base.) 
 
 Hypothenuse = I/Base 2 + Perp 2 . 
 
 What constitutes a car load (20,000 Ibs. weight) : 
 
 70 bbls. lime ; 70 bbls. cement ; 90 bbls. flour ; 6 cords 
 of hard wood ; 7 cords of soft wood ; 18 to 20 head of cattle ; 
 9000 feet board measure of plank or joists; 17,000 feet 
 siding; 1 3, 000 feet of flooring ; 40,000 shingles ; 340 bushels 
 of wheat ; 360 bushels of corn ; 680 bushels of oats ; 360 
 bushels of Irish potatoes ; 121 cu. ft. of granite ; 133 cu. ft. 
 sandstone ; 6000 bricks ; 6 perch rubble stone ; 10 tons of 
 coal ; 10 tons of cast-iron pipes or special castings. 
 
 Lubricator, for slushing heavy gears: 
 
 10 gallons, or 3J pails of tallow ; 1 gallon, or \ pail of 
 Neat's foot-oil ; 1 quart of black-lead. Melt the tallow, 
 and as it cools, stir in the other ingredients. 
 
 For cleaning brass : 
 
 Use a mixture of one ounce of muriatic acid and one- 
 half pint of water. Clean with a brush ; dry with a piece 
 of linen ; and polish with fine wash leather and prepared 
 hartshorn. 
 
 Iron cement, for repairing cracks in castings : 
 
 Mix J Ib. of flour of sulphur and \ Ib. of powdered sal 
 ammoniac with 25 Ibs. of clean dry and fine iron-borings, 
 then moisten to a paste with water and mix thoroughly. 
 
APPENDIX. 
 
 603 
 
 Calk the cement into the joint from both sides until the 
 crack is entirely filled. In heavy castings to be subjected 
 to a great pressure of water, a groove may be cut along a 
 transverse crack, on the side next the pressure, about one- 
 quarter inch deep, with a chisel ^%-inch wide, to facilitate 
 the calking in of the cement. 
 
 Alloys. The chemical equivalents of copper, tin, zinc, 
 and lead bear to each other the following proportions, ac- 
 cording to Rarikine : 
 
 Copper. 
 31-5 
 
 Tin. 
 59- 
 
 Zinc. 
 32-5 
 
 Lead. 
 
 When these metals are united in alloys their atomic pro- 
 portions should be maintained in multiples of their respec- 
 tive proportional numbers ; otherwise the mixture will lack 
 uniformity and appear mottled in the fracture, and its 
 irregular masses will differ in expansibility and elasticity, 
 ajid tend to disintegration under the influence of heat and 
 motion. 
 
 MATERIALS. 
 
 COMPOSITION. 
 
 By Equivalents. 
 
 By Weight. 
 
 Very hard bronze 
 
 Copper. 
 12 
 
 14 
 16 
 
 * 18 
 
 20 
 
 Copper. 
 4 
 
 2 
 
 3 
 4 
 
 Tin. 
 Znc. 
 
 2 
 
 3 
 
 Copper. 
 6.401 
 6.966 
 8.542 
 9.610 
 10.678 
 
 Copper. 
 
 3-877 
 1.938 
 
 1-454 
 1.292 
 
 Tin. 
 
 Zinc. 
 
 I 
 
 Hard bronze for machinery bearings 
 
 Bronze or gun-metal, contracts -j-^ in cooling 
 Bronze somewhat softer ... . 
 
 Soft bronze for toothed wheels 
 
 Malleable brass 
 
 Ordinary brass, contracts ^ in cooling 
 Yellow metal for sheathing ships 
 
 Spelter solder, for brazing copper and iron. . 
 
 Babbitt's metal consists of 50 parts of tin, i of copper, and 5 of antimony. 
 
604 APPENDIX. 
 
 Aluminum bronze, containing 95 to 90 parts of copper 
 and 5 to 10 parts of aluminum, is an alloy much stronger 
 than common bronze, and has a tenacity of about 22.6 
 tons per square inch, while the tenacity of common bronze, 
 or gun-metal, is but about 16 tons. 
 
 Manganese bronze is made by incorporating a small 
 proportion of manganese with common bronze. This alloy 
 can be cast, and also can be forged at a red-heat. 
 
 A specimen cast at the Royal Gun Factory, Woolwich, 
 in 1876, showed an ultimate strength of 24.3 tons per square 
 inch, an elastic limit of 14 tons, and an elongation of 8.75 
 per cent. The same quality forged had an ultimate resist- 
 ance of 29 tons per square inch, an elastic limit of 12 tons, 
 and an elongation of 31.8 per cent. A still harder forged 
 specimen had an ultimate strength of 30.3 tons per square 
 inch, elastic limit of 12 tons, and elongation of 20.75 per 
 cent. 
 
 The tough alloy, introduced by Mr. M. P. Parsons, will 
 prove a desirable substitute for the common bronze in hy- 
 draulic apparatus, where its superior strength and greater 
 reliability will be especially valuable. 
 
 APPROXIMATE BOTTOM VELOCITIES OF FLOW IN CHANNELS AT 
 WHICH THE FOLLOWING MATERIALS BEGIN TO MOVE. 
 
 > ,2,5 feet per second, microscopic sand and clay. 
 
 .50 " " " fine sand, 
 
 i.oo " " " coarse sand. 
 
 1.75 " " " pea gravel. 
 
 3 " " " smooth nut gravel. 
 
 4 " " " 4-inch pebbles. 
 
 5 " " " 2-inch square brick-bats. 
 
APPENDIX. 
 
 606 
 
 TENSILE STRENGTH OF CEMENTS AND CEMENT MORTARS, WHEN 
 7 DAYS OLD, 6 OF WHICH THE CEMENTS WERE IN WATER. 
 
 (Compiled from Gilmore.*) 
 
 
 BY WEIGHT. 
 
 BY VOLUME, 
 LOOSELY MEASUR'D 
 
 BY VOLUME, 
 
 WELL SHAKEN. 
 
 
 
 
 
 
 
 s .. 
 
 /I 
 
 
 
 
 
 U 
 
 m 
 
 
 
 
 
 e/5 3 
 
 ^s 
 
 
 
 
 
 
 
 ^.S'S 
 
 
 en 
 
 
 
 ^'l 
 
 
 
 
 
 
 Sj 
 
 a o a 
 
 How MIXED. 
 
 ,0 
 
 1 
 
 
 
 U- 
 
 jL fl 
 
 
 
 
 
 1 
 
 (iAro 
 
 
 Jjj 
 
 a 
 
 
 "wl^ 
 
 S'l 1 " 
 
 o-' 
 
 .j 
 
 i 
 
 
 I 
 
 TiT' 
 
 
 jy 
 
 V 
 
 
 s j 
 
 
 
 C 
 
 
 
 
 
 g 
 
 
 L 
 
 o 
 
 
 ^ 
 
 ^^ 
 
 
 1 
 
 O 
 
 
 t* 
 c 
 
 s 
 
 
 3*1 
 
 Is 
 
 1 
 
 
 ll 
 
 1g 
 
 
 O 
 
 a 
 a 
 
 1 
 
 
 
 ~ 
 
 jls 
 
 
 SB 8 
 
 O 4 O 
 
 1 
 
 O 4) 
 
 1 
 
 73 
 
 I 
 
 1 
 
 1 
 
 g 
 
 3-g- 
 
 
 0,0 
 
 K 
 
 c/! 
 
 duO 
 
 (^0 
 
 
 OH 
 
 & 
 
 w 
 
 H 
 
 
 
 
 
 
 
 
 
 
 
 
 
 Lbs. 
 
 Lbs. 
 
 Like beton agglome're'. 
 
 
 
 
 25 
 
 X 
 
 
 
 .21 
 
 
 
 
 .25 
 
 377 
 
 
 
 " common mortar. . 
 
 
 
 
 2 5 
 
 44 
 
 _ 
 
 44 
 
 
 __ 
 
 
 289 
 
 _^ 
 
 '' beton agglomere'. 
 
 
 
 
 5 
 
 I 
 
 
 
 .42 
 
 
 
 
 5 
 
 320 
 
 
 
 '' common mortar. . 
 
 
 __ 
 
 .5 
 
 44 
 
 
 
 44 
 
 
 
 
 44 
 
 222 
 
 
 
 1 beton agglome're'. 
 ' common mortar. . 
 
 
 
 
 i 
 i 
 
 I 
 14 
 
 
 
 '? 
 
 
 
 
 V 
 
 244 
 197 
 
 
 
 4 be*ton agglome're'. 
 
 
 
 
 1-33 
 
 I 
 
 
 
 X * X 3 
 
 
 
 
 x -3 
 
 179 
 
 
 
 ' common mortar. . 
 
 
 
 
 1.33 
 
 * fc 
 
 i^ 
 
 44 
 
 
 
 
 ** 
 
 129 
 
 
 
 1 beton agglome're'. 
 
 
 
 
 2 
 
 I 
 
 
 
 1.7 
 
 
 
 
 1.9 
 
 138 
 
 2804.4 
 
 41 common mortar.. 
 1 beton agglome're". 
 
 
 
 
 2 
 
 6 
 
 I 
 
 __ 
 
 if 
 
 5 
 
 
 
 5 u 9 
 
 109 
 
 66 
 
 1038.0 
 259-5 
 
 41 common mortar.. 
 
 
 __ 
 
 6 
 
 44 
 
 M 
 
 14 
 
 __ 
 
 
 35 
 
 
 ' beton agglome're'. 
 
 
 
 
 8 
 
 I 
 
 
 
 6.8 
 
 I 
 
 
 
 7.8 
 
 39 
 
 259-5 
 
 44 common mortar.. 
 4 beton agglome're'. 
 
 
 8 
 
 8 
 
 44 
 
 1 
 
 
 
 xx.6 
 
 
 
 ^~ 
 
 i4 
 
 24 
 96 
 
 104.7 
 
 14 common mortar.. 
 
 
 8 
 
 
 
 44 
 
 
 
 kt 
 
 __ 
 
 
 
 
 
 4 
 
 
 
 44 beton agglome're. 
 
 
 2 
 
 
 
 I 
 
 
 
 2.0 
 
 
 
 
 
 
 
 129 
 
 
 
 11 common mortar. . 
 1 be"ton agglomere'. 
 
 
 
 2 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 44 
 51 
 
 ~ 
 
 44 U 11 
 
 
 
 I 
 
 2 
 
 
 
 I 
 
 1.2 
 
 
 
 I 
 
 1.4 
 
 40 
 
 310.7 
 
 44 44 44 
 
 
 
 I 
 
 3 
 
 
 
 I 
 
 1.8 
 
 
 
 I 
 
 2 
 
 33 
 
 116.4 
 
 44 44 14 
 
 
 
 ! 
 
 4 
 
 
 
 I 
 
 2.4 
 
 
 
 I 
 
 2.8 
 
 22 
 
 156.0 
 
 44 44 11 
 
 - 
 
 . I 
 
 6 
 
 
 
 I 
 
 3-6 
 
 
 
 I 
 
 *J 
 
 Less than 
 10 Ibs. 
 
 52.4 
 
 11 44 14 
 
 
 
 I 
 
 8 
 
 
 
 
 
 
 
 
 
 
 
 
 
 46.5 
 
 44 14 41 
 
 i 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 
 400 
 
 846.7 
 
 44 common mortar.. 
 44 beton agglomere". 
 
 J 
 
 I 
 
 
 
 z 
 
 
 
 
 
 
 
 
 
 
 
 72 
 
 579-2 
 
 14 common mortar.. 
 
 ~ 
 
 I 
 
 ~ 
 
 ~ 
 
 ~ 
 
 ~ 
 
 ~ 
 
 ~ 
 
 ~ 
 
 
 104.7 
 
 * Vide Treatise on Coignet Be"ton, p. 28, et seq. New York, 1871. 
 
606 
 
 APPENDIX. 
 
 STANDARD DIMENSIONS OF BOLTS, WITH HEXAGONAL HEADS 
 
 AND NUTS. 
 
 Diameter 
 of bolt 
 in inches. 
 
 No. of 
 V threads 
 per in. of 
 length. 
 
 Breadth 
 of head, 
 in inches. 
 
 Thickn'ss 
 of head 
 in inches. 
 
 Breadth 
 of nut 
 in inches. 
 
 Thickness 
 of nut 
 in inches. 
 
 Weight 
 of round rod 
 per foot 
 in pounds. 
 
 Weight of 
 head and nut 
 in pounds. 
 
 t 
 
 2O 
 
 t 
 
 i 
 
 1 
 
 A 
 
 .1653 
 
 .017 
 
 T S *T 
 
 18 
 
 \ 
 
 T7T 
 
 ^ 
 
 1 
 
 2583 
 
 033 
 
 i 
 
 16 
 
 1 
 
 t 
 
 1 
 
 TV 
 
 .3720 
 
 .057 
 
 -T6 
 
 14 
 
 s 
 
 nr 
 
 
 
 i 
 
 .5063 
 
 .087 
 
 
 
 13 
 
 i 
 
 i 
 
 I 
 
 rk 
 
 .6613 
 
 .128 
 
 A 
 
 12 
 
 i 
 
 T 9 ^ 
 
 i 
 
 1 
 
 .8370 
 
 .190 
 
 1 
 
 II 
 
 i 
 
 1 
 
 I 
 
 H 
 
 r -33 
 
 .267 
 
 * 
 
 IO 
 
 4 
 
 f 
 
 4 
 
 H 
 
 1.488 
 
 43 
 
 7 
 ? 
 
 9 
 
 if 
 
 1 
 
 4 
 
 H 
 
 2.025 
 
 73 
 
 I 
 
 8 
 
 4 
 
 I 
 
 4 
 
 irV 
 
 2.645 
 
 I. 10 
 
 li 
 
 7 
 
 if 
 
 4 
 
 i| 
 
 iA 
 
 3.348 
 
 i .60 
 
 I* 
 
 7 
 
 4 
 
 4 
 
 4 
 
 ITT 
 
 4.133 
 
 2.14 
 
 If 
 
 6 
 
 2i 
 
 4 
 
 2 i 
 
 ITT 
 
 5.001 
 
 2-95 
 
 l| 
 
 6 
 
 2i 
 
 4 
 
 2 i 
 
 iA 
 
 5-952 
 
 3.78 
 
 4 
 
 si 
 
 4 
 
 T l 
 
 2^ 
 
 ixi 
 
 6.985 
 
 4.70 
 
 ij 
 
 5 
 
 2 I 
 
 J i 
 
 2 f 
 
 iii 
 
 8.101 
 
 5.60 
 
 l| 
 
 5 
 
 2| 
 
 4 
 
 2-J 
 
 IT! 
 
 9.300 
 
 7 .00 
 
 2 
 
 4! 
 
 3 
 
 2 
 
 3 
 
 2yV 
 
 10.58 
 
 8.75 
 
 2 i 
 
 4i 
 
 3f 
 
 2 i 
 
 3* 
 
 2T% 
 
 13-39 
 
 12.40 
 
 2\ 
 
 4 
 
 3f 
 
 2 i 
 
 3i 
 
 2TT 
 
 i6.53 
 
 17.00 
 
 2 ! 
 
 4 
 
 4i 
 
 2j 
 
 4j 
 
 2Tf 
 
 20.01 
 
 22.30 
 
 3 
 
 3i 
 
 4i 
 
 3 
 
 41 
 
 3rV 
 
 23.81 
 
 28.80 
 
APPENDIX. 
 
 607 
 
 WEIGHTS OF LEAD AND TIN LINED SERVICE-PIPES. 
 
 Calibre. 
 
 AAA. 
 Weight 
 per ft. 
 
 AA 
 Weight 
 per ft. 
 
 A. 
 Weight 
 per ft. 
 
 B. 
 
 Weight 
 per ft. 
 
 C. 
 
 Weight 
 per ft. 
 
 Weight 
 per ft. 
 
 D. Light. 
 Weight 
 per ft. 
 
 E . 
 
 Weight 
 per ft. 
 
 E. Light. 
 Weight 
 per ft. 
 
 Inches. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs. 
 
 Lbs, 
 
 I 
 
 1.5 
 
 1.3 
 
 1. 12 
 
 I 
 
 1. 06 
 
 0.62 
 
 
 
 0-5 
 
 
 
 * 
 
 3 
 
 2 
 
 1-75 
 
 1.25 
 
 I 
 
 0.81 
 
 
 
 0.7 
 
 0.56 
 
 I 
 
 3-5 
 
 2-75 
 
 2-5 
 
 2 
 
 i-75 
 
 1.5 
 
 1.25 
 
 I 
 
 0-75 
 
 t 
 
 4-5 
 
 3.5 
 
 3 
 
 2.25 
 
 2 
 
 1-75 
 
 i-5 
 
 1.25 
 
 I 
 
 
 
 
 
 
 
 
 
 
 I 
 
 6 
 
 4.75 
 
 4 3-25 
 
 2-5 
 
 2 
 
 
 
 1-5 
 
 
 
 I* 
 
 6 75 
 
 5-75 
 
 4-75 
 
 3-75 
 
 3 
 
 2-5 
 
 
 
 2 
 
 
 
 4 
 
 9 
 
 8 
 
 6.25 
 
 5 
 
 4-25 
 
 3-5 
 
 
 
 3-25 
 
 
 
 2 
 
 10.75 
 
 9 
 
 7 
 
 6 
 
 5-25 
 
 4 . 
 
 
 
 
 
 
 
 A manufacturer' s circular states that the following quanti- 
 ties of water will be delivered through 500 feet of their pipes, 
 of the respective sizes named, when the fall is ten feet : 
 
 Calibre . 
 
 jr inch 
 
 i inch 
 
 f inch 
 
 f inch 
 
 i inch 
 
 j i inch 
 
 
 
 
 
 
 
 
 Gallons per minute. . . 
 
 .348 
 
 .798 
 
 1.416 
 
 2.222 
 
 4.600 
 
 6-944 
 
 Gallons per 24 hours. . 
 
 576 
 
 1150 
 
 2040 
 
 3200 
 
 6624 
 
 IOOOO 
 
 A f-inch clean service-pipe connected to a J-inch tap 
 under a hundred feet head, will deliver at the sink, through 
 a common compression bib, ordinarily about three pails of 
 water, or say 8.25 gallons, or 1.1 cu. ft. of water per minute. 
 
 Lead is more generally used for service-pipes than any 
 other material, but wrought-iron pipe, lined and coated 
 with cement, or with a vulcanized rubber composition or 
 sundry coal-tar compositions and enamels, have been used 
 to a nearly equal extent within a few years past. Block- 
 tin pipe, tin-lined pipe, and galvanized iron pipe, have been 
 used also to a limited extent. 
 
608 
 
 APPENDIX. 
 
 Lead pipes of weights as in class A are used ordinarily 
 when the head of water on them does not exceed 75 feet ; 
 class AA when the head is from 75 to 150 feet ; and class 
 AAA when the head, or strain from water-ram, is great. 
 
 The strain from water-ram, in service-pipes, is very 
 much dependent on the character of the plumbing with 
 which the services connect. 
 
 METERS AND METER RATES, 1875. 
 
 CITY. 
 
 No. of 
 Meters 
 used. 
 
 Rate per 
 
 100 CU. ft. 
 
 Cents. 
 
 Kind of Meters. 
 
 Furnished by* 
 
 Boston Mass 
 
 Q74 
 
 22l 
 
 W 
 
 
 Baltimore Md 
 
 ^2O 
 
 2O 
 
 w. 
 
 
 Bridgeport, Conn . . . 
 Charlestown, Mass. . 
 Chicago 111 
 
 I 
 1 80 
 1050 
 
 26^ to 40 
 
 22 i 
 141 
 
 W. 
 W. B. & F. 
 W 
 
 Water-works. 
 Water-works. 
 
 Cleveland, O 
 
 18 
 
 iql tO 2li 
 
 W B & F 
 
 
 Columbus O 
 
 1^8 
 
 26! 
 
 B & F E Nav 
 
 
 Fitchburg, Mass 
 Fall River, " 
 Hartford Conn . 
 
 25 
 4 
 6 
 
 ni to 37 i 
 22 i 
 
 1C to 22 1 
 
 B. &F. 
 B. & F. 
 B & F D 
 
 Consumer. 
 Consumer. 
 
 Jersey City, N. J 
 Louisville Ky 
 
 208 
 
 IIQ 
 
 26! 
 20 
 
 W. 
 W 
 
 Water-works. 
 W^ater- works 
 
 Meriden, Conn 
 
 Q 
 
 26^ to 40 
 
 B & F 
 
 \Vater-works 
 
 Manchester, N.H.... 
 New York, N.Y 
 New London, Conn.. 
 New Haven, " . . 
 New Bedford, Mass. . 
 Providence, R. I 
 Portland Me 
 
 1 6O 
 
 2OO 
 20 
 
 3 
 3 
 
 1358 
 
 15 to 30 
 
 12 
 261 
 22} 
 
 22 i 
 
 22i tO 37i 
 
 B. & F. N. 
 W. 
 N. 
 N. 
 B. &F. 
 B. & F. W. 
 B. & F W. 
 
 Water-works. 
 Consumer., 
 Water-works. 
 Consumer. 
 Water-works. 
 Consumer. 
 Consumer 
 
 Springfield, Mass. . . 
 St Paul Minn 
 
 8 
 4O 
 
 22|- 
 4.O to 64.4 
 
 W. & B. & F. 
 B & F N 
 
 Water-works. 
 \Vater-works 
 
 San Francisco, Cal. . 
 Waterbury, Conn. . . . 
 Worcester, Mass 
 
 800 
 8 
 800 
 
 641 to 133 
 26! to 40 
 n to i8| 
 
 W. 
 W. B. & F. 
 B. &F. 
 
 Water- works. 
 Water-works. 
 Water- works. 
 
 The initials refer to kinds of meters, as follows : 
 
 W. Worthington. 
 
 B. & F. Ball & Fitts. 
 
 N. National Meter Co. (Gem.) 
 
 -Hagl 
 Nav. Navarro. 
 D. Desper. 
 
 * A common practice is, for the water- works to furnish the meter and main- 
 tain and control it, and to charge the consumer from ten to fifteen per cent, on 
 its original cost, annually, to cover the expense, in addition to the regular meter 
 rate for water consumed. 
 
APPENDIX. 609 
 
 RESUSCITATION FROM DEATH BY DROWNING. 
 
 Persons may be restored from apparent death by drown- 
 ing, if proper means are employed, sometimes when they 
 have been under water, and are apparently dead, for fifteen 
 or even thirty minutes. To this end 
 
 1. Treat the patent INSTANTLY, on the spot, in the open 
 air, freely exposing the face, neck, and chest to the breeze, 
 except in severe weather. 
 
 2. Send with all speed for medical aid, and for articles 
 of clothing, blankets, etc. 
 
 I. To CLEAR THE THEOAT. 
 
 3. 'Place the patient gently on the face, with one wrist 
 under the forehead. 
 
 (All fluids, and the tongue itself, then fall forwards, and 
 leave the entrance into the windpipe free. 
 
 II. To EXCITE RESPIEATION. 
 
 4. Turn the patient slightly on his side, and 
 
 (I.) Apply snuff, or other irritant, to the nostrils ; and 
 (II.) Dash cold water on the face, previously rubbed 
 briskly until it is warm. 
 
 If there be no success, lose no time, but 
 
 III. To IMITATE RESPIEATION. 
 
 5. Replace the patient on the face. 
 
 6. Turn the body gently but completely on the side, and 
 a little beyond, and then on the face alternately, repeating 
 these measures DELIBEEATELY, EFFICIENTLY, and PEESE- 
 VEEINGLY, fifteen times in the minute only. 
 
 (When the patient reposes on the chest, this cavity is 
 39 
 
610 APPENDIX. 
 
 compressed by the weight of the body, and EXPIRATION 
 takes place ; when it is tnrned on the side, this pressure is 
 removed, and INSPIRATION occurs.) 
 
 7. When the prone position is resumed, make equable 
 but efficient pressure along the spine, removing it immedi- 
 ately before rotation on the side. 
 
 (The first measure augments the EXPIRATION, and the 
 second commences INSPIRATION.) 
 
 IV. To INDUCE CIRCULATION AND WAEMTH, CONTINUE 
 THESE MEASURES. 
 
 8. Rub the limbs upwards, with FIRM PRESSURE and 
 ENERGY, using handkerchiefs, etc. 
 
 9. Replace the patient's wet covering by such other cov- 
 ering as can be instantly procured, each bystander supply- 
 ing a coat or a waistcoat. Meantime, and from time to time, 
 
 Y. AGAIN, TO EXCITE INSPIRATION,. 
 
 10. Let the surface of the body be slapped briskly with 
 the hand ; or 
 
 11. Let cold water be dashed briskly on the surface, 
 previously rubbed dry and warm. 
 
 Avoid all rough usage. Never hold up the body by the 
 feet. Do not roll the body on casks. Do not rub the body 
 with salts or spirits. Do not inject smoke or infusion of 
 tobacco, though clysters of spirits and water may be used. 
 
 The means employed should be persisted in for several 
 hours, till there are signs of death. 
 
INDEX. 
 
 The figures refer to the pages. 
 
 Acceleration of motion, 185. 
 Adjustable effluent pipe, 36^. 
 Advantages of water supplies, 29. 
 Air, resistance of, to a jet, 190. 
 44 valves, 523. 
 41 vessel, 564, 565. 
 Ajutage, an, 213. 
 
 inward projecting, 218. 
 u vacuum, 214. 
 
 Algae, fresh water, 129. _ 
 
 Analyses of lake, spring, and well waters, icjf. 
 44 u mineral waters, 143. 
 
 44 potable waters, table, 117. 
 44 " river and brook waters, 118, 120. 
 Analysis of impure ice, 136. 
 Angular force graphically represented. 175. 
 Aquatic life, purifying office of, 132. 
 
 44 organisms, 131. 
 Arago's prediction at Grenelle, 106. 
 Areas of sluice valves, 360. 
 Artesian wells, 105, 106, 108. 
 
 44 temperature of, table, 127. 
 Artificial clarification of water, 159. 
 " gathering areas, ioo. 
 u pollution of water, 152. 
 
 storage " . 84, 93, 95, 98, 99. 
 
 Aspnaltum bath for pipes, 475, 487, 490. 
 Atlantic coast/rainfall, 53. 
 Atomic theory, 162. 
 Attraction, capillary, 296. 
 Atmospheric impurities of water, 122. 
 
 pressure, 182. 
 Average consumption of water, 44. 
 
 Basins, clear-water, 550. 
 infiltration, 537. 
 
 44 settling, 50. 
 Bends and branches, 272, 275, 478, 485. 
 
 44 coefficients for, table of, 274. 
 Blow-off valves, 513. 
 Boilers, 577, 578, 580. 
 Bolts in flanges, table of, 462. 
 Bolt-holes, templet for, 460. 
 Boyden's hook-gauge, 297. 
 Branches and bends, 272, 478, 484. 
 " composite pipe, 484. 
 
 formula for flow through, 275. 
 Bucket-plunger pump, 557, 567. 
 Bursting pressure, 232. 
 
 C. 
 
 Caloric, influence of, 163. 
 Canal banks, 370. 
 
 in side hill, 370. 
 ' miner's, 375. 
 44 open, 370. 
 
 Canal revetments and pavings, 371. 
 
 slopes, 371. 
 44 stop-gates, 373. 
 Canals and rivers, observed flows in, table of^ 
 
 307. 
 
 Canals and overs, coefficients for flow in, 308. 
 Capacity for filter-beds, 552. 
 Capillary attraction, 296. 
 Cast-iron pipes, 451. 
 
 " weights of, 465, 468, 469. 
 Cast socket on wrought pipe, 483. 
 Casting of pipes, 452. 
 Cement joints of pipes, 482. 
 u lined pipes, 479. 
 44 lining ot pipes with, 481. 
 11 mortar, for lining and covering pipes, 
 
 487. 
 
 Census statistics, 31. 
 Central rain system, 49. 
 Chamber, effluent, 358. 
 " influent, 366. 
 " walls, 369. 
 
 Chandler's, Prof., remarks on wells, 140. 
 Channels, coefficients for, 308. 
 
 44 depths and relative volumes and 
 
 velocities, 328. 
 
 44 flow in. experimental data, 306. 
 44 flow in open, 299. 
 
 formulas for flow, table, 310. 
 44 inclination in, 304. 
 44 influences controlling flow in, 316. 
 44 ratios of surface to mean veloc., 315. 
 44 surface velocities, 313. 
 44 velocity of flow in, 303, 304. 
 44 velocities of given films, 311. 
 44 water supply, protection of, 431. 
 Characteristics of pipe metals, 470. 
 Charcoal clarification of water, 535, 537. 
 
 44 filters, 536. 
 Check-valve, 367, 525. 
 Chemical clarification, 532. 
 Choice of water, 587. 
 Cities, families in various, 32. 
 
 persons per family in various, 32. 
 population of various, 32. 
 44 water supplied to, 35, 36, 37. . 
 Clarification of water, artificial, 159, 532. 
 charcoal, 535, 537. 
 chemical, 532. 
 natural, 149, 530, 532. 
 Cleaning of filter-beds, 553. 
 Clear water basin, 550. 
 Climate effects, rainfall, 47. 
 Coal required for pumping, 581. 
 Coating (asphaltum) pipes. 475, 487, 490. 
 Cochituate basin, rain upon, 72. 
 Coefficients, compound tubes, 219, 220. 
 convergent tubes, 217. 
 J, table of, 271. 
 experimental, 198. 
 
 table of, 237. 
 
612 
 
 INDEX. 
 
 Coefficients for channels, Kutter's, 305. 
 
 " circular orifices, 203. 
 u " flow in conduits, 444. 
 
 " " hydrometers, 325. 
 
 * u " pipes, table of, 242. 
 
 " " rectangular orifices, 205, 206. 
 
 u " service-pipes, 528. 
 
 " u weir formulas, 287, 288. 
 
 " wide-crested weirs, 294. 
 u from Castel, 200. 
 
 u u Eytelwein and D'Aubuis- 
 
 son, 256. 
 
 " General Ellis, 201. 
 
 " " L'Abbe Bossut, 199. 
 
 u " Lespinasse, 201. 
 
 Michelotti, 198. 
 " Prony, 255. 
 w u Rennie, 199. 
 
 w increase of, in short tubes, 213. 
 
 w m, 234, 247. 
 
 " mean, for smooth and foul pipes, 
 
 248, 249, 267. 
 
 of efflux, factors of, 197, 208. 
 " " table of, 227. 
 u " entrance of jet, 267. 
 
 u flow for channels, 305, 308. 
 " *' friction of earth-work, 345. 
 
 " " table of, 495. 
 
 " issue from short tubes, 218. 
 ' " masonry frictions, 396. 
 
 w " velocity and contraction for 
 
 orifice jets, 208. 
 practical application of, 197. 
 range of, 222. 
 resistance in bends, 274. 
 u variable values of, 210. 
 
 Coffer-dams, 430. 
 
 Combined reservoir and direct systems, 525. 
 Commercial use of water, 34. 
 Compensation flow, 86. 
 
 to riparian owners, 94. 
 Composite branches, pipe, 484. 
 Composition of water, the, 112. 
 Compound tubes, 218, 220. 
 
 " coefficients for, 220. 
 Compressibility and elasticity of water, 167. 
 Concrete conduit, a 438. 
 " foundations, 368. 
 " foundations for pipes, 487. 
 " paving, 355. 
 " proportions of, 368. 
 " revetments, 429. 
 Conduit arch, thrust of, 437. 
 1 data, 445. 
 
 masonry to be self-sustaining, 437. 
 ' of concrete, 438. 
 1 of wood, 439, 441. 
 
 shells, 434. 
 
 Conduits and pipes, 223. 
 " backing of, 438. 
 
 coefficients for, 444. 
 u examples of, 431,438, 439. 
 " exposure to frost, 437. 
 " formulas for flow in, 442, 443. 
 * foundations for, 433. 
 " locked bricks for, 435. 
 u masonry, 431. 
 " mean radii of, 441, 442. 
 " protection from frost, 436. 
 " stop-gates in, 436. 
 " transmission of pressure in, 436. 
 " under pressure, 435, 439. 
 u ventilation of, 434. 
 Confervae, 129. 
 Construction of embankments, 348. 
 
 of filter-beds, 548. 
 Consumption of water, 34, 43, 503. 
 Core of an embankment, 348. 
 Cornish pump, 557, 563. 
 
 Costs of pumping water, 574, 575. 
 Crib-work foundations, 385. 
 
 " weir, 384. 
 Croton basin, rainfall upon, 72. 
 Curbs, stop-valve, 515. 
 Curved-face wall, 421. 
 Cut-off wall, embankment, 348. 
 Cycle, low, rainfalls, 69, 77, 78. 
 Cylindrical penstock, 440. 
 tubes, 222. 
 
 D; 
 
 Dams, thickness of, 387. 
 Darcy-Pitot tube gauge, 322. 
 Data from existing conduits, 445. 
 Debris, floating, 530. 
 Decimal parts of an inch and foot, 457. 
 Decomposing organic impurities, 127. 
 Densities and volumes of water, relative, 164. 
 Desmids, in fresh ponds, 129. 
 Details of stop- valves, 513. 
 Depths of pipes, 501, 502. 
 Diagonal force, 175. 
 Diagrams of pumping, 42. 
 
 " of rainfall, 55, 57, 59. 
 Diameter of sub-mains, 507. 
 
 " of supply-main, 506. 
 Dimensions of existing canals, 373. 
 *' '' filter-beds, 554. 
 " " retaining walls, 420. 
 Direct pressure system, 590. 
 Discharges of pipes, 498, 500. 
 
 ' over waste-weirs, 378, 381. 
 Domestic draught of water, 34, 508. 
 Draught, variations in, 41. 
 Duplicate pumping machinery, 590. 
 Duplication in pipe systems, 510. 
 Duty of pumping-engines, 574, 576, 580, 583^ 
 Dwellings in various cities, 32. 
 Dykes, canal and river, 371. 
 
 E. 
 
 Earth and rock, porosity of, 102. 
 
 embankments, 333, 347, 348, 353, 370; 
 " evaporation from, 89, 90. 
 " pressures against walls, 408. 
 Eastern coast rain system, 50. 
 Economy of high duty of pumping-enginesj 
 
 579 581- 
 
 " " skillful workmanship, 369. 
 
 Eddies, in weir channels, 292. 
 Effect, mechanical, of the efflux, 225. 
 Effluent chambers, 358. 
 
 " ice-thrust upon, 358. 
 Efflux, equation of, 211. 
 
 " factors of the coefficient, 197. 
 " from pipes, coefficients of, 196, 227. 
 " mechanical effect of, 225. 
 " peculiarities of jet, 207. 
 ' volume from short tubes, 194, 210, 214. 
 Elasticity and compressibility of water, 167. 
 Electric moulinet, Henry's, 326. 
 Elementary dimensions of pipes, 504. 
 Elements, the vapory, 45. 
 Embankment, a light, 353. 
 
 core materials. 339, 342, 348, 354. 
 cut-off walls, 336, 338, 348. 
 example of, 347. 
 failures, 334. 
 fine sand in, 353. 
 foundations, 335. 
 frost covering, 350. 
 gate chambers, 357, 358. 
 masonry-faced, 354. 
 materials, coefs. of friction, 345. 
 " frictional angle of^. 
 
 345- 
 
INDEX. 
 
 613 
 
 Embankment materials, proportions of, 340, 
 
 349- 
 
 weights of, 341. 
 pressures in, 343. 
 u puddle wall, 351. 
 
 puddled slopes, 356. 
 44 sheet-piling under, 339. 
 
 44 site, reconnaissance tor, 347. 
 
 slope-paving, 350. 
 44 Slopes, 344, 345, 350. 
 
 sluices, 355, 356, 358. 
 44 soils beneath, 337. 
 
 44 springs under foundation, 337. 
 
 substructure, 336. 
 ciphon waste-pipe, 358. 
 " test borings at site, 336. 
 
 treacherous strata under, 338. 
 Embankments, canal, 370. 
 Indian, 334. 
 reservoir, 333. 
 Energy of jet, 276. 
 England, supply per capita, 37. 
 Equation of motion, 186. 
 
 u " resistance to flow, 233. 
 Equilibrium destroyed, 170, 300. 
 Errors in application of formulae, 252, 257. 
 
 " " weir measurements, 296. 
 Estimates of flow of streams, 78, 94. 
 European infiltration, 544. 
 Evaporation, effect upon storage, 93. 
 examples of, 90. 
 from earth, 89, no. 
 " reservoirs, 94. 
 water, 88, 89. 
 phenomena. 87. 
 44 ratios of, table, 92. 
 
 Evaporative power of boilers, 578, 580. 
 Examples of conduits, 431, 438, 439. 
 Experimental channel data, 306. 
 
 coefficients forny drometers, 325. 
 Experiments with weirs, 234. 
 Eytelwein's coefficients, 222, 
 
 F. 
 
 Faced revetments, 429. 
 Failures of embankments, 334. 
 
 44 " walls, 427. 
 Falling bodies, 190. 
 Families in various cities, 32. 
 Fascine revetments, 371. 
 Filter-beds, 547. 
 
 44 capacity of, 552. 
 " cleaning of, 55?. 
 
 construction of, 548, 557. 
 ice upon, 556. 
 protection of, 548, 555. 
 44 temperature of, 555. 
 " vegetal growth in, 555. 
 Filters, Atkin's, 536. 
 Fire draught of water, 34, 506, 508. 
 ' extinguishment, reserve for, 44. 
 ' 4 hydrants, 516, 519, 521. 
 ' losses, effect of water upon, 26. 
 4 service, 493, 588, 589, 591. 
 
 head desirable for, 493. 
 1 supplies, diameters of pipes for, 510. 
 Fish screens, 365. 
 Flanges, diameters of valve, 462. 
 
 " of cast-iron pipes, 462. 
 Flash-boards, 378. 
 Flashy and steady streams, 71. 
 Flexible pipe-joints, 463. 
 Floats, double, gauge, 326. 
 
 maximum velocity, 328. 
 44 mid-depth, 326. 
 Flood flow, 65, 98. 
 
 44 volumes, 65, 67^ 381. 
 Floods, ratios of, to rainfalls, 62. 
 
 Floods, seasons of, 68. 
 Flow, available, for consumption, 94. 
 coefficients of, 230. 
 compensation, 86. 
 
 equivalent to given depths of rain, 81. 
 from Croton and Cochituate basins, 73. 
 
 " different surfaces, 77. 
 gauged volumes of, 277. 
 gravity the cause of, 299. 
 in seasons of minimum rain, 69. 
 increase and decrease of, 86. 
 influence of absorption and evaporation 
 
 upon, 68. 
 
 minimum, mean, and flood, 75. 
 of streams and channels, 65, 299. 
 44 water, 184. 
 over a weir, 280. 
 periodic available, 69. 
 resistance to, in channels, 232, 300. 
 sub-surface equalizers of, 70. 
 summaries of monthly statistics of, 71. 
 through orifices, 194. 
 
 pipes, 223, 508, 560. 
 short tubes, 213. 
 
 44 sluices, pipes, and channels, z6x. 
 Fluctuations of streams, 319. 
 Flush hydrant, 519, 521. 
 
 Foot and inch, equivalent decimal parts of, 457. 
 Force, loss of, in pipes, 224. 
 
 44 percussive, of particles, 221. 
 Forces, angular, 176. 
 44 equivalent, 172. 
 44 graphically represented, 175. 
 Formula, efflux from an orifice, 196, 209, 211. 
 
 4k ' 4 short pipes, 215. 
 44 for capacity of air-vessel, 566. 
 44 coal for pumping, 581. 
 44 curved-face walls, 421. 
 44 depth upon a weir, 286. 
 44 duty of pumping-engines, 576. 
 * 4 earth pressures upon walls, 410, 
 
 inclination in channels, 304. 
 power to produce flow in pipes, 
 561. 
 
 412, 413, 415, 416. 
 icli 
 
 )\V 
 
 56 
 
 44 pressure in pipes, 447. 
 
 44 pressure on submerged walls, 393, 
 
 44 resistance in channels, 301, 303. 
 4k surcharged pressure walls, 414, 
 
 416, 423. 
 
 44 triangular notch weir, 294. 
 44 velocity in channels. 303, 304. 
 44 volume at given temp., 165. 
 41 weights of cast pipes, 465, 467. 
 44 of M. Chezy, pipes, 252. 
 " Weisbach, * 257. 
 Formulas, coefficients for weir, 287. 
 
 44 for diameters of pipes, 251, 266, 269, 
 
 270, 49 8. 
 
 flood volumes, streams, 320. 
 14 flow in conduits, 442, 443.. 
 44 44 44 pipes, 254, 257. 
 
 origin of, 229. 
 
 " 44 through bends, 272. 
 44 44 u " branches, 275. 
 " " " " channels, 310. 
 41 gauging streams, 320. 
 44 head, pipes, 250, 266, 268, 270, 494. 
 44 lengths of pipes, 269, 270. 
 4k pipes, various compared, 254. 
 44 * 4 resistance to flow, 230, 234, 250. 
 
 44 thickness of pipes, table, 466. 
 44 " " " cast pipes, 453, 454, 
 
 466. 
 44 wrought pipes, 448, 
 
 450, 486. 
 
 " 44 velocity, pipes, 249, 266, 267, 268, 
 270, 498. 
 
614 
 
 INDEX. 
 
 Formulas for volume, pipes, 250, 254, 266, 498. 
 44 weir volumes, 282, 283, 284, 286. 
 " " wide-crested weirs, 293. 
 44 many incomplete, 252. 
 44 misapplication of, 316. 
 44 stability of masonry, 395, 397, 398. 
 44 velocities and times offalling bodies, 
 
 186. 
 Foundation, concrete, 386. 
 
 embankment, 335. 
 for pipes, 4 8 7 . 
 of gate chambers, 367. 
 of conduits, 433. 
 4 ' walls, 395, 406, 407. 
 under water, 430. 
 Fountain use of water, 34. 
 Francis, Jas. B., experiments with weirs, 284. 
 
 " tubes, 517. 
 
 Frankland's definition of polluted water, 137. 
 Friction, coefficient of masonry, 396. 
 in pipes, 230, 234, 250, 508. 
 of ice on canals, 372. 
 " pumping machinery, 578. 
 Frictional head, formula for, 494. 
 
 44 in pipes, 493. 494, 527. 
 stability of masonry, 395. 
 Frost curtain, 367. 
 44 disintegrates mortar, 436. 
 44 protection of conduits from, 436. 
 Fuel, expense for pumping, 581. 
 *' required " 44 575. 
 Fungi, microscopic, 129. 
 
 a. 
 
 Galleries, infiltration, 539, 540. 
 Gate chambers, 357, 367. 
 
 44 hydrants, 522. 
 Gates, stop, canals, 374. 
 Gauge, Darcy-Pitot tube, 322. 
 
 " Darcy's double tube, 322. 
 
 44 double float, 326. 
 
 44 formulas, 319. 
 
 * 4 hook, Boyden's t 296, 297. 
 
 14 maximum velocity float, 328. 
 
 44 mid-depth float, 326. 
 
 44 Pitot tube, 320. 
 
 41 rain, 63. 
 
 4 ' rule, for wens, 298. 
 
 44 tube, 317. 
 
 tube and scale, weirs, 298. 
 
 44 Woltman's, 322. 
 
 Gauges and weights of plate iron, 487, 488. 
 Gauging, hydrometer, 316, 
 
 " of mountain streams, 296. 
 
 44 rainfall, 62. 
 44 4 ' rivers, 318, 319. 
 Gears for sluice-gates, 359. 
 General rainfall, 46. 
 Geological science, application, 106. 
 Granular stability of masonry, 402. 
 Graphical representation offeree, 175. 
 Gravitation system, 588. 
 Gravity, 185, 230, 299. 
 
 centre of, 177. 
 Great rain-storms, 61. 
 Grouped rainfall statistics, 52. 
 Grouting, 353, 369. 
 
 H. 
 
 Hardening impurities, 125. 
 Hardness of water, 125. 
 Head, desirable for fire service, 493. 
 44 effective in pipe system, 493. 
 
 how to economize, 276. 
 44 loss by friction, 493. 
 subdivisions of, 225. 
 44 value of, 493. 
 Heat, units of, utilized, 578. 
 
 Heights of waves, 388. 
 Heisch's sugar test of water, 159. 
 Helpful influence of water supplies, 27. 
 Hook gauge, Boyden's, 296. 
 Hook gauge, use to detect fluctuations, 319, 
 Horse-power, to produce flow, 561. 
 Hose streams, 510, 520. 
 4k use of water, 34. 
 Hudson valley, rainfall in, 53. 
 Hydrants, 516, 517, 519, 522. 
 ' 4 high pressures, 522. 
 44 streams, 520. 
 Hydraulic mean depth. 235. 
 44 radius, 236. 
 
 44 power pumping, 589, 591. 
 44 proof of pipes, 477. 
 Hydrometers, Castellis' and others, 326. 
 
 coefficients for, 325. 
 44 gauging with, 316. 
 
 Ice covering of canals, 372. 
 44 impure, in drinking water, 135. 
 44 thrust, 358, 386. 
 Impounders, flow to, 86. 
 Impounding of water, 144. 
 Impregnation of water, 141, 152. 
 Impurities of water, 112. 
 
 44 agricultural, 134. 
 
 44 atmospheric, 122. 
 
 44 manufacturing, 134. 
 
 44 mineral, 115, 133. 
 
 organic, 116, 127, 130. 
 
 44 sewage, 134. 
 
 44 sub-surface, 123. 
 44 " deep wells, 125. 
 Inch and foot, decimal parts of, 457. 
 Incidental advantages of water supplies, 29. 
 Inclination in channels, 235, 304, 371. 
 Increase in use of water, 39. 
 Indian embankments, 334. 
 Indicator, stop-valve, 361. 
 Infiltration, 537, 540, 543, 544. 
 Influent chamber, 366. 
 Infusoria, 130. 
 Inhabitant, supply per, 40. 
 Intercepting well, 546. 
 Interchangeable pipe-joints, 469. 
 Introduction of filters, 551. 
 Insurance schedule, 29. 
 
 Investment, value of water supplies as an, 29.. 
 Iron, gauges and weights, 488. 
 44 sluice valves, 360. 
 44 -work, varnishes for, 474, 476, 489. 
 Irrigation canals, 370, 373. 
 Isolated weirs, 383. 
 
 Jets, 211, 267. 
 
 Joint mortar for pipes, 487. 
 
 Joints of cast pipes, 457, 461, 463, 469. 
 
 K. 
 
 Kutter's coefficients for channels, 305. 
 
 Lake waters, 142. 
 
 Lakes, 150. 
 
 Laying of wrought-pipes, 482. 
 
 Lead, joint, 468. 
 
 Lengths of waste- weirs, 381. 
 
 Level, use of, in gauging, 319. 
 
 Leverage of water pressure, 397. 
 
 44 resistance of walls, 402. 
 
 44 stability of masonry, 397. 
 Life of dams, 388. 
 Lining of pipes, cement, 481. 
 Logarithms of ratios, 121. 
 
INDEX. 
 
 615 
 
 Loss by evaporation, 87. 
 tk from reservoirs, 84. 
 " of head by friction, 276, 493. 
 
 M. 
 
 Mains and distribution pipes, 446. 
 
 " power to produce flow in, 561. 
 Masonry conduits^.431, 437. 
 
 coverings of waste-pipes, 357. 
 
 examples of pressure in, 403. 
 
 faced embankment, 354. 
 
 frictional stability of, 397. 
 
 granular stability of, 402. 
 
 limiting pressures in, 404. 
 
 weight leverage of, 398. 
 Materials, embankment, 339, 341. 
 Maximum velocities of flow, 508. 
 Metals, pipe, 470, 472. 
 
 " tenacities of wrought, 451, 486, 491. 
 Microscopical examination of metals, 471. 
 Mineral impurities, 115, 530. 
 springs, 142, 143. 
 
 Miners' canals, 375. 
 Misapplication of fc 
 
 "ormulae, 316. 
 
 Mississippi valley, rainfall in, 54. 
 Molecular theories, 162, 296. 
 Molecules, 185. 
 
 Moment of earth leverage, 412. 
 Monads, 130. 
 
 Monthly and hourly variations in the draught, 
 41. 
 
 fluctuations m rainfall. 56. 
 Mortar for lining and covering pipes, 487. 
 Motion, acceleration of, 185. 
 
 equations of, 186. 
 
 of a piston, 562. 
 
 of water, 184, 194. 
 u parabolic of a jet, 187. 
 Moulding of pipes, 451. 
 Moulinets, 323, 326. 
 Municipal control of water supplies, 28. 
 
 N. 
 
 Natural clarification, 149, 532. 
 
 " laws, uniform effects of, 61. 
 Necessity of water supplies, 25. 
 Noctos, 129. 
 
 O. 
 
 Ohio river valley, rainfall in, 54. 
 Open canals, 370. 
 Ordinary flow of streams, 80. 
 Organic impurities, 80, 113, 116, 531, 532. 
 Organisms, 129, 131, 133. 
 Orifices, classes of, 194. 
 ** convergent, 212. 
 
 path toward, 194. 
 cylindrical and divergent, 212. 
 " flow of water through, 194, 210. 
 Orifice-jet, form of submerged, 195. 
 peculiarities, 207. 
 ratio of minimum section, 195. 
 variations, 204. 
 velocity, 196, 208, 209. 
 
 P. 
 
 Pacific coast rainfall, 54. 
 Parabolic path of jet, 187, 
 " segment, appli 
 
 umes, 282. 
 Partitions and retaining walls, 390. 
 Paving, concrete, 355. 
 
 " embankment slope, 350. 
 Peculiar watersheds. 71. 
 Penstock, cylindrical, wood, 439, 441 
 Percolation from reservoirs, 85, 94. 
 
 ition to weir vol- 
 
 Percolation of rain, 104, in. 
 
 under retaining walls, 406. 
 Permanence of water supply essential, 585. 
 Persons per family, 32. 
 Physiological effects of the impurities of water, 
 
 Pipe 
 
 office of water, 25. 
 , adjustable effluent, 364. 
 and conduit, 223. 
 branches, composite, 484. 
 joints, cast, 457 . 4 6i, 463, 469, 483. 
 ' hub on wrought, 483. 
 dimensions of, 459, 451, 462. 
 u flexible, 463. 
 " interchangeable, 469. 
 metals, 470, 472. 
 
 kl wrought, strength of, 451, 486, 
 
 491. 
 
 resistance at entrance to, 226. 
 shells, wrought, thickness of, 448, 485, 
 
 486. 
 systems, duplication in, 510. 
 
 " illustrations, 493, 510. 
 walls, resistances of, 227, 228. 
 and sluices, embankment, 355. 
 cast-iron, 451. 
 
 thickness of, 453, 454, 455, 466. 
 weights of, 465, 468, 469. 
 ' cement joints, 482. 
 
 *' lined, 479, 481. 
 " coefficients of friction, 242, 495. 
 ' concrete foundations for, 487. 
 " depths of, 501, 502. 
 
 " sockets, 459. 461. 
 ' diameters for fire supplies, 510. 
 " elementary dimensions of, 504. 
 " flanges, table of, 462. 
 formulas for thickness of cast, 453, 466. 
 velocity, head, volume, 
 and diameter, 224, 266, 
 268, 270, 498. 
 
 " " weights of cast, 465. 
 u frictions in, 224, 495, 508. 
 hydraulic proof of, 477. 
 lead in joints, 468. 
 ' mains and distribution, 446. 
 '* preservation of surfaces, 473, 480, 489, 
 
 49 1 - 
 
 " relative capacities of, 498, 500. 
 1 short, 223. 
 " square roots of fifth powers of diameters, 
 
 400 500. 
 
 " static pressure in. 446. 
 ' sub-coefficients of flow (cO, 271. 
 ; temperatures of water in, 502. 
 " thicknesses of wrought, 447, 450, 486, 
 
 488. 
 
 u volumes of flow from, 223, 225, 495. 
 water-ram in, 448, 449. 
 wood, 491. 
 " wrought-iron, 479. 
 
 " plates for, 490. 
 Piping and water supplied, 38. 
 " rati9 to population, 35. 
 Piston motion, 562. 
 
 " pump, 557, 558. 
 Pitot tube gauge, 320. 
 Plant and insect agencies, 147. 
 " growth in reservoirs, 145. 
 Plates for wrought pipes, 490. 
 Plunger pump, 557, 563. 
 Pluviometer, 63. 
 
 Polluted water, definition of, 137. 
 Polluting liquids, inadmissible, 154. 
 Pollution question, 156. 
 
 u of water, artificial, 152. 
 Population, and relation of supply per capita, 
 
 40. 
 of various cities, 32. 
 
616 
 
 INDEX. 
 
 Portland cement for joint mortar, 487. 
 
 Porosity ot earths and rocks, 102. 
 
 Post hydrants, 517. 
 
 Power consumed by variable flow in a main, 
 
 " required to open a valve, 361, 364. 
 Practical construction of water-works, 333. 
 Precautions for triangular weirs, 295. 
 Precipitation, influence of elevation upon , 50. 
 Preservation of pipe surfaces, 473, 480, 489, 491. 
 Pressure, a line a measure of, 174. 
 " conduits under, 435, 439, 440 
 u conversion into mechanical effect, 
 
 230. 
 
 of velocity into, 227. 
 " direction of maximum effect, 176. 
 " leverage of watei, 307. 
 " of earth against walls, 408, 410, 413, 
 
 415, 416. 
 " water, 168. 
 
 " " in a conduit, 437. 
 " proportional to depth, 169. 
 " sustaining upon floating oodies, 179. 
 " transmission of, 183. 
 
 upon a unit of surface, 171. 
 
 " surfaces, 391, 393. 
 weight a. measure of, 173. 
 Pressures, artificial, 171. 
 
 at given depths, table, 172. 
 atmospheric, 182. 
 centres of, 177. 
 convertible into motion, 184. 
 from inclined columns of water, 170. 
 great in hydrants, 522. 
 horizontal and vertical effects, 177. 
 in embankments, 343. 
 limiting in masonry, 404. 
 static in pipes, 446, 448. 
 total of water, 176. 
 " upon circular areas, 179. 
 
 " curved surfaces, 178. 
 " upward upon submerged Iintels,i8i. 
 Prism of weir volumes, 282. 
 Processes for preserving iron, 474, 476, 489. 
 Profile across the United States, 48. 
 
 " of retaining walls, 407. 
 Properties of water, 113. 
 
 u of embankment materials, 342. 
 Proportions 349. 
 
 Protection of filter beds, 548, 555. 
 
 " "water supply channels, 431. 
 Prony's analysis of experiments, 255. 
 Proving press, hydraulic, 477. 
 Puddled canal bank, 370. 
 Puddle- wall, 351. 
 
 " slope, 352. 
 
 Pump, bucket-plunger, 557, 567. 
 u Cornish, 557, 563. 
 piston, 557, 558. 
 plunger, 557, 563. 
 rotary, 558. 
 Pumping of water, 557. 
 
 " diagram of, 42. 
 engines, 557, 567, 573, 577- 
 ^ adaptability of, 584. 
 " cost of supplies, 575, 582. 
 
 " attendance, 575, 582. 
 duties, 574, 579, 580, 581, 583. 
 " fuel expenses, 581. 
 
 principal divisions, 577. 
 " special trial duties, 580. 
 " values compared, 583. 
 machinery, 591, 592. 
 
 duplicate, 590. 
 
 for direct pressure, 590, 
 
 591. 
 " "' Manchester, 585. 
 
 system, 589, 590. 
 *' water, cost of, 574, 575. 
 
 Pumps, types of, 557. 
 
 " variable flow through, 550. 
 Purity of water, chief requisites for, 144. 
 Purity of water, preservation of, 148. 
 Purihcation of water, natural, 134, 157, 158. 
 
 Q. 
 Quality of water, sugar test of, 159. 
 
 R. 
 
 Radii, mean of conduits, 441, 442. 
 Rainfall, along river courses, 51. 
 diagrams of, 55, 57, 59. 
 gauging, 62. 
 general, 46. 
 
 in the United States, 53. 
 influences affecting, 60. 
 u low cycle, 69, 77, 78. 
 
 monthly fluctuations in, 56. 
 " ratio of floods to, 62. 
 
 secular fluctuations in, 60. 
 " sections of maximum, 47. 
 " statistics, review of, 46. 
 " volumes of given, 62. 
 Rain-gauge, 63. 
 Rains, river-basin, 50. 
 Rates of fire supplies, 506. 
 Ratios of evaporation, 91. 
 
 u monthly consumption, 43. 
 " monthly flow in streams, 76. 
 qualification of deduced, 99. 
 rainfall, flow, etc., table, 100, 101. 
 " standard gallons, 120. 
 " surface to mean velocities in chan- 
 nels, 315. 
 
 variable delivery of water, 564. 
 Reaction and gravity, opposition of, 230. 
 Recounoissance for embankment site, 346. 
 
 of a water-shed, 78. 
 
 Rectangular and trapezoidal walls, moments 
 of, 399. 
 weirs, 277. 
 Reducer, pipe, 478. 
 
 Relation of supply per capita to total popula- 
 tion, 40. 
 Relative values of h, h', and h"^ 253. 
 
 discharging capacities of pipes, 498, 
 
 500. i 
 
 " rates of domestic and fire draughts, 
 
 508. 
 
 Repulsion, molecular, 296. 
 Reserve for fire service, 44. 
 Reservoir coverings, 556. 
 " distributing, 353. 
 ' embankments, 333. 
 " plant growth in, 145. 
 " storage, surveys for, 347, 
 " strata conditions in, 146. 
 ' system, 598. 
 Reservoirs, subterranean, 105. 
 Resistance of the air to a jet, 190. 
 
 at entrance to a pipe, 226. 
 of masonry revetments. 417. 
 to flow, measure of, 230, 231. 
 Resistances to flow within a pipe, 227. 
 
 " in channels, 300. 
 Resultant effect of rain and evaporation, 92. 
 Retaining walls, 390. 
 
 effect of traffic on, 425. 
 for earth, table, 420. 
 front batters, 424. 
 percolation under, 406. 
 sections of, 407. 
 top breadihs, 424. 
 Revetted conduits, 431. 
 Revetments, faced and concrete, 429, 
 " final resultants, 418. 
 
I NDEX. 
 
 617 
 
 Revetments, resistance of, 417. 
 
 trapezoidal, table of, 420. 
 Riparian rights, 85. 
 Rip-rap, slope, 371. 
 River waters, 151. 
 Rivers and canals, table of flows, 307. 
 
 " basin rains, 50. 
 
 41 basins of Maine, 84. 
 
 " courses, rainfall along, 51. 
 
 " pollution committee, 154. 
 Roof for filter beds and reservoirs, 548, 555. 
 Rotary pump, 558, 
 Rubble, grouted, 353. 
 
 " masonry, 252. 
 " priming wall, 352. 
 
 S. 
 
 Sand in embankments, 353. 
 Sanitary discussions, 152. 
 " improvements, 26. 
 " office of water, 26. 
 " views, precautionary, 154. 
 Schussler's process of coating pipes, 489. 
 Screens, fish, 365. 
 Seasons of floods, 68. 
 Sections of maximum rainfall, 47. 
 Secular fluctuations in rainfall, 60. 
 Sediments, 530, ^31. 
 Service pipes, frictions in, table, 528. 
 Services, high and low, 524. 
 Settling basins, ^50. 
 Sewage impurities, 134. 
 
 dilution of, 153, 155. 
 Shells of conduits, 434. 
 Sheet-iron, gauges and weights, 488. 
 Sheet-piles, 371. 
 
 " u under embankment, 339. 
 Short-tubes, 215, 216. 
 Showers, source of, 45. 
 Sleeves, pipe, 479, 482. 
 Slope, earthwork, 344, 345. 
 
 paving exposed to frost, 355. 
 " puddled, 352. 
 
 " embankment, 356. 
 Slopes, velocities for given, 258. 
 Sluice areas, 360. 
 
 Sluice and pipes, embankment, 355. 
 " gate areas, 359. 
 4 temporary stop-gate, 359. 
 44 tunneled, embankment, 356, 358. 
 u valves, iron, 360. 
 Sines of slopes, table, 259. 
 Siphon, 182, 184. 
 
 Site for embankment, reconnoissance for, 346. 
 Smith's (A. F.) adjustable pipe, 364. 
 Soils beneath embankments, 337. 
 
 " evaporation from, no. 
 Solutions, organic, 532. 
 u in water, 112. 
 Source of showers, 45. 
 Springs, mineral, 141. 
 44 under embankments, 337. 
 u and wells, 102. 
 
 " supplying capacity of, no. 
 " waters, 141. 
 Stable use of water, 34. 
 Statistics, census, 31, 32. 
 rainfall, 46, 52. 
 Stability of masonry, 395, 397. 
 
 u u pumping machinery, 578. 
 Stand pipes, 526, 564. 
 Static pressures in pipes, 446. 
 Storage, additional required, 98. 
 basins, substratas of, 85. 
 
 44 percolation from, 85. 
 Storage of water, 84. 
 
 44 influence upon a continuous 
 supply, 99. 
 
 Storage of water, effect of evaporation on, 93. 
 
 44 required, 95. 
 Storage reservoir, 338. 
 
 embankment, 353. 
 
 supply to and draught from, 
 
 table, 96. 
 
 Strata conditions, 146. 
 Streams, available annual flow, 94. 
 " estimates of flow, 65, 78. 
 44 flashy and steady, 71. 
 gauging, 296. 
 
 minimum, mean, and flood flow, 75. 
 44 ordinary flow cf, 80. 
 u ratio of monthly flow, 76. 
 Strengths of wrought pipe metals, 451, 486, 491. 
 Stop-gates in conduits, 436. 
 Stop-valve curbs, 515. 
 
 Ludlow's, 514. 
 44 Coffin's, 493. 
 
 " Flowers', 493. 
 
 Eddy's, 511. 
 system, 511. 
 Storms, great rain. 61. 
 Sub-heads compared, 253. 
 Sub-mains, diameters of", 507. 
 Subterranean reservoirs, 105. 
 waters. 102. 
 watershed, 109. 
 waters, temperature of, 126. 
 
 uncertainties of search 
 
 for, 106. 
 
 Substrata of a storage basin, 85. 
 Supply main, diameter of, 506. 
 
 44 to, and draught from a reservoir, table, 
 
 96, 97. 
 
 Supplying capacity of watersheds, 94. 
 Surcharged pressure, earth, 414, 416, 423. 
 Surfaces, pressure of water upon, 391, 393. 
 Surveys for storage reservoir, 347. 
 Sources of water supplies, 587. 
 Symbols, definitions of, 235. 
 
 44 combined reservoir and direct, 525. 
 Systems of water supply, 585, 586. 
 44 " distribution, 493. 
 u 4t rainfall, 47,49, 50. 
 
 T. 
 
 Temperatures, artesian well, 127. 
 
 of deep sub-surface waters, 126. 
 u filter beds, 555. 
 44 water in pipes, 502. 
 Templets, for flange bolt-holes, 460. 
 Tenacities of wrought-pipe metals, 451, 486, 
 
 491. 
 
 Tests of pipe metals, 472. 
 Testing of hydrometers, 325. 
 Theory of flow over a weir, 278. 280. 
 Thickness of a curved-face wall, 422. 
 
 " dams, table, 387. 
 
 ' 4 pipes, formulas, 466. 
 
 ' walls for water-pressure, 399. 
 " " wrought-pipe shells, 447, 486, 
 
 488. 
 
 Thompson's molecular estimate, 162. 
 Thrusts of a conduit arch, 437. 
 Timber weirs, 384. 
 Transit, use in gauging, 313, 318, 319. 
 Transmission of pressures, 183. 
 Traffic, effect upon retaining walls, 425. 
 Trapezoidal revetments, table, 420. 
 Treacherous strata beneath embankments, 338. 
 Trial shafts, at embankment sites, 336. 
 Tube gauge, 317. 
 Tubes, short, 213. 
 Tubercles, in pipes, 247. 
 Turbine water-wheels. 559, 579. 
 Turned pipe-joints, 458. 
 Type curves of rainfall, 55, 57, 59. 
 
618 
 
 INDEX. 
 
 U. 
 
 Uniform effect of natural laws, 61. 
 Union of high and low services, 524. 
 Units of heat utilized, 578. 
 Use of water increasing, 39. 
 
 V. 
 
 Vacuum ajutage, 214. 
 
 imperfect, short tubes, 215. 
 " rise of water into, 182. 
 " tendency to in compound tubes, 221. 
 " under a weir crest, 292. 
 Values of ^, 271. 
 
 " " h and h', table, 264. 
 44 " pumping engines compared, 583. 
 44 " water supplies as an investment, 29. 
 Vanne conduit, 438. 
 Vapory elements, the, 45. 
 Valves, air, 523. 
 
 blow-off, 513. 
 Cornish, 569, 570. 
 check, 525. 
 " curbs, 515. 
 44 disk, 571. 
 44 double beat, 560, 570. 
 " flap, 568. 
 44 iron sluice, 360. 
 piston, 569. 
 
 power required to open, 361, 364. 
 44 stop, 493, 511, 513, 514. 
 
 k indicator, 361. 
 41 " system, 511. 
 
 1 waste, 513. 
 Variable flow through pumps, 559. 
 
 ,555- 
 , 128. 
 
 Varnishes for iron, 474, 476, 489. 
 Vegetal growth in filter beds, 
 Vegetable organic impurities 
 Velocity, conversion into pressure, 227. 
 " equation, modification ot, 270. 
 44 formula for, 249, 250. 
 Velocities in canals, 371. 
 
 44 theoretical table, 190. 
 
 of falling bodies, table, 190. 
 " for given slopes, table, 259. 
 44 ratios of surface to mean, 315. 
 
 relative, due to different depths in 
 
 channels, 328. 
 
 44 of given films, in channels, 311. 
 41 surface in channels, 313. 
 Vermin in canal banks, 371. 
 Vertical shifting of water, 365. 
 Virginia City, wrought-iron pipe, 489. 
 Voids of earths and rocks, 103. 
 Volume delivered by pipes, table, 495. 
 
 of efflux from an orifice, 194, 209. 
 44 u " formula for, 196. 
 41 flood inversely as the area of the 
 
 basin, 65. 
 Volumes, formulas for flood, 65. 
 
 flood, from watersheds, 381. 
 44 relative, due to different depths in 
 
 channels, 328. 
 of given rainfalls, 62. 
 for given depth upon weirs, 290. 
 from waste weirs, table, 380. 
 
 W. 
 
 Walls, back batters of, 422. 
 44 chamber, 369. 
 
 counterforted, 427. 
 
 curved face, table, 422. 
 
 earth pressure against, 408, 410, 412, 413, 
 
 415, 416. 
 
 elements of failure, 427. 
 end supports of, 429. 
 44 front batters of, 424. 
 
 Walls, formula of thickness for water pressure, 
 399- 
 
 44 foundations of, 395, 406, 407. 
 
 44 leverage resistance of, 402. 
 
 44 profiles of, 407. 
 
 44 retaining, 390. 
 
 44 to retain water, table, 406. 
 
 44 to sustain traffic, 425. 
 
 " top breadths, 424. 
 
 44 wharf, 426. 
 Waste pipes, embankment, 357. 
 
 44 sluice, 356. 
 
 44 weir formulas, 379. 
 
 44 u volumes, table, 380. 
 
 44 " aprons, 383. 
 44 ballast, 385. 
 
 44 weirs, 377. 
 
 discharges over, 378. 
 
 44 " forms of, 382. 
 
 44 " thickness, table, 387. 
 
 44 valves, 513. 
 Water, analyses of potable, 117. 
 
 characteristics of, 113, 159,161. 
 
 44 crystalline forms of, 165. 
 
 41 choice of, 587. 
 
 44 clarification of, 530. 
 
 44 compressibility and elasticity of, 167. 
 
 44 commercial use of, 34. 
 
 44 consumption of, 34, 503. 
 
 44 the composition of, 112. 
 
 44 domestic use, 34. 
 
 44 engine, 569. 
 
 evaporation from, 88, 89. 
 
 44 flow of, 184, 194. 
 
 44 force of falling, 388. 
 
 44 hose, use of, 34. 
 
 44 impregnations, 112, 141. 
 
 44 impurities, 112, 141. 
 
 44 molecular actions, 168, 169. 
 
 44 pressure upon surfaces, 168, 176, 391, 393. 
 
 44 pressure leverage of, 397. 
 
 44 physiological office of, 25. 
 
 effect of the impurities of,' 
 114. 
 
 44 pipes, organisms in, 129, 133. 
 plant and insect agencies in, 147. 
 
 44 pumping of, 557. 
 
 44 rarity of clear, 530. 
 
 44 ratios of variable flow, 564. 
 
 " river, 151. 
 
 44 sanitary office of, 26. 
 
 44 storage of, 84. 
 
 44 spring, 141. 
 
 44 solvent powers of, 113. 
 
 44 subterranean, 102. 
 
 44 sugar test of quality, 159. 
 
 44 supplies, gathering and delivering, 586. 
 
 44 " incidental advantages of7 29. 
 
 44 necessity of, 25. 
 
 44 supplied, 31, 35, 36, 37, 38. 40. 
 supply, permanence of, 585. 
 
 44 " systems of, 585, 586. 
 
 44 volumes and weights, table, 161, 164, 
 166. 
 
 44 vertical changes in, 365. 
 
 44 waste, 34. 
 
 44 weight of constituents, 164. 
 
 44 " pressure and motion of, 161. 
 
 44 well, 139. 
 
 44 wheels, 559, 579. 
 
 works, construction of, 333. 
 Watersheds, 71, 100. 
 
 supplying capacity of, 94. 
 Water-ram in pipes, 449. 
 Wave formula, 388. 
 Waves, heights of, 388. 
 Weir apron, 279. 
 Weir benches, 384. 
 44 caps, breadths, 386. 
 
INDEX. 
 
 619 
 
 Weir coefficients, 288, 289, 291. 
 " crests, 278, 292, 293. 
 gauging, 77. 
 overfalls, 377. 
 
 Weirs, crest contractions, 280. 
 " dimensions of, 278, 279. 
 " discharges over, table, 289, 290. 
 
 experiments with large, 284. 
 " forms of, 277. 
 " formula for wide-crested, 293 
 " " depth upon, 28 ' 
 formulas, 282, 283, 284, 286. 
 gratings in front of, 292. 
 u hook-guage for, 297. 
 " initial velocity of approach to, 285, 292. 
 " measuring, 277, 295. 
 rule gauge for, 298. 
 stability of, 279. 
 tail-water of, 292. 
 triangular notch, 294, 295. 
 " tube and scale-gauge for, 208. 
 " timber, 384. 
 
 varying lengths, 279. 
 " volumes, formulas for, 282, 283, 284, 
 
 286, 287, 293. 
 waste, 337, 383. 
 wide-crested, 293. 
 Weight, a line a measure of, 173. 
 
 Is, 341. 
 
 Weight, a measure of pressure, 173. 
 
 and volume of water, table, 166. 
 leverage of masonry, 398. 
 " of pond water, 167. 
 Weights of cast pipes, 465, 468, 4< 
 " " embankment materia 
 " " molecules, 168. 
 Well, intercepting, 546. 
 " water, 139. 
 ' waters, analyses of, 121. 
 Wells and springs, 102, no. 
 " condition of overflowing, 107. 
 " fouling of old, 140. 
 " influence upon each other, 107. 
 " impurities of deep, 125. 
 
 locations for, 139. 
 " watersheds of, 108. 
 Western rain system, 47. 
 Wharf cap-log, 426. 
 " fender and belay piles, 427. 
 " walls, 426. 
 Wood pipes, 491. 
 Woltmann's tachometer, 322. 
 Wrought-iron pipes, 479. 
 
 " pipe-joint, cast, 483. 
 1 plates, gauges, and weights, 488. 
 WyckofTs wood-pipe, 491. 
 
 
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D. VAN NOSTRAND. 11 
 
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D. VAN NOSTRAND. 13 
 
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D. VAN NOSTEAND. 15 
 
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16 SCIENTIFIC BOOKS PUBLISHED BY 
 
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D. VAN NOSTRAND. 17 
 
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 i 
 
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18 SCIENTIFIC BOOKS PUBLISHED BY 
 
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 I. CHIMNEYS FOR FURNACES, FIRE-PLACES, AND STEAM BOILERS. By 
 
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 II. STEAM BOILER EXPLOSIONS. By ZERAH COLBURN. 
 
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 XL THEORY OF ARCHES. By Prof. W. ALLAN, of the Washington and 
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 XII A PRACTICAL THEORY OF VOUSSOIR ARCHES. By WILLIAM CAIN, 
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D. VAN NOSTRAND. 19 
 
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20 SCIENTIFIC BOOKS PUBLISHED BY 
 
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 Heating and Ventilation in its Practical Ap- 
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 Shield's Treatise on Engineering 
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 25 
 
26 MILITARY BOOKS PUBLISHED BY 
 
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D. VAN NO STRAND. 27 
 
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28 MILITARY BOOKS PUBLISHED BY 
 
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 Gillmore' s Fort 
 
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 SIEGE AND REDUCTION OF FORT PULASKI, GEORGIA. By Maj.-Gen. 
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D. VAN NO STRAND. 29 
 
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30 MILITARY BOOKS PUBLISHED BY 
 
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D. VAN NOSTRAND. 31 
 
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32 MILITARY BOOKS PUBLISHED BY 
 
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D. VAN NOSTBAND. 33 
 
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J4 MILITARY BOOKS PUBLISHED BY 
 
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D. VAN NO STRAND. 35 
 
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36 MILITARY BOOKS PUBLISHED BY 
 
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D. VAN NOSTEAND. 37 
 
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38 MILITARY BOOKS PUBLISHED BY 
 
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D. VAN NO STRAND. 
 
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40 NAVAL BOOKS PUBLISHED BY 
 
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/>, VAN NOSTliANl). 41 
 
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42 NAVAL BOOKS PUBLISHED BY 
 
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