WORKING DATA FOR IRRIGATION ENGINEERS BY E. A. MORITZ, B.S.C.E.; C.E. Assoc. M. Amer. Soc. C. E. Engineer United States Reclamation Service FIRST EDITION FIRST THOUSAND NEW YORK JOHN WILEY & SONS, INC. LONDON: CHAPMAN & HALL, LIMITED 1915 Copyright, 1915, by E. A. MORITZ PUBLISHERS PRINTING COMPANY 207-217 West Twenty-fifth Street, New York PREFACE EVERY branch of engineering has its special problems which necessitate the frequent use of certain fundamental data. This requirement has led to the production of " handbooks" or "pocketbooks" to cover the requirements of the various fields and the following pages are the result of an attempt to do this for irrigation engineers. The object has been to produce a book that would result in the conservation of the time and mental energy of the user, as well as to present material not readily obtainable from other sources. Utility has been the primary aim in the selection of the material and in the arrangement of subjects. The author fully realizes that he has accomplished the de- sired object to a limited extent only. The first edition of a work of this nature must obviously be incomplete in numerous respects, but it is hoped that this defect may be remedied, in large part, in future editions if such should become necessary. To accomplish this, constructive criticisms and suggestions for additions and improvements are earnestly invited. A considerable portion of the material is original. Most of the remainder was taken from the publications and records of the United States Reclamation Service, and the author con- siders himself very fortunate in having had this prolific source of valuable information at his disposal. A few tables of a general nature were collected from various other sources. It is hoped that the book in its present form will prove to be of value to irrigation and hydraulic engineers, and the author would repeat his invitation for suggestions for its improvement so that the book may be made of the greatest use to the largest number. E. A. M. WASHINGTON, D. C., December, 1914. 7W.TY-A4 CONTENTS PAGE PREFACE . . . . . . . . . . iii LIST OF DIAGRAMS ... . . . ... ix LIST OF TABLES xi INTRODUCTION xiii CHAPTER I EXAMINATION AND RECONNOISSANCE 1 Amount of Land Available Maps Used Source of Water Supply and Quantity Available Table of Water Supply Papers Published by the Geological Survey Index Map of Principal Drainage Basins in the United States Tables of Annual Precipitation Gaging Stations Weir Measurements Current Meter Measurements Prior Water Rights Reservoirs Available. CHAPTER II INVESTIGATIONS AND SURVEYS . . . ; . . ; ..... 20 Water Duty Quantity of Water Applied to Land Monthly Variation of Use Location of Point of Diversion Location of Main Canal Determination of Irrigable Area Reservoir Surveys General Remarks on Canal Location. CHAPTER III DESIGN OF IRRIGATION STRUCTURES 29 Storage Works Evaporation Tables Seepage from Reservoirs Types of Storage Dams Spillways Maximum Run-off of Streams Outlet Works Diversion Dams Types of Diversion Dams Back- water Calculations Discharge Over Diversion Dams Head- gates Canals Capacity Seepage Losses Side Slopes Depth of Flow Bottom Width Velocities and Grades Scouring and Silting Velocities Formula for Flow Kutter's Coefficient n Free- board Rise of Water on Curves Chutes Flumes Pipes Flow of Water in Pipes Tables of Discharge of Pipes Vertical Drops Turnouts Culverts. CHAPTER IV HYDRAULIC DIAGRAMS AND TABLES ....;.. . . . . . . . . 75 Diagrams for Determining Velocities by Kutter's Formula Table of Values of Coefficient "C" Hydraulic Elements of Rec- tangular, Trapezoidal, and Circular Sections Hydraulic Elements of a Horseshoe Section Discharge and Velocities of Circular Conduits VI CONTENTS PAGE Flowing Partly Full by Kutter's Formula Discharge and Velocity of Rectangular Wood Flumes Discharge and Velocity of Small Canals in Earth Discharge and Velocity of Semicircular Steel Flumes Discharge and Velocity of Wood Stave, Cast-Iron, Steel, and Concrete Pipe Relative Discharge, Velocity, and Slope for Different Values of Kutter's n Velocity Head and Total Head Lost for Various Coefficients of Discharge Discharge of Sharp- Edged Submerged Orifices Discharge of Sluice Openings Discharge of Sharp-Edged Cippoletti Weirs Discharge of Sharp-Edged Con- tracted and Suppressed Weirs Coefficients for Velocity of Approach for Weirs Coefficients for Submerged Weirs Ly man's Table of Discharges of Suppressed Rectangular Weirs Discharge of Sup- pressed Rectangular Weirs by Bazin's Formula Tables of Multi- pliers for Broad-Crested Weirs Table of Acre-Feet and Second-Feet Equivalents Water Duty Conversion Diagram List of Hydraulic Formulas. CHAPTER V STRUCTURAL DIAGRAMS AND TABLES 203 Diagram of Excavation and Embankment for Small Canals in Level Ground Tables of Quantity of Material in Canal Prisms in Level Ground for Various Side Slopes and Any Bottom Width Tables of Quantity of Material in Canal Prisms in Sloping Ground for Various Side Slopes and Any Bottom Width Retaining Walls and Beams Formulas for Maximum Bending Moments in Beams Table of Bending Moments in Beams Formulas, Diagram, and Tables for Reinforced Concrete Design Timber Structures Table of Allowable Unit Stresses and Weight of Timber Table for Pro- portioning Wooden Beams Table of Contents in Feet B. M. of Lumber of Various Sizes and Lengths Table of Contents in Feet B. M. of Logs of Different Diameters and Lengths Table of Spacings of Bars in Concrete Pressure Pipe and Bands on Wood-Stave Pipe Diagram of Spacings of Bars in Concrete Pressure Pipe and Bands on Wood Stave-Pipe Miscellaneous Structural Data for Wood Pipe Diagram of Thickness of Shell of Riveted Steel Pipe Table of Allowable Depth of Backfill Over Steel Pipe Table of Thickness and Weight of Cast-Iron Pipe Table of Dimensions of Steel Flumes Diagram for Converting Head of Water into Pounds per Square Inch Diagram for Converting Head of Water into Pounds per Square Foot Diagram of Total Hydrostatic Pressure on a Wall One Foot Wide for Different Heads Diagram for Converting a Given Quantity of Water Falling a Given Distance into Horse-Power. CHAPTER VI MISCELLANEOUS TABLES AND DATA 257 Weights of Various Substances Convenient Equivalents Table of Inches and Fractions Expressed in Decimals of a Foot CONTENTS vii PAGE Metric Conversion Tables Table of Corrections in Feet for Curva- ture and Refraction Stadia Table Trigonometric Formulae Curve Formulae Common Logarithms of Numbers Natural Sines, Co- sines, Tangents, and Cotangents Three-Halves Powers of Num- bers Conventional Signs for Irrigation Structures Squares, Cubes, Square Roots, Cube Roots, Reciprocals, and Areas and Circumference of Circles. CHAPTER VII SPECIFICATIONS 315 Definition Discussion Subdivision of Specifications The Ad- vertisement Notice to Bidders The Proposal Guarantee of Bond Work to be Performed General Conditions Detail Speci- fications Special Conditions Canal Excavation Tunnels Exca- vation for Structures Continuous Wood-Stave Pipe Machine- Banded Wood-Stave Pipe Steel Pipe Reinforced Concrete Pipe Cast-Iron Pipe Metal Flumes Steel Highway Bridges Con- crete Paving Cement Timber Piles Structural Steel Steel Reinforcement Bars Gray Iron Castings Malleable Castings Steel Castings Rolled Bronze Cast Bronze. INDEX . . 389 LIST OF DIAGRAMS FIG. PAGE 1. Outline Map of Drainage Basins in the United States 5 2. Example of Discharge, Mean Velocity, and Area Curves 18 3. Diagram for Use in Calculating Seepage Losses in Canals 45 4. Velocities, Slopes, and Hydraulic Radii for n = .010 89 5. Velocities, Slopes, and Hydraulic Radii for n = .012 91 6. Velocities, Slopes, and Hydraulic Radii for n = .013 93 7. Velocities, Slopes, and Hydraulic Radii for n = .014 95 8. Velocities, Slopes, and Hydraulic Radii for n = .015 97 9. Velocities, Slopes, and Hydraulic Radii for n = .020 99 10. Velocities, Slopes, and Hydraulic Radii for n = .0225 101 11. Velocities, Slopes, and Hydraulic Radii for n = .025 103 12. Velocities, Slopes, and Hydraulic Radii for n = .030 105 13. Velocities, Slopes, and Hydraulic Radii for n = .035 107 14. Hydraulic Elements of Rectangular Sections Ill, 113, 115 15. Hydraulic Elements of Trapezoidal Sections, Side Slopes ^ to 1, 117, 119, 121 16. Hydraulic Elements of Trapezoidal Sections, Side Slopes 1 to 1, 123, 125, 127 17. Hydraulic Elements of Trapezoidal Sections, Side Slopes 1^ to 1, 129, 131, 133 18. Hydraulic Elements of Trapezoidal Sections, Side Slopes 2 to 1, 135, 137, 139 19-20. Hydraulic Elements of Trapezoidal Sections, Mixed Side Slopes, 141, 143 19. Hydraulic Elements of Trapezoidal Sections, Side Slopes 1 ^ to 1 ... 141 20. Hydraulic Elements of Trapezoidal Sections, Side Slopes 1% to 1. . . 143 21. Hydraulic Elements of Circular Segments 145, 147 22. Discharge of Circular Conduits Flowing Full 151, 153 23. Discharge of Rectangular Wooden Flumes, Slopes .001 to .01, 154, 155, 156 24. Discharge of Rectangular Wooden Flumes, Slopes .01 to .10, 157, 158, 159 25-26. Hydraulic Curves for Small Canals n = .0225 160, 165 27-28. Hydraulic Curves for Small Canals n = .025 163, 165 29. Discharge of Semicircular Steel Flumes 167, 169 30. Flow of Water in Wood Stave Pipe 170, 171 31. Flow of Water in Cast Iron and Monolithic Concrete Pipe 172, 173 32. Flow of Water in Riveted Steel and Jointed Concrete Pipe 174, 175 33. Relative Velocities and Slopes for Different Values of n 176 34. Theoretical Velocity Head ' 177 35. Discharge of Sharp- Edged Submerged Orifices 178 36. Discharge of Standard Cippoletti Weirs 181 37. Discharge of Rectangular Weirs 183 ix X LIST OF DIAGRAMS FIG. PAGE 38. Diagram for Converting "Acres per Second Foot" to "Depth of Water Flowing for a Given Length of Time" 196 39. Volume of Excavation and Embankment for Small Canals in Level Ground 205 40. Coefficients of Resistance of Reinforced Concrete Beams 229 41. Spacing of Bands on Wood Stave Pipe and Reinforcement Rods on Concrete Pipe 243 42. Thickness and Weight of Steel Pipe 245 43. Pressure of Water in Pounds per Square Inch 250 44. Pressure of Water in Pounds per Square Foot 251 45. Total Hydrostatic Pressure 252 46. Horse-Power of Falling Water 253 LIST OF TABLES PAGE 1. Numbers of Water-Supply Papers Containing Results of Stream Measurements 2 2-8. Annual Precipitation in Inches 6, 7, 8, 9, 10, 11, 12 9. Water Used on Projects of U. S. Reclamation Service 21 10. Water Distribution for 1912 U. S. Reclamation Service 22 11. Total Canal Losses in Per Cent of Diversions, U. S. Reclamation Service 24 12. Evaporation by Months 30, 31, 32 13. Maximum Rate of Discharge of Streams in the United States, 34, 35, 36, 37 14. Seepage Losses from Canals in Various Materials 44 15-16. Critical Velocity, or Mean Velocity at which a Canal Will Neither Silt Nor Scour 49 17. Concrete Channels Values of Kutter's Coefficient n from Ex- periments 52, 53 18. Earth Canals Values of Kutter's Coefficient n from Experiments. 54, 55, 56, 57, 58 19. Flow of Water in Smooth Straight Iron Pipes by Fanning's Formula . 68 20. Coefficients of Discharge for Submerged Tubes 84 Values of " C " for n = .010 88 Values of "C" for n = .012 90 Values of "C" for n = .013 92 Values of "C" for n = .014 94 Values of "C" for n = .015 96 Values of "C" for n = .020 98 Values of "C" for n = .0225 100 Values of "C" for n = .025 102 Values of "C" for n = .030 104 Values of "C" forn = .035.. 106 21. Values of "C" for all values of n 108, 109 Hydraulic Elements of Circular Segments 146 Hydraulic Elements of a Horseshoe Section 149 22. Circular Conduits Flowing Partly Full 150, 152 23. Semicircular Steel Flumes Freeboard, Depth, and Area for Differ- ent Conditions of Flow 166 24. Semicircular Steel Flumes Flowing Partly Full 168 25. Coefficients for Submerged Weirs 180 26. Coefficients for Velocity of Approach to Weirs 182 27. Discharge of Suppressed Rectangular Weirs for Small Heads 184 28. Discharge of Suppressed Rectangular Weirs by Bazin's Formula .... 189 28A. Multipliers of Discharge for Broad-Crested Weirs 192 28B. Multipliers of Discharge for Trapezoidal Weirs 192 28c. Multipliers of Discharge for Compound Weirs . 193 xi Xll LIST OF TABLES PAGE 29. Acre-Feet Equivalent to a Given Number of Second-Feet 194, 195 30. List of Hydraulic Formulas 197, 198, 199, 200 31. Amount of Material in Cubic Yards per 100 Linear Feet of Level Cut, Side Slopes 1 to 1 208 32. Amount of Material in Cubic Yards per 100 Linear Feet of Level Cut, Side Slopes 1^ to 1 209 33. Amount of Material in Cubic Yards per 100 Linear Feet of Level Cut, Side Slopes 2 to 1 211 34. Amount of Material in Cubic Yards per 100 Linear Feet of Level Cut, Side Slopes 3 to 1 212 35. Amount of Material in Cubic Yards per 100 Linear Feet of Cut on Sloping Ground, Side Slopes 1 to 1 214 36. Amount of Material in Cubic Yards per 100 Linear Feet of Cut on Sloping Ground, Side Slopes 1^ to 1 216 37. Amount of Material in Cubic Yards per 100 Linear Feet of Cut on Sloping Ground, Side Slopes 2 to 1 218 38. Bending Moments in Beams with Triangular Loading 223, 224 39. Areas, Weights, and Spacing of Round Rods 230 40. Areas, Weights, and Spacing of Square Rods 231 41. Quantity of Material Required for One Cubic Yard of Concrete .... 232 42. Allowable Unit Stresses and Weights of Timber 233 43. Values of M/S for Wooden Beams 234 44. Contents in Feet B. M. of Lumber 235 45. Contents in Feet B. M. of Logs 236 46. Spacing of Rods in Concrete and Bands on Wood Pipe, 237, 238, 239, 240 47. Miscellaneous Data for Wood Pipe 242 48. Thickness and Weight of Cast-Iron Pipe ...;.." 247, 248 49. Metal Flumes, Dimensions and Weights 249 50. Average Weight, in Pounds per Cubic Foot, of Various Substances . . 257 51. Convenient Equivalents 258 52. Inches and Fractions Expressed in Decimals of a Foot 259 53. Comparison of Standard Linear Units 260 54. Meters and Millimeters Converted into Feet and Inches 262, 263 55. Feet and Inches Converted into Meters and Millimeters 264 56. Correction in Feet for Curvature and Refraction 265 57. Stadia Table 266-272 58. Trigonometric Formulae 273 59. Curve Formulae 277 60. Common Logarithms of Numbers 280 61. Natural Sines and Cosines 282 62. Natural Tangents and Cotangents 284 63. Three-Halves Powers of Numbers 286 64. Conventional Signs for Irrigation Structures 291 65. Squares, Cubes, Square Roots, Cube Roots, Reciprocals, and Area and Circumference of Circles . . . 292 INTRODUCTION THE major portion of this book consists of tables and diagrams. Tables are given generally where their use does not require inter- polating for intermediate values; for example: the earthwork tables on pages 208 to 219, where the arguments of the tables are given as close as the measurements are made in the field, but in most other cases graphic representation has been preferred. Dia- grams avoid mental interpolation; they throw vividly upon the mind a picture of how the different factors vary. Logarithmic scales are generally used, and for several reasons: First, they allow covering the greatest range of values in a given amount of space; second, on these scales, most of the curves are straight or nearly so, making the reading of the diagram easier than where the lines are curved, as on natural scales; third, from whatever part of the diagram a value is read, the same degree of accuracy is obtained, which is not the case when natural scales are used. Most hydraulic calculations do not warrant the high degree of refinement generally indicated in tables, which is liable to be misleading, especially to the inexperienced. The diagrams give results that are well within the limit of accuracy of the data, and, at the same time, avoid the implication of an accuracy that does not exist. It seems desirable, before entering on a detailed explanation of the tables and diagrams, to discuss briefly the various features of irrigation engineering, in order to show more completely the applicability of the matter that follows. To this end, the usual steps in the development of an irrigation project are taken up in the order of their sequence, and data are presented that are of assistance in arriving at the proper conclusions. In discussing the various features, irrigation by gravity from surface waters is kept principally in mind, as this is by far the most important method, but most of the principles apply to irrigation by pumping as well; the main difference being that the latter method generally presents a much simpler problem in the aggregate. xiii WORKING DATA FOR IRRIGATION ENGINEERS CHAPTER I EXAMINATION AND RECONNOISSANCE Amount of Land Available. The amount of land available is generally much greater than the available water supply will cover, but a reconnoissance is always desirable to determine its location, both horizontally and in elevation, relative to the source of supply. From this is determined the probable length of the main supply canal, and it can be roughly judged whether the amount of land to be irrigated will warrant the construction of a main supply canal of the length found. The topographic sheets of the U. S. Geological Survey are exceedingly valuable for this purpose, and if such sheets are available for the territory under investigation, very little examination in the field will usually be necessary. Index maps, showing the topographic sheets available, and for sale at 10 cents each, may be obtained upon application to the U. S. Geological Survey. If such sheets are not available, a reconnoissance with hand level, aneroid barometer, and pocket compass will generally be necessary. For reference in establishing elevations, the "Dictionary of Altitudes" and pamphlets giving the results of spirit-levelling in the various States, published by the U. S. Geological Survey, are very useful. These may be obtained by application to the Director, U. S. Geological Survey, Washington, D. C. Source of Water Supply and Quantity Available. The flow of rivers comes from two general sources : rain and melting snow. Either of these is likely to produce sudden and large floods, but those produced by the former are, as a rule, much more sudden and violent, and the rivers in arid regions fed principally by rains often go dry, or almost dry, during the summer months, such as the Arkansas River, in Colorado and Kansas, and the 1 FOR IRRIGATION ENGINEERS CQ vo o t- oo CM CM CM CM IO to t- OO OS OrH CM O O OOO iHrH rH co co coeoeo coco co 00 OS O-I-H CM oo oo ososos os CM CM CMCMCM CM Ot-tTH CM CM us o t- oo os Oi-ii-i TJ TJ< T)< r}< TJ< 10 10 10 CM CM N t~t- t-t- - OS OS OS '^,-1 OS OS OS O 00 O o coco 10 Tf^m uiio m o oooo oq oo oqoooo oooo oo 00 00 OSOS OS O OOO i-l r-t T-I "* rf rJTlt Tf IO IOIO1O IOIO 1O V rfi - gj I !! rt : I 1 1 a PQ : P4 .20^ ' 1 -2 I pq e fi. o o o S 42 "- ! 1 "3 -I "3 S i si 4] 1 1 8 |g ?.! i -U 011 O g C WJ LJ I a lljlljll : 2 o *, &-.S >* o *>- .S O s5 Si v. re (y * * rt -I S 4 4" I Jl o- ft'S rt 3 S ^ ^ f I 5 "Sc ^ 5 2^ g rtrtCJ jj gti( f > S.S -g 3.3 "B S Bg = sf |i I II II & II *i 05 EXAMINATION AND RECONNOISSANCE Milk River, in Montana. Rivers fed by melting snows are much more reliable as an irrigation supply, but even these often run very low during the summer months. On account of this variable and flashy nature of streams in the arid regions, it is of the utmost importance that records be obtained not only of the total flow of the stream, but also of the monthly run-off, especially during the irrigation season. For this purpose, the records of the Hydrographic Branch of the U. S. Geological Survey are of great value. Thorough search for records from private sources should also be made. The Geological Survey records are published in various water-supply papers, a general index of the data available to date being given in the accompanying table. I. North Atlantic Coast. Includes streams flowing into the Atlantic Ocean from St. John River in Maine, to Rappahannock River, Va., inclusive. Principal streams in this division: St. Croix, Machias, Union, Penobscot, Kennebec, Androscoggin, Saco, Merrimac, Mystic, Blackstone, Connecticut, Hudson, Delaware, Susquehanna, Potomac, and Rappahannock. The streams drain wholly or in part, the States of Connecticut, Delaware, Maine, Maryland, Massachusetts, New Jersey, New Hampshire, New York, Pennsylvania, Rhode Island, Ver- mont, Virginia, and West Virginia. II. South Atlantic Coast and Eastern Gulf of Mexico. Includes streams flowing into the Atlantic Ocean and Gulf of Mexico from James River, Va., to Pearl River, Miss., inclusive. Principal streams in this division: James, Roanoke, Cape Fear, Yadkin, Santee, Savannah, Altamaha, Apalachicola, Choctawhatchee, Mobile, and Pearl. The streams drain wholly or in part the following States: Alabama, Florida, Georgia, Mississippi, North Carolina, South Carolina, and Virginia. III. Ohio River Basin. Includes Ohio River with all its tributaries. Principal streams: Allegheny, Monongahela, Beaver, Muskingum, New (or Kanawha), Scioto, Miami, Kentucky, Wabash, Cumberland, and Tennessee. The streams drain wholly or in part the following States: Alabama, Georgia, Illinois, Indiana, Kentucky, Mississippi, New York, North Caro- lina, Ohio, Pennsylvania, Tennessee, Virginia, and West Virginia. IV. St. Lawrence River Basin. Includes streams which drain into the Great Lakes and St. Lawrence River. Principal minor basins: Lake Superior, Lake Michigan, Lake Huron, Lake Erie, Lake Ontario, and St. Lawrence River. Principal streams flowing into Lake Su- perior: St. Louis, Ontbnagon, Dead, and Carp Rivers. Streams flowing into Lake Michigan are Escanaba, Menominee, Iron, Peshtigo, Oconto, Fox, St. Joseph, and Grand Rivers. Streams flowing into Lake Huron are Thunder Bay, Au Sable, Rifle, and Flint Rivers. Streams flowing into Lake Erie are Huron, St. Marys, Maumee, Sandusky, Black, and Cuyahoga. Streams flowing into Lake Ontario are Genesee, Oswego, Salmon, and Black Rivers. Streams flowing into the St. Lawrence are Oswegatchie, Raquette, Richelieu (the outlet of Lake Champlain), and St. Francis River, whose principal tributary, Clyde River, reaches it through Lake Memphremagog. The streams of this section drain wholly or in part the following States: Illinois, Indiana, Michigan, Minnesota, New York, Ohio, Pennsylvania, Vermont, and Wisconsin. V. Hudson Bay and Upper Mississippi River Basins. Include all streams which drain into Hudson Bay and the Mississippi above its junction with the Ohio (except the Missouri). The principal streams flowing into Hudson Bay from the United States are St. Mary River, Red River, and Rainy River. The principal tributaries of the upper Mississippi are Crow Wing, Sauk, Crow, Rum, Minnesota, St. Croix, Chippewa, Zumbro, Black, Root, Wisconsin, Wapsipinicon, Rock, Iowa, Des Moines, Illinois, Fox, and Kaskaskia Rivers. The streams drain wholly or in part the following States: Illinois, Indiana, Iowa, Minnesota, Missouri, North Dakota, South Dakota, and Wisconsin. 4 WORKING DATA FOR IRRIGATION ENGINEERS VI. Missouri River Basin. Includes the Missouri with all its tributaries. The principal streams in this basin are Red Rock, Beaverhead, and Jefferson Rivers, which may be con- sidered a continuous river forming the head of the Missouri; below the mouth of the Jefferson the principal tributaries are Madison, Gallatin, Prickly Pear, Little Prickly Pear, Dearborn, Sun, Marias, Judith, Musselshell, Milk, Yellowstone, Little Muddy, Little Missouri, Cheyenne, Niobrara, and Platte (including North Platte and South Platte Rivers), Kansas, Osage, and Gasconade Rivers. These streams drain wholly or in part the following States: Colorado, Iowa, Kansas, Minnesota, Missouri, Montana, Nebraska, North Dakota, South Dakota, and Wyoming. VII. Lower Mississippi River Basin. Includes all streams flowing into the Mississippi below the mouth of the Ohio. The principal streams in this division are Meramec, White, Arkansas (whose chief tributaries are Huerfano, Purgatory, Cimarron, Verdigris, Neosho, Canadian, and Mora Rivers), Yazoo, Homochitto, and Red Rivers. The streams drain wholly or in part the following States: Arkansas, Colorado, Kansas, Kentucky, Louisiana, Mississippi, Missouri, New Mexico, Oklahoma, Tennessee, and Texas. VIII. Western Gulf of Mexico Drainage Basins. Include all streams draining into the western Gulf of Mexico and into the Rio Grande. Principal streams flowing into the Gulf of Mexico above the mouth of the Rio Grande: Sabine, Trinity, Brazos, Colorado River of Texas, and Guadalupe. Principal tributaries of the Rio Grande are Rio Hondo, Rio Puerco, Pecos, and Rio San Juan. The streams drain wholly or in part the following States: Colorado, Louisiana, Mexico, New Mexico, and Texas. IX. Colorado River Basin. Includes the Colorado and its tributaries, of which the most important are Green River (considered the continuation of the Colorado), Grand River, Do- lores, San Juan, Little Colorado, Virgin, and Gila Rivers. The principal streams flowing into the Green are Newfork, Yampa, Ashley Creek, White River, Duchesne, Lake Fork, and Uinta. The principal tributaries of Grand River are Grand Lake, Frazer River, Williams Fork, Blue River, and Gunnison River. The streams of the Colorado basin drain wholly or in part the following States: Arizona, California, Colorado, Nevada, New Mexico, Utah, and Wyoming. X. Great Basin. Includes streams which do not discharge into the ocean. The basin is made up of a number of minor basins, of which the most important are Great Salt Lake, Sevier Lake, Humboldt Sink, and Truckee, Walker, Carson, and Owens River, and Honey, Mono, Malheur, Harney, Warner, Abert, Summer, Silver, and Goose Lake basins. The streams of this section drain wholly or in part the following States: California, Idaho, Nevada, Oregon, and Utah. XI. California. Includes rivers draining into the Pacific Ocean from California. Principal streams: Tia Juana, Sweetwater, San Diego, Bernardo, San Luis Rey, and Los Angeles Rivers; San Joaquin River, whose principal tributaries are Kern, Kings, Merced, Tuolumne, and Stanislaus Rivers; Sacramento River, whose principal tributaries are Pit, Feather, and American; and the following streams flowing into the Pacific Ocean above San Francisco Bay: Russian, Eel, Mad, and Klamath Rivers. With the exception of the Kla- math River, which receives a drainage from a small area in Oregon, all the streams in this division are entirely in California. XII. North Pacific Coast. Includes streams flowing into the Pacific Ocean from Oregon and Washington. Most important of these are Rogue, Umpqua, and Columbia Rivers and streams flowing into Puget Sound. The principal tributaries of the Columbia are Clark Fork, Kootenai, Spokane, Wenatchee, Yakima, Snake, Bruneau, Boise, Walla Walla, Uma- tilla, John Day, Deschute, Hood, and Willamette Rivers. The following streams flow into Puget Sound: Nisqually, Puyallup, White, Snoqualmie, and Skagit. The streams of this division drain wholly or in part the following States: Idaho, Montana, Nevada, Oregon, Utah, Washington, and Wyoming. The accompanying map shows the outlines of the above- described drainage basins. The engineer is fortunate, indeed, if he can find monthly run- off records for a number of years. When such records are not available it often happens that isolated measurements have been made which will give some idea of the run-off. If no measure- EXAMINATION AND RECONNOISSANCE f 6 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 2 ANNUAL PRECIPITATION, IN INCHES. NORTH PACIFIC STATES AND NORTH- ERN ROCKY MOUNTAIN PLATEAU 1 j * tfl 4 4 i c Year 8 3 6 1 1 i 11 1 g a X g 2 g a oJ 9 *j jj j 1 I 1 I .0 I | '1 1 5 w "3 11 | c 1872 6.03 10.10 17.93 46.90 20.24 21.40 1873 . . . 5.90 13.58 17.74 50 52 21.94 21.90 1874 . 9 73 9.58 14.97 46.17 20.11 22.40 1875 23.64 9.58 12.44 13.76 60.08 23.90 23.47 1876 21.28 5.67 16.15 ..... 11.12 54.94 ... 25.83 25.12 1877 16.35 6.47 12.91 13.80 58.30 25.57 27.88 1878 19.75 6.77 26.78 36.92 10.21 47.70 63.34 30.21 28.05 1879 13.11 9.36 16.32 45.03 17.63 62.22 73.44 33.87 28.43 1880 10.94 6.13 12.01 31.44 10.66 51.87 62.77 12.18 24.75 28.49 1881 16.88 11.91 9.87 43.68 13.56 58.05 65.56 22.68 19.94 15.54 27.77 26.54 1882 15.98 10.46 14.97 34.77 14.43 67.24 51.59 25.99 10.32 12.76 25.85 24.70 1883 14.24 8.40 11.01 22.48 15.27 51.45 41.61 14.37 10.55 15.10 20.45 24.01 1884 17.52 18.38 21.38 29.19 21.05 38.31 35.58 20.56 19.18 25.67 24.68 22.73 1885 19.69 11.80 18.37 30.91 12.56 39.59 41.95 19.01 10.99 8.37 21.32 22.54 1886 18.89 8.16 12.02 35.17 12.23 38.76 48.13 15.86 12.63 11.48 21.33 22.83 1887 11.66 8.05 11.91 37.34 11.34 54.17 61.78 20.10 14.05 18.94 24.93 21.86 1888 13.62 4.89 23.94 31.19 11.09 38.76 45.54 17.69 10.14 21.87 21.50 1889 18.46 5.75 39.26 28.12 10.95 31.76 33.75 14.27 6.71 9.40 19.84 22.64 1890 10.33 11.27 14.60 34.65 12.53 40.29 35.70 16.57 8.80 10.37 19.51 22.38 1891 15.92 9.68 23.04 46.90 13.31 47.41 58.73 16.69 19.39 19.41 27.05 23.10 1892 14.08 7.85 46.26 28.88 11.75 33.58 49.41 16.78 15.27 12.40 23.63 24.06 1893 17.35 7.85 26.46 37.86 13.87 39.03 61.62 22.00 15.48 13.31 25.48 24.04 1894 15.27 10.12 20.92 44.29 14.12 39.32 58.57 17.84 11.17 14.49 24.61 23.34 1895 11.95 6.84 25.55 29.92 7.90 30.76 46.60 13.46 10.69 10.94 19.41 24.56 1896 18.42 11.08 27.68 43.69 22.95 44.13 65.46 20.32 15.38 16.48 28.56 23.38 1897 16.74 6.66 17.40 34.83 16.98 43.01 58.50 23.84 16.16 13.30 24.74 23.68 1898 16.09 7.08 8.54 25.93 33.90 42.22 13.08 17.40 12.11 19.59 24.18 1899 17.57 8.47 23.15 42.97 14.81 42.21 62.22 20.08 11.78 17.88 26.11 23.10 1900 11.53 7.43 21.17 29.74 12.77 38.22 56.37 18.72 11.62 11.43 21.90 23.29 1901 16.08 8.73 20.76 34.37 9.59 41.05 55.08 15.99 14.71 15.03 23.14 23.71 1902 11.41 4.99 25.65 39.58 12.15 50.15 70.77 19.23 10.09 12.94 25.70 23.50 1903 14.62 6.53 20.26 29.50 9.55 35.62 56.88 16.55 11.36 16.03 21.69 22.83 1904 16.31 9.44 29.51 43.42 14.08 46.37 61.67 13.97 7.49 8.61 25.09 23.46 1905 14.23 6.42 19.67 21.14 9.77 34.10 46.43 16.68 10.08 6.76 18.52 23.21 1906 21.28 10.50 33.68 30.21 14.19 43.29 63.86 17.60 14.28 14.13 26.30 22.90 1907 19.22 11.35 17.73 42.12 15.92 42.89 51.68 17.69 12.74 13.28 24.46 22.30 Mean. . 23.89 ments whatever are available, the best that can be done as a preliminary step is to measure the slope and cross-section of the stream and calculate the probable maximum run-off, and com- pare the drainage basin with others of known run-off by means of rainfall records which may be obtained from the publications of the U. S. Weather Bureau. Tables 2 to 8 compiled by the EXAMINATION AND RECONNOISSANCE 7 TABLE 3 'ANNUAL PRECIPITATION, IN INCHES. NORTHERN ROCKY MOUNTAIN SLOPE ,& . J i 1 5 j . a j.C Q Q - i 1 Year g d 3 1 s 1 | M o 2 it * i 9 | 1 c 1 S"i 13 f! || l V V a 3 | 1 2 Q 1 o i PQ Sj 0.03 SI II J3 U 1 E 1872 18.05 32.48 19.42 14.86 16.80 13.48 19.17 17.80 1873 11.81 27.04 14.62 13.19 27.39 20.76 10.01 17.83 18.00 1874 13.46 25.75 16.24 12.64 27.63 7.58 9.71 16.14 18.22 1875 10.78 17.25 15.35 42.89 13.99 27.52 13.53 19.59 14.85 12.10 18.79 18.91 1876 15.40 20.12 11.84 32.51 19.54 30.92 25.75 18.13 12.34 5.03 19.16 19.90 1877 27.89 16.38 25.47 40.95 22.92 17.68 21.67 29.38 12.29 11.71 22.63 20.45 1878 17.96 15.51 18.62 37.05 20.19 20.23 33.83 35.72 16.11 12.64 22.79 20.63 1879 15.43 10.86 20.06 30.31! 23.50 22.61 19.31 19.76 19.67 7.34 18.89 21.22 1880 18.12 9.58 17.48 28.52 16.66 19.75 27.35 27.60 13.25 8.38 19.67 20.59 1881 33.55 12.78 22.93 45.74 14.85 15.76 19.26 29.48 14.90 11.88 22.11 20.74 1882 13.14 14.49 17.95 37.68 12.20 21.33 22.48 34.01 12.73 8.64 19.47 21.26 1883 28.50 19.49 30.01 48.92 19.91 15.66 17.88 24.96 10.82 19.24 23.54 21.39 1884 30.36 15.07 13.53 47.68 11.97 23.36 21.81 28.50 7.37 15.54 21.52 20.49 1885 23.71 15.95 22.03 36.68 20.82 13.08 17.37 22.68 15.56 15.11 20.30 20.06 1886 19.35 15.07 13.10 22.67 16.00 13.26 29.24 26.76 10.24 10.36 17.61 18.73 1887 15.71 12.49 21.68 19.92 14.26 16.33 23.36 21.97 15.43 11.82 17.30 17.54 1888 22.94 9.51 17.46 24.22 14.77 16.51 17.99 16.50 14.70 14.51 16.91 16.68 1889 19.17 14.75 20.66 22.97 15.29 11.03 11.75 17.07 8.46 14.65 15.58 17.83 1890 11.72 9.33 12.71 22.08 13.28 16.75 23.50 21.79 14.24 14.47 15.99 18.16 1891 32.34 21.43 23.36 34.92 13.18 20.50 25.93 24.31 18.98 18.97 23.39 17.88 1892 19.66 15.02 20.37 29.44 18.81 18.17 16.34 24.94 14.26 13.50 18.95 17.81 1893 10.12 8.48 13.16 26.66 14.56 13.74 20.07 23.58 15.45 9.22 15.50 18.14 1894 12.60 15.09 11.21 17.82 7.82 14.32 20.29 22.43 17.76 12.98 15.23 17.63 1895 20.31 16.12 14.58 21.69 16.85 16.92 20.60 17.38 17.07 14.76 17.63 17.48 1896 19.87 11.84 16.52 35.90 17.35 16.64 26.80 22.04 20.79 20.86 17.91 1897 21.58 15.37 17.09 21.30' 18.84 14.33 25.80 12.19 17.25 18.19 18.42 1898. . . 31.46 12.98 15.54 28.84 10.65 13.67 19.83 14.44 13.05 17.66 18.78 1899 . 28.45 9.33 13.99 26.74 20.00 15.47 16.01 20.64 12.61 14.18 17.74 18.20 1900 20.76 15.29 12.29 31.20 16.81 17.88 21.06 27.50 15.81 16.09 19.47 18.66 1901 16.06 9.10 16.44 25.08 17.04 15.59 16.50 30.16 18.36 14.99 17.93 [19.01 1902 17.70 13.35 26.27 30.48 20.04 15.95 18.97 29.12 16.85 16.50 20.52 19.10 1903 15.27 9.50 18.36 33.43 19.53 17.96 21.64 28.29 17.69 12.25 19.39 19.64 1904 17.19 14.05 23.17 25.48 9.15 14.17 27.81 26.36 9.44 15.72 18.21 20.70 1905 25.96 17.68 26.81 29.88 20.46 17.19 18.70 31.48 10.66 22.68 22.15 19.93 1906 32.54 16.84 27.99 27.59 22.06 18.22 21.21 26.00 22.01 17.65 23.21 19.40 1907 18.26 11.83 19.61 24.60 14.02 16.55 16.31 23.02 10.18 12.34 16.67 18.80 Mean 19.11 Weather Bureau contain valuable general information in regard to rainfall. If the project has any considerable size or impor- tance, nothing short of monthly run-off records for a series of years will justify its construction. This is fully borne out by the numerous failures of irrigation schemes because of insufficient water and other cases where failure was avoided only by the construction of expensive storage works. 8 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 4 ANNUAL PRECIPITATION, IN INCHES. LAKE REGION AND CENTRAL VALLEYS I , i d | | d 1 Year .y O . .2 23 i ~ jfl .5 s s o 'rt I a it a 3 ""^ 2 ^ 8 H ri I 1 | g 1 i 1 8 *r* 1 3 *3 3 1 ^ U U c g a Q U 55 Q * S 1872. 34.39 34.68 34.12 26.52 30.47 29.07 29.72 25.63 30.58 36.95 1873 31.10 41.33 41.38 52.83 50.86 45.50 36.41 34.75 34.32 40.96 37.50 1874 25.18 33.39 37.45 43.92 47.58 37.88 28.63 35.51 26.43 35.11 38.34 1875 37.27 36.91 42.58 54.58 52.93 43.00 38.06 30.66 35.71 41.30 39.64 1876.'.... 37.62 41.19 52.62 57.56 55.60 48.46 36.48 23.67 40.40 43.73 39.51 1877 41.00 33.13 34.65 39.08 39.47 41.43 41.01 28.80 35.23 37.09 40.09 1878 38.48 53.51 41.62 38.62 41.76 40.83 41.95 22.78 43.39 40.33 40.28 1879 39.97 41.52 51.60 42.88 45.41 25.70 32.82 30.71 32.39 37.17 38.02 40.17 1880 43.63 37.38 54.67 50.99 49.56 34.66 36.66 37.32 29.76 47.68 42.23 41.51 1881 45.61 34.96 47.24 48.74 32.18 37.37 56.81 44.18 39.16 45.44 43.17 41.85 1882 45.10 39.98 52.12 53.68 61.58 43.15 47.60 41.34 23.14 30.32 43.80 41.66 1883 85.32 41.13 52.35 54.12 52.54 40.10 39.69 45.86 26.70 32.57 42.04 40.38 1884 35.53 33.26 39.28 39.99 51.66 40.64 41.14 34.61 26.11 28.17 37.04 38.28 1885 34.71 39.93 33.94 39.51 31.99 45.59 35.03 44.37 25.33 28.24 35.06 35.77 1886 40.12 27.34 31.35 39.88 37.98 44.34 29.53 26.77 22.89 26.71 32.69 34.12 1887 37.88 35.36 35.08 33.08 26.75 35.30 24.60 29.13 25.85 28.97 31.20 32.77 1888 29.36 32.57 34.88 41.36 41.90 41.17 31.15 30.86 25.86 29.02 33.81 33.31 1889 31.32 32.57 30.92 38.41 37.74 33.16 25.90 34.95 16.96 21.06 30.30 33.17 1890 31.35 47.82 47.70 54.87 50.53 37.63 24.74 32.69 23.38 34.99 38.57 34.24 1891 31.61 34.18 38.44 38.23 39.56 30.53 30.14 26.54 21.74 28.83 31.98 34.51 1892 32.15 36.51 31.95 39.77 38.71 41.62 38.42 36.56 32.55 37.11 36.54 35.92 1893 33.35 33.88 44.00 39.35 48.79 39.33 25.64 27.47 25.95 34.18 35.19 31.90 1894 30.88 27.73 26.59 31.13 30.51 27.44 20.06 27.46 25.80 25.74 27.33 32.28 1895 21.59 26.84 29.33 33.54 33.57 31.20 26.80 32.38 24.26 25.04 28.46 32.20 1896 30.14 36.68 34.48 39.84 39.36 37.55 37.09 33.14 34.73 36.20 35.89 32.55 1897 32.59 24.54 43.89 42.15 44.10 40.17 27.07 25.85 30.51 30.34 34.12 33.28 1898 34.07 32.54 38.97 44.10 48.66 49.20 28.33 33.77 25.34 34.34 36.93 33.88 1899 29.93 24.53 34.69 36.87 42.42 34.61 26.73 26.49 27.54 26.41 31.02 32.05 1900 23.03 25.83 27.78 38.45 36.89 29.51 38.46 28.65 34.22 31.45 31.43 32.47 1901 25.23 38.71 17.99 30.33 31.68 24.80 19.77 24.52 25.75 28.78 26.76 31.77 1902 29.02 39.89 37.30 37.70 33.07 38.43 42.01 37.57 31.75 35.53 36.23 31.90 1903 31.54 35.41 34.69 32.46 32.91 33.81 31.43 28.09 37.88 35.88 33.41 32.53 1904 24.68 34 . 56 29.54 45.42 32.00 33.71 28.43 26.14 34.11 28.32 31.69 34.27 1905 28.14 31.90 38.69 33.29 39.48 38.54 37.50 35.36 30.76 32.00 34.56 34.03 1906 35.22 31.62 40.83 37.47 46.92 35.52 29.44 30.87 33.21 33.67 35.48 33.70 1907 22.68 34.76 44.56 38.56 45.58 41.39 34.02 35.10 23.07 30.62 35.03 33.20 Mean 35.55 In case good records are not available, and the project appears from other considerations to be a feasible one, measuring stations should be established and rain gages installed at convenient points on the irrigable area and drainage basin. If the stream is a very small one, a weir may be used for measuring the flow, but if this is not possible, a current meter station should be established. In either case, a reliable local resident should be employed to EXAMINATION AND RECONNOISSANCE TABLE 5 ANNUAL PRECIPITATION, IN INCHES. NORTH ATLANTIC STATES AND NEW ENGLAND U V i I \ > ^ d 4 Q' 1 I Year 3 c 3 M z OH 1 1 I S S B g c > >; 4 3 1 fl .S i S 1 3 PQ 2 8 PQ E z I 1 PQ S 1 1 I 1 3 C C 1 S 1872 32.25 50.62 45.78 31.25 31.91 48.36 30.86 56.95 41.00 41.90 1873 25.92 54.53 39.98 44.63 41.42 55.28 45.70 55.43 45.36 41.97 1874 42.56 31.94 43.52 39.84 37.93 30.44 39.42 46.25 34.58 50.41 39.69 42.05 1875 45.42 26.94 50.15 45.19 38.25 31.44 34.05 40.22 41.11 50.97 40.37 42.66 1876 57.99 27.53 48.96 47.40 38.19 29.26 37.01 47.39 47.96 46.54 43.82 43.58 1877 50.62 33.17 51.49 40.94 36.09 34.48 34.72 37.26 52.59 69.13 44.05 42.87 1878 51.37 41.45 65.53 46.66 49.37 60.24 38.76 34.53 60.09 51.87 49.99 42.20 1879 43.48 24.27 45.67 36.21 38.66 30.47 37.02 36.75 32.83 35.88 36.12 41.28 1880 42.44 25.21 37.30 37.34 32.54 39.26 31.97 33.58 38.83 51.84 37.03 40.86 1881 55.98 20.99 52.63 40.40 36.34 35.95 37.30 30.21 42.20 40.06 39.21 39.47 1882 47.18 25.64 43.82 46.61 33.76 33.82 38.63 45.58 46.79 57.67 41.95 41.20 1883 53.17 35.48 38.83 39.37 38.07 43.17 39.17 45.71 54.30 43.03 42.13 1884 64.53 33.37 49.18 55.34 38.90 37.07 34.82 39.34 49.96 45.05 44.76 42.85 1885 54.06 33.64 45.10 42.12 34.39 52.36 34.12 33.35 44.84 43.25 41.72 42.39 1886. . 28.47 42.14 46.73 34.01 44.85 39.21 37.24 58.17 54.33 42.79 42.79 1887 46.96 31.13 33.75 46.63 39.70 31.55 41.95 42.17 35.08 47.74 39.67 43.49 1888 53.25 33.97 45.89 52.95 44.66 33.87 39.89 44.06 45.05 56.64 45.02 44.14 1889 42.26 38.21 39.82 58.68 39.51 40.07 41.37 50.60 61.33 70.72 48.26 43.57 1890 45.02 38.51 45.93 52.30 44.89 46.55 50.61 34.02 41.59 50.22 44.96 43.43 1891 36.44 39.12 39.70 41.44 41.68 30.74 38.28 38.19 52.95 50.63 39.92 42.39 1892 32.20 42.24 37.02 38.90 34.83 45.87 32.66 34.78 42.34 49.24 39.01 39.80 1893 29.87 29.04 41.84 53.01 35!39 38.64 37^84 37.65 36.71 57.90 39.79 37^56 1894 22.84 22.96 36.62 44.17 35.11 38.92 28.17 40.34 30.85 53.09 35.31 35.82 1895 32.88 28.69 40.17 35.73 29.80 32.02 27.50 31.01 34.25 45.41 33.75 36.24 1896 31.54 28.38 37.55 37.99 27.88 37.29 44.35 32.15 31.16 44.22 31.25 36.68 1897 39.57 43.44 40.77 44.27 40.79 37.72 35.08 42.04 44.58 42.66 41.09 36.92 1898 45.16 31.78 49.86 45.12 38.77 33.50 35.76 49.23 37.72 53.14 42.00 37.79 1899 36.44 37.25 34.69 42.06 28.92 29.39 33.85 39.96 44.02 38.41 36.50 39.90 1900 47.35 34.24 44.05 41.78 30.56 35.93 25.73 40.91 41.20 39.34 38.11 39.65 1901 41.61 33.88 48.72 47.06 40.53 35.49 40.76 45.54 41.75 42.61 41.80 39.29 1902 41.41 38.36 33.93 47.07 37.48 32.91 32.22 49.76 46.58 38.48 39.82 39.47 1903 36.67 32.86 41.97 48.60 34.09 37.95 38.81 41.50 43.55 46.10 40.21 39.38 1904 38.89 29.71 39.64 41.57 31.26 35.83 33.76 39.76 40.84 42. 6C 37.39 39.08 1905 31.88 34.73 32.08 44.48 26.98 35.85 35.19 41.61 50.64 43.29 37.67 38.97 1906 39.49 29.87 40.69 41.82 32.51 33.63 31.29 51.87 52.92 49.23 40.33 38.40 1907 44.42 29.67 37.56 45.28 33.63 34.97 34.86 48.74 44.66 38.72 39.25 38.10 Mean 40.61 read the gage daily, recording the readings on suitable blanks furnished for the purpose, or a recording gage may be estab- lished which will give a continuous record of the height of water in the form of a diagram. The rain gage consists of a metal cylinder having a funnel- shaped top leading to a smaller cylinder inside having a cross- 10 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 6 ANNUAL PRECIPITATION, IN INCHES. EAST GULP STATES Year Hatteras, N. C. Charleston, S. C. Jacksonville, Fla. Key West, Fla. New Orleans, La. Galveston, Tex. Montgomery, Ala. Augusta, Ga. Memphis Tenn. Fort Smith, Ark. 1 1 a < Five-year means 1872 57.06 62.15 62.51 50.97 78.42 78.11 77.44 50.29 46.69 43.20 57.01 51.35 60.22 67.93 35.94 44.69 49.46 52.15 47.84 45.50 53.32 70.99 57.81 55.18 47.78 56.65 46.42 44.33 38.10 32.70 37.22 42.86 37.88 34.85 43.62 31.71 57.17 60.65 48.31 57.60 55.28 50.58 60.42 47.18 65.51 54.69 53.26 53.34 55.02 82.00 54.86 58.60 53.13 46.22 47.52 41.34 41.89 58.23 56.84 46.80 40.19 60.70 45.71 38.57 53.85 54.22 55.52 52.03 49.17 55.77 46.86 45.07 31.77 32.75 32.75 36.35 37.95 38.15 49.03 58.54 33.41 53.10 41.86 48.24 33.05 34.03 30.13 43.62 35.58 52.67 42.87 39.75 24.91 22.00 42.34 29.19 25.72 46.46 43.39 29.55 48.81 37.02 38.61 30.36 37.98 41.84 48.53 26.65 60.68 65.55 62.74 85.73 67.25 63.09 66.16 51.27 69.83 64.01 50.18 69.85 60.01 64.18 54.83 64.97 83.13 48.45 42.17 38.62 56.91 48.02 54.44 56.44 49.68 43.47 49.00 31.07 56.33 57.73 41.61 57.18 43.69 80.07 41.59 66.32 41.72 58.91 49.39 58.48 50.92 66.87 60.90 26.93 50.97 53.28 57.68 41.11 62.98 62.56 40.97 43.43 65.88 37.52 47.80 41.51 24.78 35.43 40.64 38.91 23.71 29.24 42.00 41.76 78.39 51.33 37.67 52.47 42.65 48.60 31.16 43.93 55.17 64.00 48.50 51.93 57.19 58.16 54.68 59.74 46.16 50.26 53.97 55.40 46.34 48.46 40.99 54.22 47.91 53.81 54.77 54.75 49.62 39.71 39.90 48.61 45.10 58.89 40.67 56.25 46.04 44.74 45.09 61.39 49.88 45.62 49.25 48.18 42.98 51.05 47.76 69.85 39.27 47.481 48. 91 41.35 55.54 43.45 52.10 45. 82' 43. 45 46.25 51.83 39.75 43.99 50.63 48.74 59.92 51.22 52.24 50.94 48.62 41.79 48.99 51.83 37.00 29.54 47.23 40.92 50.13 53.91 49.83 38.93 43.95 56.20 45.71 57.02 55.49 73.50 49.34 52.29 61.67 42.84 71.05 57.14 64.69 37.41 57.72 42.52 46.82 44.67 68.28 51.31 61.46 44.45 54.52 38.59 35.00 46.03 48.58 38.99 47.42 34.58 50.32 36.17 42.56 55.85 54.31 41.55 49.65 56.09 51.32 58.58 57.44 64.06 60.25 49.63 58.09 53.17 55.67 52.43 54.67 54.73 46.58 48.14 55.40 49.60 50.78 45.68 47.46 47.85 50.15 47.98 48.23 47.54 45.82 42.58 51.87 44.36 42.66 45.62 39.28 48.93 46.66 42.41 50.04 53.25 53.60 54.62 57.50 58.33 57.99 57.89 57.04 55.36 53.80 54.81 54.13 53.84 5F.33 51.92 50.91 50.12 49.92 49.78 48.27 48.38 47.82 46.33 46.25 45.94 44.43 45.21 46.43 45.46 45.42 44.76 44.17 44.63 44.58 44.55 44.40 1873 1874 1875 68.26 65.78 102.04 77.18 70.72 92.64 58.81 66.60 76.96 66.41 68.02 54.72 55.07 56.73 67.24 55.51 59.50 52.88 58.30 57.85 69.28 45.25 58.82 48.20 61.88 45.65 50.11 40.13 48.87 40.97 41.66 53.94 44.56 1876 1877 1878 1879 1880 1881 1882 1883 1884 1885 50^63 31.61 35.33 38.69 50.97 43.20 64.63 40.49 49.35 44.70 41.21 49.87 25.70 41.91 51.12 40.27 39.05 22.77 35.12 35.46 31.39 42.50 42.50 35.58 1886 1887 1888 1889 1890 1891 1892 1893 1894 1895 . 1896 1897 1898 1899 1900 1901 1902 1903 1904 1905 1906 1907 Mean . . sectional area of one-tenth that of the larger cylinder, so that the depths of water accumulated in the smaller cylinder magnify the actual precipitation ten times, and thus enable very small rainfalls to be accurately measured. The water depth in the small cylinder is measured at the end of each rain by a cedar stick graduated to inches and tenths of inches. Standard rain gages are generally furnished by the Weather Bureau EXAMINATION AND RECONNOISSANCE TABLE 7 11 ANNUAL PRECIPITATION, IN INCHES. WEST GULF STATES AND SOUTHERN ROCKY MOUNTAIN SLOPE 1 ^ . t . jj t & . 1 ^8 H jfj JJ J 3J 1 | B j Year "5 itf *o- o S I 1 1 M I a c *fl III" jfa 3 C/3 rt 1 1 * 2 I | c g.5 \ (<* + l>\ i * = ( 2~ ) (-r) 1 ' in which a and b are the water depths in feet at two adjacent measuring points, V a and V b the respective mean velocities in feet per second at these points, / the distance in feet between the points, and q the discharge in second-feet for the elementary area. This formula is well suited to computing discharges in canals conforming in cross-sections to their original trapezoidal or rectangular dimensions. In the other method, the discharge is computed for consecutive pairs of elementary areas, on the assumption that the velocities and the water depths for three consecutive measuring points each lie on the arc of a parabola. This method might be termed the parabolic method and the formula for computing the discharge for each pair of elementary areas is as follows: . . l q \ e~ ~) \ 6 r in which a, b, and c are the water depths in feet at three consecu- tive measuring points; V a , V b , and V c the respective mean velocities in feet per second at these points; / the distance in feet between the consecutive points, and q' the discharge in second-feet for the pair of elementary areas. This formula is more particularly applicable to river channels and old canals that have cross-sections conforming in a general way to the arc of a parabola, or to a series of arcs of different parabolas. EXAMINATION AND RECONNOISSANCE 17 The discharge measurements at a current-meter station should be taken at sufficient intervals of gage heights to permit of making accurate velocity, area, and discharge curves. For this purpose it is necessary to get well-distributed measurements from low to high stages. Special precautions are necessary in canal measurements. The canal bed at a well-selected current-meter station is generally permanent in character and a permanent rating curve could be made were it not for the fact that increased vegetable growth in the canal and on its banks, during the irri- gation season, together with accumulations of silt, decrease the discharge capacity for all gage heights during the latter part of the irrigation season. This fact must be taken into consideration in computing the quantity of water carried by a canal during the irrigation season. If the canal is cleaned during the season, the relation of discharge to gage height is again disturbed. These changing relations of discharge to gage height are the chief source of errors and difficulties in irrigation-canal hydrography. In order to determine the discharge at a current-meter sta- tion it is necessary to read the gage daily for rivers, and for canals additionally at such times as changes of stage are made. The gages should be read accurately, generally to the nearest hundredth of a foot. The current-meter measurements at a station are interpreted and extended to cover all gage heights at the station by means of curves drawn on cross-section paper. To construct these curves, the discharges in second-feet as com- puted from individual current-meter discharge measurements, the corresponding mean velocities in feet per second, and the cross-sectional areas in square feet for each measurement are plotted as abscissas, each to a convenient scale, with the common gage heights as ordinates. The most probable area curve is drawn through the area plottings and from this the accuracy of the area computations and of the soundings are checked and, in case of a shifting channel, changes in the rating section are dis- covered. The most probable velocity curve is drawn through the velocity plottings on the sheet to provide a graphic means of finding inaccuracies in the computations and noting dis- turbances in the velocity due to obstructions in the channel or changes in the velocity due to increased roughness of the channel 18 WORKING DATA FOR IRRIGATION ENGINEERS from vegetable growths in the canal. The discharge curve is then drawn through the discharge points on the cross-section paper, giving due weight to the various measurements and to products .of the mean velocity and area abscissas for various gage heights throughout the range of depths. Where the con- ditions of flow have not been changed during the season, it will generally be comparatively easy to draw a satisfactory curve. Where/ however, the relation of discharge to gage height has been affected by vegetable growth, or the introduction of other obstructions, these conditions must be given careful consideration and another curve drawn for that part of the season during which 4.0 3.5 |3.0 I" | 2 .0 i o 1 - 5 1.0 0.5 20 41 Discharge in Second-f e 3 60 80 100 120 140 It Bt 180 200 220 *_ z / X X* Le/ '6 i / S ^ < / t> * / A 'A k >< A ^ a / / / .*&, 7 / / ,~O !>; > >-"-! 00 O -^ GO Oi O O -t O GO CO O5 1> O t> O CO O5 C *4 C4 C4 00 ^ CO CO O^ t^ CO ^^ CO ^5 O^ 1 s * ^^ O^ O^ 0^ ^* ^^ O^ GO T^ ^^ CO TJH - 1 i o CM co oo Ci i CioooocoQi'^n>i>o iO*OO500l>COCOOiTtir>.rHCMiOOOi iCOtMOCMcO CO * CO <* rH CM' T}< rH rH r4 r-^ (N Oi (N T-H FH ^-1 CO (N TH : : :g t- TJH O O5 '-i 1C CO -CM -iQO -CO "-i ^COCOCOOO^H . . -0 -O^H -(N -0 rH OS CM IO rH 00 CO CM rH rH O Oi 00 IO rH Tt CO O ^lOCMt^rHCM'OqrHqqTjHCMrHqrH CO IN rH -eg u_: 3 * CO O5 CM CO OCMO' " -^ O CN i I I-H CO CO CM CO O5CO i-H CO T-H i-H CO t > * CO I s * ^^ 00 O5 1 1 was measured at the system estimated at figure is used in esti- October 22. ed to the lan ses in latera weirs, and th was turned in April 12 and turned o Idaho-Minidoka. The water deli heads of laterals. Wash.-Yakima-Sunnyside Unit. 15% of amounts measured at the he mating amount delivered to farms. re Valley. The apparently high percentage of water delivered to the land was due to the fact that water was canals through additional feeder canals not measured. ctly under the U. S. R. S. e upper system receives water directly from the main ystem receives water from the Deer Flat Reservoir. In ater was turned in February 5, in the latter system water Colo.-Uncompa diverted which wa also supplied to the c Area is for that direct Idaho-Boise. The canal. The lower the former system INVESTIGATIONS AND SURVEYS 23 This table is intended to give a general idea of what may be expected under similar conditions elsewhere. The average applications may be considered as rather high for permanent conditions for the reason that many of these lands are new and require considerably more water than will be necessary ulti- mately. In general, it may be stated that more water was applied to the land than was absolutely necessary for growing the crops, so that in time, when the irrigators become more proficient and water becomes more scarce, the quantity applied to the land will no doubt be considerably reduced. Distribution of Irrigation Water through the Season. It is not sufficient to know the total quantity of water that is required in a season, but it must also be known how the use of this water is to be distributed through the season. This is necessary for determining the sufficiency of the water supply during the irriga- tion months, when storage is not provided, and also to determine the maximum capacity of canals. It is obvious that more water is required during the hot, dry summer months than earlier and later in the season. Fortunately, a general knowledge of the variation in the requirements for the different months is sufficient, as, if necessary, the quantities used can be adjusted in a consid- erable degree to the available supply. Generally speaking, the maximum requirement may be taken as 25 to 50 per cent greater than the average. The accompanying table is useful as furnish- ing general data on the distribution of water throughout the season. This table also gives the relation of the quantity deliv- ered to the land to the quantity diverted into the main canal of the system. The difference does not represent the amount lost by seepage, as in most cases a considerable portion of the quantity diverted was wasted through wasteways and returned directly to the river. To obtain quantity lost by seepage, the quantities wasted must first be deducted from the diversion, and the re- mainder is then the sum of the quantities applied to the land, and the quantities lost by seepage. These sums, less the applied quan- tities given in the table, give the seepage losses in the entire system. These are shown in the following tabulation as far as the figures are available: 24 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 11 Project Total Canal Losses in Percent of Diversion, 1912 Project Total Canal Losses in Percent of Diversion, 1912 Yuma 32 Carlsbad 48 Orland 20 Klamath 36 Boise 37 Belle Fourche 32 Minidoka 27 Okanogan 47 Flathead 50 Sunnyside. 27 Huntley 17 Tieton 17 Sun River 26 Shoshone 36 Lower Yel'stone. North Platte . . 43 21 Average 32% Truckee-Carson . 34 NOTE. See Table 14, page 44, for seepage losses from canals in various materials. It has often been assumed in investigations of irrigation projects, that one-third of the quantity diverted would be lost by seepage and evaporation in the canal system, and the above average seems to support this assumption. A detailed consider- ation of seepage losses for the purpose of designing canals is taken up later. A loss by seepage in the entire system of one- third the quantity diverted is considered to be sufficiently ac- curate for preliminary purposes. Location of Point of Diversion. The first examination will have indicated in a general way the elevation at which it is necessary to divert in order to cover a suitable body of land, and with this knowledge the stream must be examined for a suitable location for diversion works which will give the necessary eleva- tion. In most cases it will be necessary to dam the stream, and it is then necessary to estimate the area of flooded lands in order to determine the amount of damages that will have to be paid to the owners for such flooding. For the present purposes, only a rough approximation of the flooded area is necessary, but ulti- mately careful calculations for determining the elevations of the backwater must be made. The bed and banks of the river should be examined for suitable foundations for dam and headworks, so that the general type of dam required can be determined. Cross- sections of the stream must be measured, and some topography (which can be taken at small expense) is helpful. The general type of dam and its length and height should be determined upon and an estimate of quantities prepared. INVESTIGATIONS AND SURVEYS 25 Location of Main Canal. Having determined upon the loca- tion of a point of diversion, the location of the main canal may be started. (Not infrequently it happens that the point of diversion is dependent upon the location of the main canal, especially in rough country.) From the considerations already discussed, the size and grades of the canal, upon which depends its location, may be determined. The size and grades of the canal should, of course, be adjusted to the requirements of the land to be supplied, but a rough determination will suffice for preliminary purposes, and after the location has been surveyed and platted and a better knowledge is had of the areas to be irri- gated the canal sections can readily be increased or reduced within certain limits without causing appreciable errors in the estimates. Assuming that the irrigable lands are located in an elongated valley bordered by higher lands more distant from the stream, the main canal will follow along the highest points of the irrigable area, generally skirting along the foothills, following around the wider valleys of tributary watercourses, and jumping across the narrower ones. A preliminary location for the purpose of esti- mates requires the use of a transit and level, but great refinement is not necessary. Long shots may be taken with the level and the stadia may be used for measuring distances, only angle points being set and no curves run. In very rough locations it is neces- sary to set a large number of angle points if fair estimates are desired. After the fly-line, or a portion of it, has been run, the level party should go over the line and take elevations and trans- verse slopes at sufficiently frequent intervals to enable a profile to be drawn from which to estimate earthwork quantities, and structures such as flumes, pipes, etc. Determination of Irrigable Area. The main canal will gen- erally be the upper boundary of the irrigable area, and the stream the lower boundary from which, after platting, the included area is measured. There must also be made surveys of the lands which are non-irrigable, or, in other words, not tillable, such as rocky land, swamp land, etc., and areas which are isolated, that is, too high to reach by gravity from the main canal. The boundaries of non-irrigable and isolated lands may be run by 26 WORKING DATA FOR IRRIGATION ENGINEERS transit and stadia. If the country has been subdivided into townships and sections, all surveys should be tied to land lines; otherwise it will be necessary to make surveys to tie all the above-mentioned surveys together. The areas of non-irrigable and isolated lands are measured and deducted from the total to get the net area irrigable, after which it may be advisable to modify the capacities and sizes of canal sections on which the canal location was based. These revisions may affect the esti- mates of quantities, but a relocation of the line for estimating purposes will not generally be required. Reservoir Surveys. These should be of sufficient accuracy to give the probable capacity of the reservoir within 10 to 20 per cent. If the reservoir is a natural lake, the survey should include an investigation of the possibility of storage by lowering the lake outlet by tunnel or trench excavation; the boundary of the lake should be meandered and profiles run up the slopes at frequent intervals to an elevation high enough to cover the highest elevation to which the water may be raised. The volume may then be found by measuring the areas at successive 5- or 10-foot contour intervals, and computing the volume between by the usual methods; if it is possible to lower the surface of the lake these profiles should be carried below the water surface by soundings. If the reservoir site is dry, a base line should be established, and the topography elaborated from the same by the use of the transit and stadia or plane table. From the topographic sheet the capacity is calculated as noted above. A topographic survey of the dam site should be made, together with sufficient test pits or borings to give a general indication of the nature of the foundations. A scale of 400 feet to one inch, with 10-foot contour intervals, will ordinarily be found satisfactory for the reservoir site. For the dam site, a scale of 40 feet to one inch and contour intervals not greater than five feet should ordinarily be used. The best scales and contour intervals depend upon the local conditions, but those mentioned have given satisfactory results in many surveys for quite a wide range of conditions. General Remarks on Canal Locations. In making locations of canals the question of cost as affected by location is of prime INVESTIGATIONS AND SURVEYS 27 importance. In most systems the canal excavation consti- tutes by far the greater part of the construction cost of the proj- ect, and canal maintenance constitutes a very large portion of the maintenance costs. The first cost is often relatively less im- portant than cost of operation and maintenance, and the locating engineer must keep both in mind. It is a comparatively simple matter to locate a canal so as to obtain the least quantity of earthwork, and this is susceptible of exact mathematical estab- lishment, but maintenance and operating cost are not so easily calculated. No set rules can be formulated for proper locations to give minimum operation and maintenance costs. This must be left almost entirely to the experience and judgment of the locating engineer. The value of experience in this matter can- not be overestimated, and a knowledge of operation and maintenance of canals is necessary to obtain an economic location. In locating a canal, effort should be made to keep the water section in cut as far as practicable, and high fills should be avoided as much as possible on large canals, as they are a source of endless danger and expense in operation and maintenance. One of the most important items to be kept in mind is that the water surface must be kept high enough to reach the adjacent land after an allowance has been made of sufficient drop to make a measure- ment of the water over a weir or other measuring device. This is especially true of the smaller distributaries from which the water is taken directly onto the land, and if neglected when the canal is constructed, the possibility of properly measuring the water may be irreparably lost, or the expense of rectifying the damage be very high, whereas the expense of making provision for a measurement when the canal was built would have added little to the cost. The proper drop in water surface to allow for making a measurement depends upon the quality of water to be measured, and the kind of device to be used for measuring, both of which should be definitely known before the location is made. It must also be remembered that it may be necessary to make these measurements when the canal is not operating at its max- imum capacity, and unless means are provided for checking up the water to maximum elevation the measurement must be made 28 WORKING DATA FOR IRRIGATION ENGINEERS at a lower elevation. An adjustment must be made between the cost of raising the grade of the canal, providing checks for back- ing up the water, or cutting out a certain amount of land adjacent to the canal to provide the necessary drop when the canal is not running full. CHAPTER III DESIGN OF IRRIGATION STRUCTURES To design irrigation structures properly requires a thorough knowledge of structural and hydraulic engineering. In addition to this, a knowledge of the special requirements of irrigation structures is necessary. Mechanical details of design are not here discussed, but the broad problems connected therewith are pointed out, and aids for their solution, in the form of tables and diagrams, are presented. Storage Works. The rapidly decreasing supply of unappro- priated water from the natural flow of streams has in the past few years made the problem of storage works increasingly im- portant. The problem is a very difficult one perhaps the most difficult of all that the irrigation engineer encounters and only brief mention can be made here of some of its principal features. Naturally, the first point to be decided is the water supply available for storage. This has already been discussed, but an additional factor not previously considered is the probable evaporation from the reservoir. This is especially important in shallow reservoirs. The velocity of the wind and the total wind movement have a considerable influence on the evaporation. The evaporation is greater in humid than in arid regions and increases with the temperature. For these reasons a much greater allowance must be made for the evaporation from a reservoir located in a valley on the plains than from a reservoir in the mountains where the temperatures are lower, the atmosphere more humid, and the water surface more or less protected from the sweep of the winds. Experiments made in 1909-10 by the Weather Bureau, United States Department of Agriculture, gave the figures in Table 12 for the monthly and annual evaporation at various places, mostly in the Western States. The measurements were made in pans on the ground, floating in water, or elevated on stands. Calculations made by the experimenters indicate that the evaporation from a pan 2 feet in diameter is about 75 per cent, that from a pan 4 feet in diameter is about 50 per cent, 29 30 WORKING DATA FOR IRRIGATION ENGINEERS and that from a pan 6 feet in diameter is about 30 per cent greater than the evaporation from a large pond or lake. The figures in the table may be roughly corrected on this basis; thus, TABLE 12 TOTAL AMOUNT OF EVAPORATION BY MONTHS The figures contained in these tables have not been corrected for the wind effect, the temperature effect, the vapor-pressure effect, nor for the size of the pans, but they represent the observed evaporation at the pan as located. D is the diameter of pan in feet. Number l 2 3 4 5 Station Salton Sea, 1,500 Ft. Salton Sea, 500 Ft. at Salton Sea, 7,500 Ft. at Indio, Cal. Mecca, Cal. Inland Sea Sea Position of Pans Ground D =2 D =4 D =4 Ground D=6 Ground D=6 January 5.08 3.61 3.41 3.18 2 92 February 7.42 5.01 5.09 5.08 5 00 March April 12.50 15.75 6.75 9.00 6.95 8.75 7.50 12.05 8.07 10.87 Mav. 19.00 11.00 10.50 15.84 12.72 i Lay June 21.50 13.50 13.00 16.11 14.23 July 22 15 14.77 14 03 16 34 15 21 J*"j August 18 50 12.53 12 19 13 78 13 22 September October November 15.50 13.19 7.49 12.40 9.20 6.21 12.08 9.24 5.96 12.37 8.91 5.17 10.29 8.17 4 13 December . . . . 6.42 4.67 5.25 3 00 2.98 Year 164.50 108.65 106.45 119.33 107.81 Number 6 7 8 9 Station Brawley, Cal. Mammoth, Cal. N. Yakima, Wash. Hermiston, Oreg. Position of Pans Ground D=6 Ground D=6 Ground D =4 Raft D =4 Ground D=a January 3.05 5.00 8.00 10.74 13.79 13.68 14.14 11.26 10.15 6.99 4.09 2.66 4.24 5.67 8.99 12.02 15.52 16.75 18.00 13.73 12.16 9.49 5.26 3.70 1.75 2.50 6.25 7.91 8.36 8.90 10.74 9.41 5.51 3.15 2.00 1.50 1.25 1.25 3.00 7.28 7.89 9.54 12.04 11.07 7.35 3.88 2.00 1.50 1.50 1.75 4.25 9.28 11.38 13.84 17.48 16.89 10.09 6.08 3.00 1.75 February March April . Mav. i Lay June July August September October November. December Year 103.55 125.53 67.96 68.05 97.29 DESIGN OF IRRIGATION STRUCTURES TABLE 12 (Continued) TOTAL AMOUNT OF EVAPORATION BY MONTHS 31 Number 10 11 12 Station Granite Reef, Ariz. Salt River California, O. Filtration Plant Birmingham, Ala. East Lake Reservoir Position of Pans Ground D =4 Floating D = 4 Floating D = 4 Floating D =4 Floating D =4 Ta.nua.ry 4.59 4.75 6.25 9.00 11.50 13 50 14.25 14.23 13.76 11.31 7.39 4.65 4.25 4.40 5.25 7.00 9.50 12.00 12.75 12.50 11.00 8.31 6.56 4.22 1.00 1.50 2.50 4.12 5.07 6.21 7.20 7.26 5.63 3.00 1.50 1.00 1.50 1.50 2.25 4.45 5.91 7.28 7.36 7.34 6.00 4.00 2.25 1.50 1.50 1.50 2.25 5.36 6.36 7.54 6.96 7.32 5.59 4.00 2.25 1.50 February March April May Tune Tulv August September October November December Year 115.18 97.74 45.99 51.34 52.13 Number 13 14 15 16 17 Station Dutch Flats, Nebr. Interstate Canal Minidoka Dam, Idaho. Snake River 10 Feet Above Surface Deer Flat, Idaho Boise Project Lake Kachess, Wash., 10 Feet Above Surface Ady, Kla- math, Oreg. Position of Pans Ground D =4 D =3 Ground D =3 Raft D = 4 D =3 Floating D =4 January 1.75 1.75 3.00 4.50 6.25 8.05 10.95 9.39 7.44 5.59 4.00 3.00 2.25 2.50 4.00 7.00 11.21 12.31 15.00 13.50 11.00 8.50 5.75 3.50 1.50 2.25 4.00 7.25 10.68 11.05 11.15 11.77 9.75 5.40 2.70 1.50 2.00 2.75 4.25 6.00 7.90 9.59 10.59 12.16 9.25 5.42 5.52 2.00 0.50 0.50 1.25 2.57 3.83 5.54 5.93 5.51 4.41 1.47 0.75 0.50 0.50 1.25 3.57 6.64 7.15 6.99 8.01 9.21 6.13 2.50 1.00 0.50 February March April May June Tuly August September October November December Year 65.67 96.52 79.00 77.43 32.76 53.45 32 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 12 (Concluded) TOTAL AMOUNT OF EVAPORATION BY MONTHS Number 18 19 20 21 22 23 Station Fallen, Lake Tahoe, Elephant Butte, Carlsbad. N. Mex. Alfalfa Field near Lake Avalon, Nev. Cal. N. Mex. At Reclama- tion Office ' Carlsbad Pecos River Position of Pans Floating D =4 2 Feet D =4 Ground D =4 Ground D =4 Ground D =4 Floating D =4 January February 1.75 1.75 1.75 1.75 2.50 2.75 5.00 5.50 5.00 5.25 4.50 4.50 March 2.25 1.75 4.50 8.94 8.95 5.51 April 3.25 2.00 8.00 11.68 11.09 7.45 May 5.25 3.00 11.50 12.86 10.95 10.12 June 7 86 4 25 13 45 12 40 9 06 11.05 July 9 86 6.19 11.57 12 00 10.58 12.88 J * ' August 8.70 7.08 10.48 11.03 9.32 12.00 September October 5.13 3.35 6.22 3.60 8.58 6.76 9.76 7.58 7.84 5.88 9.50 7.00 November December 2.50 2 00 2.62 2 00 3.86 3 00 5.50 5.00 5.43 5.00 5.75 4.50 Year 53.65 42.21 86.95 107.25 94.35 94.76 The true evaporation from a large pond or lake at Dutch Flats, Nebraska (No. 13), would be 65.67 -=- 1.50 = 43.8. The evapor- ation from a pan elevated 10 feet above the ground surface aver- ages about 15 per cent greater than from the same size pan on the ground; thus, the true evaporation from a 3-foot pan at the ground surface at Lake Kachess, Wash. (No. 16), is 32.76 ^ 1.15 = 28.5 inches. The seepage from the floor and sides of a reservoir may have a large influence on its storage capacity. The seepage is depend- ent upon the nature of the material composing its bottom and sides, and the location of the ground-water plane in the vicinity. The latter, together with the elevation of the water in the reser- voir, will establish the grades on which the seepage water will flow from the reservoir. It follows, then, that these grades will produce a certain velocity of water through the material in the surrounding country, and consequently the porosity of this material may have a greater effect on the volume of seepage than the porosity of the material composing the bottom and sides of the reservoir. DESIGN OF IRRIGATION STRUCTURES 33 Various types of storage dams are used, the most important being masonry, earth, rock-fill, and various combinations of these three. The best type for a particular location depends upon the nature of the foundations, profile of dam site, material available for dam construction, accessibility of site, etc. A site having good rock foundations and abutments is usually favorable for a masonry dam. If the canon walls are steep and the canon comparatively narrow, an arched masonry dam may be the best. Excavations have been dug from 50 to 100 feet deep to obtain suitable foundations for high masonry dams. Where a continuous solid rock foundation cannot be had, or where the cost of materials for a masonry dam would be prohibitive, a rock- fill or earth dam, or combination of the two, is adaptable. Every storage dam across a stream having an unregulated flow must be provided with a spillway which should preferably discharge the water some distance downstream from the toe of the dam so as not to endanger the foundations of the dam and, in the case of earth dams, cause erosion by backwash. The records of flow of a stream do not usually include the maximum probable discharge, which is exceedingly difficult to predict. The maximum discharge that might occur must be assumed several times the maximum recorded, depending upon the length of time covered by the records. Fortunately, a reservoir will generally act as a regulator of the flow, and it will not usually be necessary for the spillway to discharge the water at the same rate that it comes into the reservoir. Table 13 gives the maximum rate of discharge of streams in the United States as determined by the Hydrographic Branch of the United States Geological Survey. A study of this table will give some idea of the probable maximum discharge from a given stream. The location and design of outlet works vary with the type of dam. The outlet gates for a masonry dam are usually located on the upstream face or a short distance inside the face. Some- times they are located in a tunnel running around the dam. The latter method is preferable where practicable. Earth and rock- fill and other dams having flat slopes require the construction of an outlet tower in which the operating gates are locatecl, and WORKING DATA FOR IRRIGATION ENGINEERS TABLE 13 MAXIMUM RATE OF DISCHARGE OF STREAMS IN THE UNITED STATES * Stream and Place Drainage Area, Sq. Miles Date Cu. Ft. per Sec. per Sq. Mile Budlong Creek, Utica, N. Y 1.13 1904 12040 Sylvan Glen Creek, New Hartford, N. Y . . Pequest River, Hunts Pond, N. J Starch Factory Creek, New Hartford, N. Y. Starch Factory Creek, New Hartford, N. Y. Reels Creek, Deerfield, N. Y 1.18 1.70 3.40 3.40 4.40 1904 1904 1904 1905 1904 56.58 25.30 109.62 209.00 4836 Mad Brook, Sherburne, N. Y 5.00 1905 26200 Skinner Creek, Mannsville, N. Y 6.40 1891 124.20 Coldspring Brook, Mass 643 1886 48 40 Croton River, South Branch, N. Y Woodhull Reservoir, Herkimer, N. Y Mill Brook, Edmeston, N. Y 7.80 9.40 9.40 1869 1869 1905 73.90 77.80 241 00 Stony Brook, Boston, Mass 12.7 121.00 Great River Westfield Mass 140 71 40f Smartswood Lake, N. J 160 68 00 Williamstown River, Williamstown, N. Y . . Croton River, West Branch, N. Y 16.5 20.5 1874 34.00 5440 Beaverdam Creek, Altmar, N. Y 20.7 111 00 Trout Brook, Centerville, N. Y 23.0 50.60 Wantuppa Lake, Fall River, Mass Pequest River Huntsville N T 28.5 31 4 1875 72.00 19 30 Sawkill near mouth N J 350 22860 Whippany River, Whippany, N. J Cuyadutta Creek, Johnstown, N. Y 37.0 40.0 1903 1896 61.62 72.40 West Canada Creek, Motts Dam, N. Y Six Mile Creek, Ithaca, N. Y Sauquoit Creek, New York Mills, N. Y Roc ka way River Dover, N. J 47.5 47.5 51.5 52.5 i905 34.10 170.00 53.40 43 00 Oneida Creek, Kenwood, N. Y 59.0 1890 41 20 Flat River, R. I . 61.0 1843 120.00 Camden Creek, Camden, N. Y 61.4 1889 24.10 Nine Mile Creek, Stittville, N. Y. ......... Wissahickon Creek, Philadelphia, Pa Sandy Creek, Allendale, N. Y 62.6 64.6 68.4 1898 1898 1891 124.90 43.50 87.70 Rock Creek, Washington, D. C 77.5 126.30 Sudbury River, Farmington, Mass 78.0 1897 41.38 Peouanock River Pompton N J 780 1902 5578 Hockanum River, Conn 79.0 78.10 Nashua River Mass 84.5 1850 71.04 Independence Creek, Crandall, N. Y Passaic River, Chatham, N. J 93.2 100 1869 1903 66.50 17.20 Deer River, Deer River, N. Y 101 1869 78.10 Wanaque River, N. J Tohickon Creek, Mount Pleasant, Pa 101 102 1882 1885 66.00 112.50 Fish Creek, East Branch, Point Rocks, N. Y. Nashua River, Mass 104 109 1897 1848 80.50 104.53 Sandy Creek, North Branch, Adams, N. Y . Scantic River North Branch Conn 110 118 1897 67.30 51.80 Ramapo River, Mahawah, N. J 118 1903 105.09 *From "American Civil Engineers' Pocket Book," John Wiley & Sons, New York, t Average flow for day of maximum discharge. DESIGN OF IRRIGATION STRUCTURES TABLE 13 (Continued) MAXIMUM RATE OF DISCHARGE OF STREAMS IN THE UNITED STATES 35 Stream and Place Drainage Area, Sq. Miles Date Cu. Ft. per Sec. per Sq. Mile Rockaway River Boonton N. J 125 1902 2224 Patuxent River Laurel Md 137 1897 31 20 Meshaminy Creek, below forks, Pa Oriskany Creek, Colemans, N. Y Oriskany Creek Oriskany, N. Y 139 141 144 1894 1888 1904 97.60 55.80 2900 Perkiomen Creek, Frederick, Pa Mohawk River Ridge Mills, N. Y 152 153 1889 69.20 4640 Mohawk River, State dam, Rome, N. Y. . . Ramapo River, Pompton, N. J . 158 160 1904 1882 27.34 56 10 Fish Creek, W. B., McConnellsville, N. Y. . Unadilla River, New Berlin, N. Y Salmon River, Altmar, N. Y 187 204 221 1885 1905 32.70 40.00 27.60 Black River, Forestport, N. Y Croton River, Croton Dam, N. Y Great River, Westfield, Mass 268 339 350 39.00 74.40 151.90 East Canada Creek, Dolgeville, N. Y Moose River Ayers Mill N Y 356 407 1898 24.70 31 00 Stony Creek, Johnstown, Pa 428 70.00 West Canada Creek, Middleville, N. Y. . . . Farmington River Conn 518 584 1898 24.90 41 70 Monocacy River, Frederick, Md Passaic River, Little Falls, N. J North River, Port Republic, Va Passaic River, Dundee, N. Y 665 773 804 823 1898 1882 1896 1903 29.80 24.20 29.80 43 38 North River, Glasgow, Va 831 1896 4480 Raritan River, Boundbrook, N. J 879 1882 5930 Potomac, North Branch, Cumberland, Md. Black River, Lyons Falls, N. Y 891 897 1897 1869 22.80 4600 Schoharie Creek, Fort Hunter, N. Y Genesee River, Mount Morris, N. Y Mohawk River, Little Falls, N. Y Greenbrier River, Alderson, W. Va Black River, Carthage, N. Y Schuylkill River, Fairmount, Pa Chemung River, Elmira, N. Y James River, Buchanan, Va 948 1,070 1,306 1,344 1,812 1,915 2,055 2,058 1892 / 1894 \ \ 1896 / 1902 1897 1869 1898 1889 1896 44.00 39.20 21.83 41.60 21.20 12.20 67.10 1560 Androscoggin River, Rumford, Me 2,220 1869 25.00 Genesee River, Rochester, N. Y 2,365 1865 17.00 Hudson River, Fort Edward, N. Y 2825 1900 15 60 Shenandoah River, Millville, W. Va ...... Mohawk River, Rexford, N. Y 2,995 3,384 1898 1892 11.40 23 10 Merrimac River, Lowell, Mass 4,085 19 80 Kennebec River, Waterville, Me 4,410 1896 2520 Susquehanna, W. Branch, Williamsport,Pa. Hudson River, Mechanicsville, N. Y. . 4,500 4,500 i869 11.60 15 50 Merrimac River, Lawrence, Mass . . . 4,553 23 40 Potomac River, Dam No. 5, Md 4,640 22 20 Delaware River, Lambertville, N. J Delaware River, N. J 6,500 6 750 53.80 5000 Delaware River, Stockton, N. J Susquehanna River, Northumberland, Pa. . . 6,790 6,800 1841 1889 37.59 17.50 36 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 13 (Continued) MAXIMUM RATE OF DISCHARGE OF STREAMS IN THE UNITED STATES Stream and Place Drainage Area, Sq. Miles Date Cu. Ft. per Sec. per Sq. Mile Connecticut River Holyoke, Mass . . . 8,660 1854 21 10 Potomac River, Point of Rocks, Md Connecticut River, Hartford, Conn Potomac River Md 9,654 10,234 11 043 1897 19.40 20.30 4260 Potomac River, Great Falls, Md Potomac River Chain Bridge D. C . 11,427 11 545 1889 1893 41.20 1720 Susquehanna River, Harrisburg, Pa Coosawattee River, Carters, Ga Etowah River, Canton, Ga Tuckasegee River, Bryson, N. C 24,030 532 604 662 1894 1901 1895 1899 18.90 31.86 31.50 58.23 Little Tennessee River, Judson, N. C Broad River Carlton Ga 675 762 1901 1902 85.24 3822 Saluda River Waterloo, S. C . . . 1,056 1903 1800 Catawba River, Catawba, N. C Chattahoochee River, Oakdale, Ga Ocmulgee River, Macon, Ga 1,535 1,560 2,425 1901 1899 1902 53.10 27.92 20.97 Yadkin River Salisbury N. C 3399 1899 ' 31 60 Tallapoosa River, Milstead, Ala Coosa River Rome, Ga ... 3,840 4,001 1901 1901 18.23 1604 Broad River, Alston, S. C . . . 4,609 1901 28.44 Black Warrior River, Tuscaloosa, Ala New River, Fayette, W. Va 4,900 6,200 1900 1899 27.89 17.83 Coosa River, Riverside, Ala Savannah River Augusta, Ga 6,850 7294 1898 1888 10.53 42 50* Tennessee River, Chattanooga, Tenn Des Plaines River, Riverside, 111 21,418 630 1896 1892 20.80 905* Verdigris River, Liberty, Kans Neosho River, tola, Kans 3,067 3,670 1904 1904 16.43 20.33 Grand River, Grand Rapids, Mich Smoky Hill River Ellsworth, Kans 4,900 7980 1905 1903 10.00 1 43* Kanawha River, Charleston, W. Va. 8,900 1875 13 50 Blue River, Manhattan, Kans Republican River, Junction, Kans Mississippi River, St. Paul, Minn Kansas River, Lecompton, Kans 9,490 25,837 36,085 58,550 1903 1903 1897 1903 7.25* 1.80* 19.70 3.98 Gallinas River Las Vegas, N. Mex 90 1904 129 10 Mora River, La Cueva, N. Mex 159 1904 13970 Rapid Creek, Rapid, S. Dak 320 1904 2.85 Salt Creek, at mouth, N. Mex Hondo River, reservoir, N. Mex Canadian River, Logan, N. Mex 3,052 1,387 11,440 1904 1904 1904 4.10 4.56 12.29 a Canadian River, Taylor, N. Mex Canadian River, French, N. Mex 2,832 1,478 1904 1904 32.11 b 105.56 c Pecos River, Fort Sumner, N. Mex Pec(fs River, Roswell, N. Mex Redwater River, Belle Fourche, S. Dak Sapello River, Los Alamos, N. Mex 6,191 14,840 1,006 221 1904 1904 1904 1904 7.29 3.75 8.00 36.7 Purgatory River, Trinidad, Colo Salt River, Roosevelt, Ariz 742 5,756 1904 1893 61.2 36.0 Verde River, McDowell, Ariz 6,000 1893 24.05 d * Average flow for day of maximum discharge. a, Rate for 12 hours, b, Rate for 7 hours, c, Rate for 0.5 hour, d, Rate for 24 hours. DESIGN OF IRRIGATION STRUCTURES 37 TABLE 13 (Concluded] MAXIMUM RATE OF DISCHARGE OF STREAMS IN THE UNITED STATES Stream and Place Drainage Area, Sq. Miles Date Cu. Ft. per Sec. per Sq. Mile Salt River, Ariz Gila River, Florence, Ariz Pecos River Santa. Rosa N Mex 12,000 17,750 2,649 1891 1891 1904 24.69 7.50 17.56 Mora River Weber N. Mex 422 1904 65.70 Rio Grande, Rio Grande, N. Mex Yuba River, Bowman Dam, Cat Sweet water River, Sweetwater Dam, Cal . . Tuolumne River, Lagrange, Cal San Joaquin River, Hamptonville, Cal .... King River, State Point, Cal Kern River, Rio Bravo, Cal Sacramento River, Iron Canon, Cal Yuba River, Smartsville, Cal Feather River, Oroville, Cal Stony Creek, Fruto, Cal 11,250 19 186 1,501 1,637 . 1,742 2,345 9,295 1,220 3,350 760 1904 1895 1881 1901 1897 1904 1904 1904 1904 2.75 31.6 97.5 30.6 36.51f 25.22 2.3f 23.47 f 49.02f 31.49t 29.21f t Mean for day when discharge was a maximum. a discharge conduit running through or around the dam. In this case, also, the latter method is preferable where practicable. The gates and conduits must be designed to pass the required quantity of water at low as well as high heads corresponding to the fluctuations in the elevation of the reservoir water. To avoid the necessity of operating the gates at very high heads they are sometimes located at several levels, the upper ones being used when the water is high and the lower ones when the water is low, the water from the higher levels either shooting directly through the dam, in the case of a masonry dam, or dropping down a shaft in the outlet tower and thence through the outlet conduit, in the case of other dams. For high heads, ordinary slide gates are not suitable on account of the difficulty of operation and destructive effect of vibrations due to high velocities. For this purpose, some form of balanced cylindrical or needle valve is necessary. The use of a single gate is seldom advisable, but there should be two gates in series at each outlet, so that one will be supplemented by the other, and in case of damage to either the other can be used for regulation. This arrangement is imperative where the gates are to be submerged, and consequently inac- cessible, for long periods of time. 38 WORKING DATA FOR IRRIGATION ENGINEERS In all forms of gates and valves, air should have free access to the chamber on the downstream side of the gate to prevent the periodic formation and release of a partial vacuum, which is so destructive to gates. Where the partial vacuum can be main- tained at all stages of flow it will have no more destructive effect than that due to the increased velocity produced, but this is not usually the case. High velocities flowing smoothly have very little destructive effect on concrete (see page 47), but a smooth flow is seldom obtained in the outlet conduit of a reservoir. To protect the concrete, conduits are sometimes lined with cast iron or semi- steel, the latter being used on account of its hardness and con- sequent resistance to erosion. Diversion Dams. There are two general types of diversion dam: those on impervious foundation and those on more or less pervious foundations. These in turn may each be subdivided into fixed crest dams and movable dams. A movable crest is necessary where a fixed crest of the required height would cause the backwater to flood the country excessively during periods of high water, the movable crest being removed from the path of the water to allow the flood to pass. The minimum length of dam will generally be roughly fixed by the topographic conditions at the site, and the height to which the water must be raised is fixed by the elevation of the irrigable land which it is desired to reach. It is very desirable that a movable dam be avoided, if possible, as good dams of this kind are generally expensive to build, as well as to operate and maintain. After the maximum probable flood in the river has been estimated, high-water marks have been located, and the required elevation of diversion and length of dam preliminarily fixed, calculations must be made of the effect at high water of damming the river with a fixed crest dam to raise the water to the diversion elevation at low water. The water will obviously be raised higher, due to this artificial obstruction, than it flowed before, and this effect will extend up- stream an indefinite distance. In the case of a rapidly flowing stream confined between high banks, backing up the water may do no damage to lands upstream, but in case the opposite con- ditions obtain, the effect of damming up the water even a small DESIGN OF IRRIGATION STRUCTURES 39 amount might prove disastrous. In the latter case there may be two solutions: the length of the dam may be increased or a movable crest may be used. It will generally be necessary to make many detail calculations before the proper adjustment is reached. The principal hydraulic calculations to be made in this connection are the determination of the depth of flow over the crest and the elevation of backwater at various points up- stream. With the aid of Tables 28, 28 A, 28 B, and 28 C the depth of flow may be determined for various types of crest. If the determination of exact depth of flow is of great importance due to probable damage from backwater, it is well to select a type as close as possible to one for which definite coefficients are given. Exact backwater elevations are very difficult to determine, as theoretical calculations fail almost entirely here. It is necessary that cross-sections of the stream be obtained at various points, and the slope of the stream, and, if possible, the value of " n " in Kutter's formula determined; if this can not be experimentally determined, it must be assumed. After the foregoing data are obtained, the loss of head, or drop in water surface, of the stream is calculated in successive short reaches by means of the formula Q = A C V R S. The total drop from any point upstream, calculated in this manner, added to the maximum elevation of the water surface at the dam gives the elevation of flood water at the point in question. This is a method of successive approximation, but may be depended upon to give more exact results than any backwater formula based on theoretical considerations only. If a movable crest dam is used, the determination of depth of flow over the fixed crest need not be so exact, as a certain margin of safety can be applied in the height of the movable portion. For example: if the calculations show that a movable crest 5 feet high is required, then absolute safety may be assured by making this 5J^ or 6 feet, and this will add relatively little to the expense. Diversion dams located on pervious foundations as many diversion dams are must be designed to withstand a certain amount of upthrust, and it is usually assumed that this varies from the maximum hydraulic head at the heel to zero or a small 40 WORKING DATA FOR IRRIGATION ENGINEERS amount at the toe, or at such point as the water has egress from under the downstream apron of the dam. The unit upward pressure at any point is equal to the distance of that point from the heel of the dam divided by the total length of the path of percolation, multiplied by the depth of the water upstream. If there are cut-off or curtain walls, the path of percolation is assumed to follow around those walls. For example, the accom- panying figure represents a dam subjected to a maximum head of water above equal to H. It is assumed that the pressure of the water percolating under the dam reduces to zero at E. B C represents an impervious curtain wall, and the path of per- colation is O A B C D E. The upward pressure at B, then, is equal to n . ~ r n ,., ; similarly the pressure at D is equal to \J A. Jj C L) Hi IT vx r\ -p r\ A g r n *? ** * s obvious that the longer the apron A B DA. jj \s L) Hi and the curtain wall B C are made, the lighter may the cross- section of the dam be, and calculations should be made to deter- mine what is the most economical arrangement. The upthrust pressures must, of course, be combined with the usual horizontal and vertical pressures of water and masonry to determine the Stability of the dam. Headgates. In a stream that does not carry much silt, the headgates may be built perpendicular to the direction of flow of the stream, but in streams which do carry much silt, it will generally be necessary to build the headgates parallel, or nearly parallel, to the stream, and provide a sluicing channel through the dam in front of them in order to allow the periodic washing out of the channel; otherwise, large quantities of silt would DESIGN OF IRRIGATION STRUCTURES 41 necessarily have to be carried into the canal. The velocity through headgates must generally be held to a comparatively low figure to avoid heavy washing in the canal or the necessity of expensive paving and other protective works for long dis- tance downstream. In some cases it is necessary to protect the gate openings with a grillage or screen to keep large floating debris from enter- ing the canal. In other cases, a simple shear boom is sufficient, but this does not keep out material rolling along the bottom or carried in suspension. The kind and amount of protection depend entirely upon the nature of the stream and the location of the headworks relative to it. In streams in which fish abound, State laws sometimes require that a fish screen be placed in front of the gates to keep the fish from going down the canal. A satisfactory screen for this purpose has never been devised, the great difficulty being that in order to be effective in stopping the progress of the fish the mesh of the screen must be so small (from one-fourth to one-half inch) that the screen soon becomes clogged and interferes seriously with the regulation of water through the gates. The heavy expense of continually cleaning such a screen is obvious, and even then it is very difficult to keep a constant quantity of water flowing through the gates; the result is that the use of fish screens is not very popular. Canals. The determination of the most economical design for a canal is one of the most difficult problems with which the irrigation engineer has to deal, and there are many problems that must be considered. It is the purpose here to point out the most important of these problems and the methods of solution. Capacity. It is assumed that the engineer has before him a map showing the preliminary location of the main canal and the area to be irrigated. It is also assumed that it has been pre- liminarily determined at what points the principal laterals will divert from the main canal and the approximate areas they will irrigate. These points are marked on the map, together with the length of canal between them. The problem of capacity of canal at any point now involves the determination of the duty of water, or the amount required to be applied to the land, and 42 WORKING DATA FOR IRRIGATION ENGINEERS the determination of losses by seepage in the distribution laterals and main canal itself. The duty of water is discussed on page 20. For the purposes of main-canal design, the losses in the distri- bution system may be taken as 15 per cent of the quantity diverted from the main canal. In determining capacities it is convenient to begin at the lower end of the canal and work up, following through the same calculations for each successive reach. As an example: Suppose the accompanying figure represents the lower end of a canal; large laterals are to be taken out at points B and C. The duty of water (quantity applied to land) has been decided to be 2 acre-feet per acre per season; the irrigation season is 184 days long; the maximum capacity of canal required in mid-summer is 25 per cent greater than the average; the velocity to be used is 2.5 feet per second; the loss by seepage from the main canal is 1.5 feet in depth over the wetted area per day: The duty of 2 acre-feet per acre in a season of 184 days cor- responds to a flow of 1 c. f . s. to 182 acres. The lower reach of the main canal B A is nothing more than a lateral, and it will be included with lateral N to give a total acreage just above B of 3,000 acres. At 1 c. f. s. to 182 acres applied to the land and with a loss by seepage in the laterals of 15 per cent of the diver- sions, the required maximum discharge of main canal at B is 3000X1.25 , . = 24.2 c. f. s. If there were no seepage losses lo^ /\ (^1 O.LO) the capacity at C would be the same as at B as no laterals di- vert from the canal between these points. To determine the loss by seepage, assume the average flow in the reach C B to DESIGN OF IRRIGATION STRUCTURES 43 be 25 c. f . s. ; enter the diagram, Fig. 3, with Q = 25 as an argument and find where this line intersects the inclined line marked C = 1.5, and read the seepage loss = 1.5 c. f. s. per mile on the scale to the left for V = 1 and for V = 2.5 follow the diagonal line to the left to its intersection with the vertical line marked V = 2.5 and read the seepage loss for the case in hand to be 0.95 c. f. s. per mile, or 1.9 c. f. s. for the two miles from C to B. The required capacity at C then is 24.2 + 1.9 = 26.1 c. f. s. This process is now repeated for each suc- cessive reach above C until the head of the main canal is reached. Seepage Losses. For convenience, losses by seepage have frequently been expressed in terms of the percentage of water lost per mile, or other unit of length. This method is absolutely irrational and fortunately is rapidly falling into disuse, except for very general statements. The most rational and convenient means of stating these losses is in terms of the number of feet in depth over the wetted area of the canal prism lost in one day. The following formula* has been deduced for seepage loss: Where 5 = loss in c. f. s. per mile of canal, Q = discharge of canal in c. f. s., V = mean velocity of flow in feet per second, C = the depth in feet over the wetted perimeter lost per day, and is found from observation on existing canals. An exact expression for seepage loss involves the depth of flow, inclination of side slopes, and the ratio of depth to bottom width, but it is mathematically demonstrated in the article above referred to that the above formula which is based on side slopes of 1 J^ to 1 and a bottom width of four times the depth, gives results, for any shape or proportions of section, that are well within the limit of accuracy of the data which it is necess- ary to use in connection therewith. Observations on several hundred miles of earth canals on * See Engineering News, Vol. LXX, page 402, for the derivation of this formula and a discussion of seepage losses. 44 WORKING DATA FOR IRRIGATION ENGINEERS eight different projects of the United States Reclamation Service give the following average figures for the value of C: TABLE 14 SEEPAGE LOSSES FROM CANALS IN VARIOUS MATERIALS Kind of Material No. of Observations | Loss Cement gravel and hardpan with sandy loam 3 0.34 Clay and clay loam 5 41 Sandy loam . . 4 66 Volcanic ash 3 68 Volcanic ash with some sand 5 98 Sand and volcanic ash or clay 8 1 20 Sandy soil with some rock 3 1 68 Sandy and gravelly soil .... * . ... 8 2 20 These are generally results from canals that have been in operation from three to six years. There is usually a very noticeable reduction in seepage losses with continued use, es- pecially if the water carries fine silt, and there are instances where the most porous gravel formation has been made practi- cally watertight by a coating of silt or puddle. In designing a canal, it is probably unsafe to figure on a smaller loss than 0.5 foot over the wetted area in 24 hours in even the most imper- vious material, and after a loss of over 2 to 2.5 feet is reached the question of lining the canals will generally require very serious consideration from the point of view of value of the water and damage to adjoining lands from waterlogging. The limits within which seepage losses should be considered may, therefore, be generally defined as 0.5 foot and 2.5 feet per day over the wetted area of canal, for the minimum and maximum respec- tively. The manipulation of the equation is made very simple by the use of Fig. 3, which gives the loss by seepage in cubic feet, per second per mile of canal for a large variety of conditions. Side Slopes. The proper slope to give the sides of a canal depends upon the stability of the material. . Earth canals are generally given a slope of 1^ to 1 or 2 to 1, and these may be taken as the standard for ordinary conditions. When the channel is lined, the side slopes may be made of any inclination DESIGN OF IRRIGATION STRUCTURES 45 Jt -\ \ \ S \ ^ \ ^ ^ \ \ V \ C~ \ *i o * jT V \ \> \ \ \ \ \ \ \ s. 4 L \ * ^ \ ^V x~ s )\ o\ 3 5 9 \ \ \ \ s \ \ \ \ \ I 1 - -5 ^ ^~ ^V \ V " s. S \ O i^-* \ \ 3 c \ \ ^ \ \ \ ^ ^ \ \ \ \ ^ \ \ \ \ \ \ V \ \ y \ % \ V ^ O V ^ \ s. \ ^ \ o \ \ v \ \ \ \ \ o t? \ \ \ \ KJ \ \ \ \ \ o % V \ ^ > \ \ c >l> \ \ \ \ \ \ * -tn 1 - \ \ \ \ \ i M s::::^_ S; ^ \ -V M ^ i \ \ \ ^ ^ ^ \ \ \ \ \^ s i o o < e <: <3 i >i i , \ v q \ CO r ' J * C9 3J 2. ^ " \^ \ V\ \ \ \ \ \ \ \ s s \s\ Sss \ \ \ \ \ \ \ \ \ ^\ \ \ \ \ \ \ S ! !!|i 11 \ \ \ \ \ \ \ V \^ \ \^ \ \ \ \ \ \ \ \ \ \ fi'T -H S \ \ s^ \ \ \ \ J\ . s \ \ s . \ \\Y SSsw^ \ \s s ^V V X \ \ \ \ \ X \ \ \ ^s A ;\ ^ \ s > : v \ Sj A \ ^ X\ , s \ \ s s\ v s \ s sl^^ \ \ ^y \ \ v ^ \ \ \j s\ ' S\\ \ s sN \\ S \ \N s \ v \ S ^ ^ V V \> s^> v\ 5 ^ \\ Y N \ i ? 5? 3 = ' c c s C 3 '.1 5 \f I c > ! anK jad ^oa^-puooeg m ssoi 8St?doos=s FIG. 3. Diagram for Use in Calculating Seepage Losses in Canals. 46 WORKING DATA FOR IRRIGATION ENGINEERS up to vertical. On steep side-hill locations the slope on the hill- side is often made steeper than the other slope in order to avoid excessive excavation. Usually no difference is made between the side slopes in cut and those in fill. Depth of Flow and Bottom Width. The depth and bottom width of a canal section are obviously interdependent. It has been stated that the maximum depth to use for an irrigation canal in earth should not exceed 8 feet, and for safety and econ- omy in operation it is probable that the maximum line should be fixed at 10 feet, except for uncommonly large canals. It is very seldom that a canal is designed to have the best hydraulic ele- ments, although it is a very easy matter to make such a design. One of the principal reasons for this is that the most efficient hydraulic section is too deep for its width, and such a section will not keep its shape, but tends to broaden and become more shallow. In rock and other hard material and for lined sections the most economical section can generally be used. The best hydraulic section is the one that has the greatest hydraulic radius for a given area; such a section may be picked out by inspection from Figs. 14 to 21. For example: suppose the channel is to have 1 to 1 side slopes; the required area of cross- section is 200 square feet; what are the bottom width and depth that will give the best hydraulic section? Follow the line (Fig. 16 part 3) marked 200 at the bottom of the page to its intersection with the bottom width that gives the greatest hydraulic radius which we find to be about 9 feet; the corresponding depth is 10.3 feet; and the hydraulic radius is 5.23. In case of a rock or lined channel this section could be used, but for an earth section it would be too deep for its width. The best ratio of bottom width to depth to use for a lined or rock section is usually fixed by considerations of economy only, but for canals in earth the depth should be limited, as before stated, to about 8 or 10 feet, although canals have been built with greater depths. Ratios of bottom width to depth from 2 to 1 to 6 to 1 are commonly used, depending largely on economy of construction and operation. Canals in materials which are easily eroded and broken down require the greatest relative bottom widths. DESIGN OF IRRIGATION STRUCTURES 47 Velocities and Grades. The velocities, and correspondingly the slopes, for concrete-lined sections are practically unlimited. Velocities as high as 90 feet per second have been used on con- crete without destructive effect, but such velocities are not to be generally recommended. Velocities of 20 to 30 feet per second are common. Mr. A. P. Davis, in an article in Engineering News of January 4, 1912, sums up the results of investigations of the safe velocities on concrete as follows: " (1) That where clear water can be made to glide over concrete without disturbing its velocity or abruptly changing its direction, there is no practi- cal limit to the velocities that can be permitted without harm. (2) That concrete which is subjected to the impact of water under high velocity is rapidly eroded, and that under such con- ditions the velocities must be very carefully limited." In rock sections, unlined, velocities of 10 to 12 feet are not of ten exceeded because the section is usually so rough that the loss of head with high velocities is very great; and also because many rocks will not stand a higher velocity continuously. For canals in earth the velocity usually varies from 2 to 3 feet per second. Generally speaking, velocities less than 2 feet per second will allow the deposition of silt and over 3 feet per second will erode. There is probably not a canal in existence that does not deposit at some points and erode at others, even though the material be identical. The best velocity to use in a particular material is not subject to exact mathemat- ical calculation. The mean velocity at which silt will deposit is said to be dependent upon the depth of the water, which is no doubt true. It is a well-known fact that small canals erode at a lower mean velocity than large canals. It is probably safe to say that the velocity in the largest canals in ordinary earth should not exceed 3.5 feet per second and in the smallest laterals 2 feet per second, and that the minimum velocities should be 2 feet and 1 foot, respectively. The result of too low a velocity is not only to deposit silt, but the growth of weeds and moss is encouraged, causing the channel to become foul and require fre- quent cleaning to maintain its capacity. Of the two evils it is better to build a canal with too high rather than too low a grade, as the former can be remedied without excessive expense 48 WORKING DATA FOR IRRIGATION ENGINEERS by the construction of checks, while the latter condition is generally impossible to correct except at prohibitive expense. In some canals, checks are necessary in order to back the water up to the high turnouts during times when the canal may be running at only about one-half or two-thirds its capacity. This requirement should, however, be avoided, if possible, by locating the turnouts low enough to take out their proportional quantity at any stage of the mam canal flow. From experiments made in India, Mr. R. S. Kennedy found that the velocity at which neither silting nor scouring of the canal bed will occur depends upon: (1) the depth of water in the canal, (2) the character of the silt, and (3) the quantity of silt carried in suspension. The experiments indicated that the critical velocity varied as the 0.64th power of the depth of canal, and the equation Vs = 0.84 Z>' 64 was derived for water fully charged with fine, light sandy silt brought down by the floods of the rivers of northern India. For heavier materials the coef- ficient 0.84 is larger, and the general equation then is Vs = m Z>' 64 . Values of m have been used from 0.84 to 1.09, as indicated in the accompanying table. The equation Vs = m Z)' 64 is important to American engi- neers principally as indicating the probable variation of the scouring velocity with the depth of canal. It is generally agreed that a deep canal will stand a higher mean velocity than a shallower canal, but the above equation is probably the only attempt that has been made to express this phenomenon mathematically. It is difficult to say how closely this equation fits American canals, but it is probable that the velocity, Vs, does not increase so rapidly with increasing depth. For canals carrying large quantities of silt the equation may give the true conditions with fair accuracy, but for canals carrying fairly clear water the exponent of D is probably smaller and is probably closer to 0.5 than 0.64. The critical velocity for canals carrying fairly clear water would then be Vs = m D ' 5 . For convenience of comparison, a table has been calculated from this equation also, as it probably fits the conditions on American canals more closely than the other. It certainly agrees better with Ameri- DESIGN OF IRRIGATION STRUCTURES 49 TABLE 15 CRITICAL VELOCITY, OR MEAN VELOCITY, AT WHICH A CANAL WILL NEITHER SILT NOR SCOUR Based on Kennedy's formula Vs m D - 64 (For silt-laden waters) Depth of Channel in Fine, Light, Sandy Silt Somewhat Coarser, Light, Sandy Silt Sandy, Loamy Silt Rather Coarse Silt or Debris of Hard Soils Feet D | m = 0.84 m = 0.92 m =1.01 m = 1.09 2 1.30 1.43 1.56 1.69 2.5 1.51 1.66 1.81 1.96 3 1.70 1.87 2.04 2.21 3.5 1.88 2.07 2.26 2.44 4 2.04 2.24 2.45 2.65 4.5 2.20 2.42 2.64 2.86 5 2.35 2.59 2.82 3.05 5.5 2.50 2.75 3.00 3.25 6 2.64 2.90 3.17 3.43 7 2.92 3.21 3.50 3.80 8 3.18 3.50 3.82 4.13 9 3.43 3.77 4.12 4.46 10 3.67 4.04 4.40 4.77 11 3.90 4.29 4.68 5.07 12 4.12 4.53 4.94 5.36 TABLE 16 CRITICAL VELOCITY, OR MEAN VELOCITY, AT WHICH A CANAL WILL NEITHER SILT NOR SCOUR Based on formula Vs = m D- b (For canals carrying fairly clear water) Depth of Channel in Fine, Light, Sandy Silt Somewhat Coarser, Light, Sandy Silt Sandy, Loamy Silt Rather Coarse Silt or Debris of Hard Soils Feet D m =* 0.84 m =0.92 m = 1.01 m = 1 . 09 2 1.18 1.30 1.42 1.54 2.5 1.33 1.46 1.60 1.73 3 1.45 1.59 1.75 1.89 3.5 1.57 1.72 1.89 2.04 4 1.68 1.84 2.02 2.18 4.5 1.78 1.95 2.14 2.31 5 1.88 2.06 2.26 2.44 5.5 1.97 2.16 2.37 2.56 6 2.06 2.26 2.47 2.67 7 2.22 2.44 2.68 2.89 8 2.38 2.60 2.86 3.08 9 2.52 2.76 3.03 3.27 10 2.66 2.91 3.20 3.45 11 2.79 3.05 3.35 3.62 12 2.91 3.19 3.50 3.78 NOTE: This table is based on general hypotheses, and observation of American canals unsupported by experiments. 50 WORKING DATA FOR IRRIGATION ENGINEERS can practice. It should be remembered that this equation is not based on actual experiments, but on observation only. Formula for Flow. The tables and diagrams in this book for designing open channels are based on the Kutter formula: - 1 L + 41.6 + 4L6 in which V is the mean velocity in feet per second; R is the hydraulic mean radius; S is the " slope " or sine of the angle of inclination of the water surface; and n is an empirical coefficient varying with the roughness of the channel. The formula was derived from experiments mainly on river channels, but it has been found fairly well adapted to the calcu- lation of flow in all open channels, and the value of n has been determined for a large variety of conditions. For artificial channels the value lies between 0.010 and 0.035 for the smoothest and roughest respectively. The value for earth and rock sec- tions, unlined, is generally considered to lie between 0.020 and 0.035, and for lined channels between 0.010 and 0.015. For well- built canals in earth in good order the value lies between 0.020 and 0.025, the lower figure being applicable to the more compact materials and the latter for lighter materials and those con- taining much coarse gravel. The value 0.0225 is very generally used for canals in earth. The value of n for rock sections de- pends very largely upon the amount of smoothing off that is done. With the amount of trimming that is generally done, the value probably lies between .030 and .035, while a carelessly excavated rock channel may have a valve as high as 0.040, and a very smoothly trimmed channel may have as low a value as 0.025. If plenty of grade is available, it does not pay to smooth the channel up much, but if grade is valuable it may prove eco- nomical to do sufficient trimming to bring the value of n down to .025. The values .030 and .035 are in general use for rock sections. For wood flumes or wood-lined channels a value of n of .012 is commonly employed, and experience seems to justify this DESIGN OF IRRIGATION STRUCTURES 51 value. For concrete-lined channels n = .013 is in common use. Experiments seem to indicate that this value may be as low as .012 or even less for surfaces built against forms very smoothly finished with a steel trowel, while surfaces built without forms or with wood forms slightly uneven and not trowelled, the value is probably about .014. For any concrete surface reason- ably well made, .015 is probably the upper limit, and considering the present state of our knowledge of the subject it is not safe to use a value less than 0.012. Less is known in regard to the coefficients for steel flumes than for any other form of lining, but sufficient experiments have been made to indicate that the value is probably about .015 for rough joint flumes such as the Maginnis and about .012 for the smoother joint flumes, such as the Hess and Hinman. Some manufacturers claim values as low as .010 and .011 for their flumes, but there is not sufficient justification for the use of a value less than .012, especially since steel flumes have not been in use long enough to indicate what effect age may have on their carrying capacity. The accompanying tables * give the results of observations on concrete-lined and earth channels respectively, on projects of the United States Reclamation Service. These observations, although giving largely varying results, if carefully analyzed, indicate that the values .012 to .014, generally used for concrete channels, and .020 to .025, for earth channels, are jus- tified. The great difficulty of measuring the slope and average velocity accurately explains sufficiently the large variations shown in the table, that are not explained by differences in the condition of the channel, and it is very unlikely that more uniform results can be obtained under practical conditions. On account of the great uncertainties existing in the choice of a value of n, it is very desirable, especially for structures of great importance, to know what the hydraulic conditions would be if the value turned out to be something other than assumed. For example : A canal is under design in a material which it is known will probably erode excessively under mean velocities of 2.75 feet per second; the value of n is probably not less than * Taken from the "Reclamation Record," published by the United States Reclamation Service. 52 WORKING DATA FOR IRRIGATION ENGINEERS 3 i c B "3 g | 3 w eu X c O O W * | "is B C .1 < sS 5 " s- Jl & C t/5 (4 jg 3 < > i i O ^ jz; < H u > f Pi 1 < u II lO i i . i 1C i i i-H 1C CO CO O CO ''f CTJ CO O DESIGN OF IRRIGATION STRUCTURES 53 (N iO O5 CO iO t^ 00 CO 1C O co co O5 "tf 1 Tt< co o co i i co OCOCOO5OcO(MTfr- ( NOCOfe' ^ CO i-H O Tt< CO IO .i IIO TH C<1 CO i I (M CO CO CO - CO CO CO CO CO CO CO 54 WORKING DATA FOR IRRIGATION ENGINEERS | CJ ft 1 E $ w i *o a g H "-3 K *rt & | 1 i ta ! c 2 " HP* H ^ 55 en W u ail 1 o tig; Id U J C C u id W "ft- M SEJJ < ,4 & a w _ -s C 8| w i % 3 a o > 1 < O > E M (2 Pi a II I 8cs u,.2 u S.ti'o IT " "5 * * | O o . c = p x> >"OT3 g C C o "O CO TT' 1 O O OOOOOOOO 1 oo oo oo oo oo ' (N (N !>. i 00 *O 00 g^HTt^iO^OiO^GOt^QO QOO5O5O5O5' "COOO3CO i I^Hi Ir-li li-HC^i-^C^i *C^QOr^l>t^t^t^COCOCOCOCOCOiOiOiO i-Hi li-HrHOOOOOO'-^' (T li (i-Hi OOO DESIGN OF IRRIGATION STRUCTURES 55 e o ^2 58 u en CO (N t^. t^ O5 (N rHi-H rt , a>" o-c C3 O 8 6 g u. en II !l 3 wo 11 I IT (C^l I 1 ' Id' iC^l I 1 I 1 lT-HdC v: l-HO3' I i^i^c^^c^c^c^^c^ 56 WORKING DATA FOR IRRIGATION ENGINEERS DESIGN OF IRRIGATION STRUCTURES 57 Je s. o p 0) '2 I "S m J3 w rt ^ rt en T^ -0 *S 1 OJ .2 ^ 1 1 g ^3 cj 1* H B JS bib ^ tn rt u"S . C/D ^O ^^ en D tu 1 *o 1 1 1 T 1 i be 1 J 36S F i- 8 1 **n T3 b>. flj ^> ^ |?Si ;;&> 5lg w "3-- .? J-8 g g^fe 2 i" c If! j|n C 2 hfi-"-" S rt S g-^ffiS cn^ en S g-g S 6-S 6 ai^ .0 eg D^ iis! bfl a) g gx-fi ^ sp| g l s: sl fees- 2 r bottom; some weeds, slick, black volcanic ash. Drained sand; no weeds. * ' PQ , ^~ 32* s s* -v-^ o o com 3 O O o o CQCQ 15 O o W 3 o ^ >^< y 2 x-g-c xi loslll - .Uls * .1 .o'ffi ^ 8888888888 ^ i Ii-Hi Ir-lTHrHi-MT-HrHil O CD COO5i-l OOiOOOOfN CO IO CO ^ t^ T}H 00 O - lOrH l^c^g^c^^O^ 2 I-H CO cX)' i co DESIGN OF IRRIGATION STRUCTURES 59 .020 nor more than .025. The canal is designed on the basis of mean velocity of 2.5 feet per second, and n = .0225, and the hydraulic radius is 4. If the value of n should actually be .020, instead of .0225, as assumed, what would be the resulting velocity? Fig. 33 gives a handy means of determining this (see explanation on page 82). We read from this diagram that the relative veloci- 51 ties for n = .0225 and .020 are as . and the velocity with n = 0.20 would therefore be 2.5 X ^ = 2.81. This velocity U.4o4 is higher than is considered safe, and the designed velocity must, therefore, be reduced to 2.4 or less. In other cases it is desirable to know what effect a change in the value of n may have on the slope. This may also be ascertained from Fig. 33. A saving of a few feet in grade may be the means of reclaiming many additional acres of land, and a reduction of the value of n by lining the canal might bring this about. For example: We read from Fig. 33 that an unlined canal having a hydraulic radius of 5 feet and a value of n of .025 requires a slope of 6 = 2.69 times as great as the same canal lined so as to bring the value of n down to 0.15. This problem is most important in the smaller canals which require relatively steep slopes. Other problems present themselves in the solution of which this diagram is very useful. It is a requirement of good design to make calculations on the basis of various combinations of the hydraulic elements rather than on a single set of assumptions, as the latter may lead to disastrous results if the assumptions should prove to be erroneous. Freeboard. By freeboard is meant the vertical distance from the maximum flow water surface to the top of bank. The requirement for a certain amount of freeboard is obvious. This is not susceptible of mathematical calculation, and its value must be based on experience and accepted practice. For earth canals it is seldom made less than one foot for the smallest canals (not considering small laterals, for which the freeboard may be even less) nor greater than three to four feet for the 60 WORKING DATA FOR IRRIGATION ENGINEERS largest canals. These figures are for seasoned banks; when the banks are built, provision should be made for subsequent settle- ment and wearing down, due to travel on the banks, and in certain localities for wind erosion. For well-constructed banks an allowance of about 10 per cent should be sufficient for the former, while the latter is entirely dependent upon local condi- tions, but in most localities should not be an important item with properly maintained canals. For lined canals the freeboard is usually made relatively considerably less and is dependent in some degree upon the velocity of flow. For higher velocities the freeboard is generally increased somewhat, especially at points where changes in grade occur, on account of the uncertainties existing in the calculations of depth of flow. Under high velocities the water surface fluc- tuates more and is more disturbed even under theoretically uniform flow, so that it is necessary to add a factor of safety in additional depth of freeboard. In general, it may be stated that the freeboard for lined canals with normal velocities should be about one-half that required for earth canals of correspond- ing size. Where a lined canal having high velocities passes around a sharp curve the water piles up on the outside of the curve, due to its tendency to continue on the tangent. In such cases it is necessary to raise the lining on the outside above the normal freeboard, not only to allow for the piling up of the water but because of the greater disturbance of the water at this point. The amount the water rises on the outer side of the curve may be calculated approximately, and the value thus calculated should be increased 50 to 100 per cent to allow for the increased disturbance of the water surface. An approximate method of calculating the rise of water in passing around curves is as follows: Consider any section made up of three plane surfaces, as in the figure on opposite page: Let g = acceleration of gravity = 32.2 ft. per second, per second, V = velocity of water in feet per second, R = radius of curve in feet, DESIGN OF IRRIGATION STRUCTURES 61 F = centrifugal force, G = force of gravity. Consider a unit of mass and the forces acting on it, 72 thenF = = and G = i. Equilibrium will be established when there is no tangential force acting parallel to the surface A-B, which condition obtains when the resultant P, of F and G, is perpendicular to A-B. We can then write the following equations: p = G -v- cos 9 = F -T- sin 6 :. F = GtanO = tanO Since the velocity of the water is the same on the curve as on tangent, or only very slightly smaller, the area of cross-section remains the same, and we then equate the two areas as follows: by + fco ia + **+**y / ' / I i 2 L/Z ' / / / , ? 7 / L i 1 ,^7 TV / / / 7 ? r 005 / , / / /_] /V / 1 / / i 7 / 7 / y / / 7 ' r /// ' / / >/ ? y 7 > ^ ^ r 006 / / / / / /7 v/ 7 / / ' i ? / 7 z_ / f 777 ^/v / / / y . ' . Z. 008 / / / V// / // Z 7 ' / y ...L..L..L ?'; a .5 1 - -^ / -A / ^55v ^-^-7 L-/ / 7 ' t * .2- ^ --- .015M ' 'ft / / / / / / / / /- --<--- .02 t / / / 7 ^ y ^^ ^ I ; ^ f / / // / / / / ^ ,/ y - Z-, / ' / / / / / y , / / ' 7 /' // / / ?_, _1 / / // / / / 7 22 / / ^.7 / " Z" / \ / / . y ^ / / / / ' < [2 / / / / y / / , / ^ (. ?ji, , , E / / / ^ / ? .04 / / y / 7 i / / 7 / / / ' / V / / / y 7 "y / r 9 - - 2 . ? J > I 1 ^ I// / / ^ / / / ' ^ / ' / / // / / r i ~} ' 1 '/ / 2 / f 7 / / / lii.ii i / ^ A ^ / / / / 7 - 1 ,1 . I . f ( . * t ' / 2 / f 2 } / 2 -I-|!| i A / / ^ / 5 t-'tj-t- ;.iii ! 5 Z / t-/ 4 / 2 J / V / 1 7 t ^ y ? ^ y / / / / / / // 1 / / / / ' r 010 / ^ 2_ / / / / / / '/ / // / / f i 7 ^/ ^ / / , ' / / / / / /// '/' / ' t L ^ / / / ; _- z / ;;; 2. jfij tgi /y t/ \ 7 / = <_.^. ...,,. 015 5.5 -^ -- 5 ::;z.:j?:: v //. /- / V 1 7 7 "7 " --/- it / z / / ^ r-~-'-'/-'- 2 r -.04 - t 7 y_L ^ /// ' '/ f / / / / ^ ( ' r 05 /// / / // / / / / / / / / * ^ ^ ^' j! / i!!i 2 7 / / / 7 7 ~~f / Z ^ L / i it '> ' / /// / / / / / 7 / / //*/ ^ ^V'V 7. ~/ / / / / / / / / X 7 / / / / / / / Q Z ^ ^ ^ J / / . ' / / / / ^ 7 ^ y * 7_ * ' 1 1 t / f / / / ^ / Z ^ ' 'tt / , / f / / / / / J. L ^ ^ i > / ' / / / ^ i ^ / / / 7 / / / i // / / / } / / / ~/ j 7 / / / / / / / / / / / / / / '*/ '' ~2_ / / / / / / ' / j '/ s / / t / / / "7 / / / S / 1 y ?/ / / / / / / / / / / .3 ?Z-- :: ; Z: .25 ---/-- 7 Z- .2 t--l..l.t ~y >Tn" / \ Y~ / / Y ~ 2 2.5 3 3.5 4 5 6 1 8 9 10 15 20 25 30 35 Velocity, (feet per second) FIG. 6. 94 WORKING DATA FOR IRRIGATION ENGINEERS Suggestion: n = .014 for straight regular channels, lined with concrete, having a wooden trowelled surface in good order. VALUES OF C IN THE FORMULA V = C ^Ws Si OPE .00005 .0001 .0002 .0004 .001 . 01 and over 1 43 49 53 56 59 60 2. 56 63 67 71 73 74 3 . 65 72 76 79 81 83 0.4 0.6 72 82 79 88 83 92 86 95 88 96 89 98 0.8 90 95 99 101 102 103 1.0 96 101 104 106 107 108 1.5 107 111 113 114 115 116 2.0 115 118 119 120 121 121 3 127 127 128 128 128 128 4.0. . 135 134 133 133 133 132 6.0. . . . 146 142 140 139 139 138 10.0 158 152 148 146 145 145 20.0 174 163 158 154 153 152 HYDRAULIC DIAGRAMS AND TABLES 95 4 3.5 3 2.5 J2 ii.5 -01 w .j .25 Slope s a ~ ^/ /// .OOG .008 ;.OJ .015, .02 2 2.5 3 3.5 4 5 6 7 8 9 10 15 20 25 30 35 Velocity, (feet per second) FIG. 7. 96 WORKING DATA FOR IRRIGATION ENGINEERS Suggestion: n = .015 for straight and regular channels of ordinary brickwork, smooth stonework, rough concrete work, and foul and slightly tuberculated iron. VALUES OF C IN THE FORMULA V = C ^R~S SL OPE .00005 .0001 .0002 .0004 .001 .01 and over 0.1 . 39 44 48 50 54 54 0.2 0.3 4 51 59 66 57 65 72 61 69 76 65 73 79 66 74 80 67 76 82 6 76 81 85 87 88 90 0.8 83 88 91 93 94 95 1.0 89 93 96 98 99 99 1.5 99 103 105 106 108 107 2.0 107 109 111 112 112 112 3.0 118 119 119 119 119 119 4.0 6.0 10.0 126 137 149 125 134 143 125 132 140 124 130 138 124 130 136 123 129 136 20.0 165 154 149 146 144 143 HYDRAULIC DIAGRAMS AND TABLES 97 Slope 10 2.5 3 3.5 4 5 678910 15 Velocity, (feet per second) FlG. 8. 20 25 30 35 98 WORKING DATA FOR IRRIGATION ENGINEERS Suggestion: n = .020 for channels of compact sand and fine gravel, rough set rubble, ruined masonry, rough tuberculated iron, and canals in earth in good condition lined with well-packed gravel, partly covered with sediment, and free from vegetation. VALUES OF C IN THE FORMULA V = C ^l~R~S SL OPE .00005 .0001 .0002 .0004 .001 .01 and over 0.1 2 26 35 30 39 32 42 34 44 36 45 36 46 3 41 45 48 50 51 52 0.4 6 46 53 50 57 53 60 55 62 56 63 57 64 08 59 63 65 67 68 68 1.0 64 67 69 70 71 72 1.5 72 75 77 78 78 79 2.0 79 81 82 83 83 83 3 88 89 89 89 89 89 4 95 94 94 94 93 93 6 105 102 100 99 99 99 10 116 111 108 107 105 105 20.0 131 122 117 115 113 112 HYDRAULIC DIAGRAMS AND TABLES 99 Slope < ) I 9 z_. ... :;L ...,^ / / y / / A? fj - y* ,.004 3 / / / / f f f : J f f / 7 6 5 / y / / I / f /* / / / l ^ ^1 /' y / / / / t / / 7_ V / .006 ^ f IZ / / f / / / Jf / / y / ^ ' ' r / / 1 / / / / / ~{~7 / i 7 L ' / i i! i!2 // / / / / ( / / . ' , .008 / / "]' / ^ ^J2 / / / / y / 1 / . - 010 yM/i4 Mi/rLr A / % g % iz 11.02 2 1.5 1 .9 .8 .7 .6 .5 .4 .35 .3 .25 .2 / 2 / ~t-. Z Z!^ ^ 2t-t III 1 / -/ / ^ ? \ 7' tn t / 4 |T --.03 --.04 / j. ^7 / 1 i~i ^ // 'E7 71 / /, / / / / / / / y/-/ '777/ / ^^^ / ' / > ' / / / / f / Z / y y.05 / / ^ ///y / / / // t i ' ' / f f / / y t / / /// 7 7 / / / ' / ' / / / / f / ' > / / / /V // j. ' cL / ' / // / / / / / ' / * / f 7- L- > ' / /* ~/~ y / Z2 Z j ' /* / "/ / / / 2 ^ / / y '77 * ^ ' ^ / / y y / / \ / '7* 7.7.7- f S ^ / / i / / 2 / ,y / / f / 7 / / / y y / / f / / y / ~7 / / / / /~/2. * \ \ ^ ' t r ' / / / / / f / , j J) > 5 / 7 .' / , / / / / / / y / / / 2 * ^ ^ / / / i / / / / / / / /// 2 *j .' ^ ? t > / A / / / 2 ? / / / / // / .' /> / > ' ' / / / ' / / y ' / ' / {-J.JL * ' / / /' / / / / / & /_/ ^ y / :j:j!:jj:jj ^ 1 / \{ r/ 1 .5 2 2.5 3 3.5 4 Velocity, (f< jet '-> pe rs 3 6( JO 7 U( 1) i 10 15 20 FIG. 9. 100 WORKING DATA FOR IRRIGATION ENGINEERS Suggestion : n = .0225 for canals in earth in fair condition lined with sediment and occasional patches of algae, or composed of firm gravel without vegetation. A common figure for earth canals. VALUES OF C IN THE FORMULA V = C Bill's SL OPE .00005 .0001 .0002 .0004 .001 . 01 and over 1 22 25 27 29 30 31 2. 30 33 36 37 39 39 0.3 .... 36 39 42 43 44 45 0.4 40 43 46 47 48 49 0.6 46 50 52 54 55 55 0.8 52 55 57 58 59 60 1.0 56 59 60 62 62 63 1.5 64 66 67 68 69 69 2 70 71 72 73 73 74 3.0 4.0 79 85 79 84 79 84 79 84 79 83 79 83 6.0 94 92 90 89 89 88 10 105 100 98 96 95 94 20 120 111 106 104 102 101 HYDRAULIC DIAGRAMS ANIV TABLES 10 4 3.5 3 2.5 1.5 g *P 1 S .9 .25 Slope "^^lO CO f*C iilii i i IS z // 006 010 1.5 2 2.5 3 3.5 4 5 6 7 8 9 10 Velocity, (feet per second) 15 20 FIG. 10. 102 WORKING DATA FOR IRRIGATION ENGINEERS Suggestion: n = .025 for canals in earth of tolerably uniform cross- section, slope and alignment in average condition, the water slopes being lined with sediment and minute algae, or com- posed of loose, corirse gravel; and for very smooth rock sections. VALUES OF C IN THE FORMULA V = C "^ RS R SLOPE . 00005 .0001 .0002 .0004 .001 . 01 and over 0.1 . 20 26 31 35 41 46 49 57 62 71 77 85 96 110 22 29 34 38 44 48 52 59 64 71 76 84 92 102 24 31 36 40 46 50 54 60 64 72 76 82 89 98 25 32 37 42 47 51 55 61 65 71 76 81 88 96 27 34 39 43 48 52 56 62 66 71 75 81 87 94 27 34 39 44 49 53 56 62 66 71 76 81 86 93 0.2 0.3 4 0.6 0.8 1.0 1.5 2.0 3.0 4 6 10 . . 20 HYDRAULIC DIAGRAMS AND TABLES 103 4 3.5 8 2.5 1.2 1.5 Slope ffi ft ill.ii ooc 008 010 015 < 1.5 2 2.5 3 3J 4 5 6 7 8 9 10 Velocity, (feet per second) 15 20 FIG. 11. 104 WORKING DATA FOR IRRIGATION ENGINEERS Suggestion : n = .030 for canals in earth in poor condition, having the bed partly covered with debris, or having comparatively smooth sides and bed, but the channel partly obstructed with grass, weeds, or aquatic plants; and for average rock sections. VALUES OF C IN THE FORMULA V = C p Si OPE .00005 .0001 .0002 .0004 .001 . 01 and over 0.1.. 16 17 18 19 21 21 2 21 23 25 25 27 27 0.3 25 27 29 30 30 31 0.4 28 31 32 33 34 35 0.6 33 35 37 38 39 39 0.8 37 39 41 42 42 43 1 40 42 44 45 45 45 1 5 47 48 49 50 50 51 2.0 51 53 54 54 54 55 3.0 59 59 59 59 59 59 4 64 64 63 63 63 63 6.0 10.0 20.0 72 82 96 71 78 89 69 76 85 69 75 83 68 74 81 68 74 80 HYDRAULIC DIAGRAMS AND TABLES 105 Slope Sirs O to 2J32iM co * ia o II 1 1 8 00 10 9 8 7 6 5 4 3.5 3 2.5 1.5 .4 .35 .3 .25 < 2 2.5 3 3.5 4 5 6 7 8 9 10 Velocity, (feet per second) FIG. 12. 008 .01 .015 I .j .03 .04 15 20 106 WORKING DATA FOR IRRIGATION ENGINEERS Suggestion: n = .035 for canals in earth in bad order and regimen, having the channel strewn with stones and detritus or about one-third full of vegetation; and for rough rock sections. VALUES OF C IN THE FORMULA V = C Si OPE R .00005 .0001 .0002 .0004 .001 .01 and over 01 13 14 15 16 17 17 02 18 19 21 21 22 22 3 21 22 24 24 25 25 0.4 24 25 27 27 28 29 0.6 28 30 31 31 32 33 8 31 33 34 35 35 35 1 34 35 37 37 38 38 1 5 40 41 42 42 43 43 2.0 44 45 45 45 46 46 3.0 50 51 51 51 51 51 4.0 56 55 55 55 54 55 6 63 61 60 60 59 59 10 72 69 67 66 65 65 20 . . . . 85 79 76 73 72 71 HYDRAULIC DIAGRAMS AND TABLES 107 10 4 3.5 1.5 ffi .35 .25 Slope Hi 1.5 2 2.5 3 3.5 4 5 6 7 8 9 10 Velocity, (feet per second) ti=.085 .015 .02 .05 15 20 FIG. 13. 108 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 21 VALUES OF C FOR USE IN THE CHEZY FORMULA V = C \/R~S \ n *\ .009 .010 .011 .012 .013 .014 .015 .017 .020 .0225 .025 .030 .035 .040 Slope S = .00005 = 1 in 20,000 = 0.264 feet per mile .1 78 67 59 52 47 43 39 33 26 22 20 16 13 11 .2 100 87 77 68 62 56 51 44 35 30 26 21 18 15 .3 114 99 88 79 71 65 59 50 41 36 31 25 21 18 .4 124 109 97 88 79 72 66 57 46 40 35 28 24 20 .6 139 122 109 98 90 82 76 65 53 46 41 33 28 24 .8 150 133 119 107 98 90 83 71 59 52 46 37 31 27 1.0 158 140 126 114 104 96 89 77 64 56 49 40 34 29 1.5 173 154 139 126 116 107 99 87 72 64 57 47 40 34 2 184 164 148 135 124 115 107 94 79 70 62 51 44 38 3 198 178 161 148 136 127 118 104 88 79 71 59 50 44 *3.28 201 181 164 151 139 129 121 106 91 81 72 60 52 46 4 207 187 170 156 145 135 126 111 95 85 77 64 56 49 6 220 199 182 168 156 146 137 122 105 94 85 72 63 56 10 234 212 195 181 169 158 149 134 116 105 96 82 72 64 20 250 228 211 196 184 174 165 149 131 120 110 96 85 77 50 266 245 228 213 201 190 181 165 148 136 127 112 101 93 100 275 254 237 222 210 200 190 175 158 146 137 123 112 104 Slope 5 = .0001 = 1 in 10,000 = 0.528 feet per mile .1 90 78 68 60 54 49 44 37 30 25 22 17 14 12 .2 112 98 86 76 69 63 57 48 39 33 29 23 19 16 .3 125 109 97 87 78 72 65 56 45 39 34 27 22 19 .4 136 119 106 95 86 79 72 62 50 43 38 31 25 22 .6 149 131 118 105 96 88 81 70 57 50 44 35 30 25 .8 158 140 126 114 103 95 88 76 63 55 48 39 33 28 1.0 166 147 132 120 109 101 93 81 67 59 52 42 35 31 1.5 178 159 144 130 120 111 103 89 75 66 59 48 41 35 2 187 168 151 138 127 118 109 96 81 71 64 53 45 39 3 198 178 162 149 137 127 119 104 89 79 71 59 51 45 4 206 186 169 155 143 134 125 111 94 84 76 64 55 49 6 215 195 178 164 152 142 134 119 102 92 84 71 61 54 10 226 205 188 174 162 152 143 128 111 100 92 78 69 62 20 237 216 200 185 173 163 154 139 122 111 102 89 79 71 50 249 227 211 197 185 175 166 151 134 123 114 100 91 83 100 255 234 218 204 191 181 172 158 140 130 121 108 98 91 Slope S = .0002 = 1 in 5,000 = 1,056 feet per mile .1 99 85 74 65 59 53 48 41 32 27 24 18 15 12 .2 121 105 93 83 74 67 61 52 42 36 31 25 21 17 .3 133 116 103 92 83 76 69 59 48 42 36 29 24 20 .4 143 125 112 100 91 83 76 65 53 46 40 32 27 23 .6 155 138 122 111 100 92 85 73 60 52 46 37 31 26 .8 164 145 131 118 107 99 91 79 65 57 50 41 34 29 1.0 170 151 136 123 113 104 96 83 69 60 54 44 37 32 1.5 181 162 146 133 122 113 105 91 77 67 60 49 42 36 2 188 170 154 140 129 119 111 97 82 72 64 54 45 40 3 200 179 163 149 137 128 119 105 89 79 72 59 51 45 4 205 185 168 155 143 133 125 111 94 84 76 63 55 48 6 213 193 176 162 150 140 132 117 100 90 82 69 60 53 10 222 201 185 170 158 148 140 125 108 98 89 76 67 60 20 231 210 194 180 168 158 149 134 117 106 98 85 76 68 50 240 220 203 189 177 167 158 143 126 116 108 94 85 78 100 245 224 208 194 182 172 163 148 131 121 113 99 90 83 Values of C are the same for all slopes when R = 3.28 feet. HYDRAULIC DIAGRAMS AND TABLES 109 TABLE 21 (Concluded) VALUES OF C FOR USE IN THE CHEZY FORMULA V = C \/R~S \ n \ .009 .010 .011 .012 .013 .014 .015 .017 .020 .0225 .025 .030 .035 .040 Slope S = .0004 = 1 in 2,500 = 2.112 feet per mile .1 104 89 78 69 62 56 50 43 34 29 25 19 16 13 .2 126 110 97 87 78 71 65 54 44 37 32 25 21 18 .3 138 120 .107 96 87 79 73 62 50 43 37 30 24 21 .4 148 129 115 104 94 86 79 68 55 47 42 33 27 23 .6 157 140 126 113 103 95 87 75 62 54 47 38 31 27 .8 166 148 133 121 110 101 93 81 67 58 51 42 35 30 1.0 172 154 138 125 115 106 98 85 70 62 55 45 37 32 1.5 183 164 148 135 124 114 106 93 78 68 61 50 42 37 2 190 170 154 141 130 120 112 98 83 73 65 54 45 40 3 199 179 162 149 138 128 119 105 89 79 71 59 51 45 4 204 184 168 154 142 133 124 110 94 84 76 63 55 48 6 211 191 175 161 149 139 130 116 99 89 81 69 60 53 10 219 199 183 168 157 146 138 123 107 96 88 75 66 59 20 227 207 190 176 164 154 146 131 115 104 96 83 73 66 50 235 215 198 184 173 162 154 139 123 112 104 91 82 75 100 239 219 203 189 177 167 158 143 127 116 108 96 87 80 Slope 5 = .001 = 1 in 1,000 = 5.28 feet per mile .1 110 94 83 73 65 59 54 45 36 30 27 21 17 14 .2 129 113 99 89 81 73 66 57 45 39 34 27 22 18 .3 141 124 109 98 89 81 74 63 51 44 39 30 25 21 .4 150 131 117 105 96 88 80 69 56 48 43 34 28 24 .6 161 142 127 115 104 96 88 76 63 55 48 39 32 27 .8 169 150 134 122 111 102 94 82 68 59 52 42 35 30 1.0 175 155 139 127 116 107 99 86 71 62 56 45 38 33 1.5 184 165 149 136 124 115 108 93 78 69 62 50 43 37 2 191 171 155 142 130 121 112 98 83 73 66 54 46 40 3 199 179 163 149 138 128 119 105 89 79 71 59 51 45 4 204 184 168 154 142 133 124 110 93 83 75 63 54 48 6 211 190 174 160 149 139 130 116 99 89 81 68 59 52 10 218 197 181 167 155 145 136 122 105 95 87 74 65 58 20 225 205 188 175 163 153 144 129 113 102 94 81 72 65 50 232 212 196 182 170 160 151 137 120 110 101 89 79 72 100 236 216 200 186 174 164 155 141 124 114 105 94 85 77 Slope S = .01 = 1 in 100 = 52.8 feet per mile .1 110 95 83 74 66 60 54 46 36 31 27 21 17 14 .2 130 114 100 90 81 74 67 57 46 39 34 27 22 19 .3 143 125 111 100 90 83 76 64 52 45 39 31 25 22 .4 151 133 119 107 98 89 82 70 57 49 44 35 29 24 .6 162' 143 129 116 106 98 90 77 64 55 49 39 33 28 .8 170 151 135 123 112 103 95 82 68 60 53 43 35 31 1.0 175 156 141 128 117 108 99 87 72 63 56 45 38 33 1.5 185 165 149 136 125 116 107 94 79 69 62 51 43 37 2 191 171 155 142 130 121 112 99 83 74 66 55 46 40 3 199 179 162 149 138 128 119 105 89 79 71 59 51 45 4 204 184 167 154 142 132 123 109 93 83 76 63 55 48 6 210 190 173 160 148 138 129 115 99 88 81 68 59 52 10 217 196 180 166 154 145 136 121 105 94 86 74 65 58 20 225 204 187 173 161 152 143 128 112 101 93 80 71 64 50 231 210 194 181 168 158 150 135 119 108 100 87 78 71 100 235 214 197 184 172 162 153 139 122 112 104 91 82 75 NOTE. For slopes greater than .01 C remains practically constant. 110 WORKING DATA FOR IRRIGATION ENGINEERS Formulae: A = d P = b + A_ ~~P'' Q = A V Problem : bd Water Surface SECTION d = 2.25 What is the value of r and what is the value of the dis- charge Q when V 1.5 feet per second? Solution: Enter diagram at depth = 2.25; thence horizontally to 6 = 4; read r = 1.06 and A 9; thence vertically to V = 1.5, and read Q = 13.5. HYDRAULIC DIAGRAMS AND TABLES 111 9 2 8 "X 7 1.5 A = 2.5 Area (sq. feet) 3 3.5 4 5 Rectangnli 6789 2.5 2.5 <^^ X X 1 5 Zx st: 1.5 2.5 3 3.5 4 5 6 7 8 9 10 A = Area (sq. feet) FIG. 14 (Part 1 of 3). Hydraulic Elements of Rectangular Sections. 112 WORKING DATA FOR IRRIGATION ENGINEERS Water Surface SECTION Formulae: A = bd P = b + 2d A bd = P == b + 2d Q = A V Problem: Q= 120 7 = 5.2 r = 1.7 What is the required bottom width b and depth d ? Solution: Enter the upper diagram at Q = 120; thence horizontally to V = 5.2; thence vertically downward to a point half- way between r = 1.6 and r = 1.8, and read b = 8.5 and d = 2.83. HYDRAULIC DIAGRAMS AND TABLES 113 15 20 A = Area 25 30 35 40 50 Rectangular 70 80 90 100 1.0 10 15 20 FIG. 14 (Part 2 of 3). Hydraulic Elements of Rectangular Sections. 25 30 35 40 50 60 70 80 90 100 A =Area 114 WORKING DATA FOR IRRIGATION ENGINEERS bd Formulae: A = P = b + A r = T = Q = A V bd b+2d SECTION Problem: 6 = 850 V = 2.2 b = 80 Find d and r. Solution: Enter upper diagram at Q = 850; thence horizontally to V = 2.2; thence vertically downward to b = 80, and read d = 4.85 and r = 4.32. (NOTE. The above values of r and d may be in error by one or two figures in the third digit. That is, r may be 4.31 or 4.33, and d may be 4.84 or 4.86, depending upon the personal equation of the reader of the diagram. These differences, however, are of no practical importance.) HYDRAULIC DIAGRAMS AND TABLES 115 A =Area 250 300 350 Rectangular 400 500 600 700 800 900 1000 2000 2.0 100 150 200 250 300 350 400 500 600 700 800 900 1000 A = Area FIG. 14 (Part 3 of 3). Hydraulic Elements of Rectangular Sections. 116 WORKING DATA FOR IRRIGATION ENGINEERS Formulae : A = b d + 0.5 d 2 P = b + 2.24 d A_ b d + 0.5 d 2 r ~' = P : = b + 2.24 d Q = A V Problem: Q = 9.2 A = 8.5 ft = 4 Water Surface Find d, r, and F. Solution: Enter the diagram at Q = 9.2; thence horizontally to A = 8.5 and read V 1.08; thence vertically downward to b = 4, and read d = 1.75 and r = 1.08. HYDRAULIC DIAGRAMS AND TABLES 117 1.5 A=Area 2.5 3 3.5 4 Slopes *4 to 1 6 7 8 9 1Q 20 i x ^x i 15 10 9 o : I 5 ^ 4 3 2.5 2 2 3 4 5 g 6 2 8 I 10 -- >-. z z X x > x''; ;^;:^J<: :l ;i:i;2 x X X : | 15 : :- 7 " X X % <^-^-, .^:. ;; x_ .x 2j ' X X Z x x x x x^l X x xi^X. X' -- X _X' ;^ 12 x x- x x^ X- x ..' x'X X - 10 Si 9 X x. Z X x x u / X ^ C ijjliiijii Jip|:jg XX xC x / '<"' x / f P 6 as 4 3 25 ? z ^ 2 : - 5^^^^x$ '.^c','.^^^. >^ ^ ^ ^~ ^^ -^ 7~ . ' r Z i - x x' x X- ' X X ^ 'X ^ X X X>','Xx 'X / J x X x x ^ ~7 ^ ' x X^J X ' -xf : '^ x" ~x x X 'x X -/ -^ X x - 7 x xp^' ^/X^X' > ^ " x - OX ^x Xx 2 X x X X X x x : x x xx; - X X X^^ X XJ ' ! ' " I >: !2 Xx XJ X x - x x ' x X J xx; ^ X x XX X ! * ', ' x / X ^X**^ y > : / ^x y >_ y > 7 / x / x"^ / / y 1 / I/ x / / r x \, / / X L x A /' / X 'b / \ ^' \ / / > ^ ^> \ ^ / g' r 2 x \ x Q / ^ V ^K / ^ *i X ^ / ij V 5 X' x <^ , / ^ >t X X "* x^^ < / / "V ^ x \ 7 ^^^ y^ "^s 2 / x / x \ / / v s k / ' < y x /-- --X f x / f X \ / /^,. z_ / / / x ^ ^ ^ / ^ x x x ^ ^L x / x ^/ \ x '? / / 7n y- ~v ' \ / / / x x* * / *s ! / [ x ? /'* ?< " -^ / / ' / / ^ y ,? / / x / ^ / / L 1.5 2 2.5 3 3.5 4 56789 10 A=Area FIG. 15 (Part 1 of 3). Hydraulic Elements of Trapezoidal Sections. 118 WORKING DATA FOR IRRIGATION ENGINEERS Formulae: A = b d + 0.5 d? \ Water Surface P = b + 2.24 d A 6d + 0.5d 2 \ P '' '' b + 2.24 d b *{* Q = A V SECTION ' Problem : Q = 260 V = 24 d = 1.4 Find b and r. Solution: Velocities over 20 feet per second are not indicated on the diagram, but it can be used for any velocity which, divided into the discharge, will give an area between 10 and 100 square feet, as illustrated in the following solution of the above problem. If we divide both Q and V by 10 the quotient -y = A remains the same. We therefore enter the diagram with Q = 26 instead of 260; thence horizontally to V = 2.4 in- stead of 24; thence vertically downward to d = 1.4, and read 6 = 7 and r = 1.05. If V were greater than 26, say 28, making -y less than 10, we would divide both Q and V by 100 and use Fig. 12, enter- ing the diagram with Q = 2.6 and V = 0.28. The remain- ing steps would be the same as above. HYDRAULIC DIAGRAMS AND TABLES 119 Slopes^ to 1 70 80 90 1C 20 23 30 35 40 50 GO 70 80 90 100 FIG. 15 (Part 2 of 3). Hydraulic Elements of Trapezoidal Sections. 120 WORKING DATA FOR IRRIGATION ENGINEERS Formulae: A = b d + 0.5 d 2 \ Water Surface P = b + 2.24 d N^ 1 r- -p SECTION Q = A V Problem : b = 50 d = 10.5 V = 4.5 Find r and Q. Solution: Enter the diagram at d = 10.5; thence horizontally to b = 50 and read r = 7.9. Continuing now vertically we note that the V = 4.5 line is not intersected. We therefore divide our velocity by 10 and stop at V = 0.45 and read Q = 260. Since this value of Q corresponds to a velocity of 0.45, which is only one- tenth the velocity given, the actual value of Q is 260 X 10 = 2600. HYDRAULIC DIAGRAMS AND TABLES 121 A=Area 200 250 300 350 Slopes 1$ to 1 500 600 700 8009001000 100 150 200 250 300 350 .400 500 600 700 800 9001000 A =Area FIG. 15 (Part 3 of 3). Hydraulic Elements of Trapezoidal Sections. 122 WORKING DATA FOR IRRIGATION ENGINEERS Formulae: P = b + 2.83 d r = b + 2.83 d = A V Water Surface SECTION Problem: b = 2 d = 1.5 Find A and r. Solution : Enter the diagram at d = 1.5; thence horizontally to 6 = 2, and read A = 5.2 and r = 0.84. HYDRAULIC DIAGRAMS AND TABLES 123 A = Area Slopes 1 to 1 2.5 3 3.5 4 A = Area 8 9 10 FIG. 16 (Part 1 of 3). Hydraulic Elements of Trapezoidal Sections. 124 WORKING DATA FOR IRRIGATION ENGINEERS Water Surface SECTION Formulae: A = b d + d 2 P = b + 2.83 d A_ bd + d* ~' P '" b + 2.83 d Q = A v Problem : A = 63 r = 2.75 Find b and d. Solution : Enter the diagram at A = 63; thence follow vertically to r = 2.75 (an imaginary line three-fourths of the distance from 2.6 to 2.8), and read b = 11.5 and d = 4.05. HYDRAULIC DIAGRAMS AND TABLES 125 10 A = Area 30 35 40 Slopes 1 to 1 50 GO 70 80 90 100 25 30 35 40 50 A = Area 70 80 90 100 FIG. 16 (Part 2 of 3). Hydraulic Elements of Trapezoidal Sections. 126 WORKING DATA FOR IRRIGATION ENGINEERS Formulae: A = d -\~ (L v Water Surface / P = b - 2.83 d A bd + d 2 \ 1 / P b + 2.83 d -dr^ Q = A V SECTION Problem: For an area of 140 square feet what combination of bottom width and depth gives the greatest hydraulic radius? Solution: Enter the diagram at A = 140 and follow vertically to the point indicating the maximum value of r which is when b = 7 (to the nearest foot) and d = 8.8. The value of r is 4.38. HYDRAULIC DIAGRAMS AND TABLES 127 100 A =Area Slopes 1 to 1 250 300 350 400 500 600 700 800 900 1000 2000 150 200 250 300 350 400 500 600 700 800 900 1000 A=Area FIG. 16 (Part 3 of 3). Hydraulic Elements of Trapezoidal Sections. 128 WORKING DATA FOR IRRIGATION ENGINEERS Formulae: A = b d + 1.5 d 2 ^ Water Surface P = b + 3.61 d ~P '' b + 3.61 <2 Q = A V SECTION Problem: It is required to design a canal section to carry 14 c. f. s. with a velocity of 2.2; the section to have a bottom width equal to three times the depth. Find also the hydraulic radius. Solution : Enter the diagram at Q = 14 and follow horizontally to V = 2.2; thence vertically downward to a point which indi- cates a ratio of bottom width to depth of 3 to 1. We find this to be when b = 3.6 and d = 1.2. The corresponding hydraulic radius r is found at the same time to be 0.82. HYDRAULIC DIAGRAMS AND TABLES 129 1 20 i .' 1. 3 2 A=A 2.5 3 rea 3.5 4 5 6 i Slop 8 J es ol ) 10 15 | X :| - x. x * * ' x x x x X " x' ^ x X xxx 10 1 9 x x . X x v 3 jj|j5J = :j X ^ ^'^X' 8 7 G f 5 4 3 2.5 X X X-^-^TT; ~ 1 :^ 3 X X X' / x ^ ^ ' Xx x^ / XXX ^ x 6 x x X ^xxx/x/x^ ^x' 3jj ; ! -^x X ? X x x x x x^ x , x x xxxp/^X--^ x'x'x''' X x" x x x 2 x ^^x . X x X ' . Xx ''--' ^^'V'' '''' '""' : x 7 ^ x x X x x ^X ^X x - ? ' / / ''/ x XXx x xjx ,x , x^ X x ^^ x x" X -': .. / - ''**''*'*'''''' 'x"xx;^x x x f x< x x" x x x^ x x X x ; > / ", 1 *'''*'*''*'*'' ^ x " fff ^''' f ^X^ x 'xf x XV- x x ' X 2 3 x.- . : ^-^A X' x x .- x x 2 z 2 3 i j 5---I "I" 8 fl 2 2.5 2 x X" x< X x a X x^ 7 4 a x' 1 x \ ' 3 XV II 0.9 0.8 0.7 0.6 0.5 ] X J ^ x V ^ ,/ ^5 S ^3-' i x^ ^ x ^ ii >^V' \ X \ x x >^ / ^> ~g v 2 X x^ V ^ X" / 2 7 J.v>" 'X X / ^ ^c/ ^ 8 5 jX x' V ^ / X "* 5 9 "j ? . ' Vj x/ x /^ x' , 2 ^ C^ / 7 . ^^ 10 ^ i' /'' ' H< iX / / f / i! / > s ^^ / x / Lx / / / / X / x /r i^ x x ' /' > S- L/ / / _ / x / x / / x X / /' / x ' ' I/ """'"~" 21 -*^ x / 1 X * /x /' ^ X X / 1 1.5 2 2.5 3 3.5 4 56789 10 A=r Area FIG. 17 (Part 1 of 3). Hydraulic Elements of Trapezoidal Sections. 130 WORKING DATA FOR IRRIGATION ENGINEERS SECTION Formulae: A = b d + 1.5 d* p = b + 3.61 d A bd+1.5d* P == b + 3.61 d Q = A V Problem : Q = 500 F = 24 r = 1.4 Find A, b, and d. Solution: Neither Q = 500 nor V = 24 is given in the diagram, but since A = T? we may divide both Q and V by 10 before entering the diagram and obtain the required values of A y b, and d. Enter the diagram at Q 50, follow horizontally to V = 2.4 and read A = 20.8; thence vertically downward to r = 1.4, and read b = 8 and d = 1.92. HYDRAULIC DIAGRAMS AND TABLES 131 10 A=Area Slopes 1% to 1 15 20 25 30 35 40 50 60 70 80^90.100 200 150 FIG. 17 (Part 2 of 3). Hydraulic Elements of Trapezoidal Sections. 132 WORKING DATA FOR IRRIGATION ENGINEERS Formulae : A = b d + 1.5 d 2 X^ Water Surface p = b + 3.61 d A r P " b + 3.61 d Q = A V SECTION Problem: b = 60 d = 10.3 7 = 3 Find r, A, andQ. Solution : Enter the diagram at d = 10.3, follow horizontally to b = 60 and read r = 8.0 and A = 780. Following vertically upward we note that V = 3 is not intersected. We, there- fore, stop at V = 0.3, and read Q = 235. Since Q = 235 for V = 0.3, it will be ten times 235 for V = 3, The required value of Q, therefore, is 2350. HYDRAULIC DIAGRAMS AND TABLES 133 A = Area 200 250 30Q> 350 400 Slopes 1^ to 1 500 600 700 800 900 260 300 350 400 500 600 700 800 9001000 A = Area FIG. 17 (Part 3 of 3). Hydraulic Elements of Trapezoidal Sections. 134 WORKING DATA FOR IRRIGATION ENGINEERS Formulae : A = bd + 2d* P = b + 4.48 d A_ bd+2d* P ~~ b + 4.48 d A V ~~ Problem : "^ Water Surface A = 7.2 ^ r = 0.75 ^ T 2(1 Find b and d. SECTION Solution: Enter the diagram at A 7.2, follow vertically to r 0.75 (approximately half-way between r =0.7 and r = 0.8), and read b = 5 and d = 1.02. HYDRAULIC DIAGRAMS AND TABLES 135 A = Area Slopes 2 tol 1.5 2 2.5 15 05 3 2.5 2 3 2.5 1.5 0.8 0.7 O.G f e ^X \ 10 8 rt A II 5a 1 1.5 2 2.5 3 3.5 4 5 6 7 8 9 10 FIG. 18 (Part 1 of 3). Hydraulic Elements of Trapezoidal Sections. 136 WORKING DATA FOR IRRIGATION ENGINEERS Formulae : A = bd + 2 d 2 P = b + 4.48 d ' P b + Q = A V Problem: Q = 56 A = 44 d = 2.75 Find V, b, and r. Solution : Enter the diagram at Q = 56; follow horizontally to A = 44 and read V = 1.27; thence vertically downward to d = 2.75, and read b = 10.5 and r = 1.93. SECTION HYDRAULIC DIAGRAMS AND TABLES 137 200 150 Slopes 2tol 70 80 90 100 15 20 25 30 35 40 50 A = Area 70 80 90 100 (Part 2 of 3). Hydraulic Elements of Trapezoidal Sections. 138 WORKING DATA FOR IRRIGATION ENGINEERS Formulae : A = b d + 2 d* P = b + 4.48 d = _ P ~~ A V Water Surface SECTION Problem: A = 640 r = 6.6 Q= 1440 Find b, d, and V. Solution: Enter the diagram at A = 640; follow vertically to r = 6.6 and read b = 60 and d = 8.4; thence vertically upward to Q = 1440, and read V = 2.25. HYDRAULIC DIAGRAMS AND TABLES 139 A = Area Slopes 2tol 100 200 250 300 350 400 500 GOO 700 800 900 1000 2000 150 200 250 300 350 .400 500 600 700 800 900 1000 A = Area FIG. 18 (Part 3 of 3). Hydraulic Elements of Trapezoidal Sections. 140 WORKING DATA FOR IRRIGATION ENGINEERS Formulae: A = bd + 1.25 d 2 P = b + 3.22 d A^ bd+ 1.25 = P = & + 3.22 Q = A V Water Surface SECTION Fig. 19 may also be used for canal sections having both side slopes l to 1. The equations are: A =bd + 1.25 d 2 P = b + 3.20 d A_ bd+ 1.25 d 2 ~~ P '' 6 + 3.20 d C A V ' ~ A v SECTION tt will be noted that the area is exactly the same as for the mixed slope section above, but the wetted perimeter, and con- sequently the hydraulic radius, is slightly different. The differ- ence is, however, entirely insignificant for any practical canal section. NOTE. Mixed slopes are seldom used except for relatively large canals on steep side hills where steeper slopes are necessary on the upper side to reduce excavation. The hydraulic el- ements of smaller canals than those having a water area of 100 square feet have, therefore, not been plotted. HYDRAULIC DIAGRAMS AND TABLES 141 Slopes IK to 1 and 1 to 1 or 100 2000 100 150 200 250 300 350 400 500 600 700 800 9001000 A Area FlG. 19. Hydraulic Elements of Trapezoidal Sections. 142 WORKING DATA FOR IRRIGATION ENGINEERS Formulae : A = bd + l.75 P = b + 4.04 d A_ _ bd = P ~~ Q = A V Water Surface 1.75 b + 4.04 d SECTION Fig. 20 may also be used for canal sections having both side slopes If to 1. The equations are: A = bd+ 1.75 d 2 P = b + 4.03 d A_ _ bd+ 1.75 d 2 ~~ P ~~ & + 4.03d 2 Q = A V SECTION It will be noted that the area is exactly the same as for the mixed slope section above, but the wetted perimeter, and con- sequently the hydraulic radius, is slightly different. The differ- ence is, however, entirely insignificant for any practical canal section. NOTE. Mixed slopes are seldom used except for relatively large canals on steep side hills where steeper slopes are necessary on the upper side to reduce excavation. The hydraulic elements of smaller canals than those having a water area of 100 square feet have, therefore, not been plotted. HYDRAULIC DIAGRAMS AND TABLES 143 100 Slopes 2 to 1 and 1J to 1 or A= Area 1% to 1 200 250 300 350 400 500 600 700 800 900 1000 712000 1500 150 200 250 300 350 400 500 600 700 800 9001000 A=Area FIG. 20. Hydraulic Elements of Trapezoidal Sections. 144 WORKING DATA FOR IRRIGATION ENGINEERS Case I Segment larger than semicircle. Formulae : Full circle. A = *R* P = 2?r R A_ P '" r = .p. Case II Segment smaller than semicircle. e Segment. A = n R* - P = r = R 360 90 R sin B P 2 ~0 These equations apply to both Case I and Case II, provided the proper sign is given to sin 8. For angles 8 less than 180 degrees the second member of the equations for A and r is negative and must be subtracted. For angles 8 greater than 180 degrees the second member of the equations is positive and must be added. The hydraulic elements of segments having areas from 0.2 to 100 square feet are given in Fig. 21. For values not ob- tainable from the diagram the table on the next page or the fundamental equations above may be used. Illustrations of use of Fig. 21. 1. Example. A circular pipe having a radius of 2 feet has a depth of water of 0.95 foot. What are the area of water section and hydraulic radius? Solution. Enter the diagram at d = 0.95; follow vertically to the intersection with R = 2, and read A = 2.28 and r = 0.56. HYDRAULIC DIAGRAMS AND TABLES 145 Circular Segments 5.0 1.25 .2 .25 .3 .35 .4 .5 .6 .7 .8 .9 1.0 d = Depth, (feet) 1.5 2.0 2.5 FIG. 21 (Part 1 of 2). Hydraulic Elements of Circular Segments. 146 WORKING DATA FOR IRRIGATION ENGINEERS HYDRAULIC ELEMENTS OF CIRCULAR SEGMENTS. ALL VALUES ARE GIVEN IN TERMS OF THE RADIUS R Depth Area Wetted Perimeter Hydraulic Radius 0.1R .0588R 2 0.902R .0652R 0.2R . 163R 2 1.285R . 1268R 0.3R .294R 2 1.586R . 1852R 0.4R .448R 2 1.854R .2415R 0.5R .614R 2 2.09R .293R 0.6R .792R 2 2.32R .341R 0.7R .979R 2 2.53R .386R 0.8R 1.175R 2 2.74R .429R 0.9R 1.370R 2 2.94R .466R R 1.57R 2 3.14R .500R .1R 1.77R 2 3.34R .530R .2R 1.965R 2 3.54R .555R .3R 2.161R 2 3.75R .576R .4R 2.348R 2 3.94R .596R .5R 2.526R 2 4.19R .603R .6R 2.692R 2 4.43R .608R 1.7R 2.846R 2 4.69R .607R 1.8R 2.977R 2 5.00R .595R 1.9R 3.081R 2 5.38R .565R 2R 3.142R 2 6.28R .500R NOTE. This table is intended for use in calculating the hydraulic elements of circu- lar segments having an area greater than 100 square feet, which is the limit of the diagram. It has, however, general application and may be used for calculating any circular segment. 2. Example. What are the hydraulic radius and depth of flow of a pipe of 6 feet radius when the area is 75 square feet? Solution. Enter the diagram at A = 75; follow horizontally to the line representing R = 6, and read d = 7.55 and r = 3.4. 3. Example. For an area of 25 square feet what radius of pipe will give the greatest hydraulic radius? Solution. Enter the diagram at A = 25; follow horizontally to the point indicating the greatest hydraulic radius, which is when R = 4 feet. 4. Example. The area of a segment is 30 square feet and the depth of flow is 4 feet. What are the radius of segment and hydraulic radius? Solution. Enter the diagram at A = 30; follow horizontally to the vertical line representing d = 4, and read by inter- polation R = 5.8, also r = 2.15. HYDRAULIC DIAGRAMS AND TABLES 147 Circular Segments 8 7 1.5 2.0 2.5 3.0 3.5 4.0 5.0 6.0 7.0 8.0 9.0 10.0- d=Depth (feet) FIG. 21 (Part 2 of 2). Hydraulic Elements of Circular Segments. 148 WORKING DATA FOR IRRIGATION ENGINEERS Horseshoe Sections Sections having the upper portion in the form of a semicircle and the lower portion composed of arcs of larger radius, or of straight lines, are commonly called " horseshoe " sections. They are frequently used for tunnels in yielding material and for outlet conduits under earth dams. The horseshoe section has some hydraulic and structural advantages over circular and other sections. The hydraulic value of the section illustrated on the opposite page, for a depth of flow of 1.6 R (or clearance C = 0.4 R), may be seen by com- paring the area and hydraulic radius of this section for this condition with the same elements for a circular section as given in the table on page 146. The areas are seen to be 2.85 R 2 and 2.692 R 2 respectively, and the hydraulic radii 0.610 R and 0.608 R respectively. Structurally the horseshoe section affords more floor room and permits the building of the sides and arch of the lining before the invert is put in important factors in tunnel work. It is said that the most favorable section of the horseshoe type is when the total height is equal to the greatest width, as in the section illustrated on page 149. The calculation of the hydraulic elements of such sections is a tedious process and much labor may be saved by the use of the table on the opposite page. Slight deviations from the given section, such as making the sides below the center line straight and the bottom of two straight lines, will still allow the use of this table for preliminary calculations on which to base the size of the section. After the size and form have been decided upon, more exact calculations of the hydraulic elements can be made if desired. HYDRAULIC DIAGRAMS AND TABLES 149 HYDRAULIC ELEMENTS OF A HORSESHOE SECTION All values are given in terms of R Clearance C Area Wetted Perimeter Hydraulic Radius 3.30R 2 6.52R 0.506R 0.1R 3.24R 2 5.62R 0.576R 0.2R 3.13R 2 5.24R 0.598R 0.3R 3.01R 2 4.93R 0.610R 0.4R 2.85R 2 4.67R 0.610R 0.5R 2.69R 2 4.43R 0.607R 0.6R 2.51R 2 4.18R 0.600R 0.7R 2.32R 2 3.99R 0.582R 0.8R 2.12R 2 3.78R 0.561R 0.9R 1.93R 2 3.58R 0.539R R 1 . 73R 2 3.38R 0.512R Example 1. The section has a radius R of 5 feet. The surface of the water is one foot below the top. What are the area and hydraulic radius? Clearance C = 1/5 R = 0.2 R Area = 3.13 R 2 = 78.2 sq. ft. Hydraulic radius = .598 R = 2.99 feet Example 2. The required area of water section is 125 square feet and the clearance of water surface below top shall be 0.3 R. What is the radius? Area = 3.01 R 2 = 125 .'. R = 6.45 feet Hydraulic radius = 0.61 R = 3.93 feet Clearance C = 6.45 X 0.3 = 1.94 feet 150 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 22 CIRCULAR CONDUITS FLOWING PARTLY FULL (Kutter Formula) Values by which discharge and velocity of a circular conduit flowing full should be multiplied to obtain the discharge and velocity of the same conduit with the proportionate depth on invert given in the first column. For use with Fig. 22. D = diameter of conduit. Depth of flow Proportionate depth D i flj . D = 1 FT. D = 2 FT. D = 4 FT. D = 6 FT. D = ] OFT. 11! 7 1 V k ' 2 10 -+- - - - 1 x^ 5 1 2 1 2 s _L / s \. I 2 ! r N ./ X A, t v / 7 /x^ /* v y s J / y 7 [ j j / 1 j x^ y 5?! A, / ' -.1 y ^ L y( y / i 'x ^ y i "\ ' / ^ 1 s To' / /v / f 7 Q . f ^^ 1 \ S Q y , N{ i 1 S j \ / \ y 1 1 x >x / r r " ' / / \^ / ^ x x / 7 ! / 1 \ / ^ I ^ 5; / TJX f / N x, 7 1-1 i Xl / ^y / ^ I / \ [ y ^ ^ y y N R 1 |V N / x x y '/ \i s y , * 7 ^^>. / / ~S 2 - 5 |::: 1 I 1 ft A s ^ 4 / s s i n .2 ;j?:: "3 -;''; e8 /-- k t - - -^ -/- ^ 7^ ?/ j| s^ -f y^ ^ / _ j 2 ::!(! ~^ / ,2 / 1 42 a 45 43 51 54 57 1.5 -- ,,.J j y 1 ^ ^ 7 . 7 " I ? e ; 1 ! 7" / "I*" <7 H / ^ ^ 1 1 w / / 1 y y V ~ v / T i V / / / x / y y i \/ ' "7 "*x/ y* / j , / c/7 A ' '^*t. / / N t ~7 ~~r x,.^ A s*V s i "/ r- f / v ' s / i / f s y V / r 9 --/-- ^ s 1 ^^ /* /- 7 N j / ^ / v i' X E_V / y A y i r ^ Sv /I 7 i y X 1 ^ ! i N ^ ' /N / A / y y y ^ y y y f " r 2. ^ -( / ^ / / X / f y 1 y yk y y f j j / XS/ /v 1 f ; y 1 y ^ > ' r^ 5 --/- - f 'S 1 / 7 / s ^ y / / / / t 7 V 7 ^ / / 7 s N 1 / ^ ' y 7 .4 /- - /_ / / s x 1 (/ x / / / ^ r /^ f I y _x / / / / ^ / / J 1 S > / !' j7 / 3 ^ / / / / t / > / / / / / !! '=H / .25 -::: ::|:- /- y / V - y /IKI 2.5 3 4 5 6 7 8 9 10 15 20 25 30 40 Discharge in Cubic Feet per Second FIG. 22 (Part 1 of 2). Discharge of Circular Conduits Flowing Full by Kutter Formula. (Explanation page 78.) 152 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 22 (Concluded} CIRCULAR CONDUITS FLOWING PARTLY FULL si fli N / "^t 1< ^ X. / 1 x 1 / \ J ^ x / Xyi 5^x, / j ^ ^ ^ / N 1 V I * Z s 7 / > ( ^j N V \ ^ \ / x^ \ , V f X . j Xw / s / x^ 1 X. / > "SJ 7 \ j X j ^s, ^^ x/ X ! x / X^ ^ ^ j 2 j ** 1 J!:2 x 1 X^ ^ x ( x^ y I K / * ,y x^ f ^ s ' s / /V \ / s N j / / x ^, 2, L N v ] J v X^ "s y. X / x x f X / ' ^ 1 ^ / >S s / ^JS^ / X^ / X s/ X 7 X s ^ N y "^x V ^ X / Xs / ?", t /X N 1 N, N 1 x / V x/ / X 1 2 sJ N r 2"x,z ' * \ ^[X f s - > / x ^ y ^ X r > 7 - - ft / x^ ^x^ / Nj V / / s 1 ^ X ^ ^ ^ L x / Z 7 \ / x I ^ ^ f- 4 i^ ^^ ^ X J ^ 5:3 \ / x -/* A ' I X y 1 Xi y 1 / ^ y f ***> J > . / v, y*X" X j 1 /x ^ s 1 7 ]IiJ ^ / ' X / ^ s x x/ / ^ y X, / / ^ Z Y/ ^ "V /" ^ / x^ / /x s / / x v ^/ /x j ' 2 " V C V / x 1 ^ x x ^ V X 7 x s. ^ / \ / / ? ^ 5s v ^ / ^ v s/ ^< r 7 N / s ^ 7 / ^ J / ^x Z ')'" / N 2 / ^ V / ^ X / / ^ s / ^s t r ^xf / **t < ^ x^ ^ ^ X 1 / f x / / ^ ^ 77 >^ - > - t '*! ^ / x / ^ x / f s y X I/ & ^- 3 ^x i \ i -) i / r V -/ I \ x ( 3 t 1 ' 5 1.0 .9 .8 .7 .6 .5 .4 .3 .25 4 F x/ -/ x > X/ y ~s 7 ft I 4 S 7 7' fx- _j 7 V;-- -^ -y ^- 2 ^X ^ s ^ A 132 144 7~ x /x 1 . i ^ 7 > /* X / / ' N y ^ / x / x y i ^ / / if. / 2 > ^} L , >X. / / ^ / 1 /x 1 y / *3 *h ^ - 1 x 1 i / N .y N 1 I ^ y S ^C " s ^ /' / ^> i / / x \ 1 ^ / / \ "y l| f W ^x / / / x ^ / / N x / f \ / / f ^ ^ I x. s s / <5s ' / 4/ ?VK / 7 / ^ \ / / 1 /x t / V i 5k Z -!' ^ / ' x^ / 1 ^ ^ X 1 / f x f / x/ ^ ^ ^ A.V ' "V / f V x > y f* / / X / ^ , ^/ / \/ f / X \ / > V / s / ' F? / x/ / N -f j(- ~1 x^--/- -i /7^ / ^ 1 1 J 1 y X y 7 ^x7 x / / 0,'V ^ y / / y / >X H _y ^. 1 ^ ^. / / 3 I \ v, / / <*, / y. ' Z ' * ^ ' 7^ / / s/ / / ^ / 1 X / / ^7 7 > / \ y / ( / /- X / v,^ 1 y ^S ' i I' / / X / "** / / % j / y. / ' * > t 1 S, / ^ 7^> 7 A 'x / / 7 / , ' N / / ^ N ' j ? / / x > x/ / ; X / y ) ^ ^, / 1 ^ ^'Z / x / / / * X. / / / N y / Z K (.ill V / _ll 50 GO 70 80 90 100 150 200 250 300 400 500 Discharge in Cubic Feet per Second IG. 22 (Part 2 of 2). Discharge of Circular Conduits Flc 600 >win 700800 gFull by Kutter Formula. 154 WORKING DATA FOR IRRIGATION ENGINEERS Small Wooden-Flumes /> s II i i. i i. i i. i i 00<= >0< = >0| = >0< = >< = ) FIG. 23 (Part 1 of 3). Discharge of Rectangular Wooden Flumes. (Explanation page 80.) HYDRAULIC DIAGRAMS AND TABLES 155 Small Wooden Flumes FIG. 23 (Part 2 of 3). Discharge of Rectangular Wooden Flumes. 156 WORKING DATA FOR IRRIGATION ' ENGINEERS Small Wooden Flumes S3 -v/ 3 B o^o s M o - * fc ^ \ ^ 8, o o o o* FIG. 23 (Part 3 of 3). Discharge of Rectangular Wooden Flumes. HYDRAULIC DIAGRAMS AND TABLES 157 Small Wooden Flumes FIG. 24 (Part 1 of 3). Discharge of Rectangular Wooden Flumes. (Explanation page 80.) 158 WORKING DATA FOR IRRIGATION ENGINEERS Small Wooden Flumes 3 2 3 s S.2 5 s Vi -\ FIG. 24 (Part 2 of 3). Discharge of Rectangular Wooden Flumes. HYDRAULIC DIAGRAMS AND TABLES 159 Small Wooden Flumes is. 1 adois FIG. 24 (Part 3 of 3). Discharge of Rectangular Wooden Flumes. 160 WORKING DATA FOR IRRIGATION ENGINEERS puooog aad ^88 j FIG. 25. Hydraulic Curves for Small Canals. HYDRAULIC DIAGRAMS AND TABLES 161 x ^- ' X-- ^x ? ^^ -^ x x ^x ^ >- -** b x ^, 5 ^ - , ^ Y> / - -^ ^^> -^ / & 2 2* ^ ^ ~? \ ^y >- -^^"^ / / 1 c ! sL ^ / x / / ' s r / t / ^ s s de SI op ss l^ to 1 / / / / ^ ' / / // V t // 7) ~& I' ) 10 20 30 40 50 6( Area of Water Section FIG. 25J^. Curves for Proportioning the Section. I Use of Figs. 25 to 28 1. Problem: What slope of water surface is required for a canal to have a discharge of 60 c. f. s., a mean velocity of 2.2 feet per second, lJ/2 to 1 side slopes, and a ratio of bottom width to depth of 2 to 1? n = .0225. Also find the required bottom width and depth. Solution: In Fig. 25, at the intersection of the lines representing Q = 60 and V = 2.2 we read S = .00058. At the same time we read on the diagonal line the area of water section equals 27. To find the required bottom width and depth we now turn to Fig. 25j^ and at the intersection with the im- aginary line representing area = 27 and the line marked "b = 2d" we read d = 2.7 +; and b is therefore equal to 2.7 X2or 5.4 feet. The hydraulic elements of the canal section then are: Q = 60 [ b = 5.4 V = 2.2 d = 2.7 5 = .00058 n = .0225 Side slopes lj^ to 1 162 WORKING DATA FOR IRRIGATION ENGINEERS If the canal were to have a ratio of bottom width to depth of 3, Fig. 25 would be used in the same manner as above, but in using Fig. 25 J^ the line marked "b = 3d" would be used and we would find d = 2.45 and b = 2.45 X 3 = 7.35. The line marked " b = d" is used in a similar manner to proportion a section having this ratio. The other elements of the canal section would remain as above. The results in the latter cases would not be exact because Fig. 25 is based on a ratio of bottom width to depth of 2 to 1, but the error is not of practical significance for canals of the sizes considered. For n = .025, Fig. 26, instead of Fig. 25, is used, but Fig. 25}/2 is used in the same manner as above outlined. 2. Problem: What slope, bottom width, and depth are required for a canal to carry 5 c. f. s. if the velocity is to be 1.5 feet per second, side slopes 1^ to 1, ratio of bottom width to depth 2 to 1, and n = .025? Solution: In Fig. 28, at the intersection of the lines representing Q = 5, and V = 1.5, we read S = .0016, and interpolating between diagonal lines we find the area of water section to be 3.3 square feet. Turning now to Fig. 27J^, we read at the intersection of the imaginary line representing area =3.3 with the line marked "b = 3d" that d = 0.85 foot; hence b = 3 X 0.85 = 2.55 feet. The hydraulic elements of the canal section then are : Q = 5 V= 1.5 S = .0016 b = 2.55 d = 0.85 n = .025 Side slopes lj^ to 1 HYDRAULIC DIAGRAMS AND TABLES 163 puooag J9d ^89,1 UT FIG. 26. Hydraulic Curves for Small Canals. 164 WORKING DATA FOR IRRIGATION ENGINEERS 1.5 1.0 Bide Slopes 1^ to 1 234 Area of Water Section FIG. 27^. Curves for Proportioning the Section. HYDRAULIC DIAGRAMS AND TABLES 165 Area Square Feet 1.0 1.5 2.0 Velocity in Feet per Second 2.5 FIG. 27. Hydraulic Curves for Small Laterals. 3.0 Area Square Feet 1.0 1.5 2.0 Velocity in Feet per Second FIG. 28. Hydraulic Curves for Small Laterals. 3.0 166 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 23 SEMICIRCULAR STEEL FLUMES Freeboard, depth, and area for different conditions of flow, and multipliers for other values of n. For use with Fig. 29. FREEBOARD AND DEPTH OF FLOW IN FEET AND AREA IN SQUARE FEET I ade Number Diameter of Flume |! IJK/8 Flow .437 D for V 1.024 for Q 1.08J M Ml MULTIPLIERS FOR OTHER VALUES OF n jr of Flume in '. llii 1111 ill! iff! feQSS if I Free- Depth Free- Depth Free- Depth Free- Depth n n n board &Area board & Area board &Area board &Area .013 .014 .015 18 1'- 0" 0.083 0.417 0.062 0.437 0.050 0.450 0.042 0.458 .903 .822 .746 1.000 0.31 0.33 0.34 0.35 24 1'- Si" 0.106 0.530 0.080 0.556 0.064 0.572 0.053 0.582 .905 .826 .750 1.271 0.50 0.54 0.55 0.57 36 r-ii" 0.160 0.800 0.120 0.840 0.096 0.864 0.080 0.880 .908 .832 .762 1.920 1.13 1.21 1.25 1.28 48 2'- 6|" 0.212 1.06 0.159 1.11 0.127 1.14 0.106 1.17 .910 .836 .768 2.542 2.01 2.15 2.22 2.27 60 3'- 2J" 0.265 1.33 0.199 1.40 0.159 1.44 0.132 1.46 .912 .839 .773 3.190 3.13 3.35 3.46 3.54 72 3'-10" 0.320 1.60 0.239 1.68 0.192 1.72 0.160 1.76 .913 .842 .777 3.833 4.52 4.84 5.00 5.12 84 4'- 5J" 0.371 1.86 0.278 1.95 0.223 2.01 0.186 2.04 .914 .844 .780 4.458 6.16 6.60 6.81 6.97 96 5'- 1" 0.423 2.12 0.317 2.22 0.254 2.29 0.212 2.33 .915 .846 .782 5.083 8.03 8.60 8.87 9.10 108 5'- 8}" 0.477 2.39 0.358 2.51 0.286 2.58 0.238 2.63 .916 .847 .784 5.729 10.17 10.90 11.2 11.6 120 6 4j 0.530 2.66 0.398 2.79 0.318 2.87 0.265 2.92 .917 .848 .786 6.375 12.53 13.40 13.8 14.2 132 7'- 0" 0.583 2.92 0.437 3.06 0.350 3.15 0.292 3.21 .918 .849 .788 7.000 15.18 16.2 16.8 17.2 144 7'_ 7j" 0.637 3.19 0.478 3.35 0.382 3.44 0.318 3.51 .918 .850 .790 7.646 18.10 19.4 20.0 20.5 156 8'- 4" 0.695 3.47 0.520 3.65 0.417 3.75 0.348 3.82 .919 .851 .791 8.333 21.55 23.1 23.8 24.4 168 8'-ll" 0.743 3.72 0.557 3.90 0.445 4.01 0.372 4.09 .919 .852 .792 8.920 24.66 26.4 27.3 27.9 180 9'- 6J" 0.797 3.98 0.598 4.19 0.479 4.30 0.398 4.38 .919 .853 .793 9.562 28.36 30.4 31.3 32.1 192 10'- 2" 0.847 4.24 0.635 4.45 0.508 4.58 0.424 4.66 .920 .853 .793 10.167 32.10 34.3 35.5 36.3 204 lO'-lO" 0.903 4.51 0.677 4.74 0.542 4.87 0.452 4.97 .920 .854 .794 10.833 36.36 38.9 40.2 41.2 216 11'- 5i" 0.955 4.77 0.717 5.01 0.573 5.16 0.478 5.25 .920 .855 .795 11.458 40.80 43.7 45.1 46.2 228 12'- 1" 1.006 5.03 0.755 5.29 0.605 5.44 0.503 5.54 .921 .855 .796 12.083 45.40 48.6 50.2 51.4 240 12'- 8f" 1.060 5.30 0.796 5.57 0.636 5.73 0.530 5.84 .921 .856 .797 12.729 50.35 53.9 55.7 57.0 NOTE. In the columns marked lower figure is the area. " Depth and Area," the upper figure is the depth and the HYDRAULIC DIAGRAMS AND TABLES 167 Steel Flumes ? Diameter of Flumes v 01 1 1 1 I/I 1 1 ' [ 1 1 ! I PJJMI |i|[|||[n || |\i | y! s II III ILIs^' .009 -~-j .008 --CX--- --I !:::!:!;:: pz = S t- - :S^zi::jH: .007 -{- *\ ?- --L : jjj- --f^-- 006 2 - I . 5 J ! . . IliN 2 s s s ' \ s s ^ s s x 005 1- ^ v "S 2 V^ / ^ V_ ^^ ^v^ i^ s .004 - 5 f- x Z ^s Z Vy -< > H' Ttnil n j ^T--l^p "SSS^v,^SS SS^2"J ;;^P^BI .0035 EEEl5*E = EJ .0025 = = |E:EE:I::3 |||EEEEEEg S E i .002 -^ .0015 s^-- M ^ ^: --v,- 3 . .. S2 III* \ y ^ " s 7 .001 - - - s - - - ?i-3 !| L .0009 - J's- 0008 S ...TIi i[i!l / *% / 0007 X / / ^ j L I ft / cs :::::: | (IflOfi / t 1 L L N ^ 1 ^ / ^ s f 1 1 "s 7 7^ / 1*** T Hl)iiii|ini j|!J!!!Jj rt " .0002 y- s ^-- -/- /- " " ? 7 ||| |e',/, .00015 - :.:i(. :::: ; ; t 7 7'n" S v s / ~f i X ^ Z .0001 L- -L.. 7 ^ / T! 1.5 2 2.5 3 3.5 4 5 6 7 8 9 10 Discharge (c.f.s.) 13 20 25 30 FIG. 29 (Part 1 of 2). Discharge of Semicircular Steel Flumes. (Explanation page 81.) 168 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 24 SEMICIRCULAR STEEL FLUMES FLOWING PARTLY FULL (KUTTER FORMULA) Values by which velocity and discharge of steel flumes given by Fig. 29 should be multiplied to obtain the velocity and discharge of the same flume with the proportionate depth (ratio of depth to diameter) given in the first column. Propor- tionate D = IFt. D = 2 Ft. D = 4 Ft. D = 6 Ft. D = 10 Ft. Depth Vel'ty Dis'ge V Q V Q V Q V Q .10 .367 .0485 .384 .0508 .403 .0533 .412 .0545 .420 .0555 .11 .395 .0602 .412 .0628 .431 .0654 .441 .0666 .449 .0678 .12 .424 .0730 .441 .0761 .458 .0790 .468 .0804 .475 .0818 .13 .451 .0872 .468 .0908 .486 .0940 .494 .0953 .499 .0967 .14 .477 .103 .494 .107 .511 .110 .519 .112 .524 .113 .15 .502 .119 .520 .124 .536 .128 .544 .129 .550 .131 .16 .526 .138 .544 .142 .560 .147 .568 .148 .573 .150 .17 .552 .157 .567 .162 .583 .167 .592 .169 .597 .171 .18 .576 .178 .590 .183 .607 .188 .615 .190 .620 .192 .19 .599 .200 .613 .206 .630 .211 .638 .213 .642 .215 .20 .622 .224 .636 .230 .651 .235 .659 .238 .663 .239 .21 .644 .248 .658 .254 .672 .260 .680 .263 .684 .265 .22 .665 .274 .678 .280 .692 .287 .700 .289 .703 .291 .23 .686 .301 .698 .308 .711 .315 .718 .317 .722 .319 .24 .707 .329 .718 .336 .730 .342 .737 .347 .740 .346 .25 .727 .359 .738 .367 .748 .370 .755 .375 .758 .376 .26 .746 .390 .756 .397 .767 .400 .774 .405 .776 .407 .27 .766 .423 .774 .428 .784 .433 .791 .438 .793 .437 .28 .785 .457 .793 .461 .802 .467 .808 .471 .811 .470 .29 .803 .490 .811 .494 .819 .500 .825 .504 .827 .503 .30 .821 .524 .827 .530 .837 .536 .841 .537 .843 .538 .31 .837 .558 .843 .567 .852 .572 .856 .573 .858 .574 .32 .855 .596 .859 .603 .867 .608 .872 .608 .874 .610 .33 .871 .635 .875 .642 .882 .644 .887 .644 .888 .646 .34 .887 .674 .892 .680 .898 .682 .901 .683 .902 .684 .35 .902 .716 .908 .719 .912 .721 .915 .722 .914 .723 .36 .920 .755 .922 .761 .926 .760 .930 .760 .929 .761 .37 .934 .796 .936 .803 .940 .801 .942 .802 .942 .802 .38 .949 .838 .951 .844 .953 .842 .956 .843 .955 .843 .39 .964 .880 .965 .886 .966 .884 .968 .884 .968 .884 .40 .978 .925 .978 .928 .980 .928 .980 .928 .981 .928 .41 .991 .970 .991 .970 .992 .970 .992 .970 .993 .970 .417 .000 1.000 1.000 1.000 1.000 1.000 1.000 1.000 .000 .000 .42 .005 1.014 1.003 1.013 1.003 1.013 1.004 1.013 .004 .013 .43 .017 .058 .016 1.057 1.015 1.057 1.016 .057 .014 .057 .44 .030 .105 .028 1.105 1.026 1.102 1.027 .102 .023 .102 .45 .044 .153 .040 1.153 1.038 1.149 1.038 .145 .034 .145 .46 .057 .200 .051 1.200 1.049 1.195 1.048 .192 .045 .192 .47 .068 .248 .062 1.247 1.060 1.242 1.058 .240 .055 .239 .48 .079 .295 .073 1.294 1.070 1.287 1.068 1.283 .064 1.282 .49 .090 1.342 .084 1.341 1.079 1.335 1.078 1.330 1.073 1.327 .50 .101 1.393 .094 1.389 1.089 1.380 1.087 1.377 1.082 1.373 NOTE. For any diameter greater than 10 feet that is likely to be used in practice, the multipliers are practically the same as for the 10 feet diameter. There is a slight variation with the slope that is not accounted for in the above table. For slopes greater than .0005 the error is usually less than one per cent. For flatter slopes the error is somewhat greater. HYDRAULIC DIAGRAMS AND TABLES 169 Diameter of Flumes Steel Flumes ^=.012 .0001 30 40 50 60 708090100 150 200 250300350400 5006007008001000 Discharge (c.f.s.) FIG. 29 (Part 2 of 2). Discharge of Semicircular Steel Flumes. 170 WORKING DATA FOR IRRIGATION ENGINEERS Wood Pipe 31 oq cj '2 O O 00 t- O IS -4* CO Cl -I ' r-( O O O O 8dJd jo tnSuexi ^ooj oooi aod ;aoj FIG. 30 (Part 1 of 2). Flow of Water in Wood Stave Pipe. (See pages 65 to 69.) HYDRAULIC DIAGRAMS AND TABLES 171 O OJ 00 f 10 3 3 -255 2 QdJd jo "W 0001 -rod FIG. 30 (Part 2 of 2). Flow of Water in Wood Stave Pipe. 172 WORKING DATA FOR IRRIGATION ENGINEERS Cast Iron Pipe 8die J, :\l 4- ~- 7 ^ ^s ^S-L 1 XL ^ x [ V ? x~ ^ ?- ,7- 00 ' X s / x^ 0> L^^ 5 / - T^s~ ~"1 ^ / /^ V x^ V Tyj;~ , 5 x to Z_ x / ^ V f x ^ ^ r ' ''*/\ ! *S \ C^ y " * v / X, J X ^ / " ^ 1 / CO M 8 -f :^:: /I 5 y ^ x x x v^ 3| r?, ^ j j -^x- "*.2 OJ.Q w 9 < > 1 [[It X . x if X^ ~7 ^ N *x t " > x f or> ^ ^ >i V. obo \^ / s s V x y o g N^ / s ->J / N ^ ^o '' 9^ ^ ^x / ^ X v^ / x ^ ^" / ^ \ X I o / CO o M M . _ t ||!|! :::::::z ..,,_. C^ 3 . ^ rH 2 - .666 H % NOTE. For Contracted Weirs this diagram is not accurate for heads greater than one-third the crest-length. 184 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 27 DISCHARGE OVER SHARP-CRESTED VERTICAL WEIRS WITHOUT END CON- TRACTIONS, IN CUBIC FEET PER SECOND PER FOOT OF LENGTH OF WEIR FOR SMALL HEADS Head, in Feet Weir 0.5 Ft. High Weir 0.75 Ft. High Weir 1.00 Ft. High Weir 1 . 50 Ft. High Weir 2.00 Ft. High Weir 3.00 Ft. High Weir 4.00 Ft. High Weir 6.00 Ft. High 200 315 314 313 312 311 0.310 0.309 205 327 326 325 0.324 0.323 0.322 0.321 0.210 215 0.340 352 0.337 351 0.336 350 0.335 348 0.334 347 0.333 346 0.332 346 0.220 225 0.365 377 0.363 375 0.360 372 0.359 370 0.357 369 0.356 368 0.355 367 230 392 388 385 383 382 381 380 0.235 240 0.404 420 0.400 415 0.398 412 0.396 408 0.394 406 0.393 405 0.392 404 245 433 427 425 422 420 417 416 250 446 442 438 435 434 432 430 9 55 460 453 450 447 445 443 442 0.260 0.265 270 0.475 0.490 503 0.468 0.483 497 0.465 0.478 493 0.460 0.475 488 0.458 0.473 486 0.456 0.470 484 0.455 0.468 483 0.275 0.280 0.285 0.290 295 0.515 0.530 0.546 0.560 576 0.508 0.524 0.537 0.552 566 0.505 0.518 0.532 0.547 560 0.501 0.514 0.526 0.544 555 0.498 0.510 0.523 0.540 552 0.496 0.507 0.520 0.535 548 0.495 0.506 0.517 0.533 546 0.300 0.305 310 0.595 0.610 625 0.584 0.595 612 0.576 0.588 605 0.570 0.582 598 0.566 0.577 595 0.563 0.575 590 0.560 0.572 586 0.315 320 0.640 655 0.627 645 0.620 636 0.613 630 0.608 625 0.605 620 0.602 617 325 670 655 650 641 636 632 630 0'.330 0.335 340 0.690 0.705 720 0.672 0.690 705 0.665 0.680 697 0.656 0.670 688 0.652 0.665 683 0.647 0.660 675 0.645 0.657 673 0.345 350 0.738 755 0.720 735 0.710 726 0.703 717 0.696 712 0.692 705 0.687 702 0.355 0.360 0.365 0.370 375 0.770 0.790 0.805 0.824 840 0.752 0.772 0.786 0.802 817 0.743 0.760 0.775 0.792 805 0.732 0.750 0.764 0.780 795 0.725 0.745 0.757 0.775 790 0.720 0.737 0.750 0.766 782 0.717 0.733 0.746 0.762 777 380 860 836 825 813 805 798 795 0.385 0.390 395 0.875 0.896 910 0.853 0.870 885 0.840 0.857 870 0.826 0.845 860 0.820 0.837 852 0.810 0.830 845 0.806 0.825 838 0.400 0.405 0.410 0.415 0.420 0.930 0.950 0.970 0.990 1.005 0.905 0.922 0.940 0.956 0.975 0.893 0.910 0.925 0.943 0.958 0.875 0.895 0.910 0.925 0.943 0.870 0.885 0.903 0.917 0.935 0.860 0.875 0.895 0.908 0.924 0.855 0.870 0.885 0.903 0.917 0.850 0.860 0.876 0.895 0.910 NOTE. This table covers the same ground as the first fifteen lines of Table 28 but in greater detail. This table should not be used where the weir is submerged, nor unless the overfalling sheet is aerated on the downstream face of the weir. This table is reproduced by permission of the author, Prof. R. R. Lyman of the University of Utah. It was originally published in Trans. Am. Soc. C. E., 1914, and in a Bulletin of the U. of U. HYDRAULIC DIAGRAMS AND TABLES 185 TABLE 27 (Continued) DISCHARGE IN CUBIC FEET PER SECOND PER FOOT OF LENGTH OF WEIR Head, in Feet Weir 0.5 Ft. High Weir 0.75 Ft. High Weir 1.00 Ft. High Weir 1 . 50 Ft. High Weir 2.00 Ft. High Weir 3.00 Ft. High Weir 4.00 Ft. High Weir 6.00 Ft. High 0.425 ,020 0.995 0.977 0.963 0.952 0.942 0.935 0.926 0.430 .045 1.010 0.996 0.980 0.970 0.957 0.952 0.945 0.435 .065 1.030 1.010 0.996 0.986 0.975 0.970 0.960 0.440 .083 1.045 1.026 .010 1.000 0.992 0.985 0.976 0.445 .100 1.063 1.045 .026 1.015 1.005 1.000 0.994 0.450 .120 1.080 1.060 .040 1.030 1.015 1.010 .030 0.455 1.140 1.100 1.080 .057 1.047 1.035 1.023 .016 0.460 1.164 1.125 1.105 .085 1.074 1.056 1.050 .043 0.465 1.185 1.140 .120 .100 .090 .075 1.067 .057 0.470 .205 1.163 .143 .120 .106 .095 1.085 .077 0.475 .230 1.185 .162 .140 .125 .110 1.105 .096 0.480 .250 1.205 .185 .160 .150 .133 1.125 .115 0.485 .270 1.223 .200 .175 .163 .150 .140 .130 0.490 .290 1.245 .220 .200 .183 1.166 .160 .150 0.495 .310 1.265 .233 .215 .200 1.186 .176 1.166 0.500 .335 1.285 .263 .235 1.220 1.203 .195 1.185 0.505 .355 1.300 .280 1.250 1.236 1.220 .210 1.202 0.510 .370 1.320 .296 1.270 1.257 1.237 .225 1.220 0.515 .390 1.340 .317 1.287 1.274 1.255 .244 1.235 0.520 .415 1.360 1.335 1.305 1.290 1.273 1.260 .252 0.525 .440 1.380 1.355 1.325 1.310 1.290 1.280 .274 0.530 .465 1.405 1.375 1.346 1.330 1.310 1.300 .293 0.535 .490 1.425 1.400 1.365 1.353 1.335 1.320 .310 0.540 .510 1.440 1.415 1.385 1.365 .350 1.336 .327 0.545 .530 1.465 1.435 1.403 1.385 .365 1.355 .345 0.550 .555 1.490 1.460 1.425 1.405 .385 .370 .365 0.555 .575 1.505 1.475 1.440 .420 .400 .390 1.380 0.560 .595 1.525 1.495 1.460 .435 .415 .405 1.395 0.565 .616 1.545 1.515 1.475 .455 .435 .420 1.410 0.570 .640 1.570 1.535 1.500 .475 .455 .440 1.430 0.575 .665 1.590 1.555 1.517 .500 .475 .460 1.450 0.580 .686 1.610 1.576 1.537 .517 .495 .480 1.470 0.585 .713 1.635 1.605 1.565 .540 .520 .505 1.495 0.590 .740 1.670 1.630 1.590 .570 .545 .530 .523 0.595 .760 1.685 1.650 1.605 .585 .560 .543 .535 0.600 .790 1.700 1.675 1.625 .605 .580 .565 .555 0.605 .805 1.730 1.695 1.655 .627 .605 1.590 .580 0.610 .830 1.750 1.715 1.675 .650 .625 1.610 .600 0.615 .855 .775 1.735 1.695 .675 .650 1.630 .620 0.620 .880 .795 1.760 1.710 .690 .670 1.650 1.640 0.625 .905 .815 1.780 .730 .705 .685 1.670 1.665 0.630 .930 .845 1.805 .760 .730 .705 1.694 1.687 0.635 .955 .875 1.835 .785 .760 .725 1.710 1.700 0.640 .980 .900 1.860 .815 .790 .760 .740 1.730 0.645 2.010 .915 1.870 .820 .800 .770 .750 .740 0.650 2.035 .930 1.890 .840 .810 .780 .760 .750 0.655 2.060 .960 1.915 .860 .830 .805 .785 .775 0.660 2.085 .985 1.945 .890 .865 1.830 .815 .805 0.665 2.110 2.005 1.965 .910 .880 1.850 .830 .820 0.670 2.135 2.025 1.980 .930 .900 1.870 .850 .840 186 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 27 (Continued] DISCHARGE IN CUBIC FEET PER SECOND PER FOOT OF LENGTH OF WEIR Head, in Feet Weir . 5 Ft. High Weir 0.75 Ft. High Weir 1.00 Ft. High Weir 1.50 Ft. High Weir 2.00 Ft. High Weir 3.00 Ft. High Weir 4.00 Ft. High Weir 6.00 Ft. High 0.675 2.160 2.055 2.000 1.945 1.910 1.880 1.860 1.850 0.680 2.185 2.075 2.030 1.980 1.945 1.910 1.895 .885 0.685 2.210 2.095 2.050 1.990 1.960 1.925 1.905 .895 0.690 2.240 2.125 2.075 2.025 1.990 1.960 1.935 .925 0.695 2.260 2.150 2.095 2.040 2.005 1.970 1.945 .930 0.700 2.295 2.180 2.130 2.070 2.030 1.995 1.975 .965 0.705 2.325 2.200 2.155 2.100 2.065 2.025 2.000 .985 0.710 2.350 2.220 2.170 2.115 2.085 2.040 2.020 2.005 0.715 2.380 2.250 2.195 2.140 2.105 2.060 2.035 2.025 0.720 2.410 2.275 2.220 2.160 2.125 2.085 2.060 2.045 0.725 2.435 2.300 2.245 2.180 2.155 2.115 2.090 2.080 0.730 2.465 2.325 2.270 2.200 2.175 2.135 2.110 2.095 0.735 2.490 2.350 2.295 2.230 2.190 2.150 2.130 2.120 0.740 2.520 2.375 2.320 2.250 2.210 2.170 2.140 2.130 0.745 2.550 2.405 2.340 2.275 2.235 2.200 2.170 2.160 0.750 2.585 2.430 2.375 2.300 2.260 2.225 2.190 2.180 0.755 2.605 2.455 2.400 2.325 2.285 2.245 2.220 2.200 0.760 2.640 2.480 2.415 2.340 2.300 2.270 2.240 2.230 0.765 2.670 2.510 2.440 2.370 2.330 2.290 2.265 2.255 0.770 2.700 2.540 2.470 2.400 2.350 2.300 2.285 2.275 0.775 2.730 2.560 2.500 2.420 2.375 2.330 2.310 2.300 0.780 2.760 2.590 2.515 2.440 2.400 2.345 2.330 2.325 0.785 2.790 2.610 2.550 2.460 2.415 2.365 2.345 2.335 0.790 2.820 2.630 2.570 2.480 2.430 2.380 2.360 2.350 0.795 2.850 2.660 2.595 2.510 2.460 2.410 2.380 2.365 0.800 2.890 2.700 2.625 2.550 2.500 2.440 2.410 2.400 0.805 2.910 2.730 2.660 2.575 2.520 2.465 2.425 2.410 0.810 2.940 2.755 2.680 2.595 2.545 2.485 2.445 2.425 0.815 2.975 2.780 2.700 2.610 2.565 2.505 2.460 2.440 0.820 3.010 2.810 2.735 2.640 2.590 2.530 2.500 2.480 0.825 3.045 2.840 2.770 2.670 2.610 2.560 2.530 2.510 0.830 3.070 2.870 2.790 2.700 2.640 2,580 2.550 2.535 0.835 3.100 2.905 2.830 2.730 2.675 2.610 2.580 2.565 0.840 3.130 2.930 2.840 2.760 2.695 2.630 2.600 2.590 0.845 3.160 2 . 950 2.880 2.785 2.730 2.650 2.615 2.605 0.850 3.190 2.990 2.910 2.800 2.750 2.680 2.650 2.630 0.855 3.230 3.015 2.930 2.840 2.780 2.710 2.670 2.650 0.860 3.260 3.040 2.960 2.860 2.800 2.735 2.700 2.680 0.865 3.290 3.070 2.980 2.880 2.815 2.750 2.715 2.695 0.870 3.320 3.100 3.010 2.910 2.840 2.780 2.740 2.720 0.875 3.350 3.120 3.035 2.930 2.870 2.795 2.765 2.750 0.880 3.395 3.160 3.070 2.965 2.900 2.820 2.790 2.780 0.885 3.415 3.180 3.090 2.980 2.920 2.840 2.810 2.790 0.890 3.445 3.200 3.120 3.010 2.940 2.860 2.825 2.820 0.895 3.480 3.235 3.150 3.040 2.970 2.895 2.860 2.845 0.900 3.520 3.270 3.180 3.070 3.000 2.920 2.890 2.870 0.905 3.550 3.300 3.210 3.100 3.035 2.940 2.910 2.890 0.910 3.580 3.330 3.235 3.120 3.055 2.970 2.930 2.910 0.915 3.620 3.360 3.260 3.155 3.085 3.000 2.955 2.935 HYDRAULIC DIAGRAMS AND TABLES 187 TABLE 27 (Continued) DISCHARGE IN CUBIC FEET PER SECOND PER FOOT OF LENGTH OF WEIR Head, in Feet Weir 0.5 Ft. High Weir 0.75 Ft. High Weir 1.00 Ft. High Weir 1 . 50 Ft. High Weir 2.00 Ft. High Weir 3.00 Ft. High Weir 4.00 Ft. High Weir 6.00 Ft. High 0.920 3.655 3.390 3.290 3.180 3.110 3.030 2.980 2.960 0.925 3.690 3.420 3.325 3.210 3.140 3.055 3.010 2.990 0.930 3.720 3.445 3.350 3.230 3.160 3.075 3.030 3.010 0.935 3.760 3.480 3.380 3.250 3.180 3.100 3.060 3.040 0.940 3.800 3.510 3.405 3.290 3.210 3.130 3.080 3.060 0.945 3.830 3.540 3.430 3.315 3.240 3.150 3.110 3.090 0.950 3.870 3.580 3.470 3.350 3.260 3.180 3.140 3.120 0.955 3.900 3.610 3.500 3.380 3.295 3.200 3.165 3.140 0.960 3.940 3.640 3.540 3.400 3.325 3.235 3.190 3.170 0.965 3.980 3.680 3.570 3.430 3.355 3.260 3.210 3.190 0.970 4.010 3.700 3.590 3.450 3.370 3.275 3.235 3.200 0.975 4.040 3.740 3.625 3.490 3.405 3.310 3.270 3.250 0.980 4.080 3.770 3.650 3.520 3.430 3.330 3.290 3.270 0.985 4.120 3.800 3.690 3.555 3.460 3.365 3.320 3.300 0.990 4.150 3.830 3.710 3.580 3.480 3.380 3.340 3.320 0.995 4.180 3.850 3.730 3.590 3.510 3.400 3.360 3.330 1.000 4.230 3.900 3.780 3.640 3.555 3.440 3.400 3.375 1.010 4.300 3.970 3.840 3.710 3.600 3.500 3.450 3.420 1.020 4.380 4.030 3.900 3.760 3.670 3.560 3.500 3.480 1.030 4.450 4.100 3.970 3.820 3.720 3.600 3.560 3.540 1.040 4.520 4.170 4.040 3.880 3.780 3.670 3.620 3.590 1.050 4.610 4.240 4.120 3.950 3.850 3.730 3.670 3.650 1.060 4.800 4.320 4.180 4.020 3.910 3.790 3.740 3.710 1.070 4.760 4.370 4.220 4.070 3.960 3.830 3.770 3.750 1.080 4.820 4.430 4.280 4.130 4.010 3.890 3.820 3.800 .090 4.900 4.480 4.340 4.180 4.060 3.930 3.870 3.840 .100 4.980 4.570 4.420 4.240 4.140 3.990 3.940 3.910 .110 5.060 4.640 4.480 4.320 4.190 4.060 4.000 3.960 .120 5.150 4.710 4.560 4.370 4.240 4.120 4.050 4.010 .130 5.220 4.780 4.610 4.420 4.300 4.170 4.100 4.070 .140 5.300 4.840 4.670 4.480 4.360 4.210 4.160 4.130 1.150 5.380 4.910 4.740 4.560 4.420 4.270 4.210 4.180 1.160 5.450 4.980 4.. 800 4.610 4.480 4.330 4.260 4.220 1.170 5.510 5.050 4.870 4.670 4.540 4.380 4.320 4.280 1.180 5.600 5.130 4.950 4.740 4.610 4.440 4.380 4.340 1.190 5.680 5.200 5.000 4.800 4.660 4.500 4.420 4.400 .200 5.780 5.250 5.075 4.870 4.720 4.560 4.480 4.440 .210 5.860 5.340 4.150 4.940 4.780 4.610 4.540 4.500 .220 5.940 5.420 5.250 5.000 4.860 4.680 4.610 4.590 .230 6.000 5.460 5.270 5.050 4.910 4.720 4.640 4.610 .240 6.100 5.550 5.360 5.150 4.980 4.800 4.720 4.680 .250 6.200 5.620 5.430 5.220 5.050 4.860 4.780 4.740 .260 6.275 5.675 5.500 5.275 5.100 4.910 4.830 4.800 .270 5.750 5.560 5.325 5.180 4.970 4.890 4.850 .280 5.820 5.620 5.380 5.225 5.000 4.940 4.900 .290 5.900 5 680 5 450 5 275 5 075 5.000 4.960 .300 5.975 5.775 5.525 5.350 5.150 5.050 5.020 .310 6.060 5.850 5.600 5.425 5.225 5.130 5.080 .320 6.150 5.920 5.675 5.500 5.275 5.200 5.150 1.330 6.200 6.000 5.730 5.550 5.350 5.250 5.220 188 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 27 (Concluded) DISCHARGE IN CUBIC FEET PER SECOND PER FOOT OF LENGTH OF WEIR Head, in Feet Weir 0.5 Ft. High Weir 0.75 Ft. High Weir 1.00 Ft. High Weir 1.50 Ft. High Weir 2.00 Ft. High Weir 3.00 Ft. High Weir 4.00 Ft. High Weir 6.00 Ft. High .340 6.300 6.050 5.800 5.620 5.400 5.320 5.260 .350 .360 .370 .380 .390 .400 6.375 6.450 6.505 6.625 6.700 6.780 6.130 6.200 6.300 6.375 6.450 6.530 5.875 5.940 6.000 6.080 6.150 6.230 5.675 5.750 5.820 5.900 5.960 6.040 5.460 5.520 5.580 5.650 5.725 5.770 5.370 5.430 5.500 5.560 5.625 5.675 5.320 5.380 5.450 5.525 5.575 5.640 .410 .420 .430 .440 .450 .460 470 6.860 6.950 7.000 7.075 7.150 7.250 7 330 6.620 6.675 6.750 6.820 6.900 6.975 7 050 6.320 6.375 6.450 6.520 6.600 6.660 6 740 6.100 6.150 6.220 6.300 6.360 6.430 6 500 5.850 5.920 5.975 6.030 6.100 6.150 6 220 5.760 5.820 5.875 5.930 6.000 6.050 6 120 5.700 5.760 5.825 5.880 5.950 6.000 6 060 480 7 400 7 130 6 800 6 508 6 300 6 175 6 125 .490 .500 .510 .520 .530 7.480 7.600 7.660 7.750 7.825 7.200 7.300 7.360 7.450 7.520 6.850 6.950 7.020 7.100 7.160 6.640 6.720 6.775 6.850 6.930 6.330 6.420 6.500 6.550 6.640 6.230 6.300 6.360 6.450 6.520 6.160 6.250 6.300 6.360 6.460 .540 .550 .560 .570 .580 .590 7.900 7.980 8.075 8.150 8.250 8.300 7.600 7.660 7.730 7.820 7.900 7.960 7.230 7.300 7.400 7.450 7.525 7.560 7.000 7.040 7.120 7.180 7.250 7.300 6.680 6.740 6.800 6.860 6.940 6.975 6.575 6.625 6.700 6.740 6.800 6.850 6.500 6.560 6.630 6.680 6.750 6.780 Table 28 gives the discharge per foot of length over sharp-crested vertical weirs, without end contractions, of heights 2, 4, 6, 8, 10, 20, and 30 feet, computed from Bazin's formula. Al- though this formula is based on data obtained from experiments with heads not greater than 1.64 feet, discharges for heads of 4 feet and less computed thereby agree within 2 per cent with those obtained by use of the Fteley and Stearns formula. The discharge given by this table is corrected for velocity of approach, and the head to be used is that observed 16 feet or more upstream from the crest of the weir. HYDRAULIC DIAGRAMS AND TABLES TABLE 28 189 DISCHARGE PER FOOT OF LENGTH OVER SHARP-CRESTED VERTICAL WEIRS WITHOUT END CONTRACTIONS * [Computed from the formula Q = (o.405 + ^^) (l + 0.55 Lh \/2gh (h = observed head, in feet; p = height of weir, in feet; L = length of crest, in feet; Q = discharge, in second-feet.)] \p *\ 2 4 6 8 10 20 30 0.1 0.13 0.13 0.13 0.13 0.13 0.13 0.13 0.2 .33 .33 .33 .33 .33 .33 .33 0.3 .58 .58 .58 .58 .58 .58 .58 0.4 .88 .88 .87 .87 .87 .87 .87 0.5 1.23 1.21 1.21 1.21 1.21 1.20 1.20 0.6 1.62 1.59 1.58 1.58 1.57 1.57 1.57 0.7 2.04 1.99 1.98 1.98 1.97 1.97 1.97 0.8 2.50 2.43 2.41 2.41 2.40 2.40 2.40 0.9 3.00 2.90 2.88 2.86 2.86 2.85 2.85 1.0 3.53 3.40 3.36 3.35 3.34 3.33 3.33 1.1 4.10 3.93 3.88 3.86 3.85 3.84 3.83 1.2 4.69 4.48 4.42 4.40 4.38 4.36 4.36 1.3 5.32 5.07 4.99 4.96 4.94 4.92 4.91 1.4 5.99 5.68 5.58 5.55 5.52 5.49 5.48 1.5 6.69 6.30 6.20 6.16 6.13 6.08 6.07 1.6 7.40 6.97 6.84 6.78 6.75 6.69 6.68 1.7 8.15 7.66 7.50 7.43 7.39 7.33 7.31 1.8 8.93 8.37 8.18 8.09 8.05 7.98 7.96 1.9 9.74 9.11 8.89 8.79 8.74 8.65 8.63 2.0 10.58 9.87 9.62 9.51 9.44 9.34 9.32 2.1 11.44 10.65 10.37 10.24 10.17 10.05 10.02 2.2 12.33 11.46 11.14 10.99 10.91 10.78 10.75 2.3 13.25 12.29 11.93 11.77 11.67 11.52 11.48 2.4 14.20 13.15 12.75 12.56 12.45 12.28 12.24 2.5 15.18 14.03 13.59 13.37 13.25 13.06 13.02 2.6 16.17 14.92 14.44 14.20 14.07 13.85 13.80 2.7 17.19 15.84 15.31 15.05 14.90 14.65 14.60 2.8 18.23 16.79 16.21 15.92 15.76 15.48 15.42 2.9 19.29 17.75 17.12 16.81 16.63 16.32 16.25 3.0 20.38 18.74 18.06 17.71 17.52 17.18 17.10 3.1 21.50 19.74 19.01 18.64 18.42 18.05 17.96 3.2 22.64 20.77 19.98 19.58 19.34 18.93 18.83 3.3 23.80 21.82 20.98 20.54 20.28 19.83 19.72 3.4 24.98 22.89 21.99 21.52 21.24 20.75 20.63 3.5 26.20 23.98 23.01 22.51 22.22 21.69 21.55 3.6 27.42 25.09 24.06 23.52 23.20 22.62 22.48 3.7 28.67 26.23 25.13 24.55 24.21 23.58 23.43 3.8 29.94 27.38 26.22 25.60 25.23 24.56 24.39 3.9 31.23 28.55 27.32 26.66 26.27 . 25.54 25.37 4.0 32.54 29.74 28.45 27.74 27.32 26.55 26.35 4.1 33.87 30.96 29.59 28.84 28.39 27.56 27.34 4.2 35.22 32.18 30.75 29.96 29.48 28.59 28.35 4.3 36 ..59 33.43 31.92 31.09 30.58 29.63 29.38 4.4 37.99 34.70 33.12 32.24 31.70 30.68 30.42 * This table should not be used where the weir is submerged, nor unless the overfalling sheet is aerated on the downstream face of the weir. If a vacuum forms under the falling sheet the discharge may be 5 per cent greater than given in this table. 190 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 28 (Concluded) DISCHARGE PER FOOT OF LENGTH OVER SHARP-CRESTED VERTICAL WEIRS WITHOUT END CONTRACTIONS \J fc_N 2 4 6 8 10 20 30 4.5 39.40 35.98 34.33 33.40 32.83 31.74 31.47 4.6 40.83 37.29 35.56 34.58 33.98 32.82 32.53 4.7 42.28 38.61 36.80 35.78 35.14 33.92 33.61 4.8 43.75 39.96 38.07 37.00 36.32 35.04 34.70 4.9 45.23 41.32 39.35 38.23 37.52 36.17 35.80 5.0 46.73 42.69 40.65 39.48 38.74 37.21 36.91 5.1 48.25 44.09 41.96 40.73 39.97 38.45 38.03 5.2 49.79 45.50 43.29 42.01 41.20 39.61 39.17 5.3 51.36 46.93 44.64 43.30 42.45 40.78 40.31 5.4 52.94 48.38 46.00 44.60 43.71 41.96 41.47 5.5 54.54 49.85 47.38 45.93 45.00 43.16 42.64 5.6 56.15 51.34 48.79 47.27 46.31 44.38 43.83 5.7 57.78 52.83 50.19 48.62 47.62 45.60 45.02 5.8 59.42 54.34 51.62 49.99 48.94 46.83 46.22 5.9 61.09 55.88 53.07 51.38 50.29 48.08 47.44 6.0 62.77 57.43 54.53 52.78 51.64 49.34 48.67 6.1 64.46 59.00 56.00 54.20 53.02 50.61 49.91 6.2 66.18 60.58 57.50 55.63 54.40 51.90 51.16 6.3 67.91 62.18 59.01 57.07 55.80 53.20 52.42 6.4 69.65 63.79 60.53 58.53 57.22 54.50 53.70 6.5 71.42 65.42 62.07 60.01 58.65 55.82 54.98 6.6 73.19 67.07 63.63 61.50 60.09 57.16 56.27 6.7 74.99 68.74 65.20 63.00 61.55 58.50 57.58 6.8 76.80 70.42 66.78 64.53 63.02 59.96 58.90 6.9 78.62 72.11 68.38 66.06 64.50 61.23 60.22 7.0 80.46 73.82 70.00 67.60 66.00 62.61 61.56 7.1 82.32 75.55 71.63 69.17 67.52 64.00 62.91 7.2 84.18 77.29 73.28 70.74 69.04 65.40 64.27 7.3 86.07 79.04 74.94 72.34 70.58 66.81 65.64 7.4 87.97 80.81 76.61 73.94 72.14 68.24 67.02 7.5 89.89 82.60 78.30 75.56 73.70 69.68 68.41 7.6 91.82 84.40 80.01 77.19 75.28 71.13 69.81 7.7 93.76 86.22 81.73 78.84 76.88 72.59 71.23 7.8 95.72 88.05 83.46 80.50 78.48 74.06 72.65 7.9 97.70 89.90 85.21 82.18 80.11 75.55 74.09 8.0 99.68 91.75 86.97 83.87 81.74 77.04 75.53 8.1 101.69 93.63 88.75 85.57 83.39 78.55 76.98 8.2 103.70 95.51 90.54 87.29 85.25 80.06 78.44 8.3 105.73 97.42 92.34 89.02 86.72 81.59 79.92 8.4 107.78 99.34 94.16 90.76 88.41 83.13 81.40 8.5 109.84 101.27 96.00 92.52 90.11 84.69 82.90 8.6 111.91 103.21 97.84 94.29 91.82 86.25 84.41 8.7 113.99 105.17 99.70 96.07 93.55 87.82 85.92 8.8 116.09 107.14 101.57 97.87 95.28 89.40 87.44 8.9 118.20 109.13 103.46 99.68 97.04 91.00 88.98 9.0 120.33 111.13 105.36 101.50 98.80 92.61 90.52 9.1 122.47 113.15 107.28 103.34 100.58 94.23 92.08 9.2 124.62 115.18 109.21 105.19 102.37 95.86 93.65 9.3 126.79 117.22 111.15 107.06 104.17 97.49 95.22 9.4 128.97 119.27 113.10 108.93 105.99 99.14 96.80 9.5 131.16 121.34 115.07 110.82 107.82 100.80 98.40 9.6 133.36 123.42 117.05 112.72 109.65 102.48 100.00 9.7 135 . 58 125.51 119.04 114.64 111.50 104.16 101.62 9.8 137.82 127.63 121.05 116.57 113.37 105.85 103.25 9.9 140.06 129.74 123.07 118.51 115.25 107.56 104.88 10.0 142.31 131.87 125.10 120.46 117.14 | 109.27 106.52 HYDRAULIC DIAGRAMS AND TABLES 191 Tables 28A, 28B, and 28C give multipliers to be applied to quantities in Table 28 to determine the discharge over broad- crested weirs of various types and dimensions. Example: Sup- pose the discharge is to be computed over a rectangular weir that is 10 feet long, 12 feet high, 6 feet crest width, and has an observed head of 2.4 feet. Table 28 shows that for a height (p) of 12 feet and a head (ti) of 2.4, the discharge is 12.42 second- feet. Table 28A shows that for a height (p) of 12 feet, a crest width (c) of 6 feet, and head (ti) of 2.4 feet the multiplier is 0.797. Hence, the discharge is 12.42 X 0.797 X 10 = 99.0 second-feet. 192 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 28A MULTIPLIERS OF DISCHARGE OVER RECTANGULAR WEIR, BROAD-CRESTED (TYPE a, SEE FIGURE) [p = height of weir; c = width of crest; h = observed head; all in feet] P c 4.6 2.6 4.6 6.6 11.25 .48 11.25 .93 11.25 1.65 11.25 3.17 11.25 5.88 11.25 8.98 11.25 12.24 11.25 16.30 h 0.5 .821 .792 .806 .792 .799 .801 .786 .790 1.0 '.765 !708 .997 .899 .808 .795 .791 .794 .815 .790 1.5 .789 .709 1.00 .982 .878 .796 .796 .793 .814 .792 2.0 .814 .710 1.00 .00 .906 .815 .797 .792 .797 .793 2.5 .835 .711 1.00 .00 .985 .844 .797 .790 .796 .793 3.0 .857 .711 1.00 .00 1.00 .870 .797 .788 .794 .791 3.5 .878 .712 1.00 .00 .00 .90 .812 .787 .794 .791 4.0 .899 .714 1.00 .00 .00 .93 .834 .786 .792 .789 5.0 .940 .716 1.00 .00 .00 .97 (a) .78 .79 .78 6.0 .986 .718 1.00 .00 .00 .98 (a) .78 .78 .78 7.0 1.00 .00 .00 (a) (a) .77 .78 .77 8.0 1.00 .00 .00 (a) (a) .77 .77 .77 9.0 1.00 .00 .00 (a) (a) .77 .77 .77 10.0 1.00 .00 1.00 (a) (a) .77 .77 .77 (a) Value doubtful. TABLE 28B MULTIPLIERS OF DISCHARGE FOR TRAPEZOIDAL WEIRS [p = height of weir, in feet; c = width of crest, in feet; s = upstream slope; s' = downstream slope; h = observed head, in feet] Type b (see Figure) (see Figure) P c s s' 4.9 .33 2:1 4.9 .66 2:1 4.9 .66 3:1 4.9 .66 4:1 4.9 .66 5:1 4.9 .33 2:1 5:1 4.9 .66 2:1 2:1 4.65 7.00 4.67:1 11.25 6.00 6:1 h 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 6.0 7.0 8.0 9.0 10.0 .137 .131 .120 .106 .094 .085 .072 .064 1.048 1.068 1.080 1.085 1.088 1.087 1.084 1.081 .066 .066 .061 .052 .047 .043 .038 .035 1.039 1.039 1.033 1.026 1.020 1.017 1.012 1.009 1.009 1.009 1.005 .997 .991 .988 .984 .980 1.095 1.071 1.044 1.024 1.009 1.003 1.014 1.023 .071 .066 .053 .047 .047 1.050 1.052 1.055 1.042 1.033 1.024 1.012 .995 .983 .977 .974 .97 .97 .97 .96 .96 .96 1.060 1.069 1.054 1.012 .985 .979 .976 .973 .97 .96 .96 .95 .95 .95 HYDRAULIC DIAGRAMS AND TABLES TABLE 28C MULTIPLIERS OF DISCHARGE FOR COMPOUND WEIRS [p = height of weir, in feet; h = observed head, in feet] 193 p 4.57 4.56 4.53 5.28 11.25 11.25 11.25 11.25 11.25 11.25 Type (see Figure) d - / g h i J k / m h 5 .941 .924 .933 .962 .971 .947 1.0 1.5 2.0 2.5 3.0 3.5 4.0 5.0 6.0 .842 .866 .888 .906 .927 .945 .965 1.00 .836 .834 .831 .826 .822 .817 .812 .80 .929 .950 .953 .947 .942 .936 .931 .92 .976 .979 .988 1.000 1.016 1.032 1.044 1.05 1.039 1.087 1.109 1.118 1.120 1.127 .123 .11 .11 .033 .093 .133 .153 .163 .169 .165 1.16 1.15 .988 1.018 1.033 1.045 1.054 1.060 1.060 1.05 1.04 1.045 1.066 1.063 1.020 .997 .994 .991 .98 .98 1.033 1.042 1.035 1.033 1.045 1.054 1.057 1.05 1.04 .000 .036 .063 .085 .096 .108 .110 .10 .10 7.0 .10 1.14 1.04 .97 1.04 .09 8.0 .10 1.14 1.04 .97 1.03 .09 9.0 .09 1.14 1.03 .97 1.03 .08 10.0 .09 1.13 1.03 .97 1.03 1.08 194 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 29 ACRE-FEET EQUIVALENT TO A GIVEN NUMBER OF SECOND-FEET FLOWING FOR A GIVEN LENGTH OF TIME Second- Feet DAYS OF 24 HOURS 1 2 3 4 5 6 7 8 9 10 0.01 0.0198 .0396 0.0595 .0793 .0991 .1190 .1388 .1586 .1785 .1983 .02 .0396 .0793 .1190 .1586 .1983 .2380 .2776 .3173 .3570 .3966 .03 .0595 .1190 .1785 .2380 .2975 .3570 .4165 .4760 .5355 .5950 .04 .0793 .1586 .2380 .3173 .3966 .4760 .5553 .6347 .7140 .7933 .05 .0991 .1983 .2975 .3966 .4958 .5950 .6942 .7933 .8925 .9917 .06 .1190 .2380 .3570 .4760 .5950 .7140 .8330 .9520 1.071 1.190 .07 .1388 .2776 .4165 .5553 .6942 .8330 .9719 1.110 1.249 1.388 .08 .1586 .3173 .4760 .6347 .7933 .9520 1.110 1.269 1.428 1.586 .09 .1785 .3570 .5355 .7140 .8925 1.071 1.249 1.428 1.606 1.785 .10 .1983 .3966 .5950 .7933 .9917 1.190 1.388 1.586 1.785 1.983 .11 .2181 .4363 .6545 .8727 1.090 1.309 1.527 1.745 1.963 2.181 .12 .2380 .4760 .7140 .9520 1.190 1.428 1.666 1.904 2.142 2.380 .13 .2578 .5157 .7735 1.031 1.289 1.547 1.804 2.022 2.320 2.578 .14 .2776 .5553 .8330 1.110 1.388 1.666 1.943 2.221 2.499 2.776 .15 .2975 .5950 .8925 1.190 1.487 1.785 2.082 2.380 2.677 2.975 .16 .3173 .6347 .9520 1.269 1.586 1.904 2.221 2.538 2.856 3.173 .17 .3371 .6743 1.011 1.348 1.685 2.023 2.360 2.697 2.034 3.371 .18 .3570 .7140 1.071 1.428 1.785 2.142 2.499 2.856 3.213 3.570 .19 .3768 .7537 1.130 1.507 1.884 2.261 2.638 3.014 3.391 3.768 .20 .3966 .7933 1.190 1.586 1.983 2.380 2.776 3.173 3.570 3.966 .21 .4165 .8330 1.249 1.666 2.082 2.499 2.915 3.332 3.748 4.165 .22 .4363 .8727 1.309 1.745 2.181 2.618 3.054 3.490 3.927 4.363 .23 .4562 .9124 1.368 1.824 2.280 2.737 3.193 3.649 4.105 4.561 .24 .4760 .9520 1.428 1.904 2.380 2.856 3.332 3.808 4.284 4.760 .25 .4958 .9917 1.487 1.983 2.479 2.975 3.471 3.966 4.462 4.958 .26 .5157 1.031 1.547 2.062 2.578 3.094 3.609 4.125 4.641 5.157 .27 .5355 1.071 1.606 2.142 2.677 3.213 3.748 4.284 4.819 5.355 .28 .5553 1.110 1.666 2.221 2.776 3.332 3.887 4.442 4.998 5.553 .29 .5752 1.150 1.725 2.300 2.876 3.451 4.026 4.601 5.176 5.752 .30 .5950 1.190 1.785 2.380 2.975 3.570 4.165 4.760 5.355 5.950 .31 .6148 1.229 1.844 2.459 3.074 3.689 4.304 4.919 5.533 6.148 .32 .6347 1.269 1.904 2.538 3.173 3.808 4.442 5.077 5.712 6.347 .33 .6545 1.309 1.963 2.618 3.272 3.927 4.581 5:236 5.890 6.545 .34 .6743 1.348 2.023 2.697 3.371 4.046 4.720 5.395 6.069 6.743 .35 .6942 1.388 2.082 2.776 3.471 4.165 4.859 5.553 6.247 6.942 .36 .7140 1.428 2.142 2.856 3.570 4.284 4.998 5.712 6.426 7.140 .37 .7338 1.467 2.201 2.935 3.669 4.403 5.137 5.871 6.604 7.338 .38 .7537 1.507 2.261 3.014 3.768 4.522 5.276 6.029 6.783 7.537 .39 .7735 1.547 2.320 3.094 3.867 4.641 5.414 6.188 6.961 7.735 .40 .7933 1.586 2.380 3.173 3.966 4.760 5.553 6.347 7.140 7.933 .41 .8132 1.626 2.439 3.252 4.066 4.879 5.692 6.505 7.319 8.132 .42 .8330 1.666 2.499 3.332 4.165 4.998 5.831 6.664 7.497 8.330 .43 .8528 1.705 2.558 3.411 4.264 5.117 5.970 6.823 7.676 8.528 .44 .8727 1.745 2.618 3.490 4.363 5.236 6.109 6.981 7.854 8.727 .45 .8925 1.785 2.677 3.570 4.462 5.355 6.247 7.140 8.033 8.925 .46 .9124 1.824 2.737 3.649 4.561 5.474 6.386 7.299 8.211 9.123 .47 .9322 1.864 2.796 3.728 4.661 5.593 6.525 7.457 8.390 9.322 .48 .9520 1.904 2.856 3.808 4.760 5.712 6.664 7.616 8.568 9.520 .49 .9719 1.943 2.915 3.887 4.859 5.831 6.803 7.775 8.747 9.719 0.50 0.9917 1.983 2.975 3.966 4.958 5.950 6.942 7.933 8.925 9.917 NOTE. For larger quantities and greater number of days than given in this table it is only necessary to move the decimal point, thus, for .25 c. f. s. flowing six days we read the equivalent 2.975 acre-feet and for 25 c. f. s. the equivalent in acre -feet is 297.5. Again, .25 c. f. s. flowing sixty days = 29.75 acre-feet and 25 c. f. s. flowing sixty days = 2975 acre-feet, etc., etc. HYDRAULIC DIAGRAMS AND TABLES 195 TABLE 29 (Concluded) ACRE-FEET EQUIVALENT TO A GIVEN NUMBER OF SECOND-FEET FLOWING FOR A GIVEN LENGTH OF TIME Second- Feet DAYS OF 24 HOURS 1 2 3 4 5 6 7 8 9 10 0.51 1.011 2.023 3.034 4.046 5.057 6.069 7.080 8.092 9.104 10.115 .52 1.031 2.062 3.094 4.125 5.157 6.188 7.219 8.251 9.282 10.314 .53 1.051 2.102 3.153 4.204 5.256 6.307 7.358 8.409 9.461 10.519 .54 1.071 2.142 3.213 4.284 5.355 6.426 7.497 8.568 9.639 10.710 .55 1.090 2.181 3.272 4.363 5.454 6.545 7.636 8.727 9.818 10.909 .56 1.110 2.221 3.332 4.442 5.553 6.664 7.775 8.885 9.996 11.107 .57 1.130 2.261 3.391 4.522 5.652 6.783 7.914 9.044 10.175 11.305 .58 1.150 2.300 3.451 4.601 5.752 6.902 8.052 9.203 10.353 11.504 .59 1.170 2.340 3.510 4.680 5.851 7.021 8.191 9.361 10.532 11.702 .60 1.190 2.380 3.570 4.760 5.950 7.140 8.330 9.520 10.710 11.900 .61 1.209 2.419 3.629 4.839 6.049 7.259 8.469 9.679 10.889 12.099 .62 1.229 2.459 3.689 4.919 6.148 7.378 8.608 9.838 11.067 12.297 .63 1.249 2.499 3.748 4.998 6.247 7.497 8.747 9.996 11.246 12.495 .64 1.269 2.538 3.808 5.077 6.347 7.616 8.885 10.155 11.424 12.694 .65 1.289 2.578 3.867 5.157 6.446 7.735 9.024 10.314 11.603 12.892 .66 1.309 2.618 3.927 5.236 6.545 7.854 9.163 10.472 11.781 13.090 .67 1.328 2.657 3.986 5.315 6.644 7.973 9.302 10.631 11.960 13.289 .68 1.348 2.697 4.046 5.395 6.743 8.092 9.441 10.790 12.138 13.487 .69 1.368 2.737 4.105 5.474 6.842 8.211 9.580 10.948 12.317 13.685 .70 1.388 2.776 4.165 5.553 6.942 8.330 9.719 11.107 12.495 13.884 .71 1.408 2.816 4.224 5.633 7.041 8.449 9.857 11.266 12.674 14.082 .72 1.428 2.856 4.284 5.712 7.140 8.568 9.996 11.424 12.852 14.280 .73 1.447 2.895 4.343 5.791 7.239 8.687 10.135 11.583 13.031 14.479 .74 1.467 2.935 4.403 5.871 7.338 8.806 10.274 11.742 13.209 14.677 .75 1.487 2.975 4.462 5.950 7.438 8.925 10.413 11.900 13.388 14.876 .76 1.507 3.014 4.522 6.029 7.537 9.044 10.552 12.059 13.566 15.074 .77 1.527 3.054 4.581 6.109 7.636 9.163 10.690 12.218 13.745 15.272 .78 1.547 3.094 4.641 6.188 7.735 9.282 10.829 12.376 13.923 15.471 .79 1.566 3.133 4.700 6.267 7.834 9.401 10.968 12.535 14.102 15.669 .80 1.586 3.173 4.760 6.347 7.933 9.520 11.107 12.694 14.280 15.867 .81 1.606 3.213 4.819 6.426 8.033 9.639 11.246 12.852 14.459 16.066 .82 1.626 3.252 4.879 6.505 8.132 9.758 11.385 13.011 14.638 16.264 .83 1.646 3.292 4.938 6.585 8.231 9.877 11.523 13.170 14.816 16.462 .84 1.666 3.332 4.998 6.664 8.330 9.996 11.662 13.328 14.995 16.661 .85 1.685 3.371 5.057 6.743 8.429 10.115 11.801 13.487 15.173 16.859 .86 1.705 3.411 5.117 6.823 8.528 10.234 11.940 13.646 15.352 17.057 .87 1.725 3.451 5.176 6.902 8.628 10.353 12.079 13.804 15.530 17.256 .88 1.745 3.490 5.236 6.981 8.727 10.472 12.218 13.963 15.709 17.454 .89 1.765 3.530 5.295 7.061 8.826 10.591 12.357 14.122 15.887 17.652 .90 1.785 3.570 5.355 7.140 8.925 10.710 12.495 14.280 16.066 17.851 .91 1.804 3.609 5.414 7.219 9.024 10.829 12.634 14.439 16.244 18.049 .92 1.824 3.649 5.474 7.299 9.123 10.948 12.773 14.598 16.423 18.247 .93 1.844 3.689 5.533 7.378 9.223 11.067 12.912 14.757 16.601 18.446 .94 .864 3.728 5.593 7.457 9.322 11.186 13.051 14.915 16.780 18.644 .95 .884 3.768 5.652 7.537 9.421 11.305 13.190 15.074 16.958 18.842 .96 .904 3.808 5.712 7.616 9.520 11.424 13.328 15.233 17.137 19.041 .97 .923 3.847 5.771 7.695 9.619 11.543 13.467 15.391 17.315 19.239 .98 .943 3.887 5.831 7.775 9.719 11.662 13.606 15.550 17.494 19.438 .99 1.963 3.927 5.890 7.854 9.818 11.781 13.745 15.709 17.672 19.636 1.00 1.983 3.966 5.950 7.933 9.917 11.900 13.884 15.867 17.851 19.834 196 WORKING DATA FOR IRRIGATION ENGINEERS Water Duty 300 1 | *P 9 .2 I g m P I" Z 70 g 35 30 40 < / / 50 60 70 80 90 100 150 A = Area in Acres Supplied by One Second Foot 200 FIG. 38. Diagram for Converting "Acres per Second-foot" to "Depth of 1 9835 ^V Water Applied in Given Length of Time," W = - L ^ HYDRAULIC DIAGRAMS AND TABLES 197 *1 ' ' I M 3 g " ! "3."oJ p g'Ogg ^ . .,;' iilljl ^ll!|; 1 |l1'1l ^ <1 C) 2 2 "^ ""S "o- PQ "cS'cS'S^S^^ "^ w < P H S llllJlJl 11 p H H ffi J > Q g 1 B Ht i > s. (N o 10 i2 -s* 11 K: !, II II fcj H^ ic o HYDRAULIC DIAGRAMS AND TABLES 199 *; -r) 0) 0) gt. SO S a ^ra Wa 5 8 S H| Hi O esS II II K H5 1 U | _ u. . o :> u. ^cn o ^cn to . a .tn ^ ro "in P ">-i tti "in D ">-i r-i "^ o^ooo-go^ + ^ H O Kl O5 O i-H 200 WORKING DATA FOR IRRIGATION ENGINEERS CHAPTER V STRUCTURAL DIAGRAMS AND TABLES CHAPTER V STRUCTURAL DIAGRAMS AND TABLES Fig. 39 gives the volume of excavation and embankment in cubic yards per 100 feet for small canals in ground which is level transversely. In deriving the equations for volume of embankment two cases must be considered: Case I, where the bed of canal is below the ground surface; and Case II, where Ground Surface "//WyvvW'Mvy Case II TYPICAL SECTIONS the bed of canal is above the ground surface. The two cases are illustrated in the accompanying figure. Case I. Equations: Cut V = 3.7 (b c + 1.5 c 2 ), in cubic yds. per 100 ft. Fill F! = 7.4 [a(d + h-c) + l.5(d + h- c) 2 ] Example: Assume 6 = 3 c = 2 Enter the diagram with these arguments and read directly cut V = 44 cubic yards. To get the " fill," enter the diagram at c = 2, follow the diagonal line from this point to its intersec- tion with the vertical line marked d + h = 3 ; thence horizontally to the right to the curve marked "a = 2 " and read on the upper scale Vi = 26. The cut in this case exceeds the fill, and the former is, therefore, the controlling factor. For a cut c of 1 foot the excavation is found to be 13 cubic yards and the fill 73 203 204 WORKING DATA FOR IRRIGATION ENGINEERS cubic yards. In this case the fill is the controlling factor, as it exceeds the cut by 60 cubic yards. Case II. In this case the canal is entirely in fill, and two quantities jnust be looked out from the diagram to make up the total fill. In calculating fills, the simplest process is to calculate the sum of the two embankments considered as full trapezoidal sections with bases'" a" Referring to the diagram, it will be seen that for the condition there represented as " Case II," we must deduct from the total quantity thus obtained the volume of the lower shaded triangular prism, and add the volume of the upper shaded triangular prism. The algebraic sum of these two triangular prisms may be either positive, negative, or zero, depending upon whether the upper prism is greater than, less than, or equal to the lower prism. The general equation for this sum is E = - .617 [(3 d - b) 2 - 6 2 J. The plot of this equation on the diagram shows the positive values of E on the left of the vertical axis, negative values on the right, and zero values at the intersection of curves with the vertical axis. The complete equation for embankment in Case II is: Total volume = Fi + E = 7.4 [a (d + h + a) + l.5(d + h + Ci) 2 ] -0.617 [(3 ci-6) 2 -6 2 Example: Assume b = 2 To get FI, enter the diagram at c\ = 2 or c = 2; thence follow the diagonal line to d + h = 2; thence horizontally to the right to the curve marked a = 2 and read on the lower scale Fi = 237 c.y. Now to get E, enter the diagram at the same point, Ci = 2; thence horizontally to the right to the curve for E marked b = 2 and read 8 c.y. The net fill, then, is Fi + E = 237 - 8 = 229 c.y. If b = 3 and the other factors remain the same, E = zero, and if b = 3.5, E = + 4, the value of Fi remaining the same in all three cases, as it is independent of the bottom width of canal. STRUCTURAL DIAGRAMS AND TABLES 205 FIG. 39. Volume of Excavation and Embankment for Small Canals in Level Gu Jid. 206 WORKING DATA FOR IRRIGATION ENGINEERS The object of using two different scales for the values of Vi is merely to shorten up the diagram, the lower set of curves for Vi being a continuation of the four upper curves, and the lower scale a continuation of the upper. Fig. 39 illustrates a simple and rapid means of calculating embankment quantities on level ground. This particular diagram is offered principally as an illustration of the manner of plotting the equations, rather than for practical usefulness, although it may be considered fairly accurate for the range of values of the various factors that it covers. It will be found, however, that for continuous use such a scale is rather hard on the eyes, and larger scales are desirable, which for obvious reasons are not used here. Tables 31 to 34 give the volume of excavation in cubic yards per 100 feet of length for various center depths and side slopes, assuming the ground to be level transversely. The volume required is the difference between two triangular prisms. In the figure below is shown the cross-section of a canal that has a bottom width of 18 feet and side slopes of l| to 1. The amount of material in the prism C B F E is equal to the volume of the prism ACE minus the volume of the prism A B F. As A C E has an altitude of 16 feet and A B F has an altitude of 6 feet, the volume of each for a length of 100 feet can be obtained from the table. Opposite 16 in Table 32 is 1,422, which is the volume in cubic feet of A C E per 100 linear feet; opposite 6 is 200, which is the volume of A B F. As C BF E = AC E- A B F C BF E = 1,422- 200 = 1,222 cubic yards When working up quantities for canal excavation the volume of A B F need not be subtracted at each station, but need STRUCTURAL DIAGRAMS AND TABLES 207 be subtracted only when a change of canal section or classifica- tion of material occurs. When this is done, it is obvious that the volume to be subtracted is the volume of A B F per 100-foot station multiplied by the number of stations covered. No inter- polation is necessary, as the cuts are never measured closer than the nearest 0.1 foot. Tables 35 to 37 give the volume of excavation in cubic yards per 100 feet of length, where the surface slopes transversely, for various center depths and side slopes. They differ from Tables 31 to 34 only in that the earth surface is sloping ground instead of being level transversely. The surface slope is expressed in per cent, a 10 per cent slope being 10 vertical to 100 horizontal. In the above figure is shown a section of canal in sloping ground. The depth of center cut to A is 18 feet; entering Table 36, with a depth of 18, we read the volume of C A E = 1841. The volume of B A F is always read from the tables for level cut; this volume is found in Table 32 to be 200 cubic yards. The volume of the canal prism per 100 feet is, therefore, C A E- BAF = 1841 - 200 = 1641 cubic yards. When working up quantities for canal excavation, the volume of B A F need not be subtracted at each station, but need be subtracted only when a change of canal section or classification of material occurs. When this is done, it is obvious that the volume to be subtracted is the volume of B A F per 100-foot station multiplied by the number of stations covered. 208 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 31 AMOUNT OF MATERIAL IN CUBIC YARDS PER 100 LINEAR FEET OF LEVEL CUT Side Slopes 1 to 1 Depth of || Center Cut, in Feet 0. l. 2." 3. 4. 5. 6. .7 .8 .9 0.0 0.0 0.1 0.3 0.6 0.9 1.3 1.8 2.4 3.0 1 3.7 4.5 5.3 6.3 7.3 8.3 9.5 10.7 12.0 13.4 2 15 16 18 20 21 23 25 27 29 31 3 33 36 38 40 43 45 48 51 54 56 4 59 62 65 68 72 75 78 82 85 89 5 93 96 100 104 108 112 116 120 125 129 6 133 138 142 147 152 156 161 166 171 176 7 181 187 192 197 203 208 214 220 225 231 8 237 243 249 255 261 268 274 280 287 293 9 300 307 313 320 327 334 341 349 356 363 10 370 378 385 393 401 408 416 424 432 440 11 448 456 465 473 481 490 498 507 516 524 12 533 542 551 560 569 579 588 597 607 616 13 626 636 645 655 665 675 685 695 705 716 14 726 736 747 757 768 779 789 800 811 822 15 833 844 856 867 878 890 901 913 925 936 16 948 960 972 984 996 ,008 1,021 1,033 ,045 1,058 17 ,070 1,083 ,096 1,108 ,121 ,134 ,147 1,160 ,173 ,187 18 ,200 1,213 ,227 1,240 ,254 ,268 ,281 1,295 ,309 ,323 19 ,337 ,351 ,365 1,380 ,394 ,408 ,423 1,437 ,452 ,467 20 ,481 ,496 ,511 1,526 ,541 ,556 ,572 1,587 ,602 ,618 21 ,633 ,649 ,665 1,680 ,696 ,712 ,728 1,744 ,760 ,776 22 1,793 ,809 ,825 1,842 1,858 ,875 1,892 1,908 1,925 ,942 23 1,959 ,976 1,993 2,011 2,028 2,045 2,063 2,080 2,098 2,116 24 2,133 2,151 2,169 2,187 2,205 2,223 2,241 2,260 2,278 2,296 25 2,315 2,333 2,352 2,371 2,389 2,408 2,427 2,446 2,465 2,484 26 2,504 2,523 2,542 2,562 2,581 2,601 2,621 2,640 2,660 2,680 27 2,700 2,720 2,740 2,760 2,781 2,801 2,821 2,842 2,862 2,883 28 2,904 2,924 2,945 2,966 2,987 3,008 3,029 3,051 3,072 3,093 29 3,115 3,136 3,158 3,180 3,201 3,223 3,245 3,267 3,289 3,331 30 3,333 3,356 3,378 3,400 3,423 3,445 3,468 3,491 3,513 3,536 31 3,559 3,582 3,605 3,628 3,652 3,675 3,698 3,722 3,745 3,769 32 3,793 3,816 3,840 3,864 3,888 3,912 3,936 3,960 3,985 4,009 33 4,033 4,058 4,082 4,107 4,132 4,156 4,181 4,206 4,231 4,256 34 4,281 4,307 4,332 4,357 4,383 4,408 4,434 4,460 4,485 4,511 35 4,537 4,563 4,589 4,615 4,641 4,668 4,694 4,720 4,747 4,773 36 4,800 4,827 4,853 4,880 4,907 4,934 4,961 4,988 5,016 5,043 37 5,070 5,098 5,125 5,153 5,181 5,208 5,236 5,264 5,292 5,320 38 5,348 5,376 5,405 5,433 5,461 5,490 5,518 5,547 5,576 5,604 39 5,633 5,662 5,691 5,720 5,749 5,779 5,808 5,837 5,867 5,896 40 5,926 5,956 5,985 6,015 6,045 6,075 6,105 6,135 6,165 6,196 41 6,226 6,256 6,287 6,317 6,348 6,379 6,409 6,440 6,471 6,502 42 6,533 6,564 6,596 6,627 6,658 6,690 6,721 6,763 6,785 6,816 43 6,848 6,880 6,912 6,944 6,976 7,008 7,041 7,073 7,105 7,138 44 7,170 7,203 7,236 7,268 7,301 7,334 7,367 7,400 7,433 7,467 45 7,500 7,533 7,567 7,600 7,634 7,668 7,701 7,735 7,769 7,803 46 7,837 7,871 7,905 7,940 7,974 8,008 8,043 8,077 8,112 8,147 STRUCTURAL DIAGRAMS AND TABLES 209 TABLE 31 (Concluded) AMOUNT OF MATERIAL IN CUBIC YARDS PER 100 LINEAR FEET OF LEVEL CUT Side Slopes 1 to 1 3 47 48 49 50 51 52 53 54 55 56 57 58 59 60 .0 .1 * .3 .4 .5 .6 .7 .8 .9 8,181 8,533 8,216 8,569 8,251 8,605 8,286 8,640 8,321 8,676 8,356 8,712 8,392 8,748 8,427 8,784 8,462 8,820 8,498 8,856 8,893 8,929 8,965 9,002 9,038 9,075 9,112 9,148 9,185 9,222 9,259 9,296 9,333 9,371 9,408 9,445 9,483 9,520 9,558 9,596 9,633 9,671 9,709 9,747 9,785 9,823 9,861 9,900 9,938 9,976 10,015 10,053 10,092 10,131 10,169 10,208 10,247 10,286 10,325 10,364 10,404 10,443 10,482 10,522 10,561 10,601 10,641 10,680 10,720 10,760 10,800 10,840 10,880 10,920 10,961 11001 11,041 11,082 11,122 11,163 11,204 11,244 11,285 11,326 11,367 11,408 11,449 11,491 11,532 11,573 11,615 11,656 11,698 11,740 11,781 11,823 11,865 11,907 11,949 11,991 12,033 12,076 12,118 12,160 12,203 12,245 12,288 12,331 12,373 12,416 12,459 12,502 12,545 12,588 12,632 12,675 12,718 12,762 12,805 12,849 12,893 12,936 12,980 13,024 13,068 13,112 13,156 13,200 13,245 13,289 13,333 TABLE 32 AMOUNT OF MATERIAL IN CUBIC YARDS PER 100 LINEAR FEET OF LEVEL CUT Side Slopes 1 1 to 1 Depth of Center Cut, in Feet .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 0.0 0.0 0.2 0.5 0.9 1.4 2.0 2.7 3.6 4.5 1 5.6 6.7 8.0 9.4 10.9 12.5 14.2 16.1 18.0 20.1 2 22 24 27 29 32 35 38 41 44 47 3 50 53 57 60 64 68 72 76 80 84 4 89 93 98 103 108 112 118 123 128 133 5 139 144 150 156 162 168 174 180 187 193 6 200 207 214 222 228 235 242 249 257 264 7 272 280 288 296 304 312 321 329 338 347 8 356 364 374 383 392 401 411 420 430 440 9 450 460 470 480 491 501 512 522 533 544 10 556 567 577 589 601 612 624 636 648 660 11 672 684 697 709 722 735 748 760 774 787 12 800 813 827 840 854 868 882 896 910 924 13 939 953 968 983 998 1,012 1,028 1,043 1,058 1,073 14 1,089 1,104 1,120 1,136 1,152 1,168 1,184 1,200 1,217 1,233 15 1,250 1,267 1,284 1,300 1,318 1,335 1,352 1,369 1,387 1,404 210 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 32 (Concluded} AMOUNT OF MATERIAL IN CUBIC YARDS PER 100 LINEAR FEET OF LEVEL CUT Side Slopes 1 1 to 1 I Depth of 1 Center Cut, I in Feet .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 16 1,422 1,440 1,458 1,476 1,494 1,512 1,531 1,549 1,568 1,587 17 1,606 1,624 1,644 1,663 1,682 1,701 1,721 1,740 1,760 1,780 18 1,800 1,820 1,840 1,860 1,881 1,901 1,922 1,943 1,964 1,984 19 2,006 2,027 2,048 2,069 2,091 2,112 2,134 2,156 2,178 2,200 20 2,222 2,244 2,267 2,289 2,311 2,335 2,358 2,380 2,404 2,427 21 2,450 2,473 2,497 2,520 2,544 2,568 2,592 2,616 2,640 2,664 22 2,689 2,713 2,738 2,763 2,788 2,812 2,838 2,863 2,888 2,913 23 2,939 2,964 2,990 3,016 3,042 3,068 3,094 3,120 3,147 3,173 24 3,200 3,227 3,254 3,280 3,308 3,335 3,362 3,389 3,417 3,444 25 3,472 3,500 3,528 3,556 3,584 3,612 3,641 3,669 3,698 3,727 26 3,756 3,784 3,814 3,843 3,872 3,901 3,931 3,960 3,990 4,020 27 4,050 4,080 4,110 4,140 4,171 4,201 4,232 4,263 4,294 4,324 28 4,356 4,387 4,418 4,449 4,481 4,512 4,544 4,576 4,608 4,640 29 4,672 4,704 4,737 4,769 4,802 4,835 4,868 4,900 4,934 4,967 30 5,000 5,033 5,067 5,100 5,134 5,168 5,202 5,236 5,270 5,304 31 5,339 5,373 5,408 5,443 5,478 5,512 5,548 5,583 5,618 5,653 32 5,689 5,724 5,760 5,796 5,832 5,868 5,904 5,940 5,977 6,013 33 6,050 6,087 6,124 6160 6,198 6,235 6,272 6,309 6,347 6,384 34 6,422 6,460 6,498 6,536 6,574 6,612 6,651 6,689 6,728 6,767 35 6,806 6,844 6,884 6,923 6,962 7,001 7,041 7,080 7,120 7,160 36 7,200 7,240 7,280 7,320 7,361 7,401 7,442 7,483 7,524 7,564 37 7,606 7,647 7,688 7,729 7,771 7,812 7,854 7,896 7,938 7,980 38 8,022 8,064 8,107 8,149 8,192 8,235 8,278 8,320 8,364 8,407 39 8,450 8,493 8,537 8,580 8,624 8,668 8,712 8,756 8,800 8,844 40 8,889 8,933 8,978 9,023 9,068 9,112 9,158 9,203 9,248 9,293 41 9,339 9,384 9,430 9,476 9,522 9,568 9,614 9,660 9,707 9,753 42 9,800 9,847 9,894 9,940 9,988 10,035 10,082 10,129 10,177 10,224 43 10,272 10,320 10,368 10,416 10,464 10,512 10,561 10,609 10,658 10,707 44 10,756 10,804 10,854 10,903 10,952 11,001 11,051 11,100 11,150 11,200 45 11,250 11,300 11,350 11,400 11,451 11,501 11,552 11,603 11,654 11,704 46 11,756 11,807 11,858 11,909 11,961 12,012 12,064 12,116 12,168 12,220 47 12,272 12,324 12,377 12,429 12,482 12,535 12,588 12,640 12,694 12,747 48 12,800 12,853 12,907 12,960 13,014 13,068 13,122 13,176 13,230 13,284 49 13,339 13,393 13,448 13,503 13,558 13,612 13,668 13,723 13,778 13,833 50 13,889 13,944 14,000 14,056 14,112 14,168 14,224 14,280 14,337 14,392 51 14,450 14,507 14,564 14,620 14,678 14,735 14,792 14,849 14,987 14,964 52 15,022 15,080 15,138 15,196 15,254 15,312 15,371 15,430 15,489 15,548 53 15,606 15,664 15,724 15,783 15,842 15,901 15,961 16,020 16,080 16,140 54 16,200 16,260 16,320 16,380 16,441 16,501 16,562 16,623 16,684 16,744 55 16,806 16,867 16,928 16,989 17,051 17,112 17,174 17,236 17,298 17,360 56 17,422 17,484 17,547 17,609 17,672 17,735 17,798 17,860 17,924 17,987 57 18,050 18,113 18,177 18,240 18,304 18,368 18,432 18,496 18,560 18,624 58 18,689 18,753 18,818 18,883 18,948 19,012 19,078 19,143 19,208 19,273 59 19,339 19,404 19,470 19,536 19,602 19,668 19,734 19,800 19,867 19,933 60 20 000 STRUCTURAL DIAGRAMS AND TABLES 211 TABLE 33 AMOUNT OF MATERIAL IN CUBIC YARDS PER 100 LINEAR FEET OF LEVEL CUT Side Slopes 2 to 1 Depth of 1 Center Cut, in Feet .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 0.0 0.1 0.3 0.7 1.2 1.9 2.7 3.6 4.7 6.0 1 7.4 9.0 10.7 12.5 14.5 16.7 19.0 21.4 24.0 26.7 2 30 33 36 39 43 46 50 54 58 62 3 67 71 76 81 86 91 96 101 107 113 4 119 125 131 137 143 150 157 164 171 178 5 185 193 200 208 216 224 232 241 249 258 6 267 276 285 294 303 313 323 333 343 353 7 363 373 384 395 406 417 428 439 451 462 8 474 486 498 510 523 535 548 561 574 587 9 600 613 627 641 655 669 683 697 711 726 10 741 756 771 786 801 817 832 848 864 880 11 896 913 929 946 963 980 997 1,014 1,031 1,049 12 1,067 1,084 1,103 1,121 1,139 1,157 1,176 1,195 1,214 1,233 13 1,252 1,271 1,291 1,310 1,330 1,350 1,370 1,390 1,411 1,431 14 1,452 1,473 1,494 1,515 1,536 1,557 1,579 1,601 1,623 1,645 15 1,667 1,689 1,711 1,734 1,757 1,780 1,803 1,826 1,849 1,873 16 1,896 1,920 1,944 1,968 1,992 2,017 2,041 2,066 2,091 2,116 17 2,141 2,166 2,191 2,217 2,243 2,269 2,295 2,321 2,347 2,373 18 2,400 2,427 2,454 2,481 2,508 2,535 2,563 2,590 2,618 2,646 19 2,674 2,702 2,731 2,759 2,788 2,817 2,846 2,875 2,904 2,938 20 2,963 2,993 3,023 3,053 3,083 3,113 3,143 3,174 3,205 3,236 21 3,267 3,298 3,329 3,361 3,392 3,424 3,456 3,488 o,520 3,553 22 3,585 3,618 3,651 3,684 3,717 3,750 3,783 3,817 3,851 3,885 23 3,919 3,953 3,987 4,021 4,056 4,091 4,126 4,161 4,196 4,231 24 4,267 4,302 4,338 4,374 4,410 4,446 4,483 4,519 4,556 4,593 25 4,630 4,667 4,704 4,741 4,779 4,817 4,855 4,893 4,931 4,969 26 5,007 5,046 5,085 5,124 5,163 5,202 5,241 5,281 5,320 5,360 27 5,400 5,440 5,480 5,521 5,561 5,602 5,643 5,684 5,725 5,766 28 5,807 5,849 5,891 5,933 5,975 6,017 6,059 6,101 6,144 6,187 29 6,230 6,273 6,316 6,359 6,403 6,446 6,490 6,534 6,578 6,622 30 6,667 6,711 6,756 6,801 6,846 6,891 6,936 6,981 7,027 7,073 31 7,119 7,165 7,211 7,257 7,303 7,350 7,397 7,444 7,491 7,538 32 7,585 7,633 7,680 7,728 7,776 7,824 7,872 7,921 7,969 8,018 33 8,067 8,116 8,165 8,214 8,263 8,313 8,363 8,413 8,463 8,513 34 8,563 8,613 8,664 8,715 8,766 8,817 8,868 8,919 8,971 9,022 35 9,074 9,126 9,178 9,230 9,283 9,335 9,388 9,441 9,494 9,547 36 9,600 9,653 9,707 9,761 9,815 9,869 9,923 9,977 10,031 10,086 37 0,141 10,196 10,251 10,306 10,361 10,417 10,472 10,528 10,584 10,640 38 0,696 10,753 10,809 10,866 10,923 10,980 11,037 11,094 11,151 11,209 39 11,267 11,325 11,383 11,441 11,499 11,557 11,616 11,675 11,734 11,793 40 11,852 11,911 11,971 12,030 12,090 12,150 12,210 12,270 12,331 12,391 41 2,452 12,513 12,574 12,635 12,696 12,757 12,819 12,881 12,^43 13,005 42 13,067 13,129 13,191 13,254 13,317 13,380 13,443 13,506 13,569 13,633 43 13,696 13,760 13,824 13,888 13,952 14,017 14,081 14,146 14,211 4,276 44 14,341 14,406 14,471 14,537 14,603 14,669 14,735 14,801 14,867 4,933 212 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 33 (Concluded) AMOUNT OF MATERIAL IN CUBIC YARDS PER 100 LINEAR FEET OF LEVEL CUT Side Slopes 2 to 1 1 Depth of !| Center Cut,; | in Feet .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 45 15,000 15,067 15,134 15,201 15,268 15,335 15,403 15,470 15,538 15,606 46 15,674 15,742 15,811 15,879 15,948 16,017 16,086 16,155 16,224 16,293 47 16,363 16,433 16,503 16,573 16,643 16,713 16,783 16,854 16,925 16,996 48 17,067 17,138 17,209 17,281 17,352 17,424 17,496 17,568 17,640 17,713 49 17,785 17,858 17,931 18,004 18,077 18,150 18,223 18,297 18,371 18,445 50 18,519 18,593 18,667 18,741 18,816 18,891 18,966 19,041 19,116 19,191 51 19,267 19,342 19,418 19,494 19,570 19,646 19,723 19,799 19,876 19,953 52 20,030 20,107 20,184 20,261 20,339 20,417 20,495 20,573 20,651 20,729 53 20,807 20,886 20,965 21,044 21,123 21,202'21,281 21,361 21,440 21,520 54 21,600 21,680 21,760 21,841 21,921 22,002:22,08322,164 22,245 22,326 55 22,407 22,489 22,571 22,653 22,735 22,81722,89922,981 23,064 23,147 56 23,230 23,313 23,396 23,479 23,563 23,64623,73023,814 23,898 23,982 57 24,067 24,151 24,236 24,321 24,406 24,49124,57624,661 24,747 24,833 58 24,919 25,005 25,091 25,177 25,263 25,35025,44725,524 25,611 25,698 59 25,785 25,873 25,960 26,048 26,136 26,22426,31226,401 26,489 26,578 60 26,667 TABLE 34 AMOUNT OF MATERIAL IN CUBIC YARDS PER 100 LINEAR FEET OF LEVEL CUT Side Slopes 3 to 1 Depth of II Center Cut, in Feet .0 .1 o .3 .4 .5 .6 .7 .8 .9 0.0 0.1 0.4 1.0 1.8 2.8 4.0 5.4 7.1 9.0 1 11 1 13.4 16.0 18.8 21.8 25.0 28.4 32.2 36.1 40.1 2 44 49 54 59 64 69 75 81 87 93 3 100 106 114 121 128 136 144 152 160 168 4 178 187 196 205 215 225 235 245 256 267 5 278 289 300 312 324 336 348 361 373 387 6 400 413 427 441 445 469 484 499 514 529 7 544 560 576 592 608 625 642 659 676 693 8 711 729 747 765 784 803 822 841 860 880 9 900 920 940 961 982 1,003 1,024 1,045 1,067 1,089 10 1,111 1,133 1,156 1,179 1,202 1,225 1,248 1,272 1,296 1,320 11 1,344 1,369 1,394 1,419 1,444 1,469 1,495 1,521 1,547 1,573 12 1,600 1,627 1,654 1,681 1,708 1,736 1,764 1,792 1,820 1,849 13 1,878 1,907 1,936 1,965 1,995 2,025 2,055 2,085 2,116 2,147 14 2,178 2,209 2,240 2,272 2,304 2,336 2,368 2,401 2,434 2,467 STRUCTURAL DIAGRAMS AND TABLES 213 TABLE 34 (Concluded} AMOUNT OF MATERIAL IN CUBIC YARDS PER 100 LINEAR FEET OF LEVEL CUT Side Slopes 3 to 1 Depth of Center Cut, in Feet .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 15 2,500 2,533 2,567 2,601 2,635 2,669 2,704 2,739 2,774 2,809 16 2,844 2,880 2,916 2,952 2,988 3,025 3,062 3,099 3,136 3,173 17 3,211 3,249 3,287 3,325 3,364 3,403 3,442 3,481 3,520 3,560 18 3,600 3,640 3,680 3,721 3,762 3,803 3,844 3,885 3,927 3,969 19 4,011 4,053 4,096 4,139 4,182 4,225 4,268 4,312 4,356 4,400 20 4,444 4,489 4,534 4,579 4,624 4,669 4,715 4,761 4,807 4,853 21 4,900 4,947 4,994 5,041 5,088 5,137 5,184 5,232 5,280 5,329 22 5,378 5,427 5,476 5,525 5,575 5,625 5,675 5,725 5,776 5,827 23 5,878 5,929 5,980 6,032 6,084 6,136 6,188 6,240 6,294 6,346 24 6,400 6,453 6,507 6,561 6,615 6,669 6,724 6,779 6,834 6,889 25 6,944 7,000 7,056 7,112 7,168 7,225 7,282 7,339 7,396 7,453 26 7,511 7,569 7,627 7,685 7,744 7,803 7,862 7,921 7,980 8,040 27 8,100 8,160 8,220 8,281 8,342 8,403 8,464 8,525 8,587 8,649 28 8,711 8,773 8,836 8,899 8,962 9,025 9,088 9,152 9,216 9,280 29 9,344 9,409 9,474 9,539 9,604 9,669 9,735 9,801 9,867 9,993 30 10,000 10,067 10,134 10,201 10,268 10,336 10,404 10,472 10,540 10,609 31 10,678 10,747 10,816 10,885 10,955 11,025 11,095 11,165 11,236 11,307 32 11,378 11,449 11,520 11,592 11,664 11,736 11,808 11,881 11,954 12,027 33 12,100 12,173 12,247 12,321 12,395 12,469 12,544 12,619 12,694 12,769 34 12,844 12,920 12,996 13,072 13,148 13,225 13,302 13,379 13,456 13,533 35 13,611 13,689 13,767 13,845 13,924 14,003 14,082 14,161 14,240 14,320 36 14,400 14,480 14,560 14,641 14,722 14,803 14,884 14,965 15,047 15,129 37 15,211 15,293 15,376 15,459 15,542 15,625 15,708 15,792 15,876 15,960 38 16,044 16,129 16,214 16,299 16,384 16,469 16,555 16,641 16,727 16,813 39 16,900 16,987 17,074 17,161 17,248 17,336 17,424 17,512 17,600 17,689 40 17,778 17,867 17,956 18,045 18,135 18,225 18,315 18,405 18,496 18,587 41 18,678 18,769 18,860 18,952 19,044 19,136 19,228 19,321 19,414 19,507 42 19,600 19,693 19,787 19,881 19,975 20,069 20,164 20,259 20,354 20,449 43 20,544 20,640 20,736 20,832 20,928 21,025 21,122 21,219 21,316 21,413 44 21,511 21,609 21,707 21,805 21,904 22,003 22,102 22,201 22,300 22,400 45 22,500 22,600 22,700 22,801 22,902 23,003 23,104 23,205 23,307 23,409 46 23,511 23,613 23,716 23,819 23,922 24,025 24,128 24,232 24,336 24,440 47 24,544 24,649 24,754 24,859 24,964 25,069 25,175 25,281 25,387 25,493 48 25,600 25,707 25,814 25,921 26,029 26,136 26,244 26,352 26,460 26,569 49 26,678 26,787 26,896 27,005 27,115 27,225 27,335 27,445 27,556 27,667 50 27,778 27,889 28,000 28,112 28,224 28,336 28,448 28,561 28,674 28,787 51 28,900 29,013 29,127 29,241 29,355 29,469 29,584 29,699 29,814 29,929 52 30,044 30,160 30,276 30,392 30,508 30,625 30,742 30,859 30,976 31,093 53 31,211 31,329 31,447 31,565 31,684 31,80331,922 32,041 32,160 32,280 54 32,400 32,520 32,640 32,761 32,882 33,003 33,124 33,245 33,367 33,489 55 33,611 33,733 33,856 33,979 34,102 34,225 34,348 34,472 34,596 34,720 56 34,844 34,969 35,094 35,219 35,344 35,459 35,595 35,721 35,847 35,973 57 36,100 36,227 35,354 36,481 36,608 36,736 36,864 36,992 37,120 37,249 58 37,378 37,507 37,636 37,765 37,895 38,025 38,155 38,285 38,416 38,547 59 38,678 38,809 38,940 39,072 39,204 39,336 39,468 39,601 39,734 39,867 , 60 40,000 214 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 35 AMOUNT OF MATERIAL IN CUBIC YARDS PER 100 LINEAR FEET OF CUT ON SLOPING GROUND Side Slopes 1 to 1 < O3 * 5S| ISa SURFACE SLOPE OF GROUND IN PER CENT 10 15 20 25 30 35 40 45 50 55 60 1r\ .u 1.5 8 8 9 9 9 9 10 10 11 12 13 2.0 15 15 16 16 16 17 18 19 20 21 23 2.5 23 24 24 25 25 27 27 29 31 33 36 3.0 33 33 34 35 36 38 39 42 44 47 52 3.5 46 46 47 48 49 51 54 57 60 65 70 4.0 59 60 61 63 65 67 70 74 79 85 92 4.5 76 77 78 80 83 85 89 94 100 107 117 5.0 94 95 97 99 102 106 111 117 124 133 145 5.5 113 114 117 120 123 128 133 141 149 161 175 6.0 134 136 139 142 146 152 158 167 177 191 208 6.5 157 160 163 166 172 178 186 196 208 224 244 7.0 183 185 189 193 199 206 215 227 242 260 283 7.5 210 212 217 222 229 237 248 261 278 299 325 8.0 239 242 247 253 261 270 282 297 316 340 370 8.5 270 274 279 286 295 305 319 336 357 384 418 9.0 303 307 312 320 330 342 357 376 400 430 468 9.5 338 342 348 356 367 381 398 419 446 479 522 10.0 374 378 385 395 406 422 441 464 494 531 578 10.5 412 417 425 436 448 465 486 512 545 585 637 11.0 453 458 467 478 492 510 533 562 598 642 700 11.5 495 501 510 523 538 558 583 615 653 702 765 12.0 539 545 555 569 586 607 634 669 711 764 833 12.5 585 592 603 618 637 659 689 726 772 830 904 13.0 632 640 652 668 689 713 745 785 835 897 978 13.5 681 691 703 720 743 769 803 847 900 967 ,054 14.0 733 743 756 774 799 827 864 911 968 1,040 ,134 14.5 787 797 811 831 857 887 927 977 1,039 1,116 ,216 15.0 841 852 868 888 916 949 994 ,045 1,111 1,194 ,301 15.5 898 910 927 949 978 1,014 1,059 ,116 ,187 1,276 ,390 16.0 957 970 987 1,011 1,042 1,080 1,128 ,189 ,264 1,359 ,480 16.5 1,018 1,031 1,050 1,075 1,1-08 1,148 1,199 ,265 ,344 1,445 ,573 17.0 1,080 1,095 1,115 1,141 1,176 ,219 1,273 ,343 ,427 1,534 ,669 17.5 1,145 1,160 1,182 1,209 1,246 ,292 1,349 ,423 ,512 1,626 ,770 18.0 1,212 1,227 1,250 1,280 1,319 ,368 1,428 ,506 ,600 1,720 ,874 18.5 1,281 1,297 1,321 1,353 1,394 ,445 1,509 ,591 ,691 1,817 ,980 19.0 1,351 1,368 1,393 1,426 1,470 ,523 1,591 1,678 ,783 1,916 2,088 19.5 1,422 1,440 1,467 1,502 1,548 ,604 1,676 1,767 1,878 2,018 2,199 20.0 1,496 1,515 1,542 1,580 1,628 ,687 1,763 1,859 1,975 2,123 2,313 20.5 1,572 1,592 1,620 1,660 1,710 1,773 1,852 1,953 2,075 2,230 2,430 21.0 1,649 1,670 1,701 1,742 1,795 1,861 1,943 2,049 2,178 2,340 2,550 21.5 1,729 1,751 1,783 1,826 1,882 1,951 2,037 2,148 2,283 2,453 2,673 22.0 1,811 1,834 1,868 1,913 1,971 2,043 2,134 2,250 2,391 2,569 2,800 22.5 1,894 1,918 1,953 2,001 2,061 2,136 2,231 2,353 2,501 2,687 2,928 23.0 1,979 2,004 2,041 2,090 2,153 2,232 2,331 2,458 2,613 2,808 3,059 STRUCTURAL DIAGRAMS AND TABLES 215 TABLE 35 (Concluded) AMOUNT OF MATERIAL IN CUBIC YARDS PER 100 LINEAR FEET OF CUT ON SLOPING GROUND Side Slopes 1 to 1 Depth of |i Center Cut, i in Feet SURFACE SLOPE OF GROUND IN PER CENT 10 15 20 25 30 35 40 45 50 55 60 23.5 2,065 2,091 2,130 2,181 2,247 2,330 2,434 2,566 2,728 2,931 3,194 24.0 2,154 2,181 2,221 2,275 2,344 2,430 2,539 2,677 2,845 3,057 3,331 24.5 2,245 2,274 2,315 2,371 2,443 2,533 2,646 2,790 2,965 3,186 3,472 25.0 2,338 2,368 2,411 2,469 2,545 2,637 2,755 2,905 3,088 3,318 3,615 25.5 2,432 2,463 2,508 2,568 2,647 2,743 2,866 3,022 3,212 3,451 3,761 26.0 2,529 2,561 2,608 2,670 2,752 2,852 2,980 3,142 3,340 3,588 3,910 26.5 2,627 2,661 2,709 2,774 2,859 2,963 3,095 3,264 3,469 3,727 4,062 27.0 2,727 2,762 2,813 2,880 2,968 3,076 3,212 3,388 3,601 3,869 4,217 27.5 2,829 2,865 2,918 2,988 3,079 3,191 3,332 3,515 3,736 4,014 4,374 28.0 2,932 2,970 3,024 3,097 3,191 3,308 3,454 3,643 3,872 4,161 4,534 .28.5 3,038 3,077 3,133 3,208 3,306 3,427 3,579 3,775 4,012 4,311 4,698 29.0 3,146 3,187 3,245 3,322 3,423 3,548 3,706 3,909 4,154 4,464 4,864 29.5 3,255 3,297 3,357 3,438 3,542 3,671 3,835 4,045 4,298 4,619 5,033 30.0 3,367 3,409 3,471 3,555 3,663 3,797 3,967 4.183 4,445 4,777 5,205 30.5 3,480 3,524 3,588 3,675 3,786 3,924 4,100 4,323 4,595 4,937 5,380 31.0 3,595 3,641 3,707 3,798 3,911 4,054 4,236 4,466 4,747 5,100 5,558 31.5 3,712 3,759 3,828 3,920 4,039 4,187 4,374 4,612 4,901 5,266 5,739 32.0 3,831 3,880 3,951 4,046 4,169 4,322 4,514 4,760 5,058 5,435 5,923 32.5 3,952 4,002 4,075 4,173 4,300 4,457 4,656 4,909 5,217 5,606 6,109 33.0 4,074 4,126 4,201 4,302 4,433 4,595 4,800 5,061 5,379 5,780 6,298 33.5 4,198 4,252 4,329 4,433 4,568 4,735 4,946 5,215 5,543 5,956 6,491 34.0 4,324 4,379 4,459 4,566 4,705 4,877 5,095 5,372 5,710 6,135 6,686 34.5 4,452 4,509 4,592 4,702 4,845 5,022 5,246 5,531 5,879 6,317 6,884 35.0 4,583 4,641 4,726 4,839 4,987 5,169 5,399 5,693 6,051 6,502 7,085 35.5 4,714 4,774 4,861 4,978 5,130 5,317 5,555 5,856 6,225 6,689 7,288 36.0 4,848 4,910 5,000 5,120 5,276 5,469 5,712 6,023 6,402 6,879 7,496 36.5 4,984 5,048 5,140 5,263 5,423 5,621 5,872 6,191 6,581 7,071 7,705 37.0 5,122 5,187 5,282 5,408 5,573 5,776 6,034 6,362 6,762 7,266 7,918 37.5 5,261 5,328 5,426 5,555 5,725 5,933 6,198 6,535 6,946 7,464 8,132 38.0 5,402 5,471 5,571 5,705 5,879 6,093 6,365 6,711 7,133 7,665 8,353 38.5 5,545 5,615 5,718 5,855 6,033 6,254 6,532 6,888 7,321 7,867 8,572 39.0 5,690 5,763 5,868 6,008 6,191 6,418 6,703 7,069 7,513 8,073 8,797 39.5 5,837 5,912 6,020 6,164 6,351 6,584 6,877 7,252 7,707 8,282 9,024 40.0 5,986 6,062 6,173 6,321 6,513 6,752 7,052 7,436 7,903 8,493 9,254 40.5 6,137 6,215 6,328 6,480 6,677 6,921 7,230 7,623 8,102 8,706 9,487 41.0 6,289 6,369 6,485 6,641 6,843 7,093 7,410 7,813 8,304 8,922 9,722 41.5 6,442 6,524 6,644 6,803 7,011 7,266 7,591 8,004 8,507 9,140 9,961 42.0 6,599 6,683 6,806 6,969 7,181 7,443 7,775 8,198 8,713 9,362 10,203 42.5 6,758 6,844 6,969 7,136 7,353 7,622 7,962 8,395 8,922 9,587 10,447 43.0 6,917 7,006 7,134 7,305 7,527 7,802 8,150 8,593 9,133 9,814110,694 43.5 7,079 7,170 7,300 7,476 7,703 7,984 8,341 8,794 9,347 10,043 10,944 44.0 7,243 7,335 7,469 7,648 7,880 8,169 8,533 8,997 9,563 10,175 11,197 216 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 36 AMOUNT OF MATERIAL IN CUBIC YARDS PER 100 LINEAR FEET OF CUT ON SLOPING GROUND Side Slopes 1 1 to 1 o3 $ ^ SURFACE SLOPE OF GROUND IN PER CENT 10 15 20 25 30 35 40 45 50 55 60 0.5 1 1 1 1 1 1 1 2 2 2 6 1.0 6 6 7 7 7 8 9 11 13 18 29 1.5 12 13 13 14 15 17 19 22 28 39 65 2.0 23 23 24 26 28 38 34 41 51 70 117 2.5 36 37 38 41 44 48 55 64 80 109 183 3.0 51 53 55 58 63 69 78 92 114 157 263 3.5 70 72 75 79 85 94 106 125 155 213 357 4.0 91 94 98 104 112 123 139 163 203 278 467 4.5 113 118 124 132 141 155 176 206 257 352 590 5.0 142 146 153 162 174 192 217 255 318 435 730 5.5 172 177 185 195 211 232 262 309 384 526 882 6.0 205 211 220 233 251 276 312 368 457 624 1,051 6.5 240 248 258 273 295 324 367 431 537 735 1,233 7.0 278 287 299 317 341 375 425 500 622 852 1,430 7.5 319 329 343 363 391 430 488 574 714 978 1,641 8.0 364 375 391 414 446 491 556 654 813 ,113 1,870 8.5 411 423 441 467 503 555 627 738 918 ,257 2,107 9.0 460 474 495 524 564 622 703 827 1,029 ,409 2,364 9.5 513 528 552 583 628 691 783 922 ,146 ,569 2,633 10.0 569 585 611 647 697 765 868 1,021 ,271 ,740 2,919 10.5 627 645 673 712 768 844 956 1,125 ,401 ,918 3,217 11.0 687 708 739 781 843 927 1,049 1,235 ,537 2,104 3,531 11.5 752 774 808 855 922 1,013 1,149 1,350 ,680 2,301 3,860 12.0 819 843 879 931 ,003 1,103 1,250 1,470 1,829 2,504 4,203 12.5 888 914 954 1,010 ,089 1,197 1,356 1,595 1,985 2,717 4,560 13.0 961 989 03?, 1,093 ,178 1,295 1 467 1,725 2,147 2,939 4,933 13.5 1,036 1,066 ,112 1,178 ,269 1,396 1,581 1,860 2,316 3,170 5,318 14.0 1,114 1,147 ,196 1,267 ,365 1,502 1,701 2,001 2,489 3,410 5,721 14.5 1,195 1,230 ,284 1,359 ,465 1,612 1,825 2,146 2,669 3,657 6,136 15.0 1,279 1,316 ,374 1,454 ,568 1,724 1,952 2,297 2,857 3,914 6,567 15.5 1,366 1,406 ,467 1,553 ,674 1,841 2,085 2,453 3,051 4,179 7,012 16.0 1,455 1,498 ,563 1,654 ,784 1,961 2,221 3,613 3,250 4,453 7,472 16.5 1,547 1,593 ,662 1,759 ,897 2,085 2,362 2,779 3,456 4,735 7,945 17.0 1,643 1,691 ,765 1,868 2,014 2,214 2,507 2,951 3,670 5,027 8,435 17.5 1,741 1,792 ,870 1,979 2,134 2,346 2,656 3,126 3,889 5,326 8,937 18.0 1,841 1,896 ,979 2,094 2,258 2,482 2,809 3,308 4,114 5,636 9,456 18.5 1,945 2,002 2,090 2,212 2,385 2,622 2,967 3,494 4,346 5,953 9,988 19.0 2,051 2,111 2,205 2,334 2,516 2,766 3,130 3,686 4,585 6,279 10,535 19.5 2,160 2,225 2,322 2,458 2,650 2,913 3,299 3,881 4,828 6,614 11,097 20.0 2,272 2,341 2,442 2,586 2,787 3,064 3,472 4,083 5,079 6,957 11,673 20.5 2,387 2,460 2,566 2,717 2,929 3,220 3,648 4,289 5,337 7,310 12,265 21.0 2,506 2,581 2,692 2,851 3,073 3,379 3,828 4,502 5,600 7,670 12,871 21.5 2,627 2,705 2,822 2,988 3,221 3,541 4,013 4,719 5,870 8,040 13,491 22.0 2,751 2,832 2,955 3,129 3,373 3,708 4,201 4,941 6,147 8,417 14,127 22.5 2,877 2,962 3,090 3,272 3,527 3,878 4,394 5,168 6,429 8,804 14,775 STRUCTURAL DIAGRAMS AND TABLES 217 AMOUNT OF MATERIAL IN TABLE 36 (Concluded} CUBIC YARDS PER 100 SLOPING GROUND Side Slopes l.\ to 1 LINEAR FEET OF CUT ON > 3 0 = Angle of repose of material. (3) <' = Angle of friction between material and wall. (4) F R D is the ground surface. (5) Draw RA. (6) Produce D R. (7) Draw F B parallel to RA. (8) Draw B O parallel to A Y. (9) Describe the arc A M D on A D. (10) Draw M J_ to A D. (11) With A as center, describe arc M I. (12) Draw / C parallel to A Y. (13) Make / L = I C and draw C L. (14) The total pressure on one linear foot of wall is then equal to the area of the triangle I C L multiplied by the weight of 1 cubic foot of the material. (15) The point of application may be taken as at one- third A F from A. The average pressure equals the total divided by A F. The maximum pressure equals twice the average. (16) When R D is parallel to A D the formula for total pressure on A F is : STRUCTURAL DIAGRAMS AND TABLES 221 e wt. of 1 cu. ft. of material h = height of wall See Fig. 45 for total earth pressures on walls without sur- charge based on equivalent water pressure. Formulas for Maximum Bending Moments in Beams. The variation of pressures on any submerged wall due to water or earth is generally triangular or trapezoidal, that is, the loading at one end is greater than at the other. In the following list are given the principal formulas for calculating the bending moments due to uniform loads, triangular loads, and trapezoidal loads. The bending moments are given in inch-pounds; the loading is in pounds per linear foot; and the span is in feet. Uniform loading: W = load on beam in pounds per linear foot. / = span in feet. M = bending moment in inch-pounds. (1) M = 1.5 W I 2 , for a simple beam. (2) M = W I 2 , for negative bending moment at the supports of a fixed beam. (3) M = 0.5 W I 2 for the positive bending moment at the center of a fixed beam. (4) M = 6 W I 2 , for a cantilever beam. Triangular loading: P = load at end of beam in pounds per linear foot. (5) M = 0.77 P I 2 , for a simple beam. (6) M = 0.6 P I 2 , for the maximum negative bending mo- ment at the more heavily loaded end of a fixed beam. (7) M = 0.26 P I 2 , for the maximum positive bending mo- ment between supports of a fixed beam. (8) M = 2 P I 2 , for a cantilever beam having the base of triangular load at supported end. Trapezoidal loading: Wi = load in pounds per linear foot at lightly loaded end. 222 WORKING DATA FOR IRRIGATION ENGINEERS PI = load in pounds per linear foot at heavily loaded end. (9) M = (/* - x*} + -j (P, - IF:) (l - |) for simple beam, the point of maximum bending moment being at (10) M = Wi I 2 + 0.6 (Pi - Wi) I 2 , for the maximum nega- tive moment at the heavily loaded support of a. fixed beam. (11) M = 0.5 Wi I 2 + 0.26 (P l - Wi) / 2 , for the maximum positive (approximate) moment between supoorts; of a fixed beam. (12) M = 6 Wi I 2 + 2 (Pi - Wi) I 2 , for cantilever beams, with the heavier loading at the supported end. Table 38 gives the bending moments in thousands inch- pound units in beams one foot wide for triangular loading, that is: for loads varying uniformly from pounds per linear foot at one end to P pounds per linear foot at the other end, due to water and earth pressures. < is the angle of repose of the earth and 6 is the slope of surface of ground back of the wall. The face of the wall against which the pressure acts is assumed to be vertical and the angle of friction between earth and wall is not considered. Formulas for Reinforced Concrete Design. The theory of the design of a rectangular concrete beam reinforced on one side may be illustrated by the following diagram : Any section A-B of a reinforced concrete beam subjected to a bending moment has acting on it the forces P, representing the total stress in the steel, and PI, representing the total STRUCTURAL DIAGRAMS AND TABLES 223 O |8 r^ P o Q f Q i 111 w P O CQ O w O O S S5 H ft 55 2 O H 3 o H w U M P g W en , PH en CM u g |fi ^ O H Sow i igsi siiii a 1 llll os os o w <* * t- rH 10 CD rH rH d W CO 00 ca rH rH N CO t- d OS rji OS W 10 t- rH rH rH rH d CO t- rH i 00 Tj rH VO Tj< CO 00 rH rH rH CO ISSli s s CO t- rH *)< SSSS CO rH rH rH d IO S 2233 rH rH rH d 10 00 rH rH rH 00 Tj< rH S* rH Tl* rH IO t- 00 rj< rH rH CO rH 1 rH W O CO CO rH (O io' os IN' CD 06 rH rH (M W CO 03 .2 -J3 * E fl Jj J^ 00 to Tl-rHOSOO U5 t- 00 rH rH rH rH CO rH CO t- 00 rH r-i CO IO' 00 t-* rH rH rH rH C 00 (N* 00 rH rH rH ^ ^ III . d rH 10 (N TH 50 t- 00 CO rH t> CD CD OS 10 * 10 CD* t-* rH 1 I! oj i- en 'S'o . 00 N 00 co* * r)5 t> t> CO 00 CO CD C<3 CO CO "tf CO g -as. S - 1 * rH CO OS rH CO ^ t- q co ^J rH rH N W CO ^ J i " " o " / tn o / X 10 XXXX rH CO OS t- xxxxx CO OO 00 t- OS 00 Oi rH IO H rH eg CO o co oo oo M 00 rH t> CO CD id id cd d rH CO CO 10 kdiocod Tf CO CD kO CO O O5 rH CO Tf 10 10 t- O CD t- 00 CO 10 CO t> CO rH rH O O O rH O O O O rH xxxx rH CO 05 t-_ 05 co t- d CO T}< T} CO O rH CO rH 00 S* eo t~ t- as 00 05 rH CO 00 CO O5 CO 05 10 r^ CO CO T* 10 CD CD IO IO CD id id 06 eo Tf 10 CD C- rH O OO rH CO CO eoeeeio^i O5 IO rH O5 rH CO CO * Tf C- CO t- CO CO CO >0 t> rH rH rH rH CO CO q co 05 co TJ; CO t- CO t> CO O b-. -* CO t> CO t-. Tf CO CO rH CO Tf 10 CO O5 CO O5 CO CO CO rH rH CO CO CO lOt^COrH rHCOlOOOCO rHrHrHCO rHrHrHrHCO xxxxx CO OO 00 t> O5 CO Tj t- t- S 05 10 10 CO rH CO IO O5 10 10 < CO rH CO CO t- 05 alss Tf 10 00 10 O rH CO rH rH rH rH CO O rH 00 t> CO 05 00 10 CO CD rH qcoqco Tl 05 CO Tf Tf Tf 00 coooqca OlOrHCO 10 10 CD xxxx rH CO Cft t^ 05 CO l> O O rH CO 1! II II SrH t- Tl< CO -* CO CD rl IO CD t- rH co Tf 10 -^r 10 Ti< 10 CO 05 i C~ CO O5 CD IT- CO CO CO t CD t- CD rH t- CO O5 CO CO CO rH 00 05 CO 10 O5 CO CO CO CD rH CO CO CO Tjt SSSa -q IO O CD C- ^< t- 05 CO 00 CO CO CO Tf cd t> oi id oo IO CD t- O5 CO eocoqio O CO t- 00 10 05 TJ! d 06 d CO CO *! * t- ^ CO CO t> CO O5 CO t> CO t- rH CO CO CO * rH 10 05 05 CO t> 00 05 rH t^ CO COrH rH CO * 10 CD XXXXX CO 00 CO t> 05 06 eo OJ t> 06 CO CO CO -^ CO o O CO O ^t o co co n so II II II II II - STRUCTURAL DIAGRAMS AND TABLES 225 stress in the concrete. The stress in the steel is concentrated at one point, but the compressive stress in concrete (tensile stress from C to B is neglected, as it has no influence on the ultimate, or even the working strength of the beam) varies from zero at C to a maximum at A , the rate of increase being uniform from C to A . The summation of these stresses is represented by p l = p t whose point of application is one-third of A C below A . The resisting moment of the section, therefore, is equal to P x or PI x, and this must be equal to the bending moment, or M = P x = Pi x. The value of x for a given beam depends upon the location of the neutral axis which varies with different percentages of steel and with the quality of the concrete. This variation is slight for ordinary percentages of steel and grades of concrete used in practice and the neutral axis may be assumed to be located at 0.39 d below the top of the beam. The point of application of PI, then, is -^-r = 0.13 d below the top of the beam and the lever arm x of internal stresses is d .13 d .87 d, or J/% d, and the resisting moment is % d P. Therefore, M = . 7 / s d P and P = -=-r = Pi If f 8 represents the intensity of working stress in the steel, the area of steel required is *.,,**. ' /. "Idf. The shifting of the neutral axis has a greater influence on the fiber stress in the concrete than on the stress in the steel. On the assumption that the coefficient of elasticity of concrete is equal to 2,000,000, which corresponds to a good grade of con- crete, the position of neutral axis will vary from .3 d to .48 d below the top of beam for percentages of steel varying from 0.4 to 1.5, the ordinary range of practice. With this variation in the position of the neutral axis, the maximum fiber stress in the concrete varies from f c ' 226 WORKING DATA FOR IRRIGATION ENGINEERS for 0.4 per cent steel to/ c = -r~ for 1.5 per cent steel. These equations apply only to working stresses of about one-fourth the ultimate. Beyond this point the variation of stresses in the concrete becomes parabolic, resulting in a different set of equa- tions. For approximate design, Turneaure and Maurer give the following formulas: M = bending moment in inch-pounds /, = unit stress in steel f c = maximum fiber stress in concrete b = width of beam d = depth of beam above plane of steel p = ratio of steel area to concrete area = 7: bd for p = % 6 j- ~ ?f 8 P 3 ft If a value of p greater than & -f is used, then equation (2) /* should be used to determine b and d. If a value of p less than & y is used, equation (l) should be used for determining b and d. Js If equation (2) is used, the unit stress in the steel is given very closely by equation (1) in all cases, but if equation (1) is used for determining b and d equation (2) will not give the unit stress in the concrete unless p = /( 6 ~. For other values of p the unit Js 7.5M stress in the concrete may range approximately from f c = , , 2 for p 0.4 per cent to f c = -7-^ for p = 1.5 per cent. STRUCTURAL DIAGRAMS AND TABLES 227 Example of Use of Above Formulas. A concrete beam has a bending moment of 50,000 inch-pounds, /, is to be not greater than 12,000 and f c is to be not greater than 500. Determine b and d and the area of steel required. In order to have /, = 12,000 and/ c = 500, . _ s/ fc _ s/ x 5,000 P " /16 / /16 X 10 nnn .UU/S = 0.78 per cent. From (2) b d? = - -^^ - = 600 If b = 8 inches d = A = 8.7 inches Now, if it were desired to use 1.00 per cent of steel, equation (2) would be used and we would have b d z equal to 600 as before, while the stress in the concrete would be between 500 and 410, \ = TTdv or rou &hly> 470,* and the stress in the steel would be _ _8M_, 8X50,000 J *~ 7pbd 2 " 7X .01 X 600 If only 0.5 per cent steel were used, equation (1) would be used for finding b and d: 8 X 50,000 = 7 X 12,000 X .005 = If b = 8 d = \ = 11 inches * The stress of 500 corresponds to a percentage of steel of .78 and 410 ( = b~d? ) corresponds to a percentage of 1.5 as above stated. The assumption of a linear variation between these limits gives a stress, corresponding to 1.0 per cent steel, of 500 - f^ (500 - 410)1 = 470 pounds per square inch. 228 WORKING DATA FOR IRRIGATION ENGINEERS In this case, the stress in the steel would be 12,000 pounds per square inch, as assumed, but the stress in concrete would be , 7.5 M 7.5 X 50,000 between 500 and , , 2 = - :rr^ -- = 395; in fact, it would o (t " be very near the latter figure roughly, 370. By means of the above equations, approximate calculations can be rapidly made without the use of tables, diagrams, or com- plicated formulas, and they will be found to serve admirably for ordinary beam problems when tables or diagrams are not avail- able. Fig. 40* is a convenient diagram for proportioning rein- forced concrete beams. This diagram is based on a ratio of coefficient of elasticity of steel to coefficient of elasticity of concrete of 15. Its values correspond closely with those ob- tained from the above equations. Table 39 * for round rods and Table 40 * for square rods are convenient for use with this diagram in the design of walls and slabs. Illustrative Examples. The bending moment M in a beam is 50,000. Find the values of b, d, and p required to carry this when f c = 400 and /, = 10,000 : Solution : At the intersection of the lines marked f c = 400 and f 8 = 10,000 we read the percentage of steel equals 0.75 and M Ib d 2 = 65 .*. b d 2 = = bo 770. If b = 8 inches, d = -y = 9.8 inches from the top of beam to center of steel. Area of steel required 8 X 9.8 X .0075 = 0.59 square inches, requiring 2 J^-inch round rods. (2) The bending moment per linear foot on a concrete re- taining wall is 75,000 inch-pounds. Find the thickness of wall and size and spacing of reinforcement rods required when /, = 12,000 and f c = 500. Solution: As before read from the dia- gram T-p = 84 and p = 0.8. M_ 75,000 b d 2 = b d 2 * Reproduced by permission from "Principles of Reinforced Construc- tion," by Turneaure and Maurer, John Wiley & Sons, New York. STRUCTURAL DIAGRAMS AND TABLES 229 FIG. 40. Coefficients of Resistance of Reinforced Concrete Beams. R - M R ~bd 2 230 WORKING DATA FOR IRRIGATION ENGINEERS I CQ T-H ^H i-l 00(NOOOOT-O5(NOO C^COOl>Oir-Hrtll>T-I^JHOOCOI>-I>OOi 1 ^ ^-i ^H' ^i 00 IIS 00 O i i(NCOiO 'Tt ) cOOcDTt | Tt | t > -OOI>-'^ l OOCOCDCO' lO 'O5T-ICO ^t l O'^ H COl>-iOC v flCDO5 rH(MCOCO-^iOCOi>-OO O 232 WORKING DATA FOR IRRIGATION ENGINEERS 75,000 .'.bd 2 Since b = 12, d = = 893 8.6 inches Area of steel per foot of wall 12 X 8.6 X .008 = .83 square inch. From- Table 39 we read that ^-inch round rods spaced inches on centers will supply this area. TABLE 41 QUANTITIES OF MATERIALS REQUIRED FOR ONE CUBIC YARD OF RAMMED CONCRETE, ASSUMING A BARREL OF 3.8 CUBIC FEET PARTS IN Mix Voros IN BROKEN STONE OR GRAVEL 45%* 40 %t Cement Sand Stone Cement Sand Stone Cement Sand Stonet Bbl. Cu. Yd. Cu. Yd. Bbl. Cu. Yd. Cu. Yd. 1 2 3H .68 0.47 0.83 .61 0.45 0.79 1 2 4 .57 0.44 0.88 .50 0.42 0.84 1 2 4^ .48 0.42 0.94 .41 0.40 0.89 1 2^ 3 .66 0.58 0.70 .60 0.56 0.68 1 2^ 3^ .55 0.55 0.76 .49 0.52 0.73 1 2H 4 1.46 0.51 0.82 .40 0.49 0.79 1 2^ 4M 1.37 0.48 0.87 .31 0.46 0.83 1 2^ 5 1.30 0.46 0.92 .24 0.44 0.87 3 5 1.22 0.52 0.86 .17 0.49 0.82 3 5^ 1.16 0.49 0.90 .11 0.47 0.86 3 6 1.11 0.47 0.94 .05 0.44 0.89 4 7 0.92 0.52 0.91 0.88 0.50 0.87 4 8 0.85 0.48 0.96 0.81 0.46 0.91 * For broken stone. t For gravel or stone and gravel. Timber Structures. Various tables, etc., are given in the following pages which may be found useful in the design of timber structures. The formulas for bending moments are given on page 221. The common flexure formula for beams of any shape is: Me I where S = stress on extreme fiber in pounds per square inch M = bending moment in inch-pounds c = distance from neutral axis to extreme fiber in ins. 7 = moment of inertia in inches 4 STRUCTURAL DIAGRAMS AND TABLES 233 TABLE 42 ALLOWABLE UNIT STRESSES AND WEIGHTS OF TIMBER Kind of Timber Ten- sion COMPRESSION SHEARING Weight in Lbs. per Cubic Foot Dry* With Grain Across Grain With Grain 4 Across Grain End Bear- ing Col- umns Under 15 Diams. Factor of Safety 10 5 5 4 4 White oak 1200 700 1200 800 900 800 800 600 600 700 850 700 1400 1100 1400 1200 1100 1000 1200 1100 1000 1100 1000 800 1000 900 800 750 900 800 750 750 800 800 800 500 200 350 200 250 200 200 150 200 200 250 150 200 100 150 130 100 ioo 100 ioo 150 100 1000 500 1250 iooo '756 f 600 | 400 500 46.4 25.6 38.1 32.1 38.4 30.2 25.0 26.4 to 32.3 29.8 23.1 41.0 26.2 25.0 White pine Southern long-leaf pine Douglas fir Short-leaf yellow pine . Norway pine Spruce and eastern fir. Hemlock Cvoress v_y p Cedar Chestnut Cal. redwood Cal. spruce * The weights of green or unseasoned timbers are 20 to 40 per cent greater. The above unit stresses are recommended by the Association of Railway Superintendents of Bridges and Buildings. They are for unseasoned timber. For structures not subjected to impact, these stresses may safely be increased 25 per cent. For columns having a length greater than fifteen times the least dimen- sion, the safe end-bearing stress may be obtained by the following formula: when Si = allowable compression in column 5 = allowable end-bearing from table L = length of column in feet d = least side of column in inches 234 WORKING DATA FOR IRRIGATION ENGINEERS <& 5 g o xi ?s? &S- Q -iCOO i- i-l rH i-H (N C^ CO O I 3 2^ 15* 2% 15* 2 15* 15* 2 2 15* 15* 5* 5* 30 32 34 36 38 40 42 44 46 48 50 52 54 56 58 60 62 64 66 68 70 72 2 2 15* 15* 2 2 2 15* 15* 5% 2% 5M 1J* 1J* 1M 15* 4 4 3% 2 2 15* 15* 15* 15* 3 3 2% 2% 2M 2 4 2 2 2 15* 5 4% 3% For rectangular beams c = and / 12 and the formula becomes 5 = . a 2 The values of c and I for other shapes of cross-section may be found in any standard pocket-book. Table 43 is convenient for proportioning wooden beams. b d? M This table gives values of = -=-, where M is in foot- o /\ LA o pounds. To determine the size of a rectangular wooden beam, divide the bending moment in foot-pounds (equal to the bend- STRUCTURAL DIAGRAMS AND TABLES 241 ing moment in inch-pounds divided by 12) by the allowable stress in the wood; enter the diagram with the resulting quotient and read the depth and width of beam required. Example: A wooden beam is to be subjected to a bending moment of 50,000 foot-pounds; the allowable unit stress is 1,200 pounds per square inch; -~- = ' = 41.7. From the table we find o 1,ZUU that a 12 x 16-inch beam gives a value of -~ of 42.67. Other o combinations of b and d also approximate the desired value of MlS, and the best combination to use must be decided on economical and practical considerations. Table 46 gives the spacing, in inches, of round bars for pipes under pressure. It is intended primarily for the reinforcing bars of concrete pipes, but may also be used for determining the spacing of bands on wood pipe. Fig. 41 gives similar data, but covers a much larger range, and is especially adapted to wood stave and concrete pipe of larger sizes and greater heads than are included in the table. This diagram gives without computation the spacing of bands or rods for heads from 20 to 200 feet, diameters of pipe from 18 to 120 inches, diameters of steel rods or bands from J^-inch to 1 inch, and stresses in steel from 10,000 to 15,000 pounds per square inch. Example of Use of Diagram. Given a 60-inch diameter wood pipe with a head of water of 150 feet. What size and spacing of bands are required, the working stress in bands to be 12,000 pounds per square inch ? Solution : Enter the diagram at head = 150 feet; thence horizontally to the line for 60-inch pipe; thence down to the line for J^-inch band. Here it is noted that j^-inch bands would require a spacing of 0.57 inch. This spacing is impracticable, as is also the size of band for this pipe; we, therefore, follow diagonally to the right and note that J^-inch bands would require a spacing of 1 inch; continuing down diagonally we note that J^-inch bands would require a spacing of 1.56 inches and %-inch bands would re- quire a spacing of 2.25 inches. If it is decided to use %-inch bands, we now follow down vertically to the line for 10,000 242 WORKING DATA FOR IRRIGATION ENGINEERS pounds per square inch stress; thence diagonally to the right to the line for 12,000 pounds per square inch stress and read the spacing 2.7 inches for %-inch bands, for a 60-inch pipe under a head of 150 feet, the working stress in the bands being 12,000 pounds per square inch. The formula on which the diagram is based is shown on the drawing. Table 47 gives miscellaneous data in regard to the design and construction of wood pipe. TABLE 47 MISCELLANEOUS DATA FOR WOOD PIPE Economical Thickness of Staves MACHINE-BANDED PIPE CONTINUOUS PIPE Diameter of Pipe, Thickness of Staves, Diameter of Pipe, Thickness of Staves, Inches Inches Inches Inches 4 1A 24 1^ 6 1A 36 *H 8 IK 48 1 10 1H 60 l 5 / 8 or2y s 12 1 1% 72 2y s or 2y 2 14 1 1% 84 2y 2 or zy 8 16 18 IX 1% 96 108 2 5 /8 or 3y 8 sy 8 or zy 2 20 1* 120 3 5 / 8 or 4 24 1* 132 3% or 4^ 144 3% or 4^ MAXIMUM CURVATURE ON WHICH SOME WOOD STAVE PIPES HAVE BEEN BUILT Diameter, Thickness Radius Radius of Curve Feet Inches. Feet Diameter of Pipe 2.0 IK 58 29 2.5 4.0 4.7 5.0 7.0 2 89 83 100 106 296 Horizontal Horizontal Vertical Concave Vertical Convex Horizontal 35 21 21 21 43 These were about the sharpest curves the respective pipes would stand. Convex vertical curves (^^) are easiest to build; concave vertical curves ( ^ ) are next, and horizontal curves are the most difficult on account of the difficulty of applying the necessary pull to the pipe to throw it into the curve. NOTE. The above data on thickness of staves and maximum curvature were furnished by Mr. H. D. Coale. Chief .Engineer. Pacific Tank and Pipe Company, Portland, Ore. STRUCTURAL DIAGRAMS AND TABLES 243 s= Spacing, center to center of rod Cinches) 0.20.250.3 0.4 0.50,60.70.80.91 1,5 2 2.5 3 4 5 6 7 8 9 10 12 X S ^ " 1 ^\ ^\ \ \ \ \ S 5 ^ ^ \ ^ S V 150 \^ c v\\\ N \ \ V s \ \ X ^ . \ \\\\ ^ \ \ \ \\ s. 5i ^ s. N ^ ^ ~^s^Or' s \ \ v \ ^^ ^ \ ^^ sX ^\ \ \ \ ^ \\\ \ \ v > \ X ^^s \ \ \ v ^ \ \ \ \\ v * on ... g 90 s-S s - N - \s < jjSJ 80 - ^rN vN r^~ ^~^s \\ ' \ \ 3 70 . * \ \ ^ V !v s ! S ^ ^ V ^ ^ \ ( s V \ \ > ^ ^ s N s. \ S . ^ ^L \ \\ \ % \ V A ^- s^ s vr^S X 1 s ^\ \ \, v V^^^i,^^^ i!!: ] S N \ \\ \ z S v \>\^s,s v ^ \ x V ^ sX 40 \ ^ v\ ^ S \ \ \ x \ \ X ^\^S 11L '/ i^ Q^f P g ( \ r\C ffi x \ flw ^ \ i L ftp t 20 tt<; d x \ \ \ \ \ \ \ \ v v s 1! ^; "^ Jr iJH ^ X f X x X \ \ \ \ \ \ V \S\ N ^ \ \ ^ ^ s^ v x \N - v ^ s ^ \ % \* 1/2 1 5/ i %i 1 -8 1 S ioooo-S| iiooo g 5 12 000 S M A 13000.2" 14000| 15000 ^d (n i i i x \ X ^ \ x N " v ' \ v s > \ \ \ \ s sN S3 ^ I X \ ^ s ^ \ \ y s s v X S ^ V^ V ^ S S S \ 4 i \ *\ ^\\ \\ \ \ \ S s \ ^ ill \ V ; x \ \ S \ s \ \ s \ X V \ S x S^ S x ^ \ \\ s x \ sS o ^^ 5 ' X \ !||j| \ \ \ v s s Sl^ 1 \ \^ \ \ \ \ ^ ^ ; J 5 J S ll 111 V' 11 1 X K \ x \ \ i \ \ S \ x iv \ ^X ^ s \ X ^l| Hi? :vl|^ 1 A \ X^ l \ \ \ ^ \^\ \ \ S io;^ Formula 2-307 f- spacing in inches area of band or rod in sq.ins. unit stress in band or rod head of water in feet on centei of pipe inside radius of pipe in inches \ \\\^\\\ M$\ \ \ \ s\\\^ \A\ \ A \ \^^\^ All x \ \\^J ' xV r s s j^ 3-K 1 1 \ \ \^\ i. vvS v^N tv SM;S \ y S * ^V JA x 5S S \ H\ A v KvSi \ .\ Si ^ ^ \ 1 1.5 2 2.5 3 4 5 6 7 8 910 1 s = Spacing center to center of rod (inches) FIG. 41. Spacing of Bands on Wood Stave Pipe and Reinforcement Rods in Concrete Pipe. 244 WORKING DATA FOR IRRIGATION ENGINEERS SIZE OF WIRE USUALLY USED FOR WINDING MACHINE-BANDED PIPE Gage Number Diameter, Inches Area, Square Inches Breaking Strength at 60,000 Lbs. per Sq. In. 0. . .307 .074 4440 1 2 4 .283 .263 225 .063 .054 040 3774 3258 2388 6. 192 029 1734 8 .162 .021 1236 Fig. 42 gives the thickness of steel pipe for three different efficiencies of joint, single riveted at 55 per cent, best double riveted at 72 per cent, and lock-bar pipe at 90 per cent. The lock-bar joint is capable of developing 100 per cent efficiency; but, due to occasional defects in material or workmanship on the lock-bars, an efficiency of 90 per cent is recommended for cal- culating the thickness. The thickness given in the diagram is the net thickness of steel required to withstand the given pressure at a unit stress in the steel of 16,000 pounds per square inch. It is customary to allow a slight excess of thickness to take care of the weakening by corrosion. The following table * gives the greatest allowable depth of earth cover over steel pipe in feet. If a pipe is to be subjected to a greater pressure of earth than indicated in the table, the thickness must be increased or the pipe shell reinforced with angle irons or other suitable shapes. DIAMETER OF PIPE Thickness 30 Inches 36 Inches 42 Inches 48 Inches 54 Inches 60 Inches 72 Inches 8 5 8 '5 'i '3 12 9 6 5 4 3 2 3/ 18 12 9 7 6 4 3 _7_ 25 17 12 9 8 6 4 I/ 22 16 12 10 8 6 5 /8 15 12 9 * Figures taken from "American Civil Engineers' Pocket Book," Mansfield Merriman, Editor- in-Chief, John Wiley & Sons, New York City. STRUCTURAL DIAGRAMS AND TABLES 245 .2170 H ^ ormula it = thickness of shell in inches diameter of pipe " head of water unit stress in steel = 16 000 c. = efficiency of joint Approximate weight per linear foot: (12.5 x diameter x thickness) + 10 Ibs. Best Double Riveted 72-* :-bar 90% efficiency of joint Thickne&b In Inches (working Strees 16 000 #/n"j FIG. 42. Thickness and Weight of Steel Pipe. 246 WORKING DATA FOR IRRIGATION ENGINEERS Example oj Use of Diagram. Given a 72-inch steel pipe for a power plant under a static head of 200 feet; an allowance of 50 per cent is to be made for water-ram and 10 per cent for cor- rosion, making the total head (200 X 1.60) = 320 feet. Enter the diagram at a head of 320 feet, thence horizontally to the line for 72-inch pipe, then vertically down and read thickness slightly more than /{ 6 inch for single-riveted joint, slightly less than J{ 6 inch for double-riveted joint, and slightly more than 1 % 2 inch for the lock-bar. Single riveting is seldom used for any but unimportant and temporary structures. Carrying the above example further, we note from the foregoing table that the /16-inch shell will withstand a back-fill of 4 feet, and the "^-indi shell will withstand between 2 and 3 feet. The approximate weight of the pipe is given by the formula shown in the diagram. Table 48 gives the American Water Works Association Standards for thickness and weight of cast-iron pipe. Table 49 gives the dimensions and weights of metal flumes as manufactured by the Hess Flume Co. of Denver, Col. Fig. 43 gives the pressure of water in pounds per square inch, corresponding to heads up to 460 feet. The diagram contains two pairs of scales, those at top and left belonging to the upper line, and those at bottom and right belonging to the lower line. Example 1- What is the pressure corresponding to a head of 97 feet? Enter the diagram on the left at a head of 97 feet, thence horizontally to the upper line, thence vertically to the top scale and read 42 pounds per square inch. Example 2. What is the pressure corresponding to a head of 285 feet? Enter the diagram on the right at a head of 285 feet, thence horizontally to the lower line, thence vertically to the lower scale and read 124 pounds per square inch. Fig. 44 gives the pressure of water in pounds per square foot for heads up to 380 feet. Its construction and manner of use are similar to Fig. 33. Fig. 45 gives the total horizontal hydraulic pressure on a wall 1 foot long for heads up to 100 feet. This diagram is useful in the design of dams and retaining walls. For retaining walls for resisting earth pressures without surcharge, the pressures given by the diagram may be multiplied by 0.35 to 0.45 according to STRUCTURAL DIAGRAMS AND TABLES 247 the nature of the back-filling material, to obtain the total earth pressure. For pressures up to 30 feet, the lower line and lower scale are used. For pressures from 30 to 100 feet, the upper line and upper seals are used. Example 1- What is the total pressure on section of wall 10 feet long under a hydrostatic head of 75 feet? Enter the diagram on the left at a head of 75 feet, thence horizontally to the upper line, thence vertically to the upper scale, and read 176,000 pounds for a section of wall 1 foot long. For the 10-foot section the pressure will, therefore, be 1,760,000 pounds. Example 2. A retaining wall for earth is 25 feet high. What is the total earth pressure on a section of the wall 8 feet long? From the lower line of the diagram we read the hydro- static pressure to be 19,500 pounds per linear foot of wall. TABLE 48 CAST-IRON PIPE THICKNESS AND WEIGHT (American Water Works Association Standards) CLASS A CLASS B 100 FEET HEAD 200 FEET HEAD 43 POUNDS PRESSURE 86 POUNDS PRESSURE Nomi- nal Inside Weight per Weight per Diam- eter Thick- Thick- ness, Inches ness, Inches Foot 12-Foot Length Inches Foot 12-Foot Length Laid Laid 4 .42 20.0 240 .45 21 7 260 6 .44 30.8 370 .48 33.3 400 8 .46 42.9 515 .51 47.5 570 10 .50 57.1 685 .57 63.8 765 12 .54 72.5 870 .62 82.1 985 14 .57 89.6 1075 .66 102.5 1230 16 .60 108.3 1300 .70 125.0 1500 18 .64 129.2 1550 .75 150.0 1800 20 .67 150.0 1800 .80 175.0 2100 24 .76 204.2 2450 .89 233.3 2800 30 .88 291.7 3500 1.03 333.3 4000 36 .99 391.7 4700 1.15 454.2 5450 42 1.10 512.5 6150 1.28 591.7 7100 48 1.26 666.7 8000 1.42 750.0 9000 54 1.35 800.0 9600 1.55 933.3 11200 60 1.39 916.7 11000 1.67 1104.2 13250 72 1.62 1283.4 15400 1.95 1545.8 18550 84 1.72 1633 . 4 19600 2.22 2104.2 25250 All weights include standard sockets. 248 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 48 (Concluded) CAST-IRON PIPE THICKNESS AND WEIGHT CLASS C CLASS D 300 FEET HEAD 400 FEET HEAD 130 POUNDS PRESSURE 173 POUNDS PRESSURE Nomi- nal Weight per Weight per Inside 1*U Itw Thick- Diame- 1 niclc- ness, eter, Inches ness, Inches Foot 12-Foot Length Inches Foot 12-Foot Length Laid Laid 4 .48 23.3 280 .52 25.0 300 6 .51 35.8 430 .55 38.3 460 8 .56 52.1 625 .60 55.8 670 10 .62 70.8 850 .68 76.7 920 12 .68 91.7 1100 .75 100.0 1200 14 .74 116.7 1400 .82 129.2 1550 16 .80 143.8 1725 .89 158.3 1900 18 .87 175.0 2100 .96 191.7 2300 20 .92 208.3 2500 1.03 229.2 2750 24 1.04 279.2 3350 1.16 306.7 3680 30 .20 400.0 4800 1.37 450.0 5400 36 .36 545.8 6550 1.58 625.0 7500 42 .54 716.7 8600 1.78 825.0 9900 48 .71 908.3 10900 1.96 1050.0 12600 54 1.90 1141.7 13700 2.23 1341.7 16100 60 2.00 1341.7 16100 2.38 1583.3 19000 72 2.39 1904.2 22850 84 All weights include standard sockets. The total hydrostatic pressure on an 8-foot section, there- fore, is 19,500 X 8 = 156,000 pounds. The earth pressure will equal from 0.35 to 0.45 of this, or 55,000 to 70,000 pounds, depending upon the nature of the back-fill, the material having the steepest angle of repose producing the smallest pressure, and vice versa. Fig. 46 gives the theoretical horse-power of falling water. The diagram gives horse-powers directly for quantities up to 75 c. f . s. and falls up to 50 feet. The diagram may be used for higher values of quantity or fall by dividing by 10 before enter- ing the diagram, and then multiplying the resulting power by 10. Example 1. What horse-power is produced by 45 c.f.s. of water falling 27 feet? Enter the diagram at the lower scale at Q = 45, thence vertically to the line representing a fall of 27 feet, thence horizontally to the scale at the left and read 138 horse-power. STRUCTURAL DIAGRAMS AND TABLES 249 3-3 B I .SP5^ ^o "30 O OSC^^OS ssssss i iOOOOC5OO' i (N(N(N(N-i I OOi I TH i (-iCOiOCOI>l>QOOOO5OOi i ^^ H 2 ! ?3m the Formula 434H --at " IK \ h i !/ ^EEEEE lilllliilll lead of water in feet K ::: II 40--- I 35 30 25 20 15 10 oLLL . -220 200 140 120 40 60 80 100 120 140 p = Pressure in pounds per square inch FIG. 43. 160 180 200 STRUCTURAL DIAGRAMS AND TABLES 251 100 mTf p= Pressure in Pound 00 1000 1500 2000 2500 3000 350C Pressure of Water 18 per Sq.Foot (Pounds per Sq. Foot) 4000 4500 5000 5500 6000 75 45 : : : : - : Pressure of Water in Pounds per Squ Corresponding to Different He Calculated from Formula [[ Lfffl are Foot : : 7 ads ----------- f--- 1 i 1 i 1 i 1 -ft--- --400 -- 2 --- ---^380 2 t 4 360 ^ .2 340 _^ -t 320 2 t 300 2 t.. 280 fr 35 30 20 -- 15 10 5 -- 7 * gEE efe L. m III ill 4000 6000 8000 10000 12000 1400 jp = Pressure in Pound ^z::!:::::::::::::::: 240 ^ 1 IN 1 1 1 1| || 1 1 1| 1 1 HI [ w :__:: ::::::::: : x 160 --- - 140 120 --100 ::::::: so 16000 18000 20000 22000 24000 3 per Sq.Foot FIG. 44. 252 WORKING DATA FOR IRRIGATION ENGINEERS Total Hydrostatic Pressure p = Total Hydrostatic Pressure in Thousands of Pounds r 345 30 25 20 50 100 150 250 300 I I I I I I I I I I I' Total Hydrostatic Pressure on Walls and Dams Calculated from the Formula H 2 W* weight of a cubic foot of water H - height of wall or dam p = total pressure per linear foot Note :-For retaining walls for earth without surcharge multiply the values taken from this diagram by 0.35 to 0.45 5 10 15 20 p = Total Hydrostatic Pressure in Thousands of Pounds FIG. 45. 30 STRUCTURAL DIAGRAMS AND TABLES 253 400 Horse Power 50 45 40 35 350 250 5150 100 Theoretical Horse Power of Falling Water Calculated from Formula: HQ i n . 8.81 Q = Discharge in Cubic Feet per Second H = Fall of Water in Feet 25' 15 10 5 10 15 20 25 30 35 40 45 50 55 Quantity c.f .s.= Q FIG. 46. 70 75 254 WORKING DATA -FOR IRRIGATION ENGINEERS Example 2. What horse-power is produced by 155 c.f. s. dropping 30 feet? 155 c. f. s. is not represented on the diagram, but 15.5 c.f.s. is. We, therefore, enter at 15.5 c.f.s., and following through the same process as in example 1, read 52 horse- power. This is only one-tenth of the real horse-power, as the quantity used was only one-tenth of the real quantity. The real horse-power is, therefore, 520. Example 3. What horse-power is produced by 65 c. f . s. dropping 120 feet? 120 feet fall is not represented on the diagram, but 12 feet is. We, therefore, enter the diagram at Q = 65, and from the line representing a fall of 12 feet, read 89 horse- power. The real horse-power is, therefore, 890. Example 4. What horse-power is produced by 160 c.f.s. dropping 230 feet? In this case, both quantity and fall must be divided by 10 before entering the diagram, and the horse- power read must then be multiplied by 100. Entering the diagram with Q = 16 and H = 23 we read the horse-power to be 47. The real horse-power, therefore, is 4,700. CHAPTER VI MISCELLANEOUS TABLES AND . DATA CHAPTER VI MISCELLANEOUS TABLES AND DATA TABLE 50 AVERAGE WEIGHT, IN POUNDS PER CUBIC FOOT, OF VARIOUS SUBSTANCES Substance Weight Substance Weight Clay, earth and mud : Clay Earth, dry and loose . . . Earth, dry and shaken . Earth, dry and moderately rammed Earth, slightly moist, loose Earth, more moist, loose . . Earth, more moist, shaken Earth, more moist, moder- ately rammed Earth, as soft flowing mud Earth, as soft mud well pressed into a box . . . Mud, dry, close Mud, wet, moderately pressed Mud, wet, fluid Masonry and its materials: Brick, best pressed Brick, common hard. . . . Brick, soft, inferior Brickwork, pressed brick, fine joints Brickwork,medium quality Brickwork, coarse, inferior soft bricks Cement, pulverized, loose . Cement, pressed Cement, set Concrete, 1:3:6 Gravel, loose Gravel, rammed Masonry of granite or stone of like weight: Well dressed Well-scabbled rubble, 20 per cent mortar. Roughly scabbled rubble, 25 per cent to 35 per cent mortar. Well-scabbled dry rubble. . 122-162 72-80 82-92 90-100 70-76 66-68 75-90 90-100 104-112 110-120 80-110 110-130 104-120 150 125 100 140 125 100 72-105 115 168-187 140 82-125 90-145 165 154 150 138 Masonry and its materials (continued) : Roughly-scabbled dry rubble Masonry of sandstone or stone" of like weight weighs about seven- eighths of the above. Mortar, hardened Sand, pure quartz, dry, loose Sand, pure quartz, dry, slightly shaken.. . . Sand, pure quartz, dry, rammed Sand, natural, dry, loose Sand, natural, dry, shaken Sand, wet, voids full of water Stone Stone, quarried, loosely piled Stone, broken, loose Stone, broken, rammed. Metals and alloys Brass (copper and zinc) . . Bronze (copper and tin) . . Copper, cast Copper, rolled Iron and steel, cast Average Iron and steel, wrought. . Average Spelter or zinc Tin, cast Steel Tin Zinc Mercury (32 F.) Woods: See page 233 125 90-115 87-106 92-110 100-120 80-110 85-125 118-128 135-195 80-110 77-112 79-121 487-524 524-537 537-548 548-562 438-483 450 475-494 480 425-450 450-470 490 459 438 849 257 258 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 51 CONVENIENT EQUIVALENTS LENGTH (See Table 53) SURFACE 1 square inch = .006944 square foot = .0007716 square yard = .0000001594 acre = .0000000002491 square mile = 6.45163 square centimeters. 1 square foot = 144 square inches = square yard = .000022957 acre = .00000003587 square mile = .092903 square meters. 1 square yard = 1,296 square inches = 9 square feet = .0002066 acre = .0000003228 square mile = .83613 square meter. 1 acre = 6,272,640 square inches = 43,560 square feet = 4,840 square yards = .0015625 square mile = 208.71 feet square = .404687 hectare. 1 square mile = 4,014,489,600 square inches = 27,878,400 square feet = 3,097,600 square yards = 640 acres = 259 hectares. 1 square meter = 10,000 square centimeters = .0001 hectare = .000001 square kilometer = 1,550 square inches = 10.7639 square feet = 1.19598 square 002471 acre = .0000003861 square mile. , yards = .0002471 acre VOLUME 1 cubic inch = .004329 U. S. gallon = .0005787 cubic foot = 16.3872 cubic centimeters. 1 U. S. gallon = 231 cubic inches = .13368 cubic foot = .00000307 acre- foot = 3.78543 liters. 1 cubic foot = 1,728 cubic inches = 7.4805 U. S. gallons = .037037 cubic yard = .000022957 acre-foot = 28.317 liters. 1 cubic yard = 46,656 cubic inches = 27 cubic feet = .00061983 acre-foot = .76456 cubic meter. 1 acre-foot = 325,851 U. S. gallons = 43,560 cubic feet = 1,613^ cubic yards = 1,233.49 cubic meters. 1 cubic meter, stere or kiloliter = 1,000,000 cubic centimeters = 1,000 liters = 61,023.4 cubic inches = 264.17 U. S. gallons = 35.3145 cubic feet = 1.30794 cubic yards = .000810708 acre-foot. HYDRAULICS 1 U. S. gallon of water weighs 8.34 pounds avoirdupois. 1 cubic foot of water weighs 62.4 pounds avoirdupois. 1 second-foot = 448.8 U. S. gallons per minute = 26,929.9 U. S. gallons per hour = 646,317 U. S. gallons per day. = 60 cubic feet per minute = 3,600 cubic feet per hour = 86,400 cubic feet per day = 31,536,000 cubic feet per year = .000214 cubic miles per year. = .9917 acre-inch per hour = 1.9835 acre-feet per day = 723.9669 acre-feet per year. = 50 miner's inches in Idaho, Kansas, Nebraska, New Mexico, North Dakota, and South Dakota = 40 miner's inches in Arizona, California, Montana, and Oregon = 38.4 miner's inches in Colorado. = .028317 cubic meters per second = 1.699 cubic meters per minute = 101.941 cubic meters per hour = 2,446.58 cubic meters per day. MISCELLANEOUS TABLES AND DATA 259 1 cubic meter per minute = .5886 second-feet = 4.403 U. S. gallons per second = 1.1674 acre-feet per day. 1 million gallons per day = 1.55 second-feet = 3.07 acre-feet per day = 2.629 cubic meters per minute. 1 second-foot falling 8.81 feet = 1 horse-power. 1 second-foot falling 10 feet = 1.135 horse-power. 1 second-foot falling 11 feet = 1 horse-power, 80 per cent efficiency. 1 second-foot for 1 year will cover 1 square mile 1.131 feet or 13.572 inches deep. 1 inch deep on 1 square mile = 2,323,200 cubic feet = .0737 second-feet for 1 year. MISCELLANEOUS 1 foot per second = .68 mile per hour = 1.097 kilometers per hour. 1 avoirdupois pound = 7,000 grains = .4536 kilogram. 1 kilogram = 1,000 grams = .001 tonne = 15,432 grains = 2.2046 pounds avoirdupois. {15 pounds per square inch. 1 ton per square foot. 1 kilogram per square centimeter. Acceleration of gravity, g, = 32.16 feet per second per second. 1 horse-power = 5,694,120 foot-gallons per day = 550 foot-pounds per second = 33,000 foot-pounds per minute = 1,980,000 foot-pounds per hour = 76 kilogrammeters per second = 1.27 kilogrammeters per minute = 746 watts. TABLE 52 INCHES AND FRACTIONS EXPRESSED IN DECIMALS OF A FOOT Inches FRACTIONS OF INCHES H M H H 5 /s H y s .0000 .0104 .0208 .0313 .0417 .0521 .0625 !0729 1 .0833 .0937 .1041 .1146 .1250 .1354 .1458 .1562 2 .1667 .1771 .1875 .1980 .2084 .2188 .2292 .2396 3 .2500 .2604 .2708 .2813 .2917 .3021 .3125 .3229 4 .3333 .3437 .3541 .3646 .3750 .3854 .3958 .4062 5 .4167 .4271 .4375 .4480 .4584 .4688 .4792 .4896 6 .5000 .5104 .5208 .5313 .5417 .5521 .5625 .5729 7 .5833 .5937 .6041 .6146 .6250 .6354 .6458 .6562 8 .6667 .6771 .6875 .6980 .7084 .7188 .7292 .7396 9 .7500 .7604 .7708 .7813 .7919 .8021 .8125 .8229 10 .8333 .8437 .8541 .8646 .8750 .8854 .8958 .9062 11 .9167 .9271 .9375 .9480 .9584 .9688 .9792 .9896 12 1.0000 260 8 -IS! - WORKING DATA FOR IRRIGATION ENGINEERS I ,34 s I ! MISCELLANEOUS TABLES AND DATA 261 Table 57 is designed for use in stadia work and gives the difference in elevation corresponding to specified slant distances for vertical angles of to 20. The horizontal dis- tances corresponding to the slant distances are also given for various vertical angles. Example. With the instrument at A a vertical angle of 3 10' is observed on a point B which is distant 350 feet by stadia reading; find the difference in elevation of A and B and the horizontal distance A B. Opposite 3 10' in the first column of the table, 16.5 is found under a distance of 300 and 22.1 under a distance of 400; and interpolation for a distance of 350 feet gives 19.3 feet for the difference in elevation of A and B. Inter- polation for 350 between the values in the 300 and the 400 dis- tance columns of the horizontal distance lines at 3 and 4 gives, respectively, 349.0 and 348.2; and an additional interpolation gives, for an angle of 3 10' and a slant distance of 350, a hori- zontal distance of 348.9. The horizontal distance of A B is, therefore, 348.9 feet. Another method of making interpolations is as follows: Opposite 3 10' read as before, 16.5 feet vertical distance under the slant distance 300; then under the slant distance 500 and vertical angle 3 10' read 27.6 feet, and divide this by 10 to get the vertical distance for 50 feet equals 2.76; add this to 16.5 and obtain 19.3 as the vertical distance for 350 feet. By a similar process the horizontal distances are found. If the slant dis- tance were 355 feet the vertical distance would be 16.5 + 27.6 , 27.6 ~To~ Too" = 19 ' 5 ' anc * so on * 262 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 54 TABLE FOR CONVERTING METERS AND METERS CONVERTED INTO FEET METERS O 10 20 30 4O 5O 6O 7O 8O 9O 1OO 11O 12O 130 14O ISO 160 17O ISO 19O 2OO 21O 220 230 24O 250 26O 27O 28O 29O 30O .8083 I3I- 2 "', 164 .233 Ov 2 041 .6581 4664 -3 19 /64 .2747 295 328 .083 .8913 '/32 7000 QQQ-8 13 030 .70( 426 :Bn 45 g-3",. 492:124-5 524:^8 .7411 5494 -4'%4 .3577 666-.iar 688 -$& 70l-9 25 / 6 4 /2I .7826 764:iJSi 787:^2 820 .2083 863:8;?- 886:83- 9511;% 3-3 a /s .2801 36:j;'" 68: 2808 1Vi 0891 |Q/-6 11 /64 I04 74 05 /3 7 J 1 Vo4 .5140 107 .3223 200:lSi f . non-ir 7 ^ 202 .9389 265 298 33l: 4 3M' .7472 6 43 /64 .5555 .1721 QQC-11 49 /* 03 b .9808 /OO-9 16 / 3S 423 .7887 .4053 ~2136 ~021 6 9 -9 31 /32 .8302 -7 21 /32 6 23 85 T4468 -3V, 6 .2551 ~0 49 /64 .0634 70 r 720 .8717 000-5 55 /64 020 .4883 QCC-3 9 /i6 000 .2966 .1049 .9132 954 :f 215 OO"I ~ 6 23 /6^ 307 .5298 6-6 47 /S4 .5616 39 .3700 72 .1782 in/. -ii"/32 104 .9865 IO7-9 17/32 lO/ .7948 1 70 .603? 236:i 4 iU? .0280 30I-.K 400 .6446 -5 7 /i .4529 -3V64 .2616 .0699 /CC-10 r /32 4bO .8778 /QQ-8 15 / 6 4 430 .6861 .ino TftS ~7276 T5359 T3442 7 61 "j 525 Tno-H 17/32 /JO .9608 "769*1* ".5774 OCO-0 300 .0023 8106 4 3 9 . 42 .6508 7C -5 1 / 2 /O .4591 I08T26% |/|-0 29 /32 141 .0756 |7Q-10 39 /64 I/O .8839 -10 7 /64 .8424 1922 239*5006 272~3088 305:i','7i 337 :1S? 469 COQ bOO .3918 -2 13 /32 .2002 .0085 CQQ-9 5 V 6 4 D30 .8168 764' 5 QQfl OOU 4 i 34 .2417 -0 19 /32 .0499 ~858 7 3 895 .6666 QftQ_ 5 43 /64 320 .47 2 49 ~2832 4 994:J9 / .'i 4 n^\" .12 3 33 -8 7 /, .16 4 48 ~iVSi ~78H .5897 ~3980 .2063 Q7 / -0 11/ 64 0/4 .0146 .4395 .2478 ~.056T ~672 6 7 CQC-5 49 /64 bOb .4^10 66972893 7Q/ 704 .0976 -10 7 /8 .9059 .7142 ~ 522*5 OQQ-3 31 /32 000 .3308 .1391 -11 3 /8 .9474 Ol .7557 964-.5 6 6 7o nOTP-4 15 /32 337 .3723 5 -4-V I6.404 3 ! 2 49: 2 2 ;^ 82 ov .0207 14711% OlO-3 3 ^4 2I0.2539 .8705 Ql|-8 9 /64 011.6788 Q / / 5"/32 044.4871 .2954 .7203 50813: 541:^9 674:UM .9535 .76J 6 8 "570*1 ".3784 4 7OO-2 15 / 6 4 700.1867 .9950 .8033 -7 11 /32 .6116 -5 1 /32 .4199 -2 47 /64 .2282 .0365 836 869 902 .8448 NOTE: Values of converted even meters are expressed of 1 foot. For example 74 meters = 242 '-9 8 / 8 "or 242.781'. table. For example .3 meter = 11.811 inches = .984 ft.= To convert 147.678 meters into feet:147. 000 m= 482.282 ft, .6 = 1.986" .07 "= .229 " .008"= .026" From Engineering News.March 12, 1914, Reproduced by permission of the originator, Mr. H. P. Quick, Consulting Engineer, New York. 147.G78m=484.505 MISCELLANEOUS TABLES AND DATA 263 TABLE 54 (Concluded') MILLIMETERS INTO FEET AND INCHES WITH INCHES TO NEAREST 64 IOTHS ETC. OF i METER CONVERTED mo B'* 19 .6849 52S 851o1 6 .1098 18313? 2161347 2491& 282:i5( 3 6 3861% 413-1819 .0011 544ir p/,n-0 33 /64 040.0426 .2343 O 33 /* .8509 "6592 2 -3Vn 774:3$ 839 : .7008 938:^' 003: 9 P' 7 10-11 19/ Sa 22.9658 55"77 9 41 4 -6 63 /s .5824 I54:?; IO/ .0073 0|Q-9 25 / 32 219.8194 orn-7 31 /64 252.6231 31813s 351:8481 4I61& - 3^/64 .2820 547:lt 646:1215 .7484 .17^33 79816 . 7899 007:iSif 8 25-2^4 .2466 -0 21 /3 59:83fe I24:i! I57: 5>A 4 2 7 9 98 288T 288T71 / 30 nno 2.16 3871% 485:88. CIC-9 35 / 6 * DID .7960 682irfe 2209 748: 2 9t 879 .2 G2A 97711 9 291$ 62: 4 33t7 QC-1 47 / 64 90.1440 |Q7-ii 27 /64 127 .9523 METERS .3772 .1855 1OI-11 59/6 < 2al .9938 .8021 QC7-7 21 /64 007 .6104 390:857 423:i2?; .0357 488: 1 843e 521 :Eft 55411? 587: 37/ " 2685 .0768 .8851 CQr-8 21 /64 050 .6934 7l8-.IoT7 75i-j;a 84913% .5433 8l5-fe 948S 980:^82 O 1O 20 30 40 50 60 7O 80 90 10O 110 120 130.03 140 150 16O 170 A INCHES 3.937 7.874 11.811 15.748 19.685 23.622 27.559 31.496 35.433 .04 ,05 06 .07 180.08 190 200 21O 220 230 240 250 260 270 280 290 3OO .09 .393 .787 1.181 1.574 1.968 2.362 2.756 3.149 3.543 .001 002 .003 005 007 .008 009 .039 .078 .118 .157 .196 .236 .275 .315 .354 B FEET .3281 .6561 .984 1.312 1.640 1.968 2.296 2.624 2.952 .032 .065 .098 .131 .164 .196 .229 .262 .295 C FEET AND INCHES TO NEAREST Vs4 Q-7 7 /s" 2-3 9 /e + 2-7 1 /*"- 2m"+ r/; 2" 2% 3%, .003 .006 .009 .013 .016 .019 .023 .026 .029 '/13 '/." y; v* 1 /{ y; 1%'+ 2% ;;+3 5/ " /32 25/" /128 15/" /64 y* 1 3 Flc 6no 9 o 8S 1 2i F 4C 7m in feet and inches to nearest 64th, and also as feet and decimal Fractions of meter are read from the right hand portion of the 0-11%" .07 meter = 2.756 in=.229 ft^O^K" To convert same number to feet and inches: 147.000 m = 482 : 3%" .6 = l-H 5 /8 .07 " = 0-2M .008 " = 0-0 Ke 147.678 m = 264 WORKING DATA FOR IRRIGATION ENGINEERS aj 3 5 ^ 31 < w Hg g en u = u fc ^^ O5 1^* C^ t>* ^H ^H rH (N (N (N CO -C s 5t > - 00 O5 O5 coo(Noo O5I>*OCOi tOicOTtHfNO i ICO" ICO' iiOOOOiO i-H rH i-l i-H (N (N (N I-H cO T ( iO O iA O5 O5 O O TH T-H (N (N -COiOCOC < l'-HOOOI>-COOCO(N' iCTHt^-COOJiOi !I>(NOOTtiOcOC > I Soo T-< CO (N CO "^ iOCOCJi tOOO i-tt^COO5iOO l>cOiOCO (M' O 8O5l>- Or-i S i i IOKOC01 i COrHOOCOCO 09.54 m of the ^ II ^ |i 1 s "I *OcOOOOi (CO^ (N(N(NCOCOCO CO CO COW* T^ tely only. ering N im ngine Appr rom MISCELLANEOUS TABLES AND DATA 265 TABLE 56 CORRECTION IN FEET FOR CURVATURE AND REFRACTION (h = 0.574 Z) 2 ) D = Distance in miles Distance, in Miles .0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1 .6 .7 .8 1.0 1.1 1.3 1.5 1.7 1.9 2.1 2 2.3 2.5 2.8 3.0 3.3 3.6 3.9 4.2 4.5 4.8 3 5.2 5.5 5.9 6.2 6.6 7.0 7.4 7.8 8.3 8.7 4 9.2 9.6 10.1 10.6 11.1 11.6 12.1 12.7 13.2 13.8 5 14.3 14.9 15.5 16.1 16.7 17.3 18.0 18.6 19.3 20.0 6 20.7 21.4 22.1 22.8 23.5 24.2 25.0 25.7 26.5 27.3 7 28.1 28.9 29.8 30.6 31.4 32.3 33.2 34.1 35.0 35.9 8 36.7 37.6 38.6 39.5 40.4 41.4 42.4 43.4 44.4 45.5 9 46.5 47.5 48.6 49.7 50.7 51.8 52.9 54.0 55.1 56.3 10 57.4 58.6 59.7 60.9 62.1 63.3 64.5 65.7 67.0 68.2 11 69.5 70.7 71.9 73.2 74.5 75.8 77.1 78.5 79.8 81.2 12 82.7 84.0 85.4 86.8 88.3 89.7 91.1 92.6 94.0 95.5 13 97.0 98.5 100.0 101.5 103.1 104.6 106.2 107.7 109.3 110.9 14 112.5 114.1 115.7 117.4 119.0 120.7 122.4 124.0 125.7 127.4 15 129.1 130.9 132.6 134.3 136.1 137.9 139.7 141.5 143.3 145.1 16 146.9 148.7 150.6 152.5 154.4 156.3 158.2 160.1 162.0 163.9 17 165.8 167.8 169.8 171.7 173.7 175.7 177.7 179.7 181.8 183.8 18 185.9 188.0 190.1 192.2 194.3 196.4 198.5 200.7 202.8 205.0 19 207.1 209.3 211.5 213.7 216.0 218.2 220.4 222.7 224.9 227.2 20 229.5 231.8 234.2 236.5 238.8 241.2 243.5 245.9 248.3 250.7 21 253.1 255.5 257.9 260.4 262.8 265.3 267.7 270.2 272.7 275.2 22 277.7 280.3 282.8 285.4 288.0 290.5 293.1 295.7 298.3 301.0 23 303.6 306.2 308.9 311.5 314.2 316.9 319.6 322.3 325.0 327.8 24 330.5 333.3 336.1 338.9 341.7 344.5 347.3 350.1 352.9 355.8 25 358.6 361.5 364.4 367.3 370.2 373.1 376.0 379.0 381.9 384.9 26 387.9 390.9 393.9 396.9 400.0 403.0 406.0 409.1 412.2 415.3 27 418.3 421.4 424.5 427.7 430.8 434.0 437.1 440.3 443.5 446.7 28 449.9 453.1 456.3 459.6 462.8 466.1 469.4 472.7 476.0 479.3 29 482.6 485.9 489.3 492.6 496.0 499.4 502.8 506.2 509.6 513.0 30 516.5 519.9 523.4 526.8 530.3 533.8 537.3 540.8 544.4 547.9 31 551.5 555.0 558.6 562.2 565.8 569.4 573.0 576.7 580.3 584.0 32 587.6 591.3 595.0 598.7 602.4 606.1 609.9 613.6 617.3 621.1 33 624.9 628.7 532.5 636.3 640.2 644.0 647,9 651.7 655.6 659.5 34 663.4 667.3 671.2 675.1 679.1 683.0 687.0 690.9 694.9 698.9 35 702.9 707.0 711.0 715.1 719.1 723.2 727.3 731.4 735.5 739.6 36 743.7 747.8 752.0 756.1 760.3 764.5 768.7 772.9 777.1 781.3 37 785.6 789.8 794.1 798.4 802.6 806.9 811.3 815.6 819.9 824.2 38 828.6 833.0 837.4 841.8 846.2 850.6 855.0 859.4 863.9 868.3 39 872.8 877.3 881.8 886.3 890.8 895.3 899.9 904.4 909.0 913.5 40 918.1 922.7 927.3 931.9 936.6 941.2 945.9 950.5 955.2 959.9 266 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 57 STADIA TABLE Slant Distance 100 200 300 400 500 600 700 800 900 2' .. 0.06 0.1 0.2 0.2 0.3 0.3 0.4 0.5 0.5 4 0.12 0.2 0.3 0.5 0.6 0.7 0.8 0.9 1.0 6 0.17 0.3 0.5 0.7 0.9 1.0 1.2 1.4 1.6 8 0.23 0.5 0.7 0.9 1.2 1.4 1.6 1.9 2.1 10 0.29 0.6 0.9 1.2 1.5 1.7 2.0 2.3 2.6 12 0.35 0.7 1.0 1.4 1.7 2.1 2.4 2.8 3.1 14 0.41 0.8 1.2 1.6 2.0 2.4 2.8 3.3 3.7 16 0.47 0.9 1.4 1.9 2.3 2.8 3.3 3.7 4.2 18 0.52 .0 1.6 2.1 2.6 3.1 3.7 4.2 4.7 20 0.58 .2 1.7 2.3 2.9 3.5 4.1 4.6 5.2 22 0.64 .3 1.9 2.6 3.2 3.8 4.5 5.1 5.8 24 0.70 .4 2.1 2.8 3.5 4.2 4.9 5.6 6.3 26 0.76 .5 2.3 3.0 3.8 4.5 5.3 6.0 6.8 28 0.81 .6 2.4 3.2 4.1 4.9 5.7 6.5 7.3 30 0.87 .7 2.6 3.5 4.4 5.2 6.1 7.0 7.8 32 0.93 1.9 2.8 3.7 4.6 5.6 6.5 7.4 8.4 34 0.99 2.0 3.0 3.9 4.9 5.9 6.9 7.9 8.9 36 1.05 2.1 3.1 4.2 5.2 6.3 7.3 8.4 9.4 38 .11 2.2 3.3 4.4 5.5 6.6 7.7 8.8 9.9 40 .16 2.3 3.5 4.6 5.8 7.0 8.1 9.3 10.5 42 .22 2.4 3.7 4.9 6.1 7.3 8.5 9.8 11.0 44 .28 2.6 3.8 5.1 6.4 7.7 9.0 X 10.2 11.5 46 .34 2.7 4.0 5.3 6.7 8.0 9.4 10.7 12.0 48 .40 2.8 4.2 5.6 7.0 8.4 9.8 11.2 12.5 50 ........ .45 2.9 4.4 5.8 7.2 8.7 10.2 11.6 13.1 52 51 3.0 4.5 6.0 7.5 9.1 10.6 12.1 13.6 54 .57 3.1 4.7 6.3 7.8 9.4 11.0 12.6 14.1 56 .63 3.3 4.9 6.5 8.1 9.8 11.4 13.0 14.6 58 .69 3.4 5.0 6.7 8.4 10.1 11.8 13.5 15.2 60 .74 3.5 5.2 7.0 8.7 10.5 12.2 14.0 15.7 10 2' ... 1.80 3.6 5.4 7.2 9.0 10.8 12.6 14.4 16.2 4 1.86 3.7 5.6 7.4 9.3 11.2 13.0 14.9 16.7 6 1.92 3.8 5.8 7.7 9.6 11.5 13.4 15.4 17.3 8 1.98 4.0 5.9 7.9 9.9 11.9 13.8 15.8 17.8 10 2.03 4.1 6.1 8.1 10.2 12.2 14.2 16.3 18.3 12 . , 2.09 4.2 6.3 8.4 10.5 12.6 14.7 16.7 18.8 14 2.15 4.3 6.5 8.6 10.8 12.9 15.1 17.2 19.4 16 2.21 4.4 6.6 8.8 11.0 13.3 15.5 17.7 19.9 18 2.27 4.5 6.8 9.1 11.3 13.6 15.9 18.1 20.4 20 2.33 4.7 7.0 9.3 11.6 14.0 16.3 18.6 20.9 22 2.38 4.8 7.2 9.5 11.9 14.3 16.7 19.1 21.5 24 2.44 4.9 7.3- 9.8 12.2 14.7 17.1 19.5 22.0 26 2.50 5.0 7.5 10.0 12.5 15.0 17.5 20.0 22.5 28 2.56 5.1 7.7 10.2 12.8 15.3 17.9 20.5 23.0 30 2.62 5.2 7.8 10.5 13.1 15.7 18.3 20.9 23.5 32 2.67 5.3 8.0 10.7 13.4 16.0 18.7 21.4 24.1 34 2.73 5.5 8.2 10.9 13.7 16.4 19.1 21.9 24.6 36 2.79 5.6 8.4 11.2 14.0 16.7 19.5 22.3 25.1 38 2.85 5.7 8.5 11.4 14.2 17.1 19.9 22.8 25.6 40 2.91 5.8 8.7 11.6 14.5 17.4 20.3 23.3 26.2 42 2.97 5.9 8.9 11.9 14.8 17.8 20.8 23.7 26.7 44 3.02 6.0 9.1 12.1 15.1 18.1 21.2 24.2 27.2 46 3.08 6.2 9.2 12.3 15.4 18.5 21.6 24.6 27.7 48 3.14 6.3 9.4 12.6 15.7 18.8 22.0 25.1 28.3 50 3.20 6.4 9.6 12.8 16.0 19.2 22.4 25.6 28.8 52 3.26 6.5 9.8 13.0 16.3 19.5 22.8 26.0 29.3 54 3.31 6.6 9.9 13.2 16.6 19.9 23.2 26.5 29.8 56 3.37 6.7 10.1 13.5 16.9 20.2 23.6 27.0 30.3 58 3.43 6.9 10.3 13.7 17.1 20.6 24.0 27.4 30.9 60 3.49 7.0 10.5 14.0 17.4 20.9 24.4 27.9 31.4 Horizontal dist. 99.9 199.8 299.6 399.5 499.4 599.3 699.2 799.0 898.9 MISCELLANEOUS TABLES AND DATA 267 TABLE 57 (Continued] STADIA TABLE Slant Distance 100 200 300 400 500 600 700 800 900 2 2' 3.55 7.1 10.6 14.2 17.7 21.3 24.8 28.4 31.9 4 3.60 7.2 10.8 14.4 18.0 21.6 25.2 28.8 32.4 6 3.66 7.3 11.0 14.6 18.3 22.0 25.6 29.3 33.0 8 3 . 72 7.4 11.2 14.9 18.6 22.3 26.0 29.8 33.5 10 3.78 7.6 11.3 15.1 18.9 22.7 26.4 30.2 34.0 12 3.84 7.7 11.5 15.3 19.2 23.0 26.9 30.7 34.5 14 3.90 7.8 11.7 15.6 19.5 23.4 27.3 31.2 35.1 16 3.95 7.9 11.9 15.8 19.8 23.7 27.7 31.6 35.6 18 4.01 8.0 12.0 16.0 20.0 24.1 28.1 32.1 36.1 20 4.07 8.1 12.2 16.3 20.3 24.4 28.5 32.5 36.6 22 4.13 8.3 12.4 16.5 20.6 24.8 28.9 33.0 37.1 24 4.18 8.4 12.6 16.7 20.9 25.1 29.3 33.5 37.7 26 4.24 8.5 12.7 17.0 21.2 25.5 29.7 33.9 38.2 28 4.30 8.6 12.9 17.2 21.5 25.8 30.1 34.4 38.7 30 4.36 8.7 13.1 17.4 21.8 26.1 30.5 34.9 39.2 32 4 42 8.8 13.2 17.7 22.1 26.5 30.9 35.3 39.7 34 4.47 8.9 13.4 17.9 22.4 26.8 31.3 35.8 40.3 36 4.53 9.1 13.6 18.1 22.7 27.2 31.7 36.3 40.8 38 '. . 4.59 9.2 13.8 18.4 23.0 27.5 32.1 36.7 41.3 40 4.65 9.3 13.9 18.6 23.2 27.9 32.5 37.2 41.8 42 4.71 9.4 14.1 18.8 23.5 28.2 32.9 37.6 42.4 44 4.76 9.5 14.3 19.1 23.8 28.6 33.3 38.1 42.9 46 ! 4.82 9.6 14.5 19.3 24.1 28.9 33.8 38.6 43.4 48 4.88 9.8 14.6 19.5 24.4 29.3 34.2 39.0 43.9 50 ! 4.94 9.9 14.8 19.8 24.7 29.6 34.6 39.5 44.4 52 5.00 10.0 15.0 20.0 25.0 30.0 35.0 40.0 45.0 54 5.05 10.1 15.2 20.2 25.3 30.3 35.4 40.4 45.5 56 5.11 10.2 15.3 20.4 25.6 30.7 35.8 40.9 46.0 58 . . 5.17 10.3 15.5 20.7 25.8 31.0 36.2 41.4 46.5 60 5 23 10.5 15.7 20.9 26.1 31.4 36.6 41.8 47.1 Horizontal dist. 99.7 199.5 299.2 398.9 498.7 598.4 698.1 797.8 897.5 3 2' 5.28 10.6 15.9 21.1 26.4 31.7 37.0 42.3 47.6 4 5.34 10.7 16.0 21.4 26.7 32.1 37.4 42.7 48.1 6 5.40 10.8 16.2 21.6 27.0 32.4 37.8 43.2 48.6 8 5.46 10.9 16.4 21.8 27.3 32.7 38.2 43.7 49.1 10 5.52 11.0 16.5 22.1 27.6 33.1 38.6 44.1 49.6 12 5.57 11.1 16.7 22.3 27.9 33.4 39.0 44.6 50.2 14 .. 5 63 11.3 16.9 22.5 28.2 33.8 39.4 45.0 50.7 16 5 69 11.4 17.1 22.8 28.4 34.1 39.8 45.5 51.2 18. ....... 5.75 11.5 17.2 23.0 28.7 34.5 40.2 46.0 51.7 20 ! 5.80 11.6 17.4 23.2 29.0 34.8 40.6 46.4 52.2 22 i 5.86 11.7 17.6 23.4 29.3 35.1 41.0 46.9 52.8 24 5.92 11.8 17.8 23.7 29.6 35.5 41.4 47.4 53.3 26 5.98 12.0 17.9 23.9 29.9 35.9 41.8 47.8 53.8 28 6.04 12.1 18.1 24.1 30.2 36.2 42.2 48.3 54.3 30 ; 6.09 12.2 18.3 24.4 30.5 36.6 42.6 48.7 54.8 32 6.15 12.3 18.4 24.6 30.8 36.9 43.0 49.2 55.4 34 6.21 12.4 18.6 24.8 ; 31.0 37.3 43.5 49.7 55.9 36 6.27 12.5 18.8 25.1 31.3 37.6 43.9 50.1 56.4 38 3.32 12.6 19.0 25.3 31.6 37.9 44.3 50.6 56.9 40 3.38 12.8 19.1 25.5 31.9 38.3 44.7 51.1 57.4 '42 6.44 12.9 19.3 25.8 32.2 38.6 45.1 51.5 58.0 44 6 50 13.0 19.5 26.0 32.5 39.0 45.5 52.0 58.5 46 6.55 13.1 19^7 26^2 32^8 39.3 45.9 52.4 59.0 48 S.61 13.2 19.8 26.4 33.1 39.7 46.3 52.9 59.5 50 6.67 13.3 20.0 26.7 33.4 40.0 46.7 53.4 60.0 52 6 . 73 13.5 20.2 26.9 33.6 40.4 47.1 53.8 60.6 54 6.78 13.6 20.4 27.1 33.9 40.7 47.5 54.3 61.1 56 6.84 13.7 20.5 27.4 34.2 41.1 47.9 54.7 61.6 58 6 90 13.8 20.7 27.6 34.5 41.4 48.3 55.2 62.1 60 6.96 13.9 20.9 27 '.8 34^8 4l!? 48!7 55.7 62.6 Horizontal dist. 99.5 199 298.5 398.0 497.6 597.1 696.6 796.1 895.6 268 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 57 (Continued) STADIA TABLE Slant Distance 100 200 300 400 500 600 700 800 900 A 2' 4 4 6 8 7.02 7.07 7.13 7.19 14.0 14.1 14.3 14.4 21.0 21.2 21.4 21.6 28.1 28.3 28.5 28.8 35.1 35.4 35.7 35.9 42.1 42.4 42.8 43.1 49.1 49.5 49.9 50.3 56.1 56.6 57.0 57.5 63.1 63.7 64.2 64.7 10 12 14 16 18 7.25 7.30 7.36 7.42 7.48 14.5 14.6 14.7 14.8 15.0 21.7 21.9 22.1 22.3 22.4 29.0 29.2 29.4 29.7 29.9 36.2 36.5 36.8 37.1 37.4 43.5 43.8 44.2 44.5 44 9 50.7 51.1 51.5 51.9 52 3 58.0 58.4 58.9 59.3 59 8 65.2 65.7 66.2 66.8 67 3 20 7.53 15.1 22.6 30.2 37 7 45 2 52 7 60 3 67 8 22 7.59 15 2 22 8 30.4 38 45 5 53 1 60 7 68 3 24 7 65 15 3 22 9 30 6 OQ O 45 9 53 5 61 2 68 8 26 28 30 32 34 36 38 40 42 44 46 48 7.71 7.76 7.82 7.88 7.94 7.99 8.05 8.11 8.17 8.22 8.28 8 34 15.4 15.5 15.6 15.8 15.9 16.0 16.1 16.2 16.3 16.4 16.6 16 7 23.1 23.3 23.5 23.6 23.8 24.0 24.2 24.3 24.5 24.7 24.8 25 30.8 31.1 31.3 31.5 31.7 32.0 32.2 32.4 32.7 32.9 33.1 33 4 38.5 38.8 39.1 39.4 39.7 40.0 40.3 40.5 40.8 41.1 41.4 41 7 46.2 46.6 46.9 47.3 47.6 48.0 48.3 48.6 49.0 49.3 49.7 50 53.9 54.3 54.7 55.1 55.5 56.0 56.4 56.8 57.2 57.6 58.0 58 4 81.6 62.1 62.6 63.0 63.5 63.9 64.4 64.9 65.3 65.8 66.2 66 7 69.3 69.9 70.4 70.9 71.4 71.9 72.5 73.0 73.5 74.0 74.5 75 50 52 54 56 58 60 8.40 8.45 8.51 8.57 8.63 8 68 16.8 16.9 17.0 17.1 17.3 17 4 25.2 25.4 25.5 25.7 25.9 26 33.6 33.8 34.0 34.3 34.5 34.7 42.0 42.3 42.6 42.8 43.1 43 4 50.4 50.7 51.1 51.4 51.8 52 1 58.8 59.2 59.6 60.0 60.4 60 8 67.2 67.6 68.1 68.5 69.0 69 5 75.6 76.1 76.6 77.1 77.6 78 1 Horizontal dist. * 2' O 4 99.2 8.74 8.80 198.5 17.5 17.6 297.7 26.2 26.4 397.0 35.0 35 2 496.2 43.7 44.0 595.4 52.4 52 8 694.7 61.2 61 6 793.9 69.9 70 4 893.0 78.7 79.2 6 8.85 17.7 26 6 35 4 44 3 53 1 62 70 8 79.7 8 10 12 14 16 18 20 22 8.91 8.97 9.03 9.08 9.14 9.20 9.25 9 31 17.8 17.9 18.1 18.2 18.3 18.4 18.5 18 6 26.7 26.9 27.1 27.2 27.4 27.6 27.8 27 9 35.6 35.9 36.1. 36.3 36.6 36.8 37.0 37 2 44.6 44.8 45.1 45.4 45.7 46.0 46.3 46 6 53.5 53.8 54.2 54.5 54.8 55.2 55.5 55 9 62.4 62.8 63.2 63.6 64.0 64.4 64.8 65 2 71.3 71.7 72.2 72.7 73.1 73.6 74.0 74 5 80.2 80.7 81.2 81.7 82.3 82.8 83.3 83 8 24 9 37 18 7 28 1 37 5 46 8 56 2 65 6 74 9 84 3 26 28 9.43 9.48 18.9 19.0 28.3 28 4 37.7 37 9 47.1 47.4 56.6 56 9 66.0 66 4 75.4 75.9 84.8 85.3 30 32 34 36 38 40 42 9.54 9.60 9.65 9.71 9.77 9.83 9 88 19.1 19.2 19.3 19.4 19.5 19.7 19 8 28.6 28.8 29.0 29.1 29.3 29.5 29 6 38.2 38.4 38.6 38.8 39.1 39.3 39 5 47.7 48.0 48.3 48.6 48.8 49.1 49 4 57.2 57.6 57.9 58.3 58.6 59.0 59 3 66.8 67.2 67.6 68.0 68.4 68.8 69 2 76.3 76.8 77.2 77.7 78.1 78.6 79 85.9 86.4 86.9 87.4 87.9 88.4 88 "9 44 9 94 19 9 29 8 39 8 49 7 59 6 69 6 79 5 89 4 46 10.00 20.0 30 40 50 60 70 80 90.0 48 10.05 20 1 30 2 40 2 50 3 60 3 70 4 80 4 90.5 50 52 54 56 58 60 Horizontal dist. 10.11 10.17 10.22 10.28 10.33 10.40 98.9 20.2 20.3 20.4 20.6 20.7 20.8 197.8 30.3 30.5 30.7 30.8 31.0 31.2 296.7 40.4 40.7 40.9 41.1 41.4 41.6 395.6 50.5 50.8 51.1 51.4 51.7 52.0 494.5 60.7 61.0 61.3 61.7 62.0 62.4 593.5 70.8 71.2 71.6 72.0 72.4 72.8 692.4 80.9 81.3 81.8 82.2 82.7 83.2 791.3 91.0 91.5 92.0 92.5 93.0 93.6 890.2 MISCELLANEOUS TABLES AND DATA 269 TABLE 57 (Continued] STADIA TABLE Slant Distance 100 200 300 400 500 600 700 800 900 60 2 ' 10.45 20.9 31.4 41.8 52.3 62.7 73.2 83.6 94.1 4 ::.:::.. 10.51 21.0 31.5 42.0 52.5 63.1 73.6 84.1 94.6 6 8 10 12 10.57 10.62 10.68 10.74 21.1 21.2 21.4 21.5 31.7 31.9 32.0 32.2 42.3 42.5 42.7 42.9 52.8 53.1 53.4 53.7 63.4 63.7 64.0 64.4 74.0 74.4 74.8 75.2 84.5 85.0 85.4 85.9 95.1 95.6 96.1 96.6 14 10 79 21.6 32.4 43.2 54.0 64.8 75.5 86.3 97.1 16 10.85 21.7 32.5 43.4 54.2 65.1 75.9 '86.8 97.6 18 20 22 24 10.91 10.96 11.02 11 08 21.8 21.9 22.0 22.2 32.7 32.9 33.1 33.2 43.6 43.8 44.1 44.3 54.5 54.8 55.1 55.4 65.4 65.8 66.1 66.5 76.3 76.7 77.1 77.5 87.2 87.7 88.2 88.6 98.2 98.7 99.2 99.7 26 11.13 22.3 33.4 44.5 55.6 66.8 77.9 89.1 100.2 28 30 32 34 11.19 11.25 11.30 11 36 22.4 22.5 22.6 22.7 33.6 33.7 33.9 34.1 44.8 45.0 45.2 45.4 55.9 56.2 56.5 56.8 67.1 67.5 67.8 68.2 78.3 78.7 79.1 79.5 89.5 90.0 90.4 90.9 100.7 101.2 101.7 102.2 36 38 11.42 11.47 22.8 22.9 34.2 34.4 45.7 45.9 57.1 57.4 68.5 68.8 79.9 80.3 91.3 91.8 102.7 103.2 40 42 44 46 48 50 52 54 56 58 60 Horizontal dist. ry 2' 1 4. 6 .. 11.53 11.59 11.64 11.70 11.76 11.81 11.87 11.93 11.98 12.04 12.10 98.5 12.15 12.21 12 26 23.1 23.2 23.3 23.4 23.5 23.6 23.7 23.9 24.0 24.1 24.2 197.0 24.3 24.4 24 5 34.6 34.8 34.9 35.1 35.3 35.4 35.6 35.8 35.9 36.1 36.3 295.5 36.5 36.6 36 8 46.1 46.3 46.6 46.8 47.0 47.2 47.5 47.7 47.9 48.2 48.4 394.0 48.6 48.8 49 1 57.6 57.9 58.2 58.5 58.8 59.1 59.3 59.6 59.9 60.2 60.5 492.6 60.8 61.0 61 3 69.2 69.5 69.9 70.2 70.5 70.9 71.2 71.6 71.9 72.2 72.6 591.1 72.9 73.2 73 6 80.7 81.1 81.5 81.9 82.3 82.7 83.1 83.5 83.9 84.3 84.7 689.6 85.1 85.5 85 8 92.2 92.7 93.1 93.6 94.0 94.5 95.0 95.4 95.9 96.3 96.8 788.1 97.2 97.7 98 1 103.8 104.3 104.8 105.3 105.8 106.3 106.8 107.3 107.8 108.4 108.9 886.6 109.4 109.9 110.4 8 10 12 12.32 12.38 12.43 24.6 24.8 24.9 37.0 37.1 37.3 49.3 49.5 49.7 61.6 61.9 62.2 73.9 74.3 74.6 86.2 86.6 87.0 98.6 99.0 99.5 110.9 111.4 111.9 14 12.49 25.0 37.5 50.0 62.4 74.9 87.4 99.9 112.4 16 18 .. 12.55 12 60 25.1 25 2 37.6 37 8 50.2 50 4 62.7 63 75.3 75 6 87.8 88.2 100.4 100 8 112.9 113.4 20 22 24 26 28 30 .. 12.66 12.71 12.77 12.83 12.88 12 94 25.3 25.4 25.5 25.7 25.8 25 9 38.0 38.1 38.3 38.5 38.6 38 8 50.6 50.9 51.1 51.3 51.5 51 8 63.3 63.6 63.8 64.1 64.4 64 7 75.9 76.3 76.6 77.0 77.3 77 6 88.6 89.0 89.4 89.8 90.2 90 6 101.3 101.7 102.2 102.6 103.1 103 5 113.9 114.4 114.9 115.4 115.9 116 4 32 34 36 38 40 42 44 13.00 13.05 13.11 13.16 13.22 13.28 13 33 26.0 26.1 26.2 26.3 26.4 26.6 26 7 39.0 39.2 39.3 39.5 39.7 39.8 40 52.0 52.2 52.4 52.7 52.9 53.1 53 3 65.0 65.3 65.5 65.8 66.1 66.4 66 7 78.0 78.3 78.6 79.0 79.3 79.7 80 91.0 91.4 91.7 92.1 92.5 92.9 93 2 104.0 104.4 104.9 105.3 105.8 106.2 106 7 117.0 117.5 118.0 118.5 119.0 119.5 120.0 46 48 50 .... 13.39 13.44 13.50 26.8 26.9 27 40.2 40.3 40 5 53.6 53.8 54 66.9 67.2 67 5 80.3 80.7 81 93.7 94.1 94 5 107.1 107.6 108.0 120.5 121.0 121.5 52 54 56 58 60 13.56 13.61 13.67 13.73 13.78 27.1 27.2 27.3 27.5 27.6 40.7 40.8 41.0 41.2 41.3 54.2 54.5 54.7 54.9 55.1 67.8 68.1 68.3 68.6 68.9 81.3 81.7 82.0 82.3 82.7 94.9 95.3 95.7 96.1 96.4 108.5 108.9 109.4 109.8 110.3 122.0 122.5 123.0 123.5 124.0 Horizontal dist. 98.1 196.1 294.2 392.2 490.3 588.4 686.4 784.5 882.6 270 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 57 (Continued] STADIA TABLF Slant Distance 100 200 300 400 500 600 700 800 900 80 5' 13.92 27.8 41.8 55.7 69.6 83 5 97 4 111 4 125 3 10 15 14.06 14 20 28.1 28 4 42.2 42 6 56.2 56 8 70.3 71 84.4 85 2 98.4 99 4 112.5 113 6 126.6 127 8 20 25 30 35 40 45 50 55 60 14.34 14.48 14.62 14.76 14.90 15.04 15.17 15.31 15 45 28.7 29.0 29.2 29.5 29.8 30.1 30.3 30.6 30 9 43.0 43.4 43.9 44.2 44.7 45.1 45.5 45.9 46 4 57.4 57.9 58.5 59.0 59.6 60.1 60.7 61.2 61 8 71.7 72.4 73.1 73.7 74.5 75.2 75.9 76.6 77 3 86.0 86.9 87.7 88.4 89.4 90.2 91.0 91.9 92 7 100.4 101.4 102.3 103.1 104.3 105.2 106.2 107.2 108 2 114.7 115.8 116.9 117.8 119.2 120.3 121.4 122.5 123 6 129.1 130.3 131.6 132.5 134.1 135.3 136.6 137.8 139 1 Horizontal dist. Q 5' y 10 15 20 25 30 35 40 45 97.5 15.59 15.73 15.86 16.00 16.14 16.28 16.42 16.55 16 69 195.1 31.2 31.5 31.7 32.0 32.3 32.6 32.8 33.1 33 4 292.7 46.8 47.2 47.6 48.0 48.4 48.8 49.2 49.7 50 1 390.2 62.4 62.9 63.5 64.0 64.6 65.1 65.7 66.2 66 8 487.8 77.9 78.6 79.3 80.0 80.7 81.4 82.1 82.8 83 5 585.3 93.5 94.5 95.2 96.0 96.8 97.7 98.5 99.3 100 1 682.9 109.1 110.2 111.1 112.0 113.0 113.9 114.9 115.9 116 8 780.4 124.7 125.9 126.9 128.0 129.0 130.2 131.3 132.4 133 5 878.0 140.3 141.6 142.8 144.0 145.3 146.5 147.7 148.0 150 2 50 16 83 33 7 50 5 67 3 84 4 101 117 8 134 6 151 4 55 16 96 33 9 50 9 67 9 84 8 101 8 118 7 135 7 152 7 60 17.10 34.2 51.3 68.4 85.5 102.6 119.7 136.8 153.9 Horizontal dist. 1A 5' 1U 10 15 20 25 97.0 17.24 17.37 17.51 17.65 17 78 194-. 34.5 34.7 35.0 35.3 35 6 291.0 51.7 52.1 52.5 52.9 53.3 387.9 68.9 69.5 70.0 70.6 71 1 484.9 86.2 86.9 87.6 88.2 88 9 581.9 103.4 104.2 105.1 105.9 106 7 678.9 120.7 121.6 122.6 123.5 124 5 775.9 137.9 139.0 140.1 141.2 142 3 872.9 155.1 156.4 157.6 158.8 160 30 17 92 35 8 53 8 71 7 89 6 107 5 125 4 143 3 161 3 35 18.05 36.1 54.2 72.2 90.3 108.3 126.4 144.4 162.5 40 45 50 55 60 18.19 18.37 18.46 18.60 18.73 36.4 36.6 36.9 37.2 37.5 54.6 55.0 55.4 55.8 56.2 72.7 73.4 73.8 74.4 74.9 90.9 91.8 92.3 93.0 93.7 109.1 110.1 110.8 111.6 112.4 127.3 128.5 129.2 130.2 131.1 145.5 146.6 147.7 148.8 149.8 163.7 165.3 166.1 167.4 168.5 Horizontal dist. n 5' 10 15 20 25 30 35 40 45 50 96.4 18.86 19.00 19.13 19.27 19.40 19.54 19.67 19.80 19.94 20 07 192.7 37.7 38.0 38.3 38.5 38.8 39.1 39.3 39.6 39.9 40 1 289.1 56.6 57.0 57.4 57.8 58.2 58.6 59.0 59.4 59.8 60 2 385.4 75.5 76.0 76.5 77.1 77.6 78.1 78.7 79.2 79.7 80 3 481.8 94.3 95.0 95.7 96.3 97.0 97.7 98.4 99.0 99.7 100 4 578.2 113.2 114.0 114.8 115.6 116.4 117.2 118.0 118.8 119.6 120 4 684.5 132.1 133.0 133.9 134.9 135.8 136.8 137.7 138.6 139.6 140 5 1 770.9 150.9 152.0 153.1 154.1 155.2 156.3 157.4 158.4 159.5 160 6 867.7 169.8 171.0 172.2 173.4 174.6 175.8 177.0 178.2 179.4 180 6 55 60 Horizontal dist. 20.20 20.34 95.7 40.4 40.7 191.3 60.6 61.0 287.0 80.8 81.4 382.7 101^7 478.4 121.2 122.0 474.1 141.4 142.4 669.7 161.6 162.7 765.4 181.8 183.0 861.1 MISCELLANEOUS TABLES AND DATA 271 TABLE 57 (Continued] STADIA TABLE Slant Distance 100 200 300 400 500 600 700 800 900 -g o 5' 20.47 40.9 61.4 81.9 102.3 122.8 143.3 163.8 184.2 12 i :.. 20.60 41.2 61.8 82.4 103.0 123.6 144.2 164.8 185^4 15 20.73 41.5 62.2 82.9 103.7 124.4 145.1 165.9 186.6 20 20.87 41.7 62.6 83.5 104.3 125.2 146.1 166.9 187.8 25 21.00 42.0 63.0 84.0 105.0 126.0 147.0 168.0 189.0 30 21.13 42.3 63.4 84.5 105.7 126.8 147.9 169.0 190.2 35 21.26 42.5 63.8 85.1 106.3 127.6 148.8 170.1 191.4 40 21.39 42.8 64.2 85.6 107.0 128.4 149.8 171.2 192.5 45 21.52 43.1 64.6 86.1 107.6 129.2 150.7 172.2 193.7 50 21.66 43.3 65.0 86.6 108.3 129.9 151.6 173.2 194.9 55 21.79 43.6 65.4 87.2 108.9 130.7 152.5 174.3 196.1 60 21.92 43.8 65.7 87.7 109.6 131.5 153.4 175.3 197.3 Horizontal dist. 94.9 189.9 284.8 379.8 474.7 569.6 664.6 759.5 854.5 1Q 5' 1 10 22.05 22.18 44.1 44.4 66.1 66.5 88.2 88.7 110.2 110.9 132.3 133.1 154.3 155.3 176.3 177.4 198.4 199.6 15 22.31 44.6 66.9 89.2 111.6 133.9 156.2 178.5 200.8 20 22.44 44.9 67.3 89.8 112.2 134.6 157.1 179.5 202.0 25 22.57 45.1 67.7 90.3 112.8 135.4 158.0 180.6 203.1 30 22.70 45.4 68.1 90.8 113.5 136.2 158.9 181.6 204.3 35 22.83 45.7 68.5 91.3 114.1 137.0 159.8 182.6 205.5 40 22.96 45.9 68.9 91.8 114.8 137.7 160.7 183.7 206.6 45 23.09 46.2 69.3 92.4 115.4 138.5 161.6 184.7 207.8 50 23.22 46.4 69.6 92.9 116.1 139.3 162.5 185.7 208.9 55 23.35 46.7 70.0 93.4 116.7 140.1 163.4 186.8 210.1 60 23.47 46.9 70.4 93.9 117.4 140.8 164.3 187.8 211.3 Horizontal dist. 94.2 188.3 282.4 376.6 470.7 564.9 659.0 753.2 847.3 U 5' 10 23.60 23.73 47.2 47.5 70.8 71.2 94.4 94.9 118.0 118.6 141.6 142.4 165.2 166.1 188.8 189.8 212.4 213.6 15 23.86 47.7 71.6 95.4 119.3 143.2 167.0 190.9 214.7 20 23.99 48.0 72.0 95.9 119.9 143.9 167.9 191.9 215.9 25 24.11 48.2 72.3 96.5 120.6 144.7 168.8 192.9 217.0 30 24.24 48.5 72.7 97.0 121.2 145.4 169.7 193.9 218 2 35 24.37 48.7 73.1 97.5 121.8 146.2 170.6 194 9 219 3 40 24.49 49.0 73.5 9s!o 122^5 147.0 171.5 196.0 220.4 45 24.62 49.2 73.9 98.5 123.1 147.7 172.3 197.0 221.6 50 24.75 49.5 74.2 99.0 123.7 148.5 173.2 198.0 222.7 55 24.87 49.7 74.6 99.5 124 .4 149.2 174.1 199.0 223.9 60 25.00 50.0 75.0 100.0 125.0 150.0 175.0 200.0 225.0 Horizontal dist. 93.3 186.6 279.9 373.2 466.5 559.8 683.1 786.4 839.7 iff: 5' 25.13 50.3 75.4 100.5 125.6 150.8 175.9 201.0 226.1 1 10 25.25 50.5 75.8 101.0 126.3 151.5 176.8 202.0 227.3 15 25.38 50.8 76.1 101.5 126.9 152.3 177.6 203.0 228.4 20 ...... 25.50 51.0 76.5 102.0 127.5 153.0 178.5 204.0 229.5 ' 25 25.63 51.3 76.9 102.5 128.1 153.8 179.4 205.0 230.6 30 25.75 51.5 77.3 103.0 128.8 154.5 180.3 206.0 231.8 35 25.88 51.8 77.6 103.5 129.4 155.3 181.1 207.0 232.9 40 26.00 52.0 78.0 104.0 130.0 156.0 182.0 208.0 234.0 45 26.12 52.2 78.4 104.5 130.6 156.7 182.9 209.0 235.1 50 26.25 52.5 78.7 105.0 131.2 157.5 183.7 210.0 | 236.2 55 26.37 52.7 79.1 105.5 131 9 158 2 184 6 mo 007 A 60 26.50 53.0 79.5 106.0 132 5 159 185 5 . U i 919 t& t . * oqo c Horizontal dist. 92.4 184.8 277 .'2 M9. 462.0 554.4 646 ! 8 l . U ! 739.2 Zoo . O 831.6 272 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 57 (Concluded) STADIA TABLE. Slant Distance 100 200 300 400 500 600 700 800 900 1 /? 5' 26.62 53.2 79.9 106.5 133.1 159.7 186.3 213.0 239.6 16 10 26.74 53.5 80.2 107.0 133.7 160.5 187.2 213.9 240.7 15 26.86 53.7 80.6 107.5 134.3 161.2 188.0 214.9 241.8 20 26.99 54.0 81.0 108.0 134.9 161.9 188.9 215.9 242.9 25 27.11 54.2 81.3 108.4 135.6 162.7 189.8 216.9 244.0 30 27.23 54.5 81.7 108.9 136.2 163.4 190.6 217.9 245.1 35 27.35 54.7 82.1 109.4 136.8 164.1 191.5 218.8 246.2 40 27.48 55.0 82.4 109.9 137.4 164.9 192.4 219.8 247.3 45 27.60 55.2 82.8 110.4 138.0 165.6 193.2 220.8 248.4 50 27.72 55.4 83.2 110.9 138.6 166.3 194.0 221.7 249.5 55 27.84 55.7 83.5 111.4 139.2 167.0 194.9 222.7 250.6 60 27.96 55.9 83.9 111.8 139.8 167.8 195.7 223.7 251.6 Horizontal dist. 91.4 183 274 366 457 549 640 732 823 17 5' 1 | 10 28.08 28.20 56.2 56.4 84.2 84.6 112.3 112.8 140.4 141.0 168.5 169.2 196.6 197.4 224.6 225.6 252.7 253.8 15 28.32 56.6 85.0 113.3 141.6 169.9 198.2 226.6 254.9 20 28.44 56.9 85.3 113.8 142.2 170.6 199.1 227.5 256.0 25 28.56 57.1 85.7 114.2 142.8 171.4 199.9 228.5 257.0 30 28.68 57.4 86.0 114.7 143.4 172.1 200.8 229.4 258.1 35 28.80 57.6 86.4 115.2 144.0 172.8 201.6 230.4 259.2 40 28.92 57.8 86.7 115.7 144.6 173.5 202.4 231.3 260.2 45 29.04 58.1 87.1 116.1 145.2 174.2 203.2 232.3 261.3 50 29.15 58.3 87.5 116.6 145.8 174.9 204.1 233.2 262.4 55 29.27 58.5 87.8 117.1 146.4 175.6 204.9 234.2 263.4 60 29.39 58.8 88.2 117.6 146.9 176.3 205.7 235.1 264.5 Horizontal dist. 90.4 181 271 362 452 543 633 724 814 1 O 5'. . . 29.51 59.0 88.5 118.0 147.5 177.0 206.5 236.1 265.6 18 10 29.62 59.2 88.9 118.5 148.1 177.7 207.4 237.0 266.6 15 29.74 59.5 89.2 119.0 148.7 178.4 208.2 237.9 267.7 20 29.86 59.7 89.6 119.4 149.3 179.1 209.0 238.9 268.7 25 29.97 59.9 89.9 119.9 149.9 179.8 209.8 239.8 269.8 30 30.09 60.2 90.3 120.4 150.5 180.5 210.6 240.7 270.8 35 30.21 60.4 90.6 120.8 151.0 181.2 211.4 241.7 271.9 40 30.32 60.6 91.0 121.3 151.6 181.9 212.3 242.6 272.9 45 30.44 60.9 91.3 121.8 152.2 182.6 213.1 243.5 273.9 50 30.55 61.1 91.7 122.2 152.8 183.3 213.9 244.4 275.0 55 30.67 61.3 92.0 122.7 153.3 184.0 214.7 245.4 276.0 60 30.78 61.6 92.3 123.1 153.9 184.7 215.5 246.3 277.0 Horizontal dist. 89.4 179 268 358 447 536 626 715 805 IQo 5' i y 10 30.90 31.01 61.8 62.0 92.7 93.0 123.6 124.0 154.5 155.1 185.4 186.1 216.3 217.1 247.2 248.1 278.1 279.1 15 31.12 62.3 93.4 124.5 155.6 186.8 217.9 249.0 280.1 20 31.24 62.5 93.7 125.0 156.2 187.4 218.7 249.9 281.2 25 ...... 31.35 62.7 94.1 125.4 156.8 188.1 219 . 5 250.8 282.2 30 31.47 62.9 94.4 125.9 157.3 188.8 220.3 251.7 283.2 35 31.58 63.2 94.7 126.3 157.9 189.5 221.1 252.6 284.2 40 31.69 63.4 95.1 126.8 158.5 190.1 221.8 253.5 285.2 45 31.80 63.6 95.4 127.2 159.0 190.8 222.6 254.4 286.2 50 31.92 63.8 95.7 127.7 159.6 191.5 223.4 255.3 287.2 55 32.03 64.1 96.1 128.1 160.1 192.2 224.2 256.2 288.3 60 32.14 64.3 96.4 128.6 160.7 192.8 225.0 257.1 289.3 Horizontal dist. 88.3 177 265 353 442 530 618 706 795 MISCELLANEOUS TABLES AND DATA TABLE 58. TRIGONOMETRIC FORMULAE SOLUTION OF OBLIQUE TRIANGLES. B 273 A, B,a A,a,b C, a, 6 FORMULA. C\b,c , C, c a, 6, c in li 12 j A, B, C, a 16 (A -B) A,B C =180<>- (4 + B), & = ^Z C =iinV h ^ + * ) sin B = ^ . &, C = 180 - .sin. sin . sin C. =<-+>Sg- sin y 2 (A - B) vers ^4. JC = (s -a) (s- b) (s - c) 7T a ^ in L^-L sin _? "* " 2 Bin ^4" Table 58 is reproduced by permission from " Field Engineering," by Wm. H. Searles. 274 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 58 (Continued). TRIGONOMETRIC FORMULAE GENERAL FORMULAE. 13 sin A = . = VI cos 8 A = tan A cos A cosec A 14 15 sin A = sin A = 2 sin y A cos J-j A = vers A cot J .4 Y 14 vers 2 ^4 = 4/^ (1 cos 2 A) 16 cos A = - r = V ' 1 sin 2 ^4 = cot .4 sin .4 sec - 1 17 18 19 20 cos A = cos A = tan A = tan A = 1 vers .4 = 2 cos 2 \^A 1 = 1 2 sin 2 Jfc A cos 8 y*A sin 3 J4--1 = y % -{-}P 2 ^4 1 tan.4 sin^l B 23 cot A = sin 2 ^4 sin 2 ^4 1 + 0082^ 1 cos 2 ^4 = vers 2 .4 sin 2 ^4 24 cot A = tanj^.4 exsec A 25 vers A = 1 cos ^4 = sin A tan $A = 2 sin 2 ^ -4 26 vers A = exsec A cos ^4 27 exsec A = sec A \ = tan A tan }4A = -^ Q 1 ^- 28 29 30 31 sin *4 A sin 2^4 cos ^A cos 2 A /l cos A / vers A = 2 sin ^4 cos A /I + cos A = 2 cos 2 ^4 1 = cos* A sin'" A = 1 2 sin* A MISCELLANEOUS TABLES AND DATA 275 TABLE 58 (Concluded). TRIGONOMETRIC FORMULAE GENERAL FORMULA. 32 tan M A = *-= ~-r = cosec A cot A Sin A 1 + COSJ. -- 2+ 37 vers 2 A =2 sin* A =2 sin A coa A tan 1 -cos A 38 exsec ^ A = (1 +cos A) + V 40 sin (^d B) = sin ^ . cos B sin B . cos ^L 41 cos (AB) cos ^4 . cos B T sin ^4 . sin B 42 sin A + sin B = 2 sin J$ (4 -f B) cos ^(A B) 43 sin ^ sin 5 = 2 cos f6 (4 + B) sin J^ (^1 B) 44 cos w4 + cos B = 2 cos y z (A + B) cos ^(A B) 45 cos cos A = 2 sin ^ (4 -f 5) sin } (4 B) 46 sin 2 .4 sin 5 = cos 3 5 cos 2 A = sin (4 + B) sin (^ B) 47 cos 2 ^ sin 2 B = cos (^4 -f B) cos 04 B) -- cos ^L . cos B - cos -4 . cos B 276 WORKING DATA FOR IRRIGATION ENGINEERS D = Degree of curve. L = Length of curve. C= Length of long chord = A B. MISCELLANEOUS TABLES AND DATA TABLE 59. CURVE FORMULA 277 GIVEN. SOUGHT. FORMULAE. 1 D * 50 ~ sin^D 2 R D 8 inJ>=-- 3 A, D L =-. 4 A A A ~-P L 5 ,i z> z> = ioo-A_ 6 B, A r T = # tan l A 7 " c C = 2 R sin ^ A 8 9 : M E If = R vers ^ A E R exsec J^ A 10 T, A R J2= Tcot^ A 11 12 M E C ^7= Ttan 14 A C = 2 T cos J^ A 13 H M Jlf = T cot J^ A . vers JjjJ A 14 E, A R J2- ^ exsec Jij A 15 " T T= E cot }4 A 16 C _, j., sin ^ A exsec J A 17 M M Jf = .E7COS J^ A 18 C, A R 12- C 2 sin J A 19 20 H M T lfMoaM* T 2 COS ^ A 21 22 23 24 25 M If, A ct E R C T E T? vers % A C = 2 3f cot ^ A tan^A M vers ^ A ~~ COS % A Table 59 is reproduced by permission from " Field Engineering," by Wm. H. Searles. 278 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 59 (Continued) .CURVE FORMULA GIVEN. SOUGHT. FORMULA. 26 27 28 29 R, T R, C t A A tan ^ A = -~ T COS^A = ^.|/ (* + )(*-) 30 R, M A M vers J^ A = -=j- 31 32 R, E A R-M E exsec ^3 A = p- 33 COS^A=-^ 34 35 t r, c A C COS K A = tan W A = A / % T G V 2T+C 36 37 38 39 T, E C, M A A tan J4 A = - r - cos J^ A m a i EI a cos J^ A = C a-^4 jf a 40 M, E A 3f COS ^ A = =- 41 42 43 44 45 46 47 R, T M R, C M C M E T M E tan J4 A = A/ _E ~__ ilf JB y ra+ ^ 2 E= VT* + R*-R 2 j/(^+l)(^-|) 72 2 = tfTB + HcTTRKC) MISCELLANEOUS TABLES AND DATA TABLE 59 (Conceded). CURVE FORMULAE 279 P., II A E T, C T, E C,M .If, T, M C, E T C E T C M R M JS X c M P. T X T C E C R T M R-M C = 2VM(2R -M) T = C = 2R M- CT 2T+C (T+E}(T-E) 2M rp 2 ((72 _ 4 If 2 ) 280 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 60 Common Logarithms no 123456789 10 ooooo 00432 00860 01284 01703 02119 02531 02938 03342 03743 ii 04139 04532 04922 05308 05690 06070 06446 06819 07188 07555 12 07918 08279 08636 08991 09342 09691 10037 10380 10721 11059 13 "394 11727 12057 12385 12710 J 3033 13354 13672 13988 14301 14 14613 14922 15229 15534 15836 16137 i6435 16732 17026 i73 J 9 IS 17609 17898 18184 18469 18752 19033 19312 19590 19866 20140 16 20412 20683. 20952 21219 21484 21748 22OII 22272 22531 22789 17 23045 23300 23553 23805 24055 24304 2455 1 24797 25042 25285 18 255 2 7 25768 26007 26245 26482 26717 26951 27184 27416 27646 19 27875 28103 28330 28556 28780 29003 29226 29447 29667 29885 20 30103 30320 30535 30750 30963 3H75 31387 31597 31806 32015 21 32222 32428 32634 32838 33041 33244 33445 33646 33846 34044 22 34242 34439 34635 34830 35025 352i8 354II 35603 35793 35984 23 36i73 36361 36549 36736 36922 37io7 37291 37475 37658 37840 24 38021 38202 38382 38561 38739 38917 39094 39270 39445 39620 25 39794 39967 40140 40312 40483 40654 40824 40993 41162 41330 26 4M97 41664 41830 41996 42160 42325 42488 42651 42813 42975 27 43136 43297 43457 43616 43775 43933 44091 44248 44404 4456o 28 44716 44871 45025 45179 45332 45484 45637 45788 45939 46090 29 46240 46389 46538 46687 46835 46982 47129 47276 47422 47567 30 47712 47857 48001 48144 48287 48430 48572 48714 48855 48996 31 49136 49276 49415 49554 49693 49831 49969 50106 50243 50379 32 50515 50651 50786 50920 5^55 51188 51322 5M55 51587 51720 33 5i85i 51983 52114 52244 52375 52504 52634 52763 52892 53020 34 53148 53 2 75 53403 53529 53656 53782 53908 54033 54158 54283 35 54407 54531 54654 54777 54900 55023 55U5 55267 55388 55509 36 55630 55751 55871 5599i 56110 56229 56348 56467 56585 56703 37 56820 56937 57054 57i7i 57287 57403 57519 57634 57749 57864 38 57978 58092 58206 58320 58433 58546 58659 58771 58883 58995 39 59106 59 2I 8 593 2 9 59439 59550 5966o 59770 59879 59988 60097 40 60206 60314 60423 60531 60638 60746 60853 60959 61066 61172 41 61278 61384 61490 6i595 61700 61805 61909 62014 62118 62221 42 62325 62428 62531 62634 62737 62839 62941 63043 63144 63246 43 63347 63448 63^48 63649 63749 63849 63949 64048 64147 64246 44 64345 64444 64542 64640 64738 64836 64933 65031 65128 65225 45 65321 65418 65514 65610 65706 65801 65896 65992 66087 66181 46 66276 66370 66464 66558 66652 66745 66839 66932 67025 67117 47 67210 67302 67394 67486 67578 67669 67761 67852 67943 68034 48 68124 68215 68305 68395 68485 68574 68664 68753 68842 68931 49 69020 69108 69197 69285 69373 69461 69548 69636 69723 69810 So 69897 69984 70070 7oi57 70243 70329 70415 70501 70586 70672 51 70757 70842 70927 71012 71096 71181 71265 71349 71433 7i5i7 52 71600 71684 71767 71850 71933 72016 72099 72181 72263 72346 53 72428 72509 72591 72673 72754 72835 72916 72997 73078 73159 54 73239 73320 73400 7348o 7356o 73640 73719 73799 73878 73957 0123456789 Table 60 is reproduced by permission from " American Civil Engineers' Pocket Book, Mansfield Merriman, Editor-in-Chief. MISCELLANEOUS TABLES AND DATA 281 of Numbers from 000 to 999 n o i 2 34 56789 55 74036 74H5 74194 74273 74351 74429 74507 74586 74663 74741 56 748i9 74896 74974 75051 75128 75205 75282 75358 75435 755H 57 75587 75664 75740 758i5 75891 75967 76042 76118 76193 76268 58 76343 76418 76492 76567 76641 76716 76790 76864 76938 77012 59 77085 77*59 77232 77305 77379 77452 77525 77597 77670 77743 60 778.15 77887 77960 78032 78104 78176 78247 78319 78390 78462 61 78533 78604 78675 78746 78817 78888 78958 79029 79099 79169 62 79 2 39 79309 79379 79449 795i8 79588 79657 79727 79796 79865 63 79934 80003 80072 80140 80209 80277 80346 80414 80482 80550 64 80618 80686 80754 80821 80889 80956 81023 81090 81158 81224 65 81291 81358 81425 81491 81558 81624 81690 8i757 81823 81889 66 8i954 82020 82086 82151 82217 82282 82347 82413 82478 82543 67 82607 82672 82737 82802 82866 82930 82995 83059 83123 83187 68 83251 83315 83378 83442 83506 83569 83632 83696 83759 83822 69 83885 83948 84011 84073 84136 84198 84261 84323 84386 84448 70 84510 84572 84634 84696 84757 84819 84880 84942 85003 85065 7i 85126 85187 85248 85309 85370 85431 85491 85552 85612 85673 72 85733 85794 85854 85914 85974 86034 86094 86153 86213 86273 73 86332 86392 86451 86510 86570 86629 86688 86747 86806 86864 74 86923 86982 87040 87099 87157 87216 87274 87332 87390 87448 75 87506 87564 87622 87679 87737 87795 87852 87910 87967 88024 76 88081 88138 88195 88252 88309 88366 88423 88480 88536 88593 77 88649 88705 88762 88818 88874 88930 88986 89042 89098 89154 78 89209 89265 89321 89376 89432 89487 89542 89597 89653 89708 79 89763 89818 89873 89927 89982 90037 90091 90146 90200 90255 80 90309 90363 90417 90472 90526 90580 90634 90687 90741 90795 81 90849 90902 90956 91009 91062 91116 91169 91222 91275 91328 82 91381 9*434 91487 91540 91593 91645 91698 9i75i 91803 91855 83 91908 91960 92012 92065 92117 92169 92221 92273 92324 92376 84 92428 92480 92531 92583 92634 92686 92737 92788 92840 92891 85 92942 92993 93044 93095 93146 93197 93247 93298 93349 93399 86 93450 935oo 93551 936oi 93651 93702 93752 93802 93852 93902 87 93952 94002 94052 94IOI 94i5i 94201 94250 943oo 94349 94399 88 94448 94498 94547 94596 94645 94694 94743 94792 94841 94890 89 94939 94988 95036 95085 95134 95182 95231 95279 95328 95376 90 95424 95472 95521 95569 95617 95665 95713 9576i 95809 95856 9i 95904 95952 95999 96047 96095 96142 96190 96237 96284 96332 92 96379 96426 96473 96520 96567 96614 96661 96708 96755 96802 93 96848 96895 96942 96988 97035 97081 97128 97174 97220 97267 94 97313 97359 97405 97451 97497 97543 97589 97635 97681 97727 95 97772 97818 97864 97909 97955 98000 98046 98091 98i37 98182 96 98227 98272 98318 98363 98408 98453 98498 98543 98588 98632 97 98677 98722 98767 98811 98856 98900 98945 98989 99034 99078 98 99123 99167 99211 99255 99300 99344 99388 99432 99476 99520 99 99564 99607 99651 99695 99739 99782 99826 99870 99913 99957 01 23 4 56 789 282 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 61 SINE Natural Sines Angle o' 10' 20' 30' 40' 50' 60' o.ooooo 0.00291 0.00582 0.00873 0.01164 0.01454 0.01745 89 z 0.01745 0.02036 0.02327 0.02618 0.02908 0.03199 0.03490 88 2 0.03490 0.03781 0.04071 0.04362 0.04653 0.04943 0.05234 87 3 0.05234 0.05524 0.05814 0.06105 0.06395 0.06685 0.06976 86 4 0.06976 0.07266 0.07556 0.07846 0.08136 0.08426 0.08716 85 5 0.08716 0.09005 0.09295 0.09585 0.09874 0.10164 0.10453 84 6 0.10453 o. 10742 0.11031 0.11320 o. 11609 0.11898 0.12187 83 7 0.12187 0.12476 0.12764 0.13053 0.13341 0.13629 0.13917 82 8 0.13917 0.14205 o.i4493 0.14781 0.15069 0.15356 0.15643 81 9 0.15643 Q.I593 1 0.16218 0.16505 0.16792 0.17078 0.17365 80 10 0.17365 0.17651 0.17937 0.18224 0.18509 0.18795 o. 19081 79 ii o. 19081 0.19366 0.19652 0.19937 O. 2O222 0.20507 o. 20791 78 12 0.20791 0.21076 0.21360 0.21644 0.21928 O. 22212 0.22495 77 13 0.22495 0.22778 0.23062 0.23345 0.23627 0.23910 0.24192 76 14 0.24192 0.24474 0.24756 0.25038 0.25320 o. 25601 0.25882 75 15 0.25882 0.26163 0.26443 o. 26724 0.27004 o. 27284 0.27564 74 16 0.27564 0.27843 0.28123 0.28402 0.28680 0.28959 0.29237 73 17 0.29237 0.29515 0.29793 0.30071 0.30348 0.30625 0.30902 73 18 0.30902 0.31178 0.31454 0.31730 0.32006 0.32282 0.32557 71 19 o.3 2 557 0.32832 0.33106 0.33381 0.33655 0.33929 0.34202 70 20 0.34202 0-34475 0.34748 0.35021 0.35293 0.35565 0.35837 69 21 0.35837 0.36108 0.36379 0.36650 0.36921 0.37191 0.37461 68 22 0.37461 o.3773o 0.37999 0.38268 0.38537 0.38805 0.39073 67 23 0.39073 o.3934i 0.39608 0.39875 O.4OI42 o . 40408 0.40674 66 24 0.40674 0.40939 0.41204 0.41469 0.41734 0.41998 0.42262 65 as 0.42262 0.42525 0.42788 0.4305 1 0.43313 0.43575 0.43837 64 26 0.43837 0.44098 0.44359 0.44620 0.44880 0.45140 0.45399 63 27 0.45399 0.45658 0.45917 0.46175 0.46433 0.46690 0.46947 62 28 0.46947 0.47204 0.47460 0.47716 0.47971 0.48226 0.48481 61 29 0.48481 0.48735 0.48989 0.49242 0.49495 0.49748 0.50000 60 30 0.50000 0.50252 0.50503 0.50754 0.51004 0.51254 0.51504 59 31 0.51504 o.5 r 753 o. 52002 0.52250 o. 52498 0.52745 0.52992 58 32 0.52992 0.53238 0.53484 o.5373o 0.53975 0.54220 0.54464 57 33 0.54464 0.54708 o.5495i o.55i94 0.55436 0.55678 0.55919 56 34 0.559^ 0.56160 0.56401 0.56641 0.56880 0.57119 0.57358 55 35 0.57358 0.57596 0.57833 0.58070 0.58307 0.58543 0.58779 54 36 0.58779 0.59014 0.59248 0.59482 0.59716 0.59949 0.60182 53 37 0.60182 0.60414 0.60645 0.60876 0.61107 0.61337 0.61566 52 38 0.61566 0.61795 0.62024 0.62251 0.62479 0.62706 0.62932 Si 39 0.62932 0.63158 0.63383 0.63608 0.63832 0.64056 0.64279 50 40 0.64279 0.64501 0.64723 0.64945 0.65166 0.65386 0.65606 49 41 0.65606 0.65825 0.66044 0.66262 0.66480 0.66697 0.66913 48 42 0.66913 0.67129 0.67344 0.67559 0.67773 0.67987 0.68200 47 43 0.68200 0.68412 0.68624 0.68835 0.69046 0.69256 0.69466 46 44 0.69466 0.69675 0.69883 o. 70091 0.70298 0.70505)0,70711 45 60' 50' 40' 30' 20' xo' o' Angle COSINE Table 61 is reproduced by permission from " American Civil Engineers' Pocket Book, Mansfield Merriman, Editor-in-Chief. MISCELLANEOUS TABLES AND DATA 283 and Cosines SINE Angl e o' TO' 20' 30' 40' 50' 60' 45? 0.70711 0.70916 0.71121 0.71325 0.71529 0.71732 0.71934 44 46 o-7 I 934 0.72136 0.72337 0.72537 0.72737 0.72937 0.73135 43 47 0.73135 0-73333 0.73531 0.73728 0.73924 0.74120 0.74314 42 48 0.74314 0.74509 0.74703 0.74896 0.75088 0.75280 0.75471 41 49 0-7S47 1 0.75661 0.7585 1 o. 76041 0.76229 0.76417 0.76604 40 50 0.76604 0.76791 0.76977 0.77162 0-77347 0-7753 1 0.77715 39 51 0.77715 0.77897 0.78079 0.78261 0.78442 0.78622 0.78801 38 52 0.78801 0.78980 0.79158 0.79335 0.79512 o. 79688 0.79864 37 53 o. 79864 0.80038 0.80212 0.80386 0.80558 0.80730 0.80902 36 54 0.80902 0.81072 0.81242 0.81412 0.81580 0.81748 0.81915 35 55 0.81915 0.82082 0.82248 0.82413 0.82577 0.82741 0.82904 34 56 0.82904 0.83066 0.83228 0.83389 0.83549 0.83708 0.83867 33 57 0.83867 0.84025 0.84182 0.84339 0.84495 0.84650 0.84805 32 58 0.84805 0.84959 0.85112 0.85264 0.85416 0.85567 0.85717 31 59 0.85717 0.85866 0.86015 0.86163 0.86310 0.86457 0.86603 30 60 0.86603 0.86748 0.86892 0.87036 0.87178 0.87321 0.87462 29 61 0.87462 0.87603 0.87743 0.87882 0.88020 0.88158 0.88295 28 62 0.88295 0.88431 0.88566 0.88701 0.88835 0.88968 0.89101 27 63 0.89101 0.89232 0.89363 0.89493 0.89623 0.89752 0.89879 26 64 0.89879 0.90007 0.90133 0.90259 0.90383 0.90507 0.90631 25 65 0.90631 0.90753 0.90875 0.90996 0.91116 0.91236 0.91355 24 66 0.91355 0.91472 0.91590 0.91706 0.91822 0.91936 0.92050 23 67 0.92050 0.92164 0.92276 0.92388 0.92499 0.92609 0.92718 22 68 0.92718 0.92827 0.92935 0.93042 0.93148 0.93253 0.93358 21 69 0-9335 8 0.93462 0.93565 0.93667 0.93769 0.93869 0.93969 20 70 0.93969 0.94068 0.94167 0.94264 0.94361 0.94457 0.94552 19 71 0.9455 2 0.94646 0.94740 0.94832 0.94924 0.95015 0.95106 18 72 0.95106 .95195 0.95284 0.95372 0-95459 0.95545 0.95630 17 73 0.95630 957*5 0-95799 0.95882 0.95964 0.96046 0.96126 16 74 0.96126 .96206 0.96285 0.96363 0.96440 0.96517 0.96593 15 75 0.96593 .96667 0.96742 0.96815 0.96887 0.96959 0.97030 14 76 0.97030 .97100 0.97169 0.97237 0.97304 0.97371 0.97437 13 77 0-97437 0.97502 0.97566 0.97630 0.97692 0-97754 0.97815 12 78 0.97815 0.97875 0.97934 0.97992 0.98050 0.98107 0.98:63 ZZ 79 0.98163 0.98218 0.98272 0.98325 0.98378 0.98430 0.98481 Z0 80 0.98481 0.98531 0.98580 0.98629 0.98676 0.98723 0.98769 9 8r 0.98769 0.98814 0.98858 0.98902 0.98944 0.98986 0.99027 8 82 0.99027 0.99067 0.99106 0.99144 0.99182 0.99219 0.99255 7 83 0.99255 0.99290 0.99324 0.99357 0.99390 0.99421 0.99452 6 84 0.99452 0.99482 0.99511 0.99540 0.99567 0-99594 0.99619 5 85 0.99619 0.99644 0.99668 0.99692 0.99714 0.99736 0.99756 4 86 0.99756 0.99776 0.99795 0.99813 0.99831 0.99847 0.99863 3 87 0.99863 0.99878 0.99892 0.99905 0.99917 0.99929 0.99939 2 88 0-99939 0.99949 0.99958 0.99966 0-99973 0.99979 0.99985 Z 89 0.99985 0.99989 0.99993 0.99996 0.99998 1 . 00000 I . OOOOO 60' So' 40' 30' 20' 10' o' A ngle COSINE 284 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 62 TANGENT Natural Tangents Angl< ; o' 10' 20' 30' 40' 50' 60' 0.00000 0.00291 0.00582 0.00873 0.01164 0.01455 0.01746 89 i 0.01746 0.02036 0.02328 0.02619 0.02910 0.03201 0.03492 88 2 0.03492 0.03783 0.04075 0.04366 0.04658 0.04949 0.05241 87 3 0.05241 0.05533 0.05824 o. 06116 . 06408 0.06700 0.06993 86 4 0.06993 0.07285 0.07578 0.07870 .08163 0.08456 0.08749 85 5 0.08749 0.09042 0.09335 0.09629 .099 2 3 o. 10216 o. 10510 84 6 o. 10510 o. 10805 o. 11099 0.11394 .11688 0.11983 o. 12278 83 7 o. 12278 0.12574 0.12869 0.13165 .13461 0.13758 o. 14054 82 8 0.14054 O.I435 1 o. 14648 0.14945 0.15243 0.15540 0.15838 81 9 0.15838 0.16137 0.16435 0.16734 0.17033 0.17333 0.17633 80 10 0.17633 0.17933 0.18233 0.18534 0.18835 o. 19136 0.19438 79 XI 0.19438 0.19740 0.20042 0.20345 0.20648 o. 20952 o. 21256 78 12 0.21256 o. 21560 0.21864 o. 22169 0.22475 0.22781 0.23087 77 13 0.23087 0.23393 0.23700 0.24008 0.24316 0.24624 0.24933 76 14 0.24933 0.25242 0.25552 0.25862 0.26172 0.26483 0.26795 75 15 0.26795 0.27107 0.27419 0.27732 0.28046 0.28360 0.28675 74 16 0.28675 0.28990 0.29305 0.29621 0.29938 0.30255 0.30573 73 17 0.30573 0.30891 0.31210 0.31530 0.31850 0.32171 0.32492 72 18 0.32492 0.32814 o.33 I 36 0.33460 0.33783 0.34108 0.34433 7i 19 0.34433 0.34758 o.350 8 5 0.35412 0.35740 0.36068 0.36397 70 20 0.36397 0.36727 0.37057 0.37388 0.37720 0.38053 0.38386 69 21 0.38386 0.38721 0.39055 0.39391 0.39727 0.40065 0.40403 68 22 0.40403 0.40741 0.41081 0.41421 0.41763 0.42105 0.42447 67 23 0.42447 0.42791 0.43*36 0.43481 0.43828 0.44175 0.44523 66 24 0.44523 0.44872 0.45222 0.45573 0.45924 0.46277 0.46631 65 25 0.46631 0.46985 0.47341 0.47698 0.48055 0.48414 0.48773 64 26 0.48773 o.49 I 34 0.49495 0.49858 0.50222 0.50587 0.50953 63 27 0.50953 0.51320 0.51688 0.52057 0.52427 0.52798 0.5317! 62 28 0.5317! 0.53545 0.53920 0.54296 0.54673 0.55051 0-5543 1 61 29 0.55431 0.55812 0.56194 0.56577 0.56962 0.57348 0.57735 60 30 0.57735 0.58124 0.58513 0.58905 0.59297 0.59691 0.60086 59 31 0.60086 0.60483 0.60881 0.61280 o. 61681 0.62083 0.62487 53 32 0.62487 0.62892 0.63299 0.63707 0.64117 0.64528 0.64941 57 33 0.64941 0.65355 0.65771 0.66189 0.66608 0.67028 0.67451 56 34 0.67451 0.67875 0.68301 0.68728 0.69157 0.69588 0.70021 55 35 0.70021 0.70455 0.70891 0.71329 0.71769 0.72211 0.72654 54 36 0.72654 0.73100 0.73547 0.73996 0.74447 0.74900 0-75355 53 37 0.75355 0.75812 0.76272 0.76733 0.77196 0.77661 0.78129 52 38 0.78129 0.78598 0.79070 0.79544 0.80020 0.80498 0.80978 51 39 0.80978 0.81461 0.81946 0.82434 0.82923 0.83415 0.83910 50 40 0.83910 0.84407 0.84906 0.85408 0.85912 0.86419 0.86929 49 41 0.86929 0.87441 0.87955 0.88473 0.88992 0.89515 0.90040 48 42 0.90040 0.90569 0.91099 0.91633 0.92170 0.92709 0.93252 47 43 0.93252 0.93797 0.94345 0.94896 o.9545r 0.96008 0.96569 46 44 0.96569 0.97133 0.97700 0.98270 0.98843 0.99420 I . 00000 45 60' So' 40' 30' 20' 10' o' / ingle COTANGENT Table 62 is reproduced by permission from " American Civil Engineers' Pocket Book, Mansfield Merriman, Editor-in-Chief. MISCELLANEOUS TABLES AND DATA 285 and Cotangents TANGENT Angl B <>' 10' 20' 30' 40' So' 60' 45 . 00000 .00583 .01170 .01761 02355 .02952 03553 44 46 .03553 .04158 .04766 .05378 .05994 .06613 .07237 43 47 .07237 .07864 .08496 .09131 .09770 . 10414 . 11061 42 48 .11061 ."713 .12369 .13029 .13694 14363 1 5037 41 49 .15037 I S7 I S . 16398 .17085 .17777 . 18474 I9I75 40 50 .1.9175 . 19882 20593 .21310 .22031 .22758 23490 39 Si . 23490 .24227 .24969 2 57 I 7 .26471 .27230 .27994 38 52 .27994 .28764 .29541 .30323 .31110 3 J 904 .32704 37 53 .32704 335 11 34323 35 I 42 .35968 .36800 37638 36 54 .37638 .38484 .39336 .40195 .41061 .41934 .42815 35 55 .42815 43703 .44598 .45501 .46411 .47330 48256 34 56 .48256 .49190 .50133 . 51084 .52043 .53010 53987 33 57 .53987 .54972 .55966 .56969 .57981 .59002 . 60033 32 58 .60033 .61074 .62125 .63185 .64256 65337 .66428 31 59 .66428 .67530 .68643 .69766 . 70901 . 7 2 047 73205 30 60 .73205 . 74375 .75556 .76749 77955 .79174 . 80405 29 61 . 80405 .81649 .82906 .84177 .85462 .86760 88073 28 62 .88073 . 89400 .90741 .92098 93470 .94858 .96261 27 63 .96261 .97680 .99116 00569 .02039 .03526 .05030 26 64 .05030 06553 .08094 .09654 -11233 .12832 2.14451 25 65 I445 1 . 16090 17749 . 19430 .21132 .22857 2.24604 24 66 . 24604 .26374 .28167 . 29984 .31826 .33693 2.35585 23 67 .35585 .37504 39449 .41421 .43422 45451 2.47509 22 68 .47509 49597 .51715 53865 . 56046 .58261 2.60509 21 69 .60509 .62791 .65109 .67462 69853 .72281 2.74748 20 70 . 74748 .77 2 54 . 79802 .82391 2.85023 2.87700 2.90421 19 7i .90421 93189 .96004 .98869 3-01783 3 04749 3.07768 18 72 3.07768 3. 10842 3- I 397 2 3-i7 I 59 3 . 20406 3.23714 3.27085 17 73 3.27085 3-30521 3-34023 3-37594 3-41236 3-44951 3-48741 16 74 3-48741 3-52609 3.56557 3.60588 3.64705 3.68909 3-73205 15 75 3-73205 3-77595 3.82083 3.86671 3-91364 3.96165 4.01078 14 76 4.01078 4.06107 4.11256 4.16530 4.21933 4.27471 4.33148 13 77 4.33148 4.38969 4.44942 4.51071 4.57363 4.63825 4.70463 12 78 4.70463 4.77286 4.84300 4.91516 4.98940 5.06584 5-14455 II 79 5.14455 5.22566 5-30928 5-39552 5-48451 5.57638 5.67128 IO C 80 5.67128 5.76937 5.87080 5.97576 6 . 08444 6.19703 6.31375 9 81 6.31375 6.43484 6.56055 6.69116 6.82694 6.96823 7.H537 8 82 7-II537 7.26873 7.42871 7-59575 7.77035 7-95302 8.14435 7 83 8.14435 8.34496 8-55555 8.77689 9.00983 9-25530 9.5I436 6 84 9.5M36 9.78817 10.0780 10.3854 10. 7119 11.0594 11.4301 5 85 11.4301 11.8262 12.2505 12.7062 13-1969 13.7267 14-3007 4 86 14.3007 14.9244 15.6048 16.3499 I 7- I 693 18.0750 19.0811 3 87 19.0811 20. 2056 21.4704 22.9038 24.5418 26.4316 28.6363 2 88 28.6363 31.2416 34.3678 38.1885 42.9641 49-1039 57.2900 X 89 57.2900 68.7501 85.9398 114.589 171.885 343-774 00 60' So' 40' 30' 20' 10' o' A ngle COTANGENT 286 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 63 THREE-HALVES POWERS OF NUMBERS No. .000 .001 .002 .003 .004 .005 .006 .007 .008 .009 0.00 .0000 .OOU .0002 .0003 .0004 .0005 .0006 .0007 .0008 .0009 .01 .0010 .0012 .0014 .0015 .0017 .0019 .0021 .0022 .0024 .0026 .02 .0028 .0030 .0033 .0035 .0038 .0040 .0042 .0045 .0047 .0050 .03 .0052 .0055 .0058 .0060 .0063 .0066 .0069 .0072 .0074 .0077 .04 .0080 .0083 .0086 .0090 .0093 .0096 .0099 .0102 .0106 .0109 .05 .0112 .0116 .0119 .0122 .0126 .0130 .0133 .0136 .0140 .0144 .06 .0147 .0151 .0155 .0158 .0162 .0166 .0170 .0174 .0177 .0181 .07 .0185 .0189 .0193 .0197 .0201 .0206 .0210 .0214 .0218 .0222 .08 .0226 .0230 .0235 .0239 .0244 .0248 .0252 .0257 .0261 .0266 .09 .0270 .0275 .0279 .0284 .0288 .0293 .0298 .0302 .0307 .0311 .10 .0316 .0321 .0326 .0331 .0336 .0340 .0345 .0350 .0355 .0360 .11 .0365 .0370 .0375 .0380 .0385 .0390 .0396 .0401 .0406 .0411 .12 .0416 .0421 .0427 .0432 .0437 .0442 .0448 .0453 .0458 .0464 .13 .0469 .0474 .0480 .0486 .0491 .0496 .0502 .0508 .0513 .0518 .14 .0524 .0530 .0535 .0541 .0547 .0552 .0558 .0564 .0570 .0575 .15 .0581 .0587 .0593 .0599 .0605 .0610 .0616 .0622 .0628 .0634 .16 .0640 .0645 .0652 .0658 .0664 .0670 .0677 .0683 .0689 .0695 .17 .0701 .0707 .0714 .0720 .0726 .0732 .0739 .0745 .0751 .0758 .18 .0764 .0770 .0777 .0783 .0790 .0796 .0802 .0809 .0815 .0822 .19 .0828 .0835 .0841 .0848 .0854 .0861 .0868 .0874 .0881 .0887 .20 .0894 .0901 ,0908 .0914 .0921 .0928 .0935 .0942 .0948 .0955 .21 .0962 .0969 .0976 .0983 .0990 .0997 .1004 .1011 .1018 .1025 .22 .1032 .1039 .1046 .1053 .1060 .1068 .1075 .1082 .1089 .1096 .23 .1103 .1110 .1118 .1125 .1132 .1140 .1147 .1154 .1161 .1169 .24 .1176 .1183 .1191 .1198 .1251 .1213 .1220 .1228 .1235 .1243 .25 .1250 .1258 .1265 .1273 .1280 .1288 .1296 .1303 .1311 .1318 .26 .1326 .1334 .1341 .1349 .1357 .1364 .1372 .1380 .1388 .1395 .27 .1403 .1411 .1419 .1427 .1435 .1442 .1450 .1458 .1466 .1474 .28 .1482 .1490 .1498 .1506 .1514 .1522 .1530 .1538 .1546 .1554 .29 .1562 .1570 .1578 .1586 .1594 .1602 .1611 .1619 .1627 .1635 .30 .1643 .1651 .1660 .1668 .1676 .1684 .1693 .1701 .1709 .1718 .31 .1726 .1734 .1743 .1751 .1760 .1768 .1776 .1785 .1793 .1802 .32 .1810 .1819 .1827 .1836 .1844 .1853 .1862 .1870 .1879 .1887 .33 .1896 .1905 .1913 .1922 .1931 .1940 .1948 .1957 .1966 .1974 .34 .1983 .1992 .2001 .2009 .2018 .2027 .2036 .2045 .2053 .2062 .35 .2071 .2080 .2089 .2098 .2107 .2116 .2124 .2133 .2142 .2151 .36 .2160 .2169 .2178 .2187 .2196 .2206 .2215 .2224 .2233 .2242 .37 .2251 .2260 .2269 .2278 .2287 .2296 .2306 .2315 .2324 .2333 .38 .2342 .2351 .2361 .2370 .2380 .2389 .2398 .2408 .2417 .2427 .39 .2436 .2445 .2455 .2464 .2474 .2483 .2492 .2502 .2511 .2521 .40 .2530 .2540 .2549 .2558 .2568 .2578 .2587 .2596 .2606 .2616 .41 .2625 .2635 .2644 .2654 .2664 .2674 .2683 .2693 .2703 .2712 .42 .2722 .2732 .2742 .2751 .2761 .2771 .2781 .2791 .2800 .2810 .43 .2820 .2830 .2840 .2850 .2860 .2870 .2879 .2889 .2899 .2909 .44 .2919 .2929 .2939 .2949 .2959 .2969 .2979 .2989 .2999 .3009 .45 .3019 .3029 .3039 .3049 .3059 .3070 .3080 .3090 .3100 .3110 .46 .3120 .3130 .3140 .3151 .3161 .3171 .3181 .3191 .3202 .3212 .47 .3222 .3232 .3243 .3253 .3263 .3274 .3284 .3294 .3304 .3315 .48 .3325 .3336 .3346 .3356 .3367 .3378 .3388 .3398 .3409 .3420 .49 .3430 .3441 .3451 .3462 .3472 .3483 .3494 .3504 .3515 .3525 MISCELLANEOUS TABLES AND DATA 287 TABLE 63 (Continued) THREE-HALVES POWERS OF NUMBERS No. .000 .001 .002 .003 .004 .005 .006 .007 .008 .009 0.50 .3536 .3547 .3557 .3568 .3578 .3589 .3600 .3610 .3621 .3631 .51 .3642 .3653 .3664 .3674 .3685 .3696 .3707 .3718 .3728 .3739 .52 .3750 .3761 .3772 .3782 .3793 .3804 .3815 .3826 .3836 .3847 .53 .3858 .3869 .3880 .3891 .3902 .3913 .3924 .3935 .3946 .3957 .54 .3968 .3979 .3990 .4001 .4012 .4024 .4035 .4046 .4057 .4068 .55 .4079 .4090 .4101 .4113 .4124 .4135 .4146 .4157 .4169 .4180 .56 .4191 .4202 .4213 .4225 .4236 .4247 .4258 .4269 .4281 .4292 j .57 .4303 .4314 .4326 4337 .4349 .4360 .4371 .4383 .4394 .4406 .58 .4417 .4428 .4440 .4452 .4463 .4474 .4486 .4498 .4509 .4520 .59 .4532 .4544 .4555 .4567 .4578 .4590 .4602 .4613 .4625 .4636 .60 .4648 .4660 .4671 .4683 .4694 .4706 .4718 .4729 .4741 .4752 .61 .4764 .4776 .4788 .4799 .4811 .4823 .4835 .4847 .4858 .4870 .62 .4882 .4894 .4906 .4917 .4929 .4941 .4953 .4965 .4976 .4988 .63 .5000 .5012 .5024 .5036 .5048 .5060 .5072 .5084 .5096 .5108 .64 .5120 .5132 .5144 .5156 .5168 .5180 .5192 .5204 .5216 .5228 .65 .5240 .5252 .5264 .5277 .5289 .5301 .5313 .5325 .5338 .5350 .66 .5362 .5374 .5386 .5399 .5411 .5423 .5435 .5447 .5460 .5472 .67 .5484 .5496 .5509 .5521 .5533 .5546 .5558 .5570 .5582 .5595 .68 .5607 .5620 .5632 .5644 .5657 .5670 .5682 .5694 .5707 .5720 .69 .5732 .5744 .5757 .5770 .5782 .5794 .5807 .5820 .5832 .5844 .70 .5857 .5870 .5882 .5895 .5907 .5920 .5933 .5945 .5958 .5970 .71 .5983 .5996 .6008 .6021 .6033 .6046 .6059 .6071 .6084 .6096 .72 .6109 .6122 .6135 .6147 .6160 .6173 .6186 .6199 .6211 .6224 .73 .6237 .6250 .6263 .6276 .6289 .6302 .6314 .6327 .6340 .6353 .74 .6366 .6379 .6392 .6405 .6418 .6430 .6443 .6456 .6469 .6482 .75 .6495 .6508 .6521 .6534 .6547 .6560 .6574 .6587 .6600 .6613 .76 .6626 .6639 .6652 .6665 .6678 .6692 .6705 .6718 .6731 .6744 .77 .6757 .6770 .6783 .6797 .6810 .6823 .6836 .6849 .6863 .6876 .78 .6889 .6902 .6916 .6929 .6942 .6956 .6969 .6982 .6995 .7009 .79 .7022 .7035 .7049 .7062 .7075 .7088 .7102 .7115 .7128 .7142 .80 .7155 .7168 .7182 .7196 .7209 .7222 .7236 .7250 .7263 .7276 .81 .7290 .7304 .7317 .7330 .7344 .7358 .7371 .7384 .7398 .7412 .82 .7425 .7439 .7452 .7466 .7480 .7494 .7507 .7521 .7535 .7548 .83 .7562 .7576 .7589 .7603 .7617 .7630 .7644 .7658 .7672 .7685 .84 .7699 .7713 .7727 .7740 .7754 .7768 .7782 .7796 .7809 .7823 .85 .7837 .7851 .7865 .7878 .7892 .7906 .7920 .7934 .7947 .7961 .86 .7975 .7989 .8003 .8017 .8031 .8045 .8059 .8073 .8087 .8101 .87 .8115 .8129 .8143 .8157 .8171 .8185 .8199 .8213 .8227 .8241 .88 .8255 .8269 .8283 .8297 .8311 .8326 .8340 .8354 .8368 .8382 .89 .8396 .8410 .8424 .8439 .8453 .8467 .8481 .8495 .8510 .8524 .90 .8538 .8552 .8567 .8581 .8595 .8610 .8624 .8638 .8652 .8667 .91 .8681 .8695 .8710 .8724 .8738 .8752 .8767 .8781 .8795 .8810 .92 .8824 .8838 .8853 .8868 .8882 .8896 .8911 .8926 .8940 .8954 .93 .8969 .8984 .8998 .9012 .9027 .9042 .9056 .9070 .9085 .9100 .94 .9114 .9128 .9143 .9158 .9172 .9186 .9201 .9216 .9230 .9244 .95 .9259 .9274 .9288 .9302 .9317 .9332 .9347 .9362 .9377 .9391 .96 .9406 .9421 .9435 .9450 .9465 .9480 .9494 .9509 .9524 .9538 .97 .9553 .9568 .9583 .9598 .9613 .9628 .9642 .9657 .9672 .9687 .98 .9702 .9717 .9732 .9746 .9761 .9776 .9791 .9806 .9820 .9835 .99 .9850 .9865 .9880 .9895 .9910 .9925 .9940 .9955 .9970 .9985 288 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 63 (Continued) THREE-HALVES POWERS OF NUMBERS No. .000 .001 .002 .003 .004 .005 .006 .007 .008 .009 1.00 1.0000 1.0015 1.0030 .0045 .0060 1.0075 1.0090 1.0105 1.0120 1.0135 1.01 1.0150 1.0165 1.0180 .0196 .0211 1.0226 1.0241 1.0256 1.0272 1.0287 1.02 1.0302 1.0317 1.0332 .0347 .0362 1.0378 1.0393 1.0408 1.0428 1.0438 1.03 1.0453 1.0468 1.0484 .0499 .0514 1.0530 .0545 1.0560 1.0575 1.0591 1.04 1.0606 1.0621 1.0637 .0652 .0667 1.0682 .0698 1.0713 1.0728 1.0744 1.05 1.0759 1.0774 1.0790 .0805 .0821 1.0836 .0851 1.0867 1.0882 1.0898 1.06 1.0913 1.0928 1.0944 1.0960 .0975 1.0990 .1006 1.1022 1.1037 1.1052 1.07 1.1068 1.1084 1.1099 1.1115 .1130 1.1146 .1162 1.1177 1.1193 1.1208 1.08 1.1224 .1240 .1255 1.1271 .1286 1.1302 .1318 1.1333 1.1349 1.1364 1.09 1.1380 .1396 .1411 1.1427 .1443 1.1458 .1474 1.1490 1.1506 1.1521 1.10 1.1537 .1553 .1569 1.1584 .1600 1.1616 .1632 1.1648 1.1663 1.1679 1.11 1.1695 .1711 .1727 1.1742 .1758 1.1774 .1790 1.1806 1.1821 1.1837 1.12 1.1853 .1869 .1885 1.1901 .1917 1.1932 .1948 1.1964 1.1980 1.1996 1.13 1.2012 1.2028 .2044- 1.2060 .2076 1.2092 .2108 1.2124 1.2140 1.2156 1.14 1.2172 1.2188 .2204 1.2220 .2236 1.2252 .2268 1.2284 1.2300 .2316 1.15 1.2332 1.2348 .2364 1.2381 .2397 1.2413 1.2429 1.2445 1.2462 .2478 1.16 1.2494 1.2510 .2526 1.2543 .2559 1.2575 1.2591 1.2607 1.2624 .2640 1.17 1.2656 1.2672 .2688 1.2705 .2721 1.2737 1.2753 1 .2769 1.2786 .2802 1.18 1.2818 1.2834 1.2851 1.2867 .2883 1.2900 1.2916 1 .2932 .2948 .2965 1.19 1.2981 1.2997 1.3014 1.3030 1.3047 1.3063 1 .3079 1 .3096 .3112 .3129 1.20 1.3145 1.3162 1.3178 1.3194 1.3211 1.3228 1.3244 1.3260 .3277 .3294 1.21 1.3310 .3326 1.3343 1.3360 1.3376 1.3392 1.3409 1.3426 .3442 .3458 1.22 1.3475 .3492 .3508 1.3525 1.3541 1.3558 1.3575 1.3591 .3608 .3624 1.23 1.3641 .3658 .3674 1.3691 1.3768 1.3724 1.3741 1.3758 .3775 .3791 1.24 1.3808 .3825 .3841 .3858 1.3875 1.3892 1.3908 1.3925 .3942 .3958 1.25 1.3975 .3992 .4009 .4026 1.4043 1.4060 1.4076 1.4093 .4110 .4127 1.26 1.4144 .4161 .4178 .4194 1.4211 1.4228 1.4245 1.4262 .4278 .4295 1.27 1.4312 .4329 .4346 .4363 1.4380 1.4397 1.4414 1.4431 .4448 .4465 1.28 1.4482 .4499 .4516 .4533 1.4550 1.4567 1.4584 1.4601 .4618 .4635 1.29 .4652 .4669 .4686 .4703 1.4720 1.4737 1.4754 1.4771 .4788 .4805 1.30 .4822 .4839 .4856 .4874 1.4891 1.4908 1.4925 1.4942 .4960 .4977 1.31 .4994 .5011 .5028 .5046 1.5063 1.5080 1.5097 1.5114 .5132 .5149 1.32 .5166 .5183 .5200 .5218 1.5235 1.5252 1.5269 1.5286 .5304 .5321 1.33 .5338 .5355 .5373 .5390 1.5408 1.5425 1.5442 1.5460 .5477 .5495 1.34 .5512 .5529 .5547 .5564 1.5582 1.5599 1.5616 1.5634 .5651 .5669 1.35 .5686 .5703 .5721 .5738 1.5756 1.5773 1.5790 1.5808 1.5825 1.5843 1.36 .5860 .5878 .5895 .5912 1.5930 1.5948 1.5965 1.5982 1.6000 1.6018 1.37 .6035 .6053 .6070 .6088 1.6105 1.6123 1.6141 1.6158 1.6176 1.6193 1.38 .6211 .6229 .6246 .6264 1.6282 1.6300 1.6317 1.6335 1.6353 1.6370 1.39 .6388 .6406 .6423 .6441 1.6459 1.6476 1.6494 1.6512 1.6530 1.6547 1.40 1.6565 .6583 .6601 .6618 1.6636 1.6654 1.6672 1.6690 1.6708 1.6725 1.41 1.6743 .6761 .6779 .6796 1.6814 1.6832 1.6850 1.6868 1.6885 .6903 1.42 1.6921 1.6939 .6957 .6975 1.6993 1.7010 1.7028 1.7046 1.7064 .7082 1.43 1.7100 1.7118 .7136 .7154 1.7172 1.7190 1.7208 1.7226 1.7244 .7262 1.44 1.7280 1.7298 .7316 .7334 1.7352 1.7370 1.7388 1.7406 1.7424 .7442 1.45 1.7460 1.7478 .7496 1.7514 1.7532 1.7550 1.7569 1.7587 1.7605 .7623 1.46 1.7641 1.7659 .7677 1.7696 1.7714 1.7732 1.7750 1.7768 1.7787 .7805 1.47 1.7823 1.7841 .7859 1.7878 1.7896 1.7914 1.7932 1.7950 1.7969 .7987 1.48 1.8005 1.8023 .8042 1.8060 1.8078 1.8096 1.8115 1.8133 1.8151 .8170 1.49 1.8188 1.8206 .8225 1.8243 1.8261 1.8280 1.8298 1.8316 1.8334 1.8353 MISCELLANEOUS TABLES AND DATA 289 TABLE 63 (Continued) THREE-HALVES POWERS OF NUMBERS No. .00 01 .02 .03 .04 .05 .06 .07 .08 .09 1.5 1.838 1.856 1.874 1.892 1.911 1.930 1.948 1.967 1.986 2.005 1.6 2.024 2.043 2.062 2.081 2.100 2.120 2.139 2.158 2.178 2.197 1.7 2.216 2.236 2.256 2.276 2.295 2.315 2.335 2.355 2.375 2.395 1.8 2.415 2.435 2.455 2.476 2.496 2.516 2.537 2.557 2.578 2.598 1.9 2.619 2.640 2.660 2.681 2.702 2.723 2.744 2.765 2.786 2.807 2.0 2.828 2.850 2.871 2.892 2.914 2.935 2.957 2.978 3.000 3.022 2.1 3.043 3.065 3.087 3.109 3.131 3.152 3.174 3.197 3.219 3.241 2.2 3.263 3.285 3.308 3.330 3.352 3.375 3.398 3.420 3.443 3.465 2.3 3.488 3.511 3.534 3.557 3.580 3.602 3.626 3.649 3.672 3.695 2.4 3.718 3.741 3.765 3.788 3.811 3.835 3.858 3.882 3.906 3.929 2.5 3.953 3.977 4.000 4.024 4.048 4.072 4.096 4.120 4.144 4.168 2.6 4.192 4.217 4.241 4.265 4.290 4.314 4.338 4.363 4.387 4.412 2.7 4.437 4.461 4.486 4.511 4.536 4.560 4.585 4.610 4.635 4.660 2.8 4.685 4.710 4.736 4.761 4.786 4.811 4.837 4.862 4.888 4.913 2.9 4.938 4.964 4.990 5.015 5.041 5.067 5.093 5.118 5.144 5.170 3.0 5.196 5.222 5.248 5.274 5.300 5.327 5.353 5.379 5.405 5.432 3.1 5.458 5.484 5.511 5.538 5.564 5.591 5.617 5.644 5.671 5.698 3.2 5.724 5.751 5.778 5.805 5.832 5.859 5.886 5.913 5.940 5.968 3.3 5.995 6.022 6.049 6.077 6.104 6.132 6.159 6.186 6.214 6.242 3.4 6.269 6.297 6.325 6.352 6.380 6.408 6.436 6.464 6.492 6.520 3.5 6.548 6.576 6.604 6.632 6.660 6.689 6.717 6.745 6.774 6.802 3.6 6.830 6.859 6.888 6.916 6.945 6.973 7.002 7.031 7.060 7.088 3.7 7.117 7.146 7.175 7.204 7.233 7.262 7.291 7.320 7.349 7.378 3.8 7.408 7.437 7.466 7.496 7.525 7.554 7.584 7.613 7.643 7.672 3.9 7.702 7.732 7.770 7.791 7.821 7.850 7.880 7.910 7.940 7.970 4.0 8.000 8.030 8.060 8.090 8.120 8.150 8.181 8.211 8:241 8.272 4.1 8.302 8.332 8.363 8.393 8.424 8.454 8.485 8.515 8.546 8.577 4.2 8.607 8.638 8.669 8.700 8.731 8.762 8.792 8.824 8.854 8.886 4.3 8.917 8.948 8.979 9.010 9.041 9.073 9.104 9.135 9.167 9.198 4.4 9.230 9.261 9.292 9.324 9.356 9.387 9.419 9.451 9.482 9.514 4.5 9.546 9.578 9.610 9.642 9.674 9.706 9.738 9.770 9.802 9.834 4.6 9.866 9.898 9.930 9.963 9.995 10.03 10.06 10.09 10.12 10.16 4.7 10.19 10.22 10.25 10.29 10.32 10.35 10.39 10.42 10.45 10.48 4.8 10.52 10.55 10.58 10.62 10.65 10.68 10.71 10.75 10.78 10.81 4.9 10.85 10.88 10.91 10.95 10.98 11.01 11.05 11.08 11.11 11.15 5.0 11.18 11.21 11.25 11.28 11.31 11.35 11.38 11.42 11.45 11.48 5.1 11.52 11.55 11.59 11.62 11.65 11.69 11.72 11.76 11.79 11.82 5.2 11.86 11.89 11.93 11.96 11.99 12.03 12.06 12.10 12.13 12.17 5.3 12.20 12.24 12.27 12.31 12.34 12.37 12.41 12.44 12.48 12.51 5.4 12.55 12.58 12.62 12.65 12.69 12.72 12.76 12.79 12.83 12.86 5.5 12.90 12.93 12.97 13.00 13.04 13.07 13.11 13.15 13.18 13.22 5.6 13.25 13.29 13.32 13.36 13.39 13.43 13.47 13.50 13.54 13.57 5.7 13.61 13.64 13.68 13.72 13.75 13.79 13.82 13.86 13.90 13.93 5.8 13.97 14.00 14.04 14.08 14.11 14.15 14.19 14.22 14.26 14.29 5.9 14.33 14.37 14.40 14.44 14.48 14.51 14.55 14.59 14.62 14.66 6.0 14.70 14.73 14.77 14.81 14.84 14.88 14.92 14.95 14.99 15.03 6.1 15.07 15.10 15.14 15.18 15.21 15.25 15.29 15.33 15.36 15.40 6.2 15.44 15.48 15.51 15.55 15.59 15.62 15.66 15.70 15.74 15.78 6.3 15.81 15.85 15.89 15.93 15.96 16.00 16.04 16.08 16.12 16.15 6.4 16.19 16.23 16.27 16.30 16.34 16.38 16.42 16.46 16.50 16.53 290 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 63 (Concluded) THREE-HALVES POWERS OF NUMBERS No. .00 .01 .02 .03 .04 .05 .06 .07 .08 .09 6.5 16.57 16.61 16.65 16.69 16.72 16.76 16.80 16.84 16.88 16.92 6.6 16.96 16.99 17.03 17.07 17.11 17.15 17.19 17.22 17.26 17.30 6.7 17.34 17.38 17.42 17.46 17.50 17.54 17.58 17.62 17.65 17.69 6.8 17.73 17.77 17.81 17.85 17.89 17.93 17.97 18.01 18.05 18.09 6.9 18.12 18.16 18.20 18.24 18.28 18.32 18.36 18.40 18.44 18.48 7.0 18.52 18.56 18.60 18.64 18.68 18.72 18.76 18.80 18.84 18.88 7.1 18.92 18.96 19.00 19.04 19.08 19.12 19.16 19.20 19.24 19.28 7.2 19.32 19.36 19.40 19.44 19.48 19.52 19.56 19.60 19.64 19.68 7.3 19.72 19.76 19.80 19.85 19.89 19.93 19.97 20.01 20.05 20.09 7.4 20.13 20.17 20.21 20.25 20.29 20.33 20.38 20.42 20.46 20.50 7.5 20.54 20.58 20.62 20.66 20.70 20.75 20.79 20.83 20.87 20.91 7.6 20.95 20.99 21.03 21.08 21.12 21.16 21.20 21.24 21.28 21.32 7.7 21.37 21.41 21.45 21.49 21.53 21.58 21.62 21.66 21.70 21.74 7.8 21.78 21.83 21.87 21.91 21.95 21.99 22.04 22.08 22.12 22.16 7.9 22.20 22.25 22.29 22.33 22.37 22.42 22.46 22.50 22.54 22.58 8.0 22.63 22.67 22.71 22.75 22.80 22.84 22.88 22.93 22.97 23.01 8.1 23.05 23.10 23.14 23.18 23.22 23.27 23.31 23.35 23.40 23.44 8.2 23.48 23.52 23.57 23.61 23.65 23.70 23.74 23.78 23.83 23.87 8.3 23.91 23.96 24.00 24.04 24.09 24.13 24.17 24.22 24.26 24.30 8.4 24.35 24.39 24.43 24.48 24.52 24.56 24.61 24.65 24.69 24.74 8.5 24.78 24.83 24.87 24.91 24.96 25.00 25.04 25.09 25.13 25.18 8.6 25.22 25.26 25.31 25.35 25.40 25.44 25.48 25.53 25.57 25.62 8.7 25.66 25.71 25.75 25.79 25.84 25.88 25.93 25.97 26.02 26.06 8.8 26.10 26.15 26.19 26.24 26.28 26.33 26.37 26.42 26.46 26.51 8.9 26.55 26.60 26.64 26.69 26.73 26.78 26.82 26.87 26.91 26.96 9.0 27.00 27.04 27.09 27.14 27.18 27.23 27.27 27.32 27.36 27.41 9.1 27.45 27.50 27.54 27.59 27.63 27.68 27.72 27.77 27.81 27.86 9.2 27.90 27.95 28.00 28.04 28.09 28.13 28.18 28.22 28.27 28.32 9.3 28.36 28.41 28.45 28.50 28.54 28.59 28.64 28.68 28.73 28.77 9.4 28.82 28.87 28.91 28.96 29.00 29.05 29.10 29.14 29.19 29.23 9.5 29.28 29.33 29.37 29.42 29.47 29.51 29.56 29.61 29.65 29.70 9.6 29.74 29.79 29.84 29.88 29.93 29.98 30.02 30.07 30.12 30.16 9.7 30.21 30.26 30.30 30.35 30.40 30.44 30.49 30.54 30.58 30.63 9.8 30.68 30.73 30.77 30.82 30.87 30.91 30.96 31.01 31.06 31.10 9.9 31.15 31.20 31.24 31.29 31.34 31.38 31.43 31.48 31.53 31.58 10.0 31.62 31.67 31.72 31.77 31.81 31.86 31.91 31.96 32.00 32.05 MISCELLANEOUS TABLES AND DATA 291 TABLE 64 CONVENTIONAL SIGNS FOR IRRIGATION STRUCTURES Adopted by U. S. Reclamation Service Dam Diversion dam or weir Headworks. . 1 s * Tunnel II , * Bridge ^= Spillway ^Jlj Drainage culvert under canal Mf^ IP Box or pipe culvert under road ^ Flume Check or drop A Siphon or covered conduit /Jv Sluiceway - "C|- Turnout =^-(1) Telephones | | i Telephone line _4 Transmission line . 292 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 65 SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS, AND AREA AND CIRCUMFERENCE OF CIRCLES OF RADIUS N N AT' N* N* yi 1 N 7T.ZV2 2 *N 1 1 1 1.0000 1.0000 1.000000 3.142 6.283 2 4 8 1.4142 1.2599 .500000 12.566 12.566 3 9 27 1.7321 1.4422 .333333 28.274 18.850 4 16 64 2.0000 1.5874 .250000 50.265 25.133 5 25 125 2.2361 1.7100 .200000 78.540 31.416 6 36 216 2.4495 1.8171 .166667 113.097 37.699 7 49 343 2.6458 1.9129 .142857 153.938 43.982 8 64 512 2.8284 2.0000 .125000 201.062 50.265 9 81 729 3.0000 2.0801 .111111 254.469 56.549 10 100 1,000 3.1623 2.1544 .100000 314.159 62.832 11 121 1,331 3.3166 2.2240 .090909 380.133 69.115 12 144 1,728 3.4641 2.2894 .083333 452.389 75.398 13 169 2,197 3.6056 2.3513 .076923 530.929 81.681 14 196 2,744 3.7417 2.4101 .071429 615.752 87.965 15 225 3,375 3.8730 2.4662 .066667 706.858 94.248 16 256 4,096 4.0000 2.5198 .062500 804.248 100.531 17 289 4,913 4.1231 2.5713 .058824 907.920 106.814 18 324 5,832 4.2426 2.6207 .055556 1,017.876 113.097 19 361 6,859 4.3589 2.6684 .052632 1,134.115 119.381 20 400 8,000 4.4721 2.7144 .050000 1,256.637 125.664 21 441 9,261 4.5826 2.7589 .047619 1,385.442 131.947 22 484 10,648 4.6904 2.8020 .045455 1,520.531 138.230 23 529 12,167 4.7958 2.8439 .043478 1,661.903 144.513 24 576 13,824 4.8990 2.8845 .041667 1,809.557 150.796 25 625 15,625 5.0000 2.9240 .040000 1,963.495 157.080 26 676 17,576 5.0990 2.9625 .038462 2,123.717 163.363 27 729 19,683 5.1962 3.0000 .037037 2,290.221 169.646 28 784 21,952 5.2915 3.0366 .035714 2,463.009 175.929 29 841 24,389 5.3852 3.0723 .034483 2,642.079 182.212 30 900 27,000 5.4772 3.1072 .033333 2,827.433 188.496 31 961 29,791 5.5678 3.1414 .032258 3,019.071 194.779 32 1,024 32,768 5.6569 3.1748 .031250 3,216.991 201.062 33 1,089 35,937 5.7446 3.2075 .030303 3,421.194 207.345 34 1,156 39,304 5.8310 3.2396 .029412 3,631.681 213 .,628 35 1,225 42,875 5.9161 3.2711 .028571 3,848.451 219.911 36 1,296 46,656 6.0000 3.3019 .027778 4,071.504 226.195 37 1,369 50,653 6.0828 3.3322 .027027 4,300.840 232.478 38 1,444 54,872 6.1644 3.3620 .026316 4,536.460 238.761 39 1,521 59,319 6.2450 3.3912 .025641 4,778.362 245.044 40 1,600 64,000 6.3246 3.4200 .025000 5,026.548 251.327 41 1,681 68,921 6.4031 3.4482 .024390 5,281.017 257.611 42 1,764 74,088 6.4807 3.4760 .023810 5,541.770 263.894 43 1,849 79,507 6.5574 3.5034 .023256 5,808.805 270.177 44 1,936 85,184 6.6332 3.5303 .022727 6,082.123 276.460 45 2,025 91,125 6.7082 3.5569 .022222 6,361.725 282.743 46 2,116 97,336 6.7823 3.5830 .021739 6,647.610 289.027 47 2,209 103,823 6.8557 3.6088 .021277 6,939.778 295.310 48 2,304 110,592 6.9282 3.6342 .020833 7,238.230 301.593 49 2,401 117,649 7.0000 3.6593 .020408 7,542.964 307.876 50 2,500 125,000 7.0711 3.6840 .020000 7,853.982 314.159 MISCELLANEOUS TABLES AND DATA 293 TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS, AND AREA AND CIRCUMFERENCE OF CIRCLES OF RADIUS N N N 2 N 3 B* N* i N 7J-2V2 2 nN 51 2,601 132,651 7.1414 3.7084 .019607 8,171.283 320.442 52 2,704 140,608 7.2111 3.7325 .019231 8,494.867 326.726 53 2,809 148,877 7.2801 3.7563 .018868 8,824.734 333.009 54 2,916 157,464 7.3485 3.7798 .018519 9,160.884 339.292 55 3,025 166,375 7.4162 3.8030 .018182 9,503.318 345.575 56 3,136 175,616 7.4833 3.8259 .017857 9,852.035 351.858 57 3,249 185,193 7.5498 3.8485 .017544 10,207.035 358.142 58 3,364 195,112 7.6158 3.8709 .017241 10,568.318 364.425 59 3,481 205,379 7.6811 3.8930 .016949 10,935.884 370.708 60 3,600 216,000 7.7460 3.9149 .016667 11,309.734 376.991 61 3,721 226,981 7.8102 3.9365 .016393 11,689.866 383.274 62 3,844 238,328 7.8740 3.9579 .016129 12,076.282 389.557 63 3,969 250,047 7.9373 3.9791 .015873 12,468.981 395.841 64 4,096 262,144 8.0000 4.0000 .015625 12,867.964 402.124 65 4,225 274,625 8.0623 4.0207 .015385 13,273.229 408.407 66 4,356 287,496 8.1240 4.0412 .015156 13,684.778 414.690 67 4,489 300,763 8.1854 4.0615 .014925 14,102.610 420.973 68 4,624 314,432 8,2462 4.0817 .014706 14,526.725 427.257 69 4,761 328,509 8.3066 4.1016 .014493 14,957.123 433.540 70 4,900 343,000 8.3666 4.1213 .014286 15,393.804 439.823 71 5,041 357,911 8.4261 4.1408 .014085 15,836.769 446.106 72 5,184 373,248 8.4853 4.1602 .013889 16,286.017 452.389 73 5,329 389,017 8.5440 4.1793 .013699 16,741.547 458.673 74 5,476 405,224 8.6023 4.1983 .013514 17,203.362 464.956 75 5,625 421,875 8.6603 4.2172 .013333 17,671.459 471.239 76 5,776 438,976 8.7178 4.2358 .013158 18,145.839 477.522 77 5,929 456,533 8.7750 4.2543 .012987 18,626.503 483.805 78 6,084 474,552 8.8318 4.2727 .012821 19,113.450 490.088 79 6,241 493,039 8.8882 4.2908 .012658 19,606.680 486.372 80 6,400 512,000 8.9443 4.3089 .012500 20,106.193 502.655 81 6,561 531,441 9.0000 4.3267 .012346 20,611.990 508.938 82 6,724 551,368 9.0554 4.3445 .012195 21,124.069 515.221 83 6,889 571,787 9.1104 4.3621 .012048 21,642.432 521.504 84 7,056 592,704 9.1652 4.3795 .011905 22,167.078 527.788 85 7,225 614,125 9.2195 4.3968 .011765 22,698.007 534.071 86 7,396 636,056 9.2736 4.4140 .011628 23,235.220 540.354 87 7,569 658,503 9.3274 4.4310 .011494 23,778.715 546.637 88 7,744 681,472 9.3808 4.4480 .011364 24,328.494 552.920 89 7,921 704,969 9.4340 4.4647 .011236 24,884.556 559.205 90 8,100 .729,000 9.4868 4.4814 .011111 25,446.901 565.487 91 8,281 753,571 9.5394 4.4979 .010989 26,015.529 571.770 92 8,464 778,688 9.5917 4.5144 .010870 26,590.441 578.053 93 8,649 804,357 9.6437 4.5307 .010753 27,171.635 584.336 94 8,836 830,584 9.6954 4.5468 .010638 27,759.113 590.619 95 9,025 857,375 9.7468 4.5629 .010526 28,352.874 596.903 96 9,216 884,736 9.7980 4.5789 .010417 28,952.918 603.186 97 9,409 912,673 9.8489 4.5947 .010309 29,559.246 609.469 98 9,604 941,192 9.8995 4.6104 .010204 30,171.856 615.752 99 9,801 970,299 9.9499 4.6261 .010101 30,790.750 622.035 100 10,000 1,000,000 10.0000 4.6416 .010000 31,415.927 628.319 294 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N N* W N* N* l N 101 10,201 1,030,301 10.0498756 4.6570095 .009900990 102 10,404 1,061,208 10.0995049 4.6723287 .009803922 103 10,609 1,092,727 10.1488916 4.6875482 .009708738 104 10,816 1,124,864 10.1980390 4.7026694 .009615385 105 11,025 1,157,625 10.2469508 4.7176940 .009523810 106 11,236 1,191,016 10.2956301 4.7326235 .009433962 107 11,449 1,225,043 10.3440804 4.7474594 .009345794 108 11,664 1,259,712 10.3923048 4.7622032 .009259259 109 11,881 1,295,029 10.4403065 4.7768562 .009174312 110 12,100 1,331,000 10.4880885 4.7914199 .009090909 111 12,321 1,367,631 10.5356538 4.8058955 .009009009 112 12,544 1,404,928 10.5830052 4.8202845 .008928571 113 12,769 1,442,897 10.6301458 4.8345881 .008849558 114 12,996 1,481,544 10.6770783 4.8488076 .008771930 115 13,225 1,520,875 10.7238053 4.8629442 .008695652 116 13,456 1,560,896 10.7703296 4.8769990 .008620690 117 13,689 1,601,613 10.8166538 4.8909732 .008547009 118 13,924 1,643,032 10.8627805 4.9048681 .008474576 119 14,161 1,685,159 10.9087121 4.9186847 .008403361 120 14,400 1,728,000 10.9544512 4.9324242 .008333333 121 14,641 1,771,561 11.0000000 4.9460874 .008264463 122 14,884 1,815,848 11.0453610 4.9596757 .008196721 123 15,129 1,860,867 11.0905365 4.9731898 .008130081 124 15,376 1,906,624 11.1355287 4.9866310 .008064516 125 15,625 1,953,125 11.1803399 5.0000000 .008000000 126 15,876 2,000,376 11.2249722 5.0132979 .007936508 127 16,129 2,048,383 11.2694277 5.0265257 .007874016 128 16,384 2,097,152 11.3137085 5.0396842 .007812500 129 16,641 2,146,689 11.3578167 5.0527743 .007751938 130 16,900 2,197,000 11.4017543 5.0657970 .007692308 131 17,161 2,248,091 11.4455231 5.0787531 .007633588 132 17,424 2,299,968 11.4891253 5.0916434 .007575758 133 17,689 2,352,637 11.5325626 5.1044687 .007518797 134 17,956 2,406,104 11.5758369 5.1172299 .007462687 135 18,225 2,460,375 11.6189500 5.1299278 .007407407 136 18,496 2,515,456 11.6619038 5.1425632 .007352941 137 18,769 2,571,353 11.7046999 5.1551367 .007299270 138 19,044 2,628,072 11.7473401 5.1676493 .007246377 139 19,321 2,685,619 11.7898261 5.1801015 .007194245 140 19,600 2,744,000 11.8321596 5.1924941 .007142857 141 19,881 2,803,221 11.8743421 5.2048279 .007092199 142 20,164 2,863,288 11.9163753 5.2171034 .007042254 143 20,449 2,924,207 11.9582607 5.2293215 .006993007 144 20,736 2,985,984 12.0000000 5.2414828 .006944444 145 21,025 3,048,625 12.0415946 5.2535879 .006896552 146 21,316 3,112,136 12.0830460 5.2656374 .006849315 147 21,609 3,176,523 12.1243557 5.2776321 .006802721 148 21,904 3,241,792 12.1655251 5.2895725 .006756757 149 22,201 3,307,949 12.2065556 5.3014592 .006711409 150 22,500 3,375,000 12.2474487 5.3132928 .006666667 MISCELLANEOUS TABLES AND DATA 295 TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS 2V N 2 AT3 ** N* 1 N 151 22,801 3,442,951 12.2882057 5.3250740 .006622517 152 23,104 3,511,808 12.3288280 5.3368033 .006578947 153 23,409 3,581,577 12.3693769 5.3484812 .006535948 154 23,716 3,652,264 12.4096736 5.3601084 .006493506 155 24,025 3,723,875 12.4498996 5.3716854 .006451613 156 24,336 3,796,416 12.4899960 5.3832126 .006410256 157 24,649 3,869,893 12.5299641 5.3946907 .006369427 158 24,964 3,944,312 12.5698051 5.4061202 .006329114 159 25,281 4,019,679 12.6095202 5.4175015 .006289308 160 25,600 4,096,000 12.6491106 5.4288352 .006250000 161 25,921 4,173,281 12.6885775 5.4401218 .006211180 162 26,244 4,251,528 12.7279221 5.4513618 .006172840 163 26,569 4,330,747 12.7671453 5.4625556 .006134969 164 26,896 4,410,944 12.8062485 5.4737037 .006097561 165 27,225 4,492,125 12.8452326 5.4848066 .006060606 166 27,556 4,574,296 12.8840987 5.4958647 .006024096 167 27,889 4,657,463 12.9228480 5.5068784 .005988024 168 28,224 4,741,632 12.9614814 5.5178484 .005952381 169 28,561 4,826,809 13.0000000 5.5287748 .005917160 170 28,900 4,913,000 13.0384048 5.5396583 .005882353 171 29,241 5,000,211 13.0766968 5.5504991 .005847953 172 29,584 5,088,448 13.1148770 5.5612978 .005813953 173 29,929 5,177,717 13.1529464 5.5720546 .005780347 174 30,276 5,268,024 13.1909060 5.5827702 .005747126 175 30,625 5,359,375 13.2287566 5.5934447 .005714286 176 30,976 5,451,776 13.2664992 5.6040787 .005681818 177 31,329 5,545,233 13.3041347 5.6146724 .005649718 178 31,684 5,639,752 13.3416641 5.6252263 .005617978 179 32,041 5,735,339 13.3790882 5.6357408 .005586592 180 32,400 5,832,000 13.4164079 5.6462162 .005555556 181 32,761 5,929,741 13.4536240 5.6566528 .005524862 182 33,124 6,028,568 13.4907376 5.6670511 .005494505 183 33,489 6,128,487 13.5277493 5.6774114 .005464481 184 33,856 6,229,504 13.5646600 5.6877340 .005434783 185 34,225 6,331,625 13.6014705 5.6980192 .005405405 186 34,596 6,434,856 13.6381817 5.7082675 .005376344 187 34,969 6,539,203 13.6747943 5.7184791 .005347594 188 35,344 6,644,672 13.7113092 5.7286543 .005319149 189 35,721 6,751,269 13.7477271 5.7387936 .005291005 190 36,100 6,859,000 13.7840488 5.7488971 .005263158 191 36,481 6,967,871 13.8202750 5.7589652 .005235602 192 36,864 7,077,888 13.8564065 5.7689982 .005208333 193 37,249 7,189,057 13.8924440 5.7789966 .005181347 194 37,636 7,301,384 13.9283883 5.7889604 .005154639 195 38,025 7,414,875 13.9642400 5.7988900 .005128205 196 38,416 7,529,536 14.0000000 5.8087857 .005102041 197 38,809 7,645,373 14.0356688 5.8186479 .005076142 198 39,204 7,762,392 14.0712473 5.8284767 .005050505 199 39,610 7,880,599 14.1067360 5.8382725 .005025126 200 40,000 8,000,000 14.1421356 5.8480355 .005000000 296 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N N* NI N* ** l N 201 40,401 8,120,601 14.1774469 5.8577660 .004975124 202 40,804 8,242,408 14.2126704 5.8674643 .004950495 203 41,209 8,365,427 14.2478068 5.8771307 .004926108 204 41,616 8,489,664 14.2828569 5.8867653 .004901961 205 42,025 8,615,125 14.3178211 5.8963685 .004878049 206 42,436 8,741,816 14.3527001 5.9059406 .004854369 207 42,849 8,869,743 14.3874946 5.9154817 .004830918 208 43,264 8,998,912 14.4222051 5.9249921 .004807692 209 43,681 9,129,329 14.4568323 5.9344721 .004784689 210 44,100 9,261,000 14.4913767 5.9439220 .004761905 211 44,521 9,393,931 14.5258390 5.9533418 .004739336 212 44,944 9,528,128 14.5602198 5.9627320 .004716981 213 45,369 9,663,597 14.5945195 5.9720926 .004694836 214 45,796 9,800,344 14.6287388 5.9814240 .004672897 215 46,225 9,938,375 14.6628783 5.9907264 .004651163 216 46,656 10,077,696 14.6969385 6.0000000 .004629630 217 47,089 10,218,313 14.7309199 6.0092450 .004608295 218 47,524 10,360,232 14.7648231 6.0184617 .004587156 219 47,961 10,503,459 14.7986486 6.0276502 .004566210 220 48,400 10,648,000 14.8323970 6.0368107 .004545455 221 48,841 10,793,861 14.8660687 6.0459435 .004524887 222 49,284 10,941,048 14.8996644 6.0550489 .004504505 223 49,729 11,089,567 14.9331845 6.0641270 .004484305 224 50,176 11,239,424 14.9666295 6.0731779 .004464286 225 50,625 11,390,625 15.0000000 6.0822020 .004444444 226 51,076 11,543,176 15.0332964 6.0911994 .004434779 227 51,529 11,697,083 15.0665192 6.1001702 .004405286 228 51,984 11,852,352 15.0996689 6.1091147 .004385965 229 52,441 12,008,989 15.1327460 6.1180332 .004366812 230 52,900 12,167,000 15.1657509 6.1269257 .004347826 231 53,361 12,326,391 15.1986842 6.1357924 .004329004 232 53,824 12,487,168 15.2315462 6.1446337 .004310345 233 54,289 12,649,337 15.2643375 6.1534495 .004291845 234 54,756 12,812,904 15.2970585 6.1622401 .004273504 235 55,225 12,977,875 15.3297097 6.1710058 .004255319 236 55,696 13,144,256 15.3622915 6.1797466 .004237288 237 56,169 13,312,053 15.3948043 6.1884628 .004219409 238 56,644 13,481,272 15.4272486 6.1971544 .004201681 239 57,121 13,651,919 15.4596248 6.2058218 .004184100 240 57,600 13,824,000 15.4919334 6.2144650 .004166667 241 58,081 13,997,521 15.5241747 6.2230843 .004149378 242 58,564 14,172,488 15.5563492 6.2316797 .004132231 243 59,049 14,348,907 15.5884573 6.2402515 .004115226 244 59,536 14,526,784 15.6204994 6.2487998 .004098361 245 60,025 14,706,125 15.6524758 6.2573248 .004081633 246 60,516 14,886,936 15.6843871 6.2658266 .004065041 247 61,009 15,069,223 15.7162336 6.2743054 .004048583 248 61,504 15,252,992 15.7480157 6.2827613 .004032258 249 62,001 15,438,249 15.7797338 6.2911946 .004016064 250 62,500 15,625,000 15.8113883 6.2996053 .004000000 MISCELLANEOUS TABLES AND DATA 297 TABLE 65 (Continued} SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N AT2 N^ N* fri l N 251 63,001 15,813,251 15.8429795 6.3079935 .003984064 252 63,504 16,003,008 15.8745079 6.3163596 .003968254 253 64,009 16,194,277 15.9059737 6.3247035 .003952569 254 64,516 16,387,064 15.9373775 6.3330256 .003937008 255 65,025 16,581,375 15.9687194 6.3413257 .003921569 256 65,536 16,777,216 16.0000000 6.3496042 .003906250 257 66,049 16,974,593 16.0312195 6.3578611 .003891051 258 66,564 17,173,512 16.0623784 6.3660968 .003875969 259 67,081 17,373,979 16.0934769 6.3743111 .003861004 260 67,600 17,576,000 16.1245155 6.3825043 .003846154 261 68,121 17,779,581 16.1554944 6.3906765 .003831418 262 68,644 17,984,728 16.1864141 6.3988279 .003816794 263 69,169 18,191,447 16.2172747 6.4069585 .003802281 264 69,696 18,399,744 16.2480768 6.4150687 .003787879 265 70,225 18,609,625 16.2788206 6.4231583 .003773585 266 70,756 18,821,096 16.3095064 6.4312276 .003759398 267 71,289 19,034,163 16.3401346 6.4392767 .003745318 268 71,824 19,248,832 16.3707055 6.4473057 .003731343 269 72,361 19,465,109 16.4012195 6.4553148 .003717472 270 72,900 19,683,000 16.4316767 6.4633041 .003703704 271 73,441 19,902,511 16.4620776 6.4712736 .003690037 272 73,984 20,123,648 16.4924225 6.4792236 .003676471 273 74,529 20,346,417 16.5227116 6.4871541 .003663004 274 75,076 20,570,824 16.5529454 6.4950653 .003649635 275 75,625 20,796,875 16.5831240 6.5029572 .003636364 276 76,176 21,024,576 16.6132477 6.5108300 .003623188 277 76,729 21,253,933 16.6433170 6.5186839 .003610108 278 77,284 21,484,952 16.6733320 6.5265189 .003597122 279 77,841 21,717,639 16.7032931 6.5343351 .003584229 280 78,400 21,952,000 16.7332005 6.5421326 .003571429 281 78,961 22,188,041 16.7630546 6.5499116 .003558719 282 79,524 22,425,768 16.7928556 6.5576722 .003546099 283 80,089 22,665,187 16.8226038 6.5654144 .003533569 284 80,656 22,906,304 16.8522995 6.5731385 .003521127 285 81,225 23,149,125 16.8819430 6.5808443 .003508772 286 81,796 23,393,656 16.9115345 6.5885323 .003496503 287 82,369 23,639,903 16.9410743 6.5962023 .003484321 288 82,944 23,887,872 16.9705627 6.6038545 .003472222 289 83,521 24,137,569 17.0000000 6.6114890 .003460208 290 84,100 24,389,000 17.0293864 6.6191060 .003448276 291 84,681 24,642,171 17.0587221 6.6267054 .003436426 292 85,264 24,897,088 17.0880075 6.6342874 .003424658 293 85,849 25,153,757 17.1172428 6.6418522 .003412969 294 86,436 25,412,184 17.1464282 6.6493998 .003401361 295 87,025 25,672,375 17.1755640 6.6569302 .003389831 296 87,616 25,934,336 17.2046505 6.6644437 .003378378 297 88,209 26,198,073 17.2336879 6.6719403 .003367003 298 88,804 26,463,592 17.2626765 6.6794200 .003355705 299 89,401 26,730,899 17.2916165 6.6868831 .003344482 300 90,000 27,000,000 17.3205081 6.6943295 .003333333 298 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N AT* N 3 N* N* l N 301 90,601 27,270,901 17.3493516 6.7017593 .003322259 302 91,204 27,543,608 17.3781472 6.7091729 .003311258 303 91,809 27,818,127 17.4068952 6.7165700 .003300330 304 92,416 28,094,464 17.4355958 6.7239508 .003289474 305 93,025 28,372,625 17.4642492 6.7313155 .003278689 306 93,636 28,652,616 17.4928557 6.7386641 .003267974 307 94,249 28,934,443 17.5214155 6.7459967 .003257329 308 94,864 29,218,112 17.5499288 6.7533134 .003246753 309 95,481 29,503,629 17.5783958 6.7606143 .003236246 310 96,100 29,791,000 17.6068169 6.7678995 .003225806 311 96,721 30,080,231 17.6351921 6.7751690 .003215434 312 97,344 30,371,328 17.6635217 6.7824229 .003205128 313 97,969 30,664,297 17.6918060 6.7896613 .003194888 314 98,596 30,959,144 17.7200451 6.7968844 .003184713 315 99,225 31,255,875 17.7482393 6.8040921 .003174603 316 99,856 31,554,496 17.7763888 6.8112847 .003164557 317 100,489 31,855,013 17.8044938 6.8184620 .003154574 318 101,124 32,157,432 17.8325545 6.8256242 .003144654 319 101,761 32,461,759 17.8605711 6.8327714 .003134796 320 102,400 32,768,000 17.8885438 6.8399037 .003125000 321 103,041 33,076,161 17.9164729 6.8470213 .003115265 322 103,684 33,386,248 17.9443584 6.8541240 .003105590 323 104,329 33,698,267 17.9722008 6.8612120 .003095975 324 104,976 34,012,224 18.0000000 6.8682855 .003086420 325 105,625 34,328,125 18.0277564 6.8753443 .003076923 326 106,276 34,645,976 18.0554701 6.8823888 .003067485 327 106,929 34,965,783 18.0831413 6.8894188 .003058104 328 107,584 35,287,552 18.1107703 6.8964345 .003048780 329 108,241 35,611,289 18.1383571 6.9034359 .003039514 330 108,900 35,937,000 18.1659021 6.9104232 .003030303 331 109,561 36,264,691 18.1934054 6.9173964 .003021148 332 110,224 36,594,368 18.2208672 6.9243556 .003012048 333 110,889 36,926,037 18.2482876 6.9313008 .003003003 334 111,556 37,259,704 18.2756669 6.9382321 .002994012 335 112,225 37,595,375 18.3030052 6.9451496 .002985075 336 112,896 37,933,056 18.3303028 6.9520533 .002976190 337 113,569 38,272,753 18.3575598 6.9589434 .002967359 338 114,244 38,614,472 18.3847763 6.9658198 .002958580 339 114,921 38,958,219 18.4119526 6.9726826 .002949853 340 115,600 39,304,000 18.4390889 6.9795321 .002941176 341 116,281 39,651,821 18.4661853 6.9863681 .002932551 342 116,964 40,001,688 18.4932420 6.9931906 .002923977 343 117,649 40,353,607 18. 5202532 7.0000000 .002915452 344 118,336 40,707,584 18.5472370 7.0067962 .002906977 345 119,025 41,063,625 18.5741756 7.0135791 .002898551 346 119,716 41,421,736 18.6010752 7.0203490 .002890173 347 120,409 41,781,923 18.6279360 7.0271058 .002881844 348 121,104 42,144,192 18.6547581 7.0338497 .002873563 349 121,801 42,508,549 18.6815417 7.0405806 .002865330 350 122,500 42,875,000 18.7082869 7.0472987 .002857143 MISCELLANEOUS TABLES AND DATA 299 TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS 1 1 N N 2 N 3 N* N 351 123,201 43,243,551 18.7349940 7.0540041 .002849003 352 123,904 43,614,208 18.7616630 7.0606967 .002840909 353 124,609 43,986,977 18.7882942 7.0673767 .002832861 354 125,316 44,361,864 18.8148877 7.0740440 .002824859 355 126,025 44,738,875 18.8414437 7.0806988 .002816901 356 126,736 45,118,016 18.8679623 7.0873411 .002808989 357 127,449 45,499,293 18.8944436 7.0939709 .002801120 358 128,164 45,882,712 18.9208879 7.1005885 .002793296 359 128,881 46,268,279 18.9472953 7.1071937 .002785515 360 129,600 46,656,000 18.9736660 7.1137866 .002777778 361 130,321 47,045,881 19.0000000 7.1203674 .002770083 362 131,044 47,437,928 19.0262976 7.1269360 .002762431 363 131,769 47,832,147 19.0525589 7.1334925 .002754821 364 132,496 48,228,544 19.0787840 7.1400370 .002747253 365 133,225 48,627,125 19.1049732 7.1465695 .002739726 366 133,956 49,027,896 19.1311265 7.1530901 .002732240 367 134,689 49,430,863 19.1572441 7.1595988 .002724796 368 135,424 49,836,032 19.1833261 7.1660957 .002717391 369 136,161 50,243,409 19.2093727 7.1725809 .002710027 370 136,900 50,653,000 19.2353841 7.1790544 .002702703 371 137,641 51,064,811 19.2613603 7.1855162 .002695418 372 138,384 51,478,848 19.2873015 7:1919663 .002688172 373 139,129 51,895,117 19.3132079 7.1984050 .002680965 374 139,876 52,313,624 19.3390796 7.2048322 .002673797 375 140,625 52,734,375 19.3649167 7.2112479 .002666667 376 141,376 53,157,376 19.3907194 7.2176522 .002659574 377 142,129 53,582,633 19.4164878 7.2240450 .002652520 378 142,884 54,010,152 19.4422221 7.2304268 .002645503 379 143,641 54,439,939 19.4679223 7.2367972 .002638522 380 144,400 54,872,000 19.4935887 7.2431565 .002631579 381 145,161 55,306,341 19.5192213 7.2495045 .002624672 382 145,924 55,742,968 19.5448203 7.2558415 .002617801 383 146,689 56,181,887 19.5703858 7.2621675 .002610966 384 147,456 56,623,104 19.5959179 7.2684824 .002604167 385 148,225 57,066,625 19.6214169 7.2747864 .002597403 386 148,996 57,512,456 19.6468827 7.2810794 .002590674 387 149,769 57,960,603 19.6723156 7.2873617 .002583979 388 150,544 58,411,072 19.6977156 7.2936330 .002577320 389 151,321 58,863,869 19.7230829 7.2998936 .002570694 390 152,100 59,319,000 19.7484177 7.3061436 .002564103 391 152,881 59,776,471 19.7737199 7.3123828 .002557545 392 153,664 60,236,288 19.7989899 7.3186114 .002551020 393 154,449 60,698,457 19.8242276 7.3248295 .002544529 394 155,236 61,162,984 19.8494332 7.3310369 .002538071 395 156,025 61,629,875 19.8746069 7.3372339 .002531646 396 156,816 62,099,136 19.8992487 7.3434205 .002525253 397 157,609 62,570,773 19.9248588 7.3495966 .002518892 398 158,404 63,044,792 19.9499373 7.3557624 .002512563 399 159,201 63,521,199 19.9749844 7.3619178 .002506266 400 160,000 64,000,000 20.0000000 7.3680630 .002500000 300 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N y* jft N* N* l N 401 160,801 64,481,201 20.0249844 7.3741979 .002493766 402 161,604 64,964,808 20.0499377 7.3803227 .002487562 403 162,409 65,450,827 20.0748599 7.3864373 .002481390 404 163,216 65,939,264 20.0997512 7.3925418 .002475248 405 164,025 66,430,125 20.1246118 7.3986363 .002469136 406 164,836 66,923,416 20.1494417 7.4047206 .002463054 407 165,649 67,419,143 20.1742410 7.4107950 .002457002 408 166,464 67,917,312 20.1990099 7.4168595 .002450980 409 167,281 68,417,929 20.2237484 7.4229142 .002444988 410 168,100 68,921,000 20.2484567 7.4289589 .002439024 411 168,921 69,426,531 20.2731349 7.4349938 .002433090 412 169,744 69,934,528 20.2977831 7.4410189 .002427184 413 170,569 70,444,997 20.3224014 7.4470342 .002421308 414 171,396 70,957,944 20.3469899 7.4530399 .002415459 415 172,225 71,473,375 20.3715488 7.4590359 .002409639 416 173,056 71,991,296 20.3960781 7.4650223 .002403846 417 173,889 72,511,713 20.4205779 7.4709991 .002398082 418 174,724 73,034,632 20.4450483 7.4769664 .002392344 419 175,561 73,560,059 20.4694895 7.4829242 .002386635 420 176,400 74,088,000 20.4939015 7.4888724 .002380952 421 177,241 74,618,461 20.5182845 7.4948113 .002375297 422 178,084 75,151,448 20.5426386 7.5007406 .002369668 423 178,929 75,686.967 20.5669638 7.5066607 .002364066 424 179,776 76,225,024 20.5912603 7.5125715 .002358491 425 180,625 76,765,625 20.6155281 7.5184730 .002352941 426 181,476 77,308,776 20.6397674 7.5243652 .002347418 427 182,329 77,854,483 20.6639783 7.5302482 .002341920 428 183,184 78,402,752 20.6881609 7.5361221 .002336449 429 184,041 78,953,589 20.7123152 7.5419867 .002331002 430 184,900 79,507,000 20.7364414 7.5478423 .002325581 431 185,761 80,062,991 20.7605395 7.5536888 .002320186 432 186,624 80,621,568 20.7846097 7.5595263 .002314815 433 187,489 81,182,737 20.8086520 7.5653548 .002309469 434 188,356 81,746,504 20.8326667 7.5711743 .002304147 435 189,225 82,312,875 20.8566536 7.5769849 .002298851 436 190,096 82,881,856 20.8806130 7.5827865 .002293578 437 190,969 83,453,453 20.9045450 7.5885793 .002288330 438 191,844 84,027,672 20.9284495 7.5943633 .002283105 439 192,721 84,604,519 20.9523268 7.6001385 .002277904 440 193,600 85,184,000 20.9761770 7.6059049 .002272727 441 194,481 85,766,121 21.0000000 7.6116626 .002267574 442 195,364 86,350,888 21.0237960 7.6174116 .002262443 443 196,249 86,938,307 21.0475652 7.6231519 .002257336 444 197,136 87,528,384 21.0713075 7.6288837 .002252252 445 198,025 88,121,125 21.0950231 7.6346067 .002247191 446 198,916 88,716,536 21.1187121 7.6403213 .002242152 447 199,809 89,314,623 21.1423745 7.6460272 .002237136 448 200,704 89,915,392 21.1660105 7.6517247 .002232143 449 201,601 90,518,849 21.1896201 7.6574138 .002227171 450 202,500 91,125,000 21.2132034 7.6630943 .002222222 MISCELLANEOUS TABLES AND DATA 301 TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N jft 2V3 N? N* l N 451 203,401 91,733,851 21.2367606 7.6687665 .002217295 452 204,304 92,345,408 21.2602916 7.6744303 .002212389 453 205,209 92,959,677 21.2837967 7.6800857 .002207506 454 206,116 93,576,664 21.3072758 7.6857328 .002202643 455 207,025 94,196,375 21.3307290 7.6913717 .002197802 456 207,936 94,818,816 21.3541565 7.6970023 .002192982 457 208,849 95,443,993 21.3775583 7.7026246 .002188184 458 209,764 96,071,912 21.4009346 7.7082388 .002183406 459 210,681 96,702,579 21.4242853 7.7138448 .002178649 460 211,600 97,336,000 21.4476106 7.7194426 .002173913 461 212,521 97,972,181 21.4709106 7.7250325 .002169197 462 213,444 98,611,128 21.4941853 7.7306141 .002164502 463 214,369 99,252,847 21.5174348 7.7361877 .002159827 464 215,296 99,897,344 21.5406592 7.7417532 .002155172 465 216,225 100,544,625 21.5638587 7.7473109 .002150538 466 217,156 101,194,696 21.5870331 7.7528606 .002145923 467 218,089 101,847,563 21.6101828 7.7584023 .002141328 468 219,024 102,503,232 21.6333077 7.7639361 .002136752 469 219,961 103,161,709 21.6564078 7.7694620 .002132196 470- 220,900 103,823,000 21.6794834 7.7749801 .002127660 471 221,841 104,487,111 21.7025344 7.7804904 .002123142 472 222,784 105,154,048 21.7255610 7.7859928 .002118644 473 223,729 105,823,817 21.7485632 7.7914875 .002114165 474 224,676 106,496,424 21.7715411 7.7969745 .002109705 475 225,625 107,171,875 21.7944947 7.8024538 .002105263 476 226,576 107,850,176 21.8174242 7.8079254 .002100840 477 227,529 108,531,333 21.8403297 7.8133892 .002096436 478 228,484 109,215,352 21.8632111 7.8188456 .002092050 479 229,441 109,902,239 21.8860686 7.8242942 .002087683 480 230,400 110,592,000 21.9089023 7.8297353 .002083333 481 231,361 111,284,641 21.9317122 7.8351688 .002079002 482 232,324 111,980,168 21.9544984 7.8405949 .002074689 483 233,289 112,678,587 21.9772610 7.8460134 .002070393 484 234,256 113,379,904 22.0000000 7.8514244 .002066116 485 235,225 114,084,125 22.0227155 7.8568281 .002061856 486 236,196 114,791,256 22.0454077 7.8622242 .002057613 487 237,169 115,501,303 22.0680765 7.8676130 .002053388 488 238,144 116,214,272 22.0907220 7.8729944 .002049180 489 239,121 116,930,169 22.1133444 7.8783684 .002044990 490 240,100 117,649,000 22.1359436 7.8837352 .002040816 491 241,081 118,370,771 22.1585198 7.8890946 .002036660 492 242,064 119,095,488 22.1810730 7.8944468 .002032520 493 243,049 119,823,157 22.2036033 7.8997917 .002028398 494 244,036 120,553,784 22.2261108 7.9051294 .002024291 495 245,025 121,287,375 22.2485955 7.9104599 .002020202 496 246,016 122,023,936 22.2710575 7.9157832 .002016129 497 247,009 122,763,473 22.2934968 7.9210994 .002012072 498 248,004 123,505,992 22.3159136 7.9264085 .002008032 499 249,001 124,251,499 22.3383079 7.9317104 .002004008 500 250,000 125,000,000 22.3606798 7.9370053 .002000000 302 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N #2 N 3 N* N* l N 501 251,001 125,751,501 22.3830293 7.9422931 .001996008 502 252,004 126,506,008 22.4053565 7.9475739 .001992032 503 253,009 127,263,527 22.4276615 7.9528477 .001988072 504 254,016 128,024,064 22.4499443 7.9581144 .001984127 505 255,025 128,787,625 22.4722051 7.9633743 .001980198 506 256,036 129,554,216 22.4944438 7.9686271 .001976285 507 257,049 130,323,843 22.5166605 7.9738731 .001972387 508 258,064 131,096,512 22.5388553 7.9791122 .001968504 509 259,081 131,872,229 22.5610283 7.9843444 .001964637 510 260,100 132,651,000 22.5831796 7.9895697 .001960784 511 261,121 133,432,831 22.6053091 7.9947883 .001956947 512 262,144 134,217,728 22.6274170 8.0000000 .001953125 513 263,169 135,005,697 22.6495033 8.0052049 .001949318 514 264,196 135,796,744 22.6715681 8.0104032 .001945525 515 265,225 136,590,875 22.6936114 8.0155946 .001941748 516 266,256 137,388,096 22.7156334 8.0207794 .001937984 517 267,289 138,188,413 22.7376340 8.0259574 .001934236 518 268,324 138,991,832 22.7596134 8.0311287 .001930502 519 269,361 139,798,359 22.7815715 8.0362935 .001926782 520 270,400 140,608,000 22.8035085 8.0414515 .001923077 521 271,441 141,420,761 22.8254244 8.0466030 .001919386 522 272,484 142,236,648 22.8473193 8.0517479 .001915709 523 273,529 143,055,667 22.8691933 8.0568862 .001912046 524 274,576 143,877,824 22.8910463 8.0620180 .001908397 525 275,625 144,703,125 22.9128785 8.0671432 .001904762 526 276,676 145,531,576 22.9346899 8.0722620 .001901141 527 277,729 146,363,183 22.9564806 8.0773743 .001897533 528 278,784 147,197,952 22.9782506 8.0824800 .001893939 529 279,841 148,035,889 23.0000000 8.0875794 .001890359 530 280,900 148,877,000 23.0217289 8.0926723 .001886792 531 281,961 149,721,291 23.0434372 8.0977589 .001883239 532 283,024 150,568,768 23.0651252 8.1028390 .001879699 533 284,089 151,419,437 23.0867928 8.1079128 .001876173 534 285,156 152,273,304 23.1084400 8.1129803 .001872659 535 286,225 153,130,375 23.1300670 8.1180414 .001869159 536 287,296 153,990,656 23.1516738 8.1230962 .001865672 537 288,369 154,854,153 23.1732605 8.1281447 .001862197 538 289,444 155,720,872 23.1948270 8.1331870 .001858736 539 290,521 156,590,819 23.2163735 8.1382230 .001855288 540 291,600 157,464,000 23.2379001 8.1432529 .001851852 541 292,681 158,340,421 23.2594067 8.1482765 .001848429 542 293,764 159,220,088 23.2808935 8.1532939 .001845018 543 294,849 160,103,007 23.3023604 8.1583051 .001841621 544 295,936 160,989,184 23.3238076 8.1633102 .001838235 545 297,025 161,878,625 23.3452351 8.1683092 .001834862 546 298,116 162,771,336 23.3666429 8.1733020 .001831502 547 299,209 163,667,323 23.3880311 8.1782888 .001828154 548 300,304 164,566,592 23.4093998 8.1832695 .001824818 549 301,401 165,469,149 23.4307490 8.1882441 .001821494 550 302,500 166,375,000 23 . 4520788 8.1932127 .001818182 MISCELLANEOUS TABLES AND DATA 303 TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N 2V2 N* #* N* l N 551 303,601 167,284,151 23.4733892 8.1981753 .001814882 552 304,704 168,196,608 23.4946802 8.2031319 .001811594 553 305,809 169,112,377 23.5159520 8.2080825 .001808318 554 306,916 170,031,464 23.5372046 8.2130271 .001805054 555 308,025 170,953,875 23.5584380 8.2179657 .001801802 556 309,136 171,879,616 23.5796522 8.2228985 .001798561 557 310,249 172,808,693 23.6008474 8.2278254 .001795332 558 311,364 173,741,112 23.6220236 8.2327463 .001792115 559 312,481 174,676,879 23.6431808 8.2376614 .001788909 560 313,600 175,616,000 23.6643191 8.2425706 .001785714 561 314,721 176,558,481 23.6854386 8.2474740 .001782531 562 315,844 177,504,328 23.7065392 8.2523715 .001779359 563 316,969 178,453,547 23.7276210 8.2572633 .001776199 564 318,096 179,406,144 23.7486842 8.2621492 .001773050 565 319,225 180,362,125 23.7697286 8.2670294 .001769912 566 320,356 181,321,496 23.7907545 8.2719039 .001766784 567 321,489 182,284,263 23.8117618 8.2767726 .001763668 568 322,624 183,250,432 23.8327506 8.2816355 .001760563 569 323,761 184,220,009 23.8537209 8.2864928 .001757469 570 324,900 185,193,000 23.8746728 8.2913444 .001754386 571 326,041 186,169,411 23.8956063 8.2961903 .001751313 572 327,184 187,149,248 23.9165215 8.3010304 .001748252 573 328,329 188,132,517 23.9374184 8.3058651 .001745201 574 329,476 189,119,224 23.9582971 8.3106941 .001742160 575 330,625 190,109,375 23.9791576 8.3155175 .001739130 576 331,776 191,102,976 24.0000000 8.3203353 .001736111 577 332,929 192,100,033 24.0208243 8.3251475 .001733102 578 334,084 193,100,552 24.0416306 8.3299542 .001730104 579 335,241 194,104,539 24.0624188 8.3347553 .001727116 580 336,400 195,112,000 24.0831891 8.3395509 .001724138 581 337,561 196,122,941 24.1039416 8.3443410 .001721170 582 338,724 197,137,368 24.1246762 8.3491256 .001718213 583 339,889 198,155,287 24.1453929 8.3539047 .001715266 584 341,056 199,176,704 24.1660919 8.3586784 .001712329 585 342,225 200,201,625 24.1867732 8.3634466 .001709402 586 343,396 201,230,056 24.2074369 8.3682095 .001706485 587 344,569 202,262,003 24.2280829 8.3729668 .001703578 588 345,744 203,297,472 24.2487113 8.3777188 .001700680 589 346,921 204,336,469 24.2693222 8.3824653 .001697793 590 348,100 205,379,000 24.2899156 8.3872065 .001694915 591 349,281 206,425,071 24.3104916 8.3919423 .001692047 592 350,464 207,474,688 24.3310501 8.3966729 .001689189 593 351,649 208,527,857 24.3515913 8.4013981 .001686341 594 352,836 209,584,584 24.3721152 8.4061180 .001683502 595 354,025 210,644,875 24.3926218 8.4108326 .001680672 596 355,216 211,708,736 24.4131112 8.4155419 .001677852 597 356,409 212,776,173 24.4335834 8.4202460 .001675042 598 357,604 213,847,192 24.4540385 8.4249448 .001672241 599 358,801 214,921,799 24.4744765 8.4296383 .001669449 600 360,000 216,000,000 24.4948974 8.4343267 .001666667 304 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N 2V 2 N* N* N* 1 tT~ 601 361,201 217,081,801 24.5153013 8.4390098 .001663894 602 362,404 218,167,208 24.5356883 8.4436877 .001661130 603 363,609 219,256,227 24.5560583 8.4483605 .001658375 604 364,816 220,348,864 24.5764115 8.4530281 .001-655629 605 366,025 221,445,125 24.5967478 8.4576906 .001652893 606 367,236 222,545,016 24.6170673 8.4623479 .001650165 607 368,449 223,648,543 24.6373700 8.4670001 .001647446 608 369,664 224,755,712 24.6576560 8.4716471 .001644737 609 370,881 225,866,529 24.6779254 8.4762892 .001642036 610 372,100 226,981,000 24.6981781 8.4809261 .001639344 611 373,321 228,099,131 24.7184142 8.4855579 .001636661 612 374,544 229,220,928 24.7386338 8.4901848 .001633987 613 375,769 230,346,397 24.7588368 8.4948065 .001631321 614 376,996 231,475,544 24.7790234 8.4994233 .001628664 615 378,225 232,608,375 24.7991935 8.5040350 .001626016 616 379,456 233,744,896 24.8193473 8.5086417 .001623377 617 380,689 234,885,113 24.8394847 8.5132435 .001620746 618 381,924 236,029,032 24.8596058 8.5178403 .001618123 619 383,161 237,176,659 24.8797106 8.5224321 .001615509 620 384,400 238,328,000 24.8997992 8.5270189 .001612903 621 385,641 239,483,061 24.9198716 8.5316009 .001610306 622 386,884 240,641,848 24.9399278 8.5361780 .001607717 623 388,129 241,804,367 24.9599679 8.5407501 .001605136 624 389,376 242,970,624 24.9799920 8.5453173 .001602564 625 390,625 244,140,625 25.0000000 8.5498797 .001600000 626 391,876 245,314,376 25.0199920 8.5544372 .001597444 627 393,129 246,491,883 25.0399681 8.5589899 .001594896 628 394,384 247,573,152 25.0599282 8.5635377 .001592357 629 395,641 248,858,189 25.0798724 8.5680807 .001589825 630 396,900 250,047,000 25.0998008 8.5726189 .001587302 631 398,161 251,239,591 25.1197134 8.5771523 .001584786 632 399,424 252,435,968 25.1396102 8.5816809 .001582278 633 400,689 253,636,137 25.1594913 8.5862047 .001579779 634 401,956 254,840,104 25.1793566 8.5907238 .001577287 635 403,225 256,047,875 25.1992063 8.5952380 .001574803 636 404,496 257,259,456 25.2190404 8.5997476 .001572327 637 405,769 258,474,853 25.2388589 8.6042525 .001569859 638 407,044 259,694,072 25.2586619 8.6087526 .001567398 639 408,321 260,917,119 25.2784493 8.6132480 .001564945 640 409,600 262,144,000 25.2982213 8.6177388 .001562500 641 410,881 263,374,721 25.3179778 8.6222248 .001560062 642 412,164 264,609,288 25.3377189 8.6267063 .001557632 643 413,449 265,847,707 25.3574447 8.6311830 .001555210 644 414,736 267,089,984 25.3771551 8.6356551 .001552795 645 416,025 268,336,125 25.3968502 8.6401226 .001550388 646 417,316 269,586,136 25.4165301 8.6445855 .001547988 647 418,609 270,840,023 25.4361947 8.6490437 .001545595 648 419,904 272,097,792 25.4558441 8.6534974 .001543210 649 421,201 273,359,449 25.4754784 8.6579465 .001540832 650 422,500 274,625,000 25.4950976 8.6623911 .001538462 MISCELLANEOUS TABLES AND DATA 305 TABLE 65 (Continued] SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N AT2 N* N* N* l AT 651 423,801 275,894,451 25.5147016 8.6668310 .001536098 652 425,104 277,167,808 25.5342907 8.6712665 .001533742 653 426,409 278,445,077 25.5538647 8.6756974 .001531394 654 427,716 279,726,264 25.5734237 8.6801237 .001529052 655 429,025 281,011,375 25.5929678 8.6845456 .001526718 656 430,336 282,300,416 25.6124969 8.6889630 .001524390 657 431,649 283,593,393 25.6320112 8.6933759 .001522070 658 432,964 284,890,312 25.6515107 8.6977843 .001519757 659 434,281 286,191,179 25.6709953 8.7021882 .001517451 660 435,600 287,496,000 25.6904652 8.7065877 .001515152 661 436,921 288,804,781 25.7099203 8.7109827 .001512859 662 438,244 290,117,528 25.7293607 8.7153734 .001510574 663 439,569 291,434,247 25.7487864 8.7197596 .001508296 664 440,896 292,754,944 25.7681975 8.7241414 .001506024 665 442,225 294,079,625 25.7875939 8.7285187 .001503759 666 443,556 295,408,296 25.8069758 8.7328918 .001501502 667 444,889 296,740,963 25.8263431 8.7372604 .001499250 668 446,224 298,077,632 25.8456960 8.7416246 .001497006 669 447,561 299,418,309 25.8650343 8.7459846 .001494768 670 448,900 300,763,000 25.8843582' 8.7503401 .001492537 671 450,241 302,111,711 25.9036677 8.7546913 .001490313 672 451,584 303,464,448 25.9229628 8.7590383 .001488095 673 452,929 304,821,217 25.9422435 8.7633809 .001485884 674 454,276 306,192,024 25.9615100 8.7677192 .001483680 675 455,625 307,546,875 25.9807621 8.7720532 .001481481 676 456,976 308,915,776 26.0000000 8.7763830 .001479290 677 458,329 310,288,733 26.0192237 8.7807084 .001477105 678 459,684 311,665,752 26.0384331 8.7850296 .001474926 679 461,041 313,046,839 26.0576284 8.7893466 .001472754 680 462,400 314,432,000 26.0768096 8.7936593 .001470588 681 463,761 315,821,241 26.0959767 8.7979679 .001468429 682 465,124 317,214,568 26.1151297 8.8022721 .001466276 683 466,489 318,611,987 26.1342687 8.8065722 - .001464129 684 467,856 320,013,504 26.1533937 8.8108681 .001461988 685 469,225 321,419,125 26.1725047 8.8151598 .001459854 686 470,596 322,828,856 26.1916017 8.8194474 .001457726 687 471,969 324,242,703 26.2106848 8.8237307 .001455604 688 473,344 325,660,672 26.2297541 8.8280099 .001453488 689 474,721 327,082,769 26.2488095 8.8322850 .001451379 690 476,100 328,509,000 26.2678511 8.8365559 .001449275 691 477,481 329,939,371 26.2868789 8.8408227 .001447178 692 478,864 331,373,888 26.3058929 8.8450854 .001445087 693 480,249 332,812,557 26.3248932 8.8493440 .001443001 694 481,636 334,255,384 26.3438797 8.8535985 .001440922 695 483,025 335,702,375 26.3628527 8.8578489 .001438849 696 484,416 337,153,536 26.3818119 8.8620952 .001436782 697 485,809 338,608,873 26.4007576 8.8663375 .001434720 698 487,204 340,068,392 26.4196896 8.8705757 .001432665 699 488,601 341,532,099 26.4386081 8.8748099 .001430615 700 490,000 343,000,000 26.4575131 8.8790400 .001428571 306 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N W* N 3 N* *i 1 " N 701 491,401 344,472,101 26.4764046 8.8832661 .001426534 702 492,804 345,948,408 26.4952826 8.8874882 .001424501 703 494,209 347,428,927 26.5141472 8.8917063 .001422475 704 495,616 348,913,664 26.5329983 8.8959204 .001420455 705 497,025 350,402,625 26.5518361 8.9001304 .001418440 706 498,436 351,895,816 26.5706605 8.9043366 .001416431 707 499,849 353,393,243 26.5894716 8.9085387 .001414427 708 501,264 354,894,912 26.6082694 8.9127369 .001412429 709 502,681 356,400,829 26.6270539 8.9169311 .001410437 710 504,100 357,911,000 26.6458252 8.9211214 .001408451 711 505,521 359,425,431 26.6645833 8.9253078 .001406470 712 506,944 360,944,128 26.6833281 8.9294902 .001404494 713 508,369 362,467,097 26.7020598 8.9336687 .001402525 714 509,796 363,994,344 26.7207784 8.9378433 .001400560 715 511,225 365,525,875 26.7394839 8.9420140 .001398601 716 512,656 367,061,696 26.7581763 8.9461809 .001396648 717 514,089 368,601,813 26.7768557 8.9503438 .001394700 718 515,524 370,146,232 26.7955220 8.9545029 .001392758 719 516,961 371,694,959 26.8141754 8.9586581 .001390821 720 518,400 373,248,000 26.8328157 8.9628095 .001388889 721 519,841 374,805,361 26.8514432 8.9669570 .001386963 722 521,284 376,367,048 26.8700577 8.9711007 .001385042 723 522,729 377,933,067 26.8886593 8.9752406 .001383126 724 524,176 379,503,424 26.9072481 8.9793766 .001381215 725 525,625 381,078,125 26.9258240 8.9835089 .001379310 726 527,076 382,657,176 26.9443872 8.9876373 .001377410 727 528,529 384,240,583 26.9629375 8.9917620 .001375516 728 529,984 385,828,352 26.9814751 8.9958829 .001373626 729 531,441 387,420,489 27.0000000 9.0000000 .001371742 730 532,900 389,017,000 27.0185122 9.0041134 .001369863 731 534,361 390,617,891 27.0370117 9.0082229 .001367989 732 535,824 392,223,168 27.0554985 9.0123288 .001366120 733 537,289 393,832,837 27.0739727 9.0164309 .001364256 734 538,756 395,446,904 27.0924344 9.0205293 .001362398 735 540,225 397,065,375 27.1108834 9.0246239 .001360544 736 541,696 398,688,256 27.1293199 9.0287149 .001358696 737 543,169 400,315,553 27.1477439 9.0328021 .001356852 738 544,644 401,947,272 27.1661554 9.0368857 .001355014 739 546,121 403,583,419 27.1845544 9.0409655 .001353180 740 547,600 405,224,000 27.2029410 9.0450417 .001351351 741 549,081 406,869,021 27.2213152 9.0491142 .001349528 742 550,564 408,518,488 27.2396769 9.0531831 .001347709 743 552,049 410,172,407 27.2580263 9.0572482 .001345895 744 553,536 411,830,784 27.2763634 9.0613098 .001344086 745 555,025 413,493,625 27.2946881 9.0653677 .001342282 746 556,516 415,160,936 27.3130006 9.0694220 .001340483 747 558,009 416,832,723 27.3313007 9.0734726 .001338688 748 559,504 418,508,992 27.3495887 9.0775197 .001336898 749 561,001 420,189,749 27.3678644 9.0815631 .001335113 750 562,500 421,875,000 27.3861279 9.0856030 .001333333 MISCELLANEOUS TABLES AND DATA 307 TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N y* N^ N* N* 1 N 751 564,001 423,564,751 27.4043792 9.0896392 .001331558 752 565,504 425,259,008 27.4226184 9.0936719 .001329787 753 567,009 426,957,777 27.4408455 9.0977010 .001328021 754 568,516 428,661,064 27.4590604 9.1017265 .001326260 755 570,025 430,368,875 27.4772633 9.1057485 .001324503 756 571,536 432,081,216 27.4954542 9.1097669 .001322751 757 573,049 433,798,093 27.5136330 9.1137818 .001321004 758 574,564 435,519,512 27.5317998 9.1177931 .001319261 759 576,081 437,245,479 27.5499546 9.1218010 .001317523 760 577,600 438,976,000 27.5680975 9.1258053 .001315789 761 579,121 440,711,081 27.5862284 9.1298061 .001314060 762 580,644 442,450,728 27.6043475 9.1338034 .001312336 763 582,169 444,194,947 27.6224546 9.1377971 .001310616 764 583,696 445,943,744 27.6405499 9.1417874 .001308901 765 585,225 447,697,125 27.6586334 9.1457742 .001307190 766 586,756 449,455,096 27.6767050 9.1497576 .001305483 767 588,289 451,217,663 27.6947648 9.1537375 .001303781 768 589,824 452,984,832 27.7128129 9.1577139 .001302083 769 591,361 454,756,609 27.7308492 9.1616869 .001300390 770 592,900 456,533,000 27.7488739 9.1656565 .001298701 771 594,441 458,314,011 27.7668868 9.1696225 .001297017 772 595,984 460,099,648 27.7848880 9.1735852 .001295337 773 597,529 461,889,917 27.8028775 9.1775445 .001293661 774 599,076 463,684,824 27.8208555 9.1815003 .001291990 775 600,625 465,484,375 27.8388218 9.1854527 .001290323 776 602,176 467,288,576 27.8567766 9.1894018 .001288660 777 603,729 469,097,433 27.8747197 9.1933474 .001287001 778 605,284 470,910,952 27.8926514 9.1972897 .001285347 779 606,841 472,729,139 27.9105715 9.2012286 .001283697 780 608,400 474,552,000 27.9284801 9.2051641 .001282051 781 609,961 476,379,541 27.9463772 9.2090962 .001280410 782 611,524 478,211,768 27.9642629 9.2130250 .001278772 783 613,089 480,048,687 27.9821372 9.2169505 .001277139 784 614,656 481,890,304 28.0000000 9.2208726 .001275510 785 616,225 483,736,625 28.0178515 9.2247914 .001273885 786 617,796 485,587,656 28.0356915 9.2287068 .001272265 787 619,369 487,443,403 28.0535203 9.2326189 .001270648 788 620,944 489,303,872 28.0713377 9.2365277 .001269036 789 622,521 491,169,069 28.0891438 9.2404333 .001267427 790 624,100 493.039,000 28.1069386 9.2443355 .00126-5823 791 625,681 494,913,671 28.1247222 9.2482344 .001264223 792 627,264 496,793,088 28.1424946 9.2521300 .001262626 793 628,849 498,677,257 28.1602557 9.2560224 .001261034 794 630,436 500,566,184 28.1780056 9.2599114 .001259446 795 632,025 502,459,875 28.1957444 9.2637973 .001257862 796 633,616 504,358,336 28.2134720 9.2676798 .001256281 797 635,209 506,261,573 28.2311884 9.2715592 .001254705 798 636,804 508,169,592 28.2488938 9.2754352 .001253133 799 638,401 510,082,399 28.2665881 9.2793081 .001251564 800 640,000 512,000,000 28.2842712 9.2831777 .001250000 308 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N 7\T2 #3 N* N* 1 is 801 641,601 513,922,401 28.3019434 9.2870440 .001248439 802 643,204 515,849,608 28.3196045 9.2909072 .001246883 803 644,809 517,781,627 28.3372546 9.2947671 .001245330 804 646,416 519,718,464 28.3548938 9.2986239 .001243781 805 648,025 521,660,125 28.3725219 9.3024775 .001242236 806 649,636 523,606,616 28.3901391 9.3063278 .001240695 807 651,249 525,557,943 28.4077454 9.3101750 .001239157 808 652,864 527,514,112 28.4253408 9.3140190 .001237624 809 654,481 529,475,129 28.4429253 9.3178599 .001236094 810 656,100 531,441,000 28.4604989 9.3216975 .001234568 811 657,721 533,411,731 28.4780617 9.3255320 .001233046 812 659,344 535,387,328 28.4956137 9.3293634 .001231527 813 660,969 537,367,797 28.5131549 9.3331916 .001230012 814 662,596 539,353,144 28.5306852 9.3370167 .001228501 815 664,225 541,343,375 28.5482048 9.3408386 .001226994 816 665,856 543,338,496 28.5657137 9.3446575 .001225490 817 667,489 545,338,513 28.5832119 9.3484731 .001223990 818 669,124 547,343,432 28.6006993 9.3522857 .001222494 819 670,761 549,353,259 28.6181760 9.3560952 .001221001 820 672,400 551,368,000 28.6356421 9.3599016 .001219512 821 674,041 553,387,661 28.6530976 9.3637049 .001218027 822 675,684 555,412,248 28.6705424 9.3675051 .001216545 823 677,329 557,441,767 28.6879766 9.3713022 .001215067 824 678,976 559,476,224 28.7054002 9.3750963 .001213592 825 680,625 561,515,625 28.7228132 9.3788873 .001212121 826 682,276 563,559,976 28.7402157 9.3826752 .001210654 827 683,929 565,609,283 28.7576077 9.3864600 .001209190 828 685,584 567,663,552 28.7749891 9.3902419 .001207729 829 687,241 569,722,789 28.7923601 9.3940206 .001206273 830 688,900 571,787,000 28.8097206 9.3977964 .001204819 831 690,561 573,856,191 28.8270706 9.4015691 .001203369 832 692,224 575,930,368 28.8444102 9.4053387 .001201923 833 693,889 578,009,537 28.8617394 9.4091054 .001200480 834 695,556 580,093,704 28.8790582 9.4128690 .001199041 835 697,225 582,182,875 28.8963666 9.4166297 .001197605 836 698,896 584,277,056 28.9136646 9.4203873 .001196172 837 700,569 586,376,253 28.9309523 9.4241420 .001194743 838 702,244 588,480,472 28.9482297 9.4278936 .001193317 839 703,921 590,589,719 28.9654967 9.4316423 .001191895 840 705,600 592,704,000 28.9827535 9.4353880 .001190476 841 707,281 594,823,321 29.0000000 9.4391307 .001189061 842 708,964 596,947,688 29.0172363 9.4428704 .001187648 843 710,649 599,077,107 29.0344623 9.4466072 .001186240 844 712,336 601,211,584 29.0516781 9.4503410 .001184834 845 714,025 603,351,125 29.0688837 9.4540719 .001183432 846 715,716 605,495,736 29.0860791 9.4577999 .001182033 847 717,409 607,645,423 29.1032644 9.4615249 .001180638 848 719,104 609,800,192 29.1204396 9.4652470 .001179245 849 720,801 611,960,049 29.1376046 9.4689661 .001177856 850 722,500 614,125,000 29.1547595 9.4726824 .001176471 MISCELLANEOUS TABLES AND DATA 309 TABLE 65 (Continued} SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N N* ^3 N* N* 1 N 851 724,201 616,295,051 29.1719043 9.4763957 .001175088 852 725,904 618,470,208 29.1890390 9.4801061 .001173709 853 727,609 620,650,477 29.2061637 9.4838136 .001172333 854 729,316 622,835,864 29.2232784 9.4875182 .001170960 855 731,025 625,026,375 29.2403830 9.4912200 .001169591 856 732,736 627,222,016 29.2574777 9.4949188 .001168224 857 734,449 629,422,793 29.2745623 9.4986147 .001166861 858 736,164 631,628,712 29.2916370 9.5023078 .001165501 859 737,881 633,839,779 29.3087018 9.5059980 .001164144 860 739,600 636,056,000 29.3257566 9.5096854 .001162791 861 741,321 638,277,381 29.3428015 9.5133699 .001161440 862 743,044 640,503,928 29.3598365 9.5170515 .001160093 863 744,769 642,735,647 29.3768616 9.5207303 .001158749 864 746,496 644,972,544 29.3938769 9.5244063 .001157407 865 748,225 647,214,625 29.4108823 9.5280794 .001156069 866 749,956 649,461,896 29.4278779 9.5317497 .001154734 867 751,689 651,714,363 29.4448637 9.5354172 .001153403 868 753,424 653,972,032 29.4618397 9.5390818 .001152074 869 755,161 656,234,909 29.4788059 9.5427437 .001150748 870 756,900 658,503,000 29.4957624 9.5464027 .001149425 871 758,641 660,776,311 29.5127091 9.5500589 .001148106 872 760,384 663,054,848 29.5296461 9.5537123 .001146789 873 762,129 665,338,617 29.5465734 9.5573630 .001145475 874 763,876 667,627,624 29.5634910 9.5610108 .001144165 875 765,625 669,921,875 29.5803989 9.5646559 .001142857 876 767,376 672,221,376 29.5972972 9.5682982 .001141553 877 769,129 674,526,133 29.6141858 9.5719377 .001140251 878 770,884 676,836,152 29.6310648 9.5755745 .001138952 879 772,641 679,151,439 29.6479342 9.5792085 .001137656 880 774,400 681,472,000 29.6647939 9.5828397 .001136364 881 776,161 683,797,841 29.6816442 9.5864682 .001135074 882 777,924 686,128,968 29.6984848 9.5900939 .001133787 883 779,689 688,465,387 29.7153159 9.5937169 .001132503 884 781,456 690,807,104 29.7321375 9.5973373 .001131222 885 783,225 693,154,125 29.7489496 9.6009548 .001129944 886 784,996 695,506,456 29.7657521 9.6045696 .001128668 887 786,769 697,864,103 29.7825452 9.6081817 .001127396 888 788,544 700,227,072 29.7993289 9.6117911 .001126126 889 790,321 702,595,369 29.8161030 9.6153977 .001124859 890 792,100 704,969,000 29.8328678 9.6190017 .001123596 891 793,881 707,347,971 29.8496231 9.6226030 .001122334 892 795,664 709,732,288 29.8663690 9.6262016 .001121076 893 797,449 712,121,957 29.8831056 9.6297975 .001119821 894 799,236 714,516,984 29.8998328 9.6333907 .001118568 895 801,025 716,917,375 29.9165506 9.6369812 .001117318 896 802,816 719,323,136 29.9332591 9.6405690 .001116071 897 804,609 721,734,273 29.9499583 9.6441542 .001114827 898 806,404 724,150,792 29.9666481 9.6477367 .001113586 899 808,201 726,572,699 29.9833287 9.6513166 .001112347 900 810,000 729,000,000 30.0000000 9.6548938 .001111111 310 WORKING DATA FOR IRRIGATION ENGINEERS TABLE 65 (Continued) SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N 7V2 N* N* . * 1 4- 901 811,801 731,432,701 30.0166620 9.6584684 .001109878 902 813,604 733,870,808 30.0333148 9.6620403 .001108647 903 815,409 736,314,327 30.0499584 9.6656096 .001107420 904 817,216 738,763,264 30.0665928 9.6691762 .001106195 905 819,025 741,217,625 30.0832179 9.6727403 .001104972 906 820,836 743,677,416 30.0998339 9.6763017 .001103753 907 822,649 746,142,643 30.1164407 9.6798604 .001102536 908 824,464 748,613,312 30.1330383 9.6834166 .001101322 909 826,281 751,089,429 30.1496269 9.6869701 .001100110 910 828,100 753,571,000 30.1662063 9.6905211 .001098901 911 829,921 756,058,031 30.1827765 9.6940694 .001097695 912 831,744 758,550,528 30.1993377 9.6976151 .001096491 913 833,569 761,048,497 30.2158899 9.7011583 .001095290 914 835,396 763,551,944 30.2324329 9.7046989 .001094092 915 837,225 766,060,875 30.2489669 9.7082369 .001092896 916 839,056 768,575,296 30.2654919 9.7117723 .001091703 917 840,889 771,095,213 30.2820079 9.7153051 .001090513 918 842,724 773,620,632 30.2985148 9.7188354 .001089325 919 844,561 776,151,559 30.3150128 9.7223631 .001088139 920 846,400 778,688,000 30.3315018 9.7258883 .001086957 921 848,241 781,229,961 30.3479818 9.7294109 .001085776 922 850,084 783,777,448 30.3644529 9.7329309 .001084599 923 851,929 786,330,467 30.3809151 9.7364484 .001083424 924 853,776 788,889,024 30.3973683 9.7399634 .001082251 925 855,625 791,453,125 30.4138127 9.7434758 .001081081 926 857,476 794,022,776 30.4302481 9.7469857 .001079914 927 859,329 796,597,983 30.4466747 9.7504930 .001078749 928 861,184 799,178,752 30.4630924 9.7539979 .001077586 929 863,041 801,765,089 30.4795013 9.7575002 .001076426 930 864,900 804,357,000 30.4959014 9.7610001 .001075269 931 866,761 806,954,491 30.5122926 9.7644974 .001074114 932 868,624 809,557,568 30.5286750 9.7679922 .001072961 933 870,489 812,166,237 30.5450487 9.7714845 .001071811 934 872,356 814,780,504 30.5614136 9.7749743 .001070664 935 874,225 817,400,375 30.5777697 9.7784616 .001069519 936 876,096 820,025,856 30.5941171 9.7819466 .001068376 937 877,969 822,656,953 30.6104557 9.7854288 .001067236 938 879,844 825,293,672 30.6267857 9.7889087 .001066098 939 881,721 827,936,019 30.6431069 9.7923861 .001064963 940 883,600 830,584,000 30.6594194 9.7958611 .001063830 941 855,481 833,237,621 30.6757233 9.7993336 .001062699 942 887,364 835,896,888 30.6920185 9.8028036 .001061571 943 889,249 838,561,807 30.7083051 9.8062711 .001060445 944 891,136 841,232,384 30.7245830 9.8097362 .001059322 945 893,025 843,908,625 30.7408523 9.8131989 .001058201 946 894,916 846,590,536 30.7571130 9.8166591 .001057082 947 896,809 849,278,123 30.7733651 9.8201169 .001055966 948 898,704 851,971,392 30.7896086 9.8235723 .001054852 949 900,601 854,670,349 30.8058436 9.8270252 .001053741 950 902,500 857,375,000 30.8220700 9.8304757 .001052632 MISCELLANEOUS TABLES AND DATA 311 TABLE 65 (Concluded] SQUARES, CUBES, SQUARE ROOTS, CUBE ROOTS, RECIPROCALS N #2 N* AT* ^ l If 951 904,401 860,085,351 30.8382879 9.8339238 .001051525 952 906,304 862,801,408 30.8544972 9.8373695 .001050420 953 908,209 865,523,177 30.8706981 9.8408127 .001049318 954 910,116 868,250,664 30.8868904 9.8442536 .001048218 955 912,025 870,983,875 30.9030743 9.8476920 .001047120 956 913,936 873,722,816 30.9192497 9.8511280 .001046025 957 915,849 876,467,493 30.9354166 9.8545617 .001044932 958 917,764 879,217,912 30.9515751 9.8579929 .001043841 959 919,681 881,974,079 30.9677251 9.8614218 .001042753 960 921,600 884,736,000 30.9838668 9.8648483 .001041667 961 923,521 887,503,681 31.0000000 9.8682724 .001040583 962 925,444 890,277,128 31.0161248 9.8716941 .001039501 963 927,369 893,056,347 31.0322413 9.8751135 .001038422 964 929,296 895,841,344 31.0483494 9.8785305 .001037344 965 931,225 898,632,125 31.0644491 9.8819451 .001036269 966 933,156 901,428,696 31.0805405 9.8853574 .001035197 967 935,089 904,231,063 31.0966236 9.8887673 .001034126 968 937,024 907,039,232 31.1126984 9.8921749 .001033058 969 938,961 909,853,209 31.1287648 9.8955801 .001031992 970 940,900 912,673,000 31.1448230 9.8989830 .001030928 971 942,841 915,498,611 31.1608729 9.9023835 .001029866 972 944,784 918,330,048 31 . 1769145 9.9057817 .001028807 973 946,729 921,167,317 31.1929479 9.9091776 .001027749 974 948,676 924,010,424 31.2089731 9.9125712 .001026694 975 950,625 926,859,375 31.2249900 9.9159624 .001025641 976 952,576 929,714,176 31.2409987 9.9193513 .001024590 977 954,529 932,574,833 31.2569992 9.9227379 .001023541 978 956,484 935,441,352 31.2729915 9.9261222 .001022495 979 958,441 938,313,739 31.2889757 9.9295042 .001021450 980 960,400 941,192,000 31.3049517 9.9328839 .001020408 981 962,361 944,076,141 31.3209195 9.9362613 .001019368 982 964,324 946,966,168 31.3368792 9.9396363 .001018330 983 966,289 949,862,087 31.3528308 9.9430092 .001017294 984 968,256 952,763,904 31.3687743 9.9463797 .001016260 985 970,225 955,671,625 31.3847097 9.9497479 .001015228 986 972,196 958,585,256 31.4006369 9.9531138 .001014199 987 974,169 961,504,803 31.4165561 9.9564775 .001013171 988 976,144 964,430,272 31.4324673 9.9598389 .001012146 989 978,121 967,361,669 31.4483704 9.9631981 .001011122 990 980,100 970,299,000 31.4642654 9.9665549 .001010101 991 982,081 973,242,271 31.4801525 9.9699095 .001009082 992 984,064 976,191,488 31.4960315 9.9732619 .001008065 993 986,049 979,146,657 31.5119025 9.9766120 .001007049 994 988,036 982,107,784 31.5277655 9.9799599 .001006036 995 990,025 985,074,875 31.5436206 9.9833055 .001005025 996 992,016 988,047,936 31.5594677 9.9866488 .001004016 997 994,009 991,026,973 31.5753068 9.9899900 .001003009 998 996,004 994,011,992 31.5911380 9.9933289 .001002004 999 998,001 997,002,999 31.6069613 9.9966656 .001001001 1000 1,000,000 1,000,000,000 31.6227766 10.0000000 .001000000 CHAPTER VII SPECIFICATIONS CHAPTER VII SPECIFICATIONS SPECIFICATIONS are a definite, particularized, and complete statement of the legal and engineering or technical requirements to be met in performing the work covered thereby. The importance of having a clear, concise, and definite set of specifications is frequently minimized, especially by engineers who have not had extensive experience in carrying out important works. Even engineers of large experience sometimes minimize this important requirement because they may have been for- tunate enough to carry through their work with less extensive and detail specifications, but it is probably safe to say that the importance of the latter sooner or later becomes evident. In general, specifications, except as to the legal requirements, should not be intended as a rigid set of rules to be scrupulously followed according to the letter, but as a guide to indicate to the contractor the quantity and quality of the work that the engineer will require him to do. The language must, therefore, be definite and clear, so as to be susceptible of only one inter- pretation. This protects both the contractor and the engineer, for, if the contractor bids too low because of a misinterpreta- tion of the engineer's requirements, he either loses money or the engineer must allow him additional compensation above the contract price. In either case, friction and bad feeling may ensue with resulting detriment to the work. The specifications of the United States Reclamation Service, which have been gradually evolved during a period of twelve years' construction of important irrigation works, may well be taken as a model by irrigation engineers. Some of these specifications that have become more or less standardized are printed in the following pages, with some modifications. The specifications given are not intended to be used without modification. There might be cases where they could be so used, but the main intention is to state the important points to 315 316 WORKING DATA FOR IRRIGATION ENGINEERS be covered rather than to state how they should be covered. With this information at hand it becomes a comparatively simple matter to draw up specifications adaptable to the peculiar local conditions involved, whereas, without such information, impor- tant clauses are very liable to be overlooked. Subdivisions of Specifications. A complete set of specifica- tions consists of the following: 1. The advertisement. 2. Notice to bidders. 3. The proposal. 4. Guarantee of bond. 5. Statement of work to be performed. 6. General conditions, legal requirements, etc. 7. Detailed specifications. 8. Drawings. THE ADVERTISEMENT For public work (Federal, State, Municipal, etc.), advertising is usually required by law. Private work may or may not be advertised publicly. In any case, the value of wide publicity is evident, as by this means the greatest competition is obtained. The advertisement should state clearly, concisely, and briefly when and where bids will be received, what the work is that is to be performed, the approximate quantities involved, where the work is located, and from whom particulars may be obtained. A form commonly used by the Reclamation Service is as follows: " Washington, D. C., , 19. . " Sealed proposals will be received at the office of the United States Reclamation Service at until 2 o'clock P.M., , 19. . . , for canal excavation and structures, involv- ing about cubic yards of excavation, cubic yards of reinforced concrete, etc., etc. The work is situated " For particulars, address the United States Reclamation Service, "(s g d.) .',.;.;: " SPECIFICATIONS 317 NOTICE TO BIDDERS This should be placed in a conspicuous place at the beginning of the specifications. The purpose of this " notice " is to call particularly to the attention of bidders such requirements as they should take special cognizance of before preparing their bids, such as the requirement for certified check and guarantee of bond, whether bids may be submitted on portions of the work only, and any other instructions that the work in question may seem to make desirable. A clear and concise set of instructions under the " Notice to Bidders " will frequently simplify the comparison of the bids after they have been opened and will avoid misunderstandings. THE PROPOSAL This is the contractor's bid, and should state what he pro- poses to do. The following form is used by the Reclamation Service: " ,19... " To " SIR: " Pursuant to the foregoing advertisement, the undersigned bidder proposes to do all the work and to furnish all the material as provided by the attached specifications, and binds himself on the acceptance of this proposal to execute a contract with nec- essary bond, of which this proposal and the said advertisement and specifications shall be a part, for performing and completing said work within the time required by the specifications and at the prices named in the specifications and in the schedules hereto annexed. " The bidder furthermore agrees that, in case of his default in executing a contract with necessary bond, the proceeds of the check accompanying this proposal shall be and remain the property of the United States. " Signature " (Corporate Seal) Address . . 318 WORKING DATA FOR IRRIGATION ENGINEERS " Names of individual members of firm or names and titles of all officers of corporation " Corporation organized under the laws of the State of , GUARANTEE OF BOND This is a simple statement signed by a surety company or by individual bondsmen guaranteeing that bond to insure the faithful performance of the work will be furnished for the bidder if contract is awarded to him. The statement may be as follows: " We agree to furnish bond for this bidder, as required by these specifications, in case contract is awarded to him on the basis of this proposal. Signatures and addresses of guarantors of bond WORK TO BE PERFORMED Under this head should be stated the work that is to be done, and appropriate blanks should be provided in which the bidder can fill in his prices. The work may be listed by items with provision for a lump sum bid for each item, or it may be in the form of schedules of quantities in which the quantities of each class of work are given and blanks provided for the bidder to fill in his unit prices and total amounts. Some kinds of work, such as machinery, buildings, bridges, etc., are usually bid on by the lump sum for the entire job. Earth- work, concrete struc- tures, etc., are not readily adapted to lump-sum bidding on account of uncertainties existing in the quantities and clas- sifications. In such cases, it is more satisfactory to both con- SPECIFICATIONS 319 tractor and engineer to have an estimate of quantities and unit prices for each item. The work to be performed on large jobs may be divided into a number of schedules allowing the work to be divided among a number of contractors if such procedure should seem to be eco- nomical or desirable. On large jobs this allows small, as well as large, contractors to bid and, therefore, results hi keener com- petition. GENERAL CONDITIONS The following general clauses are used by the Reclamation Service in all specifications. (Paragraphs 20 to 28 inclusive are not used when they are not required, such as in specifications for furnishing machinery, cement, and other materials.) Special clauses applying exclusively to Government work and reference to Government bureaus and officers have been omitted. Some clauses and words unnecessary for private contracts have been modified or eliminated. Particular attention is called to the fact that these general clauses must be used with discretion, as they cover most of the legal requirements by which the con- tractor is to be bound, and it is desirable, especially on im- portant works, to have them reviewed by a legal expert. i. Form of Proposal and Signature. The proposal shall be made on the form provided therefor and shall be enclosed in a sealed envelope marked and addressed as required in the notice to bidders. The bidder shall state in words and in figures the unit prices or the specific sums, as the case may be, for which he proposes to supply the material or machinery and perform the work required by these specifications. If the proposal is made by an individual it shall be signed with his full name, and his address shall be given; if it is made by a firm, it shall be signed with the copartnership name by a member of the firm, and the name and full address of each member shall be given; and if it is made by a corporation it shall be signed by an officer with the corporate name attested by the corporate seal, and the names and titles of all officers of the corporation shall be given. No telegraphic proposal or telegraphic modification of a proposal will be considered. 320 WORKING DATA FOR IRRIGATION ENGINEERS 2. Proposal. Blank spaces in the proposal should be prop- erly filled. The phraseology of the proposal should not be changed, and no additions should be made to the items men- tioned therein. Unauthorized conditions, limitations, or provisos attached to a proposal will render it informal and may cause its rejection. Alterations by erasure or interlineation must be explained or noted in the proposal over the signature of the bidder. If the unit price and the total amount named by a bidder for any item do not agree, the unit price alone will be considered as representing the bidder's intention. A bidder may withdraw his proposal before the expiration of the time during which proposals may be submitted, without prejudice to himself, by submitting a written request for its withdrawal to the officer who holds it. No proposals received after said time will be considered. Bidders are invited to be present at the opening of proposals. The right is reserved to reject any or all proposals, to accept one part of a proposal and reject the other, and to waive technical defects, as the interests of may require. 3. Certified Check. Each bidder shall submit with his pro- posal a certified check for the sum stated in the notice to bidders, drawn to the order of If the bidder to whom an award is made fails or refuses to execute the required contract and bond within the time specified in paragraph 4, the proceeds of his check shall become the property of The proceeds of the check of the successful bidder will be returned after the execution of his contract and the approval of his bond on behalf of ; and the proceeds of the checks of the other bidders will be returned at the expiration of .... days from the date of opening proposals, or sooner if contract is exe- cuted prior to that time. 4. The Contract. The bidder to whom an award is made shall execute a written contract with and if bond is required furnish good and approved bond within .... days after receiving the forms of contract and bond for execution. If the bidder to whom an award is made fails to enter into a contract as herein provided, the award will be annulled, and an award may be made to the bidder whose proposal is next most SPECIFICATIONS 321 acceptable in the opinion of ; and such bidder shall fulfill every stipulation embraced herein as if he were the party to whom the first award was made. The advertisement, notice to bidders, proposal, general conditions, and detail specifi- cations and drawings will be incorporated in the contract. A corporation to which an award is made may be required, before the contract is finally executed, to furnish certificate of its cor- porate existence and evidence that the officer signing the con- tract for the corporation is duly authorized to do so. 5. Contractor's Bond. The contractor shall furnish bond in an amount not less than per cent of the estimated aggregate payments to be made under the contract, conditioned upon the faithful performance by the contractor of all covenants and stip- ulations in the contract. If during the continuance of the con- tract any of the sureties die, or, in the opinion of , are or become irresponsible, the may require additional sufficient sureties, which the contractor shall furnish to the satisfaction of that officer within .... days after notice. 6. Engineer. The word " engineer " used in these specifi- cations or in the contract means He will be represented by assistants and inspectors authorized to act for him. On all questions concerning the acceptability of material or machinery, the classification of material, the execution of the work, conflicting interests of contractors performing related work, and the determination of costs, the decision of the engineer shall be final. 7. Contractor. The word " contractor " used in these specifications or in the contract means the person, firm, or cor- poration with whom the contract is made by The contractor shall at all times be represented on the works in person or by a foreman or duly designated agent. Instructions and information given by the engineer to the contractor's fore- man or agent on the work shall be considered as having been given to the contractor. When two or more contractors are en- gaged on installation or construction work in the same vicinity the engineer shall be authorized to direct the manner in which each shall conduct his work so far as it affects other contractors. 322 WORKING DATA FOR IRRIGATION ENGINEERS 8. Materials and Workmanship. All materials must be of the specified quality and equal to approved samples, if samples have been submitted. All work shall be done and completed in a thorough, workmanlike manner, notwithstanding any omission from these specifications or the drawings. All materials furnished and all work done must be satisfactory to the engineer. Work not in accordance with these specifications, in the opinion of the engineer, shall be made to conform thereto. Unsatisfactory material will be rejected, and, if so ordered by the engineer, shall, at the contractor's expense, be immediately removed from the vicinity of the work. 9. Delays. The contractor shall receive no compensation for delays or hindrances to the work except when, in the judg- ment of the engineer, direct and unavoidable extra cost to the contractor is caused by the failure of the to pro- vide necessary information, material, right of way, or site for installation. When such extra compensation is claimed a written statement thereof shall be presented by the contractor not later than .... days after the close of the month during which extra cost is claimed to have been incurred. Such claim, if found correct, will be approved and the decision of the engineer, whether extra cost has been incurred and the amount thereof, shall be final. If delays are caused by specific orders to stop work given by the engineer, or by the performance of extra work, or by un- foreseen causes beyond the control of the contractor, or by the failure of to provide material or necessary in- structions for carrying on the work or to provide the necessary right of way or site for installation, then such delay will entitle the contractor to an equivalent extension of time. 10. Changes. The engineer may, without notice to the sure- ties on the contractor's bond, make such changes in the designs of materials or machinery or plans for installation or construction or in the quantities or character of the work or material required as he may deem advisable. These changes in plans for installa- tion or construction may also include modifications of shapes and dimensions of canals, dams, and other structures, and the shifting of locations to suit conditions disclosed as work pro- gresses. If such changes result in an increase or decrease of cost SPECIFICATIONS 323 to the contractor, the engineer will make such additions or de- ductions on account thereof as he may deem reasonable and proper and his action thereon shall be final. Extra work or material shall be charged for as hereinafter provided. 11. Extra Work or Material. In connection with the work covered by this contract, the engineer may order work or material not covered by the specifications. Such work or material will be classed as extra work and will be ordered in writing. No extra work will be paid for unless ordered in writing. Extra work shall be charged for at actual necessary cost, as determined by the engineer, plus .... per cent for profit, superintendence, and general expenses. The actual necessary cost will include all expenditures for materials, labor, and supplies furnished by the contractor, and a reasonable allowance for the use of shop equipment where required, but will not include any allowance for office expenses, general superintendence, or other general expenses. At the end of each month the contractor shall present in writing his claims for extra work and material and, when requested by the engineer, shall furnish itemized statements of the cost and shall permit examination of accounts, bills, and vouchers relating thereto. 12. Inspection. All materials furnished and work done under this contract will be subject to rigid inspection. The contractor shall furnish complete facilities, including the neces- sary labor for the inspection of all material and workmanship. The engineer shall have at all times access to all parts of the shop where such material under his inspection is being manufac- tured. Material that does not conform to the specifications, accepted through oversight or otherwise, may be rejected at any stage of the work. Whenever the contractor on installation or construction is permitted or directed to do night work or to vary the period during which work is carried on each day, he shall give the engineer due notice, so that inspection may be pro- vided for. 13. Errors and Omissions. The contractor will not be al- lowed to take advantage of any error or omission in these speci- fications. Suitable instructions will be given when such error or omission is discovered. 324 WORKING DATA FOR IRRIGATION ENGINEERS 14. Experience. Bidders, if required, shall present satisfac- tory evidence that they have been regularly engaged in furnishing material and machinery and constructing such work as they pro- pose to execute, and that they are fully prepared with necessary capital, machinery, and material to begin the work promptly and to conduct it as required by these specifications. 15. Specifications and Drawings. The contractor shall keep on the work a copy of the specifications and drawings and shall at all times give the engineer access thereto. Any drawings or plans listed in the detail specifications shall be regarded as part thereof and of the contract. Anything mentioned in these speci- fications and not shown in the drawings or shown in the drawings and not mentioned in these specifications shall be done as though shown or mentioned in both. The engineer will furnish from time to time such detail drawings, plans, profiles, and information as he may consider necessary for the contractor's guidance. 16. Local Conditions. Bidders shall satisfy themselves as to local conditions affecting the work, and no information derived from the maps, plans, specifications, profiles, or drawings, or from the engineer or his assistants, will relieve the contractor from any risk or from fulfilling all of the terms of his contract. The accuracy of the interpretation of the facts disclosed by bor- ings or other preliminary investigations is not guaranteed. Each bidder or his representative should visit the site of the work and familiarize himself with local conditions; failure to do so when intelligent preparation of bid depends on a knowledge of local conditions may be considered sufficient cause for rejecting a proposal. 17. Data to be Furnished by the Contractor. The contractor shall furnish the engineer reasonable facilities for obtaining such information as he may desire respecting the character of the materials and the progress and manner of the work, including all information necessary to determine its cost, such as the number of men employed, their pay, the time during which they worked on the various classes of construction, etc. 1 8. Damages. The contractor will be held responsible for and required to make good, at his own expense, all damage to SPECIFICATIONS 325 person or property caused by carelessness or neglect on the part of the contractor, his agent or employees. 19. Character of Workmen. The contractor shall not allow his agents or employees to trespass on premises or lands in the vicinity of the work. None but skilled foremen and workmen shall be employed on work requiring special qualifications, and when required by the engineer, the contractor shall discharge any person who commits trespass or is in the opinion of the engineer disorderly, dangerous, insubordinate, incompetent, or otherwise objectionable. 20. Staking Out Work. The work to be done will be staked out for the contractor, who shall provide such material and give such assistance as may be required by the engineer. 21. Methods and Appliances. The methods and appliances adopted by the contractor shall be such as will, in the opinion of the engineer, secure a satisfactory quality of work and will enable the contractor to complete the work in the time agreed upon. If at any time the methods and appliances appear inad- equate, the engineer may order the contractor to improve their character or efficiency, and the contractor shall conform to such order; but failure of the engineer to order such improvement of methods or efficiency will not relieve the contractor from his obligation to perform satisfactory work and to finish it in the time agreed upon. 22. Climatic Conditions. The engineer may order the con- tractor to suspend any work that may be damaged by climatic conditions. When delay is caused by an order to suspend work given on account of climatic conditions that could have been reasonably foreseen the contractor will not be entitled to any extension of time on account of such order. 23. Quantities and Unit Prices. The quantities noted in the schedule or proposal are approximations for comparing bids, and no claim shall be made against the United States for excess or deficiency therein, absolute or relative. Payment at the prices agreed upon will be in full for the completed work and will cover materials, supplies, labor, tools, machinery, and all other expenditures incident to satisfactory compliance with the contract. 326 WORKING DATA FOR IRRIGATION ENGINEERS 24. Removal and Rebuilding of Defective Work. The con- tractor shall remove and rebuild at his own expense any part of the work that has been improperly executed, even though it has been included in the monthly estimates. If he refuses or neglects to replace such defective work, it may be replaced by at the contractor's expense. 25. Protection of Work and Cleaning Up. The contractor shall be responsible for any material furnished him and for the care of all work until its completion and final acceptance, and he shall at his own expense replace damaged or lost material and repair damaged parts of the work, or the same may be done at his expense by He shall take all risks from floods and casualties and shall make no charge for detention from such causes. He may, however, be allowed a reasonable extension of time on account of such detention, subject to the conditions hereinbefore specified. The contractor shall remove from the vicinity of the completed work all plant, buildings, rubbish, unused material, concrete forms, etc., belonging to him or used under his direction during construction, and in the event of his failure to do so the same may be removed by at his expense. 26. Roads and Fences. Roads subject to interference from the work covered by this contract shall be kept open, and the fences subject to interference shall be kept up by the contractor until the work is finished. 27. Bench Marks and Survey Stakes. Bench marks and survey stakes shall be preserved by the contractor and in case of their destruction or removal by him or his employees, they will be replaced by the engineer at the contractor's expense. 28. Sanitation. The engineer may establish sanitary and police rules and regulations for all forces employed under this contract; and if the contractor fails to enforce these rules the engineer may enforce them at the expense of the contractor. DETAIL SPECIFICATIONS The detail specifications should state in specific terms, as far as possible, the exact nature and quality of work that the con- tractor will be required to perform so that he will be enabled to SPECIFICATIONS 327 formulate an intelligent bid. No important requirements as far as they are known should be omitted; neither should re- quirements be inserted which it is not intended to enforce. The latter practice has resulted in the tendency of contractors to assume that certain requirements will not be enforced with resultant detriment to all concerned. The more thorough the understanding between the contractor and engineer before the bid is submitted, the more satisfactory will be the results. It is not intended by the above remarks to imply that require- ments established before a contract is let must be adhered to under all circumstances. It is probably safe to say that there have been few large works constructed the specifications for which did not have to be modified in certain details. There should, however, be special reasons for such modifications, and when modifications are made without such reasons there is evi- dence of laxity on the part of the engineer in enforcing the re- quirements, or his specifications must have been poorly drawn. Happily for the engineering profession, the former happens very infrequently. The latter is usually due to lack of knowledge of the work to be done or of current practice in regard thereto. It can hardly be expected of an engineer to have a personal and detailed knowledge of the requirements of all the work coming under his supervision, and this lack of knowledge may sometimes show up in his specifications. It is customary, where the requirements in regard to details are not definitely known, to leave the specifications open on such points and to require that the contractor submit his own specifications, which shall be sub- ject to the approval of the engineer. This also applies to detail designs. This procedure is also followed when it is intended that contractors shall submit bids on their standard goods. The above remarks in regard to the detail specifications apply also to the drawings. Complete detail drawings are not always necessary, nor even desirable, as the details are nearly always changed after the work has gotten under way, and such detail drawings can be supplied after the contract has been let. The main thing to be kept in mind is that all items and conditions affecting the cost to the contractor of doing the work should be shown on the drawings as far as this is possible. 328 WORKING DATA FOR IRRIGATION ENGINEERS SPECIAL CONDITIONS i. Description of Work. 2. List of Drawings. 3. Commencement, Prosecution, and Completion of Work. Work shall be commenced by the contractor within .... days, and shall be completed within .... days after the execution of the contract on behalf of The contractor shall at all times during the continuation of the contract prosecute the work with such force and equipment as, in the judgment of the engineer, are sufficient to complete it within the specified time. 4. Failure to Complete the Work in the Time Agreed Upon. Should the contractor fail to complete the work or any part thereof in the time agreed upon in the contract, or in such extra time as may have been allowed for delays, a deduction of dollars per day for each schedule will be made for each and every day, including Sundays and holidays, that such schedule remains uncompleted after the date required for the completion. The said amounts are hereby agreed upon as liquidated damages for the loss to on account of all expenses due to the employment of engineers, inspectors, and other employees after the expiration of the time for completion and on account of the value of the operation of the irrigation works dependent thereon, and will be deducted from any money due the con- tractor under this contract, and the contractor and his sureties shall be liable for any excess. 5. Progress Estimates and Payments. At the end of each calendar month the engineer will make an approximate measure- ment of all work done and material delivered up to that date, classified according to items named in the contract, and will make an estimate of the value of the same on the basis of the unit prices named in the contract. To the estimate made as above set forth will be added the amounts earned for extra work to the date of the progress estimate. From the total thus computed a deduction of 10 per cent will be made and from the remainder there will be further deducted any amount due to from the contractor for supplies or materials furnished or services SPECIFICATIONS 329 rendered and any other amounts that may be due to as damages for delays or otherwise under the terms of the con- tract. From the balance thus determined will be deducted the amount of all previous payments and the remainder will be paid to the contractor upon the approval of the accounts. The 10 per cent deducted as above set forth will become due and payable with and as a part of the final payment to be made as hereinafter provided. When the terms of the contract shall have been fully complied with to the satisfaction of the engineer and when a release of all claims against under or by virtue of the contract shall have been executed by the contractor, final payment will be made of any balance due, including the per- centage withheld as above, or such portion thereof as may be due to the contractor. Note. Under the head of " Special Conditions " should also be stated any other requirements or conditions applying to the particular contract as a whole. SPECIFICATIONS FOR CANAL EXCAVATION i. Classification of Excavation. All materials moved in the excavation of canals and for structures, and in the construction of embankments will be measured in excavation only, to the neat lines shown in the drawings or prescribed by the engineer, and will be classified for payment as follows: Class 1. Material that can be ploughed to a depth of six inches or more with a six-horse or six-mule team, each animal weighing not less than 1,400 pounds, attached to a suitable plough, all well handled by at least three men; also all material that is loose and can be handled in scrapers, and all detached masses of rock, not exceeding two cubic feet in volume, occurring in loose material or material that can be ploughed as specified. Class 2. Indurated material of all kinds that cannot be ploughed as described under Class 1, but that, when loosened by powder or other suitable means, can be removed by the use of ploughs and scrapers, and all detached masses of rock more than two and not exceeding ten cubic feet in volume. Class 3. All rock in place not included in Classes 1 and 2, 330 WORKING DATA FOR IRRIGATION ENGINEERS and all detached masses of rock exceeding ten cubic feet in vol- ume, not included in Classes 1 and 2. Note: The above classifications may also be used for "wet" excavation, but provision must be made for separate prices for wet excavation. If there be required the excavation of any material which, in the opinion of the engineer, cannot properly be included in any of the above three classes, the engineer will determine the actual necessary cost of excavating and disposing of such material, and payment therefor as extra work will be made under the provi- sions of paragraph .... of these specifications. No additional allowance above the prices bid for the several classes of material will be made on account of any of the material being frozen. It is desired that the contractor or his representative be present during the measurement of material excavated. On written request of the contractor, made by him within ten days after the receipt of any monthly estimate, a statement of the quan- tities and classifications between successive stations included in said estimate will be furnished him within ten days after the receipt of such request. This statement will be considered as satisfactory to the contractor unless he files with the engineer, in writing, specific objections thereto, with reasons therefor, within ten days after receipt of said statement by the contractor or his representative on the work. Failure to file such written objection with reason therefor within said ten days shall be considered a waiver of all claims based on alleged erroneous estimate of quantities or incorrect classification of materials for the work covered by such statement. 2. Canal Sections. The canal sections are shown in the drawings, but the undetermined stability of the material that will form the canal banks may make it desirable during the progress of the work to vary the slopes and dimensions depen- dent thereon. Increase or decrease of quantities excavated as a result of such changes shall be covered in the estimates and shall not otherwise affect the payments due to contractor, unless it is found by the engineer that the unit cost is thereby increased, in which case the engineer will estimate, and include in the amount due the contractor, the amount of such increase. The SPECIFICATIONS 331 canal shall be excavated to the full depth and width required and must be finished to the prescribed lines and grades in a work- manlike manner. Runways shall not be cut into canal slopes below the proposed water level. Earth slopes shall be neatly finished with scrapers or similar appliances. Rock bottoms and banks must show no points of rock projecting more than 0.3 foot into the prescribed section. Above the water line the rock will be allowed to stand at its steepest safe angle and no finishing will be required other than the removal of rock masses that are loose and liable to fall. Payment for excavation of canals will be made to the neat lines only as shown in the drawings or as established by the engineer. 3. Preparation of Surfaces. The ground under all embank- ments that are to sustain water pressure, and the surface of all excavation that is to be used for embankments, shall be cleared of trees, brush, and vegetable matter of every kind. The roots shall be grubbed and burned with other combustible material that has been removed. The surface of the ground under the entire embankment shall be scored with a plough making open furrows not less than eight inches deep below the natural ground surface at intervals of not more than three feet. The cost of all work described in this paragraph shall be included in the unit prices bid for excavation. 4. Construction of Embankments. Embankments built with teams and scrapers or with dump wagons shall be made in layers not exceeding twelve inches in thickness and kept as level as practicable. The travel over the embankments during construc- tion shall be so directed as to distribute the compacting effect to the best advantage. Any additional compacting required over that produced by ordinary travel in distributing the material will be ordered in writing and paid for as extra work under the pro- visions of paragraph Embankments shall be built to the height designated by the engineer to allow for settlement, and shall be levelled on top to a regular grade. ( Note. // the engineer proposes to permit the use of machinery in canal excavation full specifications should be drafted in each individual case. Machine- built embankments must generally be rolled to make them equal in value to team-built embankments and, in order to be eco- I 332 WORKING DATA FOR IRRIGATION ENGINEERS nomical, machine-work should be several cents cheaper per cubic yard than team-work.) No embankments shall be made from frozen materials nor on frozen surfaces. Should the engineer direct that unsuitable material be excavated and removed from the site of any embankment, the material thus exca- vated will be paid for as excavation. When canal excava- tion precedes the building of structures, openings shall be left in the embankments at the sites of these structures, and, except when the construction of the structures is included in the contract, the contractor will not be required to complete such omitted embankments. The cost of all work described in this paragraph, except as herein specified, shall be included in the prices bid for excavation. 5. Disposal of Materials. All suitable material excavated in the construction of canals and structures, or so much thereof as may be needed, shall be used in the construction of embank- ments and in backfilling around structures. Where the canal is on sloping ground, all material taken from the excavation shall be deposited on the lower side of the canal unless otherwise shown in the drawings or directed by the engineer. Where the canal is on level or nearly level ground, the material from the excavation shall be deposited in embankments on both sides to form the top portions of the waterway. If there is an excess of material in excavation, it shall be used to strengthen the embankment on either side of the canal as may be directed by the engineer. Material taken from cuts that is not suitable for embankment construction and surplus material may be wasted on the right of way owned by , at such points as shall be ap- proved by the engineer. Unless otherwise shown in the drawings or directed by the engineer, no material shall be wasted in drain- age channels, nor within .... feet of the edge of the prescribed or actual canal cut. On side-hill locations all material wasted shall be placed on the lower side of the canal unless specific written authority is obtained from the engineer to waste such material elsewhere. Waste banks shall be left with reasonably even and regular surfaces. Whenever directed by the engineer, materials found in the excavation, such as sand, gravel, or stone, that are suitable for use in structures or that are otherwise re- SPECIFICATIONS 333 quired for special purposes, shall be preserved and laid aside in some convenient place designated by him. 6. Borrow Pits. Where the canal excavation at any section does not furnish sufficient suitable material for embankments, the engineer will designate where additional material shall be pro- cured. Unless otherwise shown on the drawings or directed by the engineer a berm of fifteen feet shall be left between the outside toe of the embankment and the edge of the borrow pit, with provision for a side slope of one and one-half to one to the bottom of the borrow pit. Borrowed material will be measured in excavation only, and unless the engineer gives the contractor specific written orders to excavate other than class 1 material from borrow pits, all material obtained from this source will be paid for at the unit price bid for class 1 excavation, regardless of its actual character. Payment for excavation from borrow pits will be made for only such quantities as are required for embank- ments or backfilling or such as by direction of the engineer are excavated and wasted or laid aside. 7. Overhaul. All material taken from the excavation and required for embankment or for other purposes shall be placed as directed by the engineer. The limit of free haul will be 200 feet. Necessary haul over 200 feet will be paid for at the price bid ( Note. If it is desirable, a fixed sum should be stated for over- haul] per cubic yard per hundred feet additional haul, but no allowance will be made for overhaul where the excavated material is wasted, except where such overhaul is specifically ordered in writing by the engineer. Where material is taken from borrow pits, the length of the haul will be measured along the shortest practicable route between the center of gravity of the material as found in excavation and the center of gravity of the material as deposited in each station. Where the material is taken from canal excavation, the length of the haul shall be understood to mean the distance measured along the center line of the canal from the center of gravity of the material as found in excavation to the center of gravity of the material as required to be deposited. 8. Surface and Berm Ditches. If, in the judgment of the engineer, it should be necessary to construct surface and berm 334 WORKING DATA FOR IRRIGATION ENGINEERS drainage ditches along the lines of the canal, the contractor shall perform such work and the excavation will be paid for at the unit prices bid in the schedules covering the excavation of the canal along which such surface and berm ditches are built. 9. Blasting. Any blasting that will probably injure the work will not be permitted, and any damage done to the work by blast- ing shall be repaired by the contractor at his expense. SPECIFICATIONS FOR TUNNELS 1. Excavation. The tunnel, shafts, and adits shall in all cases be excavated in such manner and to such dimensions as will give suitable room for the necessary timbering, lining, ven- tilating, pumping, and draining. The contractor shall use every reasonable precaution to avoid excavating beyond the outside lines of permanent timbering and beyond the outside neat con- crete lines where no permanent timbering is required. All drilling and blasting shall be carefully and skilfully done so as not to shatter the material outside of the required lines. Any blasting that would probably injure the work will not be per- mitted and any damage done to the work by blasting shall be repaired by the contractor at his expense, and in a manner satis- factory to the engineer. Tunnel excavation will be paid for at the price bid per linear foot. Partial excavation, as in the case of a heading, amounting to not less than one-half the full section, will be allowed for in the monthly progress estimates at one- fourth of the price named in the contract for full excavation. 2. Timbering. Suitable timbering and lagging shall be used to support the tunnel, sides, and roof wherever necessary. If practicable, this timbering may be removed before the construc- tion of the concrete lining. Timbering may be left in place, provided it is constructed in such a manner as not to weaken the concrete lining and is in accordance with designs approved by the engineer. An approved design for such permanent timbering is shown in the drawings, but in case this design is found to be inadequate, it may be modified from time to time, subject to the approval of the engineer. Lumber for timbering shall be furnished by the contractor. The cost of furnishing and placing permanent and temporary timbering shall be included in the SPECIFICATIONS 335 price per linear foot bid in the schedule for excavating the tun- nel, except that in addition thereto the contractor will be paid the sum of dollars per M feet B. M. for permanent timber- ing in place. No payment will be made for temporary timbering nor for timber used in filling cavities. In measuring permanent timbering for payment, the net length of pieces and the commer- cial cross-sectional dimensions will be taken. Nothing herein contained shall prevent the contractor from placing such tem- porary timbering as he may deem necessary nor from using heav- ier permanent timbering than that shown in the drawings, nor shall be construed to relieve the contractor from sole and full responsibility for the safety of the tunnel and for damage to person and property. 3. Concrete Lining. The tunnel shall be lined throughout with concrete. The tunnel lining side walls and arch, where permanent timbering is not required, shall have an average thickness of .... inches, with a minimum thickness of inches over projecting points of rock. The average thickness of the concrete tunnel invert shall be inches. Where permanent timber is required it shall be set back so far that the concrete lining will cover the timber at least .... inches. The concrete for such timbered portions of the tunnel will be estimated as having an average thickness of inches. If the tunnel is excavated to greater dimensions than necessary for placing the prescribed average thickness of the concrete lining, the excess space shall be solidly filled with concrete, or the lining shall be confined with forms to the prescribed thickness and properly backfilled. Concrete tunnel lining will be paid for by the cubic yard at the unit price named in the contract, measured to the neat lines shown in the drawings, based on the average thickness herein specified. 4. Lines and Grades. The contractor shall provide such forms, spikes, nails, troughs for plumb-bob lines, light, etc., and such assistance as may be required by the engineer in giving lines and grades, and the engineer's marks shall be carefully pre- served. Work in the shafts, adits, and tunnel shall be suspended for such reasonable time as the engineer may require to transfer lines and to mark points for line of grade. No allowance will 336 WORKING DATA FOR IRRIGATION ENGINEERS be made to the contractor for loss of time on account of such suspension. 5. Draining. The contractor shall drain the tunnels and adits where necessary to rid the same of standing water. Pump- ing shall be done where gravity flow to an outlet cannot be secured. 6. Lighting and Ventilating. The contractor shall properly light and ventilate the tunnel during construction. 7. Storage and Care of Explosives. Caps or other exploders or fuses shall in no case be stored or kept in the same place in which dynamite or other explosives are stored. The location and design of powder magazines, methods of transporting ex- plosives, and in general the precautions taken to prevent acci- dents must be satisfactory to the engineer; but the contractor shall be liable for all damages to person or property caused by blasts or explosions. 8. Backfilling. Any space outside of the concrete tunnel lining shall be compactly refilled at the expense of the contractor with such of the excavated material from the tunnel as may be approved by the engineer. Large cavities in the tunnel roof may be filled with waste timber. The backfilling to the springing lines of the arch shall be placed before the arch is constructed, and shall be brought up evenly on both sides of the tunnel; it shall be spread in layers not exceeding six inches in thickness and well rammed. The invert and side walls shall be braced, if required, during the placing of the backfilling. 9. Adits and Shafts. The contractor shall construct, at his own expense, such adits and shafts as he may desire to use to expedite the tunnel work. The sides and the arch of the tunnel lining situated immediately beneath the opening of each shaft shall be increased to such suitable thickness as the engineer may prescribe; and each adit shall be closed at the point where it meets the tunnel with a block of concrete averaging at least four feet in thickness, extending into the sides of the adit two feet and having a foundation two feet below the bottom of the tunnel. All concrete required for this purpose shall be furnished by the contractor at his own expense, the cement for which will be furnished to the contractor at its cost on the work. All shafts SPECIFICATIONS 337 must be completely refilled. Dumping from the top will not be allowed until the tunnel arch has been covered to a depth of at least ten feet. After the completion of the block of concrete required for closing an adit, the adit shall be refilled and the filling tamped into place for a distance of twenty feet from the tunnel. SPECIFICATIONS FOR EXCAVATION FOR STRUCTURES 1. Excavation. Unless otherwise shown in the drawings, excavation for structures will be measured for payment to lines outside of the foundation of the structures and to slopes of ; provided, that, where the character of the material cut into is such that it can be trimmed to the required lines of the concrete structure and the concrete placed against the sides of the excavation without the use of intervening forms, payment for excavation will not be made outside of the required limits of the concrete. The prices bid for excavation shall include the cost of all labor and material for cofferdams and other temporary structures and of all pump- ing, baling, draining, and all other works necessary to maintain the excavation in good order during construction. 2. Backfilling. The contractor shall place and shall compact thoroughly all backfilling around structures. The compacting must be equivalent to that obtained by the tramping of well- distributed scraper teams depositing the material in layers not exceeding six inches thick when compacted. The material used for this purpose, the amount thereof, and the manner of deposit- ing the same must be satisfactory to the engineer. So far as practicable, the material moved in excavating for structures shall be used for backfilling, but when sufficient suitable material is not available from this source, additional material shall be ob- tained from borrow pits selected by the engineer. Payment for backfilling will be made at the price per cubic yard bid therefor in the schedule. 3. Puddling. Backfilling and embankment around struc- tures within .... feet of the structure shall be made with material approved by the engineer, and where practicable shall consist of sand and gravel, with an admixture of clay equal to one-fourth 338 WORKING DATA FOR IRRIGATION ENGINEERS to one-half the volume of the sand and gravel. The material shall be deposited in water of such depth as is approved by the engineer, unless the quantity of clay predominates, in which case the engineer may in his discretion order the material depos- ited in layers of six inches or less, and compacted by tamping or rolling with the smallest quantity of water that will insure con- solidation. Payment for the work specified in this paragraph will be made at the unit price bid for puddling, and will be in addition to the payment made for excavation and overhaul. 4. Blasting. Any blasting that will probably injure the work will not be permitted and any damage done to the work by blasting shall be repaired by the contractor at his expense. SPECIFICATIONS FOR CONTINUOUS WOOD STAVE PIPE 1. Description. The pipe shall be of the continuous-stave metal-banded type with metal tongues driven into slots in the ends of the staves to form the butt joints. The alignment and profile of the pipe are shown in the drawings. Each proposal shall be accompanied by drawings showing clearly detail dimen- sions of staves, bands, and tongues, which shall comply with the requirements of the specifications. Omission of drawings from proposals or any uncertainty as to detail dimensions will be sufficient cause for rejection. 2. Material. All material of whatever nature required in the work shall be furnished by the contractor. The price bid for wood staves in place shall include the cost of all necessary tongues, and all royalties for special material or devices used in the pipe or in its construction. The price bid for bands in place shall include all necessary shoes and fastenings and asphaltum coat- ing, and all royalties for special devices used in the pipe or in its construction. 3. Diameter of Pipe. The inside diameter of the pipe shall be .... inches, measured after completion of the work. No di- ameter at any point shall differ more than !}/ per cent from the average diameter of the pipe at said point, and the average of the vertical and horizontal diameters at any point shall not be less than the specified diameter. SPECIFICATIONS 339 4. Staves. All lumber used in staves shall be Douglas fir or redwood. It shall be sound, straight-grained, and free from dry-rot, checks, wind shakes, wane, and other imperfections that may impair its strength or durability. Redwood shall be clear and free from sap. In Douglas fir sap will not be allowed on more than 10 per cent of the inside face of any stave and in not more than 10 per cent of the total number of pieces; sap shall be bright and shall not occur within 4 inches of the ends of any piece; pitch seams will be permitted in not over 10 per cent of the total number of pieces, if showing on the edge only, and if not longer than 4 inches nor wider than /(e inch; no through knots or knots at edges nor within 6 inches of ends of staves will be allowed; sound knots not exceeding J/2 inch in diameter, not falling within the above limitations, nor exceeding three within a 10-foot length will be accepted. All lumber used shall be seasoned by not less than 60 days' air drying in open piles before milling or by thorough kiln drying. All staves shall have smooth-planed surfaces and the inside and outside faces shall be accurately milled to the required circular arcs to fit a standard pattern provided by the contractor. Staves shall be trimmed perfectly square at ends and the slots for tongues shall be in exactly the same relative position for all ends and according to detail drawings furnished by the contractor. Staves shall have an average length of not less than 15 feet 6 inches and not more than 1 per cent of the staves shall have a length of less than 9 feet 6 inches. No staves shorter than 8 feet will be accepted. The finished thickness of staves shall not be less than inches. All staves delivered on the work in a bruised or injured condition will be rejected. If staves are not immediately used on arrival at the site of the work, they shall be kept under cover until used. 5. Bands. A band shall consist of one complete fastening and shall include the bolts, shoes, nuts, and washers necessary to form same. 6. Band Spacing. The distance center to center of bands shall be as marked on the profile, except that where the spacing as marked is such as to make the distances from bands to the ends of staves more than 4 inches, extra bands shall be used to keep such distances within 4 inches. 340 WORKING DATA FOR IRRIGATION ENGINEERS 7. Bolts. All bolts shall be of .... inch diameter steel and shall conform to the following specifications: (see specifications for structural steel). Bolts may have either button or bolt heads. They shall be at least as strong in thread as in body, and threads shall permit the nut to run freely the entire length of thread. Nuts shall be of such thickness as to insure against stripping of threads. 8. Shoes. There shall be .... malleable iron shoes to each band. ( Note: It is customary to use only one shoe for pipe 48 inches and smaller in diameter and two shoes for larger sizes. For very large pipe more than two may be necessary.) Shoes shall fit accurately to the outer surface of the pipe and shall have the dimensions shown on the drawing, or the con- tractor may submit for approval a drawing or sample of some other type of shoe which he may desire to furnish. If required, such shoe shall be shown under suitable test to be stronger than the bolt. The material for shoes shall conform to the following specifications : (see standard specifications for malleable castings) . 9. Tongues. Shall be of galvanized steel or iron inch thick and .... wide. Their length shall be such that when in place, they will penetrate into the sides of the adjacent staves without undue injury. The tongues and slots shall be so pro- portioned as to insure a tight fit of the tongues into the slots without danger of splitting the staves. 10. Coating of Bands. The bands shall be coated by being dipped when hot in a mixture of pure California asphalt, or equivalent. Bolts shall be bent to the required arc before dip- ping. If the bands are dipped cold they shall be left in the hot bath a sufficient length of time to insure that they have acquired the temperature of the asphalt. This coating shall be so pro- portioned and applied that it will form a thick and tough coating free from tendency to flow or become brittle under the range of temperature to which it will be subjected. Where the pipe is uncovered and exposed to the full range of atmospheric temper- atures, not less than 7 per cent and not more than 10 per cent of pure linseed oil shall be mixed with the. asphalt. 11. Erection. The pipe shall be built in a workmanlike manner. The ends of adjoining staves shall break joint at least SPECIFICATIONS 341 3 feet. The staves shall be driven in such a manner as to avoid any tendency to cause wind in the pipe and the required grade and alignment must be maintained. Staves shall be well driven to produce tight butt joints; driving bars, or other suitable means being used to avoid marring or damaging staves in driving. In rounding out the pipe, care shall be exercised to avoid damage by chisels, mauls, or other tools. The pipe shall be rounded out to produce smooth inner and outer surfaces. Bands shall be accurately spaced and placed perpendicular to the axis of the pipe. Shoes shall be placed so as to cover longitudinal joints between staves and bear equally on two staves as nearly as practicable. They shall be placed alternately on opposite sides of the pipe, so as to be out of line and cover successively on each side at least three joints. Shoes shall not be allowed to cover the butt joints. Bolts shall be hammered thoroughly into the wood to secure a bearing on 60 of the circumference of the bolt. All kinks in bolts shall be carefully hammered out. Bands shall be back-cinched to the satisfaction of the engineer so as to produce the required initial compressive stresses in the staves. All metal work shall be handled with reasonable care so as to avoid injury to the coating as much as possible. In hammering shoes into place they shall be struck so as to avoid deformation or injury. After erection the contractor shall retouch all metal work, where abraded, with an asphaltum paint satisfactory to the engineer. 12. Painting. After erection and while the pipe is dry the entire outer surface shall be given a coat of refined water-gas tar, followed by a coat of refined coal-gas tar, thinned with dis- tillate, applied with brushes or sprayed on with air pressure. Before application of the paint the surface of the pipe shall be thoroughly cleaned of dirt, dust, and foreign matter of every kind. All checks, cracks, and surface irregularities of every kind shall be thoroughly filled with paint. The finished thickness of the coating shall be not less than /( 6 inch. The cost of all work under this paragraph shall be included in the price bid for pipe in place. (Note: Redwood, not painted, is probably equal in durability to Douglas fir painted.) 13. Inspection. Final inspection of materials, as well as 342 WORKING DATA FOR IRRIGATION ENGINEERS erection, will be made on the work, but if the contractor so de- sires, preliminary inspection of staves may be made at the mill at the contractor's expense. Mill inspection, however, shall not operate to prevent the rejection of any faulty material on the work. Tests of metal work will be made at the point of manu- facture by at own expense; or they may be made at the plant by the contractor or his employees acting under the direction of the engineer or his representative; or cer- tified tests may, at the option of the engineer, be accepted in lieu of the above-mentioned tests. The contractor shall provide, at his own expense, the necessary test pieces, and shall notify the engineer or his representatives when these pieces are ready for testing. All test bars and test pieces shall be marked so as to indicate clearly the material that they represent, and shall be properly boxed and prepared for shipment if required. 14. Tests of Pipe. On completion of the work, or as soon as possible thereafter, the contractor shall make a full pressure test of the pipe. All leaks found at the time of the test shall be made tight by the contractor. If the leakage is not so large as to endanger the foundation of the pipe, the pipe shall be kept under full pressure for two days before plugging of leaks is started in order to allow the wood to become thoroughly satu- rated. The cost of making the test shall be borne by the con- tractor. 15. Payments. SPECIFICATIONS FOR MANUFACTURE OF MACHINE- BANDED WOOD STAVE PIPE 1. Description. The pipe shall be of the jointed, wood- stave, machine-banded type. 2. Lengths of Pipe Sections. Pipe shall be furnished in lengths of 10 to 20 feet and the average length shall be not less than 16 feet. Shorter sections shall be furnished only if required for making sharp curves, in which case the lengths shall not be more than one foot shorter than will be required to keep the joint opening at the outside of the curve due to throw within a limit of /{ 6 inch. 3. Material. All material of whatever nature required in SPECIFICATIONS 343 the manufacture of the pipe in accordance with these specifica- tions shall be furnished by the contractor. 4. Diameters of Pipes. The diameters of pipes shall be as listed in the schedules. No diameter of any pipe shall differ more than 1 per cent from the specified diameter of the pipe, and the average of the vertical and horizontal diameters at any point shall not be less than the specified diameter. 5. Thickness of Staves. The finished thickness of staves shall be as follows : 4" to 6" l 1/16 8" to 10" 1 1/8 12" to 14" 1 3/16 16" to 18" 1 1/4 20" to 24" 1 5/16 6. Lumber for Staves. All lumber used in staves shall be Douglas fir or redwood. It shall be sound, straight-grained, and free from dry-rot, checks, wind shakes, wane, and other imper- fections that may impair its strength or durability. Redwood shall be clear and free from sap. In the Douglas fir sap will not be allowed on more than 10 per cent of the inside face of any stave, and in not more than 10 per cent of the total number of pieces; sap shall be bright and shall not occur within 4 inches of the ends of any piece; pitch seams will be permitted in not over 10 per cent of the total number of pieces, if showing on the edge only, and if not longer than 4 inches nor wider than /{ 6 inch; no through knots nor knots at edges nor within 6 inches of ends of staves will be allowed; sound knots not exceeding J^ inch in diameter, not falling within the above limitations, nor exceeding three within a 10-foot length, will be accepted. All lumber used shall be seasoned by not less than sixty days' air drying in open piles before milling or by thorough kiln drying. All staves shall have smooth-planed surfaces, and the inside and outside faces shall be accurately milled to the required circular arcs. 7. Banding. Size and spacing of banding wire shall be designed for a working stress of 12,000 pounds per square inch on the wire. The spacing shall in no case be greater than 4 inches, center to center of wires, nor greater than will produce a 344 WORKING DATA FOR IRRIGATION ENGINEERS pressure of wire on the wood of 800 pounds per square inch as pRf calculated from the formula B = TIT where B = pressure r (JK.+ t) on wood in pounds per square inch; p = water pressure in pounds per square inch;/ = spacing of wire in inches; R = in- side radius of pipe in inches; r = radius of wire in inches; and / = thickness of staves in inches. No wire smaller than No. 8 United States Standard gage shall be used. Wire shall be of medium steel with a tight coating of galvanizing and shall have an ultimate tensile strength of 55,000 to 65,000 pounds per square inch, and capability of being bent flat on itself without fracture. The galvanizing shall pass the standard test of four immersions in a standard solution of copper sulphate and shall show no lumps of zinc. The bidder shall state in his proposal the size of banding wire he proposes to furnish. 8. Joints. Inserted joint pipe shall be furnished for diam- eters of 12 inches and less and for heads not exceeding 50 feet. For pipes of larger diameter than 12 inches, and for all pipes under more than 50 feet head, wood sleeve collars shall be fur- nished. The banding on collars shall be 50 per cent stronger than the banding on the pipe. 9. Individual Bands. Individual bands shall be used on all collars for pipe 12 inches and greater in diameter. The smallest bolts used shall be Y% mc h m diameter. The bolt shall have an ultimate tensile strength of 55,000 to 65,000 pounds per square inch; an elastic limit of one-half the ultimate tensile strength, and capability of being bent back flat on itself without fracture. The shoes shall be malleable iron, and shall be stronger than the bolts, with sufficient bearing on the wood at the tail to prevent injurious indentation in cinching. The shoes shall be sound and free from blow-holes, and shall have an ultimate tensile strength of not less than 40,000 pounds per square inch. Bidders shall submit samples or drawings of the type of shoe they propose to furnish. 10. Coating. After manufacture the outside of the pipe and collars shall be dipped in a bath of hot coal tar and asphaltum. Previous to dipping the collars in coal tar and asphaltum they SPECIFICATIONS 345 shall be dipped for a depth of 1 inch at each end for a period of ten minutes in a bath of creosote. Care should be exercised to keep the coal tar and asphaltum from the tenon ends and inside surfaces, and, if necessary, the tenons shall be wrapped with paper while being dipped. After dipping, the pipe and collars shall be rolled in fine sawdust while the coating is still soft. 11. Inspection. Inspection of pipe will be made at the mill, but the manufacturer will be held responsible for any damage in transit caused by improper loading of the pipe. 12. Marking. Each section of pipe shall be plainly marked on the inside at one end, showing the head for which the section was wound, and the number of the banding wire used. 13. Shipment. 14. Payment. SPECIFICATIONS FOR STEEL PIPE 1. Description. Steel pipe may be either of the lockbar or riveted steel type. Riveted steel shall have \ 1 courses. [ taper J Circular seams may be single-riveted and longitudinal seams shall be \ . n *V <* riveted. The bidder shall submit with his bid [ double J a drawing showing details of joints, size and spacings of rivets, etc. Failure to submit such drawing will be sufficient cause for rejection of the bid. 2. Thickness of Metal. The thickness of steel sheets shall be as follows: Length, Feet THICKNESS, INCHES Head, Feet Riveted Lockbar 346 WORKING DATA FOR IRRIGATION ENGINEERS 3. Planing and Scarfing. When necessary the edges of plates shall be prepared for caulking by planing and scarfing at the factory. 4. Riveting. The riveting and other details of longitudinal seams shall be designed to withstand the heads given in para- graph 2. The rivets for circular joints shall be of the same size as for longitudinal seams. The intensity of working stress on rivets shall be 7,500 pounds per square inch in shear and 15,000 pounds per square inch in bearing on riveted plates. All rivet spacing shall be arranged to give the greatest possible efficiency of joint. Size of rivets and rivet spacing shall be sub- mitted to the engineer for approval. All riveting shall be done in the field, but sufficient of the work done with different tem- plates must be assembled at the shop to prove the work correct. (When appropriate, shop riveting should be specified.) 5. Punching. Rivet holes may be punched and shall be no larger than is necessary to pass the required size of rivet. Drift pins shall not be used except for bringing together the several parts, and drifting with such force as to distort the holes will not be allowed. Wrongly punched plates shall not be corrected by plugging the holes and re-punching, but shall be rejected. All burrs and ragged edges on plates shall be smoothed off before the material leaves the shop. All punching shall be done at the shop before shipment. 6. Material. All steel shall be made by the open-hearth process. Steel for plates shall be of the grade known as " boiler plate." Steel for rivets shall be of the grade known as " boiler rivet steel." 7. Chemical and Physical Properties of Boiler Plate Steel. Boiler plate steel shall contain not more than .05 per cent phos- phorus, .05 per cent sulphur, and from 0.30 to 0.60 per cent manganese. It shall show an ultimate tensile strength of 55,000 to 65,000 pounds per square inch; an elastic limit of not less than one-half the ultimate tensile strength; an ultimate elongation in 8 inches of not less than 1,500,000 divided by the ultimate tensile strength; and capability of being bent, cold or quenched, 180 flat without fracture. The steel shall be in all respects such as to stand punching, caulking, and riveting without showing the SPECIFICATIONS 347 least tendency to crack. Plates shall withstand, without crack- ing of the material, a drift test made by driving a pin into a %-inch hole, enlarging same to a diameter of 1 inch. In all respects not covered in these specifications boiler plate steel shall conform to the " Standard Specifications for Boiler Steel " of the American Society for Testing Materials, adopted Aug- ust 25, 1913. 8. Chemical and Physical Properties of Rivet Steel. Steel for rivets shall contain not more than .04 per cent of phosphorus, .045 per cent sulphur, and from 0.30 to 0.50 per cent of man- ganese. It shall show an ultimate tensile strength of 45,000 to 55,000 pounds per square inch; an elastic limit of not less than one-half the ultimate tensile strength; an ultimate elongation in 8 inches of not less than 1,500,000 divided by the ultimate tensile strength, but need not exceed 30 per cent; and capability of being bent, cold or quenched, 180 flat without fracture. Rivet rounds shall be tested of full size as rolled. In all respects not covered in these specifications steel for rivets shall conform to the " Stand- ard Specifications for Boiler Rivet Steel " of the American Society for Testing Materials, adopted August 25, 1913. 9. Marking. Each plate shall be distinctly stamped with its melt or slab number. Rivet steel may be shipped in securely fastened bundles with melt number stamped on a metal tag attached. Plates and other parts shall be plainly marked for identification and assembly in the field. 10. Test Pieces. (This paragraph should state who is to furnish test pieces, what disposition shall be made of broken test specimens, etc.) n. Tests of Material. (This paragraph should state who is to make tests, at whose expense tests are to be made, etc.) 12. Shipment. 13. Erection. Erection of pipe shall be commenced at the point directed by the engineer. The contractor shall haul all material and distribute same along the trench and shall furnish a compressed-air plant and full equipment . for air riveting, and all other equipment, tools, and supplies required for the erection of the pipe and completion for service. The pipe shall be care- fully caulked and painted as the work progresses. The work of 348 WORKING DATA FOR IRRIGATION ENGINEERS assembling, riveting, and caulking shall be done by workmen experienced in this line. Riveting shall show first-class workman- ship, rivet heads shall be full and concentric with the body of the rivet, and the rivet shall completely fill the hole and thor- oughly pinch the connected pieces together. Rivets that are loose or have defective heads shall be removed and other rivets substituted therefor. 14. Painting. Inside and outside of pipe shall be covered with three coats of a reliable brand of asphalt paint which shall be subject to the approval of the engineer. Before painting all surfaces shall be thoroughly cleaned by scrubbing with wire brushes or other means as directed by the engineer. All riveted joints shall be painted before riveting. All paint shall be applied while the pipe is warm and thoroughly dry. 15. Defective Work. The contractor shall guarantee the material and workmanship furnished by him to be free from defects of material and construction, and he shall replace free of cost to any material that shall develop faults during construction or tests. 1 6. Test of Pipe. On completion of erection, or as soon as possible thereafter, the contractor shall make a full-pressure test of the pipe. The pipe shall be water-tight under this test and the contractor shall correct any defects that develop. 17. Payments. SPECIFICATIONS FOR JOINTED REINFORCED CON- CRETE PIPE 1. Description. The pipe shall be composed of concrete reinforced with steel rods or wire and built in vertical forms in lengths of .... feet; the sections being connected in the trench by concrete collars reinforced with steel. 2. Diameter of Pipe. The inside diameter of the pipe shall be inches and no diameter shall differ more than 0.5 per cent from the specified diameter of the pipe. Each section of pipe shall be a true right cylinder with the plane of the ends perpendicular to the axis of the pipe. 3. Thickness of Shell. The shell of the pipe shall have a thickness of , inches which shall be uniform around the SPECIFICATIONS 349 entire circumference. In no case will a variation of more than 10 per cent from the specified thickness be allowed. 4. Manufacture. The concrete shall be thoroughly mixed in a mechanical batch mixer. It shall be deposited in such a manner that no separation of ingredients will occur and suitable tools shall be used to settle the concrete thoroughly and produce smooth surfaces. Great care shall be exercised to maintain proper spacing of the reinforcing rods. No pipe shall be manu- factured when the temperature of the atmosphere is above 90, except by permission of the engineer. During manufacture the concrete and forms shall be protected from the direct rays of the sun, and thereafter the sections shall be kept covered for five days and they shall be kept moist for twenty days. Manufac- ture shall not be carried on in freezing weather, except in a heated enclosure, and the sections of pipe shall be prevented from freezing. Immediately after removal of the forms all de- fects in the surface of the concrete shall be smoothed up with a 1 to 1 mixture of cement and fine sand, especial care being taken to produce smooth interior surfaces. Forms shall not be removed in less than twenty-four hours after the concrete has been poured. 5. Forms. The forms used shall be subject to the approval of the engineer. All-steel forms are preferred, but wooden forms with steel linings may be used, provided the desired results can be obtained therewith. Forms shall be strong and rigid with sufficient bracing to prevent warping in handling, or pouring concrete. They shall be provided with suitable attach- ments for making the joint grooves at the ends in accordance with the drawings. A sufficient number of forms shall be pro- vided to allow the manufacture of not less than .... sections of pipe per day, or such additional number as may be necessary to complete the work within the specified time. 6. Reinforcement. The transverse reinforcement shall con- sist of medium steel rods or wire and shall be spaced as shown on the drawings. Sufficient longitudinal reinforcement shall be used to fasten the transverse rods and hold them rigidly in place. The transverse reinforcement may be either individual rods, welded or lapped and wired at the ends for a length of 24 di- 350 WORKING DATA FOR IRRIGATION ENGINEERS ameters, or it may be wound in helical coils. The latter method is preferred where its use is practicable. 7. Steel. Steel may be made by either the open-hearth or Bessemer process. It shall contain not more than 0.1 per cent phosphorus if made by the Bessemer process, and not more than 0.05 per cent if made by the open-hearth process. It shall have an ultimate tensile strength of 55,000 to 70,000 pounds per square inch; an elastic limit not less than 33,000 pounds per square inch; a minimum per cent of elongation in 8 inches of 1,400,000 divided by the ultimate tensile strength; and capability of being bent cold without fracture 180 around a pin having a diameter equal to the thickness of the test piece. Bars or wire will be subject to rejection if the actual weight of any lot varies more than 5 per cent over or under the theoretical weight of that lot. 8. Concrete. Concrete shall be composed of cement, sand, and gravel, well mixed and brought to a proper consistency by the addition of water. The proportions will depend upon the nature of component materials and upon the head of water that the pipe will be subjected to, but will vary in general from one part cement to five parts aggregate, to one part cement to six parts aggregate. The contractor shall not be entitled to any extra compensation by reason of such variations. (Note: If the contractor furnisfos the cement this paragraph must be modified so as to provide for separate prices for different mixtures.} 9. Cement. * 10. Sand. Sand for concrete shall be obtained from natural deposits. The particles shall be hard, dense, durable, non- organic rock fragments, such as will pass a )^-inch mesh screen. The sand must be free from organic matter and must contain not more than 3 per cent of clayey material or other objectionable non-organic matter. The sand must be so graded that, when dry and well shaken, its voids will not exceed 35 per cent. n. Gravel. Gravel for concrete shall consist of hard, dense, durable rock pebbles that will pass through a .... inch mesh screen and that will be rejected by a %-mch rnesh screen. (Note: Gravel is better suited for thin-shelled reinforced concrete SPECIFICATIONS 351 pipe on account of the greater ease with which it can be worked in around the reinforcement.) 12. Water. The water used in mixing concrete shall be reasonably clean, and free from objectionable quantities of organic matter, alkali, salts, and other impurities. 13. Mixing Concrete. The cement, sand, and gravel shall be so mixed and the quantities of water added shall be such as to produce a homogeneous mass of uniform consistency. Dirt and other foreign substances shall be carefully excluded. Machine mixing will be required, and the machine and its operation shall be subject to the approval of the engineer. Enough water shall be used to give the concrete a mushy consistency. If concrete is mixed in freezing weather, the sand and gravel or water shall be heated sufficiently before mixing to remove all frost. 14. Placing Concrete. No concrete shall be used that has attained its initial set, and such concrete shall be immediately removed from the site of the work. No concrete shall be placed except in the presence of a duly authorized inspector. 15. Hauling Pipe. In handling and hauling the sections of pipe great care shall be taken to avoid injury to the pipe, and suitable cradles shall be provided to avoid concentration of the entire weight on small areas. The sections of pipe shall be dis- tributed along the trench as directed by the engineer. Any pipes that are seriously injured in handling or hauling will be re- jected and shall be immediately removed from the site of the work or demolished, and the contractor shall replace the same with other sections of pipe having the same quantity of rein- forcement. 1 6. Laying Pipe. The sections of pipe shall be laid true to line and grade according to stakes established by the engineer and with only sufficient joint space between to allow for satis- factory caulking. Before making the joints the adjacent sections of pipe shall be firmly bedded or supported by blocks to pre- vent the slightest movement while the joint is being made. 17. Joints. Joints may be made by sectional collars sepa- rately moulded and set in grooves in the ends of the pipe sections, or by pouring concrete on the outside of the pipe into suitable 352 WORKING DATA FOR IRRIGATION ENGINEERS flexible forms and at the same time pointing and smoothing off on the inside with a 1 to 1 mixture of mortar. The concrete used for joints shall be equal to or better in quality than that used for the pipe. Each joint shall be reinforced with .... steel rods, or the equivalent in area of some other form of reinforce- ment satisfactory to the engineer. As soon as the joint has been made it shall be covered with wet cloths and kept so covered for ten days thereafter. If desired, after the concrete has attained its final set, damp earth may be substituted for the wet cloths. 18. Tests of Pipe. On completion of the work, or as soon as possible thereafter, the contractor shall make a full-pressure test of the pipe. All leaks found at the time of the test shall be made tight by the contractor. The cost of making the test shall be borne by the contractor. 19. Measurement. The price bid per linear foot shall be for pipe complete in place, ready for service, and shall include all material, except cement, entering into or used on the work, manufacture, hauling, laying, jointing, testing, repairing leaks, etc., until final inspection and acceptance by the engineer. The number of linear feet of pipe in place will be measured along the axis of the pipe after completion. 20. Payments. SPECIFICATIONS FOR CAST-IRON PIPE (Based on "Standard Specifications for Cast-Iron Water-Pipe " of the American Water Works Association, adopted May 12, 1908.) 1. Description. The pipes shall be made with hub and spigot joints and shall conform accurately to the dimensions and weights and shall be subjected to the tests required for class .... pipe in the " Standard Specifications for Cast-Iron Water Pipe " of the American Water Works Association, adopted May 12, 1908. They shall be straight and shall be true circles in section, with their inner and outer surfaces concentric. They shall be at least 12 feet in length, exclusive of socket. In all respects not specifically mentioned herein, the pipes and their material shall conform to the above-mentioned specifications. 2. Quality of Iron. All pipes shall be made of cast iron of SPECIFICATIONS 353 good quality, and of such character as shall make the metal of castings strong, tough, and of even grain, and soft enough to admit satisfactorily of drilling and cutting. The metal shall be made without any admixture of cinder iron or other inferior metal, and shall be remelted in a cupola or air furnace. Speci- men bars 2 inches wide and 1 inch thick loaded at the middle of a 24-inch span shall carry a load of not less than 2,000 pounds and shall show a deflection of not less than 0.3 inch before break- ing, or, if preferred, tensile tests may be made which shall show a breaking load of not less than 20,000 pounds per square inch. 3. Test Pieces. (This paragraph should state who is to fur- nish test pieces and how many, and what disposition is to be made of broken test specimens.) 4. Quality of Castings. The pipes shall be smooth, free from scales, lumps, blisters, blow-holes, sand-holes, and defects of every nature that unfit them for the use for which they are intended. No plugging or filling will be allowed. 5. Casting of Pipe. The straight pipes shall be cast in dry sand moulds in a vertical position. Pipes 16 inches or less in diameter shall be cast with the hub end up or down as specified in the proposals. Pipes 18 inches or more in diameter shall be cast with the hub end down. The pipes shall not be stripped or taken from the pit while showing color of heat, but shall be left in the flasks for a sufficient length of time to prevent unequal contraction by subsequent exposure. 6. Diameters. The diameters of the sockets and the outside diameters of the spigot ends of the pipes shall not vary from the standard dimensions by more than .06 of an inch for pipes 16 inches or less in diameter; .08 of an inch fpr 18-inch, 20-inch and 24-inch pipes; .10 of an inch for 30-inch, 36-inch, and 42-inch pipes; .12 of an inch for 48-inch, and .15 of an inch for 54-inch and 60-inch pipes. Especial care shall be taken to have the sockets of the required size. The sockets and spigots will be tested by circular gages and no pipe will be received that is defective in joint from any cause. 7. Thickness. For pipes whose standard thickness is less than 1 inch, the thickness of metal in the body of the pipe shall not be more than .08 of an inch less than the standard thickness 354 WORKING DATA FOR IRRIGATION ENGINEERS and for pipes whose standard thickness is 1 inch or more, the variation shall not exceed .10 of an inch, except that for spaces not exceeding 8 inches in length in any direction, variations from the standard thickness of .02 of an inch in excess of the allow- ance above given shall be permitted. 8. Weights. No pipe shall be accepted whose weight is more than 5 per cent less than the standard weight for pipes 16 inches or less in diameter, and 4 per cent less than the stand- ard weight for pipes more than 16 inches in diameter, and no excess above the standard weight or more than the given per- centage will be paid for. The total weight to be paid for shall not exceed for each size and class of pipe received the sum of the standard weights of the same number of pieces of the given size and class by more than 2 per cent. 9. Coating. Every pipe and special casting shall be coated, inside and out, with coal-tar pitch varnish, mixed with sufficient oil to make a smooth coating, tough and tenacious when cold and not brittle nor with any tendency to scale off. Before being dipped the pipes shall be thoroughly cleaned and shall be entirely free from rust. Castings shall have a uniform temperature of 300 F. when they are put in the vat and the coating material shall be kept heated to the same temperature. Each casting shall remain in the bath at least five minutes. 10. Marking. Each pipe shall have distinctly cast upon it the initials of the maker's name, and the weight and class letter shall be conspicuously painted in white on the inside of each pipe after the coating has become hard. 11. Inspection and Tests. All pipes shall be subjected to a careful hammer inspection. Tests of the material will be made by at its own expense, or they may be made at the plant by the contractor or his employees acting under the direction of the engineer or his representative; or certified tests may, at the option of the engineer, be accepted in lieu of the above-mentioned tests. 12. Shipment. 13. Payment. SPECIFICATIONS 355 SPECIFICATIONS FOR METAL FLUMES 1. Type of Flume. All flumes furnished under these speci- fications shall be made of metal and shall be of the semicircular, smooth-interior type. Bidders shall submit with their proposals a drawing or catalogue showing clearly the type of construction and detailed dimensions of the flume that they propose to fur- nish. Smoothness of interior surface and ease of erection will be important factors in the consideration of proposals. 2. Dimensions and Weight of Flume. The assembled flume shall have an interior diameter of .... feet .... inches, and the depth shall be that of the full semicircle. The bidder shall state the weight of the completed flume per linear foot. A com- plete flume shall consist of sheets, carrier rods, compression bars, shoes, nuts, and washers. 3. Thickness of Metal Sheets. The thickness of the metal sheets shall be sufficient to provide necessary rigidity and stiff- ness. The following minimum thicknesses shall be used: No. of Flume U. S. Standard Gage 24 to 60 22 72 to 108 v 20 120 to 156 18 168 to 204 16 216 and larger 14 For the larger sizes of flumes intermediate carrier rods or reinforc- ing ribs shall be furnished, if necessary, to maintain the true semicircular shape of the sheets when subjected to the full weight of water and the bidder shall submit a drawing or de- scription of the method of reinforcing he proposes to use. 4. Size of Carrier Rods and Compression Bars. Carrier rods shall be designed for a working stress of 8,000 pounds per square inch when subjected to the full weight of the water; provided that the smallest allowable carrier rod shall be %-inch in diameter, or its equivalent. Carrier rods shall be threaded at both ends and provided with nuts and washers. They shall be as strong in thread as in body. Compression bars shall be equivalent to or larger in cross-section than the corresponding carrier rods. Compression bars shall be provided with shoes for 356 WORKING DATA FOR IRRIGATION ENGINEERS distributing the pressures on supporting timbers. The size and shape of shoes and washers shall be such as to distribute prop- erly the pressures on the wooden timbers supporting the flume, and the average pressure on the timbers due to the full weight of the water in the flume shall not exceed 400 pounds per square inch. All carrier rods, compression bars, shoes, nuts, and washers shall be coated before shipment by being dipped when hot in a mixture of pure California asphalt, or its equivalent; not less than 7 per cent nor more than 10 per cent of pure lin- seed oil shall be mixed with the asphalt. Materials for coating shall be subject to the approval of the engineer. 5. Joints. The joints between successive sheets comprising the flume lining shall be designed to be rigid and water tight and shall offer the least possible obstruction to the flow of water through the flume. All necessary crimping of sheets to form the joints shall be done by the contractor. 6. Curves. The metal sheets for curved flumes shall be fabricated so as to conform exactly to the degree of curvature required. The engineer will furnish the contractor a list of lengths of flumes required of each degree of curvature, and the degree of curvature shall be plainly stamped on each sheet. 7. Materials for Sheets. The metal sheets shall be manu- factured from steel or pure iron, and shall be galvanized. The chemical and physical properties of the allowable mate- rials shall be as follows: Elements Considered Pure Iron Open-hearth Steel Bessemer Steel Carbon max. per cent .03 0.07 to 0.14 0.07 to 0.14 Manganese " " .03 0.34 to 0.46 1.00 Phosphorus " " .01 .03 .10 Sulphur " " .03 .05 .07 Silicon ' .01 .02 .02 Copper " " Recorded Recorded Recorded Ultimate strength 42,000-48,000 50,000-60,000 50,000-60,000 Elastic limit 22,000-30,000 25,000-35,000 25,000-35,000 Minimum elongation in 8" 25 per cent 25 per cent 25 per cent The material shall show great homogeneity of structure as exhibited by the ends of the broken test specimens. SPECIFICATIONS 357 8. Material for Compression Bars and Carrier Rods. These shall be made of medium steel and shall have an ultimate tensile strength of 55,000 to 65,000 pounds per square inch; an elastic limit of not less than one-half of the ultimate tensile strength; a minimum per cent of elongation in 8 inches of 1,400,000 divided by the ultimate strength; a silky fracture; and capability of being bent cold without fracture 180 around a pin having a diameter equal to the thickness of the test piece. 9. Material for Shoes and Washers. The bearing shoes and washers for compression bands and carrier rods may be made of either gray or malleable cast iron. Gray iron castings shall conform in all respects to the standard specifications for such castings adopted September 1, 1905, by the American Society for Testing Materials, except that no tensile test will be required. Malleable iron castings shall conform to the standard specifica- tions for such castings adopted November 15, 1904, by the American Society for Testing Materials. 10. Test Pieces. All test pieces shall be furnished by the contractor at his expense. The number and shape of test speci- mens for gray and malleable castings shall be as prescribed in the specifications of the American Society for Testing Materials specified in paragraph 9 hereof. For all other materials, at least one test specimen shall be taken from each melt, and where possible shall be cut from the finished material. Specimens not cut from finished material shall, in so far as possible, receive the same treatment before testing as the finished product. Ten- sile test pieces shall be % of an inch in diameter and shall have 8 inches of gage length. 11. Inspection and Tests. All necessary facilities and as- sistance for making inspection and tests shall be furnished to the engineer by the contractor at the expense of the contractor. Physical tests and chemicals analyses will be made by at its own expense; or they may be made at the factory by the contractor or his employees, acting under the direction of the engineer or his representative; or certified tests may, at the option of the engineer, be accepted in lieu of the above-mentioned tests. No material shall be shipped until all tests and final 358 WORKING DATA FOR IRRIGATION ENGINEERS inspection have been made, or certified tests shall have been accepted. 12. Galvanizing. The metal sheets shall have a coating of tight galvanizing. The grooving for joints and bending of sheets shall be done in such a manner as to avoid any injury^ to galvan- izing. All sheets on which the galvanizing is cracked or otherwise injured will be rejected. The galvanizing shall consist of a coat- ing of pure zinc evenly and uniformly applied in such a manner that it will adhere firmly to the surface of the metal. Each square foot of metal sheets shall hold not less than 1J/2 ounces of zinc. The galvanizing shall be of such quality that clean, dry samples of the galvanized metal shall appear^ black and show no copper-colored spots when they are four times alternately immersed for one minute in the standard copper sulphate solu- tion and then immediately washed in water and thoroughly dried. The coating shall fully and completely cover all surfaces of the material, and shall appear smooth and polished and be free from lumps of zinc. 13. Shipment. 14. Measurement and Payment. Payment will be made on the basis of the actual assembled length of flume measured along the center line and at the prices bid in the schedule. SPECIFICATIONS FOR STEEL HIGHWAY BRIDGES 1. Description. The bridge shall be of the { . nveted 1 ( pin-connected J I , ,[ truss type, having a span, center to center of end bearings, of .... feet .... inches, and a clear width between trusses of feet. The bridge shall consist of spans. 2. Stress Sheets and Loading. The bidder shall furnish with his bid a stress sheet showing the maximum stresses to which members are to be subjected, based on the following loading: / = span in feet. w = weight of steel per square foot of floor. SPECIFICATIONS 359 p = live load per square foot of floor. Dead load : w = not less than the actual weight of steel. Wooden floor =15 pounds per square foot. Live load: p = 100 io or a concentrated load of 30,000 pounds on two axles 8 feet center to center; with wheels spaced 6 feet center to center, and two-thirds of the load on one axle, assumed to occupy a space 16 feet in the direction of traffic by 12 feet at right angles thereto. Impact: for chords 25 per cent of uniform live load; for web and floor, 40 per cent of either uni- form or concentrated live load. Wind load: unloaded chord, 100 pounds per linear foot of bridge. loaded chord, 200 pounds per linear foot of bridge. Note. Neither wind nor concentrated loads are assumed to act simultaneously with uniform live load. 3. Detail Drawings. The contractor shall prepare all detail and shop drawings. Each proposal shall be accompanied, in addition to the stress sheets, by such general drawings of members and details as will clearly show the type of construction proposed at all points, and all items that are necessary to enable the engineer to determine the strength of all parts of the structure and whether, as a whole and in all its parts, it complies with these specifications. As soon as practicable after the award of the contract complete detail and shop drawings shall be furnished to the engineer by the contractor, and these shall receive the approval of the engineer before work is commenced. Working drawings shall be furnished in triplicate. The approval of gen- eral and working drawings shall not relieve the contractor from the responsibility of any errors therein. In case the engineer requires additional copies of drawings for use during construc- tion or for record these shall be furnished by the contractor with- out charge. 360 WORKING DATA FOR IRRIGATION ENGINEERS 4. Unit Stresses. The following limiting working stresses in pounds per square inch of net cross-section shall be used: Tension on rolled sections 16,000 Shear on rolled sections 9,000 Bearing on pins 20,000 Shear on pins 10,000 Bearing on shop rivets 20,000 Shear on shop rivets 10,000 Bearing on field rivets 15,000 Shear on field rivets 7,500 L Bearing on columns 16,000 70 Bearing on expansion rollers per linear inch 500 d d = diameter of roller in inches. L = unsupported length of column in inches. R = least radius of gyration in inches. No compression member shall have an unsupported length exceeding 120 times its least radius of gyration for main mem- bers, or 140 times its least radius of gyration for laterals. 5. Reversed Stresses. Members subject to reversion of stresses shall be designed to resist both tension and compression and each stress shall be increased by /(o of the smaller stress for determining the sectional area. The connections shall be de- signed for the arithmetical sum of the stresses. 6. Combined Stresses. Members subject to both direct and bending stresses shall be designed so that the greatest unit fiber stress shall not exceed the allowable unit stress for the member. 7. Net Sections. The net section of any tension flange or member shall be determined by a plane cutting the member square across at any point. The greatest number of rivet holes that can be cut by any such plane, or whose centers come nearer than 2 1/2 inches to said plane, are to be deducted from the cross-section when computing the net area. 8. Minimum Sizes. No metal less than /ie inch in thick- ness shall be used except for filling plates. The smallest angles used shall not be less than 2}/ X 2j^ X %e inches. A single angle shall never be used for a compression member. 9. Connections. All connections shall be designed to de- SPECIFICATIONS 361 velop the full strength of the members. Connecting plates shall be used for connecting all members, and in no case shall any two members be connected directly by their flanges. Angles subject to tensile stress shall be connected by both legs, otherwise only the section of the leg actually connected will be considered effective. 10. Portal Bracing. Portal bracing shall consist of straight members and shall be designed to transmit the full wind reaction from the upper lateral system into the end posts and abutments. The clear head room below portal and sway bracing for a width of 6 feet on either side of center line shall be not less than 15 feet. 11. Sway Bracing. Sway bracing of an approved type shall be provided at each panel point. 12. Lateral Systems. Upper and lower lateral systems shall be designed to resist the maximum wind pressures from either direction. The members shall be as nearly as practicable in the plane of the axes of the chords. 13. Floor System. All floor beams and stringers shall be rolled or riveted steel girders. Floor beams shall be rigidly connected to the trusses and stringers shall be rigidly connected to the floor beams. 14. Intersection of Axes of Members. The axes of all mem- bers of trusses, and those of lateral systems coming together at any apex of a truss or girder must intersect at a point whenever such an arrangement is practicable, otherwise all induced stresses and bend of members caused by the eccentricity must be. pro- vided for. 15. Batten Plates and Lattice Bars. The open sides of com- pression members shall be stayed by batten plates at the ends and by diagonal lattice bars at intermediate points. Batten plates shall be used at intermediate points when, for any reason, the latticing is interrupted. Lattice bars shall be inclined to the member not less than 60 for single latticing nor less than 45 for double latticing. 1 6. Eyebars. The thickness of eyebars shall be not less than % inch nor less than l / 7 the width of the bar. Heads of eyebars shall be formed by upsetting and forging and shall be so proper- 362 WORKING DATA FOR IRRIGATION ENGINEERS tioned as to develop the full strength of the bar. Eyebars shall be perfectly straight at the time they are bored, and all bars composing one member shall be piled, clamped together, and bored in one operation. The eyebars composing a member shall be so arranged that their surfaces are not in contact. 17. Rods. No rod shall be used which has a cross-sectional area less than % square inch. Screw-ends shall be stronger in thread than in body. 1 8. Riveting. The rivets used shall in general be % inch in diameter; smaller ones being allowable where made necessary by the size of the member, but no rivets smaller than % inch in diameter shall be used in legs of an angle iron equal to or greater than 3^ inches wide. Not less than three rivets shall be used in any main truss, portal, or lower lateral connection or in any compression strut or sway bracing, portal bracing, or upper lateral system connection. The pitch of rivets in all classes of work in the direction of the stress shall never exceed 6 inches nor be less than three diameters of the rivet. At the ends of compression members it shall not exceed four times the diameter of the rivets for a length equal to twice the width of the member. No rivet-hole center shall be less than one and one-half diameters from the edge of the plate, and whenever practicable this distance is to be increased to two diameters. The rivets when driven must completely fill the holes. The rivet heads must be round, and they must be of uniform size for the same size rivets throughout the work; they must be neatly made and concentric with the rivets and must thoroughly pinch the connected pieces together. Whenever possible, all rivets shall be machine driven. No rivet excepting those in shoe plates and roller and bed plates is to have a smaller diameter than the thickness of the thickest plate through which it passes. The effective diameter of any rivet shall be assumed the same as its diameter before driving, but in making deductions for rivet holes in tension members the diameter of the hole shall be assumed % inch larger than that of the rivet. The amount of field riveting shall be reduced to a minimum, and all details are to be made so that the field rivets can be driven readily. Rivets shall not be used in direct ten- sion. The contractor will be held responsible for the correct SPECIFICATIONS 363 fitting of all parts upon assembly in the field, and, if necessary to insure this, all members shall be assembled in the shop, and fitted before shipment. 19. Pins. All pins shall be turned smoothly to a gage and shall be finished perfectly round, smooth, and straight. All pins up to and including 3j/ inches in diameter shall fit the pin-holes within 1/50 inch; all pins over 3^2 inches in diameter shall fit their holes within 1/32 inch. The contractor must provide steel-pilot nuts for all pins to preserve the threads while the pins are being driven. 20. Camber. All trusses shall be cambered by making the top-chord section longer than the corresponding bottom-chord section by /{ 6 inch for each 10 feet of length. 21. Expansion and Contraction. Provision shall be made for changes in length due to temperature variations of at least y* inch for each 10 feet of span. 22. Roller Ends. Each truss of more than 60 feet span shall be provided with one roller end. For spans 60 feet and less a sliding end may be used. Rollers shall be turned accurately to gage and must be finished perfectly round and to the correct diameter or diameters from end to end. The tongues and grooves in plates and rollers must fit snugly so as to prevent lateral motion. Roller beds must be planed. The smallest allowable diameter of expansion rollers is 3^2 inches. 23. Anchorages. Every span must be anchored at each end to the pier or abutment in such a manner as to prevent lateral motion, but so as not to interfere with the longitudinal motion of the truss due to changes of temperature. The shoes or bolsters shall be so located that the anchor bolts will occupy a central position in the slotted holes at a temperature of 40 F. Bedplates shall be designed to distribute the load over a sufficient area to keep the pressure on the masonry below 400 pounds per square inch. 24. Hand Railing. A suitable latticed hand railing shall be provided for each truss. 25. Shop Painting. Before leaving the shop all structural steel, except as below specified, shall be thoroughly cleaned of all loose scales and rust and given one coat of good iron ore paint 364 WORKING DATA FOR IRRIGATION ENGINEERS mixed with pure linseed oil, which shall be well worked into all joints and open spaces. All surfaces of steel that will come in contact with each other shall be painted before being riveted or bolted together. Pins, pinholes, screw threads, and all finished surfaces shall not be painted, but shall be coated with white lead and tallow as soon as they are finished. MATERIAL 26. Manufacture. Structural steel shall be made by the open-hearth process and shall conform in all respects, not spe- cifically mentioned herein, to the " Standard Specifications for Structural Steel for Bridges of the American Society for Testing Materials," adopted August 25, 1913. 27. Physical and Chemical Properties of Structural Steel. Steel shall contain not more than 0.05 per cent sulphur, and not more than 0.04 per cent phosphorus for basic open-hearth nor more than 0.06 per cent phosphorus for acid open-hearth. It shall have an ultimate tensile strength of 55,000 to 65,000 pounds per square inch; an elastic limit as indicated by the drop of beam of not less than one-half the ultimate tensile strength; a mini- mum per cent of elongation in 8 inches of 1,500,000 divided by the ultimate tensile strength; a silky fracture and capability of being bent cold without fracture 180 flat on itself for material % inch thick and under; for material over % inch to and including 1 % inches around a pin having a diameter equal to the thickness of the test piece; and for material over lj^ inches thick, around a pin having a diameter equal to twice the thick- ness of the test piece. A deduction of 2.5 will be allowed in the specified percentage of elongation for each /( 6 inch in thickness below /{ 6 inch and a deduction of 1 will be allowed for each H inch in thickness above % inch. 28. Physical and Chemical Properties of Rivet Steel. Rivet steel shall contain not more than .04 per cent each of sulphur and phosphorus. It shall have an ultimate tensile strength of 45,000 to 55,000 pounds per square inch; an elastic limit as determined by the drop of beam of not less than one-half the ultimate tensile strength; a minimum per cent of elongation in 8 inches of 1,500,000 divided by the ultimate tensile strength; SPECIFICATIONS 365 a silky fracture; and capability of being bent cold without fracture 180 flat on itself. 29. Finish. Finished material must be free from injurious seams, flaws, or cracks, and have a workmanlike finish. 30. Marking. Every finished piece of steel shall have the melt number stamped or rolled upon it. Steel for pins and rollers shall be stamped on the end. Rivet steel and other small parts may be bundled, with the above marks on an attached metal tag. 31. Test Pieces. (This paragraph should state who is to furnish test pieces and how many, and what disposition is to be made of the broken test specimens, etc.) 32. Tests. (This paragraph should state who is to make tests, at whose expense tests are to be made, etc.) 33. Shipment. 34. Payment for Fabricated Material. t i ERECTION 35. Material and Labor. The contractor shall furnish all labor, tools, machinery, and materials, except wood flooring, for erecting the bridge complete in place, including all hauling, erection, and dismantling of all falsework and staging, setting of anchor bolts, and all other work necessary for the completion of the structure ready for traffic. 36. Wood Floor. Lumber for flooring shall be furnished, and put in place by the contractor and he shall furnish all necessary fastenings. Flooring shall be 4 inches thick and shall be of sound timbers of good grade, rough. A 4 x 8 inch wheel-guard shall be placed adjacent to each truss. 37. Painting After Erection. After erection all metal work shall be thoroughly cleaned of mud, grease, and other objection- able matter and evenly painted with two coats of paint of the kind and colors specified by the engineer. Linseed oil shall be used as the vehicle in mixing the paint for each of these coats, and the separate coats shall have distinctly different shades of color. All recesses which might retain water shall be filled with thick paint or some water-proof material before final painting. The first coat shall be allowed to become thoroughly dry before 366 WORKING DATA FOR IRRIGATION ENGINEERS the second coat is applied. No painting shall be done in wet or freezing weather. 38. Final Payment. SPECIFICATIONS FOR CONCRETE 1. Composition. Concrete shall be composed of cement, sand, and broken rock or clean gravel, well mixed and brought to a proper consistency by the addition of water. Ordinarily one part by volume, measured loose, of cement shall be used with parts of sand and parts of broken rock or gravel. These proportions may be modified by the engineer as the work or the nature of the materials used may render it desirable, and the contractor shall not be entitled to any extra compensation by reason of such modifications. (Note. // the contractor furnishes the cement this paragraph must be modified to provide for different prices for different mix- tures.) 2. Cement. (See specifications for cement.) 3. Reinforcement Bars. Steel bars shall be placed in the concrete wherever shown in the drawings or prescribed by the engineer. The exact position and shape of reinforcement bars are not shown in all cases in the drawings accompanying these specifications, but the contractor will be furnished supple- mental detailed drawings and lists which will give him the infor- mation necessary for cutting, bending, and spacing of bars. The steel used for concrete reinforcement shall be so secured in position that it will not be displaced during the depositing of the concrete, and special care shall be exercised to prevent any disturbance of the steel in concrete that has already been placed. 4. Sand. Sand for concrete may be obtained from natural deposits or may be made by crushing suitable rock. The sand particles shall be hard, dense, durable rock fragments, such as will pass a ^-mch mesh screen. The sand must be free from organic matter and must not contain more than 5 per cent of clayey and other objectionable non-organic material. The sand must be so graded that when dry and well shaken its voids will not exceed 35 per cent. 5. Broken Rock or Gravel. The broken rock or gravel for SPECIFICATIONS 367 concrete must be hard, dense, durable rock fragments or pebbles that will pass through a -inch mesh screen when used for plain concrete, and through a -inch mesh screen when used for reinforced concrete, and that will be rejected by a J^-inch mesh screen. 6. Water. The water used in mixing concrete must be reasonably clean and free from objectionable quantities of or- ganic matter, alkali salts, and other impurities. 7. Mixing. The cement, sand, and broken rock or gravel shall be so mixed and the quantities of water added shall be such as to produce a homogeneous mass of uniform consistency. Dirt and other foreign substance shall be carefully excluded. Machine mixing will be required unless specific authority to use hand mixing is given by the engineer. The machine and its operation shall be subject to the approval of the engineer. Hand mixing, if permitted, shall be thorough and shall be done on a clean, tight floor. In general, enough water shall be used in mixing to give the concrete the consistency ordinarily designated as " wet." Concrete containing a minimum amount of water, ordinarily designated as " dry " concrete, will be permitted only where the nature of the work renders the use of " wet " concrete impracticable. If concrete is mixed in freezing weather, the materials shall be heated sufficiently before mixing to remove all frost and maintain a temperature above 32 F., until the concrete has been placed in the work and has attained its final set. 8. Placing. Concrete shall be placed in the work before the cement takes its initial set. No concrete shall be placed in water except by permission of the engineer and the method of depositing the same shall be subject to his approval. Foundation surfaces upon which concrete is to be placed must be free from mud and debris. When the placing of concrete is to be inter- rupted long enough for the concrete to take its final set, the working face shall be given a shape, by the use of forms or other means, at the option of the engineer, that will secure proper union with subsequent work. All concrete surfaces upon or against which concrete is to be placed and to which the new concrete is to adhere, shall be roughened, thoroughly 368 WORKING DATA FOR IRRIGATION ENGINEERS cleaned, and wet before the concrete is deposited. " Dry " concrete shall be deposited in layers not exceeding 6 inches in thickness, each of which shall be rammed until water appears on the surface. " Wet " concrete shall be stirred with suitable tamping bars, shovels, or forked tools until it completely fills the form, closes snugly against all surfaces, and is in perfect and complete contact with any steel used for reinforcement. Where smooth surfaces are required a suitable tool shall be worked up and down next to the form until the coarser material is forced back and a mortar layer is brought next to the form. No concrete shall be placed except in the presence of a duly authorized inspector. 9. Finishing. The surface of concrete finished against forms must be smooth, free from projections, and thoroughly filled with mortar. Immediately upon the removal of forms all voids shall be neatly filled with cement mortar, irregularities in exposed surfaces shall be removed and minor imperfections of finish shall be smoothed to the satisfaction of the engineer. Exposed surfaces of concrete not finished against forms, such as horizontal or sloping surfaces, shall be brought to a uniform surface and worked with suitable tools to a smooth mortar finish. All sharp angles where required shall be rounded or bevelled by the use of moulding strips or suitable moulding or finishing tools. 10. Protection. The contractor shall protect all concrete against injury. Exposed surfaces of concrete shall be protected from the direct rays of the sun and shall be kept damp for at least two weeks after the concrete has been placed. Concrete laid in cold weather shall be protected from freezing by such means as are approved by the engineer. All damage to concrete shall be repaired by the contractor at his expense, in a manner satisfactory to the engineer. 11. Forms. Forms to confine the concrete and shape it to the required lines shall be used wherever necessary. Where the character of the material cut into to receive a concrete structure is such that it can be trimmed to the prescribed lines, the use of forms will not be required. The forms shall be of sufficient strength and rigidity to hold the concrete and to withstand the necessary pressure and ramming without deflection from the SPECIFICATIONS 369 prescribed lines. For concrete surfaces that will be exposed to view and for all other concrete surfaces that are to be finished smooth, the lagging of forms must be surfaced and bevel-edged or matched; provided that smooth metal forms may be used if desired. All forms shall be removed by the contractor, but not until the engineer gives permission. Forms may be used repeat- edly, provided they are maintained in serviceable condition and thoroughly cleaned before being re-used. 12. Measurement. Concrete will be measured for payment to the neat lines shown in the drawings or prescribed by the engineer under these specifications. No payments will be made for concrete outside of the prescribed lines. 13. Payment. The unit price bid for concrete shall include all material and labor entering into its construction. SPECIFICATIONS FOR PAVING 1. Dry Paving. Where shown in the drawings and where directed by the engineer, dry paving shall be placed on the embankment slopes and on the beds and banks of canals and other watercourses. The rock used for paving shall be clean, hard, dense, and durable. The dimensions of paving stone normal to the face of the pavement shall be not less than inches. They shall have an average volume of not less than of a cubic foot, not more than 25 per cent of the pieces being less than .... of a cubic foot in volume. Either boulders or quarried rock may be used if fulfilling the requirements as to quality and dimensions. If quarried rock is used, the stones shall have roughly squared, reasonably flat, upper faces. The stones shall be bedded in a layer of sand and gravel or unscreened crushed rock, having an average thickness of not less than .... inches. They shall be hand placed with close joints to the lines and grades established by the engineer, and the spaces between the stones shall be filled with spalls and gravel or crushed rock. The thickness of the paving, including the gravel layer, shall be not less than .... inches. Payment for dry paving will be made at the unit prices per square yard bid therefor in the schedules. 2. Grouted Paving. Where shown in the drawings and where directed by the engineer, grouted paving shall be placed on the 370 WORKING DATA FOR IRRIGATION ENGINEERS embankment slopes and on the beds and banks of canals and other watercourses. The rock used for paving shall be clean, hard, dense, and durable. The dimension of paving stones normal to the face of the pavement shall be not less than .... inches. They shall have an average volume of not less than .... of a cubic foot, not more than 25 per cent of the pieces being less than .... of a cubic foot in volume. Either boulders or quarried rock may be used if fulfilling the requirements as to quality and dimensions. If quarried rock is used, the stones shall have roughly squared, reasonably flat, upper faces. The stones shall be bedded in a layer of sand and gravel or unscreened crushed rock, having an average thickness of not less than .... inches. They shall be hand placed with close joints to the lines and grades established by the engineer and the spaces between the stones shall be filled with spalls and gravel or crushed rock, from which the sand or fine material has been removed by screening,, after which a mortar, composed of three parts sand and one part cement, shall be poured into the voids so as to form a water-tight surface. After the cement mortar has been added the paving shall be kept moist for forty-eight hours after the cement has reached its permanent set. The thickness of paving, including the gravel layer, shall be not less than inches. Payment for grouted paving will be made at the unit prices per square yard bid therefor in the schedules. 3. Rubble Concrete Paving. Where shown in the drawings and where directed by the engineer, rubble concrete paving shall be placed on the embankment slopes and on the beds and banks of canals and other watercourses. The rock used for paving shall be clean, hard, dense, and durable. The dimension of paving stones normal to the face of the paving shall be not less than .... inches. They shall have an average volume of not less than .... of a cubic foot, not more than 25 per cent of the pieces being less than of a cubic foot in volume. Either boulders or quarried rock may be used if fulfilling the require- ments as to quality and dimensions. If quarried rock is used the stones shall have roughly squared, reasonably flat, upper faces. The paving shall have a foundation course of sand and gravel or unscreened crushed rock not less than . . inches in thickness. SPECIFICATIONS 371 Upon this foundation course shall be placed a layer of concrete inches thick. The paving stones shall be bedded in this concrete before the concrete has taken its initial set. The stones shall be hand placed with close joints to the lines and grades established by the engineer and the spaces between- the stones shall be filled with spalls or with gravel or crushed rock from which the sand or fine material has been removed by screening, after which a mortar composed of three parts sand and one part cement shall be poured into the voids so as to form a water-tight surface. After the cement mortar has been added, the paving shall be kept moist for forty-eight hours after the cement has reached its permanent set. The thickness of paving, including the gravel layer shall be not less than .... inches. Payment for rubble-concrete paving will be made at the unit prices per square yard bid therefor in the schedule. SPECIFICATIONS FOR CEMENT 1. Definition. The cement shall be the product obtained by finely pulverized clinker produced by calcining to incipient fusion, an intimate mixture of properly proportioned argillaceous and calcareous substances, with only such additions subsequent to calcining as may be necessary to control certain properties. Such additions shall not exceed 3 per cent, by weight, of the calcined product. 2. Composition. In the finished cement, the following limits shall not be exceeded: Per cent Loss on ignition for 15 minutes 4 Insoluble residue 1 Sulphuric anhydride (SO 3 ) 1.75 Magnesia (MgO) 4 3. Specific Gravity. The specific gravity of the cement shall be not less than 3.10. Should the cement as received fall below this requirement, a second test may be made upon a sample heated for thirty minutes at a very dull red heat. 4. , Fineness. At least 92 per cent of the cement by weight shall pass through the No. 100 sieve, and at least 75 per cent shall pass through the No. 200 sieve. 372 WORKING DATA FOR IRRIGATION ENGINEERS 5. Soundness. Pats of neat cement prepared and treated as hereinafter prescribed shall remain firm and hard and show no sign of distortion, checking, cracking, or disintegration. If the cement fails to meet the prescribed steaming test, the cement may be rejected or the steaming test repeated after seven or more days, at the option of the engineer. 6. Time of Setting. The cement shall not acquire its initial set in less than forty-five minutes and must have acquired its final set within ten hours. 7. Tensile Strength. Briquettes made of neat cement, after being kept in moist air for twenty-four hours and the rest of the time in water, shall develop tensile strengths per square inch as follows : Pounds After seven days 500 After twenty-eight days 600 Briquettes made up of one part cement and three parts standard Ottawa sand, by weight, shall develop tensile strengths per square inch as follows : Pounds After seven days 200 After twenty-eight days 275 The average of the tensile strengths developed at each age by the briquettes in any set made from one sample is to be con- sidered the strength of the sample at that age, excluding any results that are manifestly faulty. The average strength of the sand mortar briquettes at twenty-eight days shall show an increase over the average strength at seven days. 8. Brand. Bids for furnishing cement or for doing work in which cement is to be used shall state the brand of cement pro- posed to be furnished and the mill at which made. The right is reserved to reject any cement which has not established itself as a high-grade Portland cement, and has not been made by the same mill for two years and given satisfaction in use for at least one year under climatic and other conditions at least equal in severity to those of the work proposed. , 9. Packages. The cement shall be delivered in sacks, bar- rels, or other suitable packages (to be specified by the engineer), SPECIFICATIONS 373 and shall be dry and free from lumps. Each package shall be plainly labelled with the name of the brand and of the manufac- turer. A sack of cement shall contain 94 pounds net. A barrel shall contain 376 pounds net. Any package that is short weight or broken, or that contains damaged cement, may be rejected, or accepted as a fractional package, at the option of the engineer. If the cement is delivered in cloth sacks, the sacks used shall be strong and serviceable and securely tied, and the empty sacks will, if practicable, be returned to the contractor at the point of delivery of the cement. On final settlement under the con- tract, ten cents will be paid the contractor for each sack furnished by him in accordance with the above requirements and not re- turned in serviceable condition. 10. Inspection. The cement shall be tested in accordance with the standard methods hereinafter prescribed. In general the cement will be inspected and tested after delivery, but partial or complete inspection at the mill may be called for in the speci- fications or contract. Tests may be made to determine the chemical composition, specific gravity, fineness, soundness, time of setting, and tensile strength, and a cement may be rejected in case it fails to meet any of the specified requirements. An agent of the contractor may be present at the making of the tests or they may be repeated in his presence. 11. Sampling. The selection of the samples for testing will be left to the engineer. The number of packages sampled and the quantity to be taken from each package will depend on the importance of the work, the number of tests to be made, and the facilities for making them. The samples should be so taken as to represent fairly the material, and, where conditions permit, at least one barrel in every fifty should be sampled. Before tests are made, samples shall be passed through a sieve having twenty meshes per linear inch to remove foreign material. Sam- ples shall be tested separately for physical qualities, but for chemical analysis mixed samples may be used. Every sample should be tested for soundness, but the number of tests for other qualities will be left to the discretion of the engineer. 12. Chemical Analysis. The method to be followed for the analysis of cement shall be that proposed by the Committee on 374 WORKING DATA FOR IRRIGATION ENGINEERS Uniformity in the Analysis of Materials for the Portland Cement Industry, reported in Tlie Journal of the Society for Chemical Industry, Vol. 21, p. 12, 1902, and published in Engineering News, Vol. 50, p. 60, 1903, and in The Engineering Record, Vol. 48, p. 49, 1903. The insoluble residue shall be determined on a 1-gram sample, which is digested on the steam bath in hydro- chloric acid of approximately 1.035 specific gravity until the cement is dissolved. The residue is filtered, washed with hot water, and the filter-paper contents digested oh the steam bath in a 5-per-cent solution of sodium carbonate. The residue is then filtered, washed with hot water, then with hot hydrochloric acid, approximately of 1.035 specific gravity, and finally with hot water, then ignited and weighed. The quantity so obtained is the insoluble residue. 13. Determination of Specific Gravity. The determination of specific gravity may be made with a standardized apparatus of Le Chatelier or other equally accurate form. Benzine (62 Baume naphtha), or kerosene free from water, should be used in making the determination. The cement should be allowed to pass slowly into the liquid of the volumenometer, taking care that the powder does not adhere to the sides of the graduated tube above the liquid and that the funnel through which it is introduced does not touch the liquid. The tem- perature of the liquid in the flask should not vary more than 1 F. during the operation. To this end the flask should be im- mersed in water. The results of repeated tests should agree within 0.01.* If the specific gravity of the cement as received is less than 3.10, a redetermination may be made as follows: Seventy grams of the cement is placed in a nickel or platinum crucible about 2 inches in diameter and heated for thirty minutes * Under the metric system the specific gravity of a solid is expressed math- ematically by the weight in grams of 1 cubic centimeter of the substance of the solid. Therefore, in using a volumenometer graduated to show volume, or displacement, in cubic centimeters: Weight of substance used, in grams Specific gravity = - : : Displacement in cubic centimeters. In the standard Le Chatelier volumenometer 64 grams of Portland cement are taken. SPECIFICATIONS 375 at a temperature between 419 C. and 630 C. After the cement has cooled to atmospheric temperature the specific gravity shall be determined in the same manner as described above. The cement should be heated in a muffle or other suitable furnace, the temperature of which is to be maintained above the melting point of zinc (419 C.) but below the melting point of antimony 630 C.)- This maximum temperature can be recognized as a very dull red which is just discernible in the dark. 14. Determination of Fineness. The No. 100 and No. 200 sieves shall conform to the standard sieve specifications of the Bureau of Standards, Department of Commerce. The deter- mination of fineness should be made on a 50-gram sample, which may be dried at a temperature of 100 C. (212 F.), prior to sifting. The coarsely screened sample should be weighed and placed on the No. 200 sieve, which, with the pan and cover attached, should beheld in one hand hi a slightly inclined position and moved forward and backward in the plane of inclination, at the same time striking the side gently about 200 times per minute against the palm of the other hand on the upstroke. The oper- ation is to be continued until not more than 0.05 gram will pass through in one minute. The residue should be weighed, then placed on the No. 100 sieve, and the operation repeated. The sieves should be thoroughly dry and clean. Determination of fineness may be made by washing the cement through the sieve or by a mechanical sifting device which has been previously standardized with the results obtained by hand sifting on equiv- alent samples. In case of the failure of the cement to pass the fineness requirements by the washing method or the mechanical device, it shall be tested by hand. 15. Mixing Cement Pastes and Mortars. The quantity of cement or cement and sand to be used in the paste or mortar should be expressed in grams and the quantity of water in cubic centimeters. The material should be weighed, placed upon a non-absorbent surface, thoroughly mixed dry if sand be used, and a crater formed in the center, into which the proper percentage of clean water should be poured; the material on the outer edge should be turned into the crater by the aid of a trowel. As soon as the water has been absorbed, the operation should be completed 376 WORKING DATA FOR IRRIGATION ENGINEERS by vigorously mixing with the hands for one minute and a half. During the operation of mixing, the hands should be protected by rubber gloves. The temperature of the room and the mixing water should be maintained as nearly as practicable at 21 C. (70 F.). 1 6. Determination of Normal Consistency. The normal consistency for neat paste to be used in making briquettes and pats should be determined by the ball method, as follows: A quantity of cement paste should be mixed in the manner de- scribed in paragraph 15, and quickly formed into a ball about 2 inches in diameter. The ball should then be dropped upon a hard, smooth, and flat surface from a height of 2 feet. The paste is of normal consistency when the ball does not crack and does not flatten more than one-half of its original diameter. Trial pastes should be made with varying percentages of water, until the correct consistency is obtained. The percentage of water to be used in mixing mortars for sand briquettes is given by the formula: in which y is the percentage of water required for the sand mortar; P is the percentage of water required for neat cement paste of normal consistency; n is the number of parts of sand to one of cement by weight, and K is a constant which for standard Ottawa sand has the value of 6.5. The percentage of water to be used for mortars containing three parts standard Ottawa sand, by weight, to one of cement is indicated in the following statement: Percentage of Water for Neat Cement Paste 18 Percentage of Water for 1 to 3 Mortars of Standard Ottawa Sand 9.5 Percentage of Water for Neat Cement Paste 24 Percentage of Water for 1 to 3 Mortars of Standard Ottawa Sand 10 5 19 9.7 25. ... 10 7 20 9.8 26 10 8 21. 10 27 11 22 . . . 10 2 28 11 2 23.. ..10.3 29.. ..11.3 SPECIFICATIONS 377 17. Determination of Soundness. Pats of neat cement paste of normal consistency about 3 inches in diameter, J^ inch in thickness at the center, and tapering to a thin edge, should be kept in moist air for a period of twenty-four hours. One pat should then be kept in air and a second in water, at the ordinary temperature of the laboratory not to vary greatly from 21 C. (70 F.), and both observed at intervals for at least twenty- eight days. A third pat should be exposed to steam at atmos- pheric pressure above boiling water for five hours. 18. Determination of Time of Setting. The time of setting should be determined by the standardized Gilmore* needles, as follows: A pat of neat cement paste about 3 inches in diameter and y^ inch in thickness with flat top, mixed at normal con- sistency, should be kept in moist air, at a temperature main- tained as nearly as practicable at 21 C. (70 F.). The cement is considered to have acquired its initial set when the pat will bear, without appreciable indentation, a needle /fc of an inch in diameter loaded to weigh J^ of a pound. The final set has been acquired when the pat will bear, without appreciable indentation, a needle /24 of an inch in diameter, loaded to weigh 1 pound. In making the test the needle should be held in a vertical position and applied lightly to the surface of the pat. The pats made for the soundness test may be used to determine the time of setting. 19. Tensile Tests. Tensile tests should be made on an approved machine. The test pieces shall be briquettes of the form recommended by the Committee on Uniform Tests of Cement of the American Society of Civil Engineers, and illus- trated in Circular 33 of the Bureau of Standards. The briquettes shall be made of paste or mortar of normal consistency. Imme- diately after mixing, the paste or mortar should be placed in the moulds, pressed in firmly by the fingers and smoothed off with a trowel without mechanical ramming. The material should be heaped above the mould, and, in smoothing off, the trowel should be drawn over the mould in such a manner as to exert a moderate pressure on the material. The moulds should be * The Gilmore needle is specified in Government specifications. Other specifications specify the Vicat needle. 378 WORKING DATA FOR IRRIGATION ENGINEERS turned over and the operation of heaping and smoothing off repeated. Not less than three briquettes should be made and tested for each sample for each period of test. The neat tests are not considered as important as the sand tests. The briquettes should be broken as soon as they are removed from the water. The load should be applied at the rate of 600 pounds per minute. 20. Storage of Test Pieces. During the first twenty-four hours after moulding the test pieces should be kept in air suffi- ciently moist to prevent them from drying. After twenty-four hours in moist air the test pieces should be immersed in water. The air and water should be maintained as nearly as practical at21C. (70 F.). 21. Standard Sand. The sand to be used shall be natural sand from Ottawa, Illinois, screened to pass a No. 20 sieve and retained on a No. 30 sieve. Sand having passed the No. 20 sieve shall be considered standard when not more than 2 grams pass the No. 30 sieve after one minute continuous sifting of a 200- gram sample. The No. 20 and No. 30 sieves shall conform to the standard sieve specifications of the Bureau of Standards, Depart- ment of Commerce. SPECIFICATIONS FOR TIMBER PILES i. Timber Piles. Piles shall be cut from sound trees; shall be close-grained and solid; free from injurious ring shakes, large and unsound or loose knots, decay, or other defects that may materially impair their strength or durability. The piles shall be cut above the ground swell and have a uniform taper from butt to tip. Short bends or bends in two directions will not be al- lowed. A line drawn from the center of the butt to the center of the tip shall lie wholly within the body of the pile. Piles shall be peeled soon after cutting. All knots shall be trimmed close to the body of the pile. The minimum diameter at the tip shall be 9 inches for lengths not exceeding 30 feet, 8 inches for lengths over 30 feet but not exceeding 50 feet, and 7 inches for lengths over 50 feet. The minimum diameter at one-quarter of the length from the butt shall be 12 inches and the maximum diameter at the butt 20 inches. (Note. The kind of timber to be specified depends upon the locality.} SPECIFICATIONS 379 SPECIFICATIONS FOR STRUCTURAL STEEL (Based on " Standard Specifications for Structural Steel for Buildings" of the American Society for Testing Materials, adopted August 25, 1913.) 1. Manufacture. Structural steel may be made by either the open-hearth or Bessemer process. Rivet steel and plate or angle material over % inch thick, which is punched, shall be made by the open-hearth process. The steel shall conform in all respects, not specifically mentioned herein, to the " Standard Specifications for Structural Steel for Buildings " of the American Society for Testing Materials, adopted August 25, 1913, and tests shall be made as provided in said specifications. 2. Chemical and Physical Properties of Structural Steel. Steel made by the Bessemer process shall contain not more than 0.10 per cent phosphorus and steel made by the open-hearth process shall contain not more than 0.06 per cent phosphorus. All structural steel shall have an ultimate tensile strength of 55,000 to 65,000 pounds per square inch; an elastic limit, as determined by the drop of the beam, of not less than one-half the ultimate tensile strength; a minimum per cent of elongation in 8 inches of 1,400,000 divided by the ultimate tensile strength; a silky fracture; and capability of being bent cold without fracture 180 flat on itself for J^-inch material and under; around a pin having a diameter equal to the thickness of the test piece for material over % inch to and including 1^ inches; and around a pin having a diameter equal to twice the thickness of the test piece for material over 1J4 inches in thickness. A deduction of 1 from the specified percentage of elongation will be allowed for each % inch in thickness above % inch; and a deduction of 2.5 will be allowed for each /{ 6 inch in thickness below % Q inch. 3. Chemical and Physical Properties of Rivet Steel. Rivet steel shall contain not more than 0.06 per cent phosphorus nor more than 0.045 per cent sulphur. It shall have an ultimate tensile strength of 48,000 to 58,000 pounds per square inch; an elastic limit of one-half the ultimate tensile strength; a mini- mum per cent of elongation in 8 inches of 1,400,000 divided by 380 WORKING DATA FOR IRRIGATION ENGINEERS the ultimate tensile strength; a silky fracture; and capability of being bent cold without fracture 180 flat on itself. 4. Finish. Finished material must be free from injurious seams, flaws, or cracks, and have a workmanlike finish. 5. Marking. Every finished piece of steel shall be stamped with the melt or blow number, except that small pieces may be shipped in bundles securely wired together with the melt or blow number on a metal tag attached. 6. Test Pieces. (This paragraph should state who is to furnish test pieces, what disposition is to be made of broken test specimens, etc.) 7. Tests. (This paragraph should state who will make tests, at whose expense tests will be made, etc.) 8. Shipment. 9. Payment. SPECIFICATIONS FOR STEEL REINFORCEMENT BARS (Based on " Standard Specifications for Billet-Steel Concrete Re- inforcement Bars " of the American Society for Testing Ma- terials, adopted August 25, 1913.) 1. Manufacture. Steel may be made by either the open- hearth or Bessemer process and the bars shall be rolled from billets. It shall conform in all respects, not specifically men- tioned herein, to the "Standard Specifications for Billet-Steel Concrete Reinforcement Bars " of the American Society for Testing Materials adopted August 25, 1913, and tests shall.be made as provided in said specifications. 2. Type of Bars. All reinforcement bars shall be of the deformed type. Bidders shall submit samples or cuts of the type of bar they propose to furnish. 3. Chemical Properties. Bars of steel made by the Besse- mer process shall contain not more than 0.10 per cent phosphorus, and not more than 0.05 per cent phosphorus if made by the open- hearth process. 4. Physical Properties. Bars of steel shall have an ultimate tensile strength of 55,000 to 70,000 pounds per square inch; an elastic limit of not less than 33,000 pounds per square inch; a SPECIFICATIONS 381 minimum per cent of elongation in 8 inches of 1,250,000 divided by the ultimate tensile strength; and capability of being bent cold without fracture 180 around a pin having a diameter equal to the thickness of the test piece for material less than % inch in thickness, and around a pin having a diameter equal to twice the thickness of the test piece for material of % mcri an d over in thickness. For each increase of ^ inch in diameter or thickness above M inch and for each decrease of /{ 6 inch in di- ameter or thickness below /(e inch, a deduction of 1 will be allowed from the specified percentage of elongation. 5. Variation in Weight. Bars for reinforcement are subject to rejection if the actual weight of any lot varies more than 5 per cent over or under the theoretical weight of that lot. 6. Finish. Finished material shall be free from injurious seams, flaws, or cracks, and shall have a workmanlike finish. 7. Test Pieces. (See " Structural Steel.") 8. Tests. (See " Structural Steel") 9. Shipment 10. Payment. SPECIFICATIONS FOR GRAY-IRON CASTINGS (Based on " Standard Specifications for Gray-Iron Castings " of the American Society for Testing Materials, adopted Sep- tember 1, 1903.) 1. Manufacture. Castings shall be of tough gray iron made by the cupola process. In all respects, not specifically mentioned herein, the castings shall conform to the " Standard Specifica- tions for Gray-Iron Castings " of the American Society for Testing Materials, adopted September 1, 1901, and tests shall be made as provided in said specifications. 2. Light Castings, Physical and Chemical Properties. Cast- ings having any section less than J/ inch thick shall be known as light castings. The sulphur content shall be not greater than 0.08 per cent. The minimum breaking load of a bar l^t inches in diameter, loaded at the middle of a 12-inch span, shall be 2,500 pounds. The deflection shall in no case be less than 0.1 inch. 3. Heavy Castings, Physical and Chemical Properties. Castings in which no section is less than 2 inches thick shall be 382 WORKING DATA FOR IRRIGATION ENGINEERS known as heavy castings. The sulphur content shall be not greater than 0.12 per cent. The minimum breaking load of a bar 1J4 inches in diameter, loaded at the middle of a 12-inch span, shall be 3,300 pounds. The deflection shall in no case be less than 0.1 inch. 4. Medium Castings, Physical and Chemical Properties. Medium castings are those not included under " light " or " heavy " castings. Their sulphur content shall be not greater than 0.10 per cent. The minimum breaking load of a bar 1}^ inches in diameter loaded at the middle of a 12-inch span shall be 2,900 pounds. The deflection shall in no case be less than 0.1 inch. 5. Finish. All castings shall be true to pattern, free from cracks, flaws, porosity, cold-shuts, blow-holes, and excessive shrinkage and shall have a workmanlike finish. 6. Test Pieces. (See "Structural Steel.") 7. Tests. (See "Structural Steel") 8. Shipment. 9. Payment. SPECIFICATIONS FOR MALLEABLE CASTINGS (Based on " Standard Specifications for Malleable Castings " of the American Society for Testing Materials, adopted Novem- ber 15, 1904.) 1. Manufacture. Malleable iron castings may be made by the open-hearth or air-furnace process. In all respects not specifically mentioned herein the castings shall conform to the " Standard Specifications for Malleable Castings " of the Ameri- can Society for Testing Materials, adopted November 15, 1904, and tests shall be made as provided in said specifications. 2. Chemical and Physical Properties. Castings shall con- tain not more than 0.06 per cent of sulphur nor more than .0225 per cent of phosphorus. They shall have a tensile strength of not less than 40,000 pounds per square inch and the elongation measured in 2 inches shall be not less than 2j/ per cent. The transverse strength of the standard test bar 1 inch square, loaded at the middle of a 12-inch span, shall be not less than 3,000 pounds per square inch; and the deflection shall be at least % mcn - SPECIFICATIONS 383 3. Finish. Castings shall be true to pattern, free from blem- ishes, scale, and shrinkage cracks, and shall have a workmanlike finish. 4. Test Pieces. (See "Structural Steel.") 5. Tests. (See "Structural Steel.") 6. Shipment. 7. Payment SPECIFICATIONS FOR STEEL CASTINGS (Based on " Standard Specifications for Steel Castings " of the American Society for Testing Materials, adopted August 25, 1913.) 1. Manufacture. Steel for castings may be made by the open-hearth, crucible, or Bessemer process. Castings shall be annealed unless otherwise specified, and in all respects not specifically mentioned herein their material and manufacture shall conform to the " Standard Specifications for Steel Castings of the American Society for Testing Materials," adopted August 25, 1913, and tests shall be made as provided in said specifica- tions. 2. Chemical and Physical Properties. Castings shall con- tain not more than 0.05 per cent of phosphorus nor more than 0.05 per cent of sulphur. Castings shall be classed as " Hard," " Medium," and " Soft," and shall have the following physical properties : Tensile strength, pounds per square inch Elastic limit Hard 80,000 36,000 Medium 70,000 31,500 Soft 60,000 27,000 Elongation, per cent in 2 inches . . 15 18 22 Contraction of area, oer cent. . 20 25 30 3. Finish. Castings shall be true to pattern, free from blemishes, flaws, or shrinkage cracks. Bearing surfaces shall be solid and no porosity shall be allowed in positions where the resistance and value of the casting for the purpose intended will be seriously affected thereby. 4. Test Pieces. (See "Structural Steel.") 5. Tests. (See "Structural Steel.") 6. Shipment. 7. Payment. 384 WORKING DATA FOR IRRIGATION ENGINEERS SPECIFICATIONS FOR FORGED OR ROLLED BRONZES (Use of Forged or Rolled Bronzes) (a) Class A and No. 1 manganese bronze have the same physical properties, but the manganese bronze is generally more reliable and also more expensive. (b) No. 2 and No. 3 manganese bronze are adaptable where greater strength is required than is furnished by No. 1, but they are less ductile. (c) Phosphor bronze is valuable where non-corrodibility is an important item, but should not be used where great strength and ductility are essential. (d) Tobin bronze is valuable for shafting, bolts, nuts, and other fastenings where a high degree of non-corrodibility is essen- tial. It is more easily forged and stamped than any of the other bronzes. 1. Kind and Quality. Forged or rolled bronze shall be made of new metal of the best grade as to purity and homogeneity. The use of scrap bronze will not be allowed. 2. Shapes. Forged or rolled bronze pieces shall be accu- rately formed as shown on the drawings. The contractor will be held responsible for the correct fitting of the parts designed to conform one with the other, so that the whole may be properly assembled in good working order. 3. Annealing. Cold working of bronze shall be avoided if possible, but when cold working is necessary the material shall be subsequently annealed. 4. Physical Properties of Class A Bronze. Class A bronze shall have the following physical properties : An ultimate tensile strength in pounds per square inch of not less than 60,000; an elastic limit of not less than one-half the ultimate tensile strength; and a minimum per cent of ultimate elongation in 2 inches of 30. 5. Physical Properties of No. i Manganese Bronze. No. 1 manganese bronze shall have the following physical properties: An ultimate tensile strength in pounds per square inch of not less than 60,000; an elastic limit of not less than one-half the ultimate tensile strength; a minimum per cent of ultimate elongation in 2 inches of 30. SPECIFICATIONS 385 6. Physical Properties of No. 2 Manganese Bronze. No. 2 manganese bronze shall have the following physical properties: An ultimate tensile strength in pounds per square inch of not less than 70,000; an elastic limit of not less than one-half the ultimate tensile strength; and a minimum per cent of ultimate elongation in 2 inches of 28. 7. Physical Properties of No. 3 Manganese Bronze. No. 3 manganese bronze shall have the following physical properties: An ultimate tensile strength in pounds per square inch of not less than 80,000; an elastic limit of not less than one-half the ultimate tensile strength; and a minimum per cent of ultimate elongation in 2 inches of 25. 8. Physical and Chemical Properties of Phosphor Bronze. Phosphor bronze shall have the following physical properties: An ultimate tensile strength in pounds per square inch of not less than 50,000; an elastic limit of not less than one-half the ulmtiate tensile strength; and a minimum per cent of ultimate elongation in 2 inches of 25. Chemical analyses of phosphor bronze shall show: Copper, 79 to 81 per cent; tin, 9 to 11 per cent; lead, 9 to 11 per cent; phosphorus, 0.7 to 1.0 per cent. The analyses shall show not more than 1 per cent of all other ingredients combined. 9. Physical and Chemical Properties of Tobin Bronze. Tobin bronze shall have the following physical properties: An ultimate tensile strength of 60,000 pounds per square inch; an elastic limit of not less than one-half the ultimate tensile strength; a minimum per cent of ultimate elongation in 2 inches of 30. A chemical analysis of the composition of Tobin bronze shall show the following per cents of materials: 59 to 63 per cent of copper; 0.5 to 1.5 per cent of tin; the remainder of zinc, with such small percentage of other ingredients as the manufacturer considers best suited to produce the specified physical properties and in- corrodibility. 10. Finish. Finished pieces of bronze shall be free from injurious seams, flaws, and cracks, and shall have a workmanlike finish. n. Markings. Large pieces of finished bronze shall be stamped with the melt number; and small pieces may be tied in 386 WORKING DATA FOR IRRIGATION ENGINEERS suitable packages or bundles, securely wired together, having the melt number on attached tags. 12. Test Pieces. The contractor shall furnish at his own expense all test pieces. At least one test piece shall be taken from each melt of bronze. The standard test pieces shall be cut from the finished material or from material from the same melt and treated in exactly the same manner. The test pieces shall be J^ inch in diameter and shall have 2 inches of gage length, except that large bars may be tested in full sizes. All test bars and test pieces shall be marked so as to indicate clearly the material they represent and shall be properly boxed and prepared for shipment if required. 13. Tests. (See "Structural Steel.") 14. Shipment. 15. Payment. SPECIFICATIONS FOR CAST BRONZES (Use of Cast Bronzes) (a) Class A bronze is adaptable for castings where physical rather than chemical properties are the more important. (b) Class B bronze is adaptable for bearings, bushings, sleeves, and all parts subject to considerable wear. (c) Class C and Class D bronze are especially adaptable to sliding surfaces in contact, such as bearing faces of gates and gate frames, Class C being used for one bearing and Class D for the other bearing in contact therewith. (d) Manganese bronze is valuable for its physical properties and is generally more expensive, but stronger and more reliable than Class A bronze. (e) Phosphor bronze is adaptable where non-corrodibility is an important factor. It is slow to heat and is a good bearing metal. i. Kind and Quality. Castings of bronze shall be made of new metal, and shall have a homogeneous structure free from cold shuts, blow-holes, porosity, flaws, patching, plugging, and other injurious imperfections. The use of bronze scrap will not be allowed. SPECIFICATIONS 387 2. Castings. Castings shall have the forms and dimensions shown in the drawings. The contractor will be held responsible for correct fitting of the parts designed to conform one with the other, so that the whole may be properly assembled in good working order. 3. Physical Properties of Class A Bronze. Class A bronze must have the following properties: An ultimate tensile strength in pounds per square inch of not less than 60,000; an elastic limit of not less than one-half the ultimate tensile strength; and a minimum per cent of ultimate elongation in 2 inches of 15. 4. Chemical Properties of Class B Bronze. Chemical an- alyses of the composition of Class B bronze shall show from 82 to 84 per cent of copper, 12J/2 to 14 J^ per cent of tin, and 2j/ to 4j/ per cent of zinc. 5. Chemical Properties of Class C and Class D Bronze. Class C bronze shall have the following chemical composition: Copper, 82.7 per cent; lead, 4.9 per cent; zinc, 5.3 per cent; and tin, 7.1 per cent. Class D bronze shall have the following chem- ical composition: Copper, 82.8 per cent; lead, 8.0 per cent; zinc, 4.4 per cent; tin, 4.8 per cent. 6. Physical Properties of Manganese Bronze. Manganese bronze must have the following physical properties: Ultimate tensile strength in pounds per square inch of not less than 60,000; an elastic limit of not less than one-half the ultimate tensile strength; and a minimum per cent of ultimate elongation in 2 inches of 20. 7. Physical and Chemical Properties of Phosphor Bronze. Phosphor bronze must have the following physical properties: An ultimate tensile strength in pounds per square inch of not less than 25,000; an elastic limit of not less than one-half the ultimate tensile strength; a minimum per cent of ultimate elongation in 2 inches of 5. Chemical analyses of the composi- tion of phosphor bronze shall show: 79 to 81 per cent copper; 9 to 11 per cent tin; 9 to 11 per cent lead; and 0.7 to 1.0 per cent phosphorus. The analyses shall show not more than 0.5 per cent of other ingredients. 8. Finish. All castings shall be finished true to pattern, and shall be free from excessive shrinkage, porosity, blow-holes, 388 WORKING DATA FOR IRRIGATION ENGINEERS and other injurious imperfections, and shall have a workmanlike finish. 9. Markings. Each casting shall be marked or tagged with the melt number from which it is made. 10. Test Pieces. The contractor shall furnish at his own expense all test pieces. At least one test piece shall be taken from each melt of bronze. The standard test pieces shall be cut from the finished material or from material from the same melt and treated in exactly the same manner. The test pieces shall be ^ inch in diameter and shall have 2 inches of gage length, except that large bars may be tested in full sizes. All test bars and test pieces shall be marked so as to indicate clearly the material they represent and shall be properly boxed and prepared for shipment if required. n. Tests. (See "Structural Steel.") 12. Shipment. 13. Payment. INDEX Acre-feet equivalents in second-feet, 194 Allowable depth of backfill for steel pipe, 244 Allowable stresses in timber, 233 Altitudes, dictionary of, 1 Areas of circles, 292 Areas, weights, and spacing of round and square bars, 230, 231 Bars, spacing of, in reinforced con- crete beams, 230, 231 Bazin's formula for rectangular weirs, with tables, 189 Beams, 220 bending moments in, 221; table, 223 coefficient of resistance of rein- forced concrete, 229 reinforced concrete, 222; dia- gram, 229; spacing of rods in, 230, 231 wooden, values of M/S, 234 Bending moments in beams, 221; table, 223 Bottom width of canals, 46 Broad-crested weirs, 191, 192, 193 Canal locations, general remarks on, 26 Canals, 25, 26 bottom width, 46 capacity, 41, 160-165 depth, 46 design, 41 diagrams for determining veloc- ities and slopes, 91-107 diagrams for design of sections, 110-147 discharge of small, 160-165 excavation for, 203-219 formula for flow, 50 freeboard, 59; on curves, 60; formula for, 61 Canals, grades, 47 Kutter formula, 50 location, 25, 26 scouring and silting velocities, 48; tables, 49 seepage losses, 43; diagram, 45; table, 44 side slopes, 44 values of "C" for, 90-109 values of n, 50; tables, 52 velocities, 47 Capacity of canals, 41 Capacity of pipes, decrease with age, 69 formulas for, 67 Cast-iron pipe, discharge, 172 thickness and weight, 247 Channels, diagrams for determining velocities and slopes, 91-107 values of coefficient "C," 90-109 Chezy formula, values of "C," 90- 109 Chutes, design, 62 Cippoletti weirs, 11 discharge, 181 Circles, circumference of, 292 Circular conduits flowing partly full, 150-153 Circular segments, hydraulic elements of, 144-147 Circumference of circles, 292 Coefficient "C" in Chezy formula, values of, 90-109 Coefficient for discharge of broad- crested weirs or dams, 191-193 Coefficient for submerged weirs, 180 Coefficient for velocity of approach to weirs, 182 Coefficients of resistance of reinforced concrete beams, 229 Columns, formula for bending mo- ment, 233 Concrete, materials required for one cubic yard, 232 389 390 INDEX Concrete pipe, discharge, 172 spacing of reinforcement bars, 237, 243 Conduits, circular, flowing partly full, 150-153 Contents in feet B.M. of logs, 236 Contents in feet B.M. of lumber, 235 Convenient equivalents, 258 Conversion diagram, "acres per sec- ond-foot" to "depth of water," 196 Conversion of linear units, 260 Conversion, English to metric units, 264 metric to English units, 262 Conversion table for acre-feet to second-feet, 194 Conversion table, inches and frac- tions to decimals of a foot, 259 Correction for curvature and refrac- tion, 265 Cosines, natural, 282 Cotangents, natural, 284 Cubes of numbers, 292 Culverts, design, 71 Current meter, description of, 14 kinds of, 14 method of making measurement with, 15 Current meter station, cable for, 15 discussion of, 13 discharge, velocity, and area curves for, 18 gagings at, 8 soundings at, 15 Curve formulae, 277 Curvature of wood pipe, 242 Curvature and refraction, correction for, 265 Dams, discharge over, 191-193 diversion (see Diversion dams) pressure on, 39, 252 storage (see Storage dams) Decrease of carrying capacity of pipes with age, 69 Depth of canals, 46 Design, formulas for reinforced con- crete, 222 Design of canals, 41 Design of chutes, 62 culverts, 71 diversion dams, 38 drops, 70 flumes, 64 headgates, 40 irrigation structures, 29 pipe lines, 65 storage works, 29 turnouts, 71 Diagrams (see list page ix) Dictionary of altitudes, 1 Dimensions of metal flumes, 249 Discharge, maximum, of streams in United States, 34 Discharge of pipes, cast-iron, 172 concrete, 172, 174 decrease with age, 69 formulas, 69 steel, 174 wood stave, 170 Discharge of Cippoletti weirs, 181 Discharge of circular conduits flowing full, 151, 153 Discharge of circular conduits flowing partly full, 150, 152 Discharge of rectangular weirs, 183- 190 Discharge of rectangular wooden flumes, 154-159 Discharge of semicircular flumes, 166-169 Discharge of sharp-edged submerged orifices, 179 Discharge of sluice gates, 179 Discharge of small canals in earth, 160-165 Discharge over dams, 191, 193 Diversion dams, backwater calculations required, 39 design of, 38 discharge over, 39, 191 discussion of, 38 movable crests, 38 on pervious foundations, 39 types of, 38 Diversion, location of point of, 24 Drainage basins list of, in United States, 3 INDEX 391 Drainage basins, outline map of, in United States, 5 rivers included in different, 3 run off from, 4, 34 Drops, inclined, 62 notched, 70 vertical, design of, 70 Duty of water, 20, 21 Duty of water, 'conversion diagram, 196 Elements, hydraulic, of rectangular sections, 110-115 of trapezoidal sections, 116-143 of circular segments, 144-147 of a horseshoe section, 149 Embankment for small canals, 203 Entrance losses, 177 Equivalents, acre-feet and second- feet, 194 Equivalent units, 258 Equivalent water pressure on retain- ing walls, 252 Evaporation, 29 Evaporation from reservoirs, 29 Evaporation tables, 30 Examination and reconnoissance, 1 Excavation for canals, 203-219 Explanation of Figs. 4^13, 75 " 14-20, 77 " 21, 78 " 22, 78 " 23-25, 80 " 26-29, 81 " 30-32, 67, 82 " 33, 82 " 34r-35, 83 " 36-37, 85 " 38, 87 " 39, 203 " 40, 228 " 41, 241 " 42, 244 " 43-45, 246 " 46, 248 Table 22, 79 " 23, 81 " 25-28, 86 " 31-34, 206 " 35-37, 207 Explanation of Table 38, 222 " 39-40, 228 " 43, 240 " 46, 241 " 57, 261 Fanning's formula for discharge of iron pipes, 68 Flumes, design of, 64 dimensions and weights of steel, 249 discharge of steel, 166-169 discharge of wooden, 154-159 Formula for flow in canals, 50 Kutter's, 50 for freeboard on curves, 60, 61 for decrease in carrying capacity of pipes with age, 69 for pressure on retaining walls, 220 Formulas, curve, 277 for bending moments in beams, 221 for canal excavation and embank- ment, 203, 204 for discharge of pipes, 67 for reinforced concrete design, 222 list of hydraulic, 197 trigonometric, 273 Fractions of inches expressed in deci- mals of a foot, 259 Gaging stations, 11, 13 Gates, discharge, 179 General remarks on canal locations, 26 Geological survey, topographic sheets, 1 water-supply papers, 2 Grades for canals, 47 Headgates, design, 40 discharge through, 179 Head required to produce veloc- ity, 177 Horsepower diagram, 253 Horseshoe section, hydraulic elements of, 149 Hydraulic curves for small canals, 160-165 392 INDEX Hydraulic diagrams (see list of dia- grams, page ix) Hydraulic elements, of rectangular sections, 110-115 of circular segments, 144-147 of a horseshoe section, 149 of trapezoidal sections, 116-143 Hydraulic equivalent units, 258 Hydraulic formulas, list of, 197 Hydraulic radius, relation to slope and velocity, diagrams, 91-107 Hydrostatic formulas, list of, 200 Inches and fractions converted to decimals of a foot, 259 Investigations and surveys, 20 Irrigable area, determination of, 25 Kutter's coefficient , 75, 76 Kutter's formula, 50 Land, amount available, 1 elevation of, 1 location of, 1 Length, equivalent units, 260 Levelling, results of spirit, in United States, 1 Linear units, conversion of, 260 List of hydraulic formulas, 197 Location of point of diversion, 24 of main canal, 25 Logarithmic diagrams, why used, 76 Logarithms of numbers, 280 Logs, contents in feet B. M., 236 Loss of head through orifices, sluice gates, pipe intakes, etc., 177 Lumber, contents in feet B. M., 235 Lyman's tables for discharge of rec- tangular weirs, 184 Materials required for one cubic yard of concrete, 232 Materials, weights of, 257 Maximum rate of discharge of streams in the United States, 34 Metal flumes, dimensions and weights, 249 discharge of, 166-169 Metric conversion tables, 262-264 Multipliers for discharge of broad- crested weirs and dams, 191- 193 Natural sines and cosines, 282 Natural tangents and cotangents, 284 Numbers, logarithms of, 280 squares, cubes, etc., 292 three-halves, powers of, 286 Numbers of water-supply papers, 2 Orifices, discharge of submerged, 179 loss of head through, 177 Outlet works for storage dams, gates for, 37 location of, 33 velocities through, 38 Pipe lines, discussion of, 65 design of, 65 Pipes, air in, 69 concrete, steel, cast iron, wood, 65 decrease of carrying capacity with age, 69 discharge of cast-iron, 172 discharge of concrete, 172, 174 discharge of steel, 174 discharge of wood stave, 170 formulas for discharge of, 67 maximum curvature of wood, 242 spacing of bands on wood stave, 237, 243 spacing of reinforcement bars in concrete, 237, 243 table of discharge by Fanning's formula, 68 thickness and weight of cast iron, 247 thickness and weight of steel, 245 thickness of staves of wood, 242 Pressure of water in pounds per square inch, 250 Pressure of water in pounds per square foot, 251 Pressure on dams, 39, 252 Precipitation, tables of, 6-12 Prior water rights, 19 Quantity of materials required for concrete, 232 INDEX 393 Rain gage, 8, 9 Reciprocals of numbers, 292 Reconnoissance, 1 Rectangular sections, hydraulic el- ements of, 110-115 Rectangular weirs, Bazin's formula and tables for, 189 diagram giving discharge of, 183 discharge of, 183-190 Francis formula, 183 Lyman's tables of discharge of, 184 Reinforced concrete beams, coefficients of resistance, 229 spacing of rods in, 230, 231 Reinforced concrete design, 222 Reinforced concrete pipe, spacing of rods in, 237, 243 Reinforcement rods in concrete pipe, spacing of, 237, 243 Relative velocities and slopes for dif- ferent values of , 176 Reservoir maps, 26 Reservoir surveys, 26 Reservoirs, 19 evaporation from, 29 seepage from, 32 Retaining walls, 220 equivalent water pressure on, 252 Rods, reinforcement for concrete pipe, spacing of, 237, 243 Runoff from streams, 4 maximum rate of, streams in United States, 34 Scouring velocities, 48; table, 49 Second-feet equivalents in acre-feet, 194 Sections, hydraulic elements of rec- tangular, 110-115 of circular, 144-147 of horseshoe, 149 of trapezoidal,' 116-143 Seepage losses, 43 Seepage losses, diagram for estimat- ing, 45 in percent of diversion, 24 table of, 44 Segments, hydraulic elements of cir- cular, 144-147 Side slopes for canals, 44 Silting velocities, 48; table, 49 Sines, natural, 282 Slope of open channels, diagrams for determining, 91-107 Sluice gates, coefficients of discharge of, 84, 179 discharge of, 179 loss of head through, 177 Spacing of bands on wood-stave pipe, 237, 243 Spacing of rods in concrete pipe, 237, 243 Spacing of round and square bars in beams, 230, 231 Specifications, 315 Advertisement, 316 detail specifications, 326 General Conditions, 319 Guarantee of Bond, 318 Notice to Bidders, 317 Proposal, 317 Special Conditions, 328 Specifications for Canal Excavation, 329 Cast Bronze, 386 Cast-iron Pipe, 352 Cement, 371 Concrete, 366 Continuous Wood- Stave Pipe, 338 Excavation for Structures, 337 Forged or Rolled Bronze, 384 Gray-Iron Castings, 381 Machine - Banded Wood - Stave Pipe, 342 Malleable Castings, 382 Metal Flumes, 355 Paving, 369 Reinforced Concrete Pipe, 348 Steel Castings, 383 Steel Highway Bridges, 358 Steel Pipe, 345 Steel Reinforcement Bars, 380 Structural Steel, 379 Timber Piles, 378 Tunnels, 334 Spillways, maximum discharge over, 33 Squares of numbers, 292 394 INDEX Stadia Tables, 266 Staves for wood pipe, thickness of, 242 Steel flumes, discharge of, 166-169 dimensions and weights, 249 Steel pipe, discharge of, 174 maximum allowable backfill for, 244 thickness of shell, 245 weight of, 245 Storage dams, outlet works for, 33 spillways for, 33 types of, 33 Storage works, dams, 33 design of, 29 discussion of, 29 study of water-supply, 29 Structures, design of, 29 Submerged orifices, discharge of, 179 Submerged tubes, coefficients of dis- charge for, 84 Submerged weirs, coefficients for dis- charge, 180 Surveys, 20 Surveys for reservoirs, 26 Tables (see list page xi) Tangents, natural, 284 Theoretical horse-power of falling water, 253 Theoretical velocity head, 177 Thickness of cast-iron pipe, 247 Thickness of staves for wood pipe, 242 Thickness of steel pipe, 245 Three-halves powers of numbers, 286 Timber, allowable stresses in, 233 weights of, 233 Timber structures, 232 Topographic sheets of United States Geological Survey, 1 Total hydrostatic pressure on walls, 252 Trapezoidal loading on beams, 221 Trapezoidal sections, hydraulic ele- ments of, 116-143 Triangular loading on beams, 221, table, 223 Trigonometric formulas, 273 Tubes, discharge coefficient for sub- merged, 84 Turnouts, design of, 71 Uniform loading on beams, 221 Value of Kutter's coefficient n, 50, 75, 176; tables, 52 Values of coefficient "C" for open channels, 90-109 Variation of velocity and slope with n, 176 Velocities, in canals, 47 ; diagrams for determining, 91-107 scouring and silting, 48; table, 49 Velocity head, 177 Velocity of approach to weirs, coef- ficients for, 182 Vertical drops, 70 Volume, equivalent units of, 258 Volume of excavation and embank- ment for small canals, 205 Volume of excavation for canals in level ground, 206, 208-213 Volume of excavation for canals in sloping ground, 207, 214-219 Walls, hydrostatic pressure on, 252 Water, horse-power produced by fall- ing, 253 maximum requirement for, 23 quantity applied to land, 20 used on projects of the U. S. Re- clamation Service, 21 variation of use through season, 22,23 Water duty, 20, 21 Water duty, conversion diagram, 196 Water pressure in pounds per square foot, 251 Water pressure in pounds per square inch, 250 Water rights, prior, 19 Water supply, papers published by U. S. Geological Survey, 2 quantity, 1 source of,,l Weight of cast-iron pipe, 247 metal flumes, 249 round and square rods, 230, 231 steel pipe, 245 timber, 233 various substances, 257 INDEX 395 Weirs, broad-crested, discharge of, Weir station, gage readings at, 8 191-193 Wooden beams, values of M /S for, 234 Cippoletti, discharge of, 181 Wooden columns, formula for, 233 coefficients for submerged, 180 Wooden flumes, discharge of, 154-159 coefficients for velocity of ap- Wood-stave pipe, discharge, 170 proach, 182 maximum curvature for, 242 discussion of, 11 size of wire used for banding, 244 rectangular, discharge of, 183- spacing of bands on, 237, 243 190 thickness of staves, 242 OV *'- O THE S^M* DAY 7/33 312523 UNIVERSITY OF CALIFORNIA LIBRARY