IRRIGATION CANALS AND OTHER Irrigation Works, INCLUDING The Flow of Water in Irrigation Canals AND OPEN AND CLOSED CHANNELS GENEKALLY, WITH TABLES Simplifying and Facilitating the Application of the Formulae of KUTTEE, D'AKCY AND BAZIN, BY p. j. FLYNisr, o. E. Member of the American Society of Civil Engineers; Member of the Technical Society of the Pacific Ooast; Late Executive Engineer, Public Works Department, Punjab, India. AUTHOR OF " Hydraulic Tables based on Kutter's Formula." . "Flow of Water in Open Channels," etc., * !' [ALL RIGHTS RESERVED *J* SAN FRANCISCO, CALIFORNIA. 1892. Entered according to Act of Congress in the year 1891, BY P. J. FLYNN, In the office of the Librarian of Congress, at Washington, D. C. & Ox, PRINTERS AND PREFACE. It is fully admitted that a work on Irrigation Canals is much needed in this country. Since this work has been in the printer's hands, I have received letters from prominent engineers, from all parts of the United States, who are anxiously awaiting its issue. The work is divided into two parts. The first part treats of Irrigation Canals and Other Irrigation Works, and the second part of the Floiv of Water in Open and Closed Channels, generally. I have aimed at making the work useful, not only to the engineer engaged in. active practice, but also to the engineering student. With this object in view I have arranged the articles, as well as I could judge, in the order in which they should follow each other. It is the first time, so far as I am aware, that a work on Irriga- tion Canals has been arranged on this plan. In preparing the work on Irrigation Canals, the best authorities have been consulted and due acknowledg- ment is given to them throughout the work. Over ninety per cent, of the matter in the Flow of Water is original. Some of it, however, has appeared before in my other publications. In order to simplify and facilitate the application of the modern and accurate formulae of Kutter, D'Arcy and 363777 IV PREFACE. Ba-zin, 1 first reduced them to the Chezy form of for- mula: v = c X \/r X V* Q = a )< c X \/r X \/s Then, for open channels I have constructed three tables: 1. Tables giving the values of , r, \/r and a\/r for a large range of channels and for several side slopes. 2. Tables giving the values of c and q/r for differ- ent grades and different values of ?i. 3. Table of slopes giving also the value of \/s. Also, for circular and egg-shaped pipes, sewers and conduits, I have constructed two tables: 1. Tables giving the values of a, r, c\/r an^ ac\/r for several values of n. 2. Table of slopes giving also the value of \/s. This is the same as Table 3 above. By making \/s a separate factor, the work of compu- tation is very much simplified. By the use of the above Tables, any problem relating to Open or Closed Channels, likely to arise in practice, can be rapidly solved. A great saving of time and labor can be gained by the use of the tables. There are thirty-seven examples relating to Open and Closed Channels, which will be of especial use to the student. Tables 30, 31 and 32 give the velocity and discharge of a large range of open channels, and Tables 68 and 69 give the velocity and discharge of circular and egg- shaped pipes, sewers and conduits with n = .013. PREFACE. At pages 8, 195, etc., is given the most complete col- lection of formulae, old and modern, sixty-nine in num- ber, that has ever before been published, in a single work, in the English language. The Floiv of Water will be useful, not only to the Irri- gation Engineer, but also to the Engineer engaged on Water Supply, Sewerage, Drainage of Land and Im- provement of Rivers, etc. The Tables of Contents of Volumes 1 and 2, and the Index of Volume 1, are very full, and will enable the reader to find any subject, referred to in the books, without loss of time. I have to acknowledge the many obligations I am under to Mr. George Spaulding, of George Spaulding & Co., printers, San Francisco, who has superintended the printing of the book, and also the plates for the illustrations. Asa specimen of splendid typography,.! refer the reader to the whole book, and particularly to the formulae and tables. P. J. FLYNN. Los Angeles, California, January 9th, 1892. TABLE OF CONTENTS. Page ARTICLE 1. Canals divided into two classes 1 Canals solely for Irrigation 1 Canals for Irrigation and Navigation combined 1 ARTICLE 2. Systems of Irrigation 2 Perennial Canals Inundation Canals Tanks or Reservoirs Wells Pumping 2 ARTICLE 3. American and Indian Canals compared 2 ARTICLE 4. Diverting the Water from the River to the land , . . . . 5 ARTICLE 5. Quantity of Water required for Irrigation 11 Duty of Water Sone Canals and Ganges Canal, India 11 Water required for navigation 12 ARTICLE 6. Depth to Bed-width of Canal, and Dimensions of Canals. 12 Cross-sections of Canals, by A. D. Foote, M. Am. Soc. C. E 13 Dimensions and grades of Canals given by T. Login, M. I. C. E. 14 ARTICLE 7. Side Slopes 17 Silting up of side slopes. . . . 18 ARTICLE 8. Grade or Slope of Bed of Canal 20 Adjustment of grade and sectional area to diminished discharge. 22 ARTICLE 9. Dimensions of Banks 26 Cross-sections of Nira Canal, India, and of Henares Canal, Spain 27 Sub-grade 28 Cross-section of canal, Central District, California 28 ARTICLE 10. A List of Irrigation Canals, giving Dimensions, Grades, etc 29 ARTICLE 11. The Surface Slope of Rivers through the Plains 32 ARTICLE 12. Safe Mean Velocities 32 Slope of bed 32 Velocity required to prevent deposition of silt or the growth of aquatic plants 33 Maximum mean velocity 34 High mean velocities 35 Velocity on Navigation Canals 35 Slope of Canals Slope too great on Ganges Canal 36 Velocities in Ganges Canal, by Major J. Crofton, R. E 37 Velocities in the Western Jumna and Baree Daub Canals, by Colonel Dyas, R. E 39 Humphreys and Abbot, on Velocities in the Mississippi 40 ARTICLE 13. Mean, Surface and Bottom Velocities 41 Bazin Rankiue Prony Dubuat 41 Revy 42 Vlll TABLE OF CONTENTS. Page ARTICLE 14. Mean Velocities from Maximum Surface Velocities 42 Ganging Channels 42 ARTICLE 15. Destructive Velocities 43 Destruction of the Deyrah Dhoon Water Courses 45 Velocities destructive to brickwork 46 ARTICLE 16. Velocity Increases with Increase in Depth 47 ARTICLE 17. Abrading and Transporting Power of Water 48 Observations on the Ganges Canal and Biver Ravee, India, and on the Loire, in France 49 Sweaton, experience Blackwell's experiments 50 Baldwin Latham's experience Sir John Leslie's formula Chailly's formula 51 Experience with bowlder flooring on Indian Canals 51 ARTICLE 18. On Keeping Irrigation Canals Clear of Silt 52 ARTICLE 19. Fertilizing Silt 56 Deposits from the Nile 56 Four kinds of water for irrigation 58 Kistna, Midnapure, Durance, Punjab Rivers ' 59 Kivers Po, Dora, Baltea, Durance, in Madras Reservoirs, Colorado 60 Idaho, Utah 61 Well Water, Punjab 62 ARTICLE 20. Silt Carried by Rivers 62 Silt ca-ried by the Nile, Godavery, Mahanuddy, Kistna, Indus, Durance, Vistula, Garonne, Rhine and Po 63 Nile, Ganges, Mississippi, Danube 64 ARTICLE 21. Improvement of Land by Silting up, Warping or Colma- tage 65 Colmatage on the Moselle, in France 66 ARTICLE 22. Equalizing Cuttings and Embankments 63 ARTICLE 23. Canal on Sidelong Ground 73 ARTICLE 24. Shrinkage of Earthwork 75 ARTICLE 25. Works of Irrigation Canals 77 ARTICLE 26. Wells and Blocks 77 Well of Sone Weir Block of Solani Aqueduct Method of Sink- ing 1 77 ARTICLE 27. Headworks of Irrigation Canals 79 Requirements for good Headworks 80 Deposition of Silt in Canals 81 ARTICLE 28. Diversion Weirs 81 Weirs Dams Anicuts Barrages 81 Canals sometimes taken from rivers without weirs 82 Kern River Dam Myapore Dam Barrage of the Nile 83 Difference between a river Weir and Dam 83 Regulator Temporary dam on crest of weir Oblique weirs ... 85 TABLE OF CONTENTS. lx Page ARTICLE 28 Diversion. Weirs. (Continued.) Proper location of dam or weir 86 Okhla Weir Godavery Anicut Turlock Weir Henares Weir Cavour Canal Weir Streeviguntum, Anicut Narora Weir Phoenix, Arizona, Brush and Bowlder Danis 7. . 87 Kern River Dam Galloway Canal 88 Weir at Head of Bear Eiver Canal, Utah Weir at Head of North Poudre Canal, Colorado 90 Headworks of Upper Ganges Canal 93 Dam and Regulator of Upper Ganges Canal at Myapore 94 The Sone, the Okhla and the Lower Ganges Weirs 98 Barrage of the Nile 97 Okhla Weir, River Juruna 102 Headworks of Sone Canals 103 Weir at head of Sone Canals Movable dam on crest of Weir. . . 104 Okhla Weir, Agra Canal 103 Streeviguntum Anicut Tambrapoorney River, Madras 109 Naroro Weir, Lower Ganges Canal, India. 110 Dowlaishwaram Branch of the Godavery Anicut 115 Turlock Weir, Tuolumne River, California 117 Bhim Tal Dam Betwa Weir Vrynwy Dam Geelong Dam Lozoya Dam 119 Henares Weir 119- 120 Proposed Weir, Cavour Canal, Italy 121 Headworks of Cavour Canal, Italy 122 A.RTICLE 29. Scouring Sluices, Under Sluices 124 ARTICLE 30. Regulators 126 Regulating Gates, Del Norte Canal 127 Idaho Canal Regulator Head 128 ARTICLE 31. Sluices Gates Movable Dams or Shutters 128 Sluice Gates, Indian Canal 129 Regulating Bridge, Regulating Apparatus for Canals 131 Sluice Gate, Henares Canal 133 Shutters of the Mahanuddy Weir 136 Formula for finding the tension 011 the chains of Shutters 137 Movable Dams on the Sone Weir 138 Tumbler Regulating Gear for Distributaries of Midnapore Canal 139 Lifting Sluice Gate 144 ARTICLE 32. The Loss of Water by Percolation under a Weir 147 Godavery Anicut or Weir 147 ARTICLE 33. Bridges Culverts 149 Formula for finding area of Culvert 150 ARTICLE 34. Aqueducts Flumes 150 Aqueduct over the Dora Baltea River Flume 011 UiT.compahgre Canal. . . 152 X TABLE OF CONTENTS. Page ARTICLE 34 Aqueducts Flumes. (Continued.) Big Drop, Grand River Ditch, Colorado Flume on Flatte Ca- nal, Colorado , 153 Aqueduct of Platte Canal, crossing Plum Creek at Acequia 155 High Flume over Malad River, Bear River Canal, Utah 156 Iron Flume over Malad River, Bear River Canal, Utah 157 Solani Aqueduct, Ganges Canal, India 158 Iron Aqueduct over the Majanar Torrent on the Henares Canal 163 ARTICLE 35. Level Crossings 164 Level Crossing at Dhunowree, Ganges Canal 166 ARTICLE 36. Superpassages 169 Ranipore Superpassage, Ganges Canal 171 Seesooan Superpassage on the Sutlej or Sirhind Canal 172 ARTICLE 37. Inverted Syphons 175 Inverted Syphon under Stony Creek, Central Irrigation Canal, California 175 Inverted Syphon carrying the Buriya torrent under the Agra Canal, India 177 Inverted Syphon canning the Hurron Creek (nullah) under the Sutlej Canal 177 Inverted Syphon carrying the Cavour Canal under the Sesia torrent 179 Wrought iron inverted Syphons on the Verdon Canal, France. . 179 Syphons on Lozoya Canal, Jucar Canal, Mijares Canal 182 ARTICLE 38. Retrogression of Levels 183 General Cautley and the Ganges Canal 185 Committee to report on Ganges Canal T. Login's work on Ganges Canal 186 Erosion at Toghulpoor Sand Hill, Ganges Canal 188 Erosion and Silting up on Eastern Jumna Canal, India 189 ARTICLE 39. Falls Drops Checks 189 Ogee Falls 192 Asufnuggur Falls, Ganges Canal 193 Vertical Falls with Water Cushions 195 Timber Fall, Canterbury Plains, New Zealand 197 Timber Fall, Turlock Canal, California - 197 Formula for depth of Water Cushion below fall 198 Raising Crest of Fall 199 Vertical Fall with Gratings 202 Vertical Fall with Grating on Baree Doab Canal 203 Computing the Spacing of Bars 206 Grating of Fall, with Horizontal Bars 210 Sliding Gate Falls on the Sukkur Canal, India 211 Fall on Calloway Canal, with Plank Panels or Flash Boards 214 Box floor for Falls. . . 214 TABLE OF CONTENTS. XI Page ARTICLE 40. Rapids 215 Kapid on the Baree Doab Canal, India 215 ARTICLE 41. Inlets 219 ARTICLE 42. Heads of Branch Canals -^. .^. . . 221 Needle Dam on the Sidhnai Canal, India 222 Kotluh Branch Head at Surranah, Sutlej Canal 225 ARTICLE 43. Escapes Relief Gates Waste. Gates 226 Location of Escape Channel , 227 Escapes on the Sone, Ganges, Agra, Naviglio Grande, Muzza and Martesana Canals 228 ARTICLE 44. Depositing Basins Silt Traps Sand Boxes 229 Trap on Canal in Idaho, by A. D. Foote, M. Am. Soc. C. E 229 Depositing Basin on the Marseilles Canal, France 230 Depositing Keservoir on the Wutchumna Canal, California 231 ARTICLE 45. Tunnels 232 Tunnels on the Merced, High Level and Henares Canals 232 Tunnels on the Marseilles and Verdou Canals San Antonio Tunnel 234 ARTICLE 46. Retaining Walls 238 ARTICLE 47. Combined Irrigation and Navigation Canals 240 Required Velocities on Canals 241 Beruegardo and Sutlej Canals Madras Canals 242 ARTICLE 48. Survey 243 Arrangement of Distributaries 245 ARTICLE 49. Distributaries Laterals Rajbuhas '252 Fall and Inverted Syphon .252 Distribution System 253 Cross-sections of Distributaries 256 Details of Distributaries 257 Cross-sections of Distributaries 261 ARTICLE 50. Submerged Dams 261 ARTICLE, 51 . Construction Canal Dredger 263 ARTICLE 52. Water Power on Irrigation Canals 268 Cigliano, Eotto and Ivrea Canals 268 Water Power on Crappone and Marseilles Canals, France , 269 Water Power on Verdon and Henares Canals 270 ARTICLE 53. Cost of Pumping and Water 270 Pumping in Egypt * 270 ARTICLE 54. Maintenance and Operation of Irrigation Canals 273 The Sources of Destruction of Canals 276 ARTICLE 55. Methods of Irrigation 279 Flooding Checks 279 Flooding in India 285 Furrow Irrigation 286 ARTICLE 56. Duty of Water for Irrigation 289 Efficiency of a Canal for Irrigation 290 xil TABLE OF CONTENTS. Pa-e ARTICLE 57. Pipe Irrigation 292 Economy of Water by the use of Pipes 294 Pipe Irrigation System, Ontario, California 296 ARTICLE 58 '. Number and Depth of Waterings 298 Marcite Irrigation Irrigation Southern California and Henares Canal 298 Esla Canal Valencia, Spain South of Prance 299 Marseilles and Bari Doab Canals Madras Colorado Prof essor G. Davidson 300 C. L. Stevenson, Utah General Scott Moncrieff, India 301 ARTICLE 59. Horary Rotation 302 ARTICLE 60. Forestry and Irrigation 304 ARTICLE 61. Rainfall 308 Statistics of Irrigation 314 ARTICLE 62. Evaporation 316 Evaporation at Kingsbridge, Tulare County, California Col- orado 316 Evaporation in Italy, Spain and India 317 Evaporation in Hyderabad, Nagpur, the Deccan and Northern India 318 Evaporation in Egypt and the South of France 320 ARTICLE 63. Percolation or A bsorption 321 Percolation in Calorado New Zealand Marterana Canal, Italy . 323 Percolation in Lombardy Marseilles Canal Canal from the Khone Agra Canal Achti Tank 324 Percolation in Palkhed Canal Ojhar Tambet Canal, Ganges Canal 325 Percolation in Ganges Canal Egypt London 326 ARTICLE 64. Drainage 327 Waterlogged land in India and Egypt 328 Waterlogged land in Colorada 329 Alkali (reh), Subsoil Drainage 330 Area Irrigated in India 331 ARTICLE 65. Defective Irrigation Alkali The affect of Irrigation on Health 332 Defective Irrigation in California ' 332 Defective Irrigation in India 335 Defective Irrigation in Europe 336 ARTICLE 66. Cost of Irrigation per acre, in different countries 336 ARTICLE 67. Annual earning of a cubic foot of water per second. . . . 338 ARTICLE 68. Cost of Canals per acre Irrigated and per cubic foot per second 339 Cost of the Ganges Canal and the Orisa Canals 339 Cost of Henares Canal, Spain, and Mussel Slough Canal, Cali- fornia. . 340 TABLE OF CONTENTS. Xlll Page ARTICLE 69. Measurement of Water Modules Meters 341 Essentials of a good Module 341 Mr. A. D. Foote's Water-meter 341 Module adopted on the Henares and Esla Canals, Spain 344 ARTICLE 70. Report on the Proposed Works of the Tulare Irrigation District 347 Borings and Trial Pits 348 Side Slopes 349 Tunnels 356 Headworks 358 Eeservoir 360 Reservoir Supply combined with Canal from Kaweah Eiver .... 362 Duty of Water 364 Reservoir Supply combined with Canal from Kaweah River .... 366 Loss from Evaporation and Seepage 368 Earthen Dams 374 Shrinkage of Earthworks 376 Canal on steep side hill ground 378 Cross-sections of Channels on side hill ground 381 Rock cutting on side hill ground with wall on lower side 382 Rainfall 583 Prevention of Waste of Water 385 Measurement of Water. . . . 385 LIST OF TABLES. Number Table. Page 1. Giving Dimensions and Grades of Canals 15 2. Giving Velocities of Channels by Kutter's formula with n = .025 17 3. Giving the Inner Side Slopes of Canals in Earth and Sandy Loam 20 4. Giving the Natural Slopes of Materials with the Horizontal Line 20 5. Giving full details of. Channels computed by Kutter's formula with n = .025 23 6. Giving a list of Irrigation Canals 30 7. Giving the Surface Slopes of Rivers through the Plains 32 8. Giving value of c , 43 9. Giving Safe Bottom and Mean Velocities of Channels 44 10. Giving Dimensions, Grades and Velocities of Masonry Chan- nels 45 11. Giving Dimensions, Grades and Velocities of Channels 47 12. Giving the Transporting Power of Water 49 13. Giving Length, Discharge, etc., of Eivers 64 14. Giving Values of the Co-efficient k 74 15. Giving Shrinkage of Different Materials 76 16. Giving Velocities and Discharge of Channels with different values of n 1 74 17. Giving Velocity in Feet per second, and Discharge in Cubic Feet per second, of Channels with Different Bed Widths, but all other things being equal, based 011 Baziii's formula for Earthen Channels 258 18. Giving the Duty of Water in Different Countries . . . . 293 19. Statistics of Irrigation 314 20. Giving Temperature and Rainfall in the south of France 330 21. Giving Cost of Irrigation per acre in Different Countries 337 22. Showing the Annual Earning of a Cubic Foot of Water per sec- ond in Different Countries 339 23. Giving the Cost of Canals per acre Irrigated, and also the Cost per Cubic Foot per second of Discharge 340 LIST OF ILLUSTRATIONS. Number of Figure. DESCRIPTION. Page 1 . Plan Diverting Water from a River 8 2. Section Diverting Water from a Eiver 8 3. Section Diverting Water from a River 8 4. Cross-Sections of Canal, by A. D. Foote, M. Am. Soc. C. E. . . 13 5. Cross-Sections of Canal, by A. D. Foote, M. Am. Soc. C. E. . . 13 6. Cross-Sections of Canal, by A. D. Foote, M. Am. Soc. C. E. . . 13 7. Cross-Sections of Canal, showing silting tip 19 8. Cross-Section of Nira Canal, India 27 9. Cross-Section of Henares Canal, Spain, in deep cutting 27 10. Cross-Section of Henares Canal, Spain, in cut and fill 27 11. Cross-Section of Canal, Central District, California 28 12. Plan showing arrangement of Channels for Silting up land, also known as Warping and Colmatage 67 13. Cross-Section explaining the Equalization of Cuttings and Embankments 69 14. Cross-Section explaining the Equalization of Cuttings and Embankments 70 15. Cross-Section explaining the Equalization of Cuttings and Embankments 73 16. Plan of Well Foundation 78 17 . Section of Well Foundation 78 18. Plan of Block Foundation 78 19. Section of Block Foundation 78 20. Cross-Section of timber Weir at head of Galloway Canal, Kern River, California 88 21. Cross-Section of Weir at head of Bear River Canal, Utah 90 22. Sectional Elevation of Crib Dam at head of North Poudre Canal, Colorado 91 23. Sectional Plan of Crib Darn at head of North Poudre Canal, Colorado 91 24. Cross-Section through center of Cribs of North Poudre Canal, Colorado 92 25. Cross-Section at ends of Cribs of North Poudre Canal, Colorado 92 26. Plan of Head- Works of Upper Ganges Canal, India 93 27. Elevation of Regulating Bridge at head of Upper Ganges Canal, India 94 28. Plan of Regulating Bridge and Dam at head of Upper Ganges Canal, India X^ 7 i LIST OF ILLUSTRATIONS. Number of Figure DESCRIPTION. Page 29. Cross-Section through Floor of Dam and Elevation of Flank of Upper Ganges Canal, India 94 30. Cross-Section through Center of Dani and Elevation of Pier of Upper Ganges Canal, India 94 31. Plan of part of the Nile Delta, showing location of Barrages and Canals 97 32. Longitudinal Section of the Rosetta Branch Barrage on the Nile 100 33. Plan of the Eosetta Branch Barrage on the Nile 100 34. Cross-Section of the Rosetta Branch Barrage on the Nile 100 35. View of the Nile Barrage 102 36. Plan of Headworks of the Sone Canals, India 103 37. Cross-Section of Weir of the Soue Canals, India 104 38. Movable Dam on Crest of Weir of the Sone Canals, India 104 39. Cross-Section of Okhla Weir or Anicut at head of Agra Canal. 10G 40. Plan of Okhla Weir or Aiiicut at head of Agra Canal 107 41. Cross-Section of Streeviguiitum Weir or Anicut, Madras 109 42. Diagram showing the Afflux during flood at Narora Weir 110 43. Cross-Section of Narora Weir or Anicut at head of Lower Ganges Canal, Ganges River, India Ill 44. Cross-Section of Godavery Weir or Anicut 116 45. Cross-Section of Turlock Weir 117 46. Cross-Section of Henares Weir 119 47. View of Stone Block Facing, Henares Weir 119 48. Bird's-eye view of Site of Headworks, Cavour Canal 122 49. Cross-Section of proposed Weir at Headworks of Cavour Canal 123 50. Plan of proposed Weir at Headworks of Cavour Canal 123 51. Cross-Section of top of proposed Weir at Headworks of Cavour Canal 123 52. Longitudinal-Section of top of proposed Weir at Headworks of Cavour Canal 123 53. Elevations of Iron Spikes 123 54. View of Myapore Regulating Bridge, Ganges Canal 126 55. Elevation of Regulating Gates of Del Norte Canal 127 56. Cross-Section of Regulating Gates of Del Norte Canal 127 57. Longitudinal-Section of Idaho Canal Regulator Head 128 58. End Elevation of Idaho Canal Regulator Head 128 59. Elevation of Sluice Gate, Cavour Canal 129 60. Cross-Section of Sluice Gate, Cavour Canal 129 61. Cross-Section of Drop-Gates on the Jumna Canal, India 129 62. Cross-Section of Drop-Gates on the Ganges Canal 129 63. Elevation of Regulating Bridge, with Lift-Gate and Sleepers. . 131 64. Plan of Regulating Bridge, with Lift-Gate and Sleepers 131 65. Elevation of Windlass for working Sleepers 131 66. Plan of Sleeper 131 67. Cross-Section of Drop-Gate for River Diuns 131 LIST OF ILLUSTRATIONS XV11 Number of Figure DESCRIPTION. Page 68. Plan of Drop-Gate for River Dams 131 69. Cross-Section of Sluice of Henares Canal 133 70. Cross-Section of Gear for Working Sluice of Henares Canal*-.-.- 133 71. Plan of Gear for Working Sluice of Henares Canal 133 72. Cross-Section of Shutters of Mahaiiuddy Weir 136 73. Cross-Section of Tumbler regulating gear for Distributaries of the Midiiapore Canal 139 74. View of Fouracre's Sluices at the Weir on the River Sone 140 75. View of Fouracre's Sluices at the Weir on the River Sone. . . . 140 76. View of Fouracre's Sluices at the Weir on. the River Sone. . . . 141 77. Section of Hydraulic Brake-Head for Shutters of Sone Weir. . 141 78. Section of Hydraulic Brake-Head for Shutters of Sone Weir. . 141 79. Cross-Section of Movable Dam, Sone Weir 142 80. Plan of Lifting Sluice Gate 144 81. Down-Stream Elevation of Lifting Sluice Gate, showing Foot- Bridge and Lifting Gear 145 82. Cross-Section, showing Lifting Sluice, shut 146 83. Cross-Section, showing Lifting Sluice, open 146 84. Plan showing End of Girder Pressing Against Free Rollers. . . 146 85. Elevation of Flume on Uncompahgre Canal, Colorado 152 86. Cross-Section of Flume on Uncompahgre Canal, Colorado. . . . 152 87. Plan of Penstock and Boom, Grand River Canal, Colorado 153 88. Longitudinal Section of Penstock and Boom Flume, Grand River Canal, Colorado 153 89. View of Platte River, with Platte Canal, Colorado 154 90. View of Aqueduct of Platte Canal ( High Line ), crossing Plum Creek at Acequia 155 91. View of High Flume over Malad River, West Branch Bear River Canal, Utah 156 92. View of Iron Flume over Malad River, Coriiine Branch Bear River Canal, Utah 157 93. View of Solani Aqueduct, Ganges Canal, India 158 94. Cross-Section of Solani Aqueduct Embankment 161 95. Elevation of Half of Solani Aqueduct 162 96. Section of Two Arches and Abutment of Solani Aqueduct 162 97. Sectional Plan of Solani Aqueduct, showing Wells and Blocks of Foundations 162 98. Plan of Half of Wrought-Iron Aqueduct over the Arroyo Ma- jauar, Henares Canal 164 99. Elevation of Wrought-Iron Aqueduct over the Arroyo Majanar, Henares Canal 164 100. Cross-Section of Wrought-Iron Aqueduct over the Arroyo Ma- janar, Henares Canal ' 164 101. Details of Wrought-Iron Aqueduct over the Arroyo Majanar, Henares Canal. . 164 XV111 LIST OF ILLUSTRATIONS. Niivnber of Figure DESCRIPTION. Page 102. Details of Wrought-Iron Aqueduct over the Arroyo Majanar, Heuares Canal 164 103. Section of End of Iron Aqueduct and Pier, showing arrange- ment to prevent leakage 164 104. Plan of Level Crossing 165 105. View of the Dhunowree Level Crossing, Ganges Canal 166 106. Plan of Eutmoo Level Crossing at Dhunowree, Gauges Canal 167 107. Plan of Escape Dani at Dhunowree Level Crossing, Ganges Canal 168 108. Longitudinal-Section of Escape Dam at Dhunowree Level Crossing, Ganges Canal 168 109. Cross-Section of Escape Dam at Dhunowree Level Crossing, Ganges Canal 168 110. View of Raiiipore Superpassage, Ganges Canal 171 111. Plan of Seesooan Superpassage, Sutlej Canal Project 173 112. Half Elevation and Half Section Superpassage, Sutlej Canal Project 1 113. Section of Wing Wall Superpassage, Sutlej Canal Project 1 114. Half Cross - Section of Seesooan Superpassage, Sutlej Canal Project 173 115. Longitudinal Section of Conduit under Stony Creek, Central Irrigation District Canal, California 178 116. Plan of Section of Conduit under Stony Creek, Central Irriga- tion District Canal, California 178 117. Section of Conduit under Stony Creek, Central Irrigation Dis- trict Canal, California 178 118. Cross-Section of Conduit under Stony Creek, Central Irriga- tion District Canal, California 178 119. Enlarged Cross-Section of one Span of Conduit under Stony Creek, Central Irrigation District Canal, California 178 120. Plan of End of Syphon for Drainage Crossing at Hurron Nullah Sirhind Canal 180 121. Section Plan of Syphon for Drainage Crossing at Hurron Nullah Sirhind Canal 180 122. Longitudinal Section of Syphon for Drainage Crossing at Hurron Nullah Sirhind Canal 180 123. Cross-Section of Syphon for Drainage Crossing at Hurron Nullah Sirhind Canal 180 124. Diagram to Illustrate Retrogression of Levels in Canals 183 125. Diagram to Illustrate Retrogression of Levels in Canals 183 126. Plan Showing the Effects of Erosion at Toghulpoor, on the Ganges Canal 188 127. Section Showing the Effects of Silting up at Toghulpoor, on the Ganges Canal 188 LIST OF ILLUSTRATIONS. XIX Number of Figure DESCRIPTION. Page 128. Cross-Section to Illustrate the Effects of Erosion on the East- ern Jumna Canal, India 189 129. Cross-Section to Illustrate the Effects of Silting ujr on-4he Eastern Jumna Canal, India 189 130. Longitudinal Section of Canal in Embankment 190 131. Longitudinal Section of Canal, showing Falls 190 132. Section of Ogee Fall with Kaised Crest 192 133. Plan of Asufnuggur Falls, Ganges Canal 193 134. View of Asufnuggur Falls, Ganges Canal 194 135. Section of Vertical Fall ; 195 136. Section of Vertical Fall, with Water Cushion, on the Baree Doab Canal 196 137. Cross-Section of Fall Constructed of Timber and Bowlders, Canterbury, New Zealand 196 138. Longitudinal Section of Fall Constructed of Timber and Bowlders, Canterbury, New Zealand 196 139. Plan of Fall Constructed of Timber and Bowlders, Canterbury, New Zealand 196 140. Cross-Section of Timber Fall with Water Cushion, Turlock Canal, California 197 141. Section of Vertical Fall with Water Cushion 198 142. Elevation, Looking Up-Stream, of Vertical Fall with Grating. 203 143. Plan of Vertical Fall with Grating 203 144. Section of Vertical Fall with Grating 2d3 145. Plan of one Bar of Grating 204 140. Section of Grating 204 147. Section of Shoe holding Grating Bar 204 148. End Elevation of Grating Bars 204 149. Plan of Bars of Grating 209 150. Plan of Bars of Grating 209 151. Section of Horizontal Bars of Grating 210 152. Plan of Fall with Sliding Gate 211 153. Section of Fall with Sliding Gate 211 154. Elevation of Fall with Sliding Gate 211 155. Section of Timber Fall with Plank Panel or Flash Boards 214 156. Plan of Rapid on Baree Doab Canal 216 157. Transverse Section at Crest and Tail of Eapid 216 158. Section of Eapid 216 159. Section of Bowlder Pavement. ........' 217 160. Plan of Inlet on a Level 219 161. Elevation of Inlet on a Level 219 162. Section of Inlet on a Level 219 163. Section of Arch and Pier of Inlet 219 164. Section of Wing Walls of Inlet 219 165. Section of Inlet with Ten Feet Fall.. 220 XX LIST OP ILLUSTRATIONS. Number of Figure DESCRIPTION. Page 166. Plan showing the Relative Position of the Regulating Bridges and Escapes at Branch Heads 221 167. Elevation of one Span of Regulating Bridge at Branch Head.. 221 168. Section of one Span of Regulating Bridge at Branch Head.. . . 221 169. Kotluh Branch Head at Suranah, Sutlej Canal 225 170. Plan of Escape Head and Regulator 227 171. Cross-Section of San Antonio Tunnel, Ontario, California 236 172. Cross-Section of Retaining Wall 239 173. Drainage Map, showing Arrangement of Distributaries 246 174. Plan showing Arrangement of Distributaries 247 175. Plan showing Arrangement of Distributaries 250 176. Section of Fall on Distributary with Aqueduct Over Tail 252 177. Plan of Fall 011 Distributary with Aqueduct Over Tail 252 178. Section of Syphon Drain for passing one Distributary under another, or under a Drainage Channel 252 179. Plan of Distribution System 253 180. Plan of Distribution System 255 181. Cross-Section of Distributary in Four Feet Cutting 256 182. Cross-Section of Distributary in Five Feet Cutting 256 183. Cross-Section of Distributary in Seven Feet Cutting 256 184. Cross-Section of Distributary in Eight Feet Cutting 256 185. Cross-Section of Distributary in Ten Feet Cutting 256 186. Cross-Section of Distributary in Cutting 261 187. Cross-Section of Distributary in Embankment 261 188. Cross-Section of Distributary in Cutting 261 189. Cross-Section of Distributary in Embankment 261 190. Canal Dredger 266 191. Plan of Irrigation by Flooding-Checks 280 192. Plan of Irrigation by Flooding-Checks 283 193. Cross-Section of Canal 283 194. Cross-Section of Distributary 283 195. Section of Country showing Two-Feet Contour Checks 283 196. Section of Country showing One-Foot Contour Checks 283 197. Plan showing Method of Furrow Irrigation 287 198. Plan of Pipe Irrigation System, Ontario, California . . . , 297 199. View of Water Meter or Module, by A. D. Foote, C. E 342 200. Inlet to Module in use on Henares Canal, Spain 344 201. Longitudinal Section of Module in use on Henares Canal, Spain 344 202. Plan of Module in use on Henares Canal, Spain 344 203. Cross-Section of Module in use on Henares Canal, Spain 344 204. Map showing the Proposed Works of the Tulare Irrigation District, California 350 205. Cross-Sections of Canal on Sidelong Ground 380 206. Cross-Section of Canal in Rock-Cutting, with Rubble Wall 011 Lower Side. . . 382 RRIGATION CANALS AND OTHER Irrigation Works. Article i. Canals divided into two Classes. Canals are divided into two great classes, those for irrigation alone, and those for irrigation and naviga- tion combined. The conditions required to develop one of the former class successfully, are: 1st. That it should be carried at as high a level as possible, so as to have sufficient fall to irrigate the land for a considerable distance, on one or both sides of it. 2d. That it should be a running stream, so as to be fed by continuous supplies of water from the parent river, to compensate for that consumed in irrigating the lands. The conditions of a canal for combined navigation and irrigation are, on the contrary, that it should be a still-water canal, so that navigation may be equally easy in both directions; and, as no water is consumed except by evaporation and absorption, and at points of transfer at locks, the required quantity of fresh supply is com- paratively small, and it is thus most economically con- structed at a low level. 25 IRRIGATION CANALS AND Article 2. Systems of Irrigation. In India there are four systems of irrigation in opera- tion, each of them on a vast scale. They are Perennial canals, Inundation canals, Tanks or Reservoirs, and Wells. The inundation canals have no dam in the river at their heads; they give a supply only during floodtime, and the largest and greatest in number aiu situated on the river Indus. Irrigation from wells is carried on, by bullock power and manual labor, each well watering from three to ten acres. In America there are three systems of irrigation, Per- ennial canals, Reservoirs and Artesian Wells. In some instances in the Western States of America, water has been developed in small quantities by constructing sub- merged dams, in the beds of, and below the surface of the ground, of streams, and, in this manner, bringing to the surface, for purposes of irrigation, water that before had flowed to waste under the bed of the river. In other cases tunnels were driven to bed rock through the gravel beds of rivers and through hillsides, to develop water sup- plies. Pumping is sometimes resorted to in America, but the most extensive pumping works in the world for pur- poses of irrigation are situated in Lower Egypt. Article 3. American and Indian Irrigation Canals Compared. In a paper in Volume I, of the Transactions of the Denver Society of Civil Engineers and Architects, by Mr. George G. Anderson, C. E., he describes the Irriga- tion canals of Colorado. This description is, in a great measure, applicable to the majority of irrigation canals in existence in America. Mr. Anderson states: " It was possible to design works on sound principles OTHER IRRIGATION WORKS. O without entering into too minute details at first, and it is to be feared that this has not been done. Regarded simply on the question of construction, it is too appa- rent that faults are numerous, alignments have been bad, grades and velocities established apparently with- out any consideration, and flumes, headworks, etc., con- structed, of which a respectable mechanic would be ashamed. Still, bad as the conditions are, they have their value to the engineer, if nothing more than in showing the mistakes to be avoided in entering upon similar works in new countries. " But by far the greater number of mistakes have been due, I think, to haste in the undertaking of the enter- prise. Too little time was given or taken by the engineer in which to make himself thoroughly familiar with the physical conformation of the country to be supplied with water. Contracts were let for construction almost "before a careful preliminary survey had been made, and the energetic contractor kept close at the heels of the locating engineer, with a consequence that a large percentage of necessarily bad alignment was made, which it is now utterly impossible or impracticable to correct. Probably the best thing that could occur to the irrigation system of northeastern Colorado to-day would be its entire blotting out from the face of the map, and reconstruction begun upon sound engineering prin- ciples." Mr. Walter H. Graves, C. E., in a paper published by the Denver Society of Engineers in 1886, states: "To determine the proper form of channel, the proper grades, slopes, etc., requires the utmost skill and intelligence on the part of the engineer. Mistakes made in the construction of a canal may not appear at first, but subsequently develop themselves by spreading disas- ter and ruin on all sides. A thousand farmers depend- 4 IRRIGATION CANALS AND ing on a canal for their water supply, at a critical peri- od, when the canal is taxed to its utmost to supply their demands, some fatal defect suddenly appears, and the canal, for the time being, is rendered useless, and before repairs are completed the crops are ruined. A catas- trophe of this kind would be almost irreparable, arid through such a disaster financial ruin might overtake an entire community. The responsibility of the engineer is often too lightly assumed by him, and too carelessly and cheaply placed by the company." The above descriptions will probably apply to over ninety per cent, of the irrigation canals and ditches in America. The weirs, headgates, bridges, drops and other works are usually temporary structures of wood. Faulty as the works are, it must be admitted that they served a good purpose in aiding in the development of the country. Without them millions of acres of land would be waste that now bear profitable crops. There is a good field for Hydraulic engineering in the im- provement of these old canals. A great change for the better has of late taken place in the design and construction of Irrigation Canals in this country, and, in some new canals, works of a more permanent character than in the old canals, are now be- ing constructed. India has the greatest number of canals that can, in many respects, be quoted as good examples. It may be thought that Indian canals are too often referred to in the following pages, but it is well to remember that the finest examples of canal construction are to be seen there, that in length, cross-sectional dimensions, dis- charging capacity, number and aggregate mileage, the Indian canals are the greatest in the world, and that their structures are permanent, that is, that very little wood or other perishable material enters into their con- struction. OTHER IRRIGATION WORKS. 5 The experience gained in other countries, where irri- gation has been practiced from time immemorial, is use- ful, especially in showing where mistakes have been made and the plans adopted to rectify them. "Though the designs may not, on the whole, suit American prac- tice, still many useful hints can be obtained from the study of the published descriptions of the works in other countries. The List of Irrigation Canals given in Article 10, shows some of the vast works carried out in India. Article 4. Diverting the Water from the River to the Land. Irrigation by means of canals is chiefly applied to tracts of country which have been formed by the gradual deposit of alluvial matter, from rivers in a state of flood. The deposit from the inundation begins to take place at the points where the velocity of the stream is checked; and this being alongside the margin of the channel, an inundation of the country through which a river passes, will leave behind it, on each side, a stratum of silt in the form of a wedge, the thick end of which is on the river bank. In the course of time, successive annual inundations. will thus have formed a slope away from each of the banks. The width of this slope will vary according to the nature and size of the river. It may be only two hundred or three hundred yards wide, or it may extend to the distance of many miles. The feature above described is not only to be found along the main channel of a river, but also along its branches. No very extensive tract of country has been formed by the inundation and consequent deposit from a single stream. On the contrary, it must have been the work of many. 6 IRRIGATION CANALS AND The channels of all rivers, unless when confined by rocks, are more or less liable to change their course. By referring to a map of any delta, the reader will observe that the characteristics of the delta form, is that a river, as it approaches the sea, should split up into two or more branches or arms, which again may be subdi- vided into smaller ones. This is well exemplified in the delta of the Nile, a diagram of which is given in the block-plan, Figure 31. Each branch of a delta has a tract of country within its influence, and serves to extend the amount of allu- vial deposit, either by raising its banks or by extending the delta seaward. It is a common occurrence to find dry beds of rivers in alluvial plains, possessing all the characteristics of the existing channels. In some cases, channels may be found of such capacity as to show, without doubt, that they are deserted beds of the main stream; in others, there may be indications of a partial and gradually di- minishing supply having reached them, which, by suc- cessive annual deposits, has curtailed their section to such an extent as to admit of their being adopted as irriga- tion channels, or if left entirely in their natural state, such channels may be silted up completely, by successive deposits from flood water and by drifted sand and dust, until they are no longer perceptible, and all that is left to mark their course is a ridge of high land. It will thus be seen that an alluvial plain is not made up of an equable deposit of alluvial matter to the right and left of the main channel of a river, but, on the contrary, by that from a number of channels, some of which may subsequently be obliterated. The fall of the country, also, instead of only following the course of the main channel, will be affected equally by all the others. Intermediate between the channels, the ground will be OTHER IRRIGATION WORKS. / low, and the line formed by the intersection of the two planes sloping away from their respective banks, will evidently indicate the course in which the drainage from those plains will tend to flow. Such lines will blTfoimd also on the extreme boundaries of a delta, receiving on one side the drainage of a portion of the delta, and on the other that of the country independent of it. After these remarks it is time to explain that the ir- rigation of a tract of country is based on very simple principles. Supposing that a supply of water is re- quired for the land near the bank of a river, which has ceased to overflow it, but which may rise to the lip of the channel, then as the country falls away from the river, it will be readily understood that a cut through the bank will give the means of irrigating the ground beyond. This may be considered the simplest form of irrigation. Again, if the surface of the river falls so considerably below the lip of the channel, as to be in- capable of supplying water to the land at a distance, by means of a cut carried at right angles to the course of the river, the difficulty may be surmounted by excavat- ing a channel in an oblique direction; for the course of a river is seldom straight for a few miles, and an artificial channel may be formed in a straight line, which will carry water to a higher level than that of the surface of the river at any point opposite to it. For every mile of its course, it thus gains something on the surface of the level of the river, and it becomes a matter of simple calculation to find how far it will have to be carried be- fore the water issues 011 the surface. For example, let the plain below B, Figure 1, require to be irrigated from the river C D. Suppose that the surface of the country from the foot hills at A, A, A, to 5, falls at the rate of two feet per mile. Let the country be traversed by a river, CD, and 8 IRRIGATION CANALS AND let the surface of the water in this river throughout its length be about twenty feet below its banks. If, then, a channel, G E, be excavated with a horizontal bed and the water at G raised very slightly by a weir in the river at this point, then the water from the river above G would flow along this channel until it reached^, a point at right angles to the river at D, whence the water might be conducted to irrigate the lower portions of the slope, E B. In like manner if the bed of the channel were made to fall one foot per mile, it would at ten miles be only ten feet below the country at E, and at twenty miles, having gained a foot per mile, it would emerge on its surface at B. OTHER IRRIGATION WORKS. 9 When, however, the ground falls at right angles to, as well as with the course of the river, the water would come to the surface of the ground at a less distance from C, than 20 miles. The case is more unfavorable, in the higher reaches of a river above the delta, where the country slopes up- wards away from the river. In this case the water for the lands farthest from the river must be brought from a part of the river nearer to its source, and the excava- tions must be deeper; or, as will often happen, the ex- pense bearing too high a ratio to the attainable advan- tage, the irrigation must be restricted to those lands which lie nearest to the source of the river, and at the lowest levels. It is the depth of the surface of the water below the bank of the river at the head of the channel, and the relative slope of the bed of the channel and the surface of the country through which it passes, which deter- mines the least length of the channel. In order to obtain command of level, and in order to get on the high ground without much heavy digging, it is sometimes necessary to locate the head of the canal high up on the river's course. For this purpose it is sometimes necessary to go either to the spot at which the river finally leaves the hills to flow through the plains, or to a point not far below that spot. Moreover, at this point the water, except in freshets, is comparatively free from silt, the great enemy of canals, and the course of the river is restricted within narrow limits, so that, by dams thrown across the river bed, we can easily divert the water into our new channel. The above considerations are so important, or rather peremptory, that they outweigh the disadvantages of the arrangement which are, indeed, very serious. For the country so close to the hills having generally an exces- 10 IRRIGATION CANALS AND sive fall, and being, moreover, intersected by hill tor- rents, the carrying of the canal through such irregular ground entails serious difficulties, which require the greatest engineering skill and a large expenditure of money to overcome them. Referring to the canal through the delta, it will be readily understood that the high ridges and the old chan- nels, above described, indicate the most suitable align- ment for a series of irrigation channels. The object would be to conduct the water from the river to the crest of such high lands, and then for the channels along them, to arrange as far as may be practicable that the ex- cavation shall be no more than sufficient to furnish the material required for the embankments, which should retain the water at as high a level as possible, consistent with their stability. If the depth of water admitted into the head of the main channel is materially less than what is due to the river at its full height, the depth of excavation at the head will increase in proportion to the difference; and it will then be our object in order to make the cutting as inexpensive as possible, tocarryvthe line of the channel through low ground, until the water would flow 011 the surface. The irrigation limit is then reached, and the channels should be continued along the highest ground that will allow of the water continuing on the same level with it or above it, as may be found most suitable for the locality. If the ground were level on both sides of the channel it would, in many cases, be indispensable to have the surface of the water above it; but on the other hand, the soil may be ill adapted for withstanding pressure, or for preventing percolation; and to avoid the occurrence of breaches it may be desir- able to keep the height of the embankments within very moderate limits. The selection of the exact spot for the head of a canal OTHER IRRIGATION WORKS. 11 is a task requiring much careful consideration. This subject will be again referred to in some of the following articles. Article 5. Quantity of Water Required for Irrigation. The source of supply for an irrigation canal having been fixed, the next point for consideration is the quan- tity of water required. This quantity depends upon: 1. The maximum quantity of land requiring irriga- tion during the same period. 2. The duty of water in the locality irrigated by the canal. The duty of water is the area irrigated annually by one cubic foot of water per second. This subject is dis- cussed in the article entitled Duty of Water. If, after an examination of the map of the irrigation district, we find that 96,000 acres require to be irrigated during one season, and we also find the duty of water in this district, or in a district similarly situated, to be 120. acres, then the quantity of water required to enter the head works of the canal is -f f - = 800 cubic feet per second. A different method of estimating the quantity has been adopted in the projects for some of the Indian canals. For the Sone Canals in India, three-quarters of a foot of water per second was estimated as sufficient for every square mile of gross area, but this area included land watered from existing wells, land lying fallow, village sites, roads, etc. For the Upper Ganges Canal in India, eight cubic feet per second w r as allowed per lineal mile of main canal, and on the Sutlej Canal, six and seven cubic feet have been taken on the same basis. If the canal is to be a navigable one, a certain mini- mum depth of water must be kept in it to float the boats 12 IRRIGATION CANALS AND as far as the navigation extends, and this must be in excess of the quantity required for irrigation. In India the following canals have provided for the purpose of navigation alone, in addition to the irriga- tion supply: On the Sone Canals 600 cubic feet per sec- ond, on the Baree Doab Canal 130 cubic feet, and on the Ganges Canal, 400 cubic feet per second. In fixing the area available for irrigation, all swamp land, sites of towns, roads, etc., not requiring water have to be deducted, and only the remaining area computed, which actually requires water. Having determined the quantity of water required, the next step is to fix the dimensions and grade of the canal. Article 6. Depth to Bed-width of Canal, and Dimen- sions of Canals. The form of cross-section of a channel is determined in a great measure: 1. By the purpose for which it is intended. 2. By the material through which it passes. 3. By the topography of the country, that is, whether it passes over a plain or along a steep hillside. A rectangular channel having a width equal to twice the depth, has a maximum discharging capacity for the same cross-sectional area. The nearer a channel ap- proaches this form the less will be its sectional area, for the same discharge, and, therefore, the more economical will it be. If the object is to convey water to a certain point without expending any of it until that point is reached, and if the material cut through will bear a high veloc- ity, then it is advisable to adopt a section having a bot- tom width equal to about twice or three times the depth, OTHER IRRIGATION WORKS. 13 and with such side slopes as may be required. All the fall available can be used so long as the velocity will not erode the bed or banks, or endanger the works. On steep hillsides, also, this form of channel can, in some cases, be used with advantage, where the material is good, as already explained. In this case the upper CROSS SECTIONS OF CANALS BY A. D. FOOTE, M. AM.SOC. C. E. FIG. 4 __. , , i <*- -r^-'f 11 ^ ^j^ -4---g g-:)_-_-Jdriii d FIG. 6 side is usually all in cut and the lower side partly in cut and partly in fill. If, however, the channel is used to supply other minor 14 IRRIGATION CANALS AND channels with water for irrigation, its depth should be small in proportion to its width, in order that, when the supply fluctuates, the surface of the water may be near the surface of the land to be irrigated. For rectangular channels, constructed of masonry or concrete, the maximum discharging channel of given area is one with a bed- width equal to twice the depth. The diagrams, figures 4 to 11, show cross-sections of some existing canals in America, India and Spain. In the List of Irrigation Canals, Article 10, the propor- tion of depth to width can be seen by inspection. It will be noticed in the Indian canals that the proportion of depth to width is less than in European and Ameri- can canals. The greater number of the Indian canals flow through sandy loam, and their mean velocity sel- dom exceeds three feet per second. In order to arrange for a low velocity, and also to keep the surface of the water in the canal, at all periods of ordinary supply, at such a level as to be able to irrigate the adjacent land, the depth has been made from one-tenth to one-twentieth of the width, except in the case of the Agra Canal, where it is one-seventh. On the Western Jumna Canal, an old canal in India, the water, in the course of years, formed for itself a channel whose depth was found, by a series of trials, to be about one-thirteenth of its width. After this, the proportion of depth to width fixed on construc- tion for the following canals in India was: on the Baree Doab Canal 1 in 15, on the Sutlej Canal 1 in 14, and on the Sone Canals 1 in 20. A rule has been proposed to make the bottom width equal in feet, to the depth in feet plus one, squared. Mr. T. Login, who was for many years an executive engineer on the Ganges Canal, has given the following table, showing approximately the sections and slopes, OTHER IRRIGATION WORKS. 15 probably best adapted for irrigation canals and water courses for Northern India. The velocities are computed by Dwyer's Where r = hydraulic mean depth in feet. tt y_ f a ]} j n f ee ^ o f surface of water per mile. " v = mean velocity in feet per second. TABLE 1. Giving dimensions and grades of canals. Cubic SECTIONS. SECTIONS. Side feet of P ! M. 05 P w 1 I chan- per CD* & P P P (t> P P P ^ CD P 5*" P P S O *-i Pf & 2. nels. second. : P' i S* ^ s & *" 8, 30 3.5 1 in 3300 340 Larimer . 45- 30 7 5 720 North Poudre 30 20 4.0 1 in 2640 450 Empire . 32 60 5 5 1400 Grand River . 35 5 1 in 2880 High Line. 70 40 7 1 in 3000 1184 Central District Merced.. . California 65" 8 60 70 6 10 1 in 10000 1 in 5280 720 3400 San Joaquin and Kind's River it 39 55 4 1 in 5280 Seventy-Six a 100 4 1 in 3520 Galloway ( t ^ 80 3.5 1 in 6600 700 Turlock it 80 20 10 1 in 666 1500 Idaho Mining and Ir- rigation Co.'s Idano Canal Co 's Idaho . . ii 75 4S' 45 40 10 4 lin 2640 1 in 3520 2585 Eagle Eock and Wil- low Creek .... <( 50 30 3 1 in 880 Phyllis . .. .. <( 54 12 5 1 in 2640 250 Arizona. . Arizona 4f 36 ' 7.5 lin 2640 1000 32 IRRIGATION CANALS AND Article n. The Surface Slope of Rivers. TABLE 7. Giving the surface slopes of rivers through the plains Name of River. s Fall in inches per mile. Name of River. S FaU in inches per mile. Mississippi above "1 Neva 000014 9 Vicksburg, Miss. / Bayou Plaquemine. 0.000050 0.000170 3 11 Ehine, in Holland. . Seine, at Paris 0.000150 0.000137 9* 8| Bayou Latorische . . Ohio, Pt. Pleasant. Tiber, at Eome 0.000040 0.000093 0.000130 2* 6 8 Seine, at Poissy .... Saone, at Eaconnay. Haiiie 0.000070 0.000040 000100 4^ 2| 6i Newka 0.000015 9J Article 12. Safe Mean Velocities. Having determined the quantity of water, and fixed the proportion of depth to width, and a minimum for both, and, if the canal is to be navigable, this minimum is to be fixed chiefly with reference to navigation facil- ities. After this there still remains a very important question to be determined before we can devise the sec- tion for our channel, that is, the slope of the bed, on which the velocity depends. If this slope is too great, the bed of the canal will be torn up, and the foundations of all bridges, drops and other works, will be endangered. The canal' bed will be cut down and retrogression of levels take place, until the velocity of the water has adjusted itself to the cohesion of the material through which it flows. Also, the level of the surface of the water in the canal will be lowered and, furthermore, the difficulties of navigation against the stream will be largely increased. If, on the other hand, the slope is too small, a larger OTHER IRRIGATION WORKS. 33 section of channel will be required to discharge a given quantity of water, and many additional works will be required, in the shape of drops, locks, etc. There will also be danger of silt being deposited in the bed, or of the canal being choked by the growth of aquatic plants. In order to provide somewhat against the deposition of silt, it is of the utmost importance that the grades and dimensions of the channels should be so arranged that the velocity of the water may not diminish from the time it enters the head of the canal until it is de- posited on the land to be irrigated. The romoval of silt, deposited by a low velocity, has caused a great deal of trouble and expense on some of the Indian canals. On the Sone Canals dredging has to be resorted to in order to keep the channels clear. In 1882 the Arrah and Buxar canals were closed to allow the silt deposited below the head-sluices at Dehri to be cleared out by manual labor. It was estimated that about forty thousand dollars would be expended in clearing out some five or six miles of canal below the headworks. On the Egyptian canals the necessity for the annual clearance of silt from the irrigation canals, has been one of the greatest evils of the irrigation system in that country. It is, therefore, of the utmost importance, to keep clear of both extremes; but it is not always easy to do so, and in general a compromise has to be made. More- over as the velocity increases rapidly with the depth, it is evident that a slope of bed which might be a very proper one for water of a certain depth, would be too great if it were necessary to increase that depth so as to throw an extra supply into the canal. The minimum mean velocity required to prevent the deposit of silt or the growth of aquatic plants is, in Northern India, taken at 1J feet per second. 34 IRRIGATION CANALS AND It is stated that, in America, a higher velocity is re- quired for this purpose, and it varies from 2 to 3J feet per second. In Spain it has been observed that a velocity of from 2 to 2J feet per second prevents the growth of weeds, but does not scour the channel. In the Inundation Canals of Sind, in India, a province watered by the Indus, it is found that with a velocity of over 2 feet per second the silt is carried on. to the fields, and, as a rule, the sand is deposited in the canal and this sand has to be cleared out every year, in order to keep the canals in working order. In Egypt, when the velocity is less than 1.8 feet per second, silt is deposited and an immense quantity of it has to be removed every year from the irrigation canals there. A velocity of over two feet per second, however, in Au- gust and September, when the Nile water is much charged with slime, prevents deposits, not only of slime but even of sand. During summer there is no silt as the water is clear. Having fixed the minimum velocity and depth of chan- nel, the required slope can be computed as explained in the examples of the application of the Tables relating to the Flow of Water. The maximum mean velocity is not, however, so easily fixed. It must, in the first place, vary with the nature of the soil of the bed. A stony bed will stand a very considerable velocity, while a sandy bed will be disturbed if the velocity exceeds 3 feet per second. Some gravel beds will bear a high velocity. Good loam with not too much sand will bear a velocity of 4 feet per second. It is better to give too great than too small a velocity, as, in the former case, measures can be adopted to pro- tect the side slopes, or falls can be made in the canal and the longitudinal slope, and, therefore, the velocity OTHER IRRIGATION WORKS. 35 reduced. In the latter case the deposition of silt will necessitate an annual clearance of the canal, at great expense, and the loss of ground along the canal-banks on which to deposit the spoil. The Cavour Canal in Italy, over a gravel bed, has a velocity of about 5 feet per second. The Naviglio Grande and the Martesana canals in Italy, which are both used largely for irrigation, have steep slopes, and their mean velocities are not less than from 5 to 6 feet per second in their upper portions. On the Aries branch of the Crappone Canal in the South of France, the mean velocity is 5.3 feet per sec- ond, and on the Istres branch of the same canal the mean velocity is 6.6 feet per second. The mean velocity of the Baree Doab Canal in India, when carrying its supply, 3,000 cubic feet per second, is about 5 feet per second over a gravel bed. The Del Norte Canal in Colorado, has a discharge of 2,400 cubic feet per second. At its head its bed-width' is 65 feet, depth of water 5J feet, and side slopes 3 to 1, therefore its velocity must be over 5 feet per second, but ,as the channel is excavated almost entirely from a coarse gravel, drift and rock, no danger is anticipated from the erosive force of the current. Again, if the navigation requirements are to be con- sidered, the maximum velocity at which a boat can be navigated against the current at a profit, is evidently a very intricate problem, depending on such varying data as the moving power employed, whether steam, animals or man; the description of boat, value of the cargo, etc. If the saving thus effected on the total traffic annually conveyed would defray the interest of the increased capital required for the proposed reduction of slope, then it would doubtless be desirable to make that reduction, looking at the question from that point of view only. 36 IRRIGATION CANALS AND But there is a limit to the reduction of slope beyond a certain minimum, as explained above, owing to the paramount necessity of preventing the deposit of silt in the canal channel, and though, with canals carrying from 2,000 to 5,000 cubic feet per second, 6 inches per mile may be taken as the minimum limit, which would, under ordinary circumstances, interfere seriously with navigation; still it must depend of course on the fall of the country and the nature of the soil, and so difficult is it often found to combine the requirements of the two purposes, irrigation and navigation, that it has been seriously proposed to provide for the latter by separate still-water channels, made alongside of the running canal itself. In the irrigation districts in this country there are numerous instances of canals and ditches with too great a slope. In other cases the woodwork of the drops has been washed away and not replaced, and by retrogres- sion of levels the fall at the drops has been added to the original slope of bed, and in this way a velocity suffi- cient to erode the bed and banks has been produced. The deep channeling has lowered the surface of the water to such an extent that the distributing channels have to be deepened at their offtake in order to obtain their supply. In some of the Indian canals, including the Upper Ganges and Jumna canals, the slope, and consequently velocity was too great, and dangerous erosion took place. To prevent dangerous channeling, expensive repairs and protective works had to be undertaken, with the additional loss of the canal for irrigation during the period that this work was going on. In computing the slope for the Ganges Canal, Sir Proby Cantley used the formula of Dubuat. This formula was often used in canal work at this time, but it is now known to be unre- OTHER IRRIGATION WORKS. 37 liable, especially for large canals. After the admission of water into the canal it was found that the velocity exceeded that originally contemplated. It was dangerous to the works and a great hindrance to navigation. Some years after the canal was in operation Major J. Crofton, R. E., was appointed to prepare plans for remodeling the canal. He made observations on the velocity in the canal, and also collected data on the same subject, which is herewith given from his report. In a portion of the channel of the Eastern Jumna Canal lying in the old bed of the Muskurra torrent, where the cur- rent seemed perfectly adjusted to a light, sandy soil, Major Brownlow, the Superintendent of the canal, found the velocities of the surface to be from 2.38 to 2.28 feet per second, or mean velocities (multiplying by 0.81), 1.928 to 1.847 feet per second. In the lower district of the same canal, near Barote .and Deola, the maximum surface velocities, with a fair supply, were found to be 2.817 and 2.507 feet per second, or mean velocity of 2.282 and 2.03 feet per second. Silt is constantly being deposited here. About 1,000 feet below the Ghoona Falls, on the same canal, in very sandy soil, with nearly a full supply of water, the maximum surface velocity was 3.077 feet per second; no erosion from bed or banks, except when -a supply, much in excess of the maximum allowed, is passing down. Below the Nyashahur bridge on the same canal, where the soil is clay, shingle and small bowlders, Lieutenant Moncrieff, K. E., found the mean surface velocity to be 6.75 feet per second, or the mean velocity about 5.47 per second. The same officer observed the surface velocity at some distance below the Yarpoor Falls in the new center division channel of the Eastern Jumna Canal, and obtained a mean of 3.96 feet per second, or about 38 IRRIGATION CANALS AND 3.21 feet per second mean velocity through entire sec- tion. The soil here is light and sandy, and the channel has been both widened and deepened by the current. In one of the rajbuhas, or main water-courses of the same canal, weeds were found growing in the bed and on the sides with a maximum surface velocity of 2.12 feet per second, or mean velocity of about 1.72 feet per second. The soil is sandy with a fair admixture of clay; silt accumulates to a troublesome extent. In another rajbuha (lateral or distributary), in the same neighborhood, a surface velocity of 2.38 feet per second, or mean about 1.93 feet per second was found. Silt deposits here, but no weeds appear to grow. In the Mahmoodpoor left bank rajbuha of the Ganges Canal, grass and weeds were found growing in the chan- nel with a maximum surface velocity of 1.72 feet per second, or mean of 1.4 feet per second. In the Buhadoorabad Lock channel, Ganges Canal y weeds appear to grow wherever the maximum surface velocity is 2.38 feet, or mean velocity 1.93 feet or under. Soil generally light and sandy. On the Ganges Canal velocities were found as follows: Below the Roorkee bridge on the main canal, where the deepened bed is covered with silt, and erosion from the sides has ceased, the mean velocity in the entire section was 2.92 feet per second; the soil sandy with a tolerable admixture of clay. In the widened channel at the Toghulpoor sand hills, 36th mile, the mean velocity with full supply was 2.53 feet per second. In the embanked channel across the Solani valley, with a supply of two inches under the present maximum on the Roorkee gauge, the mean velocity, obtained by calculation from the area of the water section there and the observed discharge through the masonry aqueduct, OTHER IRRIGATION WORKS 39 was 3.04 feet per second. The deepest portions of the channeling out here have been silted up. At the 50th mile, main line, below the Jaolee falls, with present full supply in the canal, the observed mean velocity was 3.06 feet per second. Erosion from the banks has ceased here; silt on the deepened bed, soil sandy. Above Newarree bridge, 94th mile, in a stiff clay soil, with full supply in, the observed mean velocity was 4.12 feet per second. Erosion trifling here; no silt deposit. Observations communicated by Colonel Dyas, R. E., Di- rector of Canals, Punjab. On the Hansi branch of the Western Jumna Canals, silt was deposited with mean velocities of from 2 to 2.25 feet per second. The deposition of the silt, how- ever, obviously depends on the quantity and specific gravity of the matter held in suspension by the water coming from above, and the ratio of the current veloc- 1 ities at different points along the channel. He states from observations on the channels of the Baree Doab Canal, that in sandy soil: 11 2.7 feet per second appears to be the highest mean velocity for non-cutting as a general rule, for there are soft places where the bed will go with almost any veloc- ity; but those sorts of places can be protected." Again he states: . " Bad places might be scoured out with a mean velo- city of 2.5 feet per second, but better soil would be de- posited in place of the bad with a slightly smaller velo- city than 2.5 feet; and, as the supply is not always full, there would be no fear of not getting that slightly smaller velocity very frequently. The good stuff thus deposited would not be moved again by any velocity which did not exceed 2.5 per second/' 40 IRRIGATION CANALS AND In Neville's Hydraulics, 0.83 to 1.17 feet per second are mentioned as the lowest mean velocities which will prevent the growth of weeds. This, however, will vary with the nature of the soil; vegetation also is much more rapid and vigorous in a tropical climate than that where Mr. Neville made his observations. In Captain Humphrey's and Lieutenant Abbott's re- port on the Mississippi, 1860, it is mentioned that the alluvial soil near the mouth of the river cannot resist a mean velocity of 3 feet per second; and that in the Bayou LaFourche, the last of its outlets, which resembles an artificial channel in the regularity of its section and general direction, and the absence of eddies, etc., in the stream, the mean velocity does not exceed 3 feet per sec- ond, and the banks are not abraded to any perceptible extent. From the foregoing and other observations, and tak- ing into consideration that the higher the velocity the less the works will cost, the following may be taken as safe mean velocities with maximum supply in the (re- modeled) Ganges Canal channels: 1. In the Ganges valley above Roorkee, 3 feet per second. 2. In the sandy tract generally between Roorkee and Sirdhana, 2.7 feet per second. 3. In the very light sand, such as that met with at the Toghulpoor sandhills, not higher than 2.5 feet per second. 4. And for the channels south of Sirdhana, 3 feet per second. On the branches the same data to be assumed accord- ing to similarity of the soil. There are soils, as Colonel Dyas has noted, such as light quicksand, which will not stand velocities of even 1 foot or 1J feet per second, but these are never found OTHER IRRIGATION WORKS. 41 to any great extent in one place; erosion there can only have a local influence, and such places can be protected at a trifling expense. It is channeling out on long lines which is to be feared. Article 13. Mean, Surface and Bottom Velocities. According to the formula of Baziii v b =v 10.87 i/rs. In. which i;=mean velocity in feet per second. v max Maximum surface velocity in feet per second. t> b r= Bottom velocity in feet per second , r = hydraulic mean depth in feet and s = sine of slope. Rankine states that in open channels, like those of rivers, the ratio of v to v is given approximately by the following formula of Prony in feet measures: f Irrigatiou in Southern Europe by Lieut. C. C. Scott Moncrieff. 5 66 IRRIGATION CANALS AND used to flow over a broad, gravel bed, in a number of separate streams, continually changing. A scanty crop of miserable pasturage used sometimes to spring up on the best parts of this broad channel, the rest was quite barren. This worthless strip of bowlders and gravel is now being transformed into extensive stretches of green meadow, yielding plentiful crops, and at the same time confining the river within a permanent and defined bed in a way no series of expensive embankments could easily have affected. The result of river embankments has been too often to raise the bed year by year, so that they too require to be raised. In the Moselle valley, on the other hand, the floods are allowed to flow almost un- checked over the whole of their old channel; but when they retire they leave beneficial results instead of injury behind them, and resume the same course as they did before they rose. This work was commenced by two brothers, Messrs. Dutac, in 1827, by their buying fifty acres along the left bank of the river's bed at LaGosse, a little below Epinal. At the head of this a rough bowlder dam was thrown across the river, turning about 70 cubic feet per second of its waters into a channel taken along the left of the estate. To this was given a gentle slope, which soon raised it above the river; and when lately seen the whole of the land lying between the river and the canal was a fine green meadow. The masonry works on the canal are all of the simplest kind, and require no re- mark save to notice this simplicity. The process then is as follows: Below the dam there is erected an embank- ment at such points as are required, high enough to pre- vent the full current of the river from anywhere sweep- ing over the land to be reclaimed, but not at all intended to keep it from being flooded. From the main canal are taken out little branches, and the land to be irri- OTHER IRRIGATION WORKS 67 gated by them is carefully leveled in a succession of par- allel ridges and valleys running at an angle to__ these branches. About every 25 feet along their course are little openings, admitting a stream of water about six inches wide and 'half as deep, which flows along and overflows a channel made on each ridge, running over the slopes into a similar channel in the depression below. Along this it runs into a catch-water drain, which col- lects all these little separate streams, and a little farther down commences to give the water out again to irrigate a fresh piece. Sometimes the irrigating streams are made in pairs, back to back, sometimes they run singly. The annexed diagram, Figure 12, is taken from a sketch made on the spot; a is the main canal, b the distribution channels, from which the water flows into the minor channels c, and over the ground on each side down into the dips, where the minor drainage lines d, carry it off to the main drain e, which, at a lower level, becomes in turn a distributing channel, repeating the operation. The main line a y diminishes at last into a distribution channel b, and that in time into minor channels. Of course it requires a good deal of labor to bring the gravelly bed into shape for this method of wa- tering, but once done there is very little further outlay. 68 IRRIGATION CANALS AND It is then sown with grass seed (without making any attempt to clear it of stones), and the irrigation is at once commenced. A light deposit of mud forms, every flood increases it, the irrigation is carried on incessantly, and the grass soon begins to sprout. The silt deposit proceeds fast at first where the water proceeds directly through the gravel, which acts as a fil- ter. By degrees this filtration causes a nearly imperme- able bed, through which very little of the water escapes, and just so much the more flows by the drainage-lines , and flows off without having entirely divestod itself of its particles of mud. Were it not for this the meadows would rise higher each year and soon be above the water's reach, but it is found that after a few years there is no sensible change in their level, and what fresh silt is deposited only makes good what is consumed on the vegetation. There are in America large areas of alkali land within the irrigation districts, which would be benefited by this method of silting up. Article 22. Equalizing Cuttings and Embankments. The cross-section of the water channel and its slope, or grade being determined, the next step is to fix the depth of digging. The cross-section of the canal can be fixed so that the surface of the water may be: 1. Within soil, or, in other words, all in cutting. 2. Above soil, so that all the water is carried by em- bankments. 3. Partly in cutting and partly in embankment, or in cut and fill. In some cases, for sanitary reasons, or in very per- vious soil, not suited to make good banks, where the OTHER IRRIGATION WORKS. 69 loss of water and the cost of repairs to banks are serious, it may be necessary to keep within soil. Care must be taken, however, by sinking trial pits, that a sandy^ stra- tum is not reached by deep cutting, as, in this event, much water may be wasted by absorption, and the for- mation of swamps may seriously affect the health of the district, and ruin land, by water-logging, for any useful purpose. In the second case, where the canal is all in embank- ment, there is always danger of breaches and consequent damage, and also the stoppage of irrigation when ur- gently required. In some soils the banks may require to be puddled. The third case has several advantages. "When the canal is partly in cut and partly in fill, the water has usually sufficient elevation above the land to give a com- mand of level for purposes of irrigation. It is also the most economical channel, as the cross- section can be arranged so that the earth excavated from the channel suffices for the banks, due allowance being made for shrinkage and waste. It has a further advantage, where saving of time is an object in completing a work, as there is less material to be moved than when the canal is all in cut or all in fill. The diagram, Figure 13, shows a cross-section of half of a canal, not drawn to scale, where the excavation is sufficient to make the banks, due allowance being made for shrinkage. AB shows the surface of ground which is assumed to be level. 70 IRRIGATION CANALS AND x = depth of digging which is required. d = depth from top of bank to bed of canal. (d x) = depth from top of bank to surface of ground. a = CD = half bed-width of canal. m = ratio of slopes CF = AE, that is, the ratio of horizontal to vertical distance of slope as, for instance, 2 horizontal to 1 vertical, then m = 2. b = EF = top width of bank. As the area of the excavation is to be equal to that of the embankments, we have: (x X a)-{-x X x m=b X (dx)-\-(dx) X (d x) m, that is, ~~ Now, let a = 40 feet, 6 = 6 feet, d = 7 feet, and side slopes 2 to 1, that is, m = 2, and substituting these val- ues and reducing, and we have: x 2 74 x = 140. .\ x = 1.943 feet. Figure 14 shows a cross-section where a berm at ME is required. The surface of the ground is assumed to be horizontal atHL. Let a = BK = half width of canal bed. d = AB = depth of canal from surface of berm to bed of canal. OTHER IRRIGATION WORKS. 71 x = NB = required depth of digging to give sufficient material to make the bank. A= area of bank above EC. B = area of canal below DE. Then, whatever the position of the natural surface, A and B are constants. It is required to determine the depth, BN, or x, so that the area of excavation BFLKB, shall be equal to the area of embankment EFHPQME, that is: B EFLDE = A -f EFHCE, that is: ED + FL EG + HF B- - -- x (d a?) = A+- o -- X(d aj),thatis: (ED + FL) + (EC + HF) == B A Now let EC Wj and y?= angle of BE and MQ with horizon, and = angle of HP with horizon. Then HE, = CR. cot o = (dx) cot o SF=(d x) cot /?, and HF = w -f (d x) X (cot p + cot o ) .-. EC -f HF = 2w + (d x) X (cot ft + cot e ) Now ED = AD + AE = a + d cot /? and FL = NL + NF = a + x cot ? .'. ED + FL 2a + (d -f- aj) cot /? 72 IRRIGATION CANALS AND Substituting the values of (EC -f FH) and (ED -f FL) in equation, and we have: d x / i x .'. ~n cot 6 x (a -f d cot ft + iv -f- d cot 0) = B A d (a -f w) d 2 cot ft cot From this equation the value of x can be found. Example: Given ft = = 45 and cot = cot 0=1 Let a = 50 feet, d = 8 feet, w = 4Q feet, PQ = 25 feet, QT = TM = 6 feet . -. CM == 37 feet. d 2 Then B = ad -f -^ = 432 25 + 37 A = s X 6 = 186 .*. equation becomes x 2 -^ 106^c = 432 186 720 64 32 and x = 5.53 feet Having determined the depth x, in either case, then an addition to that depth has to be made, in order to compensate for the shrinkage of the material and the waste. OTHER IRRIGATION WORKS. 73 Article 23. Canal on Sidelong Ground. It sometimes happens that the headworks of a canal are so located that the canal before it reaches the ptems has to follow along steep side-hill ground. As a rule, in such sloping ground, it will be more economical to have a deep narrow channel than the usual wide and shallow channel suitable for the plains. A section with bed width equal to or about twice the depth is better adapted to steep ground than one with a greater bed width to depth. FIG 15 The cross-section of a canal in sidelong ground is either all in cut, or partly in cut and partly in fill. In each case the upper part of the cut is triangular in shape with a horizontal base as shown in Figure 15. The outer side of the triangle has the slope of the natural ground, and the inner side the slope of the inner side of the canal in cut. Table 14, given herewith, will facilitate the computa- tion of the triangular portion. Let B = width of base. A = area of triangle. x~ angle of natural ground with horizon. y = angle of side slope of cutting with horizon. k = co-efficient, for value of which see table. B cot x cot y 74 IRRIGATION CANALS AND TABLE 14. Giving Values of the Co-efficient K. Angle of ground x in degrees Values of K for different slopes. i to 1 | to 1 1 to 1 1J to 1 1 .00877 .00880 .00888 .00896 2 .01761 .01777 .01809 .01842 3 .02655 .02691 .02765 .02844 4 .03558 .03623 . 03759 .03906 5 .04472 .04575 .04793 .05035 6 .05397 .05646 .05873 .06239 7 .06334 .06541 .06999 .07525 8 .07283 .07558 .08176 .08904 9 .08246 .08600 .09410 . 10387 10 .09220 .09670 . 10700 .11990 11 .10215 . 10765 . 12064 . 13720 12 .11230 .11900 .13510 . 15620 13 . 12250 . 13050 . 15008 .17661 14 . 13290 . 14240 .16610 . 19920 15 .14359 . 15470 . 18300 .22404 16 . 15430 . 16720 .20080 .25120 17 . 16551 . 18045 .22018 .28241 18 . 17660 . 19370 .24070 .31640 19 .18838 .20797 .26257 .35617 20 .20000 .22220 .28570 .40090 21 .21230 .23753 .31151 .45261 22 .22520 .25380 .33890 .51280 23 .23743 .26942 .35688 .58445 24 .25000 .28570 .40120 .67020 25 .26391 .30405 .43687 .77624 26 .27770 .32250 .47610 .90900 27 .29194 .34186 .51942 1.08171 28 .30670 .36200 .56750 1.31230 29 .32173 .38340 .62185 1.64652 30 .33730 .40580 .68300 2.15510 32 .37030 .4545 .8333 34 .4058 .5091 1.0373 36 .4440 .5707 1.3297 38 .4854 .641 1.7857 40 .5307 .7225 2.6041 42 .5807 .8183 44 .6364 .9345 46 .6983 1.0729 48 .7692 1.25 50 , .8488 1.475 OTHER IRRIGATION WORKS. 75 Article 24. Shrinkage of Earthwork. In the construction of embankments with earthy mat- ter, sandy loam and similar materials, whether for can-afe or reservoirs, due allowance should be made for the shrinkage or settlement of the material. The following extract, on this subject, is from a paper by the writer, on the Shrinkage of Earthwork, published in the Transactions of the Technical Society of the Pacific Coast of June, 1885: "Books of reference in the English language usually give the shrinkage of different materials, without mak- ing any allowance on account of different methods of construction and different heights of bank. For in- stance, the shrinkage of earth in general is given at about 10 per cent. Now, if 10 per cent, be sufficient for the shrinkage of a bank of that material, and 30 feet in height, constructed from the end of bank to the full height by "tipping" from wagons, surely a similar bank only 12 feet high, built up in layers, and consolidated by good scraper work, will shrink much less than 10 per cent. " In no other branch of Civil Engineering, since the time when railroads were first commenced, has such an immense quantity of work been carried out, and ex- penditures incurred, as in earthworks; and in no other branch of engineering, of equal importance, have so few experiments, on a scale adequate to the interests in- volved, been published. In other branches of engineer- ing, long, tedious and expensive experiments are carried out without any other return resulting from them than the information they give; but. experiments on earthwork could be carried out on a large scale, as actual work, and with little, if any, additional expense more than the contract price of the work. 76 IRRIGATION CANALS AND " Some of the materials are mentioned more than once, in the table given below, with a slight change in name, but the writer deems it better to give each author's own words descriptive of the material than to make a selec- tion of the materials under a fewer number of names. TABLE 15. Giving Shrinkage of Different Materials. MATERIAL. AUTHORITY. Percnt'ge of Increase + or Dimin- ution of Embnkme't toexcv'tion REMARKS. Sand Hewson 10 10 12.5 11 Q -8 1-5 addition to height of bank Shrinkage of bank 10 %. Shrinkage of bank 15 to 17%. 1-6 addition to height of bank Very light sand Graeff Light sandy earth Morris Molesworth Gravel and sand Sand and gravel Vose Trautwine Searle... . Miss. Levees, 1882. . Earth Earth Simms . . 10 Earth (scraper work) Earth (grading machine). Earth (carefully tamped) Loam & light sandy earth Loam Canadian Pacific R. R. Canadian Pacific R. R. Graeff 9 to 20 12 12 10 10 8.5 -8 Vose Trautwine Searle . . . Vose Clay and earth Yellow clayey earth Morris . .. Gravelly earth Morris Molesworth Vose.. . . Gravel .... Clay Clay Trautwine Searle... . Molesworth 10 t-20 g Clay before subsidence. . . Clay after subsidence Puddled clay Trautwine 25 15 15 + 30 + 50 + 50to -} 60 + 25 + 66 to + 75 + 60 + 42 + 60 + 50 + 70 + 25 to + 30 + 20 + 80 + 90 + 75 + 60 + Wet soil Loose vegetable surf, soil Chalk Searle Trautwine Molesworth Rock Vose Rock .... Rock Graeff Rhine Nahe Railroad. Rock Rock, large fragments.. . Hard sandstone rock, large fragments . . Searle Morris Blue slate rock, small fragments Rock, large blocks Rock, medium fragments Rock, medium unselected Rock (metal) Rock, small fragments. . . Rock fragments (loose Morris Molesworth Searle Molesworth Searle Rock fragments (careless- ly piled* Rock fragments (carefully piled) Trautwine Rock with considerable Graeff OTHER IRRIGATION WORKS. 77 Article 25. Works of Irrigation Canals. The works of irrigation canals include, weirs, dams^ regulators, sluice-gates, scouring-sluices, movable darns, bridges, culverts, aqueducts, superpassages, flumes, in- verted syphons, level crossings, inlets, drops or falls, rapids, tunnels, escapes or wastes, silt-traps or sand boxes, retaining walls, modules for measuring water, cut- tings, embankments, and, on navigable canals, locks. It is very seldom, however, that a canal has all the above works. These works are described, somewhat in detail, in the following pages. Article 26. Wells and Blocks. As wells and blocks are frequently referred to in the descriptions of the foundations of works in India, a brief description of them is herewith given. Wells for foundations are usually brick cylinders, which are sunk to a certain depth in a sandy river. After they are sunk to the required depth they are filled, or partly filled, with concrete. When the lower part only is filled with concrete, the upper part is filled in with sand over the concrete. In addition to being a foundation for weirs, wells also diminish the cross-sec- tional area of the bed of the river through which per- colation takes place. A block, as its name implies, is a block of masonry having one or more vertical holes through it. Blocks answer the same purpose in every respect as wells.' Fig- ures 16 and 17 show a plan and cross-section of one of the wells under the walls of the Sone Weir, shown in Figure 37, and Figures 18 and 19 show a plan and cross- section of one of the blocks under the piers of the Solani Aqueduct, shown in Article 34. The method pursued in 'sinking them is as follows: 78 IRRIGATION CANALS AND .iiSI i S A 1 j I V i ' ~/G./ \l ! || -r * ~ * i i I i 'i *-- g' 6! If the wells to b^ constructed and sunk are on a sand- bank in the river bed, which is dry, the sand is excavated until water is reached, then the well-curbs are placed on the level of the water, and the masonry of the well is commenced; but if a stream has to be crossed, it is OTHER IRRIGATION WORKS. 79 diverted from that part of the river, after which the water is dammed and stilled. This is, of course, often a very difficult operation where the bed of a river "con- sists of sand to a depth of, perhaps sixty feet. After the water is stilled, sand is thrown in, and an embankment formed across it, sufficiently wide to found the wells on; they are then built on it and afterwards sunk. The wells are allowed to stand from ten to fifteen days after being built, to allow the masonry to set. The wells are then sunk by excavating the sand from within them, it being generally found that the quantity of excavation is about double the cubic area of the well sunk. The wells under the walls of the Sone Weir, Figures 16 and 17, are six feet wide on exterior diameter, and are sunk from eight to twelve feet below low water mark. These wells are sunk in single rows, each well being separated from the next one, in the line crossing the river, by a space of about six inches. The inside of the wells and the craters all around them are then filled in with rubble stone, the surface to a depth of two feet inside, and be- tween, the wells being filled with concrete. Large stone slabs are then placed over the top of the wells, binding the walls to the hearting, and also bonding them to one another, and the masonry of the well is then com- menced. Wells have been sunk for foundations of bridges in sandy rivers, to a depth of over seventy feet. Article 27. Headworks of Irrigation Canals. The works at the head of a canal, for regulating and controlling the quantity of water required to be admit- ted to it, consist of a Weir across the river, by which the water is checked and diverted into it, and a Regulator across the head of the canal, by which the proper quan- tity of water is admitted. 80 IRRIGATION CANALS AND In the Regulator are fixed sliding gates, or some other device, to control the supply of water to the canal, and in the weir and near the .head gate is placed a Scouring Sluice to control somewhat the flow of water in the river past the head gate. The operation of the Weir, Scouring Sluices and Reg- ulator is so intimately connected, that a description of one of them applies more or less to the others; therefore, the descriptions given below, in the articles entitled Di- version Weirs, Scouring Sluices and Regulators, are only descriptions of different parts of the Headworks. The requirement for good headworks for an irrigation canal are the following but these are seldom to be found in one place: 1. Permanent banks, and bed, which will prevent the river from eroding the banks and endangering the regulator, etc. 2. A straight reach of the river for say half a mile up and down the river from the weir. 3. A velocity in the river as low as, or not much greater than, the velocity in the canal. The nearer the velocity in the canal approaches to that of the river, the less silt will be deposited in the former. 4. That the current of the river should flow at right angles to the center line of the canal at its head. 5. That the river at the headworks, and after the construction of the weir, shall not overflow its banks. 6. That the bank of the river at the regulator is not very high, so as not to involve very heavy digging for the first few miles of the canal. With reference to the third requirement mentioned above, Mr. C. E. Fahey, M. Inst. C. E., states:* "Transactions of the Institution of Civil Engineers, Vol. 71. OTHER IRRIGATION WORKS. 81 " If the velocity (in the river) across the mouth of a canal exceeds the proposed velocity in the canal, the result must be that the latter will soon silt up. Of course some silt will deposit in all but the largest canals, in which a high velocity can be kept up; but if a canal is led off from a point in the river where the velocity is from five to six feet per second, the water (in the Indus) at this point will have its full proportion of silt in sus- pension, and the heaviest part of this silt, namely the sand, which the above velocity was able to keep in sus- pension, will drop in the mouth of the canal, where the velocity is suddenly reduced to about three feet per second. This fact admits of no dispute. It is proved every year in the Sind Canals. If a canal is in fair order, that is, if it has a properly regulated width and bed-slope, the sandy deposit will be distributed along the upper third of the canal, the heavier sand in the first mile or so, the finer lower down, and the clay at the extreme tail, while the central portion will seldom or never re- quire cleaning. Although the velocity in the canal is not sufficient to carry on the sand, it 'is sufficient to carry on the clay, and if only escapes could be provided at the tails of all canals, which is not practicable in Sind, there would be no clay to be annually removed." Article 28. Diversion Weirs. WEIRS DAMS ANICUTS BARRAGES. A Diversion Weir is a weir built across a river to divert the water into the canal. At certain times, and always during floods, the water flows over part or the whole of this weir. A Reservoir Dam is used to impound water, and, ex- cept in very rare cases, no water flows over its top. In engineering literature the terms weir, dam, anicut in 6 82 IRRIGATION CANALS AND Madras, and barrage in Egypt, are also used to designate a weir across a river. The cross-sections of diversion weirs are as different in form as the materials of which they are constructed. The drawings in this article give several examples, show- ing the sections adopted in different countries, to suit the material available for their construction, and their foundation in the beds of the rivers across which they are constructed. Canals have frequently been taken off from rivers without weirs, but where these rivers are liable to change their beds by erosion of their banks, or where they carry large quantities of silt in suspension, it has been found impossible to regulate both the river channel and also the supply of water into canals on their banks, without a weir built right across the stream. Some canals, without weirs, have their beds at the off-take, much lower than the beds of the river from which they derive their supply, with a view of obtain- ing a supply at the low stage of the river, but this is objectionable for several .reasons, one is the great quan- tity of sand and silt likely to be carried into the canal and, therefore, the difficulty and expense of keeping the deep channel open. In some cases, in Northern India, the canal is taken out of a branch of the main river; and the permanent diversion weir is thrown across the branch only, the water being diverted from the main stream into the branch by temporary dams constructed of bowlders, which are swept away on the rise of the river, and an- nually replaced. This arrangement has chiefly been due to the very heavy expense which would be incurred in throwing a permanent dam across the main river itself. An example of this method was in operation a few years since at the headworks of the Upper Ganges Canal shown in Figure 26. OTHER IRRIGATION WORKS. 83 Dams in rivers are made solid, except at the scouring sluices, when they are called weirs. Of these, Figures 37, 39 and 43 are good examples. When they are provided with openings through their whole length, or the greater part of their length, they are called dams in India. Indeed the term dam is always, in Northern India, understood to mean an open dam, or one partly open and partly closed. Examples of this latter class of dam are to be found in the Kern River dam, Figure 20, the Myapore dam, Figure 27, and the Barrage of the Nile, Figure 32. The advantage of the Weir is that it is self-acting, re- quiring no establishment to work it, and if properly made ought to cost little for repairs. It is also a stronger construction, better able to withstand shocks from float- ing timbers, etc. Its disadvantages are, that it causes a great accumulation of silt, bowlders, etc., above it, and interferes far more than an open dam, with the normal regimen of the river. It is possible, that in certain cases, this might result in forcing the whole or part of the river water to seek another channel, and the possi- bility of this should always be taken into account; but if the river has no other channel down which it could force its way, the accumulation of material above the weir would be an advantage rather than otherwise, as adding to its strength. The advantage claimed for the open dam is that the interference with the normal action of the river is re- duced to a minimum, the strong scour obtained by open- ing its gates effectually preventing any accumulation of silt above. A dam, in India, consists of a series of piers at reg- ular intervals apart, on a masonry flooring carried right across and flush with the river bed, protected from ero- sive action by curtain w ; alls oi masonry up and down stream. 84 IRRIGATION CANALS AND The piers are grooved for the reception of sleepers or stout planks, by lowering or raising which the water passing down the river is kept under control. The in- tervals between the piers may be six to ten feet, which is a manageable length for the sleepers. If the river is navigable at the head, one or two twenty feet openings fitted with gates must be provided to enable boats to pass. The flooring must be carried well into the banks of the river on both sides, to prevent the ends of the dam being turned, and the banks and bed of the river will gener- ally require to be artificially protected for some distance, above and below the dam, to stand the violent action of the water when the gates are partially closed. The two flanks of the dam for some length are gen- erally built as weirs; that is, instead of having piers and gates, the masonry is carried up solid to a certain height so that when the water rises above that height, it may flow over the top of it. The advantage of this ar- rangement is, that it affords an escape for water in case of a sudden flood when the dam may be closed, while, when the water is low, they keep it in the center of the river and away from the flanks, and thereby create a more perfect scour. When the river is subject to sudden and violent floods, damage might be done before the sleepers could be all raised, one by one; it is better therefore to employ flood or drop-gates in such a case; that is, gates which turn upon hinges in the piers at the level of the flooring and which v/hen shut are held up by chains against the force of the water. In case of flood, the chains are loosened, the gates drop down, and the water flows over them. Should the intervals between the piers be over ten feet, there would be a difficulty in hauling the gates up again. A bridge of communication may be made between the OTHER IRRIGATION WORKS. 85 piers of the dam if required. But as it is not desirable to have it obstructed with traffic, it may be merely alight foot-bridge, or the intervals may be spanned temporally with spare sleepers. The dam and regulator are generally close together and connected by a line of revetment wall, as shown in Figures 28, 31, 40 and 48.* In some cases iron or stone posts were fixed on the crest of the weir. Planks laid horizontally are fixed in grooves in these posts to raise the water about two feet higher than the crest of the weir. These planks are removed before the occurrence of floods. The greater number of the weirs or dams across Indian rivers, and almost all those of modern date, are located at right angles to the general direction of the rivers. It is well known that the tendency of oblique weirs is to divert the strongest stream, and consequently the deep- est channel towards the bank on which the upper end of the oblique weir is situated. It was, no doubt, quite true that, in rivers where a good foundation could be obtained, there would be very little objection to oblique weirs; but in rivers such as those which had to be dealt with in India, with sandy beds and difficult foundations, they were very objectionable, for three reasons: Firstly, they induced currents parallel to the weir; Secondly, they caused a deepening of the channel above the weir, near the up-stream end, which was dan- gerous; and Thirdly, they raised the level of the water in the river at the lower end of the' weir. f Another reason is that they cost more than the straight *Roorkee Treatise on Civil Engineering. tR. B. Buckley, C. E., in Proceedings of I. C. E., Volume 60. 86 IRRIGATION CANALS AND weir, and, therefore, for all these reasons the latter weir is preferred in India. The location of the dam should be studied with a view to the avoidance of flooding the country above the dam in the high stages of the river. To prevent flooding, long and heavy embankments had to be made above the Narora weir. In order to reduce the first cost of construction, it has become a custom to build bridges and dams across streams at the narrowest point available, or to contract the stream for that purpose. This frequently involves great difficulties to the engineer in laying the piers and abutments, and also brings in an element of danger by adding to the scouring effect of the waters in the con- tracted channel. Moreover, it generally produces evil effects by the formation of shoals below the scoured-out channel. The proper location for such works, and especially for dams across a river with unstable banks, where the highest factor of safety is desired, is in the broad reaches of the stream, where the depth of water is usually less, and especially in places where a " bar " has already been formed across the river by natural causes. The dam across a river is not only analogous to a " bar" formed by natural causes, but in the scheme of irrigation by gravitation it is a "bar," and should be located and treated as such. If this is done at a broad passage of the stream, or where it has its average width, the first cost of material and workmanship may possibly be increased beyond a similar work at a contracted pas- sage; but this is not an absolute necessity, as many of the ordinary difficulties to be overcome by the engineer are much lessened, and danger to the work in progress, and when finished is much reduced during floods and ice-gorges. The adjacent banks are less liable to be torn OTHER IRRIGATION WORKS. 87 away, wing-dams are avoided, the levees are less expen- sive and less liable to abrasion and to crevasses, there is less cost for protecting works, and less cost of subsequent supervision and repairs * With three exceptions, none of the weirs described in this article raise the water higher than fourteen feet. Indeed, all the weirs in the wide, sandy rivers of India are low weirs of the type of the Okhla Weir, Figure 39, in Northern India, and of the Godavery Anicut, Figure 44, in Madras. The high weirs, the Turlock Weir, Figure 45, and the Henares Weir, Figure 46, have a cross-section not in favor in India. It is very likely that an Indian engineer would reverse these cross-sections and place the vertical side down-stream, with a water-cushion on the lower side, to receive the falling water and diminish its de- structive effect. This will be referred to when describ- ing the dams mentioned. The Cavour Canal weir has a cross-section similar to the Ogee falls first constructed on the canals in North- ern India. These falls destroyed themselves, and they had to be replaced by vertical falls with water-cushions. This is referred to in the article entitled Falls. Two of the weirs have vertical drops, the Streeviguntum Anicut, Figure 41, and Narora Weir, Figure 43. The latter, how- ever, has a water-cushion three feet in depth at the low stage of the river, while the apron of the former is laid at the level of the low-water of the river. In America there are numerous dams of a temporary character which are made of brush and bowlders. At Phoenix, Arizona, dams are formed of stakes, brush and bowlders, rendered water-tight by filling in up stream, with gravel and sand. Stakes are first driven *Irrigatioii in India, Egypt and" India, by Professor George Davidson. 88 IRRIGATION CANALS AND across the channel, and between these, bundles of fas- cines of willow trees, about three inches in diameter at their butts, are laid, with butts down stream, and weighted with a layer of bowlders; tule reeds in bundles are also used, mixed with willow and cottonwood tree. In al- ternate layers the dam is built up to the height of five feet. The willows sprout and the whole forms a mass of living brush and bowlders. When the current is too strong for a man to withstand while driving stakes, cribs are made and floated out and sunk, as was done with the fascine dam at Merced Canal head, in Cali- fornia. The cross-section of the weir of the Galloway Canal, across the Kern River, California, is shown in Figure 20. The plan of the head works of this canal is shown in the article entitled Methods of Irrigation. FIG 20 The Calloway Canal is diverted from the right bank of the Kern River, a few miles above Bakersfield. The average maximum discharge during the rainy season is probably over 19,000 cubic' feet per second. The water of the canal is diverted from the river by a very light, open, wooden weir, extending at right angles to, and en- tirely across, the river from bank to bank. The length OTHER IRRIGATION WORKS. 89 of this diversion weir is 400 feet. The weir rests on three rows of 4"xl2" anchor piles at right angles to the course of the river, and two rows of 4"xl2" sheet piHng-, at the wings parallel to the course of the stream. The piles are driven ten feet into the bed of the river. On the bed of the river and resting on the tops of the piles, and on the mud sills, to which it is securely spiked, a flooring of plank two inches thick is fixed. This floor is about thirty feet in length in the direction of the river. The trestles, A, B, C, D, Figure 20, are about four feet from center to center. These trestles support the plank- ing, A, B, two inches thick, which holds up the water and thus diverts it into the canal. There are two light foot-bridges on the weir shown at B } and C. All the planking, A, B, are shown in position. When this happens the water on the up-stream side of A, B } is level, but as shown in Figure 20 some of the planking, not on the line of the cross-section are assumed to be out and water is flowing through the weir. One man, standing on the foot-bridge, operates the two-inch flash-boards with an iron hooked rod. The total height of the weir is ten feet above the floor. The Head-Sluice or Regulator, at the head of the Gal- loway Canal, is of similar construction to the weir just described, but exceeding it by one foot in height. These head-works are in use seven years and they are reported to give satisfaction. As the whole weir is open in flood time the river bed above it has not silted up. There is not, probably in the world, a lighter or cheaper weir, of an equal length, and situated on the sandy bed of a river, that has acted so efficiently, and that costs less, for its operation and maintenance. It was a bold under- taking to attempt to control such a river, having a flood discharge of over 19,000 cubic feet per second, with such a light structure, and it well exemplifies one of the Pecu- liarities of American Engineering. 90 IRRIGATION CANALS AND The cross-section of the weir of the Bear River Canal, in Utah, is shown in Figure 21. 3&- > Cross Section Bear River Weir. Its location is well selected, as it has high rock abut- ments and a rock foundation. It is constructed of crib- work of sawn lumber. Between the crib-work it is filled in with earth and loose rock, and the up stream side, which has a slope of two to one, is filled in with rock. The down stream side has a slope of one-half to one. The lowest sills of the crib, ten inches by twelve inches, are drift bolted to the bed rock and on these planking is spiked, on the down stream side, to protect the foundation from the effect of the falling water.* The weir across the North Poudre River, at the head of the North Poudre Irrigation Canal in Colorado is, in the center, thirty feet six inches high, and 150 feet wide on the top, and it is formed in two parts. The down-stream division, or face, which gives the necessary stability against floods, consists of crib-work and stones; the up- stream or back, which renders the weir water-tight, being a vertical panel or diaphragm of timber, backed with earth, small stones, gravel and mud, thrown in without puddling. The crib-work is formed of round logs, ten inches at * American Irrigation Engineering by Mr. H.M. Wilson, M. Am. Soc. C. E., in Transactions of the American Society of Civil Engineers, Vol. 24. OTHER IRRIGATION WORKS. 91 CRIB DAM ON NORTH POUDRE IRRIGATION CANAL FIG 22 I BED OF RIVER SECTIONAL\ELEVATION JO .5 10 20 30 j 40 30 (JQ 7Q SCALE\OF FEET SECTIONAL PLAN least in diameter, joined at the ends, as in ordinary log huts, with dovetail or tongue joints. Figures 22, 23, 24 and 25, give plans and sections of the weir. Each crib is ten feet long on the face, and is fastened together with eighteen-inch treenails, two inches in diameter. The cribs are radiated so as to form, when laid close together across the stream, curved tiers of 200 feet, 216 feet, and 232 feet radius on the face. There are three of these tiers, of different heights, six feet asunder. The inte- rior of the cribs, and the spaces between the tiers, are filled with stones, and the exterior surfaces are faced with 92 IRRIGATION CANALS AND large selected blocks of stone, carefully laid so as to overlap each other like the slates or tiles of a house, and without mortar. The arrises are protected by twelve- inch square blocks, securely bolted to the cribs. The timber diaphragm is carried four feet higher than the CRIB DAM NORTH POUDRE IRRIGATION CANAL Scale 32Feet to one Inch FIG. 24 SECTION THROUGH CENTER OF CRIBS cribs and stonework of the tallest tier, to form a " slash board," which can be removed in sections in case it is found liable to be damaged by ice. The center portion of the weir for a length of sixty feet, is carried two feet CRIB DAM NORTH POUDRE IRRIGATION CANAL Scale 32Feet to one Inch- HG. 25 SECTION AT ENDS OF CRIBS higher than the sides, to throw the bulk of tne stream on to natural benches of solid quartz rock on the sides, and thereby to protect the greater part of the face, and especially the toe in the center of the stream from the abrading power of the water. OTHER IRRIGATION WORKS. 93 The weir was founded 011 stone and debris, the depth of which had not been sounded, but it was hoped that PLAN OF HEADWORKS OF UPPER GANGES CANAL. the clay thrown into the back of the weir, combined with the silting up of the river, would have the effect of putting a stop to the flow of the water, and the result has justified the expectation. At first the water leaked 94 IRRIGATION CANALS AND through and there was some difficulty in stopping it, but it was finally arrested. The weir was simply for the purpose of lifting the water high enough to enter the canal.* I Irrigation in New Countries, by Mr. P. O'Meara, M. Inst., C. E., in. Transactions of the Institution of Civil Engineers, Vol. 73. OTHER IRRIGATION WORKS. 95 The Myapore Headworks of the Upper or Original Ganges Canal are shown in the general plan, Figure 26, and in detail in Figures 27, 28, 29 and 30. This weir is an example of an " open dam," differing from the unbroken " anicuts " of Madras, and the solid weirs with scouring sluices, such as the Sone, Okhlaand Narora weirs, built in later years in Northern India. As stated by the designer, Sir P. Cautley, in the follow- ing extract, this dam is " in fact a line of sluices with gates or shutters, which are capable of being laid en- tirely open down to the bed of the river during the period of flood." This weir is designed somewhat on the plans of the Barrage of the Nile, a description of which is given below. This dam differs also from the weirs now generally constructed in regard to its position in relation to the head sluices of the canal, which are, at Myapore, placed in a "regulating bridge," situated, not on the flank revetments immediately adjoining the weir abut- ment, but two hundred feet or more down the canal. This is a defective arrangement, as the pocket thus formed between the regulator and the actual commence- ment of the canal channel is filled by an almost still back-water, when the flood-waters are pouring over the dam; and this pocket becomes shingled up, with seven or eight feet in depth of bowlders and sand, marked * * * on Figure 28, and the supply, especially at low water, is reduced until this accumulation is cleared away. The left flank of the dam abuts upon an island, in which nearly one-half of its full width is excavated. The flooring of the dam and of the regulating bridge are laid on one level, and the front line of the latter is the zero to which the whole line of the canal is refer- able, as to levels and length. The zero point for levels 96 IRRIGATION CANALS AND was fixed at the level of the bed of the river at the loca- tion of the regulator. The dam itself, which is 517 feet between the flanks, is pierced in its center by fifteen openings of ten feet wide each; the sills or floorings of each opening being raised two and a-half feet from the zero line. These floorings are so constructed, that, if necessary, they may be removed, and a flush waterway be obtained as low as zero. The piers between the above openings are eight feet in height, so that the elevated flooring leaves the depth of sluice-gate equal to five and a-half feet. The piers are fitted with grooves for the admission of planks. The Regulating Bridge, at the head of the canal, has ten bays or openings each twenty feet in width and six- teen feet in height, each bay being fitted with gates and the necessary apparatus for opening or closing them. The narrowness of the platform, only forty-four feet, contrasts strangely, at this time, with the width of other weirs, as for example the Sone, the Okhla and the Lower Ganges, shown in Figures 37, 39 and 43, but it must be remembered that the bed of the Ganges at Myapore con- sists of large and small bowlders, forming a natural talus or apron below the weir; and that owing to the back- water of the other open channels of the river, which form a water-cushion below the weir, the bed of the Myapore channel below it has a tendency to rise instead of being scoured away. The above arrangement is given to illustrate what kind of headwork was adopted when the Original Ganges Canal was projected, but of late years a new weir, across the whole Ganges River, has been constructed, two or three miles above the Mya- pore dam, which somewhat modifies the above arrange- ments.* *Koorkee Treatise on Civil Engineering OTHER IRRIGATION WORKS. 97 The Barrages of the Nile, at its bifurcation at the Ro- setta and Damietta branches, are open weirs or dams, provided with openings along their entire length. PLAN OF PART OF THE NILE DELTA SHOWING LOCATION OF BARRAGES AND CANALS. the Nile in Egypt during flood, is considerably above the level of the country, which is protected by embankments from inundation, it would have been dangerous to build 7 98 IRRIGATION CANALS AND a solid barrage, which would have still further raised the water surface, unless a length of barrage could have been obtained much in excess of the normal width of the river. A plan of the head of the Delta of the Nile, showing the positions of the barrages, is given in Figure 31, and Figures 32, 33 and 34 give the plan and longitudinal and cross-sections of the barrage of the Rosetta Branch. A view of the barrage is given in Figure 35. The Egyptians call the barrage the " Bridge of Bless- ings," for the reason that it has considerably extended the area of irrigation during the period when it is ur- gently required in Lower Egypt. The barrage crosses the Nile about twelve miles below Cairo, at the point where the river divides into two branches. The length of the western or Rosetta branch, following the sinuosi- ties of its course, is about 116 miles, and of the eastern or Damietta branch, 124 miles. The plain which they traverse, termed the Delta, presents a front to the Medi- terranean of about 180 miles, and forms by far the most valuable portion of the lands of Egypt. To form an idea of the barrage, with the aid of the drawings, imagine a bridge or viaduct of solid propor- tions established at the head of the delta, on each of the two branches of the river, and above these bridges the headworks of three great canals, destined to traverse in their course the Eastern, the Central or Delta, and the Western Provinces of Lower Egypt. If the arches of these bridges were closed by sluices, the water would of course be backed up and inundate the valley, unless it were carried off by the canals fed from the river and restrained by the banks formed to control its overflow. The water thus raised and thrown into the three canals, of which mention has been made, could then be dis- charged at will, on any of the lands of Lower Egypt OTHER IRRIGATION WORKS. 99 through openings made in the canal banks. When the -Nile commenced to rise, the sluices in the arches of the bridge would be opened gradually, until at the-time-al. the great floods, there would be 110 obstruction, except the piers of the bridges, to the passage of the waters. By this system it would be possible to regulate the height of water as desired, to increase the height of feeble floods, and to diminish somewhat the effect of violent floods by discharging water through the three main canals. M. Mougel, an able French engineer, designed the barrages, and constructed them under great difficulties. During his absence from Egypt they were condemned as unsafe, and for twenty years, from 1862 to 1882, they were never used to raise the Nile water to anything like the height originally contemplated. About the latter date, General Sir C. C. Scott Moiicrieff, K. E., took charge of the work, and since then he has so thoroughly repaired and strengthened the foundations of the bar- rages, that they now retain a head of water never at- tempted before he took charge of the works. After making a partial success of the barrages, General Moii- crieff publicly acknowledged, in the most generous manner, the great ability of M. Mougel, the original designer of the works. The following description explains the barrages as they existed, before the construction of the works to reinforce the foundations, carried out by General Moii- crieff. The Xile barrages are two open weirs thrown across the heads of the Kosetta and Damietta branches, at the apex of the Delta. Of the two branches the Kosetta has nearly twice the flood supply of the Damietta, while its bed is some six feet lower. The Damietta branch feeds eight important canals. The Kosetta barrage is l,4,S7 feet between the ftaiiks, arid the Damietta 1.709. 100 IRRIGATION CANALS AND JL.-JL OTHER IRRIGATION WORKS. 101 These barrages are separated by a revetment wall 3,280 feet in length, in the middle of which is situated the head of the Main Delta Canal. The platform 7)1 "the Rosetta barrage is flush with the river bed, being 29.8 feet above mean sea level. Its width is 151 feet and depth 11.5 feet, and it is composed of concrete overlaid with brick and stonework as shown in Figure 34. Down stream of the platform is an irregular talus of rubble pitching, varying in places from 150 to ten feet in width, and from fifty to two feet in depth. The left half of the platform is laid 011 loose sand, the right half on a barrier of rubble pitching overlying the sand. This loose stone barrier is thirty feet high, 200 feet wide at the deepest part, and tapers off to zero at the ends. It closes the deep channel of the river, and its only cementing material is the slime deposit of the Nile. This deposit is so excellent that the barrier is practically water-tight. The platform supports a regulating bridge with a lock at each end. This bridge consists of sixty- one openings each 16.4 feet wide. The lock on the left flank is 39.4 feet wide, while that on the right is 49.2 feet. Fifty-seven of the piers are 6.6 feet wide, while three of them are 11.6 feet wide; their height being 32.2 feet. The lock walls are 9.8 feet and 14.8 feet wide. The piers support arches carrying a road- way. The waterway of the barrage is 34,359 square feet, while the high flood discharge is 225,000 cubic feet per second, causing a banking up or afflux of 0.8 foot. During the floods of 1867 the floor of ten openings of the Rosetta Barrage settled 0.4 foot, producing a deflec- tion in the superstructure both horizontally and vertical- ly, and after this time no attempt was again made to raise the water so high until after the completion of the remodeling of the foundations by General Moncrieff. The Damietta Barrage has ten openings of 16.4 feet 102 IRRIGATION CANALS AND each, more than the Rosetta Barrage. The platforms and superstructures are on the same level, and exactly sim- ilar. FIG. 35. VIEW OF NILE BARRAGE. The Okhla Weir, on the River Jumna, Figure o ( J, is a mass of loose rubble stone with absolutely no founda- tion, and holds up annually ten feet of water, when the water pressure per lineal foot bears to the weight of the dam a proportion of il'j/Joo- or / . Nile sand is much finer than that in the Jumna, and will therefore require a lower co-efficient. Considering the barrage a thoroughly unsound wo-rk as to its foundations, and relying only on friction, it was determined to make the submerged weight of ma- sonry bear a ratio of fifty to the pressure of the water going to be brought on it. Springs might cause a slight subsidence of any part of the barrage, but it could not be moved as a whole. The pressure of a head of ten feet of water would be 8, 125 pounds per lineal foot. The OTHER IRRIGATION WORKS. 103 submerged weight of the platform, as first constructed, was 103,983 pounds per lineal foot. The co-efficient was -sV That this proportion might be -- 1 , it was nBeef^a-ry to make the rubble talus everywhere 131 feet wide and ten feet deep, with a submerged weight per lineal foot of 51,668 pounds. This made the submerged platform and talus together .155,651 pounds as compared to the pressure, 3,125 pounds. Since only one-third of the talus was completed in 1884, the barrage was not re- quired to hold up more that 7.2 feet of water, but on the completion of the talus in 1885, ten feet of water were held up.* The headworks of the Sono Canals, taken from the river Soiie, in India, shown in plan in Figure 36, is a good illustration of the headworks of a modern canal, taken from a river in the plains of India, and having scouring sluices with movable shutters. FIG. 36. PLAN OF HEADWORKS OF SONE CANALS. The length of the weir between the abutments, on the right and left banks of the river, is 12,550 feet, or 2.35 miles, and its crest is eight feet higher than the bed of the river. As two canals are taken off above this weir, one from each bank of the river, there are two sets of end weir scouring sluices, one at each extremity of the "Irrigation in Lower Egypt, by Mr. W. Willeocks, C. E., in Vol. 88 of Transactions of the Institution nf Civil Engineers. 104 IRRIGATION CANALS AND weir. There is also a central set of scouring sluices to provide a greater control over the regimen of the river, and to assist in keeping open a navigable channel across it, between the locks of the two canals. However, after an experience of several years, they have been found insufficient for this purpose. The pool above the weir silted up so much that when the water was level with the crest of the latter, that is, when the water was eight feet above what used to be the bed of the river, it was with difficulty that a boat drawing three feet of water FIG.37 SECTION ^_^_^ ed of ki re i WEIR AT DEHREESONE CANALS could be got across from the canal on one side to that on the other. Many islands were formed one foot or two feet above the level of the crest of the weir, and were yearly increasing. To facilitate navigation, and to raise the level of the pool with the object of obtaining a greater depth of water upon the head sluices of the canals, it was decided to put a movable dam two feet high, along the whole length of the weir. Four men can raise these shutters, when a deptli of six or eight inches of water is flowing over the crest of the weir almost as quickly as they walk. MOVABLE DAM TO BE ERECTED ALONG THE CREST OF THE SONE WEIR. Each set of scouring sluices is made up of twenty-five movable shutters of a width of twenty feet each, that is, each set is 500 feet OTHER IRRIGATION WORKS. 105 in length. These movable shutters are explained in the article entitled Sluices and Movable Dam.s. Before the construction of the weir the mean depth trf the river at time of high flood was found to be 11.64 feet, and the breadth between the banks 12, 400 feet. The river in Hood rises eight and one-half feet over the crest of the weir, and discharges about 750,000 cubic feet per second. Colonel Dickens estimated the flood discharge at 1,020,000 cubic feet per second, but his es- timate was too large. The catchment basin of the Sone is about 23,000 square miles. The weir is composed mainly of dry rubble, and is- similar in cross-section to the Okhla weir, Figure 39, but differing from that structure in having foundations to its three parallel masonry walls, which traverse the mass of dry rubble from end to end, and keep this mass to- gether. An ample supply of good stone, both for rubble and ashlar, is obtainable from quarries about five miles dis- tant. The Sone differs from the Himalayan rivers gen- erally, in being confined within a permanent channel, so that no flank defenses of any importance are neces- sary 011 the banks of the river. The three parallel walls of the dam are founded on shallow, hollow blocks, sunk with the aid of Fouracre's excavators. These blocks have thin walls; for blocks of six feet interior width a single brick thick was sufficient, \vhile for fourteen feet blocks the walls were built from one and one-half or two brick thick.* In the Bengal Revenue Report of the Public Works Department for 1889-90, it is stated that: " For many years after the construction of the Sone Weir, the recurring failures of the piers of the river * Indian Weirs, by Major A. M. Lang, K. E., Professional Papers on In- dian Engineering, Vol. VT. Second Series. 100 IRRIGATION CANALS AND sluices, owing to the inherent weakness of their design, were a constant cause of expenditure in repairs, and in 1885 it was decided to build them 011 a stronger model. The work is now completed." The Okhla Weir, Agra Canal in India, is shown in cross-section in Figure 39. This is a remarkable work, FIG. 39 SECTION AGRA CANAL OKHLA WEIR, in which the engineers of Northern India have exceeded the Madras engineers in the shallowness of foundation, in which the so-called " Madras system " was supposed to differ widely from the practice of other parts of India. In this case foundation may be said to be en- tirely dispensed with. The lowest cold water level, 649 feet above Kurrachee mean sea level, was adopted as the datum, and a trench was made for 2,438 feet across the dry sandy bed of the Jumna, eight miles below Delhi, at this level; and in this trench was built, in the winter of 1869-70, a wall four feet thick and five feet high of quartzite rubble masonry, laid in lime cement; a sloping apron of dry quartzite rubble extended five feet above this wall, and a sloping talus of similar material was laid for 100 feet below it; the floods of 1870 were allowed to pass over this weir, and left it unharmed. During the next winter, the wall was raised to its full height, of nine feet, and the talus was lengthened to 180 feet. The floods of 1871 overtopped the weir by five and a-half feet, more than 1,000,000 cubic feet per second sweeping over it, while 40,000 cubic feet broke over the left shore eubankmeiit and inundated a large tract of country. The greatest velocity was 18.6 feet OTHER IRRIGATION WORKS. 107 per second, and was found to be at forty-two feet below the crest. Stone was worked out of the talus, and deep holes, twenty feet deep, were scoured out on the stream edge. During the next winter, 1871-72, the embankments were heightened and strengthened; and 108 IRRIGATION CANALS AND 1,000,000 cubic feet of stone were expended in filling up the holes below the talus. In 1872-73, a second wall the true crest wall of the weir, parallel to, and thirty feet above the one first built was raised to a height of nine feet; the interval between the two walls being filled with dry rubble. A third wall, four feet thick and four feet deep, was inserted in the talus, forty feet below the lower wall; this has quite stopped all movement in the upper part of the talus; this wall is at the line of maximum velocity in floods. In March, 1874, the canal was opened. The total quantity of stone in the weir is 4,660,000 cubic feet. The stone is the quartzite of the ridge of Delhi, and of similar outcropping ridges in the country around. The right flank of the Okhla weir abuts on to a ridge of this rock, which has furnished an inexhaust- ible supply of material on the spot. The stone contains a large proportion of quartz, a little feldspar, and pro- toxide of iron. It is very durable and excessively hard, rendering it unsuitable (owing to the labor and expense) for finely dressed ashlar work. The river bed has silted up to the crest level; but at the canal head a clear chan- nel is kept open by the scouring action of the river sluices placed at the right end of the weir, similarly situated to those of the Narora Weir, as described below. This weir, and also the Sone and Narora weirs, have long aprons of dry rubble, and this seems to be the section selected for the modern dams, in sandy rivers, by Indian engineers. As the sandy beds of these rivers, except in the vicinity of the scouring sluices, were al- ways raised, on the up-stream side, to the level of tlio crest of the weir, consequently that portion of the work would be free from scour, and it, therefore, was given a steeper slope than the apron on the down-stream side. The Streeviguntum Weir or Aiiicut, over the Tam- brapoorney River in Madras, is shown in cross-section OTHER IRRIGATION WORKS. 109 in Figure 41. This weir, and also that across the Goda- very, Figure 44, are located in Madras, and they are there called anicuts. The Streeviguntum Weir is of the- same type as the Narora Weir, though on a smaller scale. It, however, has no water cushion, while the Norora Weir has a water cushion of at least three feet at the low stage of the river. The scouring sluices of this weir, as in the greater number of the old weirs of the Madras Presidency, have a small span. In this case there are nine vents, and each vent is only four feet in width by nine feet high. These small vents have not the scour- ing capacity of the large ones of Northern India. The Streeviguntum Weir is 1,380 feet in length be- tween the wing-walls, raised six feet above the average level of the deep bed of the river, and the width at the crown is seven and one-half feet; there is a front slope of one-half to one, and in rear a perpendicular fall on to a cut-stone apron twenty-four feet wide, and four and one-half feet in depth; beyond, there is a rough stone talus of the same depth, and thirty-six feet in width, protected by a retaining wall. The foundation of the body of the work, and of the cut-stone floor in rear, is of brick-in-linie, laid on wells sunk ten and one-half feet in the sand, and raised four and one-half feet above the wells, including the cut-stone covering; the retain- ing wall is built of stone-in -lime, and rests on a line of wells, sunk to the same depth, ten and one-half feet. The body of the aiiicut is of brick-in-lime, faced through- 110 OTHER IRRIGATION WORKS. out with cut stone, and furnished with a set of under- sluices at each extremity of the work, to let off sand and surplus water.* The Narora Weir, Lower Ganges Canal in India, is shown in cross-section in Figure 43. This canal gets its supply from the river Ganges. It is the most recent of the large and important weirs, built across wide rivers with sandy beds, and from the volume of the floods, the sandy nature of the river bed, and the absence of material on the site suitable for a weir of this description, the diffi- culties to be contended with have been very great. The dam proper is a solid wall of brick masonry 3,700 feet in length ; the floor below is of concrete, three feet thick, cov- ered over with brick work, one foot thick, and then with one foot of sandstone ashlar; and the talus below is formed f of very large masses of block kunkur, a kind of nodular limestone, brought from the quarries at thirty miles distance. The up-stream side of the weir is backed with clay puddle, pitched 011 its outer- slope with an apron of block kuriker. The length of the weir was settled by Major Jeffreys, R. | c E., as 4,000 feet, on the fol- .*<** <# ***._ lowing data: See Figure 42. & afflux =1.5 feet, when the river was at its highest was accepted as perfectly safe. ((( b) =(> feet--- maximum flood level above sill of weir. Q -maximum flood volume flowing over weir of 200,000 cubic feet per second. Z-= length of crest of weir in feet. w -6 feet per second xnvfiwe velocity of approach. * Indian Weirs, by Major A. M. Lang. Professional Papers on Indian Engineering. Vol. VI, Second Series. OTHER IRRIGATION WORKS. Ill The figures applied in D'Aubiiison's formula give: Q 3.49 I h i h + .035 w* ; 4.97 I (a b) yh + .01 -it? Computing this we find the value of ^length of weir =3,776 feet. FIG. 43. NARORA WEIR, LOWER GANGES CANAL. Colonel Brownlow, R. E., in reviewing the project and deprecating a proposed reduction of the length settled by Major Jeffreys, showed that a maximum flood of 230,- 000 cubic feet might not unreasonably be expected, and that taking into consideration the circumstances of the site, the light and friable nature of the soil of the coun- try, and the lowness of the ridge which intervenes be- tween the present channel of the river and the broad parallel trough of the Mahewah Valley, it would be very dangerous to contract the weir and raise flood levels. The necessity for well foundations, especially for a strong line of deep blocks, along the lower end of the stone floor, and also for staunching all leakage by a pud- dle of clay above the drop wall with a view of holding up all the water possible, and thus losing none of the supply when the river is at its lowest of stopping all flow under the floor to the risk of undermining arid de- stroying it and also of resisting retrogressive action below the weir, was strongly urged in Colonel Brown- low's review of the project, as will be seen from the fol- lowing extract from his report: " My reasons are, first, that all our experience in Upper India shows that where velocity of a stream is largely augmented by the construction of a barrier across it, permanent deepening of the channel below in- variably takes place; and secondly, that leakage will 112 IRRIGATION CANALS AND occur through the sandy bed underneath a dam with shallow foundations. 11 Deepening of the bed has taken place on all the tor- rents across which weirs have been thrown on the East- ern Jumna Canal, and it is now occurring at Okhla. It occurred below the Dhanowrie Dam, 011 the Ganges -Canal, until the obstruction caused by the dam was re- duced, so that the normal velocity of the torrent was nearly restored, when the channel below partially silted up again. 11 This fact alone is a very strong argument against the proposed reduction of length of weir, but as our weir at Narora will, in any case, greatly accelerate the mean velocity of the Hoods, we must be prepared both for re- trogression of levels, and the formation of very deep holes immediately below the talus of heavy material. Those at the tail of the Okhla Weir, Figure 30, after the floods of last season, were from IV) to 20 feet deep; but whereas at Okhla the materials for filling them up, and thus resisting further retrogression, are readily available, we shall at Narora have nothing but a scanty supply of block kunkur brought from long distances, or blocks of beton manufactured at considerable expense. " In the latter case, a strong line of deep blocks, sup- ported by the ruins of the talus, would stoutly resist any retrogressive action, whilst the materials for repair were being collected and prepared; while the work on shallow foundations would run the greatest risk of 'being undermined and destroyed. " It is stated that the leakage, prevented by deep well foundations, is more imaginary than real, because long before the volume entering the canal is likely to be util- ized, the bed of the river will have become silted up nearly to the crest of the dam, and the upper layers of silt will have become more or less clayey, because leak- OTHER IRRIGATION WORKS. 113 age takes place through the banks as well as through the bed, and finally because little or no leakage has been detected through the Okhla weir which has shnilow foundations. " I cannot admit that the upper layers of silt deposited in the bed of the river above are deposited by falling floods, and are swept out again by the full current of the next succeeding high flood. The scour which takes place immediately above any marked contraction of a stream, is a matter of common experience, and is easily explained by the great relative increase in the bottom velocity re- sulting from the contraction. " The banks, on the contrary, will become permanent, if the flanks of the weir are not turned, and they may ultimately become staunched by the clay brought down by the flood water. Besides, the effect of the pressure of the water 011 the banks is not worth mentioning, when compared to that 011 the sand underlying the weir. I think, therefore, that any consideration of the leakage through the banks may safely be neglected. But, even if it could not be, I do not see why we should not try and stop the leakage through the bed, because the banks are supposed likely to leak also. " The latter argument applies equally to the objection commonly urged against deep block foundations, viz: that aline of them cannot be made perfectly water-tight. It is surely better to block up T W tns of the area through which leakage can occur, than to leave it all open be- cause a perfectly water-tight partition cannot be made. " Apart from any consideration of the value in money of the water saved by a strong water-tight dam, the strongest necessity is, to my mind, laid upon us to economize every drop of the low-water supply in the river, owing to its insufficiency for the requirements of the years of drought. Common justice to the cultivating 8 114 IRRIGATION CANALS AND community, dependent on the canal, seems to me to dic- tate the adoption of every reasonable precaution for rendering the whole of the short supply available for purposes of irrigation. " I have placed the deep line of blocks at the tail of the cut-stone apron, because I think that the latter, if built at the proper level, and of a proper section, will perfectly protect the blocks from any fear of action on the up- stream side, and that the real danger to be guarded against is the cutting back and permanent deepening of the bed of the river below the weir. I have allowed only shallow foundations for the drop wall, because I consider the line of blocks underneath it sufficiently protected by the cut-stone apron and deep foundations on the down- stream side, and by the mass of heavy material on the up-stream side. The velocity of the current above the weir, although amply sufficient to sweep away the loose sand of the bed, has been proved, by the experience at Okhla, insufficient to move the heavy material of the apron." To hold the talus together, it is traversed from end to end by solid concrete walls at intervals of thirty feet and forty feet as shown in Figure 43. This plan was found to be necessary at Okhla, Figure 39, where the third wall of four feet square section was adopted as necessary, in order to check the movement in the blocks in the upper part of the talus, although it formed no part of the orig- inal design. The level of the cut-stone floor of the weir, as also of the floor of the under-sluiee, is three feet below low water level; and as the floor is five feet thick, the laying of it entailed excavation to a depth of eight feet below low water. To effect this, the upper row of blocks and lower row of wells were sunk to. full depth, and hearted with con- crete. This was done by filling the hole below the curb, and OTHER IRRIGATION WORKS. 115 the lower one or two feet of the block or well by hydraulic cement let down in skips; when this had set, it formed a water-tight plug, and enabled the well or block To~be pumped dry. The concrete core of the well or block was then put down in layers, and rammed in the ordi- nary manner. The interval between each pair of con- tiguous wells and blocks was closed by wooden piles, and the interval, included between piles and well, cleared of sand and filled with concrete. Clay puddle was also packed above the upper row of blocks. The space, thirty-three feet in width intervening between the upper row of blocks and the lower line of wells, was then di- vided into compartments of about forty feet in length, by cross lines of shallow blocks, sunk, hearted and con- nected as above described. Thus large coffer-dams were formed, which were excavated to a depth of eight feet below low water level, and the water pumped out by Gwynne's pumps, so as to allow of a three feet thick concrete floor being laid. On this a layer of brick- work one foot thick was added; and this in its turn was covered by an ash- lar floor of cut sandstone blocks one foo't in thickness. The under-sluices, forty-two vents of seven feet each, are at the extreme right abutment end of the weir, so as to keep a clear channel open along the front of the im- mediately adjoining head-sluices of the canal, whose floor is three feet above that of the weir sluices, and this allows the lowest three feet of silt-laden water to pass by without entering the canal. The crest of the weir stands seven feet above low water level, which is the level of the floor of the head-sluices, thus allowing seven feet in depth of water to pass into the canal/"" The Dowlaiswaram Branch of the Godavery Aiiicut or Weir is shown in cross-section, in Figure 44. * Indian Weirs, by Major A. M. Lang. Professional Papers on Indian Engineering, Vol. VI, Second Series. 116 IRRIGATION CANALS AND The total length between the extreme flanks of the weir is 20,570 feet. It is broken Into four sections separated by islands, and the total length of the anicut on these four sections is 11,866 feet. GOOAVERV ANICUT The longest section is the Dowlaiswaram, and the fol- lowing description of this section is taken from Colonel Baird Smith's work, " Irrigation in Southern India:" The bed of the Godavery throughout is of pure sand, and in such soil are the whole of the foundations laid. Commencing from the eastern or left bank, the first portion of the work is the Dowlaiswaram branch anicut or dam. The total length of this is 4,872 feet. The body of the dam consists of a mass of masonry resting on front and rear rows of wells, each well being six feet in diameter, and sunk six feet below the deep bed of the stream. The masonry forming the body is composed: 1st. Of a front curtain wall running along the whole length, seven feet in height, four feet in thickness at the base, with footings one foot broad on each side 10 cover the tops of the wells on which the curtain wall rests, and three feet thick at the summit. 2d. Of a horizontal flooring or waste-board nineteen feet in breadth and four feet in thickness. 3d. Of a masonry counter-arched fall twenty-eight feet in breadth and four feet thick, of which the curve is so slight that the form may be considered practically as that of an inclined plane. The waste-board and tail OTHER IRRIGATION WORKS. 117 slope are protected against the action of the stream by a covering of strongly clamped cut stones over all. 4th. Of a rough stone apron in rear formed ~oi~the most massive stones procurable, and extending about seventy or eighty feet down stream. Figure 44 does not show the apron extended so far, but it is now extended to about 150 feet, and further secured by a masonry bar. The apron, protects the rear foundation against the erosive action of the stream passing over the dam. The body of the dam rests merely on a raised interior or core of the common river sand, and no precautions to strengthen this in anyway have been considered neces- sary. On the extreme left flank of the dam is a series of works, consisting of a lock for the passage of craft, a head sluice for an irrigation channel, and an under sluice for purposes of scour and clearance from deposits. FIG. 45. CROSS-SECTION OF TURLOCK WEIR. The Turlock Weir in California, across the Tuolumne River, is shown in cross-section, in Figure 45. The 118 IRRIGATION CANALS AND original design for this weir was made by Mr. Luther Wagoner, C. E., but the water cushion was added by Mr. E. H. Barton, the present Chief Engineer of the Turlock Irrigation District. The flood discharge of the river will pass over the weir. The low weir on. the down- stream side backs up the water and forms a water cushion to receive and break the shock of the flood-water when it flows over the weir. The water-cushion has been found in India to be a most effective protection to the bed of the river from the erosion caused by falling water. The length of the weir on top is 330 feet, its max- imum height to foundation 108 feet, and the maximum height of the overfall of water ninety-eight feet. Its width at base is eighty-three feet, and the maximum pressure 6.3 tons per square foot. The weir is curved in plan, the radius to up stream face being 300 feet, and the angle 60. Bed and sides of channel is meta- morphic (quartzite after slate) rock of exceeding hard- ness. On the removal of an old dam, near the site of this weir, an inspection of the bed rock, where the fall had been ten to thirty feet over said dam for eighteen years, showed hardly any appreciable wear. Calculated for the highest flood known, that of 1862, the flow over the crest of the weir is 130,000 cubic feet per second. The subsidiary weir is located 200 feet below the main weir. It is 120 feet long on top, twelve feet in width, and twenty feet in maximum height, and it backs the water to a depth of fifteen feet on the toe of the upper or main weir, giving a water-cushion of that depth; but, during floods, there will be a depth on the toe of over forty-five feet. The volume of the dam will be about 33,000 cubic yards. Vertical falls, with water-cushions, are preferred in India to sloping or curved faces on the down-stream side OTHER IRRIGATION WORKS. 119 of works over which water falls. For stability to resist water pressure dams or weirs, with a curved profile ac- cording to the French plan, are the most suitable-pbttt, in order to avoid the erosive and destructive action of the falling water on the curved face, vertical walls with water-cushions are preferred. Numerous instances of vertical falls are to be found on the canals in Northern India, and 011 two important modern works, the Bhim Tal Dam and the Betwa Weir. Doubtless instances can be found also in modern works of dams with curved faces on the down-stream side over which water flows for example, the Vryiiwy Dam for the Liverpool water supply, and the concrete dam for the Geelong, Australia, water supply. The dam across the river Lozoya, in Spain, to impound water for the supply of Madrid, has an extraordinary vertical drop 105 feet. The back of the dam, over which the water falls, is not vertical, but has a slight batter given to it by off-sets. The flood-water, however, leaps clear over this face. During floods, when the reservoir is full, the whole discharge of the river pours over it in an unbroken WEIR OF HEN APES CANAL. sheet. It has not a water-cushion. The dam was built of ashlar, which is not the best method of construction 120 IRRIGATION CANALS AND for such a work. Uiicoursed rubble is much better suited for a dam, as there is less likelihood of percolation through its broken joints than through the regular- coursed ashlar. The cross-section of the weir of the Henares Canal, on the river Henares, in Spain, is given in Figure 46. The masonry of this weir is first-class in every respect. Its design, however, as to its cross-section, is one not adopt- ed in India. For a masonry weir, a vertical drop on the down-stream side and a water-cushion, is preferred in the latter country. The action of the water on the Ogee Falls, 011 the Ganges Canal, was found very destructive, whereas the vertical falls with water-cushion stood well. Where the Henares Canal is taken from the river, the river bed is composed of compact clay rock, mixed with strata of hard conglomerate, which had to be blasted out to fit it for the foundation of the weir. The weir itself is 390 feet in length of crest, formed on two curves of 397 and 198.5 feet, running obliquely across the river so as to be tangential to the axis of the canal. It raises the water to a height of twenty feet. Its thickness at crest is 3.14 feet, and on the general level of the river's bed, 45.8 feet. As this bed, however, was very uneven, it was necessary to carry down the thrust of the apron by a series of blocks of stones formed in steps, the last firmly embedded three feet in the rock. The body of the weir consists of hydraulic concrete; the apron is faced with cut-stone blocks, every fifth course being a bond three feet deep, and is a beautiful specimen of ma- sonry. Much pains have been bestowed on preventing the least filtration. For this purpose a channel was cut in the rock along the central axis of the weir for its whole length, and into this a line of stones was fitted, half bedded in the rock, half rising into the concrete. OTHER IRRIGATION WORKS. 121 Into each vertical joint of these stones a groove was cut an inch deep. The stones were built in cement into the rock, and the joints run with pure cement. The -con- crete was then rammed tightly round them, arid a water- tight joint thus formed. With the same object V-shaped grooves were formed in the sides of each stone of the four upper courses of the weir, as shown in Figure 46, and horizontal grooves cut to correspond with them on the upper and lower faces of each stone, as shown in Figure 47. When, therefore, the stones were set, there was formed a con- tinuous channel, one inch square, running between each, and this was filled with pure cement, poured in liquid, so as to form a tight joint between each stone. In spite of all the precautions taken the floods exerted an erosive action on the bed of the river below the weir, and a large hole was scooped out of the rock at the tail, where the apron ended.'" The head of the Cavour Canal in Italy is on the left bank of the Po, about a quarter of a mile below the Chivasso bridge. The bird's eye view, Figure 48, shows the position of the weir, regulator, uiider-sluices and escapes. In Indian canals the escapes are usually channels from the main canals to carry away any surplus water. In the bird's eye view the channels marked " Escapes" are really channels to carry away the water that is used for scour- ing purposes. These scouring or under-sluices were in- tended to prevent the silting up of the channel from the left bank of the Po to the regulator. In the bird's eye view is shown the location of the proposed weir (not yet built), placed obliquely in a curve, across the river. *Irrifjation in Southern Europe, by Lieut, (now General) C. C. Scott Moncrieff, K. E. - 122 IRRIGATION CANALS AND OTHER IRRIGATION WORKS. 123 Its length was to be 2,300 feet, forming a curve of, for the most part, 823 feet radius, but less at the ends. The design was to raise the water by means of this weir~to-a~ height of about eight feet; and of such excellent stiff soil is the bed composed, that it was thought suffi- cient to build a wall of concrete going down to only CAVOUR CANAL-DETAILS OF PROPOSED WEIR ACROSS THE PO. THE FIGURES IN BRACKETS GH (579 ^Estimated surface of water in a flood as great (5S3.52)Inlradosof3ridae near Ckivasso. "s tluit o/1839. The discharge being 143000 cubic feet S2A(n_Sitrfarji H-titcrjLr>jtl,e/lood of 1839. P er sec - J**i>'0 over a weir 1280 feet long. FIG.49 Cross section on AD. 6.56 feet below the bed, enclosed in front and rear by sheet piling, its upper portion cased in granite slabs of five inches in thickness, and the rest of blocks of rough stone forming a protection in front sloping down to a horizontal distance of sixteen feet, and in rear to twenty-six feet, with a line of sheet piling at its toe, and beyond it an apron of similar blocks, of the same width of twenty-six feet, ^ with another row of piling. 124 IRRIGATION CANALS AND The weir was intended to rest on solid abutments at the two ends, and on the end next the canal was to be supplied with a set of scouring sluices, or escapes, con- sisting of seventeen openings, each 4.6 feet in width and eight feet in height. All the bed for ninety-six feet below, and 500 feet above, is to be paved \vith splendid blocks of cut granite, brought from the neighborhood of the Lago Maggiore. From the left flank of this escape the regulating bridge is retired for a distance of about 700 feet, as shown in the bird's-eye view, Figure 48, and close to its right abutment is built a second escape of nine openings, each 5.54 feet wide and ten feet high . The floor of this escape is one foot lower than that of the regulating bridge, the more effectually to establish a scour.* Article 29. Scouring Sluices Under Sluices. These sluices are sometimes called Weir Sluices and again Dam Sluices. The first effect of the construction of a weir across a river is that the pool formed by it gradually silts up, partly by deposit, during floods, of matter in suspension in the water, and partly by the gradual forward motion of the bed of the river which exists in all streams, but is only visible to the eye in rivers with sandy beds. Islands begin to form, which would in time obstruct navigation across the river above the weir, and would prevent the water, in the dry season, from finding ac- cess to the canals led off from the pool. In rivers in India carrying sand and silt, the silting up of the bed of the river to the level of the crest of the weir seems to be inevitable. This sand and silt if not Irrigation in Southern Eiirope, by Lieut, (now General) C. C. Scott Moncrieff, K. E. OTHER IRRIGATION WORKS. 125 removed choked the head of the canal and locks, located above the weir, and stopped their supply of water. In. order to obviate these difficulties, every weir has td~t)(r furnished at one extremity, or at both extremities, ac- cording as one canal or two canals are taken off from above it, with a set of scouring sluices. In very long weirs, such as that across the Sone River in Bengal, another scouring sluice is placed in the center, to assist in keeping open a navigable channel across the river. The proper location for a scouring sluice, with respect to the regulator of a canal, is that the crest of the weir should be at right angles to the face line of the regulator, and also at right angles to the face line of the lock when the channel is navigable. This is well exemplified in the plan, of the Okhla Weir Works, Figure 40. It can be seen there that the cur- rent of the river flows flush with, and parallel to, the face line of the canal and lock, and that there is no recess for still water and consequent silting. An instance of the defective location of a regulator, with respect to the scouring sluices, is seen at the head- works of the Upper Ganges Canal, Figures 26 and 28. Here, the entrance to the canal is located over two hundred feet lower down the river than the scouring sluices, in consequence of which, the strong current flowing to the scouring sluices, is not across the face of the regulator, and there is a tendency to silt where the marks * * * are shown, on Figure 28. In the low stages of the river the silt prevents the free flow of the current towards the regulator. Another instance is in the location of the regulator of the Cavour Canal, Figure 48. The regulating bridge is located 700 feet below the weir, and the course of the current through the scouring sluices, leaves somewhat still water in the left corner, just above the sluices of 120 IRRIGATION CANALS AND OTHER IRRIGATION WORKS. 127 the regulator. When these sluices are opened the silt is washed into the canal. The flow through the scouring sluices is controHed- as explained in Article 31. The regulator should be as close as possible to the scouring sluice, and the sill of the latter should be about three feet lower than the sill of the former. Under these circumstances, when the scouring sluices are opened, the scour takes place across the whole face of the regulator, and washes away any silt or debris likely to obstruct the free flow of the supply into the canal. Article 30. Regulators. The Regulator at the head of a canal is also called, Regulating Bridge, Regulating Gate, Regulating Sluice, Head Gate, Head Sluice, Canal Sluice, Head of Canal, etc. To be precise, the regulator is the structure in which are fixed the sluice gates to control the water sup- ply to the canal. Regulating Gates Del Norte Canal Cross-Section and Elevation. U Iii India, Egypt and Italy, the regulator is sometimes part of a highway bridge, as shown in Figures 27, 32 and 48. In the latter case, however, the use of the cov- ered bridge is confined to the canal officials. The Myapore Regulating Bridge, of the Upper Ganges 128 IRRIGATION CANALS AND Canal, is shown in Figure 54. The view is taken from the down-stream end of the bridge, so that the sluice- gates, which are located on the up-stream side, are not seen. The sluice-gates of this regulator are shown in Figures 62 and 63. These sluice-gates are twenty feet in width, but regulating sluices are seldom more than six feet in width, 011 account of the difficulty of working large sluices under a great head of water. Idaho Canal Regulator Head Cross-Section and Elevation. The Reglating Gates of the Del Norte Canal, in Colo- rado, are shown in Figures 55 and 56, and Figures 57 and 58 show an Idaho Canal Regulator Head for pipe inlets.* It is usual, on Indian canals, to make the floor of the regulator at head of canal, the zero for levels on the canal. Article 31 . Sluices Gates Movable Dams and Shutters. The terms Sluices, Head Sluices, Gates, Sluice Gates and Head Gates, are variously employed to mean the sluices that are fixed in the regulator, and which are used to control the supply of water at the head of a ca- iial. The sluice gates usually used on Irrigation Canals are the sliding sluice gate Figures 55, 56, 57, 58, 59, 60, *Figures 55, 56, 57 and 58, are taken from a paper on American Irriga- tion Engineering, by Mr. H. M. Wilson, M. Am. Soc. C. E., in Vol. 24 of the Transactions of Am. Soc. C. E. OTHER IRRIGATION WORKS. 129 62, 63, 64, 65, 69, 70 and 71, the horizontal plank gate, Figures 20 and 61, and the vertical piank or needle sluice. These, and other methods not so generally in use~arc explained below. The gates of the Cavour Canal Regulator, of which there are twenty-one, are fitted with a double set of gates, and the cutwaters of the piers, on the up-stream SLUICE GATE CAVOUR CANAL. El SLUICE GATES INDIAN CANALS. Old Method on the Jumna, Improved Method on the Ganges, side, have grooves besides, for stop-planks. These latter are intended to be used in case of accident or repairs to the gates or regulator. 9 130 IRRIGATION CANALS AND The gates are of wood, braced with iron, as shown in Figures 59 and 60. They are raised by means of an iron bar four by three-quarter inches, and about eighteen feet long, firmly fastened to the center of the upper edge of the gate, and connected with diagonal bars to the lower corners to distribute the force. This bar passes through, to the platform above the highest flood level, from which the gates are worked. The bar is pierced with holes, a, a, one and one-half inches in diameter at every two inches of its length, through which, when it is required to raise it, the iron point, c, of a crow bar is put, and it is raised up hole by hole, an iron key, b, be- ing pressed at the same time through another of these holes, and resting on two cross bars to prevent it slipping down again. One man works the crow-bar while another holds the key. By pulling this out the gate falls at once, and this is important, as it is of consequence sometimes to be able to close the canal quickly. This arrangement has the great merit of simplicity and it is frequently adopted on American canals. On some of the regulators in Northern India, a drop gate is used in a simple groove, and sleepers, with a scant- ling of six inches square, are dropped upon the top of the gate. Both time and labor are required to close or open the bays, although they were only six feet in width. On the Ganges Canal regulator, however, with ten bays, having each a width of twenty feet, on which the safety of the works depended, it was necessary to devise some quicker method to economize the labor required for using the apparatus. Figures 61 and 62, show the old and also the improved method of operating the sluices. Figure 61 represents, in section, the drop gate, a, and the sleep- ers, b, b, b, opposed to the up stream current; a, repre- sents a gate five feet in depth, which is kept suspended in dry seasons, and is dropped down on the expectation OTHER IRRIGATION WOKKS. 131 of a flood; b, b } b } show the sleepers or long bars of tim- ber, which when the chains are removed from the gates, are successively dropped upon them until the bay ~ is CANAL REGULATING APPARATUS. REGULATING BRIDGE WITH LIFT-GATE & SLEEPERS Elevation. III Lift-gate. FIG. 63 DROP-GATE FOR DAMS. Elevation. . , Plan FIG.64 Plan FIG.68 WINDLASS FOR REGULATING BRIDGE. 20. FIG. 6 5 PLAN OF SLEEPER. FIG.GG 132 IRRIGATION CANALS AND closed, Figure 61. The time that this takes is equal to eighteen minutes. Figures 62, 63, 64 and 65, show the improved design gained by the use of the windlasses. The bay or sluice opening, it will be observed, is divided into three series, the lowest shutter having its sill on the floor of the reg- ulator, which is the zero level of the canal; the centrical and top shutters having their sills elevated in heights of six feet, but' working in separate grooves in the piers. The shutter marked 1, Figure 62, is dropped from wind- lass, 1; that marked 2 from windlass, 2; and that marked 3 consists of sleepers, which are raised and low- ered without the aid of a windlass. The three gates, therefore, are quite independent of each other; each has its own sill to rest upon; and the whole can, if necessary, be worked simultaneously. The great advantage of this method will be understood, by supposing that a supply of water not exceeding six feet in depth is required for canal purposes. In this case, the whole of the shutters, 2, and 3, may remain, closed; and when floods come on, the whole of the water-way may be stopped by releasing one gate only. The machinery attached to these gates is of the most simple description, intelligible to the commonest laborer on the works, and not liable to disarrangement. On some canals in India and also in other countries, Needle Dams, as they are termed, are adopted to control the supply. A horizontal bar of wood or masonry is fixed 011 the floor of, and across the opening, and a beam of timber is placed vertically over and parallel to this and fitting into sockets in the piers. Planks, called needles, about four inches scantling, are placed vertically in front of these, and are operated from the flooring of the bridge, whether permanent or temporary. This plan has been found to work well in some places. There is always OTHER IRRIGATION WORKS. 133 FIG.70 i SLUICE OF HEN ARES CANAL 134 IRRIGATION CANALS AND more leakage through a plank sluice than through a properly constructed framed sliding sluice. For the openings of Level Crossings, Drop Gates are sometimes provided. They are retained in their upright position, Figures 67 and 68, by chains against the pres- sure of the canal water from the inside, and which, on the occurrence of a flood, can be dropped down on the flooring by releasing a catch, and allowing the flood water to pass through the openings. When the flood is over, the gates are raised upright by a movable windlass, the pressure of the water being temporarily taken off by dropping planks into the groves. The sluices of the Hen ares Canal are five in number, each four feet wide. The details of these sluices are shown in Figures 69, 70 and 71. The gates are made of elmwood, and rest, on their down stream side, against pinewood frames, instead of against the edges of the stone grooves, arid thus consid- erably reducing the friction, and at the same time secur- ing a tight fit and preventing loss of water by leakage. The gates are raised by ratchets. One man can with tolerable ease raise a gate at a time. The ratchets, pin- ions, etc., are enclosed in rather heavy cast-iron boxes. This allows of no provision for suddenly dropping the gates in case of floods; but an overfall weir has been built in the left bank of the canal just below, to allow of any flood water above the full supply falling back directly again into the river. What seems a strange omission is, that the piers of the regulator are not provided with grooves for stop- planks to be used to dam out the water in case of acci- dent or repairs.* *Lieut. (now General) f. C. Scott Moiicrieff, Irrujalion in Southern En rope . OTHER IRRIGATION WORKS. 135 In the old works such as the Godavery, the Kistna, the Cauvery, and other weirs, it was the custom to make sluices with vents only six feet wide, and raised to~ordy about half the height of the flood. In these works the scouring sluices were closed in the dry season, either by balks of timber dropped one after another into the grooves in the pier, or by gates, sliding in vertical grooves, which gates were raised and lowered from above by levers working into long rods attached to the gates. This system necessitated the construction of a masonry superstructure to above the level of the highest flood, which opposed great resistance to the free flow of the floods, and stopped floating cUbrix in the river, so that the sluices not uiifrequently became choked with trees and brushwood. As these earlier works were inefficient, in the more modern works, much larger openings have been left, and movable dams have been erected, with 110 super- structure above the level of the weir, so that floods pass without obstruction over the weirs to the depth, it may be, of eighteen or twenty feet. That these movable dams may thoroughly perform their duty, it is necessary that they should be large and strongly constructed, and that they should be capable of being operated quickly. It was, therefore, attempted, in Orissa, India, to increase considerably the size of the sluice openings in the weir in the Mahanuddy River, and shutters on the plan adopted by the French engi- neers in the navigation of the Seine were constructed. The center sluices are divided into ten bays, of fifty feet each, by masonry piers. Each bay is composed of a double row of parallel timber shutters, which are fastened by wrought-iron bolts and hinges to a heavy beam of timber embedded in the masonry floor of the sluices. There are seven upper shutters and seven 136 IRRIGATION CANALS AND lower in each bay. The lower shutters are nine feet in height above the floor, and the upper seven and a-half feet. Each bay is separated from the next one by a stone pier five feet thick, in which the gearing for work- ing the shutters is fixed. FIG. 7 2 SHUTTERS OF THE MAHANUDDEE WEIR. The up-stream shutter fell up-stream, and the down- stream shutter fell down stream, so that the up-stream shutter, unless intentionally fastened down, would, in times of flood, be raised by the water getting under it and flowing against it, and would thus, automatically, shut itself, and leave the shutter below quite dry. The up-stream shutter was supported up-stream by chain ties. When it became necessary to open the sluice again, of course it would not have been practicable to lower the upper shutter against the head of water stand- ing against it, and, therefore, the lower shutter was raised and strutted up by hand, as men could walkabout with safety on the dry, down stream sluice channel, and this left a double row of shutters standing against the stream. The space between these shutters was then allowed to fill with water, and then the upper shutter, being in equilibrium, was allowed to fall back into its place on the bottom of the sluice, while the low^r shutter supported the head of water OTHER IRRIGATION WORKS. 137 If, at any time, it was required to open the sluice, the back shutter was lowered by knocking away the feet of the struts .which supported it, on the down-stream sid^, and it then fell down-stream, and the sluice was open. It has been found that in a dam constructed 011 this principle, 500 lineal feet of shutters can be easily low- ered in one hour, with a head of six feet of water, and that with a similar head an equal length can be closed in twenty-five minutes arid that three men (East Indians) standing on the floor are sufficient to knock away the back struts with safety to themselves. The back shut- ters are not damaged as they fall on the floor, because water escapes as each shutter falls, sufficient to form a a cushion for the other shutters to fall into. Twelve men are necessary to lift each of the back shutters into position/''" This kind of shutter has never been raised against a greater head of water .than about six feet nine inches. The front shutter is only used when the level of the river has fallen to at least six feet above the floor of the weir, and frequently the engineers hesitate to use the shutters until the water has fallen lower. The objection to this plan was, that the upper shutter was raised by the stream with such velocity and force that the chain ties supporting it frequently gave way, and the shutter was carried off its hinges. On one oc- casion ths front beam was pulled up from the floor. Major Allan Cunningham, R. E., has given the fol- lowing formula, for finding the tension on the chains = breadth of shutter in feet. j depth of shutter j ( stream } r mid-surface velocity (over shutter when down) in feet per second. w == weight of a cubic foot of water === 62.5 Ibs. (j = acceleration of gravity -= 32.2. T === total sudden tension of the wliole set 'of chains in Ibs. (/, = angle of inclination of chains to shutters when vertical, that is, at instant when strained taut. Total tensile stress in Ibs.- T=[ rf-H4 }wb d cosec a. v /// Example. In the sluice shutters of the Midiiapore Weir, given b .6'. 25, d 0'.5, v=12' per second, =55. Total tensile stress ^G.5- r 4 X,l^r ; ) x 62 - 5 x r) - 25 X6. 5X1. 221=75, 587 Ibs. And if there be two chains equidistant from the *T'r*W""*'i *i vX-^^s^-K^^ *'* '' v * " " ~' *"" v " v *''' "'' 1 Figs. 126, 127. Widening of Ganges Canal at Toghulpoor. The Eastern Jumna Canal, f having a discharge of 1,068 cubic feet per second, had, when originally con- structed, a grade of 372 feet in 130 miles, or at the average rate of 2.86 feet per mile. In some reaches the grade was considerably more than this. Immediately after the water was admitted into the canal the effect of a rapid current was apparent. Ketro- gression of levels on an extensive and dangerous scale took place. From the Nowgong Dam to the Muskurra River, where the fall was eight feet per mile, deep * Report on the Ganges Canal by Captain J. Crofton, E. E. t Notes and Memoranda on the Eastern Jumna Canal, by Colonel S : r P. T. Cantley, K. C. B. OTHER IRRIGATION WORKS. 189 erosion took place. A specimen cross-section 011 this reach is given in Figure 128, where the shaded portion shows the part scoured out. The silt resulting from the erosion was carried down the canal until it got to a level reach, where it was deposited, causing the TaeclT^and banks to silt up, as shown in Figure 129. The shaded part shows the silting up; the top of the bank and outside slope are shown, dressed up. Fig. 128. Erosion on Eastern Jumna Canal. To prevent the canal from being destroyed it had to be reconstructed at great expense. Fig. 129. Silting up on Eastern Jumna Canal. Twenty-three falls were constructed, being at the rate of about one fall to six miles of canal, and the grade was reduced, varying from 17 to 22 inches per mile. Article 39. Falls Drops Checks. In designing an artificial channel for the passage of a large volume of water, the first thing that presents itself for decision is the rate of slope that is to be given to the bed, to insure that velocity of current which prevents the deposition of silt, keeps the channel clear of weeds and other impediments, and, at the same time, shall not erode the bottom and sides of the channel. 190 IRRIGATION CANALS AND "When, the slope or grade of the canal is the same as the natural fall of the country through which the canal is excavated, and when the current is adjusted, as ahove explained, to prevent silting up and erosion, then the level of its bed will, of course, remain at a uniform depth below the surface of the ground. Bed of Canal in Embankment. Fig. ISO. Longitudinal Section, Canal in Embankment. Usually the slope of the country is greater than that of the canal, and, with canals having a large discharge, that is, from 1,000 to 6,000 cubic feet per second, this is invariably the case, and the excess of slope of the country has to be disposed of, either by embankments or by works variously called falls, drops, and sometimes in America, checks. Fig. 131. Longitudinal Section, Falls in Canal. In brief, then, the object of falls is to get rid of a greater declivity of bed than it is advisable to allow in mere earthen channels, and it is sought to be attained by giving at intervals sudden falls protected by masonry, between which the simple earthen bed may preserve its proper slope. Figure 130, not drawn to scale, shows a reach of a canal in embankment, five miles in length. In this five miles the grade of the country has gained 25 feet on that of the canal, and, it is obvious, that an em- OTHER IRRIGATION WORKS. .1.91 bankment is out of the question on account of its great cost, the danger of breaches in its banks and several other good reasons. To compensate, therefore, for the difference of slope, falls are constructed on irrigation canals, as they are safer arid cheaper than^enrbank- ments. Figure 131, not drawn to scale, shows how the falls are arranged so that the canal is, either in whole or in part, in soil. The canal is laid out in a series of steps t so as to keep it at a tolerably uniform, level below the surface of the country, until the flat country is reached. By this time, the supply of the canal is diminished, and it, therefore, requires a greater slope to keep up the original velocity, and usually a point will be reached where the slope of the country is the same as that fixed for the canal. When designing an irrigation canal, a minimum depth of excavation is determined, and then, when the depth of cutting becomes less than this, it is time to locate a fall. The shape and construction of falls are questions re- quiring much thought and consideration. Their loca- tion should evidently, from the diagrams, Figures 130 and 131, be near the places where the canal bed, if con- tinued without a break, would have to be carried in em- baiikmeiit above the surface of the country. Their exact location is generally made to coincide with the requirements of a highway bridge, regulator, or some other masonry work, such as are herein described, for the sake of economy, or for some other good reason. In America, falls are usually constructed of timber, and they have not only the disadvantage of being built of perishable material, but they have also other defects, the chief of which is the great velocity of the water at and near them, which often causes their destruction. 192 IRRIGATION CANALS AND Outside of America, in India, Italy and other irrigat- ing countries, the falls are permanent works, constructed of brick or stone masonry. On the best works the banks of the canal, both above and below the fall, are protected from the erosive action of the water. Six descriptions of falls are in use: 1. The Ogee Fall. 2. The Vertical Fall, with water cushion. 3. The Vertical Fall, with gratings attached. 4. The Vertical Fall, with sliding gates. 5. The Vertical or Sloping Fall, with plank panels or flash boards. 6. Rapids. Rapids are described in Article 40. Ogee Falls. There has been much difference of opinion with re- ference to the exact shape of the fall. Ogee falls, similar to that shown in Figure 132, were adopted by Sir Proby Cautley, on the Ganges Canal, with the view of deliver- ing the water at the foot of the fall as quietly as pos- sible. Fig. 132. Section of Ogee Falls. The following is a description of one of the Ogee falls on the Ganges Canal: Figure 133 shows a plan, and Fig- ure 134 a view of the Asufnuggur Fall on the Upper OTHER IRRIGATION WORKS. 193 Ganges Canal. This fall is shown attached to a bridge. The bridge consists of eight spans of 25 feet in width each, which crosses the canal on the upper levels. To the tail or apron of this bridge the ogees are attached, delivering the water into four chambers of 54| feet in width, every alternate bridge-pier being prolonged on its down-stream face, so as to divide the space, which is occupied by the lower floorings, into four compartments. In advance of the three dividing walls, which are car- ried to a distance of 84 feet from the down-stream face of the bridge, there is an open space of masonry floor- ing, which is protected by an advanced area of box- work, or heavy material filled into boxes or crates, and covered with sleepers, so as to retain the material in po- sition. IL Plan of Asufnuggur Falls. Additional defenses are given these floorings by lines of sheet piling. The flanks of the chambers below the descent are protected by revetments, equal in height to the dividing walls. Between and on the flanks of these two jetties, lines of piles and other protective arrange- ments are distributed, so as to secure the safe passage of the water over the floorings, and to admit of the cur- rents escaping from the works with as little tendency to danger as possible. The Ogee .Falls have proved fail- ures, both on the Upper Ganges and Baree Doab Canals. Col. Crofton, in his Report on the Ganges Canal, states 13 194 IRRIGATION CANALS AND OTHER IRRIGATION WORKS. 195 that the greater number of the Ogee Falls on this canal suffered injury more or less severe, in their lower floor- ings from the action of the water, and in one or two cases the brick, on edge covering to the J3geej* was stripped off, but timely repairs and protection saved the evil from spreading. Vertical Falls with Water Cushions. Vertical Falls with water cushions are illustrated in Figures 135 to 140 inclusive. Fig. 135. Section of Vertical Fall. These falls have been found much safer than the Ogee Falls. On the Baree Doab Canal, and generally 011 the new canals in India, Vertical Falls are used. These falls have a cistern on the lower side, and this cistern acts as a water cushion, and opposes a dead resistance to the falling water. The velocity of the falling water in a forward direction is also checked. To lessen the destructive action of the falling water Mr. T. Login, M. I. G. E.* secured a framework of tim- ber about five feet in height, above the crown of the Ogee Falls, instead of trusting to sleepers which were constantly giving way. By this arrangement the water was held up, so that erosive action on the bed and banks *On the Benefits of Irrigation in India, and 011 the proper Construction of Irrigation Canals by Thomas Login, M. Inst. C. E., in Proceedings of the Institution of Civil Engineers, Volume XXVII. I'JG IRRIGATION CANALS AND was prevented on the up-stream side of the canal, and it is a remarkable fact, that though there was a perpendic- ular fall of five feet or more on the crown of the Ogee, Section of Vertical Fall on Baree Doab Canal. no injury was done to the brickwork at the point where the water impinged. Probably this was owing to the water, which passed through the open spaces of the tim- ber framework, forming a cushion for the descending water . OTHER IRRIGATION WORKS. 197 Mr. Login also constructed a rough sort of submerged weir 3J feet high across the chambers of the falls, by which a cistern was formed to receive the descending mass, and in this manner diminished the destructive effect of the falling water. Figure 136 shows a vertical fall with water cushion on the Baree Doab Canal, India. It will be seen that the bed is protected for some distance, 011 the lower side, with masonry and paved flooring. Figure 137 shows a longitudinal section, Figure 138 a cross-section, and Figure 139 a plan of a vertical fall with water cushion, constructed of timber and bowlders, on a small irrigation canal on the Canterbury Plains, New Zealand.* The maximum discharge of this canal is about 50 cubic feet per second. A water gauge, for delivering the required quantity of water to one of the distributing channels, is shown by the dotted lines. Section of Timber Fall with Water Cushion. Figure 140 shows a vertical fall with water-cushion on the Turlock Canal, California. This diagram is taken from a paper by Mr. H. M. Wilson, C. E., in Transac- tions of Am. Soc. C. E., Vol. XXV. * Water Supply and Irrigation of the Canterbury Plains, New Zealand, "by George Frederick Ritso, Assoc. M. Inst. C. E., in Proceedings of the Institution of Civil Engineers. Volume LXXIV, 1883. 198 IRRIGATION CANALS AND The following formula lias been used in India to find the depth of the cistern below the lower bed of the canal. It is: x == /** X d* in which x = the required depth of cistern below the lower bed of the canal. h = the height or fall, that is, the difference of level between the surface of water above the fall and the sur- face of water below it. d = full supply depth of water in the channel. Section of Vertical Fall with Water Cushion. It has been stated that all the cisterns constructed with depths thus obtained, have answered admirably, having required but slight repairs since they were built. The very dangerous scouring and cutting action of a large body of water falling over a height of even a few feet can be readily understood. The greater the height of the fall and the depth of water, the more violent, of course, will be the action. Those on the original Ganges Canal are not higher than eight feet, but the destructive action of over 6,000 cubic feet of water per second, and having a depth on the crest of the fall of six feet or more, is very great, and nothing but the best masonry is capable of resisting it. OTHER IRRIGATION WORKS. 199 If stone of good quality can be obtained it should always be employed, laid 011 an unyielding foundation, with fine mortar joints. The banks must be protected with masonry for a considerable distance down stream, and the bed of the canal protected by a solid masonry flooring, the down stream end of which is protected by a row of sheet piling. The depth of water over the crest of a fall is less than that in the canal above the fall, and it follows that the effect of a fall occurring at the end of a canal reach is to increase the grade, and, therefore, the velocity, and to diminish the depth of water for a considerable distance above the fall. The increase of velocity and diminu- tion of depth are gradual from the point where the action commences down to the fall itself, where, of course, they attain a maximum, so that the depth of water passing over the fall is very much less, as the velocity is very much greater, than the normal depth and velocity above. This increase of velocity, before the water reaches the fall, produces a dangerous scour on the bed and banks of the canal, and in order to guard against this, it has been found necessary to head up the water at the falls on the Ganges Canal by means of sleepers dropped in the grooves of the piers, which has virtually increased the height of the fall, and has been one cause of the flooring, on the lower side of the fall, suffering in places from the violent action of the water. It has also been proposed to narrow the falls to produce the same effect. The method most commonly adopted in India is to raise the crest of the falls by a masonry weir, as shown in Figure 132. At first the crest of the fall was on the level of the bed of the canal on the upper reach. The height to which it is necessary to raise the crest of the weir may be found from the following investigation, as IRRIGATION CANALS AND given by Colonel Dyas, modified, however, bv the writer to suit the symbols used, and also Kutter's formula, as simplified in this work. v = mean velocity in feet in open channel. a = sectional area of open channel in square feet. r = hydraulic mean depth of same in feet. s == sine of slope. h = height in feet of surface of water in channel, above crest of fall. I = length of crest of fall in feet. rn co-efficient of discharge over weir varying from 2.5 to 3.5. c co-efficient of discharge of open channel. Allowing for velocity of approach, we have discharge over fall complete, that is, a free fall: but v = c X ( r s) 1 .'. v 2 = c 2 X rs substituting value of v 2 we have: (C 2 T H V- h -f- ---- ' - i* 2(/ / The discharge in channel above weir: Q = a c (/)* .-. m I (h -f c * r8 V == a c (/)* dh -f c 2 rs ^ X m 2gh+ usitalon is suppose*, to rest on, a, \\tcycr *f Ctau, , 204 IRRIGATION CANALS AND minimum. The bars are laid longitudinally with the stream, and at their lower ends, which rest on the crest of the fall, they are close together, and at the upper end they are farther apart. The teeth of a comb give a good idea of the arrangement. OTHER IRRIGATION WORKS. 205 The grating consists of a number of wooden bars resting on an iron shoe built into the crest of the fall, and one or more cross-beams, according to the length of the bars. They are laid at' a slope of one in three, and are of such length, that the full supply leveFoT^tlie water in the canal, tops their upper ends by half a foot.* The grating divides the water into a number of fila- ments or threads, and spreads the falling volume over a greater area, thus lessening very much its destructive action on the floor of the cistern. The scantling of the bars as well as of the beams should, of course, be proportioned to the weight they have to bear, plus the extra accidental strains to which they are liable, from floating timber for instance, which may possibly pass between the piers and so come in con- tact with the grating. In consideration of strains and shocks of this nature, the supporting beams are set with their line of depth at right angles to the bars instead of vertically. The dimensions of the bars used on the falls of the Baree Doab Canal, where the depth of water is 6.6 feet, are as follows: Deodar Wood. Lower end of bars, 0'.50 broad X 0'.75 deep, Upper end of bars 0.25 broad X 0.75 deep, and they are supported on two deodar beams, each measuring one foot in breadth X 1.5 feet in depth; the first beam being placed at a distance of 7.5 feet (hori- zontal measurement) from the crest of the fall, and the second 7.5 feet beyond the first beam. The bars of the grating on these falls were originally placed touching each other, side by side, at their lower *Captain J. H. Dyas in Professional Papers on Indian Engineering, Volume 3. First Series. 206 IRRIGATION CANALS AND ends, as there was not then a full supply of water in the canal. There were thus 20 bars in each 10-feet bay. Since then the number of bars has been necessarily re- duced to 19 and to 18, the latter being the present num- ber. The reduction of the number of bars and the equal spacing of the remaining bars is done with ease, as they can be pushed sideways in the iron shoo and along the beams, to which latter they are held with spiko nails. Once the correct spacing is arrived at, cleats and blocks are preferable to spike nails. The bars are undercut from the point where they leave the shoe, i. e., from the crest of tho fall, so as to make each space, as it were, "an orifice in a thin plate," and it facilitates the escape of small matters which may be brought down with the current. Large rubbish, which accumulates on the grating, is daily raked off and piled 011 one side of the fall. This is done by the es- tablishment kept up for the neighboring lock. There is considerable advantage in thus clearing the canal of rubbish, which would otherwise stick in rajbuha (dis- tributary) heads, on piers of bridges, etc., or eventually ground on the bed of the canal, and become nuclei of large lumps and silt banks. But supposing that there were no one at hand to rake the debris off, and that the grating became choked, the water would merely rise until it could pour over the top of the grating, and the rubbish would be swept over with it. Where gratings are used they act instead of a weir in checking the velocity of the water above the fulls, and the principle to be adopted in spacing the bars, is to ar- range them so that the velocity of no one thread of the stream shall be either accelerated or retarded by the proximity of the fall. This effected, it is evident that the surface of the water must remain at its normal slope, parallel to the bed of the canal, until it arrives at the grating. OTHP:R IRRIGATION WORKS. 207 To take an example, let us assume that: - mean vel. v = 0.81 v max v b = 0.62 r M ,~ (in every vertical line of the current flowing naturally *-)____ where v mean velocity in foet per cecond, t> max == surface velocity in feet per second, v b == bottom velocity in feet per second. 'Then if we make v == 2.5 foot per second, we shall have the following velocities at the given depths below the surface in a stream G foot deop: Depths below surface in feet. Velocities in feet per second REMARKS. Surface 3 . 0864 1 2 . 8909 .< 2 2.6955 Center 3 2.5 Common difference 0.1955 nearly. n 4 2 . 3046 c*&i 'fiori 11 ^m Up-stream Elevation of one span of a bridge showing the slop-boards partially applied. Section of Bridge, half roadway, with slop-boards fixed. 222 IRRIGATION CANALS AND branch canal, as shown in Figures 166 and 169. These regulators are usually combined with highway bridges constructed of masonry. On the Sone Canals, India, the original plan pro- vided for branch regulators, on the French Needle Dam plan, Figures 167 and 168, and an escape above each bifurcation, of sufficient capacity to lay both the lower channels dry, as shown in Figure 166. Where the object is to diminish the supply of water in both, it will be unnecessary to do more than open the requisite number of bays of the escape bridge. But when it is desired to keep up the whole supply in one channel, and reduce it, or altogether cut it off, in the other, it will be necessary to drop the sill beam in by the grooves, Figures 167 and 168, using the blocks and tackle, in the deep channels, for the ends near the pier, and after- wards to fix the beam in its seat by the same means. After this, using the upper beam as a bridge, the needles will be applied by hand, to such an extent as may be desired. The plan will not be so expeditious as that of the drop- gates and windlasses shown in Figure 62. It will, how- ever, provide in a simple way for all that is wanted for small regulators. By the use of a few long drop boards, let down from the parapet of the bridge, the openings could be partially closed without stopping navigation. In Figure 167 a tow-path for convenience of naviga- tion is shown under the bridge, and seven wooden needles in position to partly close the opening, and in Figure 168 the needies are shown in section, and masonry steps are shown leading from the bridge road- way to the canal. The following details of the working of a needle dam oil the Sidhiiai Canal, India, are given here: * * The Sidhiiai Canal System, by Loudon Francis MacLeaii, in Proceed- ings of the Institution of Civil Engineers, Volume CIII, 1891. OTHER IRRIGATION WORKS. 223 " The needles are made of deodar wood, and are seven feet six inches long, by five inches by three and one-half inches, with a stout handle 18 inches long, ending in a knob; they weigh 36 pounds dry and 40 pounds wet, and can be manipulated by one man. After placmg~lhe needles in position at first, they are forced up close to- gether by a man standing on the pitching below the dam, who inserts a crowbar with a wedge-shaped end into the opening, causing the needles to slide along the face of the crest wall, any leakage between them being stopped in the following way: A basket fixed to a bamboo about 10 feet long, and filled with shavings or chopped straw, or some similar substance, is slipped down in front of the leak, so that the light material may be sucked by the current into the opening, which it effectually closes. It was not found that the shock of closing on the crest wall, when first placing the needles in position, ever caused them to break when the wood was sound. "When there is a great difference of level between the water above and below the dam, a rush of water through the interstices makes it very difficult for a man to stand on the pitching below and use a crowbar. The difficulty is overcome in the following way: A piece of tarpaulin or oiled canvas, eight feet long and six broad, is fastened at one end to a wooden bar six feet four inches long, Avith handles at each extremity, and at the other end to a bar of round iron six feet four inches long and one inch in diameter. It is then rolled upon the iron bar, and placed horizontally against the needles, above where the excessive leakage occurs, and the wooden bar, which remains on the outside of the roll, is either tied or held in position by the handles; the roll is then let go, and the weight of the iron bar causes it to unroll itself down the face of the needles, at once 224 IRRIGATION CANALS AND closing all the leaks. In order that the screen may be more easily recovered, a cord is attached to a loose collar at each end of the iron bar, and when the needles have been closed up, the screen is pulled up from the bottom by these cords. ' For the purpose of regulating the height of water above the dam, it is sufficient in most cases to push some of the needles forward at the top, the water escap- ing through the open spaces left in this way; but should it be necessary to provide for a greater flow, a sufficient number of them are removed altogether. This can generally be done by hand, but if they have "jammed" from any cause, or if the pressure of the water against them is too great, they are lifted by means of a bent lever. "An eye bolt is attached to each needle just below the handle; this serves as a fulcrum for the extracting lever, and also to fasten tackle to when the pressure is too great for the needles to be drawn forward by hand. It was found dangerous to work them from the beams, which are only 18 inches wide, and after one life had been lost, and the Author himself had a narrow escape, a foot bridge was added to the dam. * * * * " Arrangements have been made to send warnings by telegraph of any rise of one foot in the Ravi at Mad- hopur and Lahore during twenty-four hours. As floods take a minimum of five days from the former, and two days from the latter place to reach Sidhnai, these warn- ings have been of the greatest service." Figure 169 is a plan of the regulator at the head of the Kotluh branch of the Sutlej Canal, designed by Major J. Crofton.* With reference to this work he states: * Report on the Sutlej Canal. OTHER IRRIGATION WORKS. 225 " The Kotluh branch will take off at an angle of 45 from the main channel, the direction of the central line remaining unaltered. A water-way of 64 feet is given to the central line, and 50 feet to the Kotluh branch, Kotluh Branch Head at Suranah, Sutlej Canal. the mean waterway of the channels below being 57.5 and 41.5 feet respectively, divided on the central into four bays, two of 14 feet each and two at the sides of 18 feet each; on the Kotluh branch, two at the sides of 18 feet each, with one central bay of 14 feet; the piers nearest the sides three feet thick, the central one two feet thick, built up to the same level as the tow-path. * * * * * -x- & * " One main object of the arrangement of the works, as shown on the plan, was to bring the bridges as close together as possible, so as partially to obviate the silting 15 226 IRRIGATION CANALS AND up, which invariably takes place in the upper channel below the point of divergence. " A drop of half a foot is given to the flooring of the Kotluh branch, for greater facility in adjusting the supply, as it is advantageous to regulate altogether, if possible, by one bridge, leaving the passage through the central line quite free. The regulation at both heads will be effected by vertical sleepers, the needles already described, their lower ends resting in a groove in the flooring, confined above between two beams rest- ing on the piers or side, retaining walls. This is an economical expedient, though, in some respects, not so efficient as the method with drop-gate, shown in Figure 62, still it will answer all the purposes of adjusting the supply. It has the advantage of dividing the entering stream into vertical films, by which the impact on the flooring will be diminished, and it can be worked by a couple of men." Article 43. Escapes Relief Gates Waste Gates. In order to provide for the control of the water in the canal, Escapes, also called Relief Gates and Waste Gates, should be made at certain intervals along the line of the canal. An excess of water in the canal, and for which an escape should be available, may arise from a breach in the canal, either at the headworks or at one of the numerous drainage channels crossing the line. Extra- ordinary floods also cause breaches in the banks, and at times the water is not required for irrigation, and there are various other causes, that point to the necessity of making ample provision, for emptying the canal, above the point in danger, in a short time. The escapes should be made of the shortest possible length, from the canal to some natural water-course, into which the water can be discharged without inun- OTHER IRRIGATION WORKS. 227 dating or damaging the country through which it flows. The dimensions of the escape channel should be fixed so as to be large enough to discharge the maximum sup- ply in the canal. The location of an escape channel will be determined by the topography of the country, but, as a rule, con- nection from the canal can be made at intervals with some natural water-course. An escape should be located above a heavy embank- ment, and above any part of the canal likely to be breached by floods. Where possible to do so, they are, in India, provided at regular intervals along the line of the canal. Where they are taken off from the canal, a double regulating- head should be built, as shown in Figure 170, one across the canal AB to prevent the water flowing down that iiimin Fig. 17O. Plan of Escape Head and Regulator. way when the escape is in use, and the other across the escape head BO to prevent the water flowing down that way when the canal is in use. Figure 166, page 221, shows the relative position of 228 IRRIGATION CANALS AND an escape to a regulating "bridge at an off-take of a branch canal 011 the Soiie Canals, India. To prevent artificial escape channels from being choked by brush, they should be occasionally cleared, other- wise, when required for use, they may be found choked and prevent the discharge of the water, thus causing an inundation and the destruction of life and property. On the Ganges Canal, India, escapes were provided every forty miles. An escape near the head of a canal is sometimes used as a scouring escape. An instance of this is on the Agra Canal, India, where a scouring escape is placed one and a-half miles below the canal head. Its waterway is somewhat in excess of that of the canal head, and the object of this is to generate velocity enough in the first one and a-half miles of the canal, to stir up and carry away the silt deposited between the escape and the canal head. In America, in order to save expense, waste gates are sometimes made in the sides of flumes, but this plan is liable to the objection that the falling water is likely to wash out the foundations and destroy the structure. A channel taken out in cutting, and connected with the water-course, would be the safer plan; the bed and banks of the channel being protected from scour, by paving or some other method. A few years since, the Naviglio Grande, the Muzzaaiid Martesana Canals, in Italy, had no sort of regulating bridge across their heads, and the flood waters were al- lowed to enter the canal with their full force, finding an exit in a series of escape-sluices and weirs. The Naviglio Grande has a number of these sluices in the first few miles of its course, and two weirs running along its side of 300 feet and 65 feetiii length, with their crests about three ieet lower than the surface of the OTHER IRRIGATION WORKS. 229 canal full-water supply. These are blocked up by strong wooden fences, closed up tightly with bundles of fas- cines. The Martesana and Muzza Canals are also fur- nished with long over-fall weirs near their heads. That the syteni has gone on so long, among an intelligent people deeply interested in their irrigation, is sufficient proof that, no very great harm can arise from it. The soil is so stiff and firm, that it is capable of resisting a heavy flood, and there are few masonry works near at hand to be damaged by it. There must, however, after a flood, be heavy deposits of gravel and silt in the canal channels. Article 44. Depositing Basins Silt Traps Sand Boxes. Depositing basins for large canals are fully described in Article 18, page 52, entitled On Keeping Irrigation Canals Clear of Silt . Small channels taken from rivers carrying large quan- tities of sand or silt, sometimes have Silt Traps or Sand Boxes located at convenient points for clearing them out. These traps intercept the sand and silt carried by the water, and prevent the rapid silting up of the channel. These silt traps are flushed out, when required, with canal water. Care should be taken to locate them in such a position that the debris does not choke the out- lets from the traps. In order to accomplish this the debris should be run into a channel that has a living- stream, or that is scoured out occasionally by flood water. In consequence of neglecting this precaution in locating some of the silt traps on the Deyrah Dhoon Irrigation channels in India, their outlets got choked and, after some time, they .became useless. Mr. A. D. Foote, M. Am. Soc. C. E., fixed a trap and small gate for the purpose of intercepting and scouring out debris in a canal from the Boise River, Idaho. This 230 IRRIGATION CANALS AND trap is a trench cut in the bottom of the canal, and run- ning diagonally upward across it from the gate. In this trench all small stones and sediment that may be loosened from the high banks by spring thaws, will be caught, and on opening the gate they will be carried out of the canal by the rapid current through the open- ing. On the Marseilles Canal, in the south of France, with a maximum capacity of 424 cubic feet per second, the water of which is used, not only for irrigation, but also for domestic use, settling basins were provided to rid the water of the sediment mechanically suspended, in order to render the water fit for domestic purposes. After several settling basins were silted up and rendered useless, one of them having a capacity of about 159,- 000,000 cubic feet, another large basin was constructed with the necessary works for flushing it out periodically. This basin has an area of fifty-seven acres, and its ca- pacity is about 81,000,000 cubic feet. It is formed by constructing a masonry dam across a valley 654 feet in length, 72 feet in height, and 55| feet in width at the base. At the end of each year, when a deposit of about five feet of sediment has accumulated at the bottom, it will be flushed out into the river Durance at a low level. Where the line of a canal passes through rolling ground, or skirts the bottom of low hills, a hollow in the ground, within a few miles of the head of the canal, is sometimes available and can be utilized for the depo- sition of silt. Sometimes a few low and cheap dams have to be built in the lower depressions. The silt-laden water enters the reservoir at its upper end. Its velocity is then checked, and it deposits its load of gravel, sand and slime, and after passing through the reservoir, it again enters the canal at its lower end, comparatively clear water. OTHER IRRIGATION WORKS. 231 No doubt it is only a matter of time for such a basin to fill up and become useless for its intended purpose, but, as the following instance will prove, a useful de- positing reservoir can, with due forethought, be made at a small expense. The Wutchumna Canal, in Tulare County, California, is taken from the right bank of the Kaweah River, at a point where this river sometimes, when the water is most required, carries large quantities of sand and silt. The clearance of this sand and silt at the close of the irrigation season, from other canals in the same district, entails heavy annual expense. When locating the Wutchumna Canal, Mr. Stephen Barton, C. E., with happy forethought, carried it through a hollow in the ground with the intention of converting the hollow into a depositing basin. This he accom- plished successfully, and the writer is not aware of any depositing basin in existence, of the same capacity as the Wutchumna reservoir, that is so well adapted to the duty it has to perform. This reservoir is situated about seven miles from the headworks of the canal, and the velocity of the canal, through this seven miles, is sufficient to prevent the de- position of sand and gravel until it enters the reservoir. Mr. W. H. Davenport, C. E., the present Superintend- ent of the Wutchumna Canal, has lately sent the writer the following additional information on this subject: " When the reservoir is at what we call low water, just now, its area is 61 acres, with an average depth of 3 feet. What we call a full reservoir is 154 acres in area, and has a depth of 7 feet above low water. The discharge of the Wutchumna Canal is 208 cubic feet per second. " There is at present an average depth of 1.25 feet of deposit over the lower water area of 61 acres. Where the ditch enters the reservoir I find a bar of sand and 232 IRRIGATION CANALS AND gravel, which the high grade of the canal has carried. This bar I estimate to have an area of 20 acres, and a depth of 3 feet. " The Wutchumna Canal has been in continual use for 10 years, drawing its supply every day without in- terruption. I think I can safely say that, the reservoir will be useful for a silt deposit for the next 100 years. The conditions are such that the reservoir can be made 6 feet deeper." Article 45. Tunnels. There are occasions, as explained further on, when a tunnel can be adopted with advantage, but they are seldom used when the supply required is over 2,000 cubic feet per second. There are no tunnels on any of the large irrigation canals in India that discharge over 2,000 cubic feet per second. The High Level Canal in Colorado, with a discharge of 1,184 cubic feet per second, has a tunnel at its head 600 feet in length. It is 20 feet wide and 12 feet high, with a grade of 1 in 1,000. The Merced Canal in California, with a discharge of 3,400 cubic feet per second, has a tunnel 1,600 feet in length, through solid rock, and another tunnel 2,000 feet in length, through ground so unstable, that it was necessary to timber its whole length, a work which re- quired over 1,000,000 feet, board measure, of redwood. In India, timber in a similar position, would, in a few years, be destroyed by the white ants. The Henares Canal in Spain, with a discharge of 177 cubic feet per second, has a tunnel 9,513 feet in length. The tunnel is lined throughout with brick. It has a semi-circular arch on top, and an inverted arch on the bottom. Its height at the center is 11.2 feet, its width at springing of invert 7.2 and its grade 1 in 3,067. OTHER IRRIGATION WORKS. 233 111 Madras, India, a tunnel is to be constructed to convey the waters of the Periar River into the Viga Val- ley for irrigation. This tunnel is in rock 6,650 feet in length. Its cross-sectional area is 80 square feet and it has a slope or grade of 1 in 75. Under certain conditions a tunnel,* when in sound rock, is preferable to an open channel for conveying water. The conditions are, that no water is required to be drawn off this part of the line, and that a heavy grade can be given. By sound rock is meant rock not subject to percolation, to any appreciable extent, that will stand the high velocity without injury by erosion, and also that will not require lining for its sides or arch- ing for its roof. When, in addition, a steep grade can be obtained, a high velocity can be given to the water, and the cross-sectional area and consequent expense reduced. In such a tunnel, the loss of water by evaporation and percolation, and the expense of maintenance are at a minimum. It has several advantages over the open channel in steep, side-hill ground. Its sides and bed are impervious to water, and it is covered from the sun- light. It shortens the line, there is no compensation to be paid for land, and it does not interfere with or cross the drainage of the country on the surface. Should it be required, at any future time to increase the carrying capacity of the canal, the discharge of the tunnel can be increased without, however,- increasing its dimen- sions. See Flow of Water. All that will be necessary is to fill all the hollows be- tween the projecting ends of the rocky bed and sides with good cement concrete, and after this to give a coat of good plaster to the surfaces in contact with the water and make them smooth. Although the section will be *Keport on the proposed Works of the Tulare Irrigation District by P. J. Flynn, C. E- 234 IRRIGATION CANALS AND diminished, still, the velocity and consequent discharge will be doubled. Let us assume the loss of water in a certain length of open channel at six per cent, of the total flow. If by adopting a tunnel line, the loss of water is only one per cent., it is evident that it would pay to expend the value of five per cent, of the water on the tunnel line above that on the open channel. Another argument in favor of the tunnel is that the amount saved yearly in maintenance capitalized could be expended on the tunnel over that upon the open channel, in order to give a fair comparison with the latter. See Flow of Watery page 52. On the Marseilles Canal, in France, there are, in all, ten miles of tunnelling, the mean velocity through them being nearly 5 feet per second. The maximum discharge of this canal is 424 cubic feet per second. . On the Verdon Canal, in France, the number of the tunnels is seventy-nine, of a total length of twelve and a-half miles, the three most important of which are respectively about three and one-fourth, two and five- eighths and one and seven-eighths miles in length . The capacity of the main canal is 212 cubic feet per second, and it has a sectional area of 113 square feet. Tunnels are employed in several instances in South- ern California, to develop water. Where there is a water- bearing strata a tunnel is driven, and in several in- stances, sufficient water has been developed to make the money expended a good paying investment, and by the use of this water for irrigation, land has been raised in value from $5 to $500 per acre. A good example of this kind of work is the San Aii- tohio Tunnel, which is being constructed at Ontario, Southern California, by F. E. Trask, Chief Engineer of the Ontario Land Improvement Co., who has supplied the following account of the work: OTHER IRRIGATION WORKS. 235 SAN ANTONIO TUNNEL. At an early date the founders of Ontario concluded they would need a larger supply of water than the one- half flow of San Antonio Creek which gave tkeinJ365 miner's inches and it was decided to tunnel for the underflow of this creek, at the point where it enters the San Bernardino Valley. Land controlling the mouth of the canon having been secured, the work of driving the tunnel began in the early part of 1883. The objective point of the tunnel was the lowest point of bed rock in the cation about one-half mile from its mouth. Here it was estimated that from eighty to one hundred feet of gravel, bowlders, etc., laid above bed rock. It was de- cided to start the tunnel about 3,000 feet south of the objective point and run on a grade of one-half inch per rod with a cross-section of twenty-eight square feet. The alignment and grade have not been strictly adhered to, although no serious changes have been introduced. The first two thousand seven hundred feet were driven through the rock and gravel formation of the canon, and required lining, which w r as as follows: the bents were of 8"x8" redwood and spaced 4 feet center to center the bed pieces were 2"x8" and the lagging 2". The clear dimensions were, height 5' 6" top width 2' bottom width 3' 6". The above portion of the tunnel has been lined in the following manner: slabs of concrete, four inches thick, were laid in hydraulic cement over the entire bottom. Between the bents and on these concrete slabs for a foundation, the side walls eight inches thick were car- ried up of concrete blocks (rock was used in some por- tions of this section), to a height of 4' 2" on which the arch was turned. The arch was composed of two seg- ments, with a tongue and groove joint at the center. These walls and arches were laid in cement, care being 236 IRRIGATION CANALS AND taken to make water-tight joints. The only deviation from this was at points where veins of water were inter- cepted, there, rectangular openings, of sufficient size and number, were left to admit the water at a height of two feet above the bottom of the tunnel. The accompany- ing section shows both the method of timbering and lining. Fig. 171. Cross-Section of San Antonio Tunnel. Bed-rock was reached at two thousand seven hundred feet, and up to January, 1891, the tunnel had penetrated six hundred feet into bed rock, making a total length of tunnel of 3,300 feet. At this time the heading was con- OTHER IRRIGATION WORKS. 237 sidered to be beyond the lowest point in bed rock, and it became necessary to investigate the material above the roof of the tunnel. For this purpose a diamond drill plant was procured, and about four months work was^ re- quired for denning the surface of bed rock. From the data thus obtained, it was found that three low points in bed rock existed one about fifty feet from the point where bed rock was first struck; another 340 feet; while a third was found to be about 200 feet beyond the head- ing of the tunnel. Up to the time bed rock was struck, the minimum flow of the tunnel has been about fifty miner's inches. On September 15, 1891, there were 137 inches; and at the present writing (October, 1891), about 300 inches have been developed. As yet the work of development above bed rock has hardly begun, and from one to two years work will be required to complete the proposed plans, when it is believed 1,000 inches will have been developed. In general terms the proposed method of development consists of a complete network of supplementary tun- nels and drifts above bed rock, and on the up stream side of the main tunnel, which will be connected by means of shafts to the main tunnel some twenty feet below. On bed rock on the doivn stream side of the main tun- nel will be built a submerged dam of sufficient height to intercept the summer underflow. Seven shafts have been used in the entire length of tunnel, and increase in depth from No. 1, 20 feet, to No. 7, 104 feet. They are unevenly spaced, the greatest run being 600 feet. Quicksand was encountered at several places and gave much trouble. Cost: The cost of driving the first twenty-seven hundred feet, including temporary wooden lining, varies from $2.50 to $20 per lineal foot. The contract for concrete lining was $2.50 per lineal foot. 238 IRRIGATION CANALS AND The -total cost for completed tunnel (2,700 feet), as above, including six shafts, was about $50,000. The cost of the 600 feet in bed rock was $8 per lineal foot. The rock being firm 110 lining of any kind is required. The supplementary tunneling, above bed rock, has not progressed far enough to justify a statement of cost, at this date. Article 46. Retaining Walls. Various complex formuke have, from time to time, been given for finding the thickness of retaining walls, and they differ considerably in the results obtained by them. Engineering Neivs , of May 24th, 1890, states with reference to this, for thickness of wall at any height: " We have our own pet formula which we want to air on this occasion. It is short and simple: ' three-seventh of the height, and throw in some odd inches for luck/ and we believe this to be more strictly arid more truly ' general ; than any one of a number of much more com- plex formulae which lie before us. It is certainly fool- hardy to build retaining walls much thinner than this formula calls for under any conditions. While expe- rience indicates that any well-built wall, proportioned in accordance with it ? is pretty sure to stand." There is more practical engineering in the above extract than in long articles discussing the pressure of the earth on the wall, under various conditions. The odd inches in the above formula are probably intended to meet the requirements of the materials composing the wall, having different specific gravity. Another rule is one-third of the height in feet plus one is equal to the thickness. This rule gives almost the same result as that given above by Engineering News . The foundation course of retaining walls has its width increased beyond the thickness of the wall, by a series of OTHER IRRIGATION WORKS. 239 steps in front, two only are shown in Figure 172. The objects of this are at once to distribute the pressure over a greater area than that of any bed joint in the body of the wall, and to diffuse that pressure more equally by bringing the center of resistance nearer to the middle of the base than it is in the body of the wall.* Fig. 172. Cross-Section of Retaining Wall. The body of the wall may be either entirely of brick, or of ashlar, backed with brick or with rubble, or of block-in-course backed with rubble, or of coursed rubble, built with mortar, or built dry. As the pressure at each bed-joint is concentrated towards the face of the wall, those combinations of masonry in which the larger and more regular stones form the face, and sustain the greater part of the pressure, and are backed with an inferior kind of masonry, whose use is chiefly to give stability by its weight, are well suited for retaining walls, special care being taken that the back and face are well tied together by long headers, and that the beds of the facing stones extend well into the wall. Along the base and in front of the retaining wall 'Rankine's Engineering. 240 IRRIGATION CANALS AND there should run a drain. In order to let the water es- cape from behind the wall, it should have small upright oblong openings through it called " weeping holes," which are usually two or three inches broad, and of the depth of a course of masonry, and are distributed at regular distances, an ordinary proportion being one weeping hole to every four square yards of face wall. The back of the retaining wall should be made rough, in order to resist any tendency of the earth to slide upon it. This object is promoted by building up the back in steps, as exemplified in Figure 172. When the material at the back of the wall is clean sand, or gravel, so that water can pass through it readily, and escape by the weeping holes, it is only necessary to ram it in layers. But if the material is retentive of water like clay, a vertical layer of stones or coarse gravel, at least a foot thick, or a dry stone rubble wall, must be placed at the back of the retaining wall, be- tween the earth and the masonry, to act as a drain. A catchwater drain behind a retaining wall is often useful. It may either have an independent outfall, or may discharge its water through pipes into the drain in front of the base of the wall. Article 47. Combined Irrigation and Navigation Canals. It has been found impracticable to combine irrigation and navigation, economically, in the same canal, and to make it a good working machine for the two purposes. In a canal intended for navigation only, a still water channel is the most suitable, and the lower its velocity is, the less obstruction will it cause to boats proceeding up stream. In an irrigation canal, on the contrary, the greater the velocity of the water, so long as it does not damage the works, the more economical and better machine it is. The cross-section of the channel can be diminished OTHER IRRIGATION WORKS. 241 in proportion to the increase in velocity of the water, and, consequently, all the works, such as headworks, embankments, cuttings, bridges, flumes, falls or drops, etc., can be diminished in size and expense. In addi- tion, locks to pass the falls would be required for naviga- tion. Mean velocities exceeding 4 feet per second cause waves, which injure the banks in the greater number of canals, especially in sandy loam. An irrigating canal requires at least, for average ground, a velocity of 2J feet per second. It follows, therefore, that when forcing its way against the current at the rate of 4 feet per second the boat is actually mak- ing headway only at the rate of 1J feet per second, and any attempt at quicker velocities would injure the banks, so that, irrespective of the loss of power, the banks could not stand if there was quick navigation. It, therefore, appears evident that for economical work- ing and the safety of the banks, an almost still water canal is required. Indian experience has fixed about 1|- feet per second as the maximum velocity which ought to be allowed in a navigable canal. The small slope would increase the number of falls required to overcome the greater surface slope of the country, and in addition, the greater cost of all the other works would make the cost of a navigable canal almost double that of the channel required for irrigation alone. Again, in a navigable channel, a certain minimum depth and width, for the passage of canal boats, must be allowed everywhere; and the amount of water required for this minimum must be allowed over and above the quantity required for irrigation. This has been referred to in Article 5, page 11, entitled Quantity of Water Re- quired for Irrigation. 16 242 IRRIGATION CANALS AND The canal of Beruegardo, in Italy, is a notable exam- ple of the great difficulty of combining navigation and irrigation in the same channel. It is with difficulty, and only by the strictest measures, that the supply for navigation is secured during the summer, on account of the urgent demand for the water for irrigation. When boats are passing, the whole of the irrigation outlets, between each pair of locks, are necessarily closed, and, with the supply accumulated in the channel by this means, the passage is effected, though with great incon- venience, and with the stoppage of irrigation from this reach of the canal during the time of the boat's transit. In his Report on the Sutlej Canal, Major Croftoii, R* E., gives some of the items which cause an increase of cost for navigation. They are, the necessity of provid- ing for a navigable communication throughout, which involves, besides lockage at the overfalls, increase of ex- cavation in the formation of tow-paths, and considerable additions to every bridge to give towing passages on either side, as well as extra height to afford headway for laden boats. Navigation appears to be satisfactorily combined with irrigation on the Madras canals, and here again, the small declivities and low velocities come into their aid. In a Report by Sir A. Cotton, on some of the Godavery channels, he mentions a mile an hour (or 1.47 feet per second) as the maximum velocity which ought to be allowed in the current of a navigable chan- nel. Were this to be taken as the basis of the calcula- tions for the Sutlej Canal (see List of Canals, page 30), the cost of the works in excavation, and falls, to over- come the superfluous slope, would be well nigh doubled. It would probably be a cheaper and more efficient plan to construct an entirely separate channel for navigation, alongside the canal, to which the latter would act as a feeder; the cost of the irrigating channel might then OTHER IRRIGATION WORKS. 243 be considerably lessened by the diminution of the ex- cavation for berms or tow-paths, and the reduction of the width of, and headway under, the bridges, to that necessary for the mere passage of water supply^ The latest information on the subject of Navigable Canals, in India, is strongly in support of the above. In the Revenue Report of the Irrigation Department of the Punjab, India, for 1889-90, it is stated with re- ference to the Sirhind, or Sutlej Canal, that: "On this, as on the other irrigation canals of Upper India, the cost of providing navigation is not likely to prove re- munerative." This is conclusive. Article 48.. Survey. The same rules which govern the survey of a railroad line are also to be observed in the survey of a canal line. There are, however, a few points which it is well to re- fer to here. The level of the floor of the head gate of the canal is a good datum for zero for levels, and the face of the up-stream head wall of the head gate is suitable for the zero of longitudinal measurement for the central channel of the canal, and the same plan can be adopted on their respective regulating head gates in fixing the same points for the branches and laterals. Correct levels are of primary importance in canal lines, and it is advisable to level twice over the same stations with the same instrument, the second levels being carried in the reversed direction to the first. In a canal carrying over 1,000 cubic feet of water per sec- ond, a few inches more or less in a mile will make a serious difference in the velocity. It is advisable to have frequent bench marks, and on permanent objects where possible, and all canal, road, railroad and other bench marks should be connected 244 IRRIGATION CANALS AND with the line of levels. A bench mark should be es- tablished close to each heavy cut and fill, crossings of all rivers, canals, bridges, aqueducts and other works on the line of canal. Where possible to do so, without extra expense, sharp curves are to be avoided. In India, in the plains, flat curves are adopted varying from 5,000 to 15,000 feet in radius. In the Isabella II Canal, in Spain, a recent work, with a discharge of only 89 cubic feet per second, the maximum radius was fixed at 492 feet and the mini- mum at 328 feet. Cross-sections should be made of all ravines and water-courses crossing the line of canal, and cross-sec- tions, at right angles to the axis of the stream, should be taken in all channels subject to flooding. The cross- sections should show the surface of the water at the date of observation, and the ordinary and highest flood marks . The waterway of all bridges and culverts and the levels of their floors, if any, and the lowest part of the superstructure should be noted. The nature of the ground should be noted, and en- quiries should be made as to whether the country is flooded, and as to whether there is any alkali land passed over by the canal line. In India, in a generally level country, the following plan is adopted preliminary to the survey for a main canal. Cross-sections are taken at intervals, perpendic- ular to the supposed water-shed. For the general alignment of the main channels between two large rivers, the interval should not exceed ten miles. For the actual location and for the minor channels, the in- terval probably should not exceed five miles, or possibly less. The cross-sections should be connected by longi- tudinal lines at their extremities, to test the accuracy of OTHER IRRIGATION WORKS. 245 the work. These levels being platted on a map on a large scale, the line of canal can.be laid down approx- imately on the map as a preliminary to the location. The levels will also show the general directions of branches and laterals, and also the natural drainage lines of the country. If the levels of the water-shed admit of it, the nearer the canal line approaches to it the better, as the interfer- ence with surface drainage of the country will then be the least possible. Having determined the lines of the main canal and its branches the next thing to do is to locate the distributaries. In order to deliver the water under the most favor- able conditions, it is clear that the irrigating channels must everywhere follow the water-sheds of the country drainage. An almost perfect arrangement of distributaries is ex- emplified in Figure 173, taken from a paper by Mr. H. M. Wilson, M. Am. Soc. C. E.* This arrangement shows the distributaries following the water-shed lines, of the country. It is seldom that such a complete dis- tributary system can be located. The first step then, is to ascertain how many water- shed lines exist, their extent and relative situations. This knowledge can only be obtained from a careful survey of the country it is designed to irrigate, care being taken to delineate on the map the course of all rivers, streams, roads, railroads, canals, etc., and the position of all hollows, swamps and the other salient points of the topography of the country. To each water-shed should be assigned a separate channel of capacity apportioned to the duty it has to perform, the two bounding streams or drainage channels being *Irrigation in India in Transactions of the American Society of Civil Engineers. Vol. XXIII. 246 IRRIGATION CANALS AND OTHER IRRIGATION WORKS. 247 248 IRRIGATION CANALS AND considered in this system as the limits to which irri- gation from any single line should be carried. This is very plainly shown in Figure 173.* Figure 174 shows a defective location of a distribution system and the proposed improvements. The difference between the location of the laterals on the two Figures 173 and 174 will be apparent on inspection. On the former the channels are kept on the water-shed lines all through, but on the latter the original channels depart so much from the water-shed that large tracts of land cannot be irrigated. Having then traced out, as above stated, on the drain- age survey map the general course of the proposed channels, it is necessary to run a series of cross-levels in order to fix the exact position of the water-shed. With the aid of the information thus obtained, the en- gineer will be enabled to locate the distributary to the best possible advantage. Some American engineers may think that too much time and labor is given, by the above method, but the experience of Indian engineers, on thousands of miles of badly located distributaries, proves that too much thought and care cannot be given to the location of these channels. For the more complete and efficient distribution of the water, minor distributaries should be taken out from the main distributaries where they may be most re- quired; but the engineer should in a measure be guided by the nature of the ground and the character of the soil. As in the case of larger works he should endeavor to secure a command of level for the purpose of afford- ing every facility for irrigation; he should avoid as far as possible crossing minor drainages or stumbling into hollows, by which his object may in any measure be de- * Professional Papers on Indian Engineering. Vol. IV. First Series. Captain W. Jeffreys, K. E. OTHER IRRIGATION WORKS. 249 feated; he should banish from his mind any idea he may entertain of the relative unimportance of this class of works; for he may be assured that nothing tends so directly to an economical distribution of the w r ater as a carefully constructed system of minor distributaries". In the system advocated above, the capacity of an irrigating channel should everywhere be exactly appor- tioned to the duty it has to perform, the section decreas- ing as the line advances until it loses itself in a small water-course. See Article 8, page 20. The level of the bed of the distributary should be fixed rather with reference to the full supply level of the canal, than to the level of the canal bed, chiefly because it is an object to keep the bed of the distributary at a suffi- ciently high level to admit of surface irrigation on. its whole line as far as possible. Moreover, the nearer to the surface that water is taken off by a distributary head, the less will be the silt which enters the distribu- tary, and the less the annual labor of clearing the bed. The bed of a distributary will, therefore, generally be from 1 to 3 feet higher than that of the main canal. When the Eastern Jumna Canal, India, was laid out, the main line was constructed by the engineers, the dis- tribution channels being left to be made entirely by the cultivators. That led to such great evils, that when the Ganges Canal was made, the main distribution channels were laid' out and constructed by the Government engi- neers; but the minor ones were still left to the cultiva- tors to make; arid on the Agra Canal a complete system of distributaries was carried out as an integral part of the scheme. Mr. Forrest* had charge for six years of one of the divisions of the Ganges Canal. It was a tail division, * Mr. K. E. Forrest, M. I. C. E., in Transactions of the Institution of Civil Engineers. Vol. LXXIII. 250 IRRIGATION CANALS AND where the supply of water was not great, while the demand was large. The engineers had to make water go as far as possible. When he first went there the waste of water was enormous. The cultivators had taken their channels in all sorts of wrong places, down roads and hollows, and across waste lands, and waste water was lying about everywhere. One great cause of loss was this: the country was studded with barren plains, and when a main distributary ran across one of them, the good land on either side was irrigated by means of little channels across the plain, as shown by the dotted lines in Figure 175, some of them over a mile Fig. 175. Plan Showing Arrangement of Distributaries. long. There was great loss in having so many chan- nels; and, as the banks were made of the silty soil of the plains, and badly made, they were always failing and flooding the plain, which no one minded, as the land was barren. For these channels were substituted properly laid out channels, AC, A E, through the middle of the good land, which, having banks made of good earth, did not break down, and if they did good lands were flooded, so that the canal establishment and OTHER IRRIGATION WORKS. 251 the cultivators had to take pains not to let them fail. The effect of the change was wonderful. Mr. Forrest had two channels, one 40, the other 50 miles long, run- ning through land of that character; and whereas he had previously not been able to get the water half way down them, he then got it down to the very tail. That led him on to making as many of these minor distribu- tion channels as he could. Each of these little water- courses was dealt with exactly as if it had been a big canal. Careful surveys were made and levels taken for it. The line was located, and the longitudinal section and cross-sections carefully fixed. Badly adjusted cross- sections caused a great loss of water. People laughed at so much pains being taken with such small channels, but the labor was not thrown away. That division be- came one of the best paying ones on the canal, and some of these channels gave a duty of 400 acres per cubic foot per second. Thus, then, the first thing was to make the distribution channels properly, and the next thing was to work them, properly. The water should be moved about and distributed by a careful system of rotation. It was better to move the water in as large volumes as possible. By a good system of rotation, it might be possible to remedy the loss of duty from the water not being used at night; the water could be run on at night to the more distant points. By a system of rotation, the evils of super- saturation could be lessened. The water was made to run through a tract only when it was wanted, and for so long as it was wanted. In some of the Ganges canal channels, the water ran only for a single day each fort- night. The water should be completely drawn from every tract in which it was not in active and imme- diate demand. 252 IRRIGATION CANALS AND Article 49. Distributaries Laterals Rajbuhas. These channels are also called Distribution Channels, Primary Channels, Ditches, etc., and they derive their supply from the Main Canal. These channels are, in every respect, a counterpart of the main canal, and require the same class of works, though on a smaller scale, as the main canal. DETAILS OF DISTRIBUTARIES. As defined for the Soane Ca**li. FcUl on & Distributary with aqueduct over fail St/fjfwn U r cu,n for paAstny onz J>istr' ouAeuy under another or vi/ef a JnusHiyt Figs. 176, 177, 178. Figure 176 illustrates a section of a fall on a distributary with a small aqueduct over its tail to carry another small distributary, and Figure 177 is a plan of the same. Figure 178 is a section of a syphon drain for passing one distributary under another, or under a drainage channel. OTHER IRRIGATION WORKS. 253 The design, location, construction and maintenance of distributaries should be as carefully carried out as that of the main canal, for on all these details the economical use of the water will chiefly depend. Those people acquainted with irrigation centers^ in America, are aware that proper attention to the minor channels of an irrigation system is very seldom given in this country. In India, on the older canals, irrigation was carried on from the main channel itself, that is the small irriga- tion outlets were fixed in the canal banks. On account of the leakage along the outside of these pipes, frequent breaches of the banks took place. During years of "T Fig. 179. Plan of Distribution System. drought the villagers cut the banks and attributed the breach to some other cause. The loss of water resulting from these practices and several other causes , were found to be so great, that the distribution (rajbuha) system is 254 IRRIGATION CANALS AND now generally adopted. In this system all pipes or tubes for the direct irrigation of land, must be taken from the lateral, and not from the main canal. Figure 179 is intended to illustrate the system of locat- ing the distribution channels in use in Northern India.* In this system, as remarked by Sir Proby Cautley, the greatest canal engineer that ever lived, we may consider the canal as answering to the reservoir or supply chan- nel, in the water supply of towns, the distributaries as the mains, and the village water-courses as the service channels. The village water-courses are not shown in any of the diagrams in this article. A and B show the methods ordinarily used there where the slope of the country is so flat as seldom to admit of the waters of the distributary being returned to the canal. In order to have the same velocity as the main canal a distributary must have a greater grade, and where the slope of the canal is parallel to the sur- face of the country, it is evident that after a channel with a greater grade than the canal has left the latter, it cannot again return its water into it. In order to have the same velocity, the grades, required for a canal and distributary, are in the inverse proportion to their hy- draulic mean depths. Where the slope of the country is greater than that of the distributary, Figure 180, C and 1), show different methods by which the tail water of the distributary is returned to the canal. C, in the diagram, gives an ex- ample how this may be done in a case where the canal is too far in soil to afford water at a proper level to irrigate close to its banks. After leaving the canal in cutting at a 1 , a 2 , etc., the distributary does not gain sufficiently on the grade of the country to be able to give surface *Sone Canal Project by Col. C. H. Dickens. OTHER IRRIGATION WORKS. 255 elevation until it arrives at 6 1 , 6 2 , etc., passing there, over a syphon or fall conveying the returning upper distrib- utary, which from loss of level in the crossing does not irrigate again till it comes to d 1 , c, etc., whence it passes over the distributary next but one below rty and irrigates the land close to the bank, before it returns by a drop into the canal. An arrangement of this kind could only be effected with a very good fall of country. Fig. ISO. Plan of Distribution System. In D, in diagram, the tail water from the upper canal is intercepted and utilized by the canal located on a lower level. The above illustrations are given to show what has 256 IRRIGATION CANALS AND been done in Northern India, where irrigation has been carried on from time immemorial, and where the British Government have developed it to an extraordinary ex- tent. In locating laterals an engineer must be careful not to attempt to be too systematic, but to be guided by his own ingenuity and the nature of the ground in each case. In the American plains, distributaries are often carried along fence lines, which form sides of either rectangular or square tracts of land. Fig. 181. Fig. 185. Figures 181 to 185 exemplify distributaries in cut de- OTHEK IRRIGATION WORKS. 257 signed for the Sone Canals, India. * Only half the bed width is shown. These illustrations are given, not only as good specimens of design, but also to show the care that is taken in India, with even the minutest details of design. Distributaries may be cleared of silt whenever the water is least required. One, or at most two clearances a year are enough for a well designed distributary. The floorings of all bridges and other masonry works, built over them, will, of course, have been carefully laid down to the proper levels, and will give so many permanent bench-marks for restoring the correct level of the beds; besides which, stakes or masonry bench-marks should be fixed at intervals, not exceeding a furlong. Major Brownlow states, that the greater the amount discharged by a distributary, the smaller will be the proportion of cost of maintenance to revenue derived. This is evident, when we consider that, other things being equal, a channel having a bed width of 12 feet, and side slopes of 1 to 1, discharges almost double the volume discharged by two, each having a bed width of 6 feet, while the cost of patrolling and repairs to banks of the 12 feet channel will be about half of that on the two 6 feet channels. When, however, the channel silts up as illustrated in Figure 7, page 19, and the side slopes average J horizontal to 1 vertical, the 12 feet channel discharges more than two 6 feet channels. The trans- porting power of large volumes of water being also greater than small volumes, the deposit of silt in the 12 feet channel will be less in proportion to the dis- charge than in the two 6 feet channels, thus doing away with the necessity of frequent clearances required in the latter. *The Sone Canal Project by Col. C. H. Dickens. 17 258 IRRIGATION CANALS AND The following table based 011 Baziii's formula (37) Floio of Water, for channels in earth, is proof of what has been stated: TABLE 17. Giving velocity in feet per second, and discharge in cubic feet per second, of channels with different bed widths, but all other things being equal, based on Baziii's formula for earthen channels. Bed width in feet. Depth in feet. Grade. Side slopes. Velocity in feet per sec. Discharge in i Side cubic feet per second. slopes. Velocity in feet per sec. Discharge in cubic feet per second. 3 3 1 ill 2500 1 to 1 1.43 25.65 'i 1 to 1 1.39 17.34 . -. j, ' 6 3 1 in '2500 i to i 1.65 44.60 ;: J to 1 1.58 35 . 59 9 3 1 in 2500 t to 1 1.80 64.66 i to 1 1.76 55.34 12 3 1 in 2500 1 to 1 1.90 85.28 j i to 1 1.87 75.83 15 3 1 in 2500 1 to 1 1.97 106.26 : MO 1 1.05 96.74 18 3 1 in 2500 I to 1 2.02 127.46 | to 1 2 . 02 117.90 By adopting large distributaries the actual amount of clearances during the year is also diminished, for a great portion of the silt which would be rapidly de- posited at the head of a small line, is carried along and dropped into the water-courses branching off from a large one. In Northern India distributaries are of various sizes discharging from 4 to 200 cubic feet per second, but ex- perience seems to prove, that irrigation may be safely and most profitably carried on from channels 18 feet wide at bottom, with side slopes of 1 to 1, the depth of water being from 3J to 4 feet, provided that the depth be kept at least 2 feet below soil for the first ten miles of its course, and that no outlets be allowed in subsequent embanked portions of the line. On the Eastern Jumna Canal during 1858-59 and 185960, the revenue from all distributaries of 12 feet OTHER IRRIGATION WORKS. 259 head water-way and upwards, amounted to $64,809, while the expenditure on their maintenance was $8,019 or .123 of the revenue. The revenue from all distri- butaries below 12 feet water-way at the head was_1133,- 524, and the cost of maintenance $28,289, or .223 of the revenue, being very nearly double the proportion in the first case. The head mentioned is the width of water-way of the regulator at the head of the distributary. For example, if a regulator at the head of a distributary has one clear opening of 12 feet between the abutments, that is called a 12-foot head, but if there is a pier in the center making two clear openings of six feet in width each, this regulator would also have a 12-foot head. The economy of water 011 the large channels is equally marked, for, during the above-named two years, the revenue was, from: Seven distributaries of 12 feet head water-way and up- wards, $64,809; Forty-nine distributaries of 6 feet head water-way and upwards, $108,216; Twenty-nine distributaries of 3 feet head water-way and upwards, $25,308; Giving an average revenue per annum of: $4,629 from a distributary of 12 feet head water-way. $1,104 from a distributary of 6 feet head water-way. $436 from a distributary of 3 feet head water-way. Measurements made gave 90, 32 and 22 cubic feet per second as the relative discharges from 12 feet, 6 feet and 3 feet heads oil this canal; from which we have as the relative values of a cubic foot of water per annum: $51 on a 12 foot distributary. $35 011 a 6 foot distributary. $20 011 a 3 foot distributary. The increased action of absorption and evaporation 260 IRRIGATION CANALS AND over the greater area covered by water of the smaller channels, accounts for the difference above shown. The depth of water in distributaries should seldom exceed 4 feet; but in carrying out a new line of irriga- tion, we should aim at keeping the surface of water at about 1 to 1J feet above the general surface of country, so as to secure irrigation by the natural flow of water. Under these conditions, breaches in the banks need never be feared, with ordinary care in their construc- tion and maintenance. This object, however, is to be kept in due subordination to the primary desiderata of a reasonable longitudinal slope, and an alignment following the watershed of the country. Where the existing supply on a distributary becomes insufficient for the demand, it will be, in the end, found more economical to increase the discharge by widening the original channel for a suitable distance, than to do so by carrying the required additional volume down from a second head, as used to be often done. Against the latter course, all the arguments before adduced hold good, while the back-water from the head which is run- ning the strongest, is sure to check the velocity of the water in the other, and so immensely accelerate the de- posit of silt.* The Roorkee Treatise states, that the system of raising water to the level of the country, where it runs below the surface of the soil, by stop dams or planks, introduced into grooves constructed for that purpose, cannot be too strongly condemned. These convert what should be a freely flowing stream, into a series of stagnant and un- wholesome pools, encourage the growth of weeds and the deposit of silt, and are in every way objectionable. Be- sides, with a reasonable slope in the surface of the coun- try, it will generally be found that, for every acre of *Koorkee Treatise on Civil Engineering. OTHER IRRIGATION WORKS. 261 land thus secured, ten can be obtained further on by the natural flow of water. Be this, however, possible or not, it is decidedly better to resort to any other means of raising the water to the level of the country than the above wasteful and unhealthy expedient. CROSS-SECTIONS OF DISTRIBUTARIES. The writer has seen, in California, land irrigated by the use of stop planks that, without their use, could not have been irrigated. No bad results whatever followed 262 IRRIGATION CANALS AND from raising the water. As a rule, there is no necessity to keep the stop planks in more than twelve hours, and in this short time little if any damage can result. It is simply a question of utilizing so many- acres of land, by raising the water for about twelve hours at certain inter- vals of time. Figures 186 to 189 show distributaries, not drawn to scale, in embankment and excavation.* Article 50. Submerged Dams. Submerged dams, also called sub-soil dams, are fre- quently constructed, across and under the beds of streams, with the object of intercepting the subterranean flow of water in channels whose beds, after rain ceases, soon become dry on the surface. In the construction of a submerged dam a trench is excavated through the sand and gravel down to the im- pervious material underlying them. After this the trench is filled with puddle, or a wall of masonry or concrete is built up to, or nearly as far as, the surface of the bed of the channel. Then, if there is no leakage, the water rises to the surface and is conveyed away, by either an open channel or a pipe. If the rocky sides of a channel or its bed are fissured, or if the bed-rock is porous, it is almost certain that no water can be intercepted. The foundation for a sub- merged dam should be, in every respect, as sound and impervious as that of a reservoir dam, but too often this has not been the case in. Southern California, as the numerous failures of submerged dams there prove con- clusively. Colonel Richard J. Hinton states! : * Irrigation by Rajbtihas (Distributaries) by Lieutenant W. S. Morton. t Irrigation in the United States. Senate Report. OTHER IRRIGATION WORKS. 263 " It is first ascertained by sinking shafts across the channel whether water is thus passing subterraneously. This will be observable in some cases by floating sub- stances traversing the shaft, but if the flow is very slow it may not be detected by this means, and coloring- the water with a dye will show it by a replacement of the colored, by pure water passing through the shaft. A subterraneous water flow is frequently brought to the surface by impervious strata traversing its course. Localities in which this occurs are the best sites for weirs. It is not probable that such natural bars are to be found in the plains, far removed from the sources of supply, and to produce them artificially in such situa- tions would necessitate very deep and probably very ex- tended walls. The trial shafts should therefore be made where the valley is well defined in character. 11 Of course these submerged dams can only bring water to the surface of the channel, where the latter is of sand or gravel, through which the water would rise, forming an artesian supply. Where the surface of the bed is of sand, in which the water could be again lost, the elevated water would of course be diverted to an im- pervious channel provided for it. Where such subter- ranean water can be intercepted a considerable supply might be expected for some months after the water ceased to flow previous to the interception, for doubtless in many cases a considerable proportion of the rainfall is absorbed and given off gradually to subterranean strata." Article 51. Construction Canal Dredger. The following brief notes are given, chiefly for the information of engineers in other countries, outside of America, and who have never seen American methods of construction. 264 IRRIGATION CANALS AND "To begin with the simplest kind of construction,* that of field ditching; the farmer does this, as a rule, with his plow, with which he can easily run a ditch of a few inches capacity across his field. If he intends to widen it while keeping it shallow, he employs the ditch plow, which consists of a blade suspended behind the shear so as to push the earth which it cuts to one side. In many soils this is found to be an invaluable implement. When the work is more roughly done, what is known as a V scraper is brought into play. This varies from a mere log of wood with a couple of old spade heads nailed in front forming a sharp prow, which is its rudest form, to a triangle some six feet wide at its wooden base, from which proceeds two long iron blades forming the acute angle. Its use is always the same. It is drawn by horses and steadied by the driver's weight so as to push the earth outwards from a simple plow furrow, or series of furrows, and thus form a ditch. When this is over six feet wide a "side wiper" is generally substituted, which is a long iron blade, lowered from a frame which rests upon four wheels, so that when drawn by a power- ful team it slants the plowed soil to one side. In light soils and for large ditches, an elaborate machine is used, which not only plows the earth, but takes it up and shoots it out upon the banks a distance of ten or twelve feet on either side, at the rate of from 600 to 1,000 cubic yards per day. But the implement most- in use for oper- ations of any extent is the iron " scraper," well known in Victoria as the " scoop/' which is found in many forms, sometimes it runs sledgewise, sometimes upon wheels, and ingeniously fitted so as to be tilted without effort. For a long pull, wheels are considered best, and for steep banks runners have the preference. The kind ^Irrigation in Western America, Egypt and Australia by the Honorable Alfred Deakin, M. P., Victoria. OTHER IRRIGATION WORKS. 265 of soil to be moved and worked upon, and the length of haul, are always taken into account in determining the class of scoop used. There is another implement known as the buck scraper, which for ordinary farming use in light soils, and in practiced hands, accomplishcs^re- markable results. It consists of a strong piece of two inch timber, from six feet to nine feet long, and one foot three inches high, with a six inch steel plate along its face projecting two inches below its lower edge, and is strength- ened with cross-pieces at the back, where there is a pro- jecting arm, upon which the driver stands. Like the ordinary scraper it is also found on wheels and runners, and in many patterns, and is drawn by a pair of horses. Instead of taking up the earth as the scraper does, it pushes the soil before it, and, when under good com- mand, does such work as check-making, ditch excavat- ing, or field levelling, in sandy soils, with marvellous rapidity." A novel method of excavating a canal has been adopted in Northern California. It is illustrated in Figure 190, which is a view of a canal dredger invented and operated by the San Francisco Bridge Company. It is now in use digging the main canal of the Central Ir- rigation District, which is fifteen feet deep, six miles long, sixty feet wide at the bottom and one hundred feet wide at the top. The following description of this machine is taken from the California Irrigations st of August 1, 1891: "The bid of the Bridge Company for this work was about thirty thousand dollars lower than that of any of their competitors. It was the only firm of contractors who figured on doing this work by machinery; the other contractors estimated on doing it by the old method of scrapers and horses. " The machine, a cut of which is herewith presented, 266 IRRIGATION CANALS AND OTHER IRRIGATION WORKS. 2b i was conceived, invented and designed by the Bridge Company for the carrying out of its contract, and it has proved remarkably well adapted to the work and is in every way a success. It would have been absolutely impossi- ble to have excavated this ditch in the oldiw^w-ith scrapers, owing to the presence of water, which in the summer months stood about two feet deep in the ditch, and in the winter months was often as deep as five to seven feet. The designers of the machine anticipated this condition, and ingeniously arranged the machine to rest on the original ground at the foot of the spoil bank at the top of the ditch, and not on the bottom of the ditch as steam excavators usually do. A standard-gauge railroad track is laid 011 either side of the ditch, as may be seen in the cut; 011 each of these tracks are located three very heavy railroad trucks, similar to flat earsonly shorter; on these trucks are rested the three trusses that span the ditch and carry the car, which runs on double track standard-gauge, and on which is located all the ex- cavating and transporting machinery, as shown in the illustration. The cars on the tracks on either bank are moved forward eight or ten feet at each shift by means of wire ropes worked by steam drums, fastened to " dead men/' or anchors fixed in the ground 100 or 200 feet ahead of the machine; then the excavating chain and buckets are lowered, by means of another steam gypsy, until the buckets come in contact with the ground, and the car is started across the transverse track by means of another steel cable worked by a steam drum; and the buckets, as the machine passes transversely across the ditch, take a cut off the top of the ditch of the whole area of the eight or ten feet which the machine moved forward, and when the machine arrives at the other side of the ditch, the boom is again lowered and the car started back, and another cut is excavated by the buckets. 268 IRRIGATION CANALS AND " This operation is repeated until this section of the ditch is taken out clear to the bottom, then the ladder is raised hy a steam drum so that the buckets clear the ground, and the side cars are again run ahead another eight or ten feet as before, and the buckets are again lowered until they come in contact with the ground, and the car started on the transverse track again. The buckets dump or discharge into a hopper, the bottom of which is inclined and reversible, and the material after falling into a hopper falls down over this incline bottom, which delivers it on the rubber belt conveyor, which carries it to the spoil bank. When the machine passes the center of the ditch, the bottom of the hopper is tilted to the other side and the material is thrown 011 the other conveyor, which delivers it on the opposite bank." Article 52. Water Power on Irrigation Canals. Water power is utilized to a far greater extent on the canals of France, Spain and Italy than it is on the irri- gation canals of India or America. The Hon. Alfred Deakiii, M. P., gives an account of the application of the water power of an irrigation canal for the purpose of irrigating land on a higher level than the canal.* He states that: " On the Cigliano Canal, above Saluggia, is the only instance in Italy in which the motive power of water is used on a large scale in connection with irrigation. Three canals, the Rotto carrying 565 cubic feet per sec- ond; the Cigliano, carrying 1,766 oubic feet per second; and the Ivrea, carrying 600 cubic feet per second, round the side of a steep hill, one above the other in the order named. The waters of the highest, the Ivrea, feed the *Irrigation in Western America, Egypt and Italy. OTHER IRRIGATION WORKS. 269 Cigliano, while the waters of the Cigliano, by a fail of twenty-one feet into the Rotto, generate a sufficient force to lift part of the waters which have been poured from the Ivrea to the crest of the hill sixty-two feet above it, and 130 feet above the Cigliano. From This height it is distributed over the surrounding plateau, which is 164 feet above any natural water supply. The first cost of the machinery employed was $140,000, and a further outlay of $20,000 was incurred before it could raise twenty-five cubic feet per second, the volume de- sired. The working expenses are small, but capitalizing the rent paid to the government for. the water, the total cost of the work amounts to $200,000, or nearly $8,100 per cubic foot per second. From such illustrations it is evident that, ingenious and economical as many of their works are, the Italians appraise the value of water almost as highly as the Southern Californians, and are prepared to undertake the most expensive and difficult works where it cannot be obtained without them." To show the extent to which the water power of irri- gation canals has been utilized in other countries the following examples are given: The Crappone Canal in France, having a capacity of from 350 to 500 cubic feet per second, moves thirty-three mills situated on its course. On the Marseilles Canal in France, the owners of one hundred and seven mills use the fall of the water in the canal for motive power, developing about 2,000 horse- power. Probably over twenty per cent, of its revenue is derived from this source, and the tariff for the use of the water for motive power at the numerous falls along the canal was, a few years since, $40 per horse-power per annum. A horse-power was fixed at 43,296 pounds of water falling through one foot per minute. The water, after being used for motive power, had to be returned 270 IRRIGATION CANALS AND to the company's canal at a lower level, and not appro- priated for any other purpose, except by special arrange- ment. When the water was not used by subscribers for irrigation, it could be employed temporarily for motive power at the rate of $5 per horse-power per month. On the Verdon Canal in France, there existed, some time since, at the numerous falls along the canal, water power to the extent of 2,000 horse-power, which was fixed to be let at $40 per horse-power per annum. The water power of the Henares Canal in Spain, has been estimated at 3,630 horse-power for nine months, and 1,450 horse-power for the rest of the year. Article 53. Cost of Pumping and of Water.* Fearing the failure of the immense masonry barrage (described at page 97), which crosses both branches of the Nile, a short distance below Cario at the head of the Delta, upon which the supply of water to the perennial canals largely depends, the Government in 1885 made an agreement with the Irrigation Society of Behera, by which 'it undertook to pay $210,000 a year for thirty years for a supply up to a certain level, with a maximum of about 2,604 cubic feet per second at Low Nile, lifted by two powerful sets of steam pumps into the Western Canal or Rayah Behera. The weir has since been ren- dered secure, but the agreement indicates the value of water and the difficulty of obtaining it, even in parts of Egypt. Owing to the defective alignment of some, and the silting up of other canals, the task of raising the water a second time from the channels to the fields has been cast upon a large, if not the largest, body of the cultivators. In 1864, according to Figari Bey, the * Irrigation in Western America, Egypt and Italy, by the Honorable Alfred Deakin, M. P. of Victoria, Australia. OTHER IRRIGATION \VORKS. 271 number of sakiyehs or wooden water-wheels used in Central and Lower Egypt was about 50,000, turned by 200,000 oxen and managed by 100,000 persons, who watered 4,500,000 acres. The water-wheels are of sev- eral varieties, costing 011 the average, with the~~well, $150 each, that most in use sufficing for five acres, or ten acres if worked day and night, and employing three bullocks and two men on each shift. In the estimate of Figari Bey, some steam pumps were probably overlooked; for twenty years later there were 2,000 of these at work in lower Egypt, with coal ranging from $10 to $20 per ton. It can now be bought in Alexandria for $5 per ton. The cost of steam pumping is about $1.50, but the price at which it can be hired varies from $2 up to $5 per acre. If paid in kind the charge is often one-fifth of a cotton, and one-quarter of a rice crop, as the latter requires more water. A ten- horse power engine gives an ample supply for 100 acres during the season. There are also "shadoofs" (Egyp- tian water-lifters or swing buckets) innumerable in con- stant employ, which require six men to keep watered one acre of cotton or sugar-cane or two of barley. " If the thin deposit of mud left by the departing river is kept moist its value remains at par. If the hot sun is allowed to play upon it unopposed, it soon becomes baked, and curls up into tiny cylinders; then, breaking into fragments, it falls dead and worse than useless. Therefore, the process of irrigation must begin at once. The rude sakiyeh and the ruder shadoof are kept going night and day, and give employment to tens of thous- ands of people, and cattle as well.* The cost of this incessant labor cannot be estimated. (t There is the greatest dearth of accurate statistics, "f and especially of statistics which would show what is * "The Modern Nile," G. L. Wilson, Scribner, September, 1887. t Public Works Report 1884. 272 IRRIGATION CANALS AND paid for the water and what is produced by it. Though twenty-eight taxes were repealed in 1880, and others have been removed since, the taxation now ranges from $5 to $10 per acre, and sometimes, in Upper Egypt, amounts to more than twenty per cent, of the gross an- nual value of the farm. Over 1,000,000 acres of the irrigated land belongs to the State, the Fellahin upon them being its tenants, with a life interest and a title to their improvements; half as much is included in great estates, while the balance is in the hands of small proprietors. Omdehs, or notables, and sheiks, who control the village communes, often own estates of 1,000 or even 2,000 acres, but the holdings of the great majority of their constituents, who are working pro- prietors, are very small. The Crown tenants, of course, pay rent, but all pay a " land tax " of from $1 to $8 per acre, which might be more properly named a water rent, as no tax is levied if no water is given. It is clear that, if in addition to the taxes, there is the cost of pumping, and four months' labor taken by the corvee, the produce must be great to yield any profit to the culti- vator. The cost of the crop, including taxes and pump- ing, averages $25 per acre. The value of land averages $60 per acre in Upper Egypt, and from $100 to $125 in Lower Egypt, but it not unfrequently reaches $100 in the one and $300 to $350 in the other. Its variation may be judged from the fact that rents run from 50 cents to $50 per acre. Labor, of course, is plentiful and cheap wages averaging from 32 cents to 14 cents per day but, on the other hand, the agricultural imple- ments employed are of the most primitive character; the plough used is made on the same model as is delineated upon monuments thousands of years old, and the Nile mud, though freely and easily worked after the subsidence of the water, requires constant attention throughout the year. OTHER IRRIGATION WORKS. 273 Article 54. Maintenance and Operation of Irrigation Canals. The defective design and construction of the greater number of irrigation canals in this country, haye_been already referred to. But this is not all, for the mainte- nance is equally bad. Repairs are seldom carried out in a thorough and workmanlike manner. Weeds, bushes, and even trees, are allowed to grow in, and obstruct the' channels. Brush is allowed to collect and form obstructions to the flow. In some places the chan- nel gets silted up and bars are formed, and in other places extensive erosion takes place. A great loss of water takes place from defective banks and leaky flumes. The channel, in some cases, floods large areas of land, causing serious loss of water. The side slopes arid grades of the canals are allowed to take care of them- selves, and when breaches occur in the banks, the re- pairs are done in a hurried and slipshod way. Any- thing is good enough to fill in the breach in the banks. When drops are washed out they are seldom replaced,, then retrogression of levels takes place, and the surface of the water gets lower and lower, until the velocity of the current has adjusted itself to the material cut through, and the channel has established its regimen. In conse- quence of the scouring out of the bed of the channel, the sub-soil water passed through is lowered, causing in some cases, great injury to the land. If the channel has fall enough, and it usually has too much fall, it is assumed that the canal can take care of itself. For the proper conservancy of the canal it should be closed once a year, at least, for repairs. Stakes should be set in the bed, to grade, and the silt removed to this level. The banks should be trimmed up, and all weeds, brush and other obstructions removed. Weirs, head- works, bridges, flumes, sluices, drops., etc., should be 18 274 IRRIGATION CANALS AND put in thorough repair. This will be found the cheap- est method in the end, and, by this means, the water can be kept in better control, and the canal worked to much better advantage, than when it is allowed to fall into bad repair. Telephone service should be established along the line of the canal, and a roadway on one bank will be found useful. The official in charge, whether engineer or superintendent, should be informed every day by the patrolman of the quantity of water flowing into the canal at the head works, and also the quantity discharged at each irrigation outlet. He should also be immediately informed of any breach in the canal banks, or anything else likely to cause damage, or a partial obstruction to, or complete stoppage of irrigation in its main or dis- tributary channels. The Indian, Egyptian and Italian Irrigation Canals are closed, at least once a year, for clearance of silt and repairs in general. Some of the Indian canals . are closed for about six weeks annually. The Naniglio Grande, or Grand Canal of the Ticino in Italy, is closed twice a year. An instance of frequent closing is given on one of the small Indian canals. In the Irrigation Revenue Report of the Bombay Presidency, for 1889-90, it is stated that: "The Palkhed Canal was closed six times during the year for clearance of silt, aquatic plants," etc. Mr. Walter H. Graves, C. E., has made some remarks on this subject which will be found useful here. He states: * " Maintenance and superintendence are matters of considerable importance in the management and success of any enterprise, but especially important in irrigation ^Irrigation and Agricultural Engineering in Transactions of the Denver Society of Civil Engineers for June, 1886. OTHER IRRIGATION WORKS. 275 plants, for obvious reasons. The roadbed and rolling stock of a railroad might be allowed to deteriorate for some length of time without seriously impairing the operation of the road, but deterioration in the head- works and channel of a canal means speedy paralysis . " The sources of impairment of canal property are: " First. As to the channel. The water itself carried by the canal, by the erosion of the banks and channel, and the filling of the channel by the deposition of sedi- ment. " This is a process of self destruction. "Second. From the storm or flood water. The de- nuding of the banks by the erosive action of the elements is a constant source of destruction, although it is a com- paratively small item. From the very nature of the alignment or location of the canal it must intercept to a greater or less extent the slope, and consequently the drainage of the country it traverses. If ample provis- ion is made to transfer the flood or drainage water across the canal by means of flumes, culverts, etc., destruction from this source is largely prevented. But, as a rule, provisions of this character are wholly neglected. In many cases, where the slope of the country is sufficient, there is no upper bank to the canal, and the drainage channels are allowed to empty directly into it. Thus the surface water of the entire country above the canal is gathered into it, and the result is, in such cases, a constant rebuilding and repairing of banks. " Third. The destruction of the channel, and espec- ially the banks, by the range cattle, which can only be prevented by fencing the canal. " The deterioration in the structures of a canal are: "First. The head works. If these are of such a character as to be proof against the strain and force of the annual floods, and to meet the requirements of the 276 IRRIGATION CANALS AND wide range of the fluctuations of the average mountain stream they must be very complete and expensive struc- tures, and quite out of the reach of the average company. The class of work usually adopted, however, is such as to make the liability of destruction and the cost of re- pair important items in the subject of maintenance. "Second. Applying to all structures is decay. Tim- ber intervening between water and earth, and alter- nately soaked and dried, is particularly subject to decay, and the life of wooden structures can scarcely be pro- longed beyond six or eight years. 11 Third. Incendiarism. Strange as it may appear, this has proven, in the experience of the larger canal companies, an item of considerable importance. 11 The subject of maintenance directly involves that of superintendence. An ignorant or an indifferent superintendent can increase the cost of maintenance many fold. " Where incipient disaster may easily and cheaply be curtailed by intelligent vigilance on the part of the superintendent, serious calamities often occur by reason of his carelessness and ignorance. As a case in point, a leak of apparently insignificant proportions was allowed to exist for some time through the embankment adjoining the head-gate of one of the largest canals in Colorado, when it suddenly assumed a magnitude beyond control, until it had almost completed the destruction of the head-gate, a structure costing several thousand dol- lars. In this case as in many others similar, bad super- intendence was credited to bad engineering. 11 It seems to be quite the custom in Colorado to select canal superintendents from among any class of men ex- cept engineers, the very men best fitted by experience and training for such work." In India the irrigation canals are always under the OTHER IRRIGATION WORKS. 277 control of the engineers of the Public Works Depart- ment. They control the movement and distribution of the water, and carry out all repairs and additions to the works. In order to know at all times the quantity of water available they have numerous gauges, the read- ings of which reach the controlling office every day, and it is a rule that he should write them into his gauge book with his own hand. There is one arrangement, however, which, though it works well in India, is not suited for this country, that is, executive and assistant engineers engaged on the canals there, usually have powers of an assistant magis- trate for the protection of canal property. The following extract is pertinent to this subject:* " It is too commonly supposed that when the canal is once constructed, there remains little for the executive engineer to do worthy of a man of any experience, abil- ity or education. This is a very great mistake. There may be no great works left to construct, but there are sure to be many small ones requiring much experience and precision to execute properly. There are many points of the purest science still undetermined, such as the true formulae for the discharge of large bodies of water in open .channels, or over weirs, the amount of loss by percolation and evaporation; the effect on the velocity of a stream of a large percentage of silt carried along. The executive engineer may have besides, to train and do battle with rivers of great size, or the not less troublesome hill torrents. He may have in his charge a series of weirs which have to be constantly watched and protected, while repairs, often of the most important character have to be executed within the space of only a few days when the canal can be closed. *ltoorkee Treatise 011 Civil Engineering. 278 IRRIGATION CANALS AND Alongside of his weirs he may have locks to superin- tend. His rajbuhas (laterals or distributaries) ought to be a source of constant interest, requiring extension and improvements, while he will find, as he goes on irrigating, that drainage has to be attended to and arti- ficial cuts to be laid out, to correct the over-saturation which only the best administration can prevent from taking place, and to ward off the malaria which over- saturation produces. 11 Besides all this, no man should consider it beneath his attention to exercise almost independent control over a large body of water, bringing in a revenue every year of $200,000 to $300,000, and also of being a source of wealth to the country of at least four times that amount. " He should possess a general knowledge of the agri- culture of the district, and know at what season the va- rious crops most want watering, and what soils most require it. If he is fond of forestry, he will find room for gratifying his taste in cherishing and extending the plantations along the banks of his canal, and may render lasting benefits to the country by the introduction of new trees. " Among lesser matters, he may turn his attention to utilizing the water power of his canal, a subject which must claim attention as the country progresses. If the above subjects do not possess sufficient interest for the engineer, he had better choose some other line than the irrigation department. " Nor ought he to look for employment on a running canal if he is not prepared for a life of constant moving about, at all seasons of the year. He must expect but little of the pleasures of society, or domestic life, and be prepared for many a long, hot day, by himself, in the canal inspection house." OTHER IRRIGATION WORKS. 279 Article 55. Methods of Irrigation. The methods of irrigation are generally classed under four heads, as follows: 1st. .Flooding. 2d. By distribution through furrows or ditches. 3d. Sub-surface irrigation by pipes. 4th. Sprinkling. Of the four methods mentioned, only the first two will be referred to in the following pages, as almost all irrigation 011 a large scale is carried 011 under these heads. Of the above four methods, flooding is most generally practiced, and on the most extensive scale. The flood- ing is usually done in embanked compartments. These compartments vary in size. In India, they are some- times as small as 400 square feet, whilst in Egypt, they are often several square miles in extent. The following, on methods of irrigation, is compiled mainly from a paper in the Minutes of Proceedings of the Institution of Civil Engineers for 1883, by P. O'Meara, C. E., on Irrigation in Northeastern Colorado, and also from a paper by the Hon. Alfred Deakin, M. P., of Victoria, Australia, on American Irrigation. FLOODING. The easiest, simplest and cheapest method of irriga- tion is by flooding. By this method, the water is directed to cover the whole area under cultivation to a depth varying according to the crop and the quality of the soil. This plan is the most wasteful of water, but cannot be avoided in the cultivation of cereals. The only work it involves in the field is that necessary to permit an even flow of water. With a regular slope this work is sometimes trifling, but, as a rule, some preliminary outlay is required for leveling irregu- 280 IRRIGATION CANALS AND larities, or else providing for the equal distribution of the stream from points of vantage. m 4i To secure the highest degree of economy under the OTHER IRRIGATION WORKS. 281 flooding method, inequalities are removed from the sur- face of the land, which is then divided by small raised mounds, called " checks," into compartments, each of which is connected with a lateral or branch drain, lead- ing from a lateral by one or more rudely constructed sluice boxes, or other cheap contrivances. The objects of these compartments are threefold, namely: 1, To check the water and to cause it to flow laterally; 2, To arrest the flooding as soon as the amount supplied is sufficient for moistening the soil to the extent deemed beneficial; 3, To diminish the inequality in the depths moistened, which necessarily arises in the circulation of water from a central point. Figure 191 exhibits the distributing ditch taken from the main canal, the gates leading from the distributing ditch to the compartment.'* The compartment flooded is the third from the main canal, and in case the two upper compartments were first flooded, their surplus water would flow through the gates shown in the checks, into the third compartment. Small gates are shown in the three checks for draining the compartments when it is deemed they have had sufficient water. The smaller the compartments the less will be the re- sulting inequality, but the greater the expense of con- structing and the labor of using them. Lands nearly level and lands with retentive soil admit of the largest compartments, with a given margin for inequality of moistening. The maximum of size is perhaps obtain- able when the slope from the point of application is about 1 inch in 100 feet. On nearly level lands the size of the compartments may be directly proportioned to the volume of water in application. The extent of this volume is limited by the difficulty of controlling it, *Report of the Senate Committee on the Irrigation and Reclamation of Arid Lauds. 282 IRRIGATION CANALS AND and the damage it would do to the soil or crop if too large. Laterals of three or four cubic feet per second for broken land, and of six or seven cubic feet when the land is unbroken, are manageable under favorable cir- cumstances, by one irrigator, although those which are in use where compartments have been tried in Colorado are much smaller. The whole of the volume in. appli- cation may be admitted into one compartment through several openings, or into several compartments through one or more openings. In the former case the com- partments may be larger, because the inequality of absorption depends 011 the time of flooding. This, to come within the margin fixed for inequality of absorp- tion, must, in the absence of statistics for different soils, be arrived at by a tentative process, and the size of the compartments then proportioned to the volume or vol- umes in application. When the fall is slight, shallow ditches are run, in Colorado, from 50 feet to 100 feet apart in the direction of the fall; when the land is steeper they are carried diagonally to the slope, or are made' to wind around it, and from there, by throwing up little dams from point to point, the whole field is inexpensively flooded. When the fall is still greater and the surface irregular, ridges are thrown up along the contour lines of the land, marking it off into plots called "checks," on the whole of the interior of which water will readily and rapidly reach an equal depth on the contour line. When one plot is covered the check is broken and the water ad- mitted so as in the same way to cover the next plot. Figure 192 shows the contour checks beginning at the main canal, and compartments supplied by a ditch or distributary running almost parallel on each side of the compartments. Figure 193 shows a cross-section of main canal; Figure 194, a cross-section of distributary, OTHER IRRIGATION WORKS. 283 and Figures 195 and 196, cross-sections showing checks.* The ridges, checks or levees must have rounded crests and easy slopes, or else they interfere with the use of farming machinery, such as plows, headers, etc. By means of diagonal furrows and checks, remarkable re- sults are obtained, even in very broken country. By their means it is claimed that, in Colorado one man can irrigate twenty-five acres per day. Where checks have not been used upon ground with an acute incline the water has soon worn deep channels through it, utterly ruining it for agricultural purposes; or again, where the water has been allowed to flow too freely, the conse- quence has been that all the fertilizing elements of the soil have been washed away. In flooding, the aim is, therefore, to put no more water upon the land than it will, at once and equally, absorb or can part with with- out creating a current sufficient to carry off sediment. The neglect of these precautions has caused the aban- donment of several settlements made in Utah before the art of Irrigation was properly understood.- *Beport of the Senate Committee ou the Irrigation and Reclamation of Arid Lands. 284 IRRIGATION CANALS AND Both the depth and number of floodings are varied according to soil and crop. With a clay the water- ings are light and frequent, while with a sandier quality they are heavier and rarer. Much, too, depends upon the distance and nature of the sub-soil. There is considerable uncertainty with regard to the measure- ments given for flooding. It is sometimes so low that it will give a depth of only two or three inches, and at other times it will give a depth of five to ten inches at a single watering. There are cases in which as many feet have been used. The number of waterings is best deter- mined by the crop itself, and the most skillful irrigators are those who study its needs and take care to supply these needs, without giving an excess of water. The quantity used alters, therefore, from season to season, so that only an average can be given. See Article 58. In Colorado, where water is used more lavishly than in any other State, some good judges have agreed that an average of 14 inches should be ample, and this is certainly not too low. Where the soil is liable to be- come hard, and will retain moisture, wheat is often grown with two floodings, one before the ground is ploughed and the other when it is approaching the ear. When two waterings are given after sowing, one is given when the wheat commences to "tiller," and the other when it reaches the milky stage. Where irriga- tion does not precede the plowing, it is postponed as long after the appearance of the crop as possible. Sometimes wheat has three, or even as many as four, floodings, but this is unusual, as over-watering occasions "rust." Experience shows that it is easy to exceed the quantity required by the crop, and that every excess is injurious. Extravagance is the common fault, so much so that the most successful irrigators are invariably those who use the least water. The less water, indeed, OTHER IRRIGATION WORKS. 285 with which grain can be brought to maturity, the finer the yield. Colonel Charles L. Stevenson states, with reference to the methods of irrigation in use in. Utah: * "Each farmer has canals leading from the main one to every field, and generally along the whole length of the upper side of each field. Each field has little fur- rows, a foot or more apart and parallel with each other, running either lengthwise or crosswise or diagonally across, as the slope of the land requires. Into these furrows the water is turned, one or more at a time, as the quantity of water permits, until it has flowed nearly to the other end, when it is turned into the next fur- rows, and so on until all are watered. 11 This is the usual custom, but where the soil is made of clay this method is not so good and another is used. This method is to throw up little embankments six inches high around separate plats of land that are of uniform level, and turn the water in until the plat is full to the top, when the water is drawn off to the next lower plat, and so on to the end. This enables the water to soak in more and so does more good, but where the soil is porous, as is generally the case, it is not so good a method as it wastes water." FLOODING IN INDIA. In India, and also Egypt, flooding is universally practiced. There are two methods adopted in India in supplying water for irrigation, known as flush and lift. In flush irrigation the water flows by gravitation on to the land to be irrigated. In lift irrigation the water reaches the land at such a low level that it cannot flow over the surface of the land to be irrigated. This * Irrigation Statistics of the Territory of Utah, by Colonel Charles L. Stevenson, C. E. 286 IRRIGATION CANALS AND necessitates power of some kind, usually manual labor, to raise the water sufficiently to enable it to flow over the land. It is, therefore, to the interest of the irri- gator to economize water, and in view of this fact the officials of the Ganges and Jumna Canals charge for lift irrigation only two-thirds of the rates charged for flow. The proportion of flow to lift irrigation, on the Sone Canals, in Bengal, in 1889-90, was 96.3 to 3.7. During the same period on the Mazzafargarh Canals, in the Punjab, the proportion of flow to lift was as 96.1 to 3.9, but on the Shahpur Inundation Canals, in the same Province, the proportion of flow to lift irrigation was 85 to 15. There is usually more lift irrigation on inun- dation canals than on perennial canals. So great was the loss from waste of water in India, some years since, that it was seriously proposed to sup- ply all the water at such a level that it should be raised some height, however small, in order to bring it to the surface of the land to be irrigated. It would then be to the interest of the irrigators to prevent waste, and the duty of water would, in this way, be materially increased. FURROWS. Peas and potatoes are not irrigated by flooding, but from furrows four feet to ten feet apart, and this is found the most economical and most successful system for vines and fruit trees. The direction of the furrows is chosen so as to give a fall of from one inch to three inches per 100 feet. The expenditure of water is much less under this than under the flooding method. When the furrows are deep and narrow the practice is similar in principle, though less effective than the pipe method of irrigation, which will be described further on. Irri- gation can, in fact, be carried on without flooding the intervening soil, moistening in the latter case taking place beneath the surface, and losses from evaporation OTHER IRRIGATION WORKS. 287 being thereby largely diminished. It is evident that the depth of the furrows should be in some degree pro- portioned to the depth of the roots of the crop culti- vated. Figure 197 illustrates how land is irrigated by furrows.* Fig. 197. Plan Showing Method of Furrow Irrigation. Under the flooding system the ground, if not pro- tected from the sun, cakes quickly. When the water is run down furrows drawn by a plow between the plants, this caking is avoided and the water soaks quickly to the roots. When flooding was practiced in orchards it *Irrigatioii by W. H. Graves, C. E. Transactions of Denver Society of Civil Engineers, 1886. 288 IRRIGATION CANALS AND was found to bring the roots to the surface and enfeeble the trees, so that they needed frequent waterings. Sometimes the furrows feed a small hole at the foot of the tree, from which the water soaks slowly in. When this is done mulching is found desirable over the hole to reduce the loss by evaporation. The general rule is to protect the trees by small ridges, so that the water does not affect the surface within three or four feet of them. The simple furrow, however, is most generally in use. Oranges are watered three or four times in summer; vines once, twice, or often not at all after the first year or two; and other fruits according to the caprice of the owner, the necessities of the season and the nature of the soil, one to four times. It is impossible to be more exact. An even greater difference, comparatively, in the quantity of water used obtains in the furrow irrigation of fruit trees and vines, than has been noted in regard to cereals. To such an extent does this prevail that, not only do districts differ, but of two neighbors who cultivate the same fruits in contiguous orchards, having exactly the same slope and soil, one will use twice or thrice as much water as the other. To attain the best results the trees must be carefully watched, and sup- plied with only just enough water to keep them in a vigorously healthy condition. Another all important principle, as to which there is no question, and which is testified to on every hand is, that the more thoroughly the soil is cultivated, the less water it demands, a truth based partly y 110 doubt, upon the fact that the evaporation from hard, unbroken soil is more rapid than from tilled ground, which retains the more thoroughly distributed moisture for a longer period. OTHER IRRIGATION WORKS. 289 Major Corbett published some articles in the Profes- sional Papers on Indian Engineering to prove that, by the adoption of superior cultivation, the necessity of irrigation would be very much diminished- in-iidia. The native plow enters the ground for only a few inches, and below that depth there is a hard crust that prevents the water from filtering down. He contended that by breaking up this hard crust by deep plowing, and by carrying the cultivation deeper, that there would not be the same necessity for irrigation as was required after shallow plowing, for the reason that evaporation from the land would not take place to the same extent. For the irrigation of cereals, works are required on a larger scale, proportionately, than for fruit, because in the first case the water is demanded in greater quantities, at particular- times, while in the latter the supply can be more evenly distributed throughout the year, though, of course, the irrigating season with both is much the same. Winter and autumn irrigations are growing in favor. Land which receives its soaking then, needs less in sum- mer, and is found in better condition for plowing. It is argued that moisture is more naturally absorbed in that season and with greater benefit. Everywhere the verdict of the experienced is, that too much water is be- ing used, and the outcry against over-saturation in summer is but one of its forms. Article 56. Duty of Water for Irrigation. The duty of water is that quantity required to irrigate a certain area of land. In English-speaking countries, it is usually expressed by stating the number of acres that a continuous flow of one cubic foot per second. will irrigate. Thus, if a stream discharging 40 cubic feet of 19 290 IRRIGATION CANALS AND water per second is all expended in irrigating 8,000 acres of land, then its duty is equivalent to 200 acres, that is, each cubic foot per second irrigates 200 acres. The duty varies from 35 to 2,200 acres per cubic foot per second. The duty is sometimes expressed by the average depth of water over the whole land, and again, by the cubic contents, as, for instance, the number of cubic yards per acre. The duty of water is influenced by different circum- stances and varies according to the following condi- tions: 1. With the character and conditions of the soil and sub-soil. 2. Configuration of the land. 3. The depth of water-line below surface of ground. 4. Rainfall. 5. Evaporation and temperature. 6. The method of application employed. 7. Length of time the land has been irrigated. 8. Kind of crop. 9. The quantity of fertilizing matter in the water. 10. The experience of the irrigators. 11. The method of payment for the water, whether by the rate per acre irrigated or by payment for the actual quantity of water used. Payment according to the actual quantity of water used is a good method to make the irrigators use the water with economy. Mr. J. S. Beresford, C. E., in a paper on the Duty of Water,* enters very fully into all the causes of waste of water. He states, under the heading: " Efficiency of a Canal. Take the Ganges Canal. We * Professional Papers on Indian Engineering, Vol. V, Second Series. OTHER IRRIGATION V^ORKS. 291 may look on it as a great machine composed of many parts, and go about calculating its efficiency in the same way as that of a steam engine. This irrigating machine is made up of four important parts, which arequite separate, and, as things stand at present, at least two of them depend on different interests. They are as follows: 11 1. Main Canal. " 2. Distributaries. " 3. Village water-courses. " 4. Cultivators who apply the water to the fields. "Each cubic foot of water entering the head of a canal is expended as below: " 1st. In waste by absorption and evaporation in passing from canal head to distributary head. " 2d. In waste from same, cause in passing from dis- tributary head to village outlet. " 3d. In waste from same cause in passing along village water-course to the fields to be watered. " 4th. In waste by cultivators, through carelessness in not distributing the water evenly over the fields, causing evaporation, and the ground to get saturated to an unnecessary depth in places. (See page 250.) " 5th. In useful irrigation of land. " Our object is plainly to increase the fifth by the re- duction of all the rest." All over the irrigating districts of America, where irrigation is carried on from earthen channels, the duty is low. We see in Table 18 that the average duty in India is over 200 acres, and it is doubtful if the average in America is half of that quantity. There is one fact that may account for this great difference. In America the greater part of the land irrigated is virgin soil, and this may account for the great quantity of water used. In India, on the contrary, the land has been irrigated 292 IRRIGATION CANALS AND for centuries and the average rainfall is greater than in the arid region of America. A great portion of the land now irrigated by canal water in India was irriga- ted from wells before the construction of the canals. Whatever the cause may be, the fact is apparent, that the duty of water in America is far below that of India. We have already seen, in page 249, how Mr. A. E. Forrest, C. E., by simply improving the distributaries, raised the duty of water in one of the divisions of the Ganges Canal to 400 acres. There is no good reason why such a duty of water should not be reached in many districts of America. As the area of irrigated land increases so will the value of water increase, and irrigators will then be compelled to keep their main and distributing channels in good order, to use the water at night to prevent all waste and to put no more on the land than is sufficient to mature a crop. The following table, showing the duty of water in different countries, is compiled from various sources and includes a table given by Mr. A. D. Foote, C. E., in his Report on Irrigating Desert Lands in Idaho: TABLE OTHER IRRIGATION WORKS. Giving the duiy of water iu different countries. 293 LOCALITY. COUNTRY. Duty of water. REMARKS. Eastern Jumna Canal India.. . . India . . Acres. 306 240 E. B. Dorsey, C. E. F C Danvers. Ganges Canal Canals of Upper India Canals of India average Bari Doab Canal India India India India 232 267 250 155 E. B. Dorsey, C. E. E. B. Dorsey, C. E. Lieut. Scott Moncrieff, R. E. F C. Danvers. Madras Canals (Rice) Tanjore 'Rice) Swat River Canal, 1888-89. Swat River Canal, 1889 90. Western Jumna Canal, 1888-89. Western Jumna Canal, 1889-90. Bari Doab Canal, 1888-89. B'iTi Doab Canal, 1889-90 Sirhind Canal, 1888-83. Sirhind Canal, 1889-90. Chenab Canal, 1888-89. Chenab Canal, 1889-90 Nira Canal, 1888-S9. Genii Canal ... India India India India India India India India India India India India. .. . India 66 40 216 177 143 179 201 227 180 180 154 154 186 240 George Gordon. Roorkee Treatise Civil Engineering. Revenue Report of the Irrigation Dep't, Punjab, 1889-90. Bombay Report, 1889-90. E B Dorsey C E Elche Spain... . Spain ... . 1072 2200 George Higgin, C. E. George Higgin, C. E Jucar (Rice) Spain 35 George Higgin C E Spain 157 George Higgin C E Canals of Valencia Spain ... . 242 140 E. B. Dorsey, C. E. Transactions ICE vol 65 Canals south of France Sen, or Lower Nile Canals Sen, or Lower Nile Canals Canals, Northern Peru Canals, Northern Chili Canals, Lombardy Canals, Piedmont < Marcite France . . Egypt .. . Egypt . . Peru Chili Italy Italy Italy 70 350 274 160 190 90 60 1 to 18 George Wilson, C. E. London Times, 18 Sept., 1877. Russian Pasha, 1883. E. B. Dorsey, C. E. No rainfall. E. B. Dorsey, C. E. No rainfall. Baird Smith, R. E. Including Rice. Baird Smith, R. E. Including Rice. Columbani and Brioschi. Sen Canals, Southern France Sen Canals, Victoria France . . . Australia 60 200 Lieut. Scott Moncrieff, R. E. The Honorable Alfred Deakin, M. P Sweetwater, San Diego Pomona, San Bernardino California. California. California 500 500 500 William Fox, M. Inst., C. E. ~) -p. William Fox, M. Inst,, C. E. V ' William Fox, M Inst.. C. E. ) s y stenL California California 80 to 150 San Diego California 1500 James D Schuyler, C. E. Canals of Utah Territory Canals of Colorado Canals of Cache la Poudre , Utah Colorado.. Colorado. . Colorado 100 100 193 55 C. L. Stevenson, C. E. Nettleton, State Engineer, Colorado. Prof Mead, C. E. P O'Meara C E Article 57. Pipe Irrigation. Four things are necessary in order to get the greatest possible duty of water. They are: 1. That the water should he sold or supplied by measurement. 2. That it should he conveyed to the actual point of use in impervious channels, and best of all in pipes. 3. That its use should he continuous, that is, at night as well as by day. 21)4 IRRIGATION CANALS AND 4. That it should be used intelligently and with a dvie regard to economy. The use of pipes refers only to small supplies of water. For large supplies earthen channels are the most economical, not o^ water, but of money. If the above four conditions are observed the duty of water, especially for fruit land, will be increased to a great extent, with a corresponding increase in the area of land irrigated. The use of pipes made of plate iron, vitrified clay, concrete, wood bound with iron bands, open channels made of asphalt or concrete, and reservoirs lined with asphalt or concrete, is steadily increasing in Southern California. The pipe system has been adopted with great success in Bear Valley, Pomona, Ontario, Riverside, San Ber- nardino, Los Angeles, and many other localities in Southern California, and this is conclusive proof, that the great expense attending their construction, is more than counterbalanced by the great saving of water effected by their use. By the pipe system the distribu- tion of water is better under control, and easier man- aged, than by open channels. Fred. Eaton, M. Am. Soc. C. E., of Los Angeles, has supplied the following relative to irrigation by pipes: * " The duty of our streams would be extended by ex- tending the present ditches by pipe systems. Experi- ence has taught us that by economizing the water it is not only the water that we save in seepage alone, but the distribution. The convenience that these pipe systems offer in the distribution of water is a great economizer. We find that we can get along with a half or a third the * Quoted in Irrigation in the United States by Richard J. Hiiitou. U. S. Department of Agriculture. OTHER IRRIGATION WORKS. 295 water that we get in running it around in ditches. It was thought that the San Gabriel was being used up by irrigating 2,000 acres, but it has been used since for irrigating 12,000 acres, and it can be increased by the pipe system. The duty of one-fiftieth of a cubicToot per second throughout the valley, under the pipe system, would be one inch to ten acres; that is, for vegetables and all kinds of crops. It depends altogether on the character of the soil. A soil that is well sub-drained, that is, composed of gravel, will require much less water. Such sub-soil is a natural drain, and for that reason water will go a great deal farther on that kind of land than it will on an impervious sub-soil. Taking the aver- age in the San Gabriel Valley, with ten acres, you can irrigate all kinds of crops, orange trees, and all kinds of vegetables. " The cost runs from $15 to $50 per acre. The cement pipes are not cheaper than the pressure pipes, because it requires a good many more of them, arid they are not so convenient as the pressure pipes. We generally use sixteen iron. It is practically the sixteenth of an inch thick. A four-inch pipe is more difficult to make than a sixteen-inch. We put asphaltum on, but it is impos- sible to keep it from being knocked off in spots, and these spots rust there. We cannot inspect them closely enough to get at them all and paint them over. In or- dinary soil where there is no alkali, it will wear fif- teen or sixteen years. I put in pipes fifteen years ago that are doing service now. The Pasadena pipes were eleven inches with eighteen iron. That system was put in in 1873 and served up to this year. We have not many storage facilities up in the mountains, they are confined practically to the foothills and the valleys. We have to bring our water down and make our reservoir in the valley/' 2"96 IRRIGATION CANALS AND The following description of the pipe system of Onta- rio, California, is by F. E. Trask, Chief Engineer of the Ontario Land Improvement Company: PIPE IRRIGATION SYSTEM, ONTARIO, CALIFORNIA. A portion of the Ontario tract of 11, 000 acres is under cultivation receiving its water supply from San Antonio Canon by means of a pipe system of main, sub-mains and laterals. The accompanying plat shows only a por- tion of the north end of the tract, the letters A A z A 3 , B B B 3 , and C C C, marking the location of mains, sub- mains and laterals respectively. Lots are 696 feet by 627 feet, or about ten acres each in area. The general slope of the land is southeast, and the grade varies from thirteen (13%) per cent, at the north end shown on plat to one (1%) per cent, at the south end of the tract, which is not included in the plat. The principal main, A A A z , brings the water from the canon, around the foothills, and down the same, to the head of the colony land, where, running east and west, this main supplies the laterals C C C. Sub-mains BB B s , or as commonly designated, the sup- plementary mains, take water from the main line, A A A^ near the foothills and run diagonally through the colony, .furnishing water to the laterals, C C C, at points some miles south of their heads, to compensate for that already expended by the latter. For example the lat- teral A$ B$ has supplied four lots by the time it reaches B$. At $3 a new supply is received into the lateral A 3 B 3 from the sub-main B B B?,, which is used to irrigate land lying south of B^. Laterals C C C are designed to carry water without pressure and deliver the same at the highest corner of each lot. They are parallel to each other and average about six miles in length. Each line is designed to irri- OTHER IRRIGATION WORKS. 297 gate one tier of lots and is located three feet within the boundary of such tier, as shown on diagram. The diameter and grades of the laterals C C C are given on the plat for the section it represents; below which the 2U8 IRRIGATION CANALS A\:> grade constantly decreases to the south end of the tract where the grade is flattened, i. e., about one per cent.; but the diameter of pipes remain the same. Stand pipes of fourteen (14") or sixteen (16") inches diameter are placed in the pipe lines, C G 0, at points where water is to be delivered to the land. In each stand pipe an iron slide gate is set; this can be dropped to close the whole pipe line or to a sufficient depth to in- tercept the required volume of water, as the case may be. The greater portion of the pipe used in this system has been manufactured from cement concrete at conven- ient points in the tract. Properly located and designed, the pipe system for the irrigation of fruit lands is much more economic than any of the older methods, and irrigators can ill afford to adopt flume or ditch systems where the topography admits of the pipe system being used. Article 58. Number and Depth of Waterings. The number and depth of waterings given to land vary very much in different countries. The greatest quantity is used in the Marcite cultiva- tion of Italy and the south of France, where water is poured over the meadow lands during the- winter, in quantity sufficient to cover them to a depth of more than 300 feet, and where the, duty has been as low, in some cases, as one acre to one cubic foot of water per second. (See Table 18.) The other extreme is reached of a small expenditure of water by the pipe system of orchard agriculture in Southern California, where a cubic foot of water per second was estimated to irrigate from 500 to 1,500 acres. The Henares Canal, in Spain, gives twelve waterings. Each watering is equal to about 916 cubic yards, which OTHER IRRIGATION WORKS. 299 gives a depth of 0.57 foot for one watering, equal to 6.8 feet in depth for twelve waterings. The Esla Canal, also in Spain, gives twelve waterings. Each watering is equal to about 850 cubic yards, which gives a total depth on the land of about 6.3 feel.~ In Valencia, in Spain, where it is vory hot, wheat is watered four or five times, giving about 200 acres per cubic foot per second. In other parts of Spain a depth of two and one-half to three inches was considered ample for an irrigation, and two irrigations in the seasons were held to be sufficient. In some of the gardens of Valencia, Spain, only from 13 to 20 acres per foot are irrigated. Here, however, there are at least two crops a year and a part is devoted to rice. In the new canal from the Rhone, in France, the summer waterings will generally be twenty in number, given once a w r eek, and representing a total depth of one metre or 3.28 feet. In the south of France the time for irrigation com- mences on the 1st of April, and terminates on the 30th of September. The standard quantity of water adopted in the country is one litre (.0353 cubic feet) of water sup- posed to flow continuously for six months, per hectare (2.471 acres). This quantity of water would cover the ground to a depth of about 62J inches; consequently it gives fourteen irrigations, each of about four and one- half inches; twenty irrigations of about three inches, or forty-three irrigations of about one and one-half inch depth of water. There is no fixed rule in the south of France as to the number of irrigations for such crops which require periodical irrigating, during the whole season, as this must necessarily depend, to a great extent, upon the nature of the land, whether light or heavy, whether fiat 300 IRRIGATION CANALS AND or sloping. In most cases the water is given by the companies once a week, which would be equal to twenty- six irrigations during the season. The Marseilles Canal gives the water forty-three times during the season. Experiments, near the Bari Doab Canal, in India, showed that an average depth of 0.24 feet on the whole surface represents a thorough watering of the average soil of the district, sandy loam, and that for sandy soils 0.31 feet in depth, and therefore the amount of water necessary for an average watering of one acre is 0.24 X 43,560 = 10,454 cubic feet. Wheat in a dry season requires five waterings; the first for preparing the land for plowing at 10,500 cubic feet, and four for the standing crop of 8,000 cubic feet, gives 42,500 cubic feet in all necessary for each crop of wheat that is an average depth of less than one foot. In Madras 6,000 cubic yards of water are usually given to irrigate an acre of rice. This is equivalent to a depth of 3.7 feet. In Colorado the expenditure of water for a single irrigation is generally reckoned at about twelve inches in depth. Of irrigations the number applied to the land in one season is about three, in exceptionally dry ones, four. The English company in Colorado has a water right equivalent to a depth of 42.84 inches. Professor George Davidson, of San Francisco, says that the best authorities assume a depth of from 10 to 12 inches of water to the production of a crop of wheat, barley and maize, when applied in waterings of four times two and a half inches or three times four inches. The smaller of these results is almost identical with the amount deduced from observation in the great valley of California, where a rainfall of 10J inches, fairly distri- buted, has insured a large crop of wheat, etc. OTHER IRRIGATION WORKS. 301 Colonel Charles L. Stevenson, C. E., states, with reference to Utah*: " Each farm generally has the right to use the water so many hours once a week or once in 10, 12 or l^days, as the particular valley and the time of year require. The crops are supposed to get a good soaking at every watering." General Scott Moncrieff states, with reference to irri- gation in India: " For the wheat crop which is grown in the cold season, four waterings are quite enough, and almost 110 other crop requires more, except rice and sugar-cane, which are sometimes irrigated as often as twelve times, and are watered by a rainy season as well. From actual experiments in the Northwest Provinces of India, in the months of December and February, when it is by no means very warm weather, I found that one cubic foot of water per second would irrigate in. twenty-four hours 4.57 acres of rough, uncleaned ground previous to plow- ing, and that this same discharge was enough for 5.64 acres of a well-cleaned and level field of young wheat. These results give depths of water of 5.1 inches and 4.1 inches. A safe mean in Northern India is to reckon five acres in twenty-four hours as the area to be watered by one cubic foot per second, where, as is general, the soil is light. " We may further take fifty oays as about the greatest interval there allowed to elapse between two waterings, and so we shall obtain 5 X 50 - 250 acres as the duty to be got out of each cubic foot per second, that is, .28 litre (.009886 cubic feet) per hectare (2.47 acres), sup- posing it can be used at this rate all the year round, and this is not more than has been done more than once on * Irrigation Statistics of the Territory of Utah. 302 IRRIGATION CANALS AND the Eastern Jumna Canal. The discharge then is measured at the head of the canal, and the water prob- ably runs on an average more than 300 miles before it actually reaches the field to be watered. It is usual to deduct twenty per cent, for the loss by filtration, evap- oration, etc., en route, and yet a duty as high as this has been proved attainable without making allowance for the deduction. Of these 250 acres, about eighteen per cent, usually consists of rice, and as much more of sugar-cane, each requiring a large amount of water; fifty per cent, of wheat and barley, and the rest of in- ferior crops, only watered once or twice. The rain, of which for the greater part falls in June, July and Au- gust, consists of about 40 inches a year more certainly than in Castile. The heat and consequent evaporation must be considerably greater." Article 59. Horary Rotation. Water is supplied for purposes of irrigation: 1. By fixed outlet or by measurement. 2. By the area of land irrigated to certain crops. 3. By Horary Rotation. The latter method of supply will be now considered. In order to obtain the greatest duty from water, it should be used at night as well as during the day. An irrigating channel passes through the lands of sev- eral proprietors. A period of rotation- is fixed for this channel. This period varies according to the nature of the crop, rice for example requiring a more rapid rota- tion than wheat. Each landowner can then have the full volume of the channel turned 011 to his land, once in the period of rotation, for a certain number of hours, according to the quantity to which he is entitled. This method is applicable only to laterals or distribu- OTHER IRRIGATION V/ORKS. oOT> taries, having a small discharge, which a landowner can handle with economy. It is clear that the quantity of water to which any sin- gle employer of a canal, common to several, ajn.d_jregu- lated by horary rotation, is entitled, is in direct propor- tion to the total volume of the canal, and the number of hours during which he is entitled to possess it, and in inverse proportion to the number of days over which rotation extends. Hence we have the following general formula: N where: Q the quantity appertaining to a single consumer in continued discharge. T === the number of hours or days during which he has the right to the whole volume of the canal. Q l = the volume of channel in cubic feet per second, or any other fixed measure. N = the number of days over which the rotation ex- tends. Example. Let 10 days be the period of rotation, and the channel has a supply of 20 cubic feet per second, of which a consumer is entitled to a continuous supply of one-twentieth part or one cubic foot per second. He wishes to change this continuous for an intermittent sup- ply ^Q_10XJ = Qi : 20 Therefore, he is entitled to the full supply for half a day or twelve hours. His name is placed on the list, say sixth, and he gets the full supply turned on at a fixed hour and turned off at a fixed hour. also. Arrangements can be made to have another consumer's gate opened as this one is being closed, and, in this manner, the full 304 IRRIGATION CANALS AND supply of the channel is delivered on the land continu- ously. Mr. R. E. Forrest, C. E.,* states: " That by a good system of rotation it might be possible to remedy the loss of duty from the water not being used at night; the water could be run on at night to the more distant points. By a system of rotation the evils of supersat- uration could be lessened. The water was made to run through a tract only when it was wanted and for so long as it was wanted. In some of the Ganges Canal chan- nels the water ran only for a single day each fortnight. The water should be completely withdrawn from every tract in which it was not in active and immediate de- mand." Article 60. Forestry and Irrigation. The preservation of the forests, and the extensive planting of trees, should proceed simultaneously with the development of irrigation in this country. A stop should be put, and at an early date, to the ruthless de- struction of the forests of this country, especially at the head-waters of the rivers, for if this is not done, what has happened in. other countries is sure to happen here, and districts which are now fertile will, in the lapse of time, become barren wastes. A large forest, is in fact, an immense reservoir, which slowly but surely gives out its supply for the wants of man. The greater part of its loss by percolation is again utilized to supply the streams, and it requires no dams or other expensive works. The Government send out engineering parties to locate the sites of reservoirs, whilst, at the same time, they permit nature's own reser- * Transactions of the Institution of Civil Engineers, Volume LXXHI 1883. OTHER IRRIGATION WORKS. 305 voirs, the forests, to be destroyed in the interest of a few individuals. Parts of Persia that are now desert were, within his- toric times, fertile lands, which supported deftse___riopu.- lations and yielded large revenues. During long periods of time, different large armies, with their countless hosts of camp followers, passed across the country and cut- down the trees for fuel. The inhabitants of the country did the same thing, and no trees were planted to replace those that were destroyed. During the existence of the forests the rain fell at regular intervals, and in moderate quantities, and, in this way, was an aid in the cultiva- tion of the land and in maturing the crop. After the destruction of. the forests the rain fell, in dense showers, at irregular intervals, thus doing more harm than good, and as a result of this the population gradually dimin- ished until the land became a desert. In America, an army of wood-cutters is constantly em - ployed in destroying the forests. It takes a short time to destroy a forest, but many a year, equal to several generations of men, to reproduce it. Mr. Allan Wilson, Mem. Inst. C. E., states* with ref- erence to Southern India: " In former times when the tanks (reservoirs) were in good repair, trees were largely planted, and, as is always the case, vegetation attracted the moisture, and the mon- soon could always be depended upon. Now, since these works have fallen into decay, the vegetation has disap- peared, and the monsoon has been precarious and insuf- ficient." Every year we read in the press of destructive floods taking place in the old country, and these floods are almost all due to the destruction of the forests. * On Irrigation in India in Transactions of the Institution of Civil En- gineers. Vol. XXVII. 1867-68. 20 306 IRRIGATION CANALS AND The Indian Government, some years since, recognized the importance of this matter, and organized a Forest Department, somewhat on the hasis of the Public Works Department, and already the good results of this policy are admitted by all those in India who have given any attention to the subject. The following extract on the Objects of Forest Manage- ment* are pertinent here. " Forest management has two objects in view: " 1. To produce and reproduce certain useful mate- rial. "2. To sustain or possibly improve certain advan- tageous natural conditions. " In the first case we treat the forest as a crop, which we harvest from the soil, take care to devote the land to repeated production of crops. As agriculture is prac- ticed for the purpose of producing food crops, so forestry is in the first place concerned in the production of wood crops, both attempting to create values from the soil. " In the second case we add to the first conception of the forest as a crop, another, namely, that of a cover to the soil, which, under certain conditions, and in certain locations, bears a very important relation to other con- ditions of life. " The favorable influence which the forest growth exerts in preventing the washing of the soil and in re- tarding the torrential flow of water, and also in checking the winds and thereby reducing rapid evaporation, fur- ther in facilitating subterranean drainage and influenc- ing climatic conditions, on account of which it is desirable to preserve certain parts of the natural forest growth and extend it elsewhere; this favorable influence is due to the dense cover of foliage mainly, and to the mechan- * What is Forestry, by B. E. Fernow, Chief of the Division of Forestry, U. S. Department of Agriculture. OTHER IRRIGATION WORKS. 307 ical obstruction which the trunks and the litter of the forest floor offer. " Any kind of tree growth would answer this purpose, and all the forest management necessary wotild^be to simply abstain from interference and leave the ground to nature's kindly action. " This was about the idea of the first advocates of for- est protection in this country; keep out fire, keep out cattle, keep out the ax of man, and nothing more is needed to keep our mountains under forest cover forever. "But would it be rational and would it be necessary to withdraw a large territory from human use in order to secure this beneficial influence? It would be, indeed, in many localities, if the advantages of keeping it under forest could not be secured simultaneously with the em- ployment of the soil for useful production, but rational forest management secures both the advantages of favor- able forest conditions and the reproduction of useful material. Not only is the rational cutting of the forest not antagonistic to favorable forest conditions, but in skillful hands the latter can be improved by the judi- cious use of the ax. " In fact the demands of forest preservation on the mountains and the methods of forest management for profit in such localities are more or less harmonious; thus the absolute clearing of the forest on steep hill- sides, which is apt to lead to dessicatioii and washing of the soil, is equally detrimental to a profitable forest man- agement, necessitating, as it does, leplaiitiiig under dif- ficulties. "Forest preservation, then, does not, as seems to be imagined by many, exclude proper forest utilization, but, on the contrary, these may we'll go hand in hand, preserving forest conditions while securing valuable ma- terial; the first requirement only modifies the manner, in which the second is satisfied." 308 IRRIGATION CANALS AND Article 61. Rainfall. In considering the growth of any crop, the annual rainfall should not so much bo taken into account as the particular portion of the rainfall that fell during the irrigating season, and its distribution during that time. In the majority of irrigation countries it was not the deficiency of rainfall throughout the year, but the fact that the rain fell at unsuitable times, that rendered irrigation essential. In some famine years in India, the aggregate of the rainfall throughout the year was more than ample to mature the crops, but it was almost useless for purposes of cultivation, as it fell at the wrong time. The Honorable Alfred Deakin, M. P., of Victoria, states*: " The arid area of the United States, by the terms of Major Powell's definition, includes only lands where the rainfall is under 20 inches per annum. Over the great belt in which irrigation has so far had its chief develop- ment, the record for a series of years gives but little more than half that quantity, so that 10 to 12 inches may be taken as a fair average, though the extremes show a much wider variation. In Northern California, and among the mountains to the east, the rainfall rises to 40 inches, while in the deserts of Southern California it falls to four inches. "In Western Kansas the fall, not infrequently, reaches 20 inches; but there, as with us, this is so irregular that the farmer who relies solely upon a natural supply loses more by the dry seasons than he can make in those which are more propitious. The question as to whether settlement increases the rainfall in the West, as it has increased it in the Mississippi Valley, is still undetermined; for, though popular Irrigation in Western America, Egypt and Italy. OTHER IRRIGATION WORKS. 309 opinion is decidedly in the affirmative, the State En- gineer of Colorado points out that official records so far do not support the assertion. The exceptions to this are that Salt Lake, Utah, appears to be steadily_gaining in depth, and that dew is now observed at Greeley, in Northern Colorado, a phenomenon quite unknown until irrigation had been practiced for some years. Nor does the mere amount of rainfall indicate sufficiently the necessity for an artificial supply of water, unless also the seasons in which it falls are taken into account. In parts of Dakota and Minnesota, where the rainfall only averages about 20 inches, dry farming is carried on; while in districts of Texas, where the figures are as high, it would be impossible to obtain the same results without irrigation. The explanation is that in Dakota nearly seventy-five per cent, of the rain falls in the season when the farmer needs it, as against about fifty per cent, in Texas. Indeed, a gradation may be ob- served in this scale from north to south, since in Kansas some sixty-five per cent, of the rain falls in the spring, and summer, while in the extreme south, as at San Diego, only half of the whole rainfall, nine inches, falls in the spring, and is consequently useless for agricul- ture. There is some irrigation in Dakota, as also in Iowa and Wyoming, but not nearly so much as in the States to the southward, where, even if the rainfall were as high, its distribution would render it insufficient. A glance at the rainfall statistics of Victoria will show that, roughly speaking, one-half of it might be included in the arid area, or in that portion of the sub-humid area in which irrigation is little less essential. " The valleys of the north and the great plains of the northwest, as well as the belt of level country imme- diately to the north and west of Port Phillip and the eastern coast of Gippsland, all feel the need of a regular 310 IRRIGATION CANALS AND rainfall. Still, there is little of what would be called in America, desert land. The irrigated districts of South- ern California are hotter and drier than any portion of our colony, resembling, indeed, the climate of Algiers, rather than that of Southern Europe. There it is always grassless and almost rainless in many seasons, while in the country beyond Swan Hill, though the rainfall drops to ten inches and even less, there are still numerous seasons in which a fair crop of grass can be obtained. In Victoria, the difficulty for the most part is, that the supply is sometimes insufficient, often irregular, or distributed so as to leave the crops unsupplied at a par- ticular period. The critical season is generally that in which the crop is ripening, toward the end of spring and beginning of summer. A glance at our rainfall statistics for the last four years gives Horsham an average fall of about sixteen inches, and Kerong of about ten inches, of which at the first rather more, and at the second rather less, than twenty-five per cent, falls in the three months, September, October and Novem- ber. If an emergency watering could always be obtained during this period, our northern farmers would be sure of a harvest, while, as it is, they run the risk of a com- plete failure every two or three years. So far as rainfall is concerned, then, Victoria appears to be in as good a position as any of the irrigated States except Western Kansas. Enough rain can be calculated upon to ma- terially decrease the quantity of water required to be artificially supplied, and, in exceptional years, to ren- der irrigation unessential. Though there have been, at long intervals, years in which this state of things has been reached in South-western America, yet they are so few as to but little affect the average. To make the comparison perfect, the fall in the various seasons in OTHER IRRIGATION WORKS. 311 Victoria would need to be tabulated for a number of years. The soil of its several districts would also have to be carefully analyzed, for it is to be remembered that one lesson of American experience is that soils w r hich to the ' dry farmer ' gave but faint promise of any productive- ness, have proved extremely fertile when exposed to fre- quent saturation and continuous cultivation. The quan- tity of water needed is also affected by temperature, for the higher it reaches the more water is demanded. The loss by evaporation has not yet been determined for the several States, but, it is stated, that in very arid tracts, it rises to over sixty inches per annum. As favored in rainfall as America, Victoria is less favored than India, Italy or France, where the precipi- tation is often twice as great. The fact that irrigation is resorted to under such conditions should be borne in mind, when we consider the wisdom of securing an artificial supply in places where the yearly fall is often sufficient." The Statistical Review of the Irrigation Works of India for 1887-88, has the following on rainfall: " It has not infrequently been assumed that the probabilities of the success of a new irrigation project can be gauged by a consideration of the incidence of the rainfall on the tract commended. The rainfall is, no doubt, one of the chief factors to be considered, but the statistics of rainfall* show conclusively that there must be other factors of at least equal, if not greater, weight, which must be taken into account in determin- ing the success or failure of an irrigation system. For example, the rainfall in Bombay is generally scanty, while at Madras it is copious, but in the former case the irrigation works are entirely unremuiierative, whereas in Madras they are, with one exception, most lucrative. Not given in this work. 312 IRRIGATION CANALS AND " Even a more striking instance can be found in Madras itself. The Gauvery Canals, which irrigate a larger area and pay a far higher percentage on capital than any other system in India, lie in a district where the average rainfall is 53.9 inches in the year; whilst the Kurnool Canal, which is the most conspicuous failure of all irrigation works in India, lies within 300 miles of the Cauvery, in the same Province, in a tract where the average rainfall is 28.9 inches, or ->nly slightly more than half that which falls on the Cauvery Canals. The causes which produce these striking dif- ferences are but little understood, and the available statistics afford no clue to them. It may, however, be said that in Madras the temperature is generally so equable that it is possible to grow two, and even three, crops of rice on the same field during the year; this is not possible in the more variable climate of Bengal, where the total rainfall is not greatly different from that of Madras. It may be that this climatic difference ex- plains the great discrepancy in the results obtained in the two Provinces. It should also be noted that the actual amount of the rainfall is of less importance than its distribution. Differences in soil and in methods of cultivation have also great weight in determining the success of an irrigation project. * * * * What- ever the causes may be which should determine the results obtained, it must be admitted that much ignor- ance has prevailed concerning them, and this has led to the construction of many works :vhich have signally failed to produce the results which were anticipated by their projectors." The following extract is taken from Engineering News of May 11, 1889:- " There is no part of California where the people are more in earnest about irrigation than in Colusa County, OTHER IRRIGATION WORKS. 313 California (see page 175), where they have an annual rainfall of 30 inches. There are tw r o classes of lands requiring irrigation here one, lands which will yield crops without irrigation, but which will double their yield under the influence of a regular supply of wafer- say a cubic foot per second to 150 acres during the growing season; the other, desert lands, which will yield nothing at all without an artificial supply of water, either from a system of irrigation works or artesian wells." The following table is from a paper by Mr. P. O'Meara, M. Inst. C. E., in the Transactions of the Institution of Civil Engineers, Vol. LXXIII: 314 IRRIGATION CANALS ANL> TABLE 19. Statistics CROP. COUNTRY OR LOCALITY. 4> P ^ < tr** 85 .E2 P *l l| I IP 53.1? Cereals, wheat, oats, etc Cereals, wheat, oats, etc Cereals, wheat, oats, etc Cereals, wheat, oats, etc Cereals, wheat, oats, etc Cereals, wheat, oats, etc Lower Bengal, Patna Southern India, Madras .... Punjab, Lahore North Italy, Piedmont Bouches-tlu-Rhone Hungary, Debreczin Inches. 2.21 7.33 4.29 17.50 6.30 14 26 Inches 9 9 None None 5 None Inches 11.21 16.33 4.29 17.50 11.30 14 26 2 to 4 2 to 1 None None 1 to 3 Cereals, wheat, oats, etc Cereals, wheat, oats, etc Cereals, wheat, oats, etc Cereals, wheat, oats, etc .... Spain, Alcalti Yorkshire, Ferry Bridge. . . . Ireland, Dublin Minnesota 6 12.73 13.04 10 35 None None None None 6. 12.73 13.04 10 35 None None None None Cereals wheat oats etc . 11 23 11 23 None Cereals, wheat, oats, etc Missouri, Lower 13 None 13 None Cereals, wheat, oats, etc .... 11 25 None 11 25 None Cereals, wheat, oats, etc Cereals, wheat, oats, etc Rice A crop Colorado, Poudre Valley... ( Colorado, Fort Collins ) i Agricultural College. y 5.67 4.50 25 33 43 None 26 48.67 4.50 51 33 3 None Rice, B crop Lower Bengal, Patna 30 44 40 70 44 Rice, A crop Rice, B crop Southern India, Madras. . . . Southern India, Madras. . . . 10.31 38 06 26 40 36.31 78 06 Rice Spain, Valencia 7 29 139 146 29 Rice North Italy, Piedmont 25 19 62 87 19 100 Rice, upland Japan, Yeddo Lower Bengal Patna 51. 45 83 None 60 51. 105 83 None Sugar Cane Southern India, Madras. . . . 48 56 60 108 56 Sugar Cane Sub Himalayas, Ranikhet.. 48 56 43 56 None Sugar Cane Jamaica 40 80 40 80 None Natal Ottawa Estate 38 78 None 38 78 Sugar Cane Mauritius 47 to 90 17 to 90 Potatoes Colorado Poudre Valley 6 6 12 2 Potatoes Ireland, Dublin 16 None 16 Summer Meadows Colorado, Poudre Valley... 6 43 49 Summer Meadows .... South of France 9 60 69 Italy 22 42 64 18 Summer Meadows . Ireland, Dublin 8 22 8 22 Bouches-du-Rhone 9 37 5 46 50 g 5 11 Indian Corn North Italy 22. 23.58 45.58 6 Indian Corn Hungary, Debreczin 12 79 12 79 Natal Coast Districts 24 59 24 59 Cotton Central India, Sutna 43 43 g None g None 33 48 None 33 48 None Vines California, San Bernardino.. 2. 3 to 12 5 to 15 2 to 4 California, Riverside 10 05 10. 20 05 California, Riverside 10.05 .5 10.55 Orange Trees Natal Durban 49 74 None 49.74 None OTHER IRRIGATION WORKS. 315 of Irrigation. IRRIGATION SKA., ON. HM *|f Mean Temper- ature. AUTHORITY. REMARKS. j Satn. 100. 60 2 70 6 Allan Wilson Blandford's rainfall tables Dec. to Apr., inc Oct to Mar inc 65.6 51 79.7 63 Allan Wilson Blandford's rainfall tables. Blandford's rainfall tables Col. Baird Smith George Wilson Chiolich's rainfall tables George Higgin Feb to July inc 50. Beardmore's rainfall tables Signal Officers' ramf'll returns Signal Offiders' rainf '11 returns Signal Officers' rainf '11 returns Signal Officers' rainf '11 returns The Author Prof Blount 73 86 Allan Wilson Aug. to Dec., inc June to Aug , inc 57! 60. 76.1 86. W. W. Hunter Allan Wilson 63 81. W W. Hunter Mar. to Sept., inc Mar. to Aug., inc Mar to Aug., inc *59 72.3 77 8 George Higgin Col. Baird Smith Con. Gen Van Buren .... Allan Wilson 139 refers to dotation, not to Total annual rainfall given. Jan. to Dec., inc 65. 82.3 60 3 Allan Wilson Col Greathead , 4 Mem. of Geological ^ Manual of Geology. Jan. to Dec., inc.. ("Natal Colonist,'') I Oct., 1879. / The Author The Author The Author The Author ( One cutting, flooding without George Wilson ! . . ! Col. Baird Smith Beardmore's tables. George Wilson Six cuttirgs. ' 'Colorado Farmer" .... / Four cuttings in third and Col Baird Smith Chiolich. The Author ( Rainfall Returns of Durban 65 84 9 Col. Greathead ... In black cotton soil. May to Aug., me " Colorado Farmer". . . . June to Aug., inc / March to May, and > 63. 85.1 George Higgin f W. W. Hunter, "Imperial \ Gazetter," vol. iv, p. 48 J. ( one irrigation in Oct j Mar. to Sept., inc Report /Ordinary flooding system. Mar to Sept inc Report J Asbestine sub-irrigation sys- ( tern. Total annual rainfall. 316 IRRIGATION CANALS AND Article 62. Evaporation. In countries where irrigation is conducted on an ex- tensive scale, the evaporation, that is, the depth of water evaporated annually, does not materially differ. The records of experiments given below in America, Italy, France, Spain, India and Egypt, prove this. The records of evaporation published by the State Engineering Department of California, show that the mean annual evaporation at Kingsburg bridge, Tulare County, California, for the four years from 1881 to 1885 was 3.85 feet in depth, when the pan was in the river, which is equal to an average depth of one-eighth of an inch per day for a whole year. For the same period the evaporation, when the pan was in air, was 4.96 feet in depth, that is, equal to a mean daily depth of evaporation throughout the year, of less than three-sixteenths of an inch per day. The greatest evaporation was in the month of August, when it was more than one-sixth of the evaporation for the whole year. The average for this month is one-third of an inch per day. During the months when the largest quantity of water is used for irrigation in this district, the table shows that the mean evaporation was: For March one-twelfth of an inch per day. For April one-twelfth of an inch per day. For May one-fifth of an inch per day. Mr. Walter H. Graves, C. E., states:* lt Evaporation is very nearly a constant quantity. * * * * * * * * Observation and experiment by the writer in various parts of Colorado tend to show that evaporation ranges * Irrigation and Agricultural Engineering in Transactions of the Den- ver Society of Engineers 1886. OTHER IRRIGATION WORKS. 317 from .088 to .16 of an inch per day, during the irrigat- ing season. " To some people these depths of evaporation may ap- pear very small. Let us, therefore, examine_the_result of observations in other countries: Colonel Baird Smith, in his work 011 Italian Irrigation states that, in the north of Italy and center of France, the daily evaporation varies from one-twelfth to one- ninth of an inch per day; while in the south and under the influence of hot winds it increases to between one- sixth and oiie-fifth of an inch per day. In 1867 the total evaporation in Madrid, 8pain,*was sixty-five inches in depth. In July of the same year according to the returns of the Royal Observatory, it was 13J inches in depth or less than half an inch per day, and in May of the same year it was only one-quarter of an inch per day. July was the hottest month in 1867, and it was estimated that during this month the total evaporation of the Henares Canal, carrying 105 cubic feet per second, or 5,250 miner's inches, under a fo-ur inch head, amounted to only three-fourths of one per cent, of the total flow. W. W. Culcheth, C. E.,f states as the result of his in- vestigation on the Ganges Canal in Northern India, that for evaporation, one-quarter of an inch per day over the wetted surface may be taken as the average loss from, a canal. Dr. Murray Thompson's J experiments in the hot sea- son in Northern India, with a decidedly hot wind blow- ing, gave an average result of half an inch in depth evaporated in twenty-four hours. * Irrigation in Spain, by George Higgin, M. Inst. C. E., in Transac- tions of the Institution of Civil Engineers. Volume XXVII. 1867-68. t Transactions of the Institution of Civil Engineers. Volume LXXIX. J Professional Papers on Indian Engineering. Vol. V. Second Series. 318 IRRIGATION CANALS AND In Hyderabad in the Dec-can, in India, it was found that the mean evaporation from a tank or reservoir was 0.165 inch per day. In Nagpur, in India, * the total depth evaporated from October, 1872, to June, 1873, was four feet, which, dis- tributed over the period of the experiment, 242 days, gives an average depth of .0165 feet, or 0.198 inch, being about one-fifth of an inch per day. Colonel Fyfe, R E.,f states that in large reservoirs in India, about two square miles in area, the amount of evaporation, that he made allowance for was about three feet in depth per annum in the Deccan, and something less in the Concan district in India. Major Allan Cunningham, R. E.,J conducted experi- ments, lasting twenty-five months, from 1876-79, to measure the evaporation from the Ganges Canal. He states that, the most remarkable feature of the results is their extreme smallness, amounting to only about one- tenth of an inch per day on the average near Roorkee; whereas one-half inch per day is said to be a common rate in India for evaporation on land. This led at first to the suspicion of the introduction of water from with- out; but after considering the possible sources of this, namely, leakage, spray, rain, dew, wilful tampering, it still seems that the results may be accepted as substan- tially correct. The real cause of the small evaporation appears to be the unusual coldness of the canal water, for instance, on May 22, 1877, at 2:30 p. M.,the temper- ature of the air was 165 in the sun, and 105 in the shade, whilst that of the water was only 66 inside the * The Nagpur Waterworks, by A. E. Binnie, M. Inst. C. E., in Trans- actions Institution of Civil Engineers. Vol. XXXIX. t Transactions Institution, of Civil Engineers. Vol. XXXIX. 1874-75. t Kecent Hydraulic Experiments in Transactions of the Institution of Civil Engineer:}. Vol. LXXI. 1883. OTHER IRRIGATION WORKS. 319 pan and 65 in the canal; also the highest recorded tem- perature of the canal water was only 75i. The canal, in fact, takes its supply from the Ganges, a snow-fed river, at its exit from the hills. It was, indeed, found that the canal evaporation in- creased with distance from the head of the canal at Hurdwar on the Ganges. Thus, out of the forty results, twenty-eight were taken near Roorkee, and twelve near Kamhera, at distances of eighteen and fifty-two and one- half miles from the head-works; the evaporation at the latter was much the larger, comparing, of course, sim- ilar seasons, being about 0.15 inch against 0.10 inch on an average. This is, no doubt, due to the gradual heat- ing of the water under the hot sun, with increased dis- tance from the head. Taking the Roorkee estimate of one-tenth of an inch per day, the total evaporation from the whole surface of the canal and its branches, about 487,000,000 square feet, amounts to about forty-seven cubic feet per second, which is about T |^ part of the full supply of the canal, or in other words, ten minutes full supply daily. Little connection could be traced between the evapor- ation and the meteorological elements; the temperature of the water, which depends chiefly on the amount of snow water in the Ganges, being probably the governing elemont. M. Lemairesse's* observations at Pondicherry, in French India, give a daily evaporation of from three- tenths to half an inch in depth per day. Trautwine made observations in the Tropics and he found the evaporation from ponds of pure water to be at the rate of one-eighth of an inch per day, but he * The Irrigation of French India in Professional Papers on Indian En- gineering, Volume I. Second Series. 320 IRRIGATION CANALS AND observes that the air in that region is highly charged with moisture. Mr. Willcocks, C. E., in his work on Egyptian Irriga- tion, states that Linant Pasha considered the evapora- tion in Upper Egypt, as about equal to one-third of an inch per day throughout the year. As a result of his own observations, Mr. Willcocks gives the evaporation for one year in Upper Egypt, as equal to six feet in depth, and in Lower Egypt, as equal to 2.4 feet in depth. The following table given by General Scott Moncrieff, R. E., shows the general conditions of temperature and rainfall, as measured at Orange, eighteen miles north of Avignon, and at Marseilles in France, for periods of thirty and twenty years respectively: TABLE 20. Giving temperature and rainfall in the South of France. MEAN TEMPEKATURE. Greatest ! Greatest Annual I No. of Summer Winter. Whole y'r. degrees. degrees. in inches. in the year. Orange . . . 71 41 56 104 5 26.6 96 Marseilles. 70 45 59 87 22 12.8 59 This table shows, in a striking way, the modifying in- fluence which the sea has over climate, the extreme range at Marseilles being only 65, while at Orange, ninety-three miles distant, it is 99. The annual rain- fall, scanty as it is, does not fully denote the extent to which this part of France suffers from drought, for at Avignon it often happens that there is not a shower of rain during the three hottest months of June, July and August. The evaporation in the plains of Languedoc, not far distant, has been estimated at .079 inch per diem, and it is probably about the same in Provence. OTHER IRRIGATION WORKS. 321 Article 63. Percolation. Taking a broad view of percolation in channels and reservoirs, through their beds and banks, it denotes infiltration, seepage, absorption and even leakage. If the leakage is of a large quantity through a bank of earth, that bank is not likely to last long. " In every new canal, through sandy loam, the loss by percolation at first is very serious. Gradually the ground gets saturated, and at the same time the inter- stices of the porous material of the bed and banks get filled up with particles of clay, which diminish the per- colation. The bed of a canal acts as an elongated filter, It is well known that the sand of a water works filter bed, if not periodically washed, or if not replaced with clean sand, the interstices between the particles of sand get filled with silt, and the filter ceases to act, or acts so slowly as to be practically useless. The same thing takes place in a canal, but at a slower rate than in a filter bed. There is less deposit in an irrigation canal, in the same time, than in a filter bed, as the greater part of the finer particles of silt do not deposit in it, but are carried in suspension until the water reaches the land to be irrigated."* Mr. Walter H. Graves, C. E., in a paper read before the Society of Engineers in Denver, Colorado, in 1866, states: " The factor of seepage is a variable one, depending mostly upon the nature of the soil, and gradually grows less through a long term of years. Evaporation is very nearly a constant quantity, depending on the altitude of the locality and the prevailing meteorological conditions. In calculating for the loss from these sources, evapora- * Report on the proposed Works of the Tulare Irrigation District, Cali- fornia, by P. J. Flynii, C. E. 21 322 IRRIGATION CANALS AND tion and seepage, in the older canals about twelve per cent, should be deducted from the carrying capacity." Mr. P. O'Meara, in a paper in the Minutes of Pro- ceedings of Inst. C. E. for 1883, states: " From a short time after irrigation is established in any district, the quantity of water required will grad- ually become less,, till an equilibrium is established between the amount of water supplied in the irrigating season, and the quantity removed by filtration and evaporation. 11 It is a question whether, supposing irrigation were carried out to its full extent in Colorado, there would be any loss of irrigating power other than that due to evaporation. Losses occurring through absorption and surface flow are not final. The waters absorbed or wasted reappear, probably with undiminished volume, lower down in the streams." Mr. Boyd, President of the State Board of Agriculture of Colorado, in a communication to the Institution of Civil Engineers in 1883, states: " In a volume of six cubic feet per second of water flowing in a lateral two miles in length, not less than one-tenth would be lost by soaking and evaporation." Mr. E. B. Dorsey, C. E., in a paper in the Transac- tions of the Am. Soc. C. E., Volume 16, 1887, states: "That in some of the Colorado canals the loss from evaporation and seepage is estimated at fifty per cent., which is excessive, and shows that the canal is con- structed in bad soil, or that there must be something the matter with the construction. Twenty per cent, ought to be, under ordinary circumstances, a liberal loss from these causes, and this should largely diminish as the banks and bottom of the canal become compact." Mr. George G. Anderson, C. E.,* made measurements * Transactions of the American Society of Civil Engineers. Volume XVI, 1887. OTHER IRRIGATION WORKS. on the High Line Canal, in Colorado, in the middle of July, 1886, and found that where 156 cubic feet per second were passing into the head-gates only 80 cubic feet per second were passing a point 45 miles from Jhe head-gates, and 110 water was used for any purpose in the intermediate distance. This was during the very hottest and driest period of an unusually hot and dry summer in Colorado. The soil through which this canal passes is in many places very pervious. There are long stretches of fine sand, and in places the canal bottom is in rock badly fissured. The alignment of the canal is very crooked, and, no doubt, a great loss is ex- perienced from this source. It is to be expected that this serious loss will gradually diminish as the canal bed and sides become compact and puddle naturally. But to estimate a smaller loss from these causes than twenty-five per cent, would scarcely be wise." In a paper by Mr. C. Greaves,* he showed that the per- colation through ordinary soil, as compared with sand, was only about one-third, whereas the evaporation from- a surface of ordinary soil was four times that from a surface of sand. Mr. G. F. Kitso, C. E., in his description of the irri- gation of the Canterbury Plains, New Zealand, states: t " Of the canals in alluvial soil that the percolation is small, as the constant tendency of channels is to silt up and to become more water-tight." The Martesana Canal, in Italy, of a capacity of 981 cubic feet per second and twenty-eight miles in length, was estimated to have lost from evaporation, seepage, and illegal abstraction, 3.75 cubic feet per second per mile of canal. We have here, however, an additional source of loss, that by illegal abstraction. * Transactions of the Institution of Civil Engineers. Vol. XLV, 1876. t Transactions of the Institution of Civil Engineers. Vol. LXXIV, 1883. 324 IRRIGATION CANALS AND Engineers in Lombardy calculate the absorption in each watering, of about four inches in depth, as ranging from one-third to one-half of the total quantity of water employed. This is when the general period of rotation is about fourteen days. From observation, it has been concluded that the balance of the water reaches chan- nels at a lower level, and is again available for the irri- gation of lower lands. On the Marseilles Canal, in France, the losses by per- colation, evaporation, and at the settling or silt basins, was estimated at 58 cubic feet per second, or sixteen per cent, of the full supply of 353 cubic feet per second. Ribera estimated the total loss from evaporation and percolation on the Isabella Canal, in Spain, a masonry- lined channel, at two per cent. Nadault de Buffoii gives the average percentage of loss on canals from evaporation and percolation at 15 per cent, of the total volume carried. He does not, how- ever, mention under what circumstances such a percent- age may be expected. In a project for a canal from the Rhone, in France, of over 2,000 cubic feet per second, it was calculated that one-sixth would be lost by evaporation, percola- tion, etc. In designing the Agra Canal, India, the loss by ab- sorption and percolation was estimated at 0.23 cubic feet per 100 cubic feet per mile of canal. After the completion of the Ashti Tank, in India, ob- servations were made, and it was found that, out of a supply of 1,348,192,450 cubic feet, the loss from evapora- tion, percolation and seepage through the subsoil of the tank combined, amounted, in a year, to 233,220,240 cubic feet, or about 18 per cent, of the supply. In the Irrigation Revenue Report of Bombay for 1889-90, it is stated, as the result of gaugings, that the OTHER, IRRIGATION WORKS. 325 Ashti Tank lost during the year by evaporation, absorp- tion, etc, 7.08 feet in depth of water over its mean area. In the same Report the result of some experiments in the loss of water in small canals was given: __ " On the Palkhed Canal, 14.87 miles in length, there was a loss by leakage and evaporation of 0.44 cubic feet per second per mile, or nearly forty-eight per cent, of the supply. " Before taking observations for leakage experiments all the irrigating outlets were closed; gaugings were made with ordinary floats and were read in each mile, which gave the average result of loss as forty-eight per cent. The only feasible way of reducing the leakage seems to be to keep the canals clear of silt arid weeds. No other precautions seem practicable, unless in the way of man- aging all outlets better, escapes included. " On the Ojhar Tambat Canal (1.75 miles in length) there was a loss of 0.49 cubic foot per second, or nearly thirty per cent, of the supply." The percentage of loss on the above canals is very great, and it is seldom that the loss is so great in a channel carrying silt, and that has been in use for some years. When the Ganges Canal was flowing at least 6,000 cubic feet per second, during October, 1868, a year of drought, Colonel H. A. Brownlow, II. E., estimated the loss by absorption at twenty per cent. He states that the es- timate of loss by absorption (twenty per cent.) may be considered somewhat low for a year of drought, but that the long continued high supply in the canal must, after some time, have checked, in a great measure, the drain upon itself by fully saturating the adjacent ground. In fact, the greater ease with which the gauges were kept up during October and November, as compared with August and September, was a matter of common re- mark at the time. 326 IRRIGATION CANALS AND In the original design of the Ganges Canal its dis- charge, at full supply, was fixed at 6,750 cubic feet per second. Of this quantity, it was assumed that 1,000 cubic feet per second would be lost by evaporation, ab- sorption and navigation, and that the remainder would be available for irrigation. Mr. J. S. Beresford, C. E., states as the result of In- dian experience, that old canals give higher duties of water than new canals, or, in other words, that there is less loss of water through the material forming the channel in old than in new canals. Sir B. Baker, C. E., has stated:* "In a porous soil like that of Egpyt, ii was impossi- ble to confine water simply by raising the bank, because it would find its way by percolation underneath, and it came up to the surface and washed the salt out and killed vegetation. He had ascertained that the water percola- ted at the rate of about one mile from the river in a week. That is to say, the water in. a well one mile from the river would begin to rise about a week after the water in the river had begun to rise. It would be seen that that was an exceedingly important matter as affecting many questions of drainage in London. If the tide were not of twelve hours but a week's interval, the greater part of the low-lying districts in London would be much in- jured by the percolation of tidal water; but at present it did not follow up quickly enough to exert a destructive hydrostatic pressure upon the thin basement walls of houses near the river." Transactions of the Institution of Civil Engineers. Vol. LXXIII, 1883. OTHER IRRIGATION WORKS. 327 Article 64. Drainage. As a rule, the drainage of irrigated land will take care of itself, if the natural drainage channels are left free and unobstructed. If it is found that, before irrigation is introduced into a district, the country is flooded and water-logged after rains, then it is likely to be in a worse condition after the land is irrigated, and drainage will be absolutely necessary for the success of the irrigation and the health of the district. In many cases in this country, although irrigation dates back but a few years, the natural drainage outlets have been converted into irrigation channels, with the very worst results. In. this way, while the supply to be drained off had been increased in quantity, the drain- age channels have been diminished in carrying ca- pacity. If the subsoil and surface water cannot escape freely by the natural channels, super-saturation follows, and the ground becomes water-logged. Stagnant water is very injurious to crops, and it generates disease and pesti- lence. Many irrigation districts in this country show the evil effects of too much irrigation combined with defective drainage. One of the least evils is a dense and troublesome growth of weeds, and as a consequence waste land. The cultivator suffers in. health and pocket. To construct irrigation canals without efficient surface drainage, and, as has sometimes been the case, to obstruct the natural drainage of the country, by the mproper location of canals, without making adequate provision for allowing the surface drainage to pass away, tend to the certain formation by artificial means, of those evils that exist in the neighborhood of natural swamps, and hence, the importance of paying every attention in the preparation of projects, and the construction of works, 328 IRRIGATION CANALS AND with the view of avoiding those -defects which, if per- mitted in the first instance, will certainly have to be remedied at some future time, at considerable cost, both direct and indirect. Whatever excuses may have been admissible in past years, when the science of construct- ing irrigation works was less understood than it is at the present day, no justification can now be pleaded for the repetition of similar errors. On the reconstruction of the Western Jumna Canal in 1820, after a suspension of its usefulness for more than half a century, the original mistake of a bad location was repeated. Instead of being carried along the water- shed lines it was taken through the drainage of the coun- try, by interfering with which, serious consequences re- sulted in the creation of swamps and the occasional sub- mergence of lands which might, by a proper location, have been brought under cultivation. But besides ren- dering lands uncultivatable, and so curtailing the extent of area capable of growing for a poor and highly taxed people, the healthfulness of the neighborhood of these swamps became seriously impaired, and the population was found to be on the decrease in the vicinity. In some cases land became waterlogged, and therefore use- less, for cultivation, whilst in others it became covered with a peculiar saline efflorescence, known as alkali in America, and reh in India. After investigating the above state of affairs, the Indian Government adopted meas- ures to abate the evils of the defective irrigation. Egypt is now suffering from the super-saturation of its land and want of proper drainage. Mr. W. Willcocks, Asso. Inst. C. E., states: * " The canals are so disproportionately large during flood, that they send down into the lower lands further * Irrigation in Lower Egypt in Transactions of the Institution of Civil Engineers. Vol. LXXXVIII. 1886-87. OTHER IRRIGATION WORKS. 329 north such an excessive volume of water, that all the canals, escapes, and drainage cuts are full to overflowing with flood water, and are in consequence unable to per- form their proper functions. The country daring jlood is divided into a number of islands surrounded by water at a high level. The natural consequence is that salt efflorescence is greatly on the increase in the lands under cultivation.' 7 Again he states: " The conversion of all the drainage cuts into irriga- tion canals, was all that was needed to destroy the higher lands. This soon followed." There are several districts in California where a few years since the great want was water, but where, at the present time, the pressing want is drainage. A small percentage of the quantity of water required a few years since to irrigate a certain area, is now sufficient to insure a crop, as the sub-soil is so saturated with water, that very little flooding is now required in comparison with the first few years after the introduction of irrigation. The same thing has happened in Colorado. Mr. Gr. G. Anderson, C. E., states: * " In Colorado, as in most other irrigation countries, the necessity of carrying on drainage and irrigation simultaneously is being impressed upon practical men more and more every year. Although it is a rare oc- currence when these works are successfully conducted together, it is regrettable to note the large and yearly increasing area of low-lying lands going to waste, and which are during the irrigating season stagnant swamps breeding disease. The frequency of typhoid fever and other epidemics in the fall of the year, is doubtless due * The Construction, Maintenance and Operation of Large Irrigation Canals in Transactions of the Denver Society of Civil Engineers and Ar- chitects, Vol. I. 330 IRRIGATION CANALS AND to this cause, so that, from a sanitary point of view at least, drainage must be speedily undertaken." To avoid this defective irrigation, some means should be adopted in irrigation districts, to prevent the use of the natural drainage channels, for any purpose what- ever, but that of conveying away the drainage water that reaches them. A good effect will be produced by restoring to their natural state such drainage outlets as have been con- verted into irrigation channels, and, if required, their carrying capacity can be increased by widening and deepening them and taking out the sharp bends. An annual clearance of debris, brush and weeds will have a good effect in keeping up their discharging capacity. A great deal has been written, usually by mere theo- rists, on subsoil drainage in connection with irrigation. In an able paper by Mr. H. Scougall, C. E.,* he states: " Now, to prevent the appearance of alkali on our lands, water must be used sparingly for irrigation pur- poses, and not a drop more than is actually necessary to promote the growth of our crops should be poured 011 the land." This is quite right and to the point. Again he states: " No good system of irrigation should be without drainage; that is, drains some 18 or 36- inches below the surface which will carry off all surplus water." Whilst it is a fact that no perfect system of irrigation should be without subsoil drainage, still it is a hard fact, that 110 country in the world requiring irrigation, can at the present moment pay for such a system as is indicated by Mr. Scougall and at the same time pay for an irrigation system. Doubtless, exceptionally small areas * The Construction of Canals for Irrigation Purposes read before the Polytecthnic Society of Utah, March, 1891. OTHER IRRIGATION WORKS. 331 can be pointed out, having the two systems in opera- tion, but what we refer to is a combined system covering a large area such as is commanded by the Agra Canal in India, or the Galloway Canal in California. To show the immense magnitude of such work if ap- plied to the irrigation districts of India, the following extracts are taken from the Statistical Review of the Irrigation Works of India, 1887-88: At the end of the financial year, 1887-88, there were completed in India 5,520 miles of main canals and 17,155 miles of distributaries, and these works irrigated over 10,000,000 acres. This includes only the great works. The Minor works irrigated 2,000,000 acres more. There were, therefore, over 12,000,000 acres of land irrigated in 1887-88. The subsoil drainage of this area of land could not be carried out, to a successful completion, by any country in the world, that is, as a paying investment. For large districts the subsoil drainage would cost much more than any irrigation system by open earthen channels. The cost at present prohibits the use of sub- soil drainage on an extensive scale. If all the drainage channels are improved to their outfall into some river, and new open drainage cuts made where required, then this will, as a rule, prevent surface flooding and super-saturation of the soil, and this is as much as can be done under the present financial condi- tion of irrigated countries. 332 IRRIGATION CANALS AND Article 65. Defective Irrigation Alkali The Effect of Irrigation on Health. The chief objections urged against irrigation are the unhealthfulness that follows the super-saturation of the soil, and the injury to the land caused by alkali, known in india as "reh." These two evils can, in a great measure, be avoided by using only just sufficient water to mature the crop, but not enough to saturate the whole sub-soil. The returns of the duty of water in America, go to prove that, as a rule, too much water is used. India, Egypt and America are suffering from alkali in the land, and the evil is on the increase. Engineering News of February 26th, 1887, contains the following paragraph: 11 Professor Hilgard, of the State University of Cali- fornia, warns the people of the Pacific Coast that land irrigation may be overdone. He says that more atten- tion must be paid to under-drainage, and sustains his arguments by existing conditions in the irrigated plains of Fresno, Tulare and Kern, where there was formerly no moisture within thirty or forty feet of the surface, while water now is found almost anywhere within three to five feet. The roots of trees and vines have been forced to the surface and the alkali accumulating through centuries is also brought upward. He recommends as a remedy, laws providing for proper location and con- struction of the ditches. 7 ' Where water is available frequent washing of the sur- face of alkali land will do much to reclaim it. The land should be flooded to a depth of a few inches, and left in this condition for a few days, then drawn off, and again flooded with fresh water, and this operation should be repeated until the surface of the land is cleared of alkali. OTHER IRRIGATION WORKS. 333 Opinions as to the effect of irrigation on health are somewhat conflicting, and for this reason we give below opinions from different sources on this subject. Dr. H. S. Orine, Member of the State Board of Health of California, states, with reference to the influence of Irrigation on Health*: " The effect of the irrigation of the agricultural lands, particularly in California, upon public health is one of growing importance, and inasmuch as the available evidence bearing upon the subject is somewhat contra- dictory, it is necessary to note the conditions of locality, with respect to soil, temperature, humidity and drain- age, wherever irrigation is practiced. " Although irrigation has been carried on in Cali- fornia since the first establishment of the early missions by the Franciscan Fathers, more than a century ago, very little progress has been made in the scientific application of the system, the object of the cultivator being apparently only to get the water upon his land, without regard to the method employed. The application of the water used in irrigation varies greatly in manner, but may be described as two different methods, viz: first, by flooding the whole surface of the land from open ditches (Zanjas); and second, by sub- irrigation, that is a conveyance of the water through pipes beneath the surface of the ground, which have openings at intervals, protected by upright pipes. So far as the effect on health is concerned the latter method will not be considered, because of the very lim- ited extent to which sub-irrigation is being applied. In the case of the application of water by flooding the land from open ditches, the various reports made by impartial authorities, are, in some respects, conflicting. * Appendix to the Eighth Biennial Eeport of the State Board of Health, California. 334 IRRIGATION CANALS AND For instance, in Los Angeles, Ventura, Santa Barbara, San Bernardino and San Diego counties, where irriga- tion has been carried on for over a hundred years, the testimony is strong to the point that, there is no striking difference in the amount of malarial diseases, whether irrigation is practised or not. On the other hand, if we consult the records of some other portions of Cali- fornia, we find an increase of malarial fevers with the increase of irrigation, too intimately connected to be overlooked. The reasons for this are not difficult to dis- cover. In Los Angeles and other valleys in extreme Southern California, where the soil is, as a rule, sandy or gravelly loam of unknown depth, the water in irri- gation either sinks into the ground, or, if there is much surface slope, immediately drains at, or near, to the sur- face. In such sections of country there is great free- dom from malarial diseases. Along the bottom lands of rivers where the slope is insufficient to insure good drainage, or where the soil is constantly saturated, the case is different. Here there is more or less intermit- tent and remittent fever during the warmer season of the year. In the case of swamp or overflowed lands, especially those having a heavy adobe soil, as well as those which remain wet and boggy from the winter rains, and are in summer kept in a saturated condition by artificial means, containing also an excess of decom- posing vegetable matter and many stagnant pools, ma- larial diseases of the most pronounced type are very prevalent. In such localities all zymotic diseases are much worse in summer than in winter, a consequence which naturally results from the high tempt-rature and increased evaporation. The fact that the people, living in these low, wet adobe sections of country, are depend- ent upon impure or surface water for drinking arid do- mestic purposes, greatly aggravates the difficulty. In- OTHER IRRIGATION V.'ORKS. 335 deed, it has been more than once demonstrated that people living in a " fever and ague" country are tol- erably exempt from the fever if they drink only pure water. In referring to defective irrigation in India, the En- gineer, London, of June 23, 1871, has the following: "It is notorious that wherever irrigation is carried on, cruel malarious diseases as surely follow, and unless Dr. CutlifiVs report, in 1869, ' On the Sanitary Condition of the lands watered by the Ganges and Jumna Canals ' very greatly errs, it is very questionable whether the aggregate increased mortality in a number of years, due to irrigation, does not even exceed what that of a pe- riodic famine would be. "There are very extensive portions of the irrigated districts where subsoil drainage would not only be prac- ticable but easy, and would entirely remedy many of the existing evils distinctly traceable to over irrigation. "Nothing beyond an extension of surface drainage appears even yet to be contemplated; but until such works are regarded as merely the basis of subsoil drain- age to follow, we can look for little real improvement in the system of agriculture in India." India is not able to pay now, and it is not likely that she will ever be able to pay, fora system of subsoil drain- age. (See Article 64.) On the subject of defective irrigation, we have more recent information, which is herewith given in the tes- timony of Dr. W. W. Hunter, who has had long expe- rience in India: * " Even irrigation itself occasionally displaced a popu- lation, and, in several parts of India, created a safeguard against dearth only at the cost of desolating the villages by malaria." Life of Lord Mayo, page 326, Vol. 2. 336 IRRIGATION CANALS AND We have additional information on the same subject relative to Europe, given by Mr. G. J. Burke, M. Inst. C. E.,* who had a large experience on Irrigation Works in India: He was of the opinion that: " Drainage and irrigation ought to go together; but how many engineers had seen both drainage and irri- gation properly carried out at the same time? He cer- tainly never had. He had seen many of the irrigated districts in Europe, and nearly all in India, and the result of his experience was, that in the irrigating sea- son, when the canals were full, the low-lying lands became swamps, generating disease and pestilence; and he had 110 doubt that a good deal of unhealthiness, in countries where canal-irrigation was extensively prac- tised, was owing to the neglect of drainage to carry off the surplus water." Article 66. Cost of Irrigation per acre in different countries. In America, as a rule, the land and water go together, and the only expense the landowner is subject to is, that of maintenance of the Canal. In India, on the contrary, the Government owns all the great canals and sells the water to the cultivators. In the Statistical Review of the Irrigation of India, 1887-88, it is stated that the rates which are charged for the use of water for irrigation vary very largely in dif- ferent parts of India and for different crops. In some cases a charge is made for a single watering, and in others a special rate is taken for water used during certain months, but generally the charge is an average rate for irrigating the crop to maturity. Excluding very excep- *Transactions of the Institution of Civil Engineers. Vol. LXXIII, 1883. OTHER IRRIGATION WORKS. 337 tional cases, it may be said that this rate varies from forty cents an acre for rice crops in some parts of Ben- gal and Sind, up to eight dollars, which is not an extreme rate in Bombay for sugar cane crops. The average rate is less than $1.20 an acre. (The rupee is here assumed as equal to forty cents.) In the Punjab Revenue Report on Irrigation for 1889- 90, it is stated that the average water rate for this year, for the Western Jumna Canal was about one dollar per acre. TABLE 21. Giving cost of irrigation per acre in different countries. CANAL OR LOCALITY. COUNTRY. Rate per acre in dollars. AUTHORITY. Ganges Canal India. $1 12 F. C Danvers, C E Trans ICE vol 33 Eastern Jumna Canal. . . Western Jumna Canal. . . Baree Doab Canal India (Rice) Madras North West Provinces . . Soonkasela Canal . India... . India... . India... . India... . India... . India... . India. 1 16 1 20 1 17 2 50 3 00 1 25 3 00 F. C. Danvers, C. E. Trans. I. C. E., vol. 33.' F. C. Danvers, C. E. Trans. I. C. E., vol. 33. F. C. Danvers, C. E. Trans. I. C. E., vol. 33. G. J. Burke, C. E. Trans. I. C. E., vol. 73. J. B. Morse, C. E. Trans. I. C. E., vol. 73 J. B. Morse, C. E. Trans. I. C. E.. vol. 73. J. H Latham. C E Trans ICE vol 34 Ceylon Lower Fgypt Alpines Canal Ceylon. . Egypt.. . France. . 50 5 00 $2 to 3 J. B. Morse, C. E. Trans. I. C. E., vol. 73. Gen. Scott Moncrieff 19th century Feb.. 1885. George Wilson, C. E. Trans. I. C E., vol 101 Canal from Rhone Marseilles Canal Verdon Canal France. . France. . France. . 10.00 6 50 5 50 Engineering, 29 June, 1877. George Wilson, C. E. Trans. I. C. E., vol. 51 George Wilson, C. E. Trans. I C E , vol 51 Henares Canal Esla Canal Colorado Truckee Valley, Nevada.. Spain.. . Spain America . America . 7 25 5 75 f 1 50 to $3 500 George Wilson, C. E. Trans. I. C. E., vol. 51. George Wilson, C. E. Trans. I. C. E., vol. 51. R. J. Hinton Irrigation in the United States. Quoted by A. D. Foote, C. E. 22 338 IRRIGATION CANALS AND Article 67. Annual earning of a cubic foot of water per second. The following extract is taken from a work by the Honorable Alfred Deakin, M. P., of Victoria.* " At Los Angeles, California, water is sold by what is called a " head," which under their loose measurement, varies from two cubic feet to four cubic feet per second, at $2 per day or $1.50 per night in summer within the city, twice that price outside of its boundaries, and half the price in winter. At Orange, Southern California, and its neighboring settlements, the price for a flow of about two cubic feet per second is 12.50 for twenty-four hours or $1.50 per day and $1 per night, and in winter $1.50 for twenty-four hours. At Riverside the cost is about $1.90 per day or $1.25 per night, for a cubic foot per second, or $3 for the twenty-four hours. These prices varying indefinitely as the conditions of sale vary, furnish but an insecure basis for any generalization. Possibly a better idea of the importance of water, than can be derived from any list of purchases and rentals in particular places, may be obtained by a glance at its cap- ital value. It has been calculated that the flow of a cubic foot per second for the irrigating season of all future years is worth from $75 to $125 per acre in grain or grazing country, to $150 in fruit lands. This is the price paid to apply such a stream to a special piece of land for as long as the farmer may think necessary, the knowledge that an excess of water will ruin his crop being the only limit. But if a flow of a cubic foot per second were brought in perpetuity without any limit to the acreage to which it might be applied, or the time or circumstances of applying it, the capital value of such a stream in Southern California to-day would be at least $40,000. * Irrigation in Western America, Egypt and Italy. OTHER IRRIGATION WORKS. 339 The following table is compiled from various sources: TABLE 22. Showing the annual earning of a cubic foot per second in different countries. NAME OP CANAL. Annual earning of a cubi : foot per second. AUTHORITIES. Ganges, 1866-67... Gauges, 1867-68. . . Ganges, 1868-69... Eastern Jumna. 1866-67 . . . Eastern Jumna, 1867-68... Eastern Jumna, 1868-69. . . Western Jumna 187 195 262 261 260 326 249 164 220 295 80 75 11000 1875 33 Russel Aitken. C. E. Trans. I. C. E., 1871-2. Russel Aitken, C. E. Trans. I. C. E., 1871-2. Russel Aitken, C. E. Trans. I. C. E., 1871-2 (year of drought). Russel Aitken, C. E. Trans. I. C. E., 1871 2 (year of drought). Russel Aitken, C. E. Trans. I. C. E., 1871-2 (year of drought). (Year of drought.) F. C. Danvers, C. E. (year of drought). F. C Danvers, C. E. (year of drought). Col. W H. Greathead. Trans. I. C. E., vol. 35. Col. W H. Greathead. Trans. I. C. E., vol. 35. Colonel Baird Smith. Colonel Baird Smith. George Higgin, C. E., in Trans. I. C. E., vol. 27. George Higgin, C. E., in Trans. I. C. E., vol. 27. H. M.Wilson, C. E., in Trans. Am. Soc. C. E.,1890. Ganges, 187071... Eastern J umna, 1870-71 . . . Piedmont Lombardy Henares, Spain (Janals in Colorado Article 68. Cost of Canals per Acre Irrigated and per cubic foot per second. The following table is taken from the most reliable sources available, but no doubt there are errors in it as the account of cost varies by different authorities. It is merely given to show approximately the cost of ir- rigation canal work in different countries. It is almost impossible to make anything like an accurate comparison of the cost of works in different countries, there are so many different matters entering into the subject. For example, the Ganges Canal is estimated to have cost $2,487, per cubic foot per second, whilst the Orissa canals are stated to have cost only $1,000. The former canal, however, has a greater number per mile of expensive works, such as bridges, falls, regulators, level crossings, superpassages, etc. The Orissa system of canals is situated in a deltaic country, which has a slope some- what approaching to that of the canals, and, as a ne- cessary consequence, very much fewer heavy works are required than on the Ganges Canal which cross the drain- age of the lower Himalayas. 340 IRRIGATION CANALS AND Again, the Henares Canal, in Spain, is stated to have cost, per cubic foot per second, more than twelve times as much as the Mussel Slough Canal in California, but then the works of the former are infinitely superior to the latter. It is very likely that in the end the Henares Canal will be the cheaper of the two, as its annual re- pairs will cost less, and the works being permanent, there will be no renewals of bridges, aqueducts, etc. Table 23 is compiled from a table given by Mr. Ed- ward Bates Dorsey, M. Am. Soc. E. C.,* and from other sources of information. TABLE 23. Giving the cost of canals per acre irrigated, and also the cost per cubic foot per second of discharge. NAME OF CANAL. COUNTRY. COST OF WORKS. Per acre Irrigated. Per cubic foot per second for water used per year. Western Jumna India .... India. . . . India. . . . India India .... India. . . . India .... India. . . . India .... India .... Colorado Colorado Colorado Colorado California California California California California California Idaho . . . France. . . France.. . France. . . Spain.. . . $10 88 6 11 26 50 36 80 28 80 35 00 32 00 29 00 39 00 15 00 10 83 59 33 6 25 9 63 52 75 7 30 7 18 2 16 35 67 81 25 46 66 $1765 2487 1990 2330 2170 1965 2600 1000 280 125 549 287 1025 549 1507 584 277 189 4305 2830 15330 7500 Eastern Jumna Sutlej or Sirhind Ganges (with navigation) Ganges (without navigation, ^ deducted) .... Baree Doab Sone Bellary Low Level. Tomba^anoor The Orissa system Fort Morgan . . Del Norte. High Level . ... Uncompahgre Cajon . . . Seventy-six . Santa Clara Valley Irrigation Co Riverside Mussel Slouch King's River North Side . Idaho Mining & Irrigation Co. (estimated).. Marseilles.. Carpentaras Verdon Henares Irrigation in Transactions of the American Society of Civil Engineers. Vol. XVI, 1887. OTHER IRRIGATION WORKS. 341 Article 69. Measurement of Water. Modules. Meters. It is not likely that the greatest duty of water will be reached until it is sold by measure. It will then-4>6 to the interest of the user of water to economize it to the fullest extent. The machines used to measure water in irrigation canals are generally known as modules, or meters. The principal objects to be sought in a module are: 1. That it should deliver a constant quantity of water with a varying depth or head of water in the sup- ply channel. 2. That it should expend very little head in deliver- ing the constant quantity. 3. That it should be so free from friction as not to be easily deranged, and that sand or silt in the water would not affect its working. 4. That it should be cheap, and so simple in con- struction that any ordinary mechanic accustomed to that line of work should be able to make or repair one'. It is of great importance that there -should be no intricate or concealed machinery, not only from its liability to derangement, but because there is then so much more liability to an alteration in the discharge, without its being noticed by the official in charge. It is also of importance to have, if possible, such a measure as can be easily inspected by those using the water, in order that each man may, if he pleases, satisfy himself that the proper quantity of water is flowing into his channel. Mr. A. D. Foote, M. Am. Soc. C. E., has invented a water meter which goes very far to satisfy all the above conditions. Professor L. G. Carpenter gives the follow- ing description of this water-meter.* *Oii the measurement and division of water. 342 IRRIGATION CANALS AND " In Figure 199, A is the main ditch with a gate D, forc- ing a portion of the water into box B. This has a board on the side towards the main ditch, with its upper edge at such a height as to give the required pressure at the orifice. Then if the water be forced through B, the amount in excess of this pressure will spill back into the ditch. If the box B is made long enough, and the spill-board be sharp edged, nearly all the excess will spill back into the ditch G, thus leaving a constant head at the orifice." Fig. 199. View of Water Meter, or Module, by A. D. Foote, C. E. Mr. Foote thus describes this meter: * " For months it has done its work in a very satisfac- tory manner, seldom clogging and never varying in its delivery to an appreciable amount. " The whole value of the meter depends upon the long *A Water-Meter for Irrigation in Transactions of the American Society of Civil Engineers, Vol. XVI 1887. OTHER IRRIGATION WORKS. 343 weir, perhaps better described as an excess or returning weir, which returns all excess of water in the box back to the ditch, and thus keeps the pressure at the delivery orifice practically uniform. l( I am w 7 ell aware that the measurement is not abso- lutely accurate or uniform; but if it is remembered that the variation in delivery is only as the square root of the variation in head, and that, owing to the long ex- cess weir the variation in head is only a small portion of the variation in the delivery ditch, it will be seen that actual delivery through the orifice is very nearly uniform. " There need be but an inch or two loss of grade in the ditch, as but very little more water should be stopped than is delivered through the orifice. The gate or other obstruction in the ditch should back the water suf- ficiently to keep the excess weir clear, and at the same time keep, say, a quarter of an inch of water on its crest, and the surface of the water in the box should then be exactly four inches above the center of the delivering orifice. 11 The principle of the long excess weir can be used for delivering water through an open notch or weir, but it is more accurate with a pressure or head, and the greater the head the greater the accuracy, as will readily be seen . ' ' Any one using the meter will naturally adapt it to their own circumstances and desires. It is cheaply con- structed and easily placed in position, costing from four to six dollars; quickly adjusted, as the gates do not have to be precisely set; needs no oversight or supervision (if properly locked as they should be) until a change in volume is desired; will deliver a large or small quantity, which is a great convenience, as the irrigator usually wants a small stream continuously and a large stream on 344 IRRIGATION CANALS AND irrigating day; is riot likely to clog, as floating leaves and grass pass over the excess weir. Half-sunken leaves may catch in the orifice, but as it is to the farmer's in- terest to keep that clear, he will probably attend to it. " To me, however, the greatest merit the method pos- sesses (excepting its accuracy) is that the irrigator him- self, with his pocket-rule, can, at any time, demonstrate to his entire satisfaction that he is getting the full amount of water he is paying for." Whilst Mr. Foote believes that the main ditch need not lose more than a few inches fall, that is from A to C, Mr. "VV. H. Graves, C. E., who has introduced the meter on large canals, prefers at least a foot. The module adopted 011 the Henares and Esla canals, in Spain, * is illustrated in Figures 200, 201, 202 and 203. MODULE IN USE ON HENARES CANAL F1G.200 n~ FIG.201 CROSS SECTION PLAN., "The water is measured by being discharged over a knife-edged iron weir, shown at E, Figure 201. The water flows from the main canal into the distributary A, irrigation in Spain, by Geogre Higgin, M. Inst. C. E., in Transactions of the Institution of Civil Engineers. Vol. XXVII, 1867-68. OTHER IRRIGATION WORKS. 345 Figure 202, from which place it is admitted into the chamber (7, by a sluice working in the* division wall B. From G the water passes into the second chamber I), where the weir is fixed at E. The communication, be- tween the two chambers, G and D, is made by narrow slits, and the water arrives at the weir without any per- ceptible velocity, and perfectly still. The weirs vary from 3.28 feet to 6.56 feet in breadth, according to the quantity of water required to be passed over. On the wall of the outer chamber is fixed a scale, with its zero point at the level of the weir edge, and by means of this scale, any person can satisfy himself that the proper dotation of water is flowing into the distribution chan- nel. By managing the sluice the guard can regulate to a nicety the height of water to be passed over the weir. This module has several good points. The sys- tem of measurement is that which possesses the most fixed rules in hydraulics, and gives the most constant results; it is simple, and almost incapable of derange- ment; it will serve equally well for turbid waters as for. clear ones; it can take off the waters with the least pos- sible loss of head a most important point in countries having a slight surface grade, where the loss of a few feet of headway would prevent the irrigation of many thousand acres. The canal official can see at a glance whether the proper amount of water is passing into the channel, and the irrigators can satisfy themselves on the same point. The only reasonable objection to this mo- dule is, that any sudden variation in the head of water in the canal will affect the discharge, which will con- tinue to be greater or less than it ought to be, according to circumstances, until the official comes round again. This is undoubtedly true, * * * but in most well- regulated canals there is never likely to be any serious variation in the head of water in twenty-four hours. 346 IRRIGATION CANALS AND There is, or should be, a man in charge of the head- works, whose special duty it is to see that a constant body of water is admitted into the canal. If the river is flooded, he must close the gates; if it diminishes he must open them. The water taken off from the Henares and Esla canals, for the different water-courses is a fixed quantity, and that passed on to the lower portion is, therefore, likewise variable. The only cause of a sud- den change of head would be in the case of a sudden and heavy fall of rain; but to provide against this at every one or two miles, there is a waste weir, 'or escape, which would immediately carry off the surplus waters; and even if a little more was discharged through the module for a short time, no inconvenience would result from this." OTHER IRRIGATION WORKS. 347 REPORT ON THE PROPOSED WORKS OF THE TULARE IRRIGATION" DISTRICT, CALIFORNIA, BY P. J. FLYNN, CIVIL AND HYDRAULIC ENGINEER, MAY, 1890. To the Honorable, the President and Board of Directors of the Tidare Irrigation District : GENTLEMEN: In accordance with your instructions, 1 have investigated several routes, in order to select the best line, for a canal to convey 500 cubic feet of water per second, or 25,000 miner's inches, under a four inch head, from the Kaweah River to the site of your pro- posed reservoir. I have also, in this report, according to your instructions, given explanations with reference to objections made to certain parts of the works. I herewith submit for your consideration plans and profiles and also detailed estimates of the cost of these lines. I also submit tabular statements giving details as to dimensions, grades, etc., of each line. (Only one of these tables referring to Middle Level Canal, No. 1, is given in this pamphlet.) ESTIMATES. The estimated cost of each line is as follows: High Level Canal $ 744,456 Middle Level Canal, No. 1 659,273 Middle Level Canal, No. 2 664,94!) Middle Level Canal, No. 3 669,389 Low Level Canal 695,983 Each estimate includes the cost of head works on the Kaweah River, canal line to reservoir, including tunnels, dam and outlet works at reservoir, canal through the 348 IRRIGATION CANALS AND plains from the reservoir to the district and the compen- sation to be paid for land for the reservoir and canal .lines. To the total cost of the above twenty per cent, has been added, that is, ten, per cent, for loss on sale of bonds, and ten per cent, for contingencies. This twenty per cent, is included in the estimates given above. I recommend the adoption of the line designated Middle Level Canal, No. 1, for the following reasons: 1. It is the cheapest line. 2. With the exception of the High Level Canal there will be less loss of water by percolation than on the other lines. 3. Also with the exception of the High Level Canal, the cost of annual repairs will be less. Briefly stated, the works on this line include head works on the Kaweah River, thence one mile in length of canal to a flume 100 feet long at Horse Creek, thence a canal 2.75 miles long to a tunnel 700 feet long. After this tunnel comes a canal 2,400 feet in length, then follows another tunnel 1,100 feet long and thence 4.59 miles of canal to reser- voir. The total length of this canal is 9.15 miles. No water is drawn from the canal between the river and the reservoir. At the reservoir there is a large dam and outlet works, and from the reservoir a canal twenty-five miles long brings the water to and through the Tulare District. The district has an area of about 40,000 acres. PRICES. The prices for work are fixed as near the current rate of labor and materials as could be ascertained. BORINGS AND TRIAL PITS. In order to make an accurate estimate borings were taken, with a light steel rod, at every hundred feet where the rock was cohered with earth. This work was done at slight expense as the ground at the time was OTHER IRRIGATION WORKS. 349 thoroughly saturated with water. A few trial pits were also sunk. SIDE SLOPES. The side slopes in cuttings vary with the nature_of Jbhe material cut through. In fill the top of the banks is 6 feet in width and 1J feet above the surface of the water. For one mile from the head works the side slopes, both inside and outside the canal, are 2 horizontal to 1 ver- tical. With this exception the banks in fill, when not protected by dry rubble, have slope sides of 1J to 1 on the inside of the canal, and 2 to 1 on the outside. I give a short description of the different lines reported on. HIGH LEVEL CANAL. The head of this canal is on the left bank of the Ka- weah River in Section 33, T. 17 S., R. 28 E. From this point this canal runs via A, B, C, D, E, X, F, G, M, S, (see map) to reservoir at S. The head of the canal for about 200 feet is through granite, and for the next 5,000 feet to Horse Creek at B, it is through bowlders, gravel and sand. For about 3,000 feet from the Kaweah river this line is in cut and the balance is in fill, about 500 feet in 13 feet fill. This is the largest fill on any of the lines. Horse Creek is passed by a flume 100 feet long. After this for 500 feet the line runs along a bold rocky bluff, the method of passing which is described under the heading, side-hill work. From this point to D via B, C, D (see map), 7,400 feet in length, the line has frequent sharp curves and runs in steep side-hill ground. The channel is fourteen feet wide at bottom, with a depth of water of seven feet, and with side slopes of J horizontal to 1 vertical. This part of the line has been kept as much as possible in five feet cut to prevent loss of water by percolation and breaches. The material cut through IRRIGATION CANALS AND is sandy loam, usually covering, for a few feet in. depth, decomposed granite or solid granite. Solid granite shows at the surface at several places, and for about half a mile after leaving Horse Creek Carlo 11, there are large granite bowlders scattered over the surface of the ground, some of them measuring as much as several cubic yards. In order to avoid the steep side-hill ground from C to V via C, H, I, T, K, V (see map), the line C, D, E, having a tunnel D, E, 7,500 feet long, was investigated. By this tunnel the line passes through the range of hills that run parallel to, and on the south OTHER IRRIGATION WORKS. 351 side of the Kaweah River. This tunnel is in granite. In cross-section it has a level bed 10 feet 3 inches wide, with vertical sides 7 feet high and a segmental top. Its grade is 1 in 300. From E this canal runs via E, X, F, G, M, S, for 3.7 miles to the reservoir. This part of the line is on fairly level ground, through sandy loam, and no difficulty is met with. This part of the canal has a bed width of thirty-three feet, a depth of water of six feet, the side slopes next to the water 1|- to 1, and the outer slope 2 to 1. The top of the bank is six feet wide and 1| feet above the surface of the water in the canal. Its grade is 1 in 7,000, and its mean velocity two feet per second. The total length of this line is 7.58 miles. MIDDLE LEVEL CANAL NO 1. This canal, which is the line recommended for adop- tion, is the same as the High Level Canal from the head works on the Kaweah river at A (see map) to C, that is for about 2.5 miles. From C to V, via C, H, I, T, K, V, it runs in a tortuous course, on rough, steep, side-hill ground, through sandy loam, rotten granite and solid granite. Large granite bowlders are scattered over the surface of this route. It will be necessary not only to clear the line of these bowlders, but also to clear the hill side above the canal line of all large bowlders that are likely, during rainy weather, to roll down and fall into the canal. From to I for 7,800 feet the canal has a bed width of 14 feet, depth of water of 7 feet, side slopes of J to 1, and a grade of 1 in 1000 or 5.28 feet per mile. At I, this line goes by a tunnel 700 feet long in granite, under the pass near Mr. Marx's house, and it emerges from this tunnel 011 the south side of the range of hills that run parallel to, and south of the Kaweah River. The lower end of the tunnel is situated at the head of Lime Kiln canon. This canon joins at its lower 352 IRRIGATION CANALS AND end with the plain that stretches from the Lime Kiln to the pass M, S (see map), that leads to the reservoir. From I, this line runs along bold, rocky side-hill ground for 2,400 feet to the beginning of a tunnel in granite 1,100 feet long. The method of passing this place is the same as that adopted in passing the rocky bluff near Horse Creek, and is explained under the heading Side- Hill Work. From the beginning of the 700. foot tunnel to the lower end of the 1,100 foot tunnel, the line runs through granite. Through this length of 4,200 feet the channel has the same dimensions and grade, that is, in cross-section, bottom level and 9 feet in width, sides vertical and 7 feet high to surface of water. The grade for the tunnels and canal for this length of 4,200 feet is 1 in 200, or 26.4 feet per mile. The velocity in this part of the line is very high, 8.15 feet per second, but the channel is well able to bear this velocity, as it is composed of granite and rubble masonry, the latter having a coat of hard plaster composed of Portland cement and sand. From the lower end of the 1,100 foot tunnel this line falls 22.6 feet in 1,100 feet by 13 vertical drops, and horizontal reaches to K, and the cross-sec- tional dimensions are the same as the last section, hav- ing a bed width of 9 feet. From K the line runs for 4,700 feet to V, along the steep, side-hill ground, through sandy loam and rock. The channel here has a bed width of 14 feet with sides as heretofore described. From V this line runs to X, and thence for 18,400 feet to the reservoir via V, X, F, G, M, S, and from X to reservoir it is the same, in every respect, as the High Level Canal. At V the depth of the canal changes from 7 to 6 feet, and the surface of the water in the channel is assumed to drop one foot near this place. From Horse Creek to V for 4.68 miles the canal has a high velocity sufficient to wash away loams and similar soils. OTHER IRRIGATION WORKS. 353 Where the canal channel, 14 feet in width, passes through these materials the bed and banks have a lining of dry rubble in order to prevent erosion. The supe- riority of this line over the Middle Level Canals, Eos. 2 and 3, lies in its smaller cross-section and higher grade from K to V, and also in following the line of the High Level Canal from X to S. The depth of cutting through the pass from M to S is less on this line than on lines Nos. 2 and 3. There are two tunnels on this line, one of 700 and the other of 1,100 feet in length. The indi- cations are that these tunnels are in solid granite and will not need timbering or lining. The length of this line is 9.15 miles. The following table gives the dimensions and grades of the different sections of the Middle Level Canal, No. 1, from the headworks to the reservoir. The velocities are computed by Kutter's formula with n = .025. The required discharge is 500 cubic feet per second. o "i 8 ^; 5-d , 1 a h a S i $ jjSy n 1-1 I ^ ^ s 2 O 02 i | d 1 0"- "GO 53 d O *M i 55 1 1 2 11 I s 5200 2600 2.03 54. 3.5 1 to 2 213.5 2.49 532-(i) 100 200 26.4 16. 4. Vertical. 64. 8. 513-(2) 400 200 26.4 9. 7. Vertical. 63. 8.15 513 14200 1000 5.28 14. 7. i to 1 110.25 4.65 513 700 200 26.4 9. 7. Vertical. 63. 8.15 513-(3) 2400 200 26.4 9. 7. Vertical. 63. 8.15 513 1100 200 26.4 9. 7. Vertical. 63. 8.15 513 1100 9. 7. Vertical. 63. 8.15 513-(4) 4700 1000 5.28 14. I to 1 110.25 4.65 j i tj \- s: / r.i.r 14400 7000 0.754 33. 6. H to 1 252. 2. 504-(5) 4000 20. 7. 1 to 1 189. 2.55 500-(6) (1.) This section begins at head works. (2.) Flume, drop of 0.5 feet. (3.) Tunnel, drop at tunnel mouth 0.5 feet. (4.) Level reaches and vertical drops. (5.) Bed continuous, drop 1 foot in surface water. (6.) Level reaches and vertical drops. 23 354 IRRIGATION CANALS AND MIDDLE LEVEL CANAL, NO. 2. This canal is the same, in every respect, as Middle Level Canal No. 1, from the head works at A to K (see map). At K it drops four feet lower than Canal No. 1, in order to avoid bad ground from K to V. From K to V it is in a slope of 1 in 7,000, whereas Canal No. 1 has in this distance a slope of 1 in 1,000. From V this line runs to the reservoir via V, G, M, S, through moderately level ground. This part of the line is in sandy loam and there is no difficulty in it. There are two tunnels on this line, having a total length of 1,800 feet. The length of this line is nine miles. MIDDLE LEVEL CANAL NO. 3. This canal is the same, in every respect, as Middle Level Canal No. 2, from the head works at A to the res- ervoir at S (see map), with the exception of that part from I to K. From I this canal runs to K via I, R, K, all in open cutting. This part is 7,000 feet in length. It is very tortuous and runs on steep side-hill ground, through sandy loam and rock. Large granite bowlders are scattered over the surface and embedded in the sandy loam that covers the bed rock. From the lower end of the 700 foot tunnel at I, the line falls forty-three feet in 1,100 feet by fourteen vertical drops and level reaches. Of all the lines .this has the shortest length of tunnel, 700 feet. From the last drop below I it runs in a channel of the same di- mensions and grade that Middle Level Canal No. 2 has from K to S, and it joins with this channel on the same level at K. It has the greatest length of any of the lines, of difficult, broken, side-hill ground. The length of this line is 9.38 miles. OTHER IRRIGATION WORKS. 355 LOW LEVEL CANAL. The headworks of this canal are situated on the left bank of the Kaweah River in Section 36, T. 17 S., R. 27 E. The river is here over 500 feet wide and it is divided into two channels. The great body of the water flows in the channel near the left bank, and the river has a decided set towards this bank. There is, however, always danger in such a wide river bed that the main channel, after a heavy flood, might change to the right bank. In such a case it would be very expensive work to excavate a channel from the right branch to the head works of this canal. The head works of Middle Level Canal No. 1 are not exposed to this danger as explained further on. At the side of the head works of the Low Level Canal the left branch of the river is about 150 wide on the surface of the water, and its low water depth about four feet. The site for the head works is in solid granite. A dam in the river, at this place, would be a costly work as, to be effective, it should reach from bank to bank. From the head works at N this line runs via N, 0, P, L, M, S, to the reservoir at S. From the head works at N the line runs across the flat above the left bank of the river to the base of the hill at 0. This line is 1,850 feet in length, through sandy loam and hard-pan. This part has a bed width of thirty-one feet, five feet in depth of water, side slopes of J to 1 and a grade of 1 in 2,500. From O this line runs through the hill in a tunnel to P for 2,850 feet in limestone. From P the line runs through the plain east of the Wachumna Hill, thus avoiding all side-hill work, to a tunnel under the pass, M, S. The canal through the plain has a bottom width of thirty feet, a depth of seven feet and side slopes of 1 to 1 with a grade of 1 in 8,000. After passing through the tunnel 3, 300 feet in length, 356 IRRIGATION CANALS AND the line runs for 2,000 feet more to the reservoir at S, through sandy loam, hard-pan and granite. There are two tunnels on this line of a total length of 6,350 feet. The tunnels have in cross-section a level bed 10 feet 3 inches in width, vertical sides with a depth of water seven feet and a segmental roof. The grade is 1 in 300. This line is the shortest of the five routes. Its length is 5.59 miles. TUNNELS. Under certain conditions a tunnel, when in sound rock, is preferable to an open channel for conveying water. The conditions are that no water is required to be drawn off this part of the line, and that a heavy grade can be given. By sound rock is meant rock not subject to percolation, to any appreciable extent, that will stand the high velocity without injury by erosion, and also that will not require lining for its sides or arch- ing for its roof. When, in addition, a steep grade can be obtained, a high velocity can be given to the water, and the cross-sectional area and consequent expense re- duced. In such a tunnel the loss of water by evaporation and percolation and the expense of maintenance is at a minimum. It has several advantages over the open channel in steep, side-hill ground. Its sides and bed are impervious to water and it is covered from the sunlight. It shortens the line, there is no compensation to be paid for land, and it does not interfere with or cross the drainage of the country on the surface. Should it be required at any future time to increase the carrying capacity of the canal, the discharge of the tunnel can be increased, without, however, increasing its dimen- sions. All that will be necessary is to fill all the hollows be- tween the projecting ends of the rocky bed and sides OTHER IRRIGATION \VQRKS. 357 with good cement concrete, and after this to give a coat of good plaster to the surfaces .in contact with the water and make them smooth. Although the section will be diminished, still the velocity and consequent xlis_charge will be doubled. Let us assume the loss of water in a certain length of open channel at six per cent, of the total flow. If, by adopting a tunnel line, the loss of water is only one per cent., it is evident that it would pay to expend the value of five per cent, of the water on the tunnel line above that on the open channel. Another argument in favor of the tunnel is, that the amount saved yearly in maintenance capitalized could be expended on the tunnel over that upon the open channel in order to give a fair comparison with the lat- ter. The above are good reasons in favor of the High Level Canal. But, on the other hand, there are two very weighty objections to this route. The principal one is the time the tunnel would take in construction. Under favorable circumstances, and with granite of medium hardness, this tunnel could be constructed in. two years; but, should circumstances turn out unfavor- able, and very hard rock as well as water be encoun- tered, the time might be increased to four years and the cost of driving also very much enhanced. The estimated cost of the High Level Canal is $85,000 more than that of the Middle Level Canal, No. 1. If that were the only difference and after taking everything into considera- tion, then in my opinion the High Level Canal would be the best of the five lines, but on account of the uncer- tainty as to time and cost, I recommend the next best line, the Middle Level Canal, No. 1. 358 IRRIGATION CANALS AND HEADWORKS OF MIDDLE LEVEL CANAL, NO. 1. The headworks of this canal are situated on the left bank of the Kaweah River, in Section 36, T. 17 S., R. 27 E. At this site the Kaweah River is well adapted for the headworks of an irrigation canal, in fact, it would be extremely difficult to find in any locality a more fa- vorable location for such a work. It is in a single channel, in a well-defined, permanent, rocky bed, free from sand, silt, gravel and bowlders. The depth of dig- ging at the head is only about eleven feet in rock for about 200 feet in length, and for a mile from the head the greatest depth of digging is only sixteen feet, and this in gravel or bowlders. At low water the greatest width of the river at this place is about 150 feet, and the greatest depth about four feet. At high water its greatest surface width is probably not more than 300 feet. At about 500 feet below this point there is a sudden fall in the rocky bed of the river, and below this fall the channel widens considerably, to 800 feet in some places; and its bed is covered with debris composed of bowlders, gravel, sand and silt. At low stages of the river, in the irrigating season, when water for irrigation is most needed, a large percentage of it is lost by percolation through this porous bed. If, at some future time, in order to economize water and reduce expenses, all canals and ditches on the left bank of the Kaweah River, from Wachumna Hill, to the mouth of Cross Creek, should combine and take out the water from the river in one canal, then this is the proper location for the headworks. With a good permanent dam across the river immedi- ately below the headworks, every cubic foot of water coming down the Kaweah River can be intercepted at this point and diverted into the canal. In seasons of great drought, when every cubic foot of water counts for so much, it is of the utmost importance to be able to OTHER IRRIGATION WORKS. 359 utilize the water that now runs to waste in the porous river bed. The canal can get its supply without a dam in the river, but to be able to intercept all the flow in the low stages of the river, a dam would be necessary. In order to prevent the silting up of the river bed above the dam to its crest, and the choking of the canal head by debris, under-sluices would be required. If the above- mentioned combination of ditch owners should find the building of such a dam necessary, then, by opening these under-sluices in said dam when required, the cur- rent will carry away any debris deposited opposite the head gates and keep the latter clear. For the reasons above given the place selected for the location of the headworks has advantages over every other place that I have seen on the river. These ad- vantages are: 1. Its elevation above the reservoir is sufficient to give a steep grade to the canal through the bad, rocky ground, and thus diminish its cross-section and expense. 2. The river is in a single, narrow channel, in a per^ maiient bed free from debris. 3. The foundation for the headworks of the most stable and permanent kind, a bed of solid granite. 4. The face line of the head gates can be located on the bank of, and parallel to the direction of the current in the river, and by this means it can be kept clear of the debris. 5. With a dam across the river, and regulating shut- ters at the head of canal, there will be a command of the w r ater for irrigation, and the water that at low stages of the river is now lost in the bed below can be intercepted and utilized. By closing the regulating shutters at any time the supply can be cut off from .the canal and its bed laid dry. 6. On account of the advantages of site above ex- 360 IRRIGATION CANALS AND plained permanent head works can be constructed at moderate expense. RESERVOIR. The reservoir has an area, when full, of 657 acres, and it contains 635,340,000 cubic feet of water. Its water- shed has an area, including the reservoir, of twenty square miles. It has an earthen dam 56 feet high at the deepest part. Its greatest depth of water is 50 feet, and its average depth 22.2 feet. The dam contains, includ- ing puddle and rip-rap, 923,000 cubic yards of material. Its length is 3,800 feet. Its top is 16 feet wide and 6 feet above the level of crest of waste weir that is above the surface of a full reservoir. At the deepest part the dam is 296 feet wide at the base. Its outer slope is 2 horizontal to 1 vertical, and its inner slope facing the water 3 to 1. This slope is to be faced with rip-rap. Under the center of the dam, and for its whole length, a trench is to be sunk to, and into the impervious clayey loam, and afterwards filled with puddle to about two feet above the surface of the ground. The dam will be constructed in thin layers of selected clayey loam well consolidated. An ample waste weir with its crest 6 feet below the top of the dam will be made at each end of the dam, and it will be arranged also so that the out- let can be used as an additional waste channel. The outlet will be through a tunnel in solid rock and through the spur of the hill at the south end of the dam. The outlet will be entirely unconnected with the dam, which will have no pipe or culvert running through it. The tower or chamber connected with the outlet tunnel will be of ample dimensions and of good masonry. The specifications will enter into more details about materials and mode of construction. The dimensions given for the dam are those adopted OTHER IRRIGATION WORKS. 361 in the best practice throughout the world. Theory has little to do with the design of an. earthen dam. Ex- perience in different parts of the world has shown that w r ith good materials* and careful construction a dam of the above dimensions can be made perfectly afe. Statements have been made that there is 110 necessity for a reservoir, that all that is required is a canal from the Kaweah River to the district, that there has hereto- fore been ample water in the river for all the require- ments of irrigation, and that it, therefore, follows that there will be an ample supply in the future. In a work entitled " Physical Data and Statistics of California," published by the State Engineering De- partment of California, there are tables giving the flow of the Kaweah River at Wachumna Hill for six years, from 1878 to 1884 inclusive. The drainage area of the Kaweah River at this place is 619 square miles. From these tables I have compiled the table 1 at the end of this report. For those more accustomed to compute the flow of water by miner's inches than by cubic feet per second, I give the equivalent of the average flow in that unit of measurement. Fifty of these inches are equivalent to one cubic foot per second. The miner's inch used is that under a mean head of four inches. From an inspection of these tables it will be evident that the expectation of ample supply in a very dry year, such, for instance, as 1879, is not well founded. There are over twenty canals and ditches drawing their water from the Kaw^eah River that will have a prior right to the use of the w T ater, and to which they are legally entitled, before the Tulare Irrigation District can take its supply from that river. I here give the names of some of these canals. They are Wachumna Canal, People's Consolidated, Kaweah Canal, Farmers' 362 IRRIGATION CANALS AND Ditch, Evans' Ditch, Tulare Canal, Packwood, Mill Creek, Outside Creek, Cameron Creek, Lower Cross Creek, Ketchum Ditch, Hayes Ditch, Hambletoii Ditch, Meherton Ditch. In addition to the ahove there are some small ditches not mentioned in this list. The table shows that the average flow of the river in May, 1879, was only 774 feet. This is the month in which water is most urgently required for irrigation. The only safe rule by which to arrive at the available supply in a year of drought is, to take the least flow of the river when water is most in demand. The canals and ditches mentioned above are entitled to more than 774 cubic feet per second. It is very likely that all the canals have never drawn the full supply to which they are entitled at the same time during the period of least supply. The time, however, is sure to come when they will do so. As the country is thickly settled the de- mand for water will increase until every available cubic foot that can be drawn from the river will be utilized on the land. Under these circumstances, in a very dry year it is evident that there will not be sufficient water to save the crops that are depending for their supply on the canal alone. In such a deplorable state of affairs the loss to the district in a year of great drought would be more than the total cost of the reservoir. The reservoir is intended to insure a supply during the period of the low stage of the river, and to prevent a water famine on the irrigable lands of the Tulare Irrigation District. The canal alone no doubt will bring a supply during years of average or more than average rainfall, but it is sure to fail when most required in seasons of great drought, for the sufficient reason that there will be no water supply. During this year there is an abundance of water avail- OTHER IRRIGATION WORKS. 363 able, but it is well to remember that we are after hav- ing a most unusual wet winter, and it is of still more importance to remember that extraordinary seasons of drought happen periodically, and that in only one such season the use of the storage water from the reservoir will more than repay the expenditure incurred on the dam. Without a reservoir in such a year the canal will be a dry channel unable to supply the perishing crops with water. In the months between irrigating seasons, when there is not such a large quantity drawn from the river for irrigation, the water that now runs to waste, during that period, can be taken to fill the reservoir, and there will thus be a storage reserve to be used only when it is ur- gently required in April and May. In. the meantime, after the reservoir is full, any water that may be drawn from the river can be allowed to flow down to the dis- trict and be used for irrigation. For instance: Let the reservoir be filled at the end of the irrigating season, when there is always an abundant supply of water in the river from the melting snow. Now, from this pe- riod until the following irrigating season in April, the supply obtained from the river flows to and out of the reservoir, keeping it full. In case, however, that the supply from the river should at any time in a dry year fail, there will still be a full reservoir stored for use. In average years, however, the reservoir can be filled several times from freshets and melting snow, and by this means at the periods of irrigation there will be a larger supply available at certain intervals than could be obtained from the river by the canal alone. The above facts prove that to have, in all seasons, an effective system of irrigation works for this district, a storage reservoir is essential. Statements have been made that, after completion, a 364 IRRIGATION CANALS AND full reservoir would not be capable of irrigating one section, that is, 640 acres of land. I now proceed to prove that these statements very much exaggerate the probable loss from evaporation and percolation. The quantity of water required to irrigate land varies very much. The number of acres that a cubic foot per second, or fifty miner's inches will irrigate is known as THE DUTY OP WATER. This varies from 50 in wheat lands, in some parts of America, to 1,600 in fruit land in Southern California. When this high duty is reached the water is conducted in pipes, and it is used with economy. In Elche, in Spain, where water is very scarce, a cubic foot per second irrigates 1,000 acres of land. General Scott MoncriefT, R. E., gives the duty that can be got out of one cubic foot of water per second in Northern India, at 250 acres, and he states that there is frequently fifty days between each irrigation. J. S. Beresford, C. E., states that five inches in depth is a safe allowance for one watering in Northern India. I have heard an experienced irrigator in this district, Tulare, state that he gave over six feet in depth, at one watering, to a piece of land having a sandy soil. He had an unlimited supply of water and the quantity used he measured from the supply channel. Prof. George Davidson in his Report on Irrigation, states that: " The amount of water required for a crop of wheat, barley, maize, etc., is almost identical with the amount deduced from observations in the great valley of Cali- fornia, where a rainfall of 10| inches, fairly distributed, will insure a crop/' " The capacity of a canal may, therefore, be fairly estimated by assuming that 12 inches of water over the OTHER IRRIGATION WORKS. 365 surface of the irrigable land will, if properly applied, be amply sufficient for the maturing of one grain crop; and hence, knowing the capacity of a canal, we can de- termine the area its water will irrigate." In one of his lectures before the Academy of Sciences at San Francisco, Prof. Davidson says on the same sub- ject: " In estimating the total acres that can be irrigated from a given supply, allowance must be made for the amount lying fallow, woodland, marsh, roads, streams, towns, etc. In India, the average under cultivation each season is only one-third of any given area; in this country we might safely estimate it at two-thirds of any irrigation district." Experienced irrigators state that in this district, as a rule, one watering some time in May will save the crops, vines and fruit trees, and that fruit trees and vines can, with careful cultivation, tide over one dry season, with less than an average depth of six inches over the land. From the instances given it will be seen that there is a wide diversity in the quantity of water used per acre to irrigate land. The reservoir, when full to the level or waste weir, will contain 635,340,000 cubic feet, equivalent to 4,752,- 660,870 U. S. standard gallons of water. If we reduce this quantity by thirty-six per cent, for evaporation and percolation, up to the point of delivery to the irrigators, we have left for purposes of irrigation 406, 617, 600 cubic feet. This is the quantity that, after the loss by evapo- ration and seepage, would be given to the irrigators for use on their land in a very dry year in April or May. This quantity is sufficient to cover 11,200 acres to a depth of ten inches or 18,600 acres to a depth of six inches. It is the opinion of irrigators well informed on the 366 IRRIGATION CANALS AND requirements of this district, that this quantity of water, used with economy, would be sufficient to save the crops, fruit trees arid vines, and tide over a very dry year in this district. Doubtless, during the first few years after the opening of the canal the loss of water will be more than thirty- six per cent., but as explained under the heading Evap- oration and Percolation, the loss from seepage will de- crease with the age of the canal and also as the sub-soil gets saturated with water. The Fresno District is a no- table instance of the saturation of sub-soil. A small percentage of the quantity of water used at first to irri- gate a certain area is now sufficient to insure a crop. I am informed that the distribution channels that I constructed in 1877, to irrigate the twenty acre lots of the Central California Colony at Fresno, have since been leveled and filled up, as the sub-soil is so saturated with water that very little flooding is now required. There is a deeper porous sub-soil in this district and, therefore, it is not likely that its saturation will be to the same extent as that of Fresno, but it will probably be sufficient to diminish the quantity of water now re- quired to irrigate a certain area in this district. I am informed that already there is a sensible rise in the sub- soil water, in and around Tulare, which is attributed to the seepage from the irrigation channels in the district. The storage capacity of one full reservoir, at a time when there is no additional supply flowing into it from the Kaweah River, would supply a canal having a dis- charge of 500 cubic feet per second or 25,000 miner's inches for fifteen days, and, when there is no outflow from the reservoir, it would take an equal length of time for the supply canal from the river to fill it. In the period of greatest demand for irrigation, in years of ordinary rainfall, there will be a supply from OTHER IRRIGATION WORKS. 307 the river, flowing into the reservoir to add to its greatest storage reserve. This supply from the river will be a material addition to the irrigating capacity of the reser- voir. As an instance let us assume that during the pefToch of irrigation 500 cubic feet per second are drawn from a full reservoir, while it is, at the same time, receivin;;- 200 feet per second in excess of all losses, including evap- oration and percolation. In this instance the reservoir and canal combined will give a supply for irrigation of 500 cubic feet per second for twenty-four and one-half davs and will, during this time, cover 24,297 acres to a depth of one foot. Without the reservoir the 200 cubic feet per second supplied by the canal would cover two-fifths of that area, equal to 9,719 acres. Without the additional 200 cubic feet per second by the canal, the reservoir alone would give a supply of 500 feet per second for fifteen days, and would cover 14,585 acres to a depth of one foot. I append a table showing the great increase of the irrigable capacity of the reser- voir supplemented by a supply from the river. The first column of the table gives the number of cubic feet per second supplied by the canal from the river to the reservoir. The second column gives the number of days supply for irrigation at the rate of 500 cubic feet per second, that the full reservoir of 635,340,000 cubic feet can give when supplemented by the quantity in column one. The third column gives the number of acres that can be covered to a depth of one foot by 500 cubic feet per second, in the number of days given in second column. The fourth column gives the number of acres that the canal supply in the first column, but without the reser- 368 IRRIGATION CANALS AND voir, can cover to a depth of one foot in the number of days given in the second column. Canal from Kaweah River, cubic feet per second. Reservoir and Canal gives a supply of 5(iO cubic feet per second for days Reservoir and Canal cover to a depth of one foot acres Canal alone without res- ervoir cover to a depth of one foot acres 15. 14,585 50 16.3 16,202 1,616 100 18.4 18,235 3,650 150 21. 20,833 6,248 200 24.5 24,297 9,719 250 29.4 29, 157 14,570 2f5 30. 29,759 15,174 300 36.8 36,483 21,897 350 49. 48,595 34,016 400 73.5 72,899 58,314 450 147. 145,792 131,206 Aii inspection of this table will show the necessity for a reservoir in a dry year. With a supply of 100 cubic feet per second, 5,000 miner's inches, the canal alone, in 18.4 days will cover 3,650 acres to a depth of one foot, whilst the reservoir, plus this supply, will irrigate 18,- 248 acres to the same depth in the same time. In the former case there would be blighted crops over a large area, and in the latter, on the contrary, there would be sufficient water, if used economically, to save the crops throughout the district. LOSS FROM EVAPORATION AND SEEPAGE. There is a popular belief that the loss of water from the surfaces of rivers, canals and reservoirs is much greater than is actually the case. The records of evaporation at Kingsburg bridge, Tulare county, published by the State Engineering de- partment of California, are given in the tables at the end of this report. From Table 12 it will be seen that the mean annual evaporation at Kingsburg bridge for the four years from 1881 to 1885 is 3.85 feet in depth, OTHER IRRIGATION WORKS. 369 when the pan is in the river, which is equal to an aver- age depth of one-eighth of an inch per day for a whole year. For the same period the evaporation, when the pan was in air, was 4.96 feet in depth, that is, equal to a mean, daily depth of evaporation throughout theTyuar, of less than three-sixteenths of an inch per day. The greatest evaporation is in the month of August, when it is more than one-sixth of the evaporation for the whole year. The average for this month is one- third of an inch per day. During the months when the largest quantity of water is used for irrigation in this district, the table shows that the mean evaporation is:- For March one-twelfth of an inch per day. For April one-twelfth of an inch per day. For May one-fifth of an. inch per day. To some people these depths of evaporation may ap- pear very small. Let us, therefore, examine the result of observations in other countries: Colonel Baird Smith, in his work on Italian Irriga- tion, states that in the north of Italy and center of France, the daily evaporation varies from one-twelfth to one-ninth of an inch per day; while in the south, and under the influence of hot winds, it increases to between one-sixth and one-fifth of an inch per day. In July, 1867, the evaporation in Madrid, according to the returns of the Royal Observatory, was 13J inches in depth, or less than half an inch per day; and in May of the same year it was only one-quarter of an inch per day. July was the hottest month in 1867, and it was estimated that during this month the total evaporation of the Henares Canal, carrying 105 cubic feet per second, or 5,250 miner's inches, amounted to only three- fourths of one per cent, of the total flow. W. W. Culcheth, C. E., states as the result of his in- 24 370 IRRIGATION CANALS AND vestigation on the Ganges Canal, in Northern India, that for evaporation, one-quarter of an inch per day over the wetted surface may be taken as the average loss from a canal. Dr. Murray Thompson's experiments in the hot season in Northern India, with a decidedly hot wind blowing, gave an average result of half an inch in depth evaporated in twenty-four hours. M. Lemairesse's observations at Pondicherry, in French India, give a daily evaporation of from three- tenths to half an inch in depth per day. Trautwiiie made observations in the Tropics and he found the evaporation from ponds of pure water to be at the rate of one-eighth of an inch per day, but he ob- serves that the air in that region is highly charged with moisture. The above quoted observations, although they do not prove the accuracy of the Kingsburg experiments, still they give results, in warm climates, so close to each other that, for all practical purposes, the latter experi- ments may be accepted as correct. Let us now investigate the loss of water from the reservoir by evaporation: Let us assume that the reservoir is full on the 31st of July, and that it receives no water from the river from this time until it is drawn upon for watei for irrigation on April 1st, of the following year. Allow twenty days for the reservoir to become empty and the surface ex- posed to evaporation during this time is equal to the surface at full supply for half the time, or ten days. From Table 12 we find the average evaporation for four years to be as follows: OTHP:R IRRIGATION WORKS. 371 August 0.861 feet in depth September 0.615 October 0.289 November 0.174 December 0.104 January 0.081 February 0.091 March, one-third of 0.075 2.290 This shows a total depth evaporated during this time equal to 2.29 feet, but the average depth of the reservoir at full supply level is 22.2 feet, and therefore the evapo- ration is, in round numbers, 10 per cent, of the full reservoir. To this will have to be added evaporation of twenty days in April in the main canal and small ditches, dur- ing the time that the reservoir is being emptied. If we take the length of the main canal at 40 miles and the width of water surface at 66 feet, we have an area of 320 acres, and if we allow the same area for the smaller ditches, we have 640 acres for twenty days in April, or in round numbers, the same area as the reser- voir, 657 acres. The evaporation, Table 12, is given as 0.286 feet in depth for the whole month of April. As the water from the reservoir will pass over the heated, dry bed of the canal, let us allow the evaporation for the twenty days in April to be as much as that of the whole month, or 0.286 feet in depth. This depth on 657 acres is equal to 1.3 per cent, of the mean depth of the reser- voir. This shows that the evaporation from reservoir and channels below reservoir is less in volume than 12 per cent, of the full reservoir. The observations made last year at the Merced reser- voir are in support of these deductions, the evaporation having been found less than that given in Table 12. There is usually more loss of water from seepage in earthen channels than from evaporation. 372 IRRIGATION CANALS AND In every new canal, through sandy loam, the loss by absorption at first is very serious. Gradually the ground gets saturated, and at the same time the interstices of the porous material of the bed and banks get filled up with particles of clay, which diminish the percolation. The bed of a canal acts as an elongated filter. It is well known that the sand of a water-works filter-bed, if it is not periodically washed, or replaced with clean sand, the interstices between its particles get filled with silt and the filter ceases to act, or acts so slowly as to be practically useless. The same thing takes place in. a canal, but at a slower rate than in a filter-bed. There is less deposit in a canal, as the greater part of the finer particles of silt do not subside until the water reaches the land to be irrigated. At first, after the completion of the canal, probably not more than 25 per cent, of the irrigable land of the district will require water. Gradually, as time goes on, small fruit farms will increase in number, and with them the area of land requiring water. At the same time the percentage of loss by percolation will decrease, and a larger quantity of water will be available than at the first opening of the canal. The loss by percolation will be most serions in the sandy reaches of the canal. These sections can be taken in hand and puddled, one at a time, during the annual repairs, and the puddling thus spread over several years and charged to the working expenses. The puddling can be done at a time when the canal is not used ior irri- gation purposes. Ribera estimated the total loss from evaporation and percolation in the Isabella Canal, in Spain, a masonry- lined channel, at two per cent. In the Ganges Canal, in India, the largest irrigation canal in the world, with a discharge of 5,000 cubic feet OTHER IRRIGATION WORKS. 373 per second, or 250,000 miner's inches, the loss in 1873- 74, from all causes, including evaporation, seepage and waste, was 69 per cent. The length of main and branch canals of all sizes was, however, at this time,_overji,000 miles long. The length of main canal alone was 648 miles. It is admitted that water was very wastefully used, and this, together with the great length of the channels, accounts for the extraordinary loss. P. O'Meara, C. E., in writing on the results of irriga- tion in this country, attributes the principal loss of water to evaporation, and he states that: " The question of evaporation was so important that it was doubtful if any loss of irrigating power occurred in Colorado, other than that which was due to it.' 7 Walter H. Graves, C. E., in a paper read before the Society of Engineers, in Denver, Colorado, in 1886, states: "The factor of seepage is a variable one, depending mostly upon the nature of the soil, and gradually grows less through a long term of years. Evaporation is very nearly a constant quantity. * * * In calculating the loss from these sources in the older canals, about twelve per cent, should be deducted from the carrying capacity. Observation and experiment by the writer in various parts of Colorado, tend to show that evaporation ranges from .088 to .16 of an inch per day, during the irriga- ting season. From what has been written, it will be seen that the loss from evaporation and seepage combined varies from twelve per cent, in Colorado to sixty-nine per cent, in India. As a fair average, therefore, thirty-six per cent, is allowed for the loss of water from these causes, in computing the capacity for irrigation of the reservoir and canal of the Tulare Irrigation District. 374 IRRIGATION CANALS AND EARTHEN DAMS. Several objections, not founded on facts, have been urged against the reservoir, and it has been stated that an earthen dam cannot be built to impound water at a depth of fifty feet. This is a mistake. Facts prove the contrary. There is no good reason to doubt that what has been well done before in thousands of cases, in put- ting a large quantity of good clayey loam together to retain water, can be done again. There are thousands of earthen |dams in different parts of the world, impounding water to a depth of 50 feet or more, that are in use to-day, and that possess as much stability as the modern brick houses in which are living millions of people. Properly constructed, on a good foundation, and with a waste weir large enough to carry off the greatest rainfall, an earthen, dam can be con- structed to have as much stability, and as long a life, as any iron railroad bridge in the country. An ample waste weir is the safety-valve of a reservoir. If, by any means, the waste weir is contracted so as to diminish its discharging capacity below its requirement for the maximum rainfall, then the dam is in danger. There would be as much sense in bolting down the safety valve of a steam engine, as in obstructing a waste weir of a reservoir, and still we read that the latter has been done and caused frightful loss of life. The top of the dam must also be kept to the level of its original height above the crest of the waste weir. Al- lowing the top of the dam to settle below its intended height is just as bad as raising the waste weir an equal distance. In the construction of the dam provision must be made for settlement by adding a certain percent- age to its height. It is as essential to keep a dam, its waste weir and outlet in repair, as it is to keep a house or bridge in the OTHER IRRIGATION WORKS. 375 same condition. Some people assert that if a dam is built it should be of masonry, as, in their opinion, this is the only material that can safely resist the pressure and erosion of the water. A masonry or concrete dam requires to ba founded on the solid rock. Clay or impervious clayey loam is not a suitable foundation for it. This is the reason why, in so many instances, the underground work on a masonry dam has cost more than that above ground, as it has to be taken down to bed rock. A masonry dam founded 011 clay, or other compressible material, is likely to settle and crack, and thereby cause serious trouble and expense, or its total destruction. On the other hand, while an earthen dam can, with safety, be founded on solid rock, still, its best foundation is in good clay, clayey loam, hard-pan or other similar material imper- vious to water. The reservoir dam proposed has for the greater part of its length a good foundation, at little depth, in clayey loam or hard-pan, and for this reason an earthen dam has been selected as being the most suitable for the location. During the last few years railroad bridges have broken down under passenger trains, causing fearful loss of life, and Buddenseick buildings have tumbled down either during erection or soon after completion. These accidents have not prevented people from traveling by rail or living in brick houses. Experience has proved that an earthen dam can be constructed so as to be as safe and stable as any bridge or building in the world. In this State, the Merced darn and the dams of the Spring Valley Water Company of San Francisco, are examples of safe construction. Some of them are in use for over twenty years. India can show thousands of dams that have been in use for over a century, and that are perfectly safe now. 376 IRRIGATION CANALS AND In the Presidency of Madras, the official records show that there are over 43,000 reservoirs in use at the present time. In an official return issued by the Irrigation De- partment of Bombay, on the 1st of September, 1877, there is a list of seventeen dams, either completed or in progress of construction, the lowest of which is 41 feet and the highest 101 feet high, and this is the work of only a few years. This shows that the Indian engineers have, from long experience, the fullest confidence in the stability of their earthen dams. Is it to be credited that the progressive American of the present time is not able to construct an earthen dam as well as the natives of India of the last century? As pertinent to this subject an extract is given from a paper by the writer, published in the Transactions of the Technical Society of the Pacific Coast for June, 1885, on the SHRINKAGE OF EARTHWORK. "Embankments in India are often constructed by basket work, the material being carried in saucer shaped wicker baskets, containing less than a cubic foot. In the construction of embankments to retain water, this basket work is done in thin layers of less than nine inches in depth, the earth being roughly leveled up as it is deposited from the baskets, and then well punned with wooden or cast-iron rammers, weighing about twelve pounds. In addition, the constant tramping of the men, women and children employed in carrying the baskets, so consolidates the bank as to make it im- pervious to water. The layers of earth are sometimes watered. Embankments constructed in this manner shrink or settle very little after they are finished. They are, in fact, an approach to puddle work, though not nearly so expensive. The writer has constructed many OTHER IRRIGATION WORKS. 377 embankments with a grading machine, tipping from wagons from grade, wheel-barrows, hand-cars, carts, scrapers and punned basket work, and of all these he believes that punned basket work settles the least, and is the best suited for hydraulic work, and the next best work to it for a similar purpose is that done by scrapers. 11 Thousands of embankments, and some of them counted among the largest and oldest dams in the world, have been constructed in India, by basket work, with- out any puddle wall or puddle lining; and some of them, that have been looked after and kept in repair, are as good, if not better, at the present day than when they were originally constructed, hundreds of years since. This kind of work is done much cheaper there than earthwork in this country. " The writer has constructed embankments in the Punjab, the lead being from 100 to 200 feet, for three rupees per thousand cubic feet, that is, at the rate of four cents per cubic yard." The numerous reservoirs for the water supply of cities all over the United States are proof that earthen dams in large numbers, and of a greater height than 50 feet, have been constructed during the last forty years in America. These dams are as safe as the ordinary railroad struc- tures, and many of them are located in the midst of a dense population. The failure of earthen dams in. the United States is mainly due to the cupidity of companies or corrupt con- tractors. Another cause of failure is the too common belief that any ordinary laborer, that any man who has used a scraper on a county road, is fitted to superintend the construction of an earthen reservoir dam. Materials that would in some instance be suitable for a county road or a railroad embankment, would be likely to cause 378 IRRIGATION CANALS AND destruction to a reservoir dam, and even with proper materials more care lias to be taken in constructing the latter than the former, and also a different method of raising the embankment has to be adopted. It is safe to assert that over fifty per cent, of all the dams in the world, constructed as part of the works for the water supply of cities are built of earth. Long experience has shown the dimensions required for dams. With these dimensions, good material prop- erly put together, a tower and outlet pipe through a tunnel in solid rock, the face of the dam covered with rip-rap, and an ample waste weir, an earthen dam can be made as safe as any structure on the best constructed railroads. Some anxiety has been expressed about danger to the dam from gophers, but it appears that they do 110 sensible damage to the Merced or Spring Valley dams of this State already referred to. CANAL ON STEEP SIDE HILL GROUND. In the description of the different lines already given, frequent mention is made of steep side-hill work. Fol- lowing the lines of the canal on the map from Horse Creek by the distinguishing letters, B, C, H, I,T, K,V, and also the loop, I, R, K, almost all the work for this distance is on steep side-hill ground, the slope in some instances being as high as twenty-six degrees, that is, a slope of two horizontal to one vertical. The material is sandy loam, hard-pan, disintegrated rock and solid granite. The depth of the rock from the surface varies consider- ably. Sandy loam is usually a surface covering of the other materials, and varies in depth from a few inches to six feet and more. It is much more difficult to carry a canal discharging 500 cubic feet of water per second, or 25,000 miner's inches, along such ground than it is to carry a railroad or county road. OTHER IRRIGATION WORKS. 379 Hydraulic miners, who have had to construct ditches and keep them in repair, know the great difficulty and expense of keeping a ditch to convey twenty-five cubic feet of water, or 1,250 miner's inches, in repair.^ How much more difficult, then, must it be, to convey twenty times that quantity in one ditch, that is 500 cubic feet of water per second. Other things being equal, the less the cross-sectional area of the channel, the less will be its cost, and the less the annual expense for repairs, when the velocity is kept within the limiting resistance of the materials of which the channel is composed, that is, when it is not so great as to abrade the bed and banks. These considerations led to the adoption of the cross- section having a bottom width equal to twice the depth, for the steep, side-hill work, with the exception of the crossing of the bluff at Horse Creek, and that part of the line between the 700 and 1,100 feet tunnels. The dimensions are, bed width 14 feet, depth of water 7 feet, side slopes { to 1. With a grade of 1 in 1 ; 000, that is, 5 feet 3 inches per mile, the velocity in this channel, according to Kutter's formula with TI= .025, is 4.65 feet per second, and the discharge 500 cubic feet per second. The levels through the hills admit of the grade given without adding materially to the length of the tunnels, and the material cut through is, on the whole, suitable for a high velocity. When the material cut through is sandy loam, or other materials that the high velocity of 4.65 feet per second in this canal would wash away, pro- tection is afforded the banks by a facing of dry rubble masonry, and the bed will be protected with stone pav- ing. Rock is in abundance all along the hillsides for this work. It has been stated that this channel will not discharge 500 cubic feet per second, and that a more suitable one would be a section with a bed of 50 feet, a depth of 380 IRRIGATION CANALS AND water 3|- feet, with side slopes of 2 to 1. The latter sec- tion, with a slope of two feet per mile will, according to Kutter's formula with n= .025, give a velocity of 2.5 feet per second and a discharge of 500 cubic feet per second. The small section will discharge just as much as this large one, and its cost will be much less. The principal objection to the large section is its expense. Fig. 205. feet, and the sur- face of the water in the small channel, be at the same level as in the larger one, the advantage is still in favor of the smaller section. Where it can be done with ad- vantage the intention is to keep the adopted section a, /, g, h, in about five feet depth of cutting, at the point, /, that is, that the vertical depth of the bed at /will be five feet below the surface of the ground at a. As the depth of water in this section is 7 feet there will be 2 feet in depth of water in embankment. The top of the bank will be 6 feet wide and will be 1J feet above the \vater, and its outer slope in earth 2 to 1, that is, for every two feet horizontal there will be one foot vertical. If necessary, the cross-section will be varied to suit the ground, keeping the depth of water seven feet in all cases in side-hill ground. As a rule, the best but most expensive plan, for a canal in loamy soil in steep side-hill, is to put the section in cut equal to the full depth of the water. In passing the bold rocky point at Horse Creek, and also in that portion of the line between the tunnels I and T, the rock will be taken out in the shape of a right-angled triangle, as shown in cross-section at a, d, c, Figure 206. Then a wall of uncoursed rubble masonry in liine mortar will be built on the lower side. The inner side of this wall will have a coat of plaster composed of Portland cement and sand. As an additional precaution to prevent percolation, a groove will be cut in the rock under the wall, which 382 IRRIGATION CANALS AND groove will be filled with concrete and this concrete will be joined with and form part of the rubble wall. The cross-section of the channel inside the rubble wall will be nine feet on a level bed, with vertical sides. The wall will be eight feet high, two feet wide on top and Fig. 206. five feet on the bottom, with the side next the water vertical and the outside battered. The grade of this channel will be 1 in 200 or 26.4 per mile. The cross- section and grade of this channel, from its bed to the surface of the water, will be the same as that of the tun- nels at each end of it. This section of the line from the upper end of the 700 foot tunnel to the lower end of the 1,100 foot tunnel will be the best part of the line. There will be less loss of water by evaporation and percolation, less expense in annual repairs, and less danger of breaches than in any other part of the line through the hills of an equal length. It has before been mentioned that the discharge through the tunnels can be doubled by giving the bot- tom and sides a smooth plastered surface. The same OTHER IRRIGATION WORKS. 383 thing can be done in the channel 2,400 feet in length, between the two tunnels which has the same sectional area as the latter. This is a fact well known to hydraulic engineers, that the new and improved^formulse give an increased discharge in proportion to the smooth- ness of the material over which the water flows. This fact was not taken into account in the old formulae, which are now known not to give the true discharge under all conditions of channel. Materials for building the rubble will cost very little. After the excavation there will be sufficient rock for the work at hand; the bed of the Kaweah River, a short distance away, will supply the sand required; lime is burned within half a mile of the work, and water is in abundance in Mr. Pogue's ditch. In the remainder of side-hill ground from Horse Creek to V, a similar sec- tion, 16 feet wide on bottom, can, 110 doubt, be adopted in several places, but this can be ascertained only after the surface covering of sandy loam is removed. This part of the line has a grade of 1 in 1000, or 5.28 feet per mile. A level bed 16 feet in width, with vertical sides, hold- ing seven feet in depth of water with this grade, will, according to Kutter's formula, with n = .025, give a velocity of 4.53 feet per second, and a discharge of 507 cubic feet per second. RAINFALL. An inspection of the rainfall of Tulare given in tables* will show that, during the ten years from 1874 to 1884, three years had total depth of rainfall for each year of less than four inches, three years of less than seven inches, three years of less than ten .inches, and one year * Tables not given in this Report. 384 IRRIGATION CANALS AND of 11.65 inches, which was the maximum during this period. This plainly shows the necessity for irrigation, in this district and nothing further will be said 011 this subject. A rainfall of 10 to 12 inches properly distributed will mature a crop in this district. The catchment basin of the reservoir, including the area of the latter, is 20 square miles. The reservoir is a little more than one square mile in area. In order to show the height which a large rainfall would raise the reservoir, let us assume that the reser- voir is full to the level of waste weir, and that no water can flow out of it through the waste weir or otherwise. In this state of affairs let the canal flow 500 cubic feet per second for one hour, whilst at the same time an ex- traordinary rainfall of three inches per hour takes place, of which 50 per cent, reaches the reservoir. At the end of one hour the reservoir would have risen 2 feet 7 inches, leaving the top of the dam 3 feet 5 inches above the surface of the water. This is a state of the reservoir not possible under any circumstances. The waste weirs will be always open and discharging to the capacity of the depth of water on them. A very heavy rainfall usually lasts but a short time, and the large capacity of the reservoir prevents a dangerous elevation of its surface during heavy rains. The total length of the waste weirs at each end of the dam must be made of sufficient capacity to carry off the flood water (computed by Dicken's formula), in addition to 500 cubic feet per second from the Kaweah River. A sufficient length of waste weir will be given so that the depth of water on its crest will not be greater than three feet. This would leave the top of the dam three feet above the surface of flood water. OTIIKR IRRIGATION WORKS. 385 PREVENTION OP WASTE OF WATER. Two methods have been adopted to prevent waste of water. One by measurement and the second by making the irrigators raise all the water they use from Uie_su.p- ply canals. There are two methods used in India, in supplying water, known as flush and lift. In flush irrigation the water flows by gravitation on to the land to be irrigated. In. lift irrigation the water reaches the land at such a low level that it cannot flow over the sur- face of the land to be irrigated. This requires power of some kind, usually manual labor, to raise the water sufficiently to enable it to flow over the land. So great was the loss from waste in India some years since, that it was seriously proposed to supply all the water at such a level, that it should be lifted some height, however small, before it could be used. It would then be to the interest of the irrigators to prevent waste. In this country the best method to prevent waste is by MEASUREMENT OF WATER. A meter for measuring water for irrigation purposes must be cheap and simple in construction and must cause little loss of head. No machine has yet been in- vented that fulfills all these conditions. The great dif- ficulty is the fluctuation of the level of the water in the main canal. It is believed, however, that a machine can be de- vised to fulfill these conditions that will give a close approximation to the quantity of water used. When the same method of measurement is used toward all the irrigators they will be treated on perfect equality and no one will have good reason to complain of in- justice more than another. 25 386 IRRIGATION CANALS AND DRAINAGE. As a rule the drainage of irrigated land will take care of itself, if the natural drainage channels are left free and unobstructed. These channels should not be used as drainage channels and also for purposes of irrigation. Nature, the best engineer, located them to convey water from the land. They cannot, with advantage, be used for irrigation and drainage, and when so used the worst results invariably follow. If the sub-soil and surface water cannot escape freely by the natural channels, super-saturation follows and the ground becomes water-logged. We have not to go far to see the evil effect of too much irrigation with defective drainage. A dense growth of weeds on the land and enervating malaria are the sure followers of bad drainage. To avoid this, stringent rules should be enforced to prevent the use of the natural drainage channels for any purpose whatever, but that of conveying away the drainage water that reaches them. EMPLOYMENT OF LOCAL LABOR. A great deal of the work, including all the earthwork, could be done by petty contract or day labor, and, in this way, employment could be given, after the harvest is over, to a large number of the residents of the district, who would be willing to do the work. In what I have above written, I have covered all the points contained in your instructions to me. In con- clusion I have to acknowledge the assistance, which as Directors of Tulare Irrigation District, individually and collectively, you have at all times given me. Respectfully presented, P. J. FLYNN. INDEX. Page Abbot (see Humphrej^s). Abraidiug Power of Water. . .43-51 62-65 Absorption (see Percolation). Abyssinia 63 Acequia 153 Afflux on Weir 101, 110 Africa, Lakes of Central 63 Alginet Syphon, Spain 182 Alkali (reh) 19, 68, 328, 329 330, 332, 336 American and Indian Irrigation Canals Compared 2-5 American Irrigation 279 American Society of Civil En- gineers, Transactions of. .61, 128 172, 197, 245, 322, 340, 342 Anderson, G. G 2, 329 Anicut (see also Weirs). 81, 87, 95 108, 109, 115 Atella, Spain 182 Apron... 87, 96, 106, 108, 109, 114 117, 120, 121, 123, 193 Aquatic Plants (see weeds). Aqueducts.... 46, 79, 150-164, 175 ! 228, 241, 252 j Ashlar. 105, 108, 110, 115, 119, 120 j Ashti Tank, or Keservoir. .324, 325 Asphalt 174, 294, 295 Astronomer Boyal, English ... 49 Asufnuggur Falls .... 192, 193, 194 Atbara Kiver 63 Aymard, M 182 Back-water 96, 98, 260 Baker, Sir B 57, 326 Bakersfield 88 Banks (see Embankments). Banks, Dimensions of Canal.. 26-29 Bar... 86, 111, 273 Page Barota 37 Barrage (see also. Weirs) . 81, 96, 98 99, 101, 102, 270 Barrage of the Nile .81, 82, 83, 95, 197 Bars of Grating, Plan of 209 Barton, Stephen 234 Bayou La Fourche 40 Bayou Plaquemine 32 Bazin 41, 42, 185, 258 Beas Kiver 150, 151 Bench Marks 254, 244, 257 Bends in Canals 28 Bengal Revenue Report 105 Beresford, J. S 290, 326, 364 Berm 27, 28 Berthoud, Captain Edward L. 18, 28 Betwa Weir 119 Beton (see Concrete). Bhim Tal Dam 119 Binnie, A. B -318 Blackwell, T. E 50 Blocks, Foundation. 77, 78, 79, 105 111, 112, 113, 114, 115 Boats on Canals 104, 241 Bombay Presidency Irrigation Beport 274 Boom 153 Borings 348, 349 Bowlders... 46, 51, 87, 88, 96, 150 163, 186, 215, 217, 218, 351 Boyd, Mr.... 322 Branch Canals 221 Breast Wall 177 Bridge.... 84, 86, 98, 99, 127, 149 152, 169, 185, 191, 193, 241 Bridge Foot 85, 89, 101, 146 ' ' Bridge of Blessings " 98 Browne, Major J 62 Brownlow, Major. 37, 111, 187, 257 Brunei .. .147 388 INDEX. Page Buffon, Nadault de 324 Buriya Torrent 177 Burke, G. J 336 Cairo, in Egypt 198, 270 California Irrigationist 265 Canals, A List of Irrigation . 29, 30 31 Canals divided into Two Classes. 1, 2 Canal, Agra.. 14, 30, 106, 177, 228 324, 331 Canal, Alpines 31 Canal, Arizona 31 Canal, Aries 35 Canal, Arrah 33 Canal, BareeDoab.. 12, 14, 30, 35 39, 150, 193, 195, 197, 202-205 215, 217, 300 Canal, Bear Kiver, Utah 90, 157 159 Canal, Beruegardo 242 Canal, Boise Kiver 229 Canal, Buxar 33 Canal, Calloway.31, 88, 89, 214, 331 Canal, Cajon 340 Canal, Carpentaras 31 Canal, Cauvery 312 Canal, Cavour..25, 30, 35, 87, 121 122, 125, 129, 152, 179 Canal, Central Irrigation, Dis- trict Calif ornia ... 25, 28, 31, 175 176 177 Canal, Cigliano 30, 268, 269 Canal, Citizens, Colorado 31 Canal, Crappone 31, 35, 269 Canal, Del Norte 31, 35, 128 Canal, Delta, Main, Egypt 30 Canal, Eagle Rock and Willow Creek 31 Canal, Elche 293 Canal, Empire 31 Canal, Esla 299, 344-346 Canal, Forez 293 Canal, Fort Morgan 31 Canal, Ganges, Lower. .30, 110, 151 Page Canal, Ganges, Upper.. 12, 26, 29 30, 38, 40, 82, 95, 112, 120, 125 127, 130, 158, 159, 161, 166, 167 170, 185-187, 192, 193, 198, 199 228, 249, 251. 286, 290, 292, 304 Canal, Genii 293 317, 325, 335, 339 Canal, Grand River, Colorado.. 17 31, 153 Canal, Hansi Branch, Western Jumna Canal 39 Canal, Henares.27, 30, 87, 119, 120 134, 163, 270, 298, 317, 340, 344 345, 346 Canal, High Line, Colorado. . . 31 232, 323 Canal, Ibrahimia 30 Canal, Idaho Canal Co.'s. . .31, 128 Canal, Idaho Mining & Irriga- tion Co.'s 31 Canal, Isabella II, 30, 244, 324 Canal, Istres 35 Canal, Ivrea 30, 268 Canal, Jucar, The Royal 50, 182 Canal, Jumna, Eastern. . . 1, 30, 37 112, 188, 249, 258, 286, 302 Canal, Jumna 36, 335 Canal, Jumna, Western. 14, 30, 39 286, 328 Canal, Kotluh, branch of Sutlej Canal 224, 225 Canal, Kurnool 312 Canal, Larimer 31 Canal, Lorca 293 Canal, Lozoya, Spain 182 Canal, Marseilles. .31, 230,269, 234 300, 324 Canal, Martesaua.. .30, 35, 228, 229 259, 323 Canal, Mazzafargarh 286 Canal, Merced, 31, 88, 232 Canal, Midnapore 139 Canal, Mijares 182 Canal, Mussel Slough, Califor- nia.. . 340 INDEX. 389 Page Canal, Muzza 30, 228, 229 Canal, Nagar (flood) 30 Canal, Naviglio Grande. 35, 228, 274 Canal, North Poudre. . .31, 153, 157 Canal, ttira 27, 293 Canal, Ojhar Tarnbat 325 Canal, Orissa 340 Canal, Ourcq 31 Canal, Palkhed 274, 325 Canal, Phyllis 31 Canal, Platte, High Line.. 154, 155 Canal, Quinto Sella 25 Canal, Eotto 30, 268, 269 Canal, New, from Khone, . . .299 324 Canal, Sahel 30 Canal, San Joaquin and King's Kiver 31 Canal, Santa Clara 340 Canal, Seventy-six 31 Canal, Sirsawiah 30 Canal, Sone. ... 14, 30, 33, 103, 222 228, 256, 257, 286 Canal, Sooiikasela 30 Canal, St. Julian 31 Canal, Subk 30 Canal, Sukkur 210-212 Canal, Sutlej or Sirhind 11, 14 29, 30, 172, 177, 225, 242, 243 Canal, Grand, of Ticino 30 Canal, Turlock, California. .31, 197 Canal, Tomtaganoor 340 Canal, Uncompahgre. .31, 152. 531 215 Canal, Verdon, France. . . . 179, 234 270 Canal, Wutchumna 231 Canterbury Plains, New Ze- land 197, 323 Carlet, Spain 182 Syphon (see Inverted Syphon). Carpenter, Prof. L. G 341 Catch water Drain 28, 67, 240 Cautley, SirProby.36, 95, 185, 186 187, 192, 254 Cavour Canal, Weir 87 Cement, Hydraulic 115, 121 Central California Colony 366 Chains 84, 134, 146 Chailly 51 Chains, Formula for Finding Tension on 137 Channeling 36 Channels, Economical 69, 73 Channels, Deep and Narrow.. . 73 Channel, Maximum Discharg- ing 12, 14 Checks or Drops (see Falls)... . Checks for Flooding. .281, 282, 283 Check-making 265 1 Chivasso Bridge, Italy 121 Chukkee Torrent 150 Cistern, Depth of, below Fall.. 198 Clamped, Cut Stones 116 Clearance of Silt from Canals.. 19 21, 24, 25, 33, 35, 52, 55, 257, 258 273, 274, 330 Coast Range of Mountains, Cal- ifornia 176 Coffer Dams 115 Colorado, Faulty Designs and . Construction of Canals in. . . 34 Colorado, Irrigation in.. . .279, 282, 283 Colmatage 65-68 Compartments by Checks. .281, 282 Colusa 175 Concrete .77, 79, 110, 112, 114, 115 119-123, 159, 176, 179, 237, 262 294, 375, 385 Construction 262 Corbett, Major 289 Cost of Canals per acre Irrigated and per Cubic Foot per Sec- ond 295, 339 340 Cost of Irrigation per acre in Different Countries. 272, 336, 337 Cost of Pumping and of Water. 270-272 Cotton, Sir A 242 Crest of Fall, Raising 199 390 INDEX. Page Crest of Weir 103, 104, 105, 107 108, 112, 115, 124, 125, 360, 374 384 Crevasses 87 Cribs 88, 90, 92, 186 Crofton, Major.... 26, 161, 186, 193 224, 242 Cross-section of Channels. . 13, 19 27, 28, 69, 70, 256, 261, 380, 382 Cross-section on Steep Hill side 13, 380 Crown of Weir (see Crest of Weir) Culcheth, W. W 317 Culverts 149, 150, 177 Cunningham, Major Allen. 137, 318 Curbs, Well 78, 114 Curtain Walls 33, 111, 114 Curves 28, 244 Cuttings 68, 70, 241 Cylinders 77, 159 Darns, Bowlder 66, 82 Dams, Earthen, for Reservoirs. 374 375, 376 Dam in Eiver, Location of. .86, 90 Dams, Masonry, for Reservoirs 375 Dams, Reservoir.. 360-364, 374-376 Dams in Rivers. . .9, 83, 84, 85, 230 358-360 Dams, Submerged. .2, 237, 262, 265 Dam, Temporary 87, 88 Damietta, branch of the Nile. . 97 98, 99, 101, 102 Danube 64 D'Arcy 147, 185 Daubisson Ill Davenport, W. H 231 Davidson, Prof. G 87, 300, 364 Deakin, The Hon. Alfred.. 268, 270 279, 308, 338 Defective Irrigation. . . .33, 332-336 Dehri 33 Delhi 106, 108 Delta. . . .6, 7, 10, 59, 98, 270, 339 Page Delta of the Nile 6, 98 Denver Society of Civil En- gineers 2, 3, 18, 274, 287, 290 316, 321, 329, 373 Deodar Wood 205 Deola 37 Depositing Basins. . .46, 52, 56, 58 229-232 Depth to bed, width of Canal .. 12-17 241 Development of Water. . .2, 234-2.38 Deyrah Dhoon Water Courses . 45 229 Dhunowree Dam 112 Dhunowree Level Crossing. 166, 167 170 Diamond Drills 237 Dickens, Col. C. H.. . . 105, 254, 257 Dimensions of Canals 12-17 Distributaries.. .19, 29, 36,67, 184 197, 245, 246-262, 277, 281, 282 291, 292 Ditching 264 Diversion, Weirs (see Weirs). Dora Baltea Aqueduct in Italy. 152 153 Dora Baltea River 60 Dorsy, E. B 61, 322, 340 Dove-tail Joints 91 Dowlaiswaram Branch of God- avery Anicut 115, 116 Drainage.. 7, 26, 28, 29, 67, 68, 275 277, 327-331, 386 Drainage Area of Rivers. . . .64, 150 Drainage, Main, in London... 50 Dredger, Canal. . : 263, 265-268 Dredging 33,52, 55 Drift Bolts 90 Drifts, Tunnel 237 Drop, Big, Grand River Canal, Colorado 153 Drop Gate 84, 134, 169, 226 Drops (see Falls) Drop Wall (see Curtain Wall). INDEX. 391 Page Drought 113 Dubuat's Formula... 36, 41, 43, 185 Dupuit 147 Dutac, Messrs 66 Durance Eiver, Silt in.. 59, 6) (54) 196 Molesworth's modification of Kutter's formula (40) (55) 196 Flynn's modification of Kutter's formula (40) (56) 196 Lampe's formula (57) 196 Weisbach's formula (58) 197 Prony's formula (59) 197 Eytelwein's formula is (60) 197 Another formula of Eytelweiii (61) 197 D'Aubisson's formula (62) 197 Hawksley's formula (63) 197 Poncelet's formula (64) 197 Blackwell's formula (65) 197 Neville's formula (66) 197 TABLE OF CONTENTS. Vll Hughes' modification of Eytelwein's formula (61) (67) 197 Blackwell's modification of Eytelwein's formula (61) (68) 198 Kirkwood's formula for tuberculated pipes (69) 198 ARTICLE 15. Remarks on the formulae 198 Major Alleu Cunningham's experiments -rr . 200 48-inch Glasgow water pipes 201 Table 34 Giving the value of c in the formula v = c^/rs in ten dif- ferent formulse 203 ARTICLE 16 Values of c and cv^for Circular Channels flowing full. Slopes greater than 1 in 2640 204 Table 35 Giving the value of c for different values of \/r and s in Kutter's formula with n = .013 204 ARTICLE 17 Construction of Tables for Circular Channels 205 ARTICLE 18 The Tables as a Labor-Saving Machine ..... 206 Table 36 Giving the discharge in cubic feet per second, of Circular and Egg-shaped Sewers, based on Kutter's formula, with n = .013 207 Table 37 Giving the velocity in feet per second in Pipes, Sewers, Con- duits, by Kutter's formula, with n = .011 207 ARTICLE 19 Discussion on Kutter's formula 208 Table 38 Giving the co-efficients of discharge, c, in Circular Pipes, of different diameters and different grades, with n .013 211 Table 39 Giving values of c, the co-efficient of discharge, according to different modifications of Kutter's formula, with n = .013 213 Table 40 Giving the mean velocity in feet per second, of pipes of dif- ferent diameters and grades, with n -~= .013 214 Mr. Guilford Molesworth's note 215 ARTICLE 20 Flynn's modification of Kutter's formula 215 Table 41 Giving the value of K, for use in Flynn's modification of Kutter's formula 216 Table 4% Giving values of \/r for Circular Pipes, Sewers and Con- duits of different diameters 217 ARTICLE 21 D^Arcy's formula 217 Four feet Glasgow Water Pipes 218 D'Arcy's formula for finding the mean velocity in clean cast-iron pipes 220 D'Arcy's formula for finding the velocity in old cast-iron pipes . . 222 ARTICLE 22 Comparison of the co-efficients for small diameters, of the Formula* of D'Arcy, Kutter, Jackson and Fanning 223 Table 43 Of co-efficients (c),- from the formulae of D'Arcy, Kutter, Jackson and Fanning 224 ARTICLE 23 Pipes, Sewers, Conduits, etc., having the same velocity . . . 226 Table 44 Pipes, Sewers and Conduits having the same valocity and the same grade, but with different velocities and different values of n, based on Kutter's formula 227 Vlll TABLE OF CONTENTS. Page Table 45 Egg-shaped Sewers having the same velocity and the same grade, but with different dimensions and different values of n, based on Kutter's formula 228 ARTICLE 24 Pipes, Sewers and Conduits having the same discharge. . 228 Table 46 Pipes, Sewers and Conduits having the same grade and the same or nearly the same discharge, but with different diameters and different values of n 229 ARTICLE 25 Egg-shaped Seiuers 230 ARTICLE 26 Explanation and Use of the Tables 231 Pipes, Sewers and Conduits 231 Example 21 Given the diameter, length, fall and value of n of an inverted Pipe Syphon, to find its mean velocity and discharge. . . . 231 Example 22 Given the discharge and cross-sectional dimensions of a rectangular, masonry Inverted Syphon, to find its grade or fall from the surface of water at inlet to its outlet 232 Example 23 Given the diameter and grade of a Pipe, to find its mean velocity and discharge by D'Arcy's formula (51) for clean cast-iron pipes 234 Example 24 Given the grade, mean velocity and value of n of a Cir- cular Sewer to find its diameter 235 Example 25 Given the discharge, grade and value of n of a Circular Sewer to find its diameter 236 Example 26 Given the diameter, the value of n and the mean velocity in a Pipe to find its inclination or grade 236 Example 21 Given the diameter, discharge and value of n of a Cir- cular Conduit flowing full to find the slope or grade 237 Example 28 To find the diameter in three sections of an intercepting sewer, with increasing discharge, the grade or inclination being the same throughout, and the value of n being given 237 Example 29 To find the value of c and n of a pipe 239 Example 30 Given the diameter of an old pipe, to find the diameter of a new pipe to discharge double that of the old pipe 240 Example 31 Given the discharges and grades of a system of pipes to find the diameters 240 Example 32 To find the dimensions of an Egg-shaped Sewer to re- place a Circular Sewer 242 Example 33 To find the diameter of a Circular Sewer whose dis- charge, flowing full depth, shall equal that of an Egg-shaped Sewer flowing one-third full depth 243 Example 34 In the same way as in Example 33, we can find the diameter of a Circular Sewer, whose velocity flowing full shall equal the velocity of an Egg-shaped Sewer flowing one-third full depth 243 Example 35 To find the dimensions and grade of an Egg-shaped Sewer flowing full, the mean velocity and discharge being given. . 243 TABLE OF CONTENTS. IX Page Example 36 The diameter and grade of a Circular Sewer being given, to find the dimensions and grade of an Egg-shaped Sewer, whose discharge, flowing two-thirds full depth, shall equal that of the Circular Sewer flowing full depth, and whose mean velocity at the same depth shall not exceed a certain rate . _^, ._.. 244 Example 37 To find the dimensions and grade of an Egg-shaped Sewer, to have a certain discharge when flowing full, and whose mean velocity shall not exceed a certain rate when flowing two- thirds full depth 245 Table 4? Giving the hydraulic mean depth, r, for Circular Pipes, Conduits and Sewers , 248 Table 48 For Circular Pipes, Conduits, etc., flowing under pressure. Based on D'Arcy's formula for clean cast-iron pipes. Value of the factors a, c\/r and ac\/r 249 Table 49 For Circular Pipes, Conduits, etc., flowing under pressure. Based on D'Arcy's formula for old cast-iron pipes lined with de- posit. Value of the factors a, c-v/Fand ac\/r. 251 Table. 50 For Circular Pipes, Conduits, Sewers, etc. Based on Kut- ter's Formula with n = .009. Value of the factors a, c\/r and ac\/r 253 Table 51 For Circular Pipes, Conduits, Sewers, etc. Based 011 Kut- ter's formula with ?i = .01. Values of the factors a, c\/r~ and ae-v/F 255 Table 52 For Circular Pipes, Conduits, Sewers, etc. Based on Kut- ters formula with ?i = .011. Values of the factors a, cv"Y"aiid ac^/r 257 Table 53 For Circular Pipes, Conduits, Sewers, etc. Based 011 Kut- ter's formula with n -012. Values of the factors a, c\/r and ac^/r 259 Table 54 For Circular Pipes, Conduits, Sewers, etc. Based 011 Kut- ter's formula with n = .013. Values of the factors a, c\/r and ac^/r 261 Table 55 For Circular Pipes, Conduits, Sewers, etc. Based on Kut- ter's formula with n = .015. Values of the factors a, c\/r and acx/r ; 263 Table 56 For Circular Pipes, Conduits, Sewer's, etc. Based on Kut- ter's formula with w = .017. Values of the factors a, c\/r and ac^/r. . . 265 X TABLE OF CONTENTS. Page Table 57 For Circular Pipes, Conduits, Sewers, etc. Based on Kut- ter's formula with n = .020. Values of the factors a, c-^/r and ac^/7 266 Table 58 Giving the value of the hydraulic mean depth, r, for Egg- shaped Sewers flowing full depth, two-thirds full depth, and one- third full depth 267 Table 59 Egg-shaped Sewers flowing full depth. Based on Kutter's formula with n = .011. Values of the factors a, c\/r~a,ud ac-^/r.. 268 Table 60 Egg-shaped Sewers flowing two-thirds full depth. Based on Kutter's formula with n = .011. Values of the factors a, c^/7 and ac-^/r 269 Table 61 Egg-shaped Sewers flowing one-third full depth. Based on Kutter's formula with n .011. Values of the factors a, c^/r and ac^r 270 Table 62 Egg-shaped Sewers flowing full depth. Based on Kutter's formula with n = .013. Values of the factors a, cv'Fand ac-^/^r. . 271 Table 63 Egg-shaped Sewers flowing two-thirds full depth. Based on Kutter's formula, with n = .013. Values of the factors a, c\/r~and acx/? 7 7 272 Table 64 Egg-shaped Sewers flowing one-third full depth. Based on Kutter's formula with n =. .013. Values of factors a, c^/c and acVr 273 Table 65 Egg-shaped Sewers flowing full depth. Based on Kutter's formula, with n = .015. Values of the factors a, c\/r^aud ac\/r. 274 Table 66--Egg-shaped Sewers flowing two-thirds full depth. Based on Kutter's formula, with n = .015. Values of the , cv'r'and ac\/~275 Table 67 Egg-shaped Sewers flowing one-third full depth. Based on Kutter's formula, with n = .015. Values of the factors a, c\/r and ac-s/r~ , 276 Table 68 Giving Velocities and Discharges of Circular Pipes, Sewers and Conduits. Based on Kutter's formula, with n = .013 277 Table 69 Giving Velocities and Discharges of Egg-shaped Sewers. Based on Kutter's formula, with n = .013. Flowing full depth. Flowing f full depth. Flowing $ full depth 279 j> r ^ LIST OF ILLUSTRATIONS Page 1 Trapezoidal Channels 30 2 Rectangular Channel 30 3 V-Flume 30 4 Cross-section of Egg-shaped Sewer 230 5 Profile of Inverted Syphon 231 FLOW OF WATRR IRRIGATION CANALS AND Open and Closed Channels Generally. Article i. Introduction. Almost all the old hydraulic formulsG, given below, for finding the mean velocity in open and closed chan- nels have constant co-efficients, and are therefore correct, for only a small range of channels. They have often been found to give incorrect results with disastrous effects, as 011 the Rhone, in France, and the Upper Ganges Canal, India. The results of the gauging of large rivers, such as the Mississippi, by Humphrey and Abbott; the Irrawaddy, by Gordon; the Upper Ganges Canal, by Cunningham; small open channels, by Bazin and D'Arcy, and cast-iron pipes by D'Arcy, prove con- clusively the inaccuracy of the old formulae and the accuracy, within certain limits, of the formulae of Kutter, Bazin and D'Arcy. Ganguillet and Kutter thoroughly investigated the American, French and other experiments, and they gave, ,as a result of their labors, the formula now generally known as Kutter's formula. 2 FLOW OF WATER IN There are so many varying conditions affecting the flow of water, that all hydraulic formula) are only ap- proximations to the correct result, and the hest that an engineer can do is to use the most correct of all the known formulae. Major Allan Cunningham, R. E., carried out experi- ments, on a most extensive scale, lasting over four years, (1874-79), on the Upper Ganges Canal, near Roorkee, India. Major Cunningham states: '* " The main object of the undertaking was to interpo- late something between Mr. Bazin's experiments on small canals and the experiments on American rivers, chiefly with a view to discharge measurement on large canals, the proper measurement of such discharge being of great practical importance, but hitherto attended with much uncertainty. For any such work there are good opportunities in India from its system of canals, both large and small, pre-eminent among which is the Ganges Canal. ' The extensive scale of the operations can be judged from the following abstract: * "* * "The total number of velocity measurements was about 50,000, Besides these, there were many occasional special experiments, which together form an important addition. * * * " An important feature in this work is the great range of conditions and data, and therefore of results obtained, this being essential to the discovery of the laws of com- plex motion. Thus the velocity work was done at thirteen sites, differing much in nature, some being of brick, some of earth; in figure, some being rectangular, some trapezoidal; and in size, the surface-breadth vary- ing from 193 feet to 13 feet, and the central depth from * Recent Hydraulic Experiments in the Minutes of Proceedings of the Institution of Civil Engineer's, Volume 71. OPEN AND CLOSED CHANNELS. 3 11 feet to 8 inches. At one of the sites the ranges of some of the conditions and results were: central depth, from 10 feet to 8 inches; surface slope, from 480 to 24 per million; velocity, from 7.7 feet to 0.6 feet per-seeond; cubic discharge, from 7,364 to 114 cubic feet per second. * * * " After discussing various known formulae for mean velocity, the only ones that appeared worth extended trial were Bazin's * formulas for the co-efficients ft and 0, and Kutter's for the co-efficient C. Accordingly, the values of these co-efficients, from the published Tables, have been printed alongside the experimental mean serial values, seventy-six of /? and eighty-three of C. As to Bazin's two co-efficients (ft, C), the discussion shows that neither is reliable, and that the use of the former with surface-velocity leads to under-estimation of mean velocity, and that the latter is defective in not contain- ing s. As to Kutter's co-efficient (7, the discrepancies between the eighty-three experimental and computed values were: 11 Thirteen, over 10 per cent. " Five, over 7J per cent. " Fifteen, over 5 per cent. " Seventeen, over 3 per cent. " Thirty-three, under 3 per cent. " Now in all the discrepancies over 10 per cent., it was found that the state of water was unfavorable for the slope-measurement. Taking this into account, along with the varied evidence in Kutter's work, it seems fair to accept Kutter's co-efficient as of pretty general appli- cability; also that when the surface slope measurement is good, it will give results seldom exceeding 7J per cent, error, provided that the rugosity-co-efficient of the * "Eecherches experimentales sur Fecoulement de Feau dans les cauaux decouverts." 4 FLOW OF WATER IN formula be known for the site. For practical applica- tion extreme care would be necessary about the slope- measurement, and the rugosity-co-efficient could only be determined, according to present knowledge, by special preliminary experiments at each site. * " The accuracy of the D'Arcy-Bazin experiments, on which so much stress had been laid, had never been questioned. The suggestion that the failure of their co- efficients, when applied to the Roorkee results, was due to the disparity of proportions of the D'Arcy-Bazin canals, and the Ganges Canal, was very likely correct, and amounted to an admission of the want of generality of those co-efficients, as urged in 'the paper. * * " Much special experiment was done (with surface slope measurement), and with the definite result that Kutter's formula was the only one not requiring velocity measurement of pr?tty general applicability, and would under favorable conditions, give results differing by not more than 7J per cent., from actual velocity measure- ments. This was surely a definite and important re- sult," The above is conclusive as to the correctness of Kutter's formula. For small open channels D'Arcy and Bazin's formulae, and for cast-iron pipes D'Arcy's formulae, are generally accepted as being approximately correct. Engineers, who desire to keep up with the progress of Hydraulic Science, now generally use one or all of the formulae of Kutter, D'Arcy and Bazin, in prefer- ence to the old and inaccurate formulae formerly in universal use. The objection to the former formulas, however, is that they are in a form not adapted for rapid work, and that they are tedious and troublesome in application. The object of this work by the writer is to simplify and facilitate the application of these formulae, so as to OPEN AND CLOSED CHANNELS. 5 effect a great saving of both time and labor, which is a matter of great importance to an engineer in active practice. Article 2. The application of Kutter's Formula simpli- fied and facilitated by the use of the Tables. The plan on which the tables are constructed will be briefly stated here, and their use will be fully explained in Article 13. The solution of problems, relating to open channels given in this work, is similar to the methods given by the writer in No. 67 of Van Nostrand's Science Series (1883), entitled Hydraulic Tables based on Kutter's Form- ula, and also given in No. 84 (1886), entitled The Flow of Water in Open Channels, Pipes, Sewers and Conduits. The present work is based on the same principles, and is intended to facilitate and simplify the computations relating to Open Channels in a somewhat similar way to that already adopted for closed channels. Kutter's formula for measures in feet is: n and putting the first factor on the right hand side of the equation =c, we have: v.s = c X }r X Q = av = cXa \/r X j/s The factors on the right hand side of the equation are tabulated, for different grades and dimensions of chan- nel, and also for different surfaces of channel over which the water flows. The tables give the value of c, c-[/r, a, r } ]/r, a\/r and \/s. All that is then necessary, for the 6 FLOW OF WATER IN solution of any problem relating to open channels, is to find out in the tables the value of the factors for the channel under consideration, and to substitute these values in such of the formulae, 41 to 49, as may be suit- able for the work in hand, and then, by simple multi- plication and division, the solution of the problem can be quickly obtained. For example : Find the velocity in a channel having a bottom width of 18 feet, a depth of 2 feet, side slopes of 1 to 1, a grade of 1 in 1000 and -n=.0275. In Table 8 we find under a bed width of 18 feet, and opposite a depth of 2 feet, that \/rI.3. In Table 25, with n= . 0275, under a slope of 1 in 1000, and opposite V/'/'=1.3, we find the value of q/V=73.9. In Table 33, opposite 1 in 1000, we find \/~s=. 031623. Substituting the values of c\/r and v/s, in formula (41), we have: v ---= 73.9 X .031623 = 2.33 feet per second. This is a much quicker method than computing the velocity by working out Kutter's formula (40). Article 3. Formulae for Mean Velocity in Open Channels. In the following formulae and in what follows: v = mean velocity in. feet per second. t> max = maximum surface velocity in feet per second. v b = bottom velocity in feet per second. Q discharge in cubic feet per second. a = area of cross section of water in square feet. p = wetted perimeter or length of wetted border in lineal feet. w = width of surface of water in channel in feet. OPEN AND CLOSED CHANNELS. 7 r hydraulic mean depth in feet; = area of r = -- = < cross section in square feet, divided by ? ^ wetted perimeter in lineal feet. h = fall of water surface in any distance Z. I = length of water surface for any fall A. s = fall of water surface (h) in any distance (I) divided by that distance '== ~r= sine of slope. L / fall in feet per mile. c = co-efficient of mean velocity. ( the natural co-efficient depending on the nature , j = of the bed; that is, the lining or surface of the channel over which the water flows. g = acceleration of gravity = 32.16. The following extract on the value of g is from Mer- rimaii's Hydraulics: "The symbol g is used in hydraulics to denote the acceleration of gravity; that is, the increase in velocity per second for a body falling freely in a vacuum at the surface of the earth. * * * * " The following formula of Pierce, which is partly theoretical and partly empirical, gives the value of g in feet for any latitude Z, and any elevation e above the sea level, e being taken in feet: g = 32. 0894(1 -{-0.0052375 sin 2 Z) (1 0.0000000957e), and from this its value may be computed for any locality. " For the United States the practical limiting values are L == 49, e = 0; whence g = 32 . 186; L = 25, e = 10000 feet; whence g = 32.089. The value of the acceleration is taken to be, unless otherwise stated, g = 32.16 feet per second; 8 FLOW OF WATER IN from which the frequently recurring quantity j/% is found to be j/20 =8.02. "If greater precision be required, which will rarely be the case, g can be computed from the formula for the particular latitude and elevation above the sea." The following collection of formulae, for finding the mean velocity in open channels, is compiled from various authorities. It is believed that such a collection will be useful, not only for reference, but also for comparison of the old with the most modern and accurate formulae. It is also believed to contain almost all the formula} in general use at various times and places up to date. All the formulae are given in feet measures. D'Aubisson's Taylor's Downing's Beardmore's Leslie's Pole's formula for large ) -, ., . [i>= and rapid rivers } /1X (1) Leslie, for small streams: v = 68 j/rs (2) Stevenson, for streams over ) n/3 / /0 \ v = 96 yrs (3) 2,000 cubic feet per minute \ Stevenson, for streams under ) ac . \v = 69 i/T8 (4) 2,000 cubic feet per minute ) D'Aubisson, for velocities ) nr , /rx U = 95.6vAs (5) over 2 feet per second ) D'Aubisson : v = (8976 . 5rs + . 012) -- . 109 (6) Beardmore v = 94 . 2 \/rs (7) Eytelwein:v = 93.4 \/rs (8) OPEN AND CLOSED CHANNELS. 9 Eytelwein : v = (8975 . 43 r s + . 011589)* . 1089 ... (9) Neville, straight rivers with velocity \ ^ __ ^ 3 up to 1 . 5 feet per second ( _ Neville, straight rivers with velocity ) v __ 93 g /-; above 1.5 feet per second \ Neville. v = 140 ^/rs 11 f^rs (12) Dwyer:v = 0.92 \/2fr (13) This formula corresponds with v = 94 . 2 i/rs. Dupuit:=6 (r)*X(s)fc ........ (27) Ganguillet and K utter condemn Hagen's formulae as tl absolutely useless." Tanning's formula: v= . . (28) \ m j 2qrs and in =-- Humphrey's and Abbot's formula:- vc= .! 1 . 00816 + (225rj8*)> . 09&* I 2 ' 4 ^^- ..... (29) ( \ ) 1+1' 1 AQ Where 6= function of depth for small streams and v l = value of first term in expression for v. For rivers whose hydraulic mean depth exceeds 12 or 15 feet, b may be assumed to be 0.1856, which will make the numerical value of the term involving b so small that it may be generally neglected, reducing the above equation to ^={(22^18*)* .0388} 2 ...................... (30) Gauchler's formulae: When s is greater than .0007, that is greater than 1 in 1429, (;)*= 1.219XfciXr*XS* ....................... (31) When s is less than .0007, that is less than 1 in 1429 ............. ............. (32) OPEN AND CLOSED CHANNELS. 11 TABLE 1. Giving the values of the co-efficients, k lf k.,, to be em- ployed in Gauchler's formulae for canals and rivers and other open channels: NATURE OF CHANNEL. s greater than .0007 s less than .( Masonry, cut stone and mortar. . . From 8.5 to 10 " 7.6 " 8.5 From 8.5 8.0 to 9.0 " 8.5 Masonry sides; earth bottom " 6.6 " 7.6 " 77 "80 Small water-courses in earth free of weeds " 5.7 "6.7 " 70 " 7.7 Small water-courses in earth, grass on slopes . " 5.0 "5.7 6.6 " 7.0 Rivers Nil 6.3 " 7.0 Molesworth's formula: v = \/kr8 TABLE 2. Giving the value of the co-efficients k in Molesworth's formula for canals and rivers. NATURE OF CHANNEL. VALUES OF k FOR VELOCITIES. Less than 4 feet per second. More than 4 feet per second. Brickwork 8800 8500 Earth 7200 6800 Shingle . ... 6400 5900 Rough, with bowlders.. . . 5300 4700 In very large channels, rivers, etc., the description of the channel affects the result so slightly that it may be practically neglected, and assumed=from 8,500 to 9,000. Bazin's formulae: For very even surfaces, fine plastered sides and bed, planed planks, etc v= J 1-^.0000045 (34) 12 FLOW OF WATER IN For even surfaces, such as cut stone, brickwork, un- planed planking, mortar, etc.: v = -Jl-i-. 000013 (4. 354+-^ XiA*.. . (35) \ \ r/ For slightly uneven surfaces, such as rubble masonry: < i/rx (36) For uneven surfaces, such as earth: v = Jl--. 00035 ^0.2438 +- - - W vA* ............ (37) A modification of Bazin's formula (37), known as D'Arcy Bazin's: (38) . .08534r +0.35 Brandreth's modification of Bazin's formula (37) is: 2r X V / / .......................... (39) V/7 + 1.7066r where /= fall in 5,000 feet, which is the length of the old English mile, now used on Indian irrigation canals. Kutter's formula is: (' 1^1+41. n v = / X\/T8 (40) and calling the first term of the right-hand side of the equation equal c, we have Chezy's formula: v=cX\/rs = c X v/^X V~* (41) ^==---- (42 > OPEN AND CLOSED CHANNELS. x V -\/ s 13 (43) V d / .... cyr _ ( - ... Y . (44) Vr/ Now <2=av=aXcv/rX\/8" ) . (45) ==a t/FXcXv/* ) :'...= . (46) r acv/r - ^ . (47) i/s v/<- . (48) ac\/f / V . (49) \ac\/ T / ,_ F Q . (50) X \/s a \/r X Article 4. Remarks on the Formulae. Most of the old formulae have constant co-efficients, and therefore give accurate results for only one channel, having a hydraulic mean radius of a certain value. Only four of the authorities, whose formula are given in Article 3, have taken into account the nature of the material forming the surface of the channel. These are Gauchler, Bazin, Molesworth and Kutter. The value of the co-efficients in Bazin's formulae depends on the nature of the surface of the material over which the water flows, and also the hydraulic mean depth. These co-efficients are not affected by the slope. For small channels of less than 20 feet bed Bazin's formula, for earthen channels in good order, gives very fair results, and tables based on it have been used by the Irrigation Departments in Northern India, for com- 14 FLOW OP WATER IN puting the velocities in the distributing channels (raj- buhas), but Kutter's formula is superseding it there, as in almost all other countries where its accuracy has been thoroughly investigated. The formulae of Gauchler, Molesworth and Kutter have varying co-efficients, which depend for their value on three things : The hydraulic mean depth, The slope or grade of bed, and The nature of the surface of the material, or the wetted peimeter, over which the water flows. The following table shows the value of c, in Kutter's formula, for a wide range of channels in earth, that will cover anything likely to occur in the ordinary practice of an engineer. TABLE 3. Values of c for earthen channels by Kutter's formula. Slope B =.035 ^/r in feet. v'V in feet. I in 0.4 1.0 1.8 2.5 4.0 ! 0.4 1.0 1.8 2.5 4.0 c c c c c c c c c c 1000 35.7 62.5 80.3 89.2 99.9 19.7 37.6 51.6 59.3 69.2 1250 35.5 62.3 80.3 89.3 100.2 19.6 37.6 51.6 59.4 69.4 1667 35.2 62.1 80.3 89.5 100.6 19.4 37.4 51.6 59.5 69.8 2300 34.6 61.7 80.3 89.8 101.4 19.1 37.1 51.6 59.7 70.4 3333 34. 61.2 80.2 90.1 102.2 18.8 36.9 51.6 59.9 71.0 5000 33. 60.5 80.3 90.7 103.7 18.3 36.4 51.6 60.4 72.2 7500 31.6 59.4 80.3 91.5 106.0 17.6 35.8 51.6 60.9 73.9 10000 30.5 58.5 80.3 92.3 107.9 17.1 35.3 51.6 60.5 75.4 15840 28.5 56.7 80.2 93.9 112.2 16.2 34.3 51.6 62.5 78.6 20000 27.4 55.7 80.2 94.8 115.0 15.6 33.8 51.5 63.1 80.6 All inspection of the tables will show the difference in the value of c, caused by the difference in slope, and also of hydraulic mean depth. It shows, for instance, that OPEN AND CLOSED CHANNELS. 15 with n = .0225 and a slope of 1 in 1000 the value of c corresponding to \/r = 0.4 is 35.7, while the value of c corresponding to ]/r === 4.0 is 99.9, or an increase of about 180 per cent. By the old formulae the channel, with the small hydraulic mean depth, would have the same co-efficient as the larger channel, and would there- fore give very inaccurate results. We also see that with the same \/r = 4.0, the value of c for a slope of 1 in 1000 is 99.9, and the value of c for a slope of 1 in 20000 is 115.0, or an increase of about 15 per cent., while with \/r = 0.4 there is a decrease from 35.7 to 27.4, or a decrease of about 23 per cent. We again find that when \/r = 1.8 (which is the near- est value of i/rto 1.811) the co-efficients for the same value of n are the same for all slopes ; that when \/r has a less value than 1.8 the co-efficients increase with an increase of slope, and when \/r has a greater value than 1.8 the co-efficients increase with the decrease of slope. D'Arcy's formuke will be referred to in the Article on the Flow of Water in Pipes, etc . Article 5. Bazin's Formula for Channels in Earth. For small channels in earth in moderately good order Bazin's formula (37) gives a tolerable close approxima- tion to the mean velocity. Table 30, giving mean velocities and discharges up to 20 feet bed width, was computed for the Punjab Irriga- tion Department by Captain Allen Cunningham, E. E. The table was computed by a modification of Bazin's formula (37) given by Captain A. B. Brandreth, R. E., for channels whose beds and sides are of earth.* * Volumes 4 and 5 of 'Second Series of Professional Papers on Indian Engineering. 16 FLOW OF WATER IN This modified form formula (39) was adopted, as it was better suited for computation of tables than Bazin's formula (37). This formula is: 2r x i/y , 7+ 1.7066 r where /is the fall in 5,000 feet, in feet. The length of the old English mile now used on Indian canals is 5,000 feet. In order to show how the modified form of Bazin is derived, it is given below. Bazin's formula for earthen channels is: 1 1\ X l/rs .00035 + (.2438 + -\ ) but y'rs = i/r X J * = 2 v/7- X J-^ \ 5000 \ 20000 substitute this value of -\/r8 and reduce and *J I xVrX J '' \ .00008533 ? + .00035 \ 20000 2r X i// V/7 -{- 1.7066 r Article 6. Comparing Kutter's and Bazin's Formulae. The following table gives a comparison between the results obtained by Bazin's formula (37) for earthen channels, and Kutter's formula with ?i .025 and n .0275, and it shows that, for the given channels, Bazin's formula agrees very nearly with Kutter n = .0275 up to 3 feet in depth, and with Kutter n = .025 from 3 to 5 feet in depth. It is also shown that Bazin's formula is almost a mean between Kutter with n = .025, OPEN AND CLOSED CHANNELS. 17 and n = .0275; that is, that it almost suits canals and rivers in earth of tolerably uniform cross-section, slope and direction, in moderately good average order and regimen and free from stones and tceeds, and also canals ancljriverft in earth beloiv the average in order and regimen. The results again show that it gives too low a velocity for canals in earth above the average in order and regimen with n = .0225 or a less value of n, and it further shows that it gives too high a velocity for canals and rivers in earth, in rather bad order and regimen, having stones and weeds occasionally, and obstructed by detritus, n = .030. Bazin's formula (37) gives correct results for earthen channels with only one value of n, while Kutter's formula is suited to any channel having either a very rough, medium or very smooth surface. TABLE 4. Giving the velocity and discharge of earthen channels ac- cording to the formulae of Bazin and also Kutter. v mean velocity in feet per second. Q = discharge in cubic feet per second. Bed width 10 feet. Side slopes 1 to 1. Slope 1 in 2500. <^/7= .02. B i ?i ffi* [ i Bazin, for Earthen Kutter, Kutter, & ^ P" CD P ^ Channels. ! n = .025 n = .0275 P" a 02 \/r ? ^ fll r*" CD : ^" ; v Q ; v Q v Q 1.0 11.00 0.858 0.93 0.83 9.17 0.97 10.67 0.87 9.57 1.5 17.25 1.211 .10 1.14 19.63| 1.26 21.73 1.14 19.66 2.0 24.00 1.533 .24 1.40 33.56 1.51 36.24 1.36 32.64 2.5 31.25 1.831 .35 1.63 50.85 1.72 53.75 1.56 48.75 3.0 39.00 2.110 .45 1.83 71.48 1.91 74.49 1.73 67.47 3.5 47.25 2.375 .54 2.02 95.46 2.08 98.28 1.89 89.30 4.0 56.00 2.628 .62 2.19 122.81J 2.24 125.44 2.03 113.68 4.5 65.25 2.871 .70 2.35 1153. 611 2.39 155.95 2.17 141.59 5.0 75.00 3.107 .76 2.51 !l87.91!| 2.53 189.75 2.29 1171.75 1 ! i i i i 18 FLOW OF WATER IN Bed width 20 feet. Side slope 1 to 1. Slope 1 in 2500. x/ = -02. B" & CD |i 5' 3^ * Baziii, for Earthen : Channels. Kutter, n = .025 Kutter, n .0275 V Q V Q V g 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 21.00 32.25 44.00 56.25 69.00 82.25 96.00 110.25 125.00 0.920 1.330 1.715 2.078 2.422 2.751 3.066 3.369 3.661 0.96 1.15 1.31 1.44 1.55 1.66 1.75 1.83 1.91 0.89 1.24 1.54 1.81 2.05 2.28 2.48 2.67 ! 2.85 18.66 39.85 67.74 101.80 141.68 187.15 238.03 294.21 555.64 \ 1.02 1.36 1.64 1.89 2.12 2.32 2.50 2.67 2.83 21.42 43.86 72.16 106.31 146.28 190.82 240.00 294.37 353.75 0.91 1.22 1.48 1.71 1.91 2.10 2.27 2.43 2.58 19.11 39.34 65.12 96.19 131.79 172.72 217.92 267.91 322.50 Article 7 Value of n. The accuracy of Kutter's formula depends, in a great measure, on the proper selection of the co-efficient of roughness n. Experience is required in order to give the right value to this co-efficient, and, to this end, great assistance can be obtained in making this selection, by consulting and comparing the results obtained from experiments on the flow of water already made in dif- ferent channels. In some cases it would be well to provide for the con- tingency of future deterioration of channel, by selecting a high value of n, as, for instance, where a dense growth f weeds is likely to occur in small channels, and also where channels are likely not to be kept in a state of good repair. Table 5, giving the value of n for different materials, is compiled from Kutter, Jackson and Hering, and this value of n applies also, in each instance, to the surfaces of other material equally rough. OPEN AND CLOSED CHANNELS. 19 Table 5. Giving the value of n for different channels. 7i = .009, well-planed timber, in perfect order and align- ment; otherwise, perhaps .01 would be suitable. n .010, plaster in pure cement : planed timber ; glazed, coated, or enamelled stoneware and iron pipes ; glazed surfaces of every sort in perfect order. n = .011, plaster in cement with one-third sand in good condition; also for iron, cement, and terra-cotta pipes, well joined and in best order. n = .012, unplaned timber, when perfectly continuous on the inside; flumes. 7i = .013, ashlar and well-laid brickwork ; ordinary metal; earthenware and stoneware pipe in good condition, but not new ; cement and terra-cotta pipe not well jointed nor in perfect order; plaster and planed wood in imperfect or inferior condi- tion ; and, generally, the materials mentioned with n .010, when in imperfect or inferior con- dition. 9 < 65 0048751 4 36 98 01190 23 6 triangular 45.. . . rectangular 0.65 0.65 0.004655 0022136 4.36 6 5 1.87 85 0.0119 13 7 52 004889 6 5 6 0119 8 46 0081629 6 5 52 0115 9 72 0014678 6 5 91 0129 10 46 0058744 6 5 55 0117 11 42 0083805 6 5 49 0114 18 19 0.65 49 0.0045988 0042731 3.9 2 6 0.91 82 0.0114. 0114 *>0 32 0059829 1 6 62 0114 27 RAMMED GRAVEL f- to i inches thick semi- circular 75 0013639 3 28 1 34 0163 4 | to inches thick rect- angular 0.65 0049736 6 85 0170 12 13 14 15 16 17 1 ? BATTENS PLACED 1 inch apart rectangular (( < < i f 2 inches ' ( i < < Ashlar rectangular . . 0.75 0.55 0.49 0.95 0.69 0.63 1 77 0.0014678 0.0059664 0.0088618 0.0014678 0.0059976 0.0088618 0008400 6.4 6.4 6.4 6.4 6.4 6.4 8 5 1.01 0.65 0.59 1.31 0.88 0.78 3 0.0149 0.0147 0.0149 0.0208 0.0211 0.0215 0133 3 39 Brickwork rectangular . . Ashlar 0.55 59 0.0050250 0081 3.0 3 9 0.65 85 0.0129 0129 32 RUBBLE, Rather damaged rectan- gular.. 52 10076 5 9 63 0167 FLOW OF WATER IN TABLE 5. (Continued.) SERIES OF BAZIX. r in feet. s Breadth at water sur- face in feet Depth in feet. n No. 33 EUBBLE, Rather damaged rectan- gtila,r . 65 036856 5 9 88 0170 1.4 1.3 1.6 1.5 44 Rather damaged new... . With deposits on the bed, rectangular 0.63 0.72 0.82 0.88 1 47 0.060 0.029 0.014 0.0122 00032 3.28 3.28 3.28 3.28 6 56 0.95 1.18 1.54 1.60 2 62 0.0180 0.0184 0.0182 0.0192 0204 46 35 With deposits on the bed, rectangular Damaged rubble trape- zoidal 1.31 1 21 0.00032 0.014221 6.56 4.9 2.29 2.29 0.0210 0.0220 OTHER OBSERVATIONS : Gontenbachschale, new rubble semi -circular . . G'rumbachschale semi- circular, damaged Gerbebachschale semi- circular, damaged 0.32 0.46 0.19 0.044 0.09927 0.168 5.5 8.5 3.7 59 0.82 0.29 0.0145 0.0175 0.0185 Alpbachschale semi-cir- cular, much damaged . . Marseilles Canal 0.72 2 87 0.0274 00043 8.2 19.6 1.18 4.4 0.0230 . 0244 Jard Canal I 97 . 0004 19.6 4.4 0.0255 Chesapeake Ohio Canal . . Canal in England .. 3.7 2 43 0.000698 000063 22.6 17 7 7.9 3 9 0.033 0184 Lanter Canal, at Newbury Pannerden Canal, in Hol- land 1.81 10 2 0.000664 000224 29.5 558. 1.8 9.8 0.0262 . 0254 Canal of Marmels 2 31 0005 26 2 2 6 0301 Linth Canal 7 8 0.00034 123. 10.8 0.0222 Hiibengraben 6 0013 4 8 8 0237 Hockenbach 87 000787 11 1 1 1 0.0243 Speyerbach . 1 46 000667 16.4 1.9 0.0260 Mississippi. . 65 6 000667 2493. 16.4 0.0270 Bayou Plaquemine 16 8 0.00017 275. 25.6 0.0294 Bayou La Fourche 13 1 00004 220 23 o 0200 Ohio, Point Pleasant Tiber, at Rome 6.7 9.4 0.000093 0.00013 1066. 239. 7.9 14.8 0.0210 0.0228 Newka . 17 4 000015 886. 21 0.0252 Newa 35 4 0.000014 1214. 19.7 0.0262 Weser 9.5 0.0002 394. 9.8 0.0232 Elbe . 10.9 0.00031 315. 43.6 0.0285 Rhine, in Holland 12.4 0.00015 1312. 14.7 0.0243 Seine at Paris 12 1 0.000137 0.025 Seine at Poissy 13.4 0.00007 0.026 Saone at Raconnay 11 8 00004 0.028 Haine . . 5.2 0.0001 0.026 OPEN AND CLOSED CHANNELS. 23 TABLE 5. (Continued.) SERIES OF BAZIN. r in feet. s Breadth at water sur- face in feet Depth in feet. n CHANNELS OB TRUCTED BY DETKITU3. Rhine, at Speyer 9 7 000112 1440 9.7 026 Rhine at Germersheim 10.8 000247 748 0.0227 Rhine, at Basle 6.9 0.001218 660 9.1 0.03 Lech 3.1 0.00115 157 3.8 . 022 Saalach . 1 4 0011 68 2 1 027 Salzach.. 4 1 0012 38 11 8 028 Issar 3.9 0025 164 4 4 0305 Escher Canal 4.0 003 72 4 9 03 Plessur 3.5 00965 42 4 6 027 Rhine, at Rhiuewald .79 0142 14 .99 031 Mosa, at Misox Rhine, at Domleschgerthal . . . Simme, at Leuk .... 1.2 1.9 1.6 0.01187 0.0075 0.0105 13 16 1.3 2.4 0.031 0.035 0.0345 In order to show to what extent the value of n affects the velocity and discharge of channels, two examples are given in table 6. TABLE 6. Showing the effect of the co-efficient of roughness n on the velocity in channels. Value of Bed width in feet. Depth in feet Side Slopes. Grade in feet per mile. Mean velocity in feet Discharge in cubic feeb per : per second. second. .0225 10 2 1 to 1 '. " 8 3.32 79.7 .025 10 2 8 2.96 71.0 0275 10 2 8 2.67 64.1 .03 10 2 8 2.43 58.3 .035 10 2 8 2.05 49.2 .0225 80 5 Hto l 2 3.49 1527. .025 80 5 2 3.15 1378. .0275 80 5 2 2.87 1256. .03 80 5 2 2.64 1155. .035 80 5 2 2.28 998. In the first channel with a bed-width of 10 feet, the difference in results shows that with a value of n = .0225 the channel has a discharge of over 60 per cent, more than when its value of ?i = .035. This shows the great necessity of keeping small irrigation channels clear of 24 FLOW OF WATER IN sand bars, brush, weeds, grass and other obstructions to the flow. Again, in the larger channel with a bed-width of 80 feet, the difference in results, obtained from the highest and lowest values of n, given in table 6, shows a varia- tion of over 53 per cent, in the velocity and discharge. It is shown that the smaller the channel the greater is the percentage of loss by keeping it in a bad state of repair. Article 8. Side Slopes. Tables 8, 9, 11 and 13 are computed for channels hav- ing side slopes of 1 to 1, 1 to 1, 1| to 1, and vertical or rectangular. When the bed width is greater .than 60 feet, the side slopes have very little effect on the velocity. Table 7, given below, well exemplifies this. Six channels are given, with varying bed widths, depths and grades, and each channel has five different side slopes. On inspec- tion, it will be seen that the change in the side slope makes no appreciable change in the velocity so long as the bed width, depth and grade or longitudinal slope remains the same. For instance, with a bed width of 70 feet, a depth of 1 foot, and a slope of 1 in 5000, the mean velocity is 0.74 feet per second for the five side slopes. Again, with a bed width of 300 feet, a depth of 14 feet, and a grade of 1 in 20,000, the mean velocity varies so little that it is substantially the same for the five channels, the greatest velocity being 2.35 feet per second, and the least velocity 2.32 feet per second. The table shows, however, that the discharge is increased with the increased flatness of the slopes. In Table 8, with side slopes of 1 to 1, the values of the factors a, \/r and a\/r are given for channels up to OPEN AND CLOSED CHANNELS. 25 a bed width of 300 feet. In Tables 9, 11 and 13, the values of these factors are given only for channels up to a bed width of 60 feet. For all channels having a greater bed width than 60 feet, and side slopes differeitt-fr-orn 1 to 1, the velocity can be found for a channel with the same bed width, but with side slopes of 1 to 1, and this will be the velocity required. To find the discharge, this velocity can be multipled by the area of channel. For example, let the velocity and discharge be required for a channel Jiaving a bed width of 160 feet, depth of 10 feet, a grade of 1 in 15,840, or 4 inches per mile, and with n = .025, and side slopes of li to 1. As the tables do not give the value of the factors for a channel of these dimensions with side slopes H to 1, let us look out, in Table 8, the value of ]/r for a similar channel, but with side slopes of 1 to 1, and we find that it is equal to 3.005. Now the actual value of \/r for a side slope of 1J to 1 is equal to 2.988, so that, practically, the value given in Table 8 is correct. Now, working out the velocities, we find that side slopes of 1 to 1 give a mean velocity of 2.09 feet per sec- ond, and side slopes of 1J to 1 give a velocity of 2.08 feet per second, as shown in Table 7. The discharge, however, is increased in proportion to the increase of area of the channel by the increased flatness of the slopes. This is shown by the last column of Table 7, showing the discharge of the channels. In the instance just given, Table 7 shows that with side slopes of 1 to 1 the discharge is 3553.7 cubic feet per second, but with side slopes of 1J to 1 the discharge is 3631.3 cubic feet per second. 26 FLOW OF WATEK IN TABLE 7. Showing the velocity and discharge of channels having different side slopes. ?i=.025. Bed 70 feet. Depth 1 foot. Slope 1 in 5,000. n=.0'25. CROSS SECTION n r Vr c-v/r Vs Velocity in feet per second. Discharge in cubic feet per second. Eectangular 70.0 0.972 0.986 52.438 .014142 0.7415 51.91 I to 1 70.5 .976 .988 52.604 .014142 0.744 52.45 I to 1 71.0 .975 .987 52.521 .014142 0.743 52.75 Hto l 71.5 .971 .986 52.438 .014142 0.742 53.05 2 to 1 72.0 .969 .983 52.189 .014142 0.738 53.14 Bed 70 feet. Depth 6 feet. Slope 1 in 5,000. n = .025. CROSS SECTION a r V'r c\/r vA Velocity in feet per second. Discharge in cubic feet per second. Rectangular i to 1 420 438 5.122 5 258 2.263 2 293 179.504 182 744 .014142 014142 2.5385 2 5844 1066.2 1132 1 to 1 . 456 5 243 2 289 182 312 014142 2 5782 1175 7 H to 1 . 474 5 172 2 270 180 260 014142 2 5492 108 3 2 to 1 492 5.081 2.254 178.532 .014142 2.5248 1242.2 Bed 160 feet. Depth 2 feet. Slope 1 in 15,840. ?* = .025. ! Velocity in Discharge CROSS SECTION I a r Vr cVr ^/ s \ feet per | second. feet per second. Rectangular 320 1.951 1 . 397 89.715 .007946 0.7129 228.1 i to 1 322 1.958 1.413 91.074 .007946 0.7237 233.0 1 to 1 324 1.956 1 . 398 89.810 .007946 0.7136 231.2 1| to 1 326 1.950 1 . 396 89.620 .007946 0.7121 232.1 2 to 1 328 1.942 1.393 89.335 .007946 0.7099 i 232.8 Bed 160 feet. Depth 10 feet. Slope 1 in 15,840. n = .025. j - " Velocity in Discharge CROSS SECTION CL T Vr cVr Vs feet per second. in cubic feet per second Rectangular 1600 1650 8 889 9.048 2.981 3.008 260.334 263.420 .007946 .007946 2.0686 2.0931 3309.8 3453.6 1 to 1 1700 9.029 3.005 263.075 .007946 2.0904 3553.7 H to 1 ..... 1750 8,926 2.988 261.132 .007946 2.0750 3631.3 2 to 1 1800 8.793 2.965 258.510 . 007946 2.0541 3697.4 OPEN AND CLOSED CHANNELS. 27 Bed 300 feet. Depth 2 feet. Slope 1 in 20,000. n= .025. " ! ' Velocity in; Dtachajge CROSS SECTION a \ r \/r c^/r Vs feet per second. ill CUBIC feet per second. Rectangular 600 1.974 1.405 90.490 .007071 0.6399 "38T.9 | to 1 602 1.977 1.406 90.588 .007071 0.6405 385.6 1 to 1 604 1.976 1.405 90.490 .007071 6399 386.5 Uto 1 .... 606 1 . 973 1.404 90.384 .007071 0.6391 387.3 2 to 1 608 1.968 1.403 90.294 .007071 0.6385 388.2 Bed 300 feet. Depth 14 feet. Slope 1 in 20,000 n == .025. CROSS SECTION & ^ ^/r c\/r \/s Velocity in feet per second. .Discharge in cubic feet per second. Rectangular 4200 12.835 3.583 330.594.007071 2.3376 9818 | to 1 . 4298 12.973 3.600 332.600.007071 2.3518 10108 1 to 1 i 4396 12.940 3.597 332. 246;. 007071 2.3493 10328 H to 1 4494 12.823 3.581 i 330. 358 '.007071 2 . 3360 10498 2 to 1 4592 12.664 3.560 327.8801.007071 2.3184 10646 Article 9. Open Channels Having the Same Velocity. Channels having the same slope, the same value of n, and also the same value of ]/r } have the same velocity. For example, a channel 70 feet wide on hot torn, depth of water 4 feet, side slopes 1 to 1, grade 1 in 1,544, and n = .03, has a mean velocity of 2.98 feet per second. The \/T of this channel will be found in Table 8, = 1.9, and if we examine this table we find channels of the following dimensions that have the same value of V/r, and therefore the same velocity. Bed 70 feet, depth 4 feet, \/r = 1.9 Bed 45 " 4.25 " i/r = 1.9 Bed 25 " " 4.75 " .\/r = 1.9 Bed 20 " " 5 " ^ = 1.9 Bed 14 " " 5.50 " /r = 1.9 28 FLOW OF WATER IN These five channels have the same velocity. They have, however, different discharges, varying with the area of each channel. Channels having the same velocity can also be found having side slopes of J to 1 and 1J to 1, and also rectangular in section. Article 10. Open Equivalent Discharging Channels. Channels having the same, or nearly the same, value of i/r and a have the same discharging capacity. For example, a channel having a bed width of 12 feet, depth 3 feet, side slopes of 1 to 1, a grade of 5 feet per mile, and n = .0275, has a discharge of 123.75 cubic feet per second. Now all channels with the same area, 45 square feet, and the same value of \/r = 1.482, will have the same discharge when s and n are the same. An inspection of Table 8, with side slopes of 1 to 1, will show channels of a nearly equivalent discharge, thus: Bed 10 feet, depth 3.25 feet, \/r = 1.498, a = 43 Bed 15 " " 2.75 " ^/r = 1.464, a = 48.8 Again, a depth or width being first given, the corres- ponding width or depth to give the required discharge can be found after a few trials. Article n. Interpolating. In tables 15 to 27 inclusive, there is given a column headed " diff.", which gives the differences of c and c \/r, equivalent to a difference of value = .01 in j/V, and this column will be found useful in interpolating values of c and c \/r between those given in the tables. For instance, we have a channel which has a grade of 1 in 1000, its value of n = .02 and \/r= 1.44, and we want the value of c corresponding to this value of y/r. OPEN AND CLOSED CHANNELS. 29 In Table 22, n = .02 and under a slope of 1 in 1000, the nearest value to \/r = 1.44 that we find is 1.4, and the value of c opposite this 82.6. The column of differ- ences shows that for a value of \/r = .01 the correspond- ing value of c =.22, therefore .22x4 = .88 has to be added to 87.6 thus: \/r =1.4 and corresponding value of c = 82.6 I/V = 0.04 and corresponding valve of c = 0.88 . \ |//' == 1. 44 and corresponding value of c = 83.48 Frequently in the examples, in order to avoid long explanations, it is proposed to find the value of c or c y/r, equivalent to a value of \/r not given in the tables, but it is understood that the method of interpolation, just explained, is intended to be used to find the values of c and c \/r. Article 12. Preliminary Work. In the examples given below, the values of the fac- tors are in some cases taken to several places of decimals. Where strict accuracy is not required, as in preliminary designs, interpolation may be omitted and the compu- tations can be still further reduced by working to fewer places of decimals. For instance, at the end of Example 3, we have: Q = a \/r X c X vA = 729.5 X 81.4 X .016854 = 1000 cubic feet per second. Instead of taking a \/r = 729.5 le.t us omit decimals and take it = 729, and in table 23 with n = .0225 under a slope of 1 in 3333 and opposite \/r = 1.9 we find, 30 FLOW OF WATER IX omitting decimals that c = 82, and for 1 in 3520 let us take v/ = .0168 instead of .016854. Substituting these values in formula (45) we have: Q = 729X 82 X .0168 = 1004 cubic feet per second, being in excess less than one-half of one per cent, which is near enough for preliminary work for all practical purposes. V-FLUME. Article 13. Explanation and Use of the Tables. After the dimensions, slope, etc., of the channel have been determined by the use of the Tables, it is advisa- ble, in order to take every precaution to obtain accuracy, that, as a final check, the work should be computed by Kutter's formula (40). OPEN AND CLOSED CHANNELS. 31 EXAMPLE 1. To find mean velocity and discharge of a canal. Required the mean velocity and discharge of a canal having a bed width of 70 feet, a depth of water of '4~feBt, with side slopes of 1J to 1, a longitudinal slope or grade of 1 in 1544, and with the co-efficient of the surface of the material of the bed =.03. State also the quantity of land this canal will irrigate, the duty of water being 190 acres per cubic foot per second. The velocity and discharge may be found by three methods: First, by arithmetic. Second, by logarithms. Third, by the tables in this work. We will compute the above example by each of these methods. 1. Computing by arithmetic: s = 1544 == .000647668, and v/* = .025449. In Table 33 of slopes, the value of s and \/s can be found quickly by inspection. Area of water section = (70H-6)X4=304 Perimeter of water section 70+2 X v/6 2 +4~ 2 --=84. 42 fy r\ A Hydraulic mean depth r= =^. ^==3. and yr y^.601 = 1.9 K utter 's formula is: 1.811 .00281 32 FLOW OF WATER IN Substituting the values of n, s and r above given, in this formula, we have: , ^ ^ , -00281 .03 X i/3.6 X. 000647668 Computing this equation we find v=2.98 feet per second; and Q=2.98X 304=906 cubic feet per second. 2. Computing by logarithms: First, we compute the value of each term in the nu- merator of the large parenthesis, and take their sum. Second, we compute the value of each term in the de- nominator, and take their sum. Third, find the value of numerator divided by denom- inator, and this is equal to c. Fourth, find the value of \/rs and multiply it by e, and this last result is equal to v. From log 1.811= 0.2579 Deduct log .03 = -2.4771 1.7808 log of 60.370 The second term is 41.600 From log .00281 =3.4487 Deduct log .0006477 = 4.8114 0.6373 log of.. 4.338 .*. Numerator in large parenthesis 106.308 For the denominator we add the values already found of the second and third terms of the numerator: OPEN AND CLOSED CHANNELS. 33 41.600+4.338=45.938=45.94 nearly, and log of 45.94 = 1.6622. From log .03 -2.4771 deduct log 3.601--2 = 0.2782 =2.1989 -1.8611- log of 0.7262 Add first term in denominator.. .1.000 1.7262 106.308 Andc = As v=q/V, we have now to find value of \/rs log 3.601 0.5564 log .0006477= -4.8114 -3.3678 and this-f-2= 2.6839, the number corresponding to which is ,0483=i/rs .-. v=cvAvs=61. 59 X. 0483 = 2.975 feet per second. Q=aX?;=304x2.975=904.4 cubic feet per second 3 Computing by tables in this work. Look out, in Table 11, under bed width 70 feet, and opposite depth 4 feet, and we find a=304, r=3.601, j/V = 1.9, a-\/r = 578. Look out, in Table 26, where 7i = .03 and ] >=1.9, and under the slope 1 in 1666 (which is the nearest slope to 1 in 1544), and we find c=61.6, and q/r= 117.0. In Table 33 the nearest slope to 1 in 1544 is 1545, and the \/* of 1545 -=.025441. Sub- stitute the values of c\/r and \/ s in formula (41), v=c\/rX\/s and we have v=117x. 025441=2.98 feet per second. Q=va=2. 98X304=906 cubic feet per second. 34 FLOW OF WATER IN Now, as a check on this, we substitute the values of the other factors given, and we have =61. 6X1.9X. 025441 = 2. 99 feet per second. Q=cXa v / rX\/s =61. 6X578X. 025441=906 cubic feet per second. As each cubic foot per second will irrigate 190 acres of land, we have 906X190 = 172,140 acres, the area which the canal can irrigate. This example shows the great saving of time and labor effected by the use of the tables, and with the additional advantage of having a check on the accuracy of the work. EXAMPLE 2. Given the discharge, bottom width and depth to find the grade of channel. A canal is designed to discharge 410 cubic feet per second. It is to be 30 feet on bed, 4 feet deep, with side slopes of 1 to 1. What is the grade necessary to pro- duce the given discharge, the value of n being .025 ? First method : The area of section=136 square feet, and Q 410 "=== 3 feet ' Look out, in Table 8, under a bed width of 30 feet and a depth of 4 feet, and we find \/r = 1.81. In Table 32, with a value of ?i=.03, the slope of 1 in 13,23 is found in a channel of the given dimensions to produce a velocity of 3 feet per second. Now, in Table 24, with 7i=.025, and under a slope of 1 in 1250, w r hich is the nearest slope to 1323, and op- posite y / r=1.8, we have c=72.3; and similarly, in Table 26, with n = .03 we have ci = 60.2. OPEN AND CLOSED CHANNELS. 35 But I : li : : c-f : and between slopes 1 in 2500 and 1 in 3333, we interpolate, and find the value of c to be = 95, and c X \/r=95X3.03 = 287.85. Now, formula (43), l/^^^ Look out, in Table 33 of slopes, and opposite y / .s= .019104, the nearest one in the table to .019107, we find the slope to be 1 in 2740, which is the slope required. EXAMPLE 5. Given the discharge, velocity and grade of a channel, to find the bed icidth and depth. What must be the bed width and depth of a canal to discharge 300 cubic feet per second, at a mean velocity of 2 feet per second ? The side slopes are 1J to 1; in- clination, 16 inches to the mile; and ?i=.025. OPEN AND CLOSED CHANNELS. 39 In Table 33, we find 16 inches in a mile = a slope of 1 in 3960, and also v/s=. 015891. Q 300 By formula (46), a= -^-^ISO square feet. By formula (42), ^=--=- = Look out now, in Table 24, with n = .025, and under slope 1 in 3333 (which is nearest to 1 in 3960), and we get cv/r=119.9, value of y^l.7 cv/r=130.1, value of |A' = l-8 Therefore for cv/r=125.9, value of \/r may be taken at 1.75. .-. a X i/r=150 X 1.75 = 262.5 Look now in Table 11, and under the same bed width for a value of v/Y=1.75, and a;/V 262.5, and we find the nearest values of these factors to be, under a bed width of 35 feet and depth 3.5 feet, v/?=1.72, and a\/r =,242.4; and, depth 3.75 feet, v/r=1.77, and a\/r= 269.6. Now ?.62.5 242.4=20.1, and 269.6242.4=27.2. .\ 27.2 : depth .025 :: 20.1 : .19, the required increased depth, approximately, over 3.5 feet is 0.19 feet. The approximate depth is therefore 3.5 + 0.19 = 3.69 feet As a check, we will now find the discharge with this depth, 3.69 feet, and a bed width of 35 feet. The area of section = 149.57 square feet. The perimeter = 48.01. a 149.57 The value of r= = 48 Q1 =3.1154. And v/?=1.77. 40 FLOW OF WATER IN In Table 24, with n = .025, and under a slope of 1 in 3333, we find, when V/r=1.7 , that c=70.5 and by interpolation, y 7 ?' 0.07, that c= 1.3 and .-. \/r=1.77, that c = 71.8 Now substitute values of c, y^' } and \/s, in formula (41) t'==c X \/r X v/, and we have: v=71.8 X 1.77 X .015891 = 2.0195 feet per second; and Q=av=149.57 X 2.0195=302 cubic feet per second. This is near enough for most purposes, but if the ex- act dimensions be required, one square foot can be taken off the area by diminishing either the depth or bed width of channel, and as the velocity is 2 feet per second, the discharge will then be 300 cubic feet per second. EXAMPLE 6. Gauging a stream to find its velocity and discharge, and the number of acres it is capable of irri- gating. It is required to ascertain how many acres of orchard land a stream will irrigate, the duty of the water being assumed at 400 acres per cubic foot per second. In a straight reach of the stream/and where it was tolerably uniform, three cross-sections were taken 300 feet apart. The first had an area =22. 3 square feet, and wetted perimeter = 14.76 lineal feet. The second had an area = 23.1 square feet, and wetted perimeter = 14.07 lineal feet. The third had an area = 23.9 square feet, and wetted perimeter = 13.68 lineal feet. The surface slope of the stream was found, by level- OPEN AND CLOSED CHANNELS. 41 ing, to fall 0.287 feet in 600 feet. As the stream was irregular, and was choked occasionally with vegetation, the value of n was assumed at .03. We have now the information required to find the discharge of the^steeam. Add the three areas, and divide by 3, and we get the mean area = 23.1 square feet. Again add the three wetted perimeters and divide by 3, and we find the mean perimeter = 14.17 lineal feet. Now r ==- =^==1.83, p 14. 1/ and v/n53 = 1.28 feet. A slope of 0.287 feet in 600 feet = 1 in 2090, and Table 33 for this slope, \/s=. 021874. In Table 26, with 71 = .03, we do not find a slope of 1 in 2090. We do, however, for 1 in 1666, and \/r=1.2, that c=49.4; and for 1 in 2500, and v/r=1.2, that c=49.2; and as 1 in 2090 is about a mean of these slopes, we take for vA-=1.2, that c= 49.3 and for y^0.08, that c= 1.76 therefore for v/r=1.28, that c= 51.06 Substituting the values of c, \/r, and \/s, in formula (41), v=c\/rX }/&, we have v=51.06xl.28x.021874=1.43 feet per second. Q=va= 1.43x23. 1=33.033 cubic feet per second. But as each cubic foot per second is capable of irri- gating 400 acres, we have 33.033 X 400 === 13,213 acres, the quantity of land the stream is capable of irrigating. 42 FLOW OF WATER IN EXAMPLE 7. Given the dimensions of a canal in earth, to find the width of a masonry channel having the same discharge, the two channels having the same depth and grade . A canal in earth, with n =.0275, a bed of 50 feet, depth 4 feet, side slopes of J to 1, and a grade of 2 feet per mile, is passed over a river by a masonry aque- duct. The aqueduct is to be rectangular in cross-sec- tion, with the same depth as the canal, and the same grade. What must be the width of the masonry channel to discharge the same quantity of water as the canal, its value of n being taken =.017 ? This value of n is taken high, .017, as the bed and sides of the aqueduct are to be roughly plastered. For earthen channel, Q=c i Xv //r X ]/ s - Substitute the values of the factors at the right-hand side of the equation, and we have Q=66.9X 391 X. 019463 =509 cubic feet per second. We have now to fix the width of a masonry channel to discharge 509 cubic feet per second, with a depth of 4 feet, a slope of 2 feet per mile, and n = .017. By formula (47), Now look out the value of ayr, in Table 13, for rec- tangular channels, .and also the value of c in Table 21, with n = .017, until we find that the product of the fac- tors av/rXc=26152. In Table 13 we find, under bed width 35 feet and depth 4 feet, that av/r=248.9, and its corresponding \/r= 1.778=1.8 nearly. At the same time we find, in Table OPEN AND CLOSED CHANNELS. 43 21, 7i=.017, that under a slope of 1 in 2500, and opposite V/r=1.8, the value of c = 106.2, and we have 248.9 >< 106.2 = 26433, which is near enough to 26152; therefore the required width is 35 feet. As a check on this work, look out, in Table 13, the value a\/ r for a rectangular channel 35 feet wide and 4 feet deep, and substitute this, and also the value of cand s, in formula (45), = 106.2X 248.9 X .019463 = 514 cubic feet per second, which is near enough for all practical purposes, EXAMPLE 8. Increased discharge of an earthen channel by clearing it of grass and u-eeds. A. drainage channel originally excavated to a bed width of 12 feet, a depth of water of 4 feet, with side slopes of 1 to 1, and a grade of 1 in 1760, or 3 feet per mile, has been for some years neglected, and its bed and banks are covered with long grass and weeds. Assuming its value of n in this state .035, what will be its in- crease in discharge when it is cleared of all grass, weeds and sharp bends ? In the latter case we will assume Let us first find the discharge in the obstructed chan- nel. In Table 8 we find a=64, and \/r = 1.657. In Table 33 we find, opposite a slope of 1 in 1760, that V/* = 023837. In Table 27, with n=.Q35 under slope of 1 in 1666.7 (which is the nearest to 1 in 1760), and opposite \/r = 1.657, the value of c=49.55. 44 FLOW OF WATER IN Now substitute the values of a, c, \/r and y^s , in formula (45), Q=ac\/rX\/s = 64 X 49.55 X 1-657 X .023837 = 125.3 cubic feet per second, being the discharge of the obstructed channel. Let us now find the discharge of the same channel after it has been cleared, at slight expense, of brush, weeds, silt deposit, sharp bends, etc., so as to bring its value of ??,:=. 025. In Table 24, with 7i=.025, under a slope of 1 in 1666.7 and opposite \/r =1.657 (found by interpolation), the value of c=69.87. Now substitute this value of c with the given values of a, \/.r and \/s in formula (45), and we have: Q = 64 X 69.87 X 1.657 X .023837 ==: 176.6 cubic feet per second, being the discharge of the improved channel. We thus see that by clearing out the channel its dis- charge has been increased by more than 40 per cent. EXAMPLE 9. Increase of discharge by improving in smooth- ness the masonry surface of a channel. A semi-circular open channel of coarse rubble set dry, of 2 feet radius and a grade of 1 in 500, and with n=.02, is to be improved by filling up all interstices, and giving its surface a coat of medium smooth plaster, so as to make its value of ?i=.013. What is the percentage of increase in discharge of the improved channel ? The hydraulic mean depth, r, of a circular channel flowing full or half full is equal to half the radius, there- fore r of this channel = 1, and \/r = 1. OPEN AND CLOSED CHANNELS. 45 The value of c for all slopes greater than 1 in 1000 is the same as for 1 in 1000. In Table 22, with n=.02, under a slope of 1 in 1000 and opposite ^/V 1, the value of c=71.5. In Table 33, opposite a slope of 1 in 500, the value of V/s .044721. Substitute the values of c, \/r and \/~s in formula (41), and v=71.5xlX- 044721 v=3.2 feet per second, the velocity of the channel with a surface of coarse rubble. Now, to find the velocity in plastered channel. Look out, in Table 19, ?i .013, and under a slope of 1 in 1000, and opposite y'V = 1, we find c\/r = 116.5. Substitute the values of c\/r and \/s , and we have v=116.5x. 044721 =5.2 feet per second, the mean velocity in the plastered channel; which shows an increase in velocity and discharge of 63 per cent. over the coarse rubble channel. EXAMPLE 10. To find the velocity and discharge of a channel having bed width, depth and side slopes not given in the tables. What is the velocity and discharge of a channel hav- ing bed width 110 feet, depth of water 7.2 feet, side slopes 2 to 1, and grade 1 in 5000, the value of n being equal to .0275? a = 110 + (7.2 X 2) X 7.2 = 895.68 square feet. 46 FLOW OF WATER IN In Table 29 of length of side slope, we find, under a slope of 2 to 1 and opposite 1 foot, 4.472 feet. Multiply this by the depth, 7.2, and we have the length of two side slopes, and, therefore: p = 110 + (4.472 X 7.2) = 142.2 895.68 '= I42-2 6 - 3 and v/?~ =v/*^3=2.51. In Table 25, with ?i=.0275, under a slope of 1 in 5000, and opposite i/?=2.61, the value of t:=75.5. In Table 33, opposite a slope of 1 in 5000, the value of v/=. 014142. Substitute the values of c, \/r and \/s in formula (41), v =-- c X i/r X i/s and v = 75.5 X 2.51 X .014142 = 2.68 feet per second, and Q av -895.68x2.68 = 2400 cubic feet per second. EXAMPLE 11. Given the discharge, grade and ratio of bed ^u^dth to depth, to find bed width and depth. A mining ditch is to discharge 130 feet per second, and its grade is 1 in 1000. What must be its bed width and depth the ratio of bed width to depth being as 2 to 1 ? Its side slopes are to be |- to 1, and its value of n = .025. By Table 33, a slope of 1 in 1000 has v/e=. 031623. Substitute the value of ,s and also the value of Q given in formula (47), Q 130 OPEN AND CLOSED CHANNELS. 47 Now look out the value of the factors c and a\/r t in Tables 10 and 24, until their product is equal or nearly equal to 4111. The value of c is found in Table 24 with -n = .025, under the given slope 1 in 1000, and opposite- the y/V corresponding to the value of a\/r. After inspection, we find in Table 10, under a bed width 8 feet and depth 4 feet, that a\/r =61.47, and \/r = 1.54. Also in Table 24, with ?i=.025, under a slope of 1 in 1000 and opposite v/V=1.54, we find c=67.9; therefore, acv/r-=61. 47x67. 9=4131, which is sufficiently near to 4111 for practical work. Let us check this discharge. =67. 9X61. 47 X- 031623 = 132 cubic feet per second. The dimensions of the channel are therefore 8 feet wide on bed, 4 feet deep, and with side slopes of J to 1. EXAMPLE 12. Diminution of discharge of channel by grass and weeds. The above channel, Example 11, after construction, has not been repaired or cleaned out for several years. It is obstructed by grass and weeds, and its value of n increased to .035. Find the percentage of diminution of discharge. In Table 27, with ?i=.035, under a slope of 1 in 1000 and opposite \/r = 1.54, we find c=47.8. Substituting this value, and also the values a\/r and ]/,s, in formula (45), we have: =47. 8X61.47X- 031623 =92.9 cubic feet per second. 48 FLOW OP WATER IN This shows that, in this case, the grass and weeds di- minished the discharge by about 30 per cent, of the original discharge. EXAMPLE 13. Given discharge, velocity and the ratio of bed width to depth, to find the slope or grade. A canal is to discharge 3000 cubic feet per second. Its mean velocity is to be 2.5 feet per second. Its bed width is to be 15 times the depth, its side slopes 1 to 1, and its value of 7i=.0'25. Find the slope required. Q 3000 tt= = =1200 square feet. Letic^depth; then p=(8.66xl5)-j-(8.66x2.828) = 154.39 a 1200 = p = 154.39 ==7 ' 7 ' y^r : =\/T.JT2= < 2.8 nearly. In order to aid in the selection of the slope, look out in Table 32, with rc = .03, under bed width 140 feet, depth 9 feet, and we find, as a rough approximation, that the slope for a velocity of 2| feet per second 11453 -1-4822 is=- g -- =8138, that is, 1 in 8138. But as the slope for 7i=.025 is flatter than when 7i=.03, we may assume a flatter slope than 1 in 8138. The nearest slope to this in the tables is 1 in 10000. We now find in Table 24, with rt=.025, under a slope of 1 in 10000, and opposite v/?=2.8, that c\/r = 245.3. OPEN AND CLOSED CHANNELS. 49 Now substitute the values of c\/r and v in formula (43), v/s= T= C\/T 2.5 and we have v/s oTc~q =.010191. Now look out in Table 33, and the nearest value of \/* to this will be found opposite a slope of 1 in. 9600. As a check on this, find value of c in Table 24, under a slope of 1 in 10000, and opposite \/r = 2.8, we find it equal to 87.0. =87. 6X2.8X. 010191 =2.5 feet per second Q=at;=1200-x2.5 =3000 cubic feet per second. EXAMPLE 14. Given the bed width, depth and grade of a channel not given in the tables, to find the velocity and discharge. A canal has a bed width of 80 feet, a depth of six feet, and side slopes of 1J to 1. Its grade is 1 in 5000, and its value of ?i=.025. Find its velocity and discharge. The table for channels with side slopes of 1^ to 1 does not extend beyond a bed width of 60 feet; but, as before explained, the velocity in channels having a greater bed width than 60 feet is not practically changed by a change in the side slopes usually adopted; that is, as an instance, the velocity in a channel 80 feet wide and 6 feet deep, with side slopes of 1 to 1, is practically the same as a channel having the same width and depth but with side slopes of 1| to 1. Let us, therefore, find first the velocity in the former channel. 4 50 FLOW OF WATER IN In Table 8, with side slopes of 1 to 1, under a bed width of 80 feet, and opposite a depth of 6 feet, the value of v/r=2.307. In Table 24, with ?i=.025, and under a slope of 1 in 5000, we find, corresponding to a value of i/V=2.3Q7, that the value of c=80.7. In Table 33 of slopes, and opposite a slope of 1 in 5000, the v" =.014142. Substitute the values of c, \/r and \/s in formula (41), and we have v=80.7 X 2.307 X .014142 2.63 feet per second. = 1404 cubic feet per second. Let us now check this. The area of a channel 80 feet on bed, 6 feet deep, and with side slopes of 1J to 1, is equal to (80 + 6 X 15) X 6 = 534 square feet. In Table 29 of length of side slopes, we find opposite a depth of 6 feet, and under a slope of 1J to 1, that the length of the two side slopes = 21.634 feet. To this has to be added bed width 80 feet, making the perimeter = 101, 634 feet. a 534 Now r = im aoA 5.2541 p 101.634 and v/r = 2.292. We have already found that the value of \/r with side slopes of 1 to 1 is 2.307, showing a difference of less than 1 per cent, with side slopes of 1J to 1. We therefore see that, for all practical purposes, the velocity found from the tables with side slopes of 1 to 1 is sufficiently correct. OPEN AND CLOSED CHANNELS. 51 EXAMPLE 15. To find the value of c and n in an open channel. A channel is gauged, and its perimeter is found equal to 26.48 lineal feet, and its area equal to 63 squaTC~feet. Its discharge is 101.5 cubic feet per second, and the slope of its water surface is equal to 22 inches per mile. Find the value of c and n. a 63 = ^"=2QA8 = and v/r=v/2".4"=1.55 Q 101.5 v = = = 1.61 feet per second. a bo In Table 33, .Mid opposite 22 inches per mile, \/s~ .018634. Substituting the value of \/s t v and s in formula, v , c ,- -, we have Vr X Vs 1.61 _ "1.65X .018634 = A slope of 1 in 2500 is the nearest in the tables of n to 22 inches per mile. Now look under the .different values of n, and under a slope of 1 in 2500, and opposite J/T 1.55, and the value of c that is nearest to 55.8 will be found under the required value of n. In this case, in Table 26, under a value of 7i=.03, and under a slope of 1 in 2500 and opposite y / r=1.5, we find the value of c=55.2, which is the nearest value in the tables to 55.8. Therefore, the required value of c 55.8, and n=.Q3. As a check on this, look out in Table 26, with ti=.03, under a slope of 1 in 2500, and opposite \/r=1..55 t and 02 FLOW OF WATER IN c is found, by interpolation, =56. 1 . Substitute this value of c, and also the values of \/r and \/s, in formula (41), v=cXl/rX\/# and we have v=56.lx 1.55 X .018634 = 1.62 feet per second. EXAMPLE 16. To find the velocity and discharge of a brick aqueduct by Seizin's formula, the dimensions and grade being given. An aqueduct constructed of brick work, rectangular in cross-section, 4 feet wide on bottom, and with ver- tical sides, carries 2 feet in depth of water and has a slope of 1 in 160, What is its velocity and discharge by Bazin's formula for open channels ? In Table 13 for rectangular channels, we find under a bed width 4 and opposite depth 2 that \/r=l. As the channel is of brick-work, it comes under the head of the second type of Bazin's channels, formula (35), by which Table 28 is computed. Now, in Table 28, and opposite l/r=l, we find that C]/T = 118.5. We also find, in Table 33, and opposite a slope of 1 in 160, that \/s=. 079057. Substituting this value and also the value of cy/r in formula (41), we have v=118.5X- 079057=9. 37 feet per second and Q=av=8x9. 37=74. 96 cubic feet per second. EXAMPLE 17. Increase of discharge of a channel in rock- cutting by plastering its surface. Near the head of a small irrigation canal the supply of water is carried in a rock-cutting 10 feet wide at bot- tom, 12 feet wide at surface of water 5 feet in depth, and having a slope of 1 in 880. OPEN AND CLOSED CHANNELS. 53 The water supply carried in this cutting being insuf- ficient, it is determined to increase the supply without, however, increasing the cross-sectional area of channel or its slope. The bottom and sides of the rock-cutting are very rough, and in order to give them a smoother surface and increase the discharge, it is determined to fill up all the hollows in them with masonry, and after this to lay on carefully a coat of cement plaster with one-third sancl,andto make the surfaces in contact with the water smooth and even. After the plastering is finished the dimensions of the channel will be: width at bottom 9.8 feet, width at water surface 11.8 feet, depth of water 4.9 feet, and the slope as before, 1 in 880. It is assumed that a near approximation to the value of n for the rock-cutting =.0225, and for the plastered channel n=. Oil. Find the increase in discharge in the plastered chan- nel over that in the original channel. In the original channel area 55 r= 7-3 = r = s- A 5=2.7228 wetted perimeter 20 . 2 j/V== v/2.7228 = 1.65 Table 33 shows, for a slope of 1 in 880, that \/s= .03371. Table 23 shows, by interpolation, under a slope of 1 in 1000 (which has the same co-efficient as a slope of 1 in 880), and opposite \/r=1.65, that cv/r=128.4. Substitute the values of \/s and c[/r t in formula (41), and we have: v=128.4X- 03371=4.328 feet per second. Now, Q=va=4. 328x55=238 cubic feet per second. 54 FLOW OF WATER IN a 52.92 In the plastered channel r= - =pr7Q~===2^67 and iA=v / 2.673:=1.64 nearly. In Table 17, with ?i=.011, we find, by interpolation, under a slope of 1 in 1000 and opposite \/r=1.64, that the value of c\/r=2Q4.2. Substituting this value of c\/r and \/s , in formula (41), and we have: v=264.2X- 03371 = 8.9 feet per second, and Q=va=S. 9x52.92=471 cubic feet per second. We here see the effect of a smooth surface in increas- ing the velocity and discharge of a channel. Although the cross-sectional area has been diminished, still the effect of giving a smooth surface to the channel has been to more than double its velocity and to almost double the discharge. The old formula would give almost the same velocity and discharge to the two channels, as these formulae do not take into account the surfaces exposed to the flow of water. FLUMES. EXAMPLE 18. To find the velocity and discharge of a rect- angular fiume. A rectangular flume 8 feet wide, and flowing 4 feet in depth of water, has a slope of 1 in 500. The flume is old, and its surface exposed to the flow of water is rough. Its value of n is, therefore, taken as =.015. Find its velocity and discharge. In Table 13, for rectangular channels, under a bed of 8 feet, and opposite a depth of 4 feet, we find i/?=l-414. As the value of c for all slopes steeper than 1 in 1000 is the same as for 1 in 1000, we now find in Table 20, OPEN AND CLOSED CHANNELS. 55 with ?i = .015, under a slope of 1 in 1000, and with \/r = 1.414, that the value of c by interpolation =112.25. In Table 33 of slopes, we find that 1 in 500 has_a_ value V/*= .044721. Substitute these three values in formula (41), v = cX V T X V* and we have v = 112.25 X 1.414 X .044721 ' =7.1 feet per second. Q = av = 32 X 7.1 = 227. 2 cubic feet per second. EXAMPLE 19. To find the velocity and discharge of a V- flume. A right-angled V-flume is flowing with a depth of water in the center of 9 inches and grade of 1 in 180. Find its velocity and discharge. The flume is new and made of uiiplaned timber, and its surface exposed to the water continuous on the iii- side, and in fairly good condition. Its value of n may therefore be taken =.012, but, to be on the side of safety, it is taken =.013. In Table 14, for V-flumes with 7i=.013, and opposite a depth of .75 feet, we find a=. 56 square feet, c'v/V=44.55, and ac\/r=24;.95. In Table 33 of slopes, we find for a slope of 1 in 180 that i/ii= . 074536. Substitute the values of c\/r and \/~s in formula (41), and we have v=44. 55 X- 074536 =3.32 feet per second; and Q=a ^=.56x3.32 = 1.86 cubic feet per second. 56 FLOW OF WATER IN As a check on this we have formula (45), Q=ac]/rX y' * Substitute values, and Q=24.95x. 074536 = 1.86 cubic feet per second. EXAMPLE 20. Given bed ividth, depth and discharge of a rectangular flume, to find its grade or slope. Find, by Kutter's formula, the slope of a flume con- structed of unplaned planks, 5 feet wide at bottom, with vertical sides 2J feet high, in order that it may discharge 102 cubic feet per second. In Table 13 under a bed width of 5 feet and opposite a depth of 2.5 feet, we find \/r == 1.118 = 1.12, nearly. Let us assume that Table 18, with n = .012, is appli- cable to this channel and in it, under a slope of 1 in 1000, we find l/r=l.l that c = 131.6 V/r=0.02 that c= 0.7 .-. v/?=1.12 that c=132.3 v= =TH- =8.16 feet per second. a J. z . o Substitute the value of c, \/r, and ?;, in formula (43), 1/8=-- /= and we have cXVr 8.16 "= 13273^02= - 0550 '- Now look out, in Table 33, the nearest value of \/s to this, and we find it to be opposite a slope of 1 in 330, which is the slope required. OPEN AND CLOSED CHANNELS. 57 TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1. Values of the factors r=area in square feet, and r ~.~ hydraulic mean depth in feet, and also \/r and a^r for use in the formula- v = c X \/r~ X \/*~ and Q c X a*/r~ X \A~ BED 1 FOOT. BED 2 FEET. Depth in Feet. a r ; \/r i a-*/r a r VT a\/r Depth in Feet. 0.5 0.75 0.311 0.577 .433 1.25 0.366 .605 .756 0.5 0.75 1.31 0.425 0.652 .856 1 2.06 0.500 .707 1.46 0.75 1. 2. 0.522 0.723; 1.45 3. 0.621 .788 2.36 1. 1.25 2.81 0.620 0.787' 2.21 i 4.06 0.734 .856 0.48 1.25 1.5 3.75 0.715 0.846 3.17 5.25 0.841 .917 4.8 1.5 1.75 4.81 0.809 0.899 4.32 6.56 0.942 .971 6.4 1.75 2. 6. 0.901 0.950 5.70 8. 1.045 1.022! 8.2 2. 2*26 9.56 1.143 1.069 10.2 2.25 2.5 11.25 1.240 1.113 12.5 2.5 2.75 13.06 1.336 .156 15.1 2.75 3. 15. 1.431 .196 17.9 3. 3.25 17.06 1.525 .235 21.1 3.25 3.5 19.25 1.618 .272 24.5 3.5 3.75 21.56 1.703 .305 28.1 3.75 4. 24. 1.803 .342 32.2 4. BED 3 FEET. BED 4 FEET. Depth Depth in Feet. a r Vr a\/r a r \/r \ a\/r in Feet. 0.5 1.75 0.396 0.629 1.1 2.25 0.416 0.645 1.5 0.5 0.75 2.81 0.549 0.741 2.1 3.56 0.582 0.763 2.7 0.75 1. 4. 0.686 0.828 3.3 5. 0.732 0.856 4.3 1. 1.25 5.31 0.812 0.901 4.8 6.56 0.871 0.933 6.1 1.25 1.5 6.75 0.932 0.965 6.5 8.25 1.000 .000 8.3 1.5 1.75 8.31 1.045 1 . 022 8.5 10.06 .124 .060 10.7 1.75 .> 10. 1.155 1.075 10.8 12. .243 .115 13.4 2. 5! 25 11.81 1.261 1.123 13.3 14.06 .357 .165 16.4 2.25 2.5 13.75 1.365 1.168 16.1 16.25 .468 .211 19.7 2.5 2.75 15.81 1.466 1.211 19.1 18.56 .576 .255 23.3 2.75 3. 18. 1.567 1.252 22.5 21. .682 .297 27.2 3. 3.25 20.31 1.666 1.290 26.2 23.56 .786 .339 31.5 3.25 3.5 22.75 1.764 1.328 30.2 26.25 1.889 .375 36.1 3.5 3.75 25.31 1.831 1.364 34.5 29.06 1.990 .411 41.0 3.75 4. 28. 1 . 956 1.398 39.1 32. 2.090 .446 46.3 4. 4.25 30.81 2.051 1.432 44.1 35.06 2.189 .480 51.9 4.25 4.5 33.75 2.146 1.465 49.4 38.25 2.287 .512 57.8 4.5 4.75 36.81 2.240 1.497 55.1 41.56 2.384 .544 64.2 4.75 5. 40. 2.333 1.527 61.1 45. 2.480 1.575 70.9 5. 58 FLOW OF WATER IN TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1 . Values of the factors a = area in square feet, and r = hydraulic mean, depth in feet, and also ^/7~i\i\d a^/'r~for use in the formula; v = c X V~ X V~ aiid Q c, X t<*/7~ X V#~ BED 5 FEET. BED 6 FEET. Depth in Feet. a r \/r a-^/r a r V'' a\/r Depth in Feet. 0.5 2.75 0.429 O.G55 1.8 3.25 0.438 0.662 2.15 0.5 0.75 4.31 0.607 0.779 3.4 5.06 0.623 0.781 3.95 0.75 1. 6. 0.766 0.875 5.2 7. 0.793 0.891 6.2 1. 1.25 7.81 0.915 0.956 7.5 9.06 0.950 0.975 8.8 1.25 1.5 9.75 .054 1.027 10. 11.25 1.098 1.048 11.8 1.5 1.75 11.81 .186 1.089 12.9 13.56 1.238 1.113 15.1 1.75 7 14. .314 1.147 16.1 16. 1.373 1.172 18.8 2 2.25 16.31 .436 1.198 19.5 18.56 1.502 1.226 22.8 2.25 2.5 18.75 .553 1.246 23.4 21.25 1.626 1.275 27.1 2.5 2.75 21.31 .668 1.292 27.5 24.06 1.747 1.321 31.8 2.75 3. 24. .780 1 . 334 32. 27. 1 1.864 1.365 36.9 ; 3. 3.25 26.81 .889 1.374 36.8 30.06 1.9791 1.407 42.3 ! 3.25 3.5 29.75 i .997 1.413 42. 33.25 2.091 1.446 48.1 3.5 3.75 32.81 2.103 1.450 47.6 36.56 2.201 1.483 54.2 3.75 4. 36. 2.207 1.486 53.5 40. 2.311 1.520; 60.8 4. 4.5 42.75 2.412 1.533 65.5 47.25 2.523 1.589 75.1 4.5 5. 50. 2.612 1.616 80.8 55. 2.731 1.653 90.9 5. 6. 66. 3.004 1.733J 114.4 72. 3.134 1.770| 127.4 6. BED 7 FEET. BED 8 FEET. Depth Depth in Feet. a r ; \/r a\/r a r ^/r a^/r in Feet. 0.5 3.75 0.446 0.667 2.50 4.25 0.451 0.672 2.85 0.5 0.75 5.81 0.637 0.798 4.64 6.56 0.648 0.805 5.28 0.75 1. 8. 0.814 0.902 7 22 9. 0.831 0.911 8.2 1. 1.25 10.31 0.979 0.989 10.2 11.56 1.002 .000 11.6 1.25 1.5 12.75 1.134 1.065 13.6 14.25 1.164 .079 15.4 1.5 1.75 15.31 1.281 1.132 17.3 17.06 1.318 .152 19.7 1.75 2. 18. 1.422 1.192! 21.5 20. 1.464 .210 24.2 2. 2.25 20.81 1.560 1.249 26. 23.06 1.606 .267 29.2 2.25 2.5 23.75 1.688 1.300J 30.9 26.25 1.742 .320 34.7 2.5 2.75 26.81 1.815 1.347 36.1 29.56 1.873 .368 40.4 2.75 3. 30. 1.938 1.392 41.8 33. 2.002 .415 46.7 3. 3.25 33.31 2.057 .434 47.8 35.56 2.069 .439 51.2 3.25 3.5 36.75 2.169 .473 54.1 40.25 2.269 .506 60.6 3 5 3.75 40.31 2.290 .513 61. 44.06 2.368 .539 67.8 3.75 4. 44. 2.403 .550 68.2 48. 2.486 .577 75.7 4. 4.5 51.75 2.623 .619 83.8 56.25 2.714 .647 92.6 4.5 5. 60. 2.838 .684 101. 65. 2.936 713i 111.3 5. 6. 78. 3.254 .804 140.7 84. 3.364 1.834 154.1 6. OPEN AND CLOSED CHANNELS. 59 TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1 . Values of the factors a = area in square feet, and r = hydraulic mean depth in feet, and also \/r and a^/r for use in the formulas v = c X Vr X V and Q = c X a^r X % BED 9 FEET. BED 10 FEET. Depth 1 Depth in Feet. a r Vr a\/r a r vT a^/r in Feet. 0.5 4.625 0.444 0.667 3.08 5.25 0.460 0.678 3.56 0.5 0.75 7.031 0.632 0.795 5.59 8.06 0.665 0.815 7.01 0.75 1 . 10. 0.845 0.919 9.19 11. 0.858 0.926 10.2 1. \.25 12.81 1.022 1.011 12.95 14.06 1.039 .019 14.3 1.25 1 .5 15.75 1.189 1.090 17.2 17.25 1.211 .100 19. 1.5 1.75 18.81 1.349 1.161 21.8 20.56 1 . 375 .173 24.1 1. o 22 1.501 1 . 225 27. 24. 1.533 .238 29.7 2.75 2^25 25! 31 1.650 1.284 32.5 27.56 1.684 .290 35.6 2.25 2.5 28.75 1.789 1.330 38.2 31.25 1.831 1.353 42.3 2.5 2.75 32.31 1 . 927 1.388 44.8 35.06 1.972 1.404 49.2 2.75 3. 36. 2.059 1.435 51.7 39. 2.110 1.452 56.6 3. 3.25 39.81 2.189 1.479 58.9 43.06 2 . 244 1.498 64.5 3.25 3.5 43.75 2.315 1.521 66.5 47.25 2.375 1.541 72.8 3.5 3.75 47.81 2.439 1.562 74.7 51.56 2.502 1 . 582 81.6 3.75 4. 52. 2.560 1.600 83.2 56. 2.628 1.621 90.8 4. 4.5 60.75 2.796 1.672 101.6 65.25 2.871 1.694 110.5 4.5 5. 70. 3.025 1.739 121.7 75. 3.107 1.763 132.2 5. . 5.5 79.75 3.248 1.802 143.7 85.25 3.336 1.826 155.7 5.5 6. 90. 3.466 1.862 167.6 96. 3.560 1.887 181.2 6. BED 11 FEET. BED 12 FEET. Depth Depth in Feet. a r \/r a\/r~ a r \/r u\/r in Feet. 0.5 5.625 0.453 0.674 3.79J 6.25 0.466 0.682 4.26 0.5 0.75 8.531 0.643 0.802 6.84 9.56 0.677 0.823 7.87 0.75 1. 12. 0.868 0.932 11.2 13. 0.877 0.936J 12.2 1. 1.25 15.31 1.053 1.026 15.7 16.56 1.066 1.032 17.1 1.25 1.5 18.75 1 . 230 1.109 20.8 20.25 1.246 1.116 22.6 1.5 1.75 22.31 1.399 1 . 183 26.4 24.06 1.420 1.192! 28.7 1.75 2 26. 1.561 1.249 32.5 28. 1.586 1.259 35.3 2 2' 25 29.81 1.719 1.311 39.1 32.06 1.746 1.321; 42.4 2^25 2.5 33.75 1.868 1.367 46.1 36.25 1 . 901 1.3791 50. 2.5 2.75 37.81 2.015 1.419 53.7 40.56 2.051 1.432 58.1 2.75 3. 42. 2.156 1.466 61.6 45. 2.197 1.482i 66.7 3. 3.25 46.31 2.291 1.5J3 70.1 49.56 2.339 1.529; 75.8 3.25 3.5 50.75 2.428 1.558 79.1 54.25 2.477 1.5741 85.4 3.5 3.75 55.31 2.561 1.600 88.5 59.06 2.612 1.616 ! 95.4 3.75 4. 60. 2.689 1.640 98.4 64. 2.745 1.657 106. 4. 4.5 69.75 2.940 1.715 119.6 74.25 3.003 1.733 128.7 4.5 5. 80. 3.182 1.784 142.7 85. 3.252 1.803 153.3 5. 5.5 90.75 3.417 1.848 167.7 96.25 3.493 1.869; 179.9 5.5 6. 102. 3.647 1.910 194.8 108. 3.728 1.931: 20S.6 6. 60 FLOW OF WATER IN TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1. Values of the factors a area in square feet, and r = hydraulic mean depth in. feet, and also \/r and a\/r for use in the formulas v = c X \/r X -s/s" and Q = c X a^r X \/*~ BED 13 FEET. BED 14 FEET. Depth in Feet. a r Vr a\/f a r x/r a 4.5 132.75 3.519 1.876 249. 155.25 3.633 1.906 295.9 4.5 4.75 141.31 3.677 1.917 270.9 165.06 3.800 1.949 321.7 4.75 5. 150. 3.831 1.957 293.6 175. 3.965 1.991 348.4 5. 5.25 158.81 3.985 1.971! 313. 185.06 4.126 2.031 375.9 5.25 5.5 167.75 4.136 2.034 341.2 195.25 4.286 2.070 404.2 5.5 5.75 176.81 4.285 2.070 366. 205.56 4.443 2.108 433.3 5.75 6. 186. 4.432 2.105 391.5 216. 4.599 2.145 463.3 6. 6.25 195.31 4.576 2.1391 417.8 N 226.56 4.752 2,179 493.7 6.25 6.5 204.75 4.720 2.172 444.7 237.25 4.903 2.214 525.3 6.5 6.75 214.31 4.861 2.205 472.6 j 248.06 5.053 2.248 557.6 6.75 7. 224. 5. 2.236 500.9 I 259. 5.201 2.281 590.8 7. 7.25 233.81 5.138 2.267 530. 270.06 5.347 2.312 624.4 7.25 7.5 243.75 5.274 2.296 559.7 281.25 5.492 2.344 659.2 7.5 7.75 253.81 5.409 2.325 590.1 292.56 5.635 2.374 694.5 7.75 8. 264. 5.541 2.354 621.5 304. 5.776 2.403 730.5 8. 8.25 274.31 5.675 2.382 653.4 315.56 5.917 2.432 767.4 8.25 8.5 284.75 5.806 2.408 685.7 327 . 25 6.055 2.460 805. 8.5 8.75 295.31 5.936 2.436 719.4 339.06 6.193 2.488 843.6 8.75 9. 306. 6.065 2.463 753.7 j! 351. 6.329 2.515 882.8 9. OPEN AND CLOSED CHANNELS. 63 TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1. Values of the factors a = area in square feet, and r = hydraulic mean depth in feet, and also \/~ a- 11 ^ \/F~for use in the formulae v = c X \/~ X -v/Tand Q = c X ov/T X \A~~ BED 35 FEET. BED 40 FEET. Depth in Feet. _ a r Vr a^/r a r vT a-v/r Depth in Feet. 0.75 23.06 0.621 .788 18.2 30.56 0.726 .852 26. 0.75 1. 36. 0.952 .976! 35.1 41. 0.957 .978 40.1 1. 1.25 45.31 1.176 1.082; 49. 51.56 1.184 1.0881 56.1 1.25 1.5 54.75 1.395 i.181! 64.7 62.25 1.407 1.190; 74.1 1.5 1.75 64.30 1.610 1.269! 81.6 73.06 1.625 1.275; 93.2 1.75 2. 74. 1.820 1.349 99.8 84. 1.840 1.356 113.9 2. 2.25 83.81 2.026 1.4231 119.3 95.06 2.050 1.432 136.1 2.25 2.5 93.75 2.228 1.493 140. 106.25 2.257 1.502! 159.6 2.5 2.75 103.81 2.426 1.557 161.6 117.56 2.460 1.568! 184.3 2.75 3. 114. 2.622 1.619 184.6 129. 2.661 1.631! 210.4 3. 3.25 124.31 2.815 1.678 208.6 140.56 2.838 1.685 236.8 3.25 3.5 134.75 3.001 1.732 233.4 152.25 3.051 1.747 266. 3.5 3.75 145.31 3.197 1.788 259.8 164.06 3.242 1.801 295.5 3.75 4. 156. 3.368 1.835 286.3 176. 3.431J 1.852 326. . 4. 4.25 166.81 3.547 1.883 314.1 188.06 3.615 1.901 357.5 4.25 4.5 177.75 3.724 1.930 343.1 200.25 3.798 1.949 390.3 4.5 4.75 188.81 3.898 1.974 372.7 212.56 3.977 1.994 423.8 4.75 5. 200. 4.070 2.017 403.4 225. 4.155 2.038 458.6 5. 5.25 211.31 4.239 2.059 435.1 237.56 4.331 2.081 494.4 5.25 5.5 222.75 4.406 2.099 467.6 250.25 4.504! 2.122 531. 5.5 5.75 234.31 4.571 2.138i 501. 263.06 4.676 2.162 567.7 5.75 6. 246. 4.733 2.176 535.3 276. 4.844 2.201 607.5 6. 6.25 257.81 4.894 2.212 570.3 289.26 5.015 2.239 647.7 6.25 6.5 269.75 5.053 2.248 606.4 j 302.25 5.1771 2.2',5 687.6 6.5 6.75 281.81 5.206 2.282 643.1 315.56 5.340 2.311 729.3 6.75 7 . 294. 5.365 2.316 680.9 329. 5.501 2.343 770.8 7. 7.25 306.21 5.517 2.349 719.3 342.56 5.661 2.379) 815. 7.25 7.5 318.75 5.671 2.381 758.9 356.25 5.830 2.414 860. 7.5 7.75 331.31 5.821 2.416 800.4 370.06 5.976 2.444 904.4 7.75 8. 344. 5.968 2.443 840.4 384. 6.13-2 2.4761 950.8 8. 8.25 356.81 6.117 2.473 882.4 398.06 6.285 2.507 997.9 8.25 8.5 369.75 6.262 2.502 925.1 412.25 6.437 2.537 1046. 8.5 8.75 382.81 6.4071 2.531 968.9 426.56 6.588 2.566 1095. 8.75 9. 396. 6.550 2.559 1013. 441. 6.737 2.596 1145. 9. 9.5 422.75 6.833 2.614 1105. 470.25 7.107 2.666 1254. 9.5 10. 450. 7.111 2.666 1200. 500. 7.322 2.706 1353. 10. 84 FLOW OF WATER IN TABLE 8: Channels having a trapezoidal section, with side slopes of 1 to 1. Values of the factors a = area in square feet, and r = hydraulic mean depth in feet, and also v^aiid a-^/T^ioT: use in the formula} v = c X V~ X -x/JTaiicl Q = c X BED 45 FEKT. BED 50 FEET. Depth in a r x/r '' a\/r a r ^/r a\/r Depth in Feet. ! Feet. 1. 46. 0.962 0.981 45.1 51. .964 0.982 50.1 1. 1.5 69.75 1.416 1.19G 83. 77.25 1.424 1.193 92.2 1.5 1.75 81.81 1.638 1.280 104.7 90.56 1.648 1.284 116.3 1.75 94. 1.856 1.362 128.1 104. 1.868 1 . 367 142 . 2 2. 2^25 106.31 2.071 1.439 153. 117.56 2.086 1.444 169.8 2.25 2.5 118.75 2.280 1.510 179.3 131.25 2.300 1.516 199. 2.5 2.75 131.31 2.488 1.577 207.1 145.06 2.511 1.584 229.8 2.75 3. 144. 2.692 1.641 236.3 159. 2.719 1.649 262.2 3. 3.25 156.81 2.894 1.701 266.7 173.06 2.927 1.711 296.1 3.25 3.5 169.75 3.092 1.758 298.4 187.25 3.126 1.768 331.1 3.5 3.75 182.81 3.288 1.813 331.4 201.56 3.326 1.823 367.4 3.75 4. 196. 3.481 1.86G 365.7 216. 3.523 1.877 405.4 4. 4.25 209.31 3.671 1.916 401. 230.56 3.717 1.928 444.5 4.25 4.5 222.75 3.859 1.964 437.5 245.25 3.910 1.977 484.8 4.5 4.75 236.31 4.044 2.011 475.2 2G0.06 4.100 2.025 526.6 4.75 5. 250. 4.227 2.05G 514. 275. 4.287! 2.070 569.2 5. 5.25 263.81 4.408 2.100 554. 290.06 4.473 1 2.115 613.5 5.25 5.5 277.75 4.587 2.142 594.9 305.25 4.656 2.158 658.7 5.5 5.75 291.81 4.763 2.182 636.7 320.56 4.838 2.199 704.9 5.75 6. 306. 4.938 2.222 679.9 336. 5.017- 2.240 752.6 6. 6.25 320.31 5.106 2.260 723.9 351.56 5.195, 2.279 801.2 6.25 6.5 334.75 5.281 2.298 769.3 367.25 5.371 2.317 850.9 6.5 6. 75 349.31 5.450 2.335 815.6 383.06 5.544 2.354 901.7 6.75 7 . 364. 5.617 2.370 862.7 399. 5.716 2.391 954. 7. 7.25 378.81 5.783 2.405 910.3 415.06 5.887 2.426 1007. 7.25 7.5 393.75 5.947 2 . 439 960.4 431.25 6.056 2.461 1061. 7.5 7.75 408.81 6.109 2.472 1011. 447 . 56 6.223 2.495 1117. 7.75 8. 424. 6.269 2.504 1062. 464. 6.389 2.527 1173. 8. 8.25 439.31 6.429 2.536 1114. 480.56 6.553 2.560 1230. 8.25 8.5 454.75 6.587 2.566 1167. 497.25 6.716 2.591 1288. 8.5 8.75 470.31 6.743 2.597 1221 . 514.06 6.877! 2.622 1348. 8.75 9. 486. 6.898 2.626 1276. 531. 7.037 2.653 1409. 9. 9.5 517.75 7.204 2.684 1390. 565 . 25 7.353 2.711 1532. 9.5 10. 550. 7.505 2.740 1507. 600. 7.665 2.770 1662. 10. 10.5 582.75 7.801 2.793 1628. 635.25 7.971 2.823 1793. 10.5 11. 616. 8.093 2.845 1753. 671. 8.273 1 2.874 1928. 11. OPEN AND CLOSED CHANNELS. 65 TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1 . Values of the factors a = area in square feet, and r == hydraulic mean depth in feet, and also ^/r~and a\/r~for use in the formula) v = c X V~ X VJTand Q = c X a*/r~ X %/" BED 60 FEET. BED 70 FEET. Depth in Feet. a r x/r a\/r a r Vr a-\/r Depth in Feet. 1. 61. 0.971 0.985 60.1 71. 0.975 0.987 70.1 1. 1.5 92.25 1.436 .199 110.6 107.25 1.445 1.200 128.7 1.5 2. 124. 1.889 .377 170.7 144. 1.903 1.346 193.8 2 2.25 140.06 2.110 .452 203.4 162.56 2.129 1.459 237.2 2 '.25 2.5 156.25 2.330 .526 238.4 181.25 2.352 1.534 278. 2.5 2.75 172.56 2.546 .595 275.2 200.06 2.572 1.604 320.9 2.75 3. 189. 2.760 .661 313.9 219. 2.790 1.670 365.7 3. 3.25 205.56 2.971 .724 355.2 238.06 3.006 1.734 412.8 3.25 3.5 222.25 3.180 1.783 396.3 257.25 3.220 1.794 461.5 3.5 3.75 239.06 3.386 1.838 439.4 276.56 3.431 1.852 512.2 3.75 4. 256. 3.590 1.895 475.1 296. 3.640 1.908 564.8 4. 4.25 273.06 3.791 1.947 531.6 315.56 3.847 1.961 618.8 4.25 4.5 290.25 3.991 1.998 579.9 335.25 4.052 2.013 674.9 4.5 4.75 307.56 4.188 2.046 629.3 355.06 4.256 2.063 732.5 4.75 5. 325. 4.384 2.095 680.9 375. 4.457 2.111 791.6 5. 5.25 342.56 4.577 2.139 732.7 395.06 4.656 2.158 852.5 5.25 5.5 360.25 4.768 2.183 786.4 415.25 4.858 2.204 915.2 5.5 5.75 378.06 4.957 2.226 841.6 435.56 5.049 2.247 978.7 5.75 6. 396. 5.145 2.268 898.1 456. 5.243 2.289 1043.8 6. 6.25 414.06 5.330 2.309 956.1 476.56 5.435 2.331 1110.9 6.25 6.5 432.25 5.515 2.348 1014.9 497.25 5.626 2.372 1179.5 6.5 6.75 450.56 5.697 2.387 1075.5 518.06 5.815 2.411 1249. 6.75 7. 469. 5.877 2.424 1136.8 539. 6.002 2.450 1320.6 7. 7.25 487.56 6.056 2.461 1199.9 560.06 6.188 2.487 1392.9 7.25 7.5 506.25 6.234 2.497 1264.1 581.25 6.373 2.524 1467.1 7.5 7.75 525.06 6.409 2.531 1328.9 602.56 6.555! 2.560 1542.6 7.75 8. 544. 6.584 2.566 1396. 624. 6.736 2.596 1619.9 8. 8.25 563.06 6.757 2.599 1463.4 645.56 6.917 2.630 1697.8 8.25 8.5 582.25 6.928 2.632 1532.5 667.25 7.095 2.664 1777.6 8.5 8.75 601.56 7.098 2.664 1602.6 689.06 7.272 2.696 1857.7 8.75 9. 621. 7.267 2.696 1674.2 711. 7.448 2.729 1940.3 9. 9.5 660.25 7.600 2.759 1821.6 755.25 7.797 2 '.790 2107.1 9.5 10. 700. 7.929 2.816 1971.2 800. 8.140 2.853 2282.4 10. 10.5 740.25 8.253 2.873 2126.7 845.25 8.478 2.912 2461.4 10.5 11. 781. 8.572 2.928 2286.8 891. 8.8121 2.968 2644.5 11. 66 FLOW OF WATER IN TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1 . Values of the factors a = area in square feet, and r hydraulic mean depth in feet, and also \X~and a\/r for use in the formulae v = c X \/'>~ X vT~and Q = c X a^/T X \A~ BED 80 FEET. BED 90 FEET. Depth in Feet. a r v/r a^/r a r \/V a\/r Depth in Feet. 1. 81. 0.978 .989 80.1 91. 0.980 .990 90.1 1. 2. 164. 1.915 1.384J 227.0 184. 1.923 1.387 255.2 2. 2.25 185.06 2.143 1.464 270.9 207.56 2.154 1.467 304.5 2.25 2.5 206.25 2.369 1.539 317.4 231.25 2.382 1.543 356.8 2.5 2.75 227.56 2.592 1.610 366.4 255.06 2.609 1.612 411.2 2.75 3. 249. 2.814 1.678 417.8 279. 2.833 .683 469.6 3. 3.25 270.56 3.034 1.742 471.3 303.06 3.055 .748 529.7 3.26 3.5 292.25 3.251 1.803 526.9 327.25 3.276 .810 592.3 3.5 3.75 314.06 3.466 1.862 584.8 351.56 3.494 .869 657. J 3.75 4. 336. 3.680 1.918 644.4 376. 3.711 .926 724.2 4. 4.25 358.06 3.891 1.973 706.5 400.56 3.926 .981 793.5 4.25 4.5 380.25 4.101 2.025 770. 425 . 25 4.139 2.034 865. 4.5 4.75 402.56 4.308 2.076 835.7 450.06 4.351 2.086 938.8 4.75 5. 425. 4.514 2.125 903.1 475. 4.562 2.136 1015. 5. 5.25 447 . 56 4.719 2.172 972.1 500.06 4.769 2.184 1092. 5.25 5.5 470.25 4.921 2.218 1043. 525 . 25 4.976 2.231 1172. 5.5 5.75 493.06 5.122 2.263 1116. 550.56 5.181 2.276 1253. 5.75 6. 516. 5.321 2.307 1190. 576. 5.397 2.320 1336. 6. 6.25 539.06 5.519 2.349 1266. 601.56 5.587 2.364 1455. 6.25 6.5 562.25 5.715 2.391 1344. 627.25 5.788 2.406 1509. 6.5 6.75 585.56 5.909 2.431 1423. 653.06 5.986 2.446 1597. 6.75 7. 609. 6.102 2.470 1504. 679. 6.184 2.487 1689. 7. 7.25 632.56 6.293 2.508 1586. 705.06 6.380 2.526 1781. 7.25 7.5 656.25 6.484 2.546 1671. 731.25 6.575 2.564 1875. 7.5 7.75 680.06 6.672 2.583 1757. 757.56 6.769 2.602 1971 7.75 8. 704. 6.860 2.619 1844. 784. 6.961 2.6381 2068. 8. 8.25 728.06 7.046 2.654 1932. 810.56 7.152 2.674 2167. 8.25 8.5 752.25 7.230 2.689 2023. 837.25 7.342 2.710 2269. 8.5 8.75 776.56 7.414 2.723 2115. 864.06 7.530 2.744 2371. 8.75 9. 801. 7.595 2.756 2208. 891. 7.717 2.778 2475. 9. 9.25 825.56 7.777 2.789 2302. 918.06 7.903 2.811 2581. 9.25 9.5 850.25 7.956 2.821 2399. 945.25 8.088 2.844 2688. 9.5 9.75 875.06 8.134 2.852 2496. 972.56 8.271 2.876 2797. 9.75 10. 900. 8.312 2.883 2595. 1000. 8.454 2.907 2907. 10. 10.5 950.25 8.663! 2.943 2797. 1055.25 8.816 2.969 3133. 10.5 11. 1001. 9.009! 3.001 3004. 1111. 9.173 3.028 3364. 11. 12. 1104. 9.689 3.113 3437. 1224. 9.876 3.142 3846. 12. OPEN AND CLOSED CHANNELS. 67 TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1 . Values of the factors a area in square feet, and r= hydraulic mean depth in feet, and also %/~ and a\/r~ for use in the formula v = c X \/~ X \/~ and Q = c X ajr X -J* BED 100 FEET. BED 120 FEET. Depth in Feet. a r Vr a-v/V a r \/r a\/r Depth in Feet. 1. 101. 0.982 0.991 100.1 121. 0.985 0.992 120. 1. 2. 204. 1.931 1.389 283.4 244. 1.942 1.393 339.9 2. 2.25 230.06 2.163 1.470 338.2 275.06 2.177 1.475 405.7 2.25 2.5 256.25 2.393 1.546 396.2 306.25 2.410 1.552 475.3 2.5 2.75 282.56 2.622 1.619 457.5 337.56 2.642 1.625 548.5 2.75 3. 309. 2.848 1.687 521.3 369. 2.872 1.695 625.5 3. 3.25 335.56 3.073 1.752 587.9 400.56 3.101 1.761 705.4 3.25 3.5 362.25 3.296 1.816 657.8 432.25 3.328 1.824 788.4 3.5 3.75 389.06 3.517 1.875 729.5 464.06 3.553 1.885 874.8 3.75 4. 416. 3.737 1.933 804.1 496. 3.777 1.943 963.7 4. 4.25 443.06 3.955 1.988 880.8 528.06 4. 2. 1056. 4.25 4.5 470.25 4.171 2.042 960.3 560.25 4.221 2.054 1151. 4.5 4.75 497.56 4.386 2.094 1042. 592.56 4.441 2.107 1249. 4.75 5. 525. 4.600 2.145 1126. 625. 4.659 2.158 1349. 5. 5.25 552.56 4.811 2.193 1212. 657.56 4.876 2.208 1452. 5.25- 5.5 580.25 5.021 2.241 1300. 690.25 5.092 2.256 1557. 5.5 5.75 608.06 5.230 2.287 1391 . 723.06 5.306 2.303 1665. 5.75 6. 636. 5.437 2.331 1483. 756. 5.519 2.349 1776. 6. 6.25 664.06 5.643 2.375 1577. 789.06 5.731 2.394 1889. 6.25 6.5 692.25 5.848 2.418 1674. 822.25 5.942 2.437 2004. 6.5 6.75 720.56 6.050 2.460 1773. 855.56 6.151 2.480 2122. 6.75 7. 749. 6.252 2.500 1873. 889. 6.359 2.521 2241. 7. 7.25 777.56 6.452 2.540 1957. 922.56 6.566 2.562 2364. 7.25 7.5 806.25 6.652 2.579 2079. 956.25 6.772 2.602 2488. 7.5 7.75 835.06 6.849 2.617 2185. 990.06 6.976 2.641 2615. 7.75 8. 864. i 7.046 2.654 2293. 1024. 7.179 2.679 2743. 8. 8.25 893.06 7.241 2.691 2403. 1058.06 7.382 2.717 2875. 8.25 8.5 922.25 7.435 2.726 2514. 1092.25 7.583 2.753 3007. 8.5 8.75 951.56 7.628 2.762 2628. 1126.56 7.783 2.790 3143. 8.75 9. 981. 7.819 2.796 2743. 1161. 7.982 2.825 3280. 9. 9.25 1010.56 8.010 2.830 2860. 1195.56 8.180 2.860 3419. 9.25 9.5 1040.25 8.199 2.863 2978. 1230.25 8.376 2.894 3560. 9.5 9.75 1070.06 8.387 2.896 3099. 1265.06 8.572 2.928 3704. 9.75 10. 1100. 8.575 2.928 3221. 1300. 8.767 2.961 3849. 10. 10.5 1160.25 8.946 2.991 3470. 1370.25 9.153 3.025 4145. 10.5 11. 1221. 9.313 3.051 3725. 1441. 9.536 3.088 4450. 11. 11.5 1282.25 9.675 3.110 3988. 1512.25 9.915 3.149 4762. 11.5 12. 1344. 10.03 3.167 4256. 1584. 10.29 3.208 5081. 12. FLOW OF WATER IN TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1. Values of the factors a area in square feet, and r hydraulic mean depth in feet, and also -x/~and a\/r~for use in the formulae v = c X Vr~ X \/~and Q = c X a->/r~ X \A~~ BED 140 FEET. BED 160 FEET. Depth in Feet. a r \/r a\/r a r V^ a\/r Depth in Feet. 1. 141. 0.987 0.9931 140. 161. 0.989 0.994 160. 1. 2. 284. 1.950 .396 396.5 324. 1.956 1.398 453. 2. 2.25 320.06 2.187 .465 468.9 365.06 2.194 1.481 540.7 2.25 2.5 356.25 2 422 .556 554.3 406.25 2.432 1.559 633.3 2.5 2.75 392.56 2^656 .630 639.9 447 . 56 2.668 1.639 733.6 2.75 3. 429. 2.889 .699 728.9 489. 2.902 1.704 833.3 3. 3.25 465.56 3.121 .767 822.6 530.56 3.136 1.771 939.6 3.25 3.5 502 . 25 3.351 .831 906.1 572.25 3.368 1.835 1050. 3.5 3.75 539.06 3.579 .892 1020. 614.06 3.599 1.897 1165. 3.75 4. 576. 3.807 .951 1124. 656. 3.829 1.957 1284. 4. 4.25 613.06 4.033 2.008 1231. 698.06 4.058 2.014 1406. 4.25 4.5 650.25 4.258 2.063 1341. 740.25 4.286 2.070 1532. 4.5 4.75 687.56 4.481 2.117 1456. 782. 56i 4.512 2.124 1662. 4.75 5. 725. 4.703 2.169 1573. 825. 4.738 2.177 1796. 5. 5.25 762.56 4.924 2.219 1692. 867.56 4.962 2.228 1933. 5.25 5.5 800.25 5.144 '2.268 1815. 910.25 5.185 2.277 2073. 5.5 5.75 838.06 5.363 2.315 1940. 953.06 5.407 2.325 2216. 5.75 6. 876. 5.581 2.362 2069. 996. 5.628 2.372 2363. 6. 6.25 914.06 5.797 2.408 2201. 1039.06 5.848 2.418 2512. 6.25 6.5 952.25 6.013 2.452 2335. 1082.25 6.067 2.463 2666. 6.5 6.75 990.56 6.226 2.495 2471. 1125.56 6.285 2.507 2822. 6.75 7. 1029. 6.439 2.538 2612. 1169. 6.498 2.549 2980. 7. 7.25 1067.56 6.651 2.579 2753. 1212.56 6.717 2.592 3143. ! 7.25 7.5 1106.25 6.862 2.620 2898. 1256.25 6.927 2.632 3306. 7.5 7.75 1145.06 7.072 2.659 3045. 1300.06 7.146 2.673 3475. 7.75 8. 1184. 7.280 2.700 3197. 1344. 7.359 2.713 3646. 8. 8.25 1223.06 7.488 2.736 3346. 1386.06 7.561 2.750 3812. 8.25 8.5 1262.25 7.695 2.774 3501. 1432.25 7.782 2.790 3996. 8.5 8.75 1301.56 7.900 2.811 3659. 1476.56 7.992 2.827 4174. 8.75 9. 1341. 8.105 2.847 3818. 1521. 8.201 2.864 4356. 9. 9.25 1380.56 8.289 2.882 3979. 1565.56 8.410 2.900 4540. 9.25 9.5 1420.25 8.511 2.917 4143. 1610.25 8.617 2.936 4728. 9.5 9.75 1460.06 8.713 2 . 952 4310. 1655.06 8.823 2.970 4916. 9.75 10. 1500. 8.912 2.985 4478. 1700. 9.029 3.005 5109. 10. 10.5 1580.25 9.312 3.051 4821. 1790.25 9.437 3.072 5499. 10.5 11. 1661. 9.707 3.116 5176. 1881. 9.843 3.137 5901. 11. 11.5 1742.25 10.098 3.178 5537. 1972.25 10.24 3.200 6311. 11.5 12. 1824. 10.49 3.249 5926. 2064. 10.64 3.262 6733. 12. 13. 1989. 11.252 3.354 6671. 2249. 11.43 3.381 7604. 113. OPEN AND CLOSED CHANNELS. TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1. Values of the factors a = area in square feet, and r hydraulic mean depth in feet, and" also \fr~ and a\/r~ior use in the formulae v = c X VV~ X \A~~ and Q = c X BED 180 FEET. BED 200 FEET. Depth Depth in f t Feet. r Vr a\/r a r Vr a\/r in Feet. 1. 181. 0.990 0.995 180.1 201. 0.991! 0.995 200. 1. 2 364. 1.961 1.400 509.6 404. 1.964 .402 566.4 2. 2^5 456.25 2.439 1.562 712.7 506.25 2.445 .564 791.8! 2.5 2.75 502.56 2.676 1.636 822.2 557.56 2.683 .638 913.3 2.75 3. 549. 2.913 1.706 936.6 609. 2.921 .709 1041. 3. 3.25 595.56 3.148 1.774 1057. 660.56 3.158 .777 1174. 3.25 3.5 642.25 3.382 1.839 1181. 712.25 3.393 .842 1312. 3.5 3.75 689.06 3.615 1.901 1310. 764.06 3.628 .905 1456. 3.75 4. 736. 3.847 1.961 1443. 816. 3.862 1.965 1603. 4. 4.25 783.06 4.078 2.019 1581. 868.06 4.094 2.023 1756. 4.25 4.5 830.25 4.308 2.075 1723. 920.25 4.326 2.080 1914. 4.5 4.75 877.56 4.537 2.130 1869. 972.56 4.557 2.134J 2075. 4.75 5. 925. 4.765 2.183 2019. 1025. 4.787 2.1881 2243. 5. 5.25 972.56 4.991 2.234 2173. 1077.56 5.015 2.239J 2413. 5.25 5.5 1020.25 5.217 2.284 2330. 1130.25 5.243 2.290 2588. 5.5 ' 5.75 1068.06 5.442 2.333 2492. 1183.06 5.470 2.339 2767. 5.75 6. . 1116. 5.666 2.380 2656. 1236. 5.697 2.387! 2950. 6. 6.25 1164.06 5.889 2.427 2825. 1289.06 5.921 2.433 3136. 6.25 6.5 1212.25 6.111 2.472 2997. 1342.25 6.146 2.479! 3327. 6.5 6.75 1200.56 6.332 2.516 3172. 1395.56 6.370 2.524 3522. 6.75 7. 1309. 6.552 2.560 3351. 1449. 6.592 2.567' 3720. 7. 7.25 1357.56 6.770 2.602 3532. 1502.56 6.814 2.610 3922. 7.25 7.5 1406.25 6.973 2.641 3714. 1556 . 25 7.035 2. 6521 4127. 7.5 7.75 1455.06 7.206 2.684 3905. 1610.06 7.255 2.693 4336. 7.75 8. 1504. 7.422 2.724 4097. 1664. 7.474 2.734 4549. 8. 8.25 1553.06 7.638 2.763 4291. 1718.06 7.693 2.773 4764. 8.25 8.5 1602.25 7.853 2.802 4490. 1772.25 7.910 2.812 4984. 8.5 8.75 1651.56 8.066 2.840 4690. 1826.56 8.127 2.851 5208. 8.75 9. 1701. 8.279 2.877 4920. 1881. 8.343 2.888 5432 . 9. 9.25 1750.56 8.491 2.914 5101. 1935.56 8.558 2.925 5662. 9.25 9.5 1800.25 8.702 2.950 5311. 1990.25 8.773 2.962 5895. 9.5 9.75 1850. 8.913 2.985 5522. 12045. 8.986 2.997 6129. 9.75 10. 1900. 9.122 3.020 5738. 2100. 9.199 3.033 6369. 10. 10.5 2000. 9.539 3.089 6178. 2210. 9.622 3.102 6855. 10.5 11. 2101. 9.952 3.154 6627. 2321. 10.04 3.169 7355. 11. 11.5 2202. 10.36 3.220 7091. 2432. 10.46 3.234 7865. 11.5 12. 2304. 10.77 3.282 7562. 2544. 10.87 3.298 8390. 12. 13. 2509. 11.59 3.406 8546. 2769. 11.69 3.417 9462. 13. 14. 2716. 12.37 3.517 9552. 2996. 12.50 3.536 10594. 14. i 70 FLOW OF WATER IN TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1. Values of the factors a = area in square feet, and r== hydraulic mean depth in feet, and also -v/^and a%/r~for use in the formula) v = c X -\/r~X \A~and Q = c X a^/r~ X \/~ BED 220 FEET. BED 240 FEET. Depth in Feet. a r x/r a\/r a r Vr a\/r Depth in Feet. 2. 444. 1.968 1.403 622.9 484. 1.970 1.404 679.5 2. 2.5 556.25 2.450 1 565 870.5 606.25 2.454 1.567 950 2.5 3. 669. 2.928 1.711 1145. 729. 2.934 1.713 1249. 3. 3.25 725.56 3.166 1.779 1291. 790.56 3.173 1.781 1408. 3.25 3.5 782.25 3.403 1.845 1443. 852.25 3.411 1.847 1574. 3.5 3.75 839.06 3.638 1.907 1600. 914.06 3.647 1.910 1746. 3.75 4. 896. 3.874 1.968 1763. 976. 3.884 1.971 1924. 4. 4.25 953.06 4.108 2.027 1932. 1038.06 4.119 2.030 2107. 4.25 4.5 1010.25 4.341 2.083 2104. 1100.25 4.353 2.086 2295. 4.5 4.75 1067.56 4.573 2.138 2282. 1162.56 4.587 2.141 2489. 4.75 5. 1125. 4.805 2.192 2466. 1225. 4.820 2.195 2689. 5. 5.25 1182.56 5.035 2.244 2654. 1287.56 5.053 2.248 2894. 5.25 5.5 1240.25 5.265 2.294 2845. 1350.25 5.283 2.298 3103. 5.5 5.75 1298.06 5.494 2.344 3043. 1413.06 5.514 2.348 3318. 5.75 6. 1356. 5.722 2.392 3244. 1476. 5.744 2.397 3538. 6. 6.25 1414.06 5.949 2.439 3449. 1539.06 5.973 2.444 3761. 6.25 6.5 1472.25 6.176 2.485 3659. 1602.25 6.201 2.490 3990. 6.5 6.75 1530.56 6.402 2.530 3872. 1665.56 6.429 2.536 4224. 6.75 7. 1589. 6.626 2.574 4090. 1729. 6.655 2.580 4461. 7. 7.25 1647.56 6.850 2.617 4312. 1792.56 6.881 2.623 4702. 7.25 7.5 1706.25 7.074 2.660 4539. 1856.25 7.106 2.666 4949. 7.5 7.75 1765.06 7.296 2.701 4767. 1920.08 7.331 2.708 5199. 7.75 8. 1824. 7.518 2.742 5001. 1984. 7.554 2.748 5452. 8. 8.25 1883.06 7.738 2.782 5239. 2048.06 7.777 2.789 5712. 8.25 8.5 1942.25 7.959 2.821 5479. 2112.25 8.000 2.828 5973. 8.5 8.75 2000.56 8.178 2.860 5722. 2176.56 8.221 2.867 6240. 8.75 9. 2061. 8.397 2.898 5973. 2241 . 8.442 2.906 6512. 9. 9.25 2120.56 8.614 2.935 6224. 2305.56 8.639 2.939 6776. 9.25 9.5 2180.25 8.832 2.972 6480. 2370.25 8.882 2.980 7063. 9.5 9.75 2240.06 9.047 3.007 6736. 2435.06 9.100 3.017 7347. 9.75 10. 2300. 9.264 3.044 7001. 2500. 9.319 3.053 7633. 10. 10.5 2420.25 9.693 3.113 7534. 2630.25 9.753 3.123 8214. 10.5 11. 2541. 10.12 3.181 8083. 2761. 10.18 3.190 8808. 11. 11.5 2662.25 10.54 3.247 8644. 2892.25 10.61 3.257 9420. 11.5 12. 2784. 10.96 3.315 9229. 3024. 11.04 3.323 10059. 12. 13. 3029. 11.80 3.435 10405. 3289. 11.88 3.44611334. 13. 14. 3276. 12.62 3.552 11636. |3556. 12.72 3.56612681. 14. 15. 3525. 13.46 3 669 12933. 3825. |l3.54 3.680 14076. 15. 16. 3776. 14.24 3.774 14251. 4096. 14.36 3.789 15520. 16 OPEN AND CLOSED CHANNELS. 71 TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1. Values of the factors a = area in square feet, and r = hydraulic mean depth in feet, and also ^/~&nd. a^/r~ior use in the formulae v = c X V^X xA~and Q = c X N/~ X BED 260 FEET. BED 280 FEET. Depth in Feet. a r \/r a^/r a r v/r a\/r Depth in Feet. 2 524. 1.972 1.404! 735.7 564. 1.974 1.405 792 A 2. 2.5 656.25 2.457 1.567 1028. 706.25 2.460 1.568 1107. 2.5 3. 789. 2.939 .714 1352. 849. 2.943 1.716 1457. 3. 3.25 855.56 3.178 .783 1525. 920.56 3.183 1.784 1642. 3.25 3.5 922.25 3.417 .849 1705. 992.25 3.423 1.850 1836. 3.5 3.75 989.06 3.655 .912 1891. 1064.06 3.662 1.914 2037. 3.75 4. 1056. 3.892 .973 2083. 1136. 3.900 1.977 2246. 4. 4.25 1123.06 4.129 2.032 2282. 1208.06 4.136 2.034 2457. 4.25 4.5 1190.25 4.364 2.089 2486. 1280.25 4.373 2.091 2677. 4.5 4.75 1257.56 4.599 2.145 2697. 1352.56 4.610 2.147 2904. 4.75 5. 1325. 4.833 2.198 2912. 1425. 4.845 2.201 3136. 5. 5.25 1392.56 5.067 2.251 3135. 1497.56 5.079 2.254 3376. 5.25 5.5 1460.25 5.299 2.302 3361. 1570.25 5.313 2.305 3619. 5.5 5.75 1528.06 5.531 2.352 3594. 1643.06 5.546 2.355 3869. 5.75 6. 1596. 5.762 2.400 3830. 1716. 5.778 2.404 4125. 6. 6.25 1664.06 5.993 2.448 4074. 1789.06 6.010 2.452 4387. 6.25 6.5 1732.25 6.223 2.494 4320. 1862.25 6.241 2.498 4652. 6.5 6.75 1800.56 6.452 2.541 4575. 1835.56 6.470 2.544 4670. 6.75 7. 1869. 6.680 2.585 4831. 2009. 6.701 2.589 5201. 7. 7.25 1937.56 6.908 2.628 5092. 2082.56 6.930 2.632 5481. 7.25 7.5 2006.25 7.134 2.671 5359. 2156.25 7.159 2.676 5770. 7.5 7.75 2075.06 7.361 2.713 5630. 2230.06 7.386 2.718 6061. 7.75 8. 2144. 7.586 2.754 5905. 2304. 7.613 2.759 6357. 8. 8.25 2213.06 7.811 2.795 6186. 2378.06 7.840 2.800 6659. 8.25 8.5 2282.25 8.035 2.835 6470. 2452.25 8.066 2.840 6964. 8.5 8.75 2351.56 8 . 258 2.874 6758. 2526.56 8.290 2.879 7274. 8.75 9. 2421. 8.481 2.912 7050. 2601. 8.515 2.918 7590. 9. 9.25 2490.56 8.703 2.950 7347. 2675.56 8.739 2.956 7909. 9.25 9.5 2560.25 8.925 2.987 7647. 2750.25 8.962 2.993 8231. 9.5 9.75 2630.06 9.146 3.024 7953. 2825.06 9.185 3.031 8563. 9.75 10. 2700. 9.366 3.060 8262. 2900. 9.407 3.067 8894. 10. 10.5 2840.25 9.804 3.131 8893. 3050.25 9.849 3.138 9572. 10.5 11. 2981. 10.24 3.200 9539. 3201. 10.29 3.203 10253. 11. 11.5 3122.25 10.67 3.266 10197. 3352.25 10.73 3.276 10982. 11.5 12. 3264. 11.10 3.332 10876. 3504. 11.16 3.341 11707. 12. 13. 3549. 11.96 3.458 12272. 3809. 12.. 02 3.467 13206. 13. 14, 3836. 12.80 3.578 13725. 4116. 12.88 3.589 14772. 14. 15. 4125. 13.64 3.693 15234. 4425. 13.72 3.705 16395. 15. 16. 4416. 14.47 3.804 16798. 4736. 14.56 3.815 18068. 16. 18. 5004. 16.09 4.012 20076. 5364. 16.21 4.026 21595. 18. 72 FLOW OF WATER IN TABLE 8. Channels having a trapezoidal section, with side slopes of 1 to 1. Values of the factors a = area in square feet, and r = hydraulic mean depth in feet, and also ^/r~ a,nd. a\/r for use in the formulae v = c X Vr~X -x/~and Q = c X a^/7~X \/s~ BED 300 FEET. Depth in Feet. a r Vr~ a\/r 2. 604. 1.976 1.405 846. 2.5 756.25 2.463 1.569 1187. 3. 909. 2.947 1.717 1561. 3.25 985.56 3.188 1.777 1751. 3.5 1062.25 3.428 1.851 1966. 3.75 1139.06 3.667 1.915 2181. 4. 1216. 3.906 1.976 2403. 4.25 1293.06 4.144 2.035 2631. 4.5 1370.25 4.382 2.093 2868. 4.75 1447.56 4.619 2.149 3111. 5. 1525. 4.855 2.203 3360. 5.25 1602.56 5.090 2.256 3616. 5.5 1680.25 5.325 2.307 3876. 5.75 1758.06 5 . 559 2.358 4145. 6. 1836. 5.792 2.406 4417. 6.25 1914.06 6.025 2.455 4699. 6.5 1992.25 6.257 2.501 4983. 6.75 2070.56 6.489 2.547 5274. 7. 2149. 6.720 2.592 5570. 7.25 2227.56 6.950 2.636 5872. 7.5 2306.25 7.180 2.679 6178. 7.75 2385.06 7.392 2.719 6485. 8. 2464. 7.637 2.764 6810. 8.25 2543. 7.865 2.804 7131. 8.5 2622.25 8.092 2.845 7460. 8.75 2701.6 8.319 2.884 7791. 9. 2781. 8.545 2.923 8129. 9 25 2860.6 8.773 2.962 8473. 9.5 2940.25 8.995 2.999 8818. 9.75 3020. 9.219 3.036 9169. 10. 3100. 9.443 3.073 9526. 10.5 3260.25 9.889 3.144 10250. 11. 3421. 10.33 3.214 10995. 11.5 3582.25 10.77 3.281 11753. 12. 3744. 11.21 3.348 12535. 13. 4069. 12.08 3.476 14144. 14. 4396. 12.94 3.597 15812. 15. 4725. 13.80 3.715 17553. 16. 50.56 14.64 3.826 19344. OPEN AND CLOSED CHANNELS. 73 TABLE 9. Channels having a trapezoidal section, with side slopes of to 1. Values of the factors a ~ area in square feet, and r = hydraulic mean depth in feet, and' also v/~and a\/r for use in the formulae v = c X \/i r X v/s" and Q = c X o BED 1 FOOT. BED 2 FEET. Depth in Feet. a r Vr a^/r a r x/F a\/r Depth in Feet. 0.5 0.62 0.293 0.54 0.34 1.12 0.359 0.60 0.68 0.5 0.75 1.03 0.385 0.62 0.64 1.78 0.484 0.69 1.24 0.75 1. 1.50 0.464 0.68 1.02 2.50 0.590 0.77 1.92 1. 1.25 2.03 0.535 0.73 1.48 3.28 0.684 0.83 2.71 1.25 1.5 2.62 0.602 0.78 2.04 4.12 0.770 0.88 3.62 1.5 1.75 3.28 0.668 0.82 2.69 5.03 0.851 0.92 4.64 1.75 2. 4.00 0.731 0.86 3.43 6.00 0.927 0.96 5.78 2. 2.25 7.03 .000 1.00 7.03 2.25 2.5 8.12 .070 1.03 8.41 2.5 2.75 9.28 .139 1.07 9.90 2.75 3. 10.50 1.217 1.10 11.5 3. 3.25 11.78 .271 1.13 13.3 3.25 3.5 13.12 .337 1.16 15.2 3.5 3.75 14.53 .399 1.18 17.2 3.75 4. 16.00 1.462 1.21 19.4 4. BED 3 FEET. BED 4 FEET. Depih iu Feet. a r \/r a-\//* a , v~ a\/r Depth in Feet. 0.5 1.62 0.394 0.63 1.02 2.12 0.411 0.64 1.37 0.5 0.75 2.53 0.541 0.73 1.87 3.28 0.578 0.76 2.50 0.75 1. 3.50 0.668 0.82 2.86 4.50 0.722 0.85 3.82 1. 1.25 4.53 0.782 0.88 4.00 5.78 0.851 0.92 5.33 1.25 1.5 5.62 0.885 0.94 5.29 7.35 0.969 0.98 7.01 1.5 1.75 6.78 0.981 0.99 6.72 8.53 .078) 1.04 8.86 1.75 2. 8.00 .071 1.03 8.28 10.00 .180 1.09 10.9 2. 2.25 9.28 .156 1.07 9.98 11.53 .277 1.13 13.0 2.25 2.5 10.62 .237 1.11 11.8 13.12 .369 1.17 15.4 2.5 2.75 12.03 .315 1.15 13.8 14.78 .456 1.21 17.8 2.75 3. 13.50 .391 .18 15.9 16.50 .541 .24 20.5 3. 3.25 15.03 .464! 1.21 18.2 18.28 .623 .27 23.3 3.25 3.5 16.62 1.536 .24 20.6 20.12 .702 .30 26.3 3.5 3.75 18.28 1.606 1.27 23.2 22.03 .779 .33 29.4 3.75 4. 20.00 1.675 .29 25.9 24.00 .854 .36 32.7 4. 4.25 21.78 1.742 .32 28.8 26.03 .957 .39 36.2 ! 4.25 4.5 23.62 1.809 1.35 31.8 28.12 2.000 .41 39.8 4.5 5. 27.50 1.939 1.39 38.3 32.50 2.1411 .46 47.6 5. 74 FLOW OF WATER IN TABLE 9. Channels having a trapezoidal section, with side slopes of | to 1 . Values of the factors a = area in square feet, and r -- hydraulic mean depth in feet, and also -^/^aud a\/V for use in the formulae v = c X ^/r~ X \A~ and Q = c X a^/T X \S*~~ BED 5 FEET. BED 6 FEET. Depth in Feet. a r Vr a\/r a r \/r a\,/r Depth in Feet. 05. 2.625 .429 .65 1.72 3.125 .439 .66 2.07 0.5 0.75 4.031 .604 .77 3.14 4.781 .623 .78 3.78 0.75 1. 5.500 .760 .87 4.79 6.500 .789 .89 5.77 1. 1.25 7.031 .902 .95 6.68 8.281 .942 .97 8.04 1.25 1.5 8.625 1.032 1.02 8.76 10.12 .082 .04 10.53 1.5 1.75 10.28 .156 .08 11.04 12.03 .214 .10 13.31 1.75 2. 12.00 .267 .13 13.51 14.00 .337 .16 16.19 2. 2.25 13.781 .374 .17 16.16 16.031 .453 .21 19.33 2.25 2.5 15.625 .476 .21 18.98 18.125 .564 .25 22.67 2.5 2.75 17.531 .572 .25 21.98 20.281 .669 .29 26.21 2.75 3. 19.500 .666 .29 25.16 22 . 500 .778 .33 29.94 3. 3.25 21.531 .755 .33 28.52 24.781 .868 .37 33.87 3.25 3.5 23.625 1.834 .36 32.06 27 . 125 . 984 .40 37.99 3.5 3.75 25.781 1.928 .39 35.78 29.231 2.032 1.43 42.31 3.75 4. 28.000 2.008 .42 39.68 32.000 2.223 1.46 46.83 4. 4.5 32.625 2.166 .47 48.02 36.625 2.280 1.52 56.45 4.5 5. 37.500 2.318 .52 57.09 42.5001 2.474! 1.57 66.85 5. 6. 48.00 2.606 .61 77.28 54.00 2.781! 1.67 90.05 6. BED 7 FEET. BED 8 FEET. Depth Depth in Feet. ct r v*r~ a\/r a r v^r a\/r in Feet. 0.5 3.62 0.447 .67 2.42 4.12 0.452 .67 2.77 0.5 0.75 5.53 0.637J .79 4.43 6.28 0.649 .80 5.06 0.75 1. 7.5 0.812 .90 6.76 8.5 0.830 .91 7.74 1. 1.25 9.53 0.973 .99 9.40 10.78 0.999 1. 10.77 1.25 1.5 11.62 .123 .06 12.31 13.12 .156 1.07 14.11 1.5 1.75 13.78 .263 .12 15.49 15.53 .304 1.14 17.74 1.75 2. 16.00 .395 .18 18.90 18.00 .443 1.20 21.63 2. 2.25 18.28 .519 .23 22.54 20.53 .576 1.25 25.78 2.25 2.5 20.62 .639 .28 26.40 23.12 .702 1.30 30.17 2.5 2.75 23.03 .751 .32 30.48 25.78 .822 1.35 34.80 2.75 3. 25.50 .859 .36 34.78 28.5 .938 1.39 39.67 3. 3.25 28.03 .965 .40 39.29 31.28 2.049 1.43 44.77 3.25 3.5 30.62 2.067 .44 44.01 34.12 2.156 1.47 50.10 3.5 3.75 33.28 2.163 .47 48.95 37.03 2.260 1.50 55.68 3.75 4. 36.0 2.258 .50 54.10 40. 2.361 1.54 61.47 4. 4.5 41.62 2.439 .56 65.02 46.12 2.554 1.60 73.71 4.5 5. 47.5 2.613 .62 76.78 52.50 2.737 1.65 86.86 5. 6. 60.0 2.939 .71 102.85 66. 3.081 1.76 115.85 6. OPEN AND CLOSED CHANNELS. 75 TABLE 9. Channels having a trapezoidal section, with side slopes of \ to 1. Values of the factors a = area in square feet, and r = hydraulic mean depth in feet, and also \/7 and a^/r for use in the formulae v = c X Vr X N/Tand Q = c X a^/r X V* BED 9 FEET. BED 10 FEET. Depth in n D r Feet. a r v/r aVr Co r Vr a\/r Feet. 0.5 4.62 .457 .676 3.12 5.12 .461 .68 3.48 0.5 0.75 7.03 .659 .812 5.71 7.78 .666 .81 6.37 0.75 1. 9.5 .845 .919 8.73 10.5 .858 '.93 9.73 1. 1.25 12.03 1.02 1.01 12.15 13.28 1.038 1.02 13.54 1.25 1.5 14.62 1.184 1.09 15.91 16.12 1.192 1.1 17.72 1.5 1.75 17.35 1.344 .16 20. 19.03 1.367 .17 22.26 1.75 2 20. 1.485 .22 24.37 22. 1.52 .23 27.13 2. 2.25 22.78 1.624 .28 29.03 25.03 1.665 .29 32.31 2.25 2.5 25.62 1.756 .33 33.96 28.12 1.804 .34 37.78 2.5 2.75 28.53 1.883 .38 39.15 31.28 1.937 .39 43.54 2.75 3. 31.5 2.005 .42 44.61 34.5 2.065 .44 49.57 3. 3.25 34.53 2.121 .46 50.31 37.78 2.188 .48 55.88 3.25 3.5 37.62 2.236 .5 56.26 41.12 2.308 .52 62.46 3.5 3.75 40.78 2.346 1.54 62.47 44.53 2.422 .56 69.31 3.75 4. 44. 2.446 1.57 68.91 48. 2.534 .59 76.41 4. 4.25 47.28 2.555 1.6 75.59 51.53 2.642 .63 83.77 4.25 4.5 50.62 2.656 1.63 82.51 55.12 2.748 .66 91.38 4.5 5. 57.5 2.849 1.69 97.06 62.5 3.097 .72 107 . 36 5. 6. 72. 3.212 1.79 129.03 78. 3.48 .82 142.35 6. BED 11 FEET. BED 12 FEET. Depth Depth in Feet. a r v/r a-v/r a r Vr a^/r in Feet. 0.5 5.625 .464 .68 3.8 6.12 .467 .68 4.2 0.5 0.75 8.531 .673 .81 7. 9.28 .679 .82 7.6 0.75 1. 11.5 .869 .93 10.7 12.5 .878 .94 11.7 1. 1.25 14.531 1.053 1.02 14.9 15.78 1.067 .03 16.3 1.25 1.5 17.625 1.228 1.11 19.5 19.1 .244 .12 21.3 1.5 1.75 20.78 1.393 1.18 24.5 22.5 .414 .19 26.8 1.75 2. 24. 1.551 1.25 29.9 26. .578 .26 32.7 2. 2,25 27.281 1.702 1.31 35.6 29.5 .732 .32 38.9 2.25 2.5 30.625 1.846 1.36 41.6 33.1 .882 .37 45.5 2.5 2.75 34.031 1.984 1.41 47.9 36.8 2.028 .42 52.4 2.75 3. 37.5 2.118 1.46 54.6 40.5 2.165 .47 59.6 3. 3.25 41.03 2.246 1.5 61.5 44.3 2.299 .52 67.1 3.25 3.5 44.63 2.372 1.54 68.7 48.1 2.427 .56 75. 3.5 3.75 48.3 2.492 1.58 76.2 52. 2.551 .6 83.1 3.75 4. 52. 2.607 1.61 84. 56. 2.674 1.64 91.6 4. 4.5 59.6 2.83 1.68 100.3 64.1 2.905 1.7 109.3 4.5 5. 67.5 2.021 1.74 117.8 72.5 3.128 1.77 128.2 5. 5.5 75.6 3.245 1.8 136.2 81.1 3.338 1.83 148.2 5.5 6. 84. 3.444 1.85 155.8 90. 3.541 1.88 169.4 6. FLOW OF WATER IN TABLE 9. Channels having a trapezoidal section, with side slopes of \ to 1. Values of the factors a area in square feet, and r = hydraulic mean depth in feet, and also ^/r and a^/r for use in the formulae v = c X Vr X v'a" and Q = c X a\/r X \/$ BED 13 FEET. Depth in Feet. a r VV a\/r 0.5 6.62 .469 .68 4.5 0.75 10. 6.682 .82 8.5 1. 13.5 .886 .94 12. 1.25 17. 1.076 .03 17.7 1.5 20.6 1.26 .12 23.2 1.75 24.3 1.437 .2 29.2 2. 28. 1.603 .27 35.4 2.25 31.8 1.764 .33 42.2 2.5 35.6 1.915 .38 49.3 2.75 39.5 2.063 .44 56.8 3. 43.5 2.207 .49 64.6 3.25 47.5 2.344 .53 72.8 3.5 51.6 2.479 .57 81.3 3.75 55.8 2.609 .61 90.1 4. 60. 2.734 .65 99.2 4.5 68.6 2.975 .73 118.4 5. 77.5 3.189 .79 138.7 5.5 86.6 3.423 1.85 160.3 6. 96. 3.634 1.91 183. BED 14 FEET. a r v^ a\/r Depth in Feet. 7.12 All .69 4.9 0.5 10.8 .689 .83 8.9 0.75 14.5 .893 .94 13.7 1. 18.3 .09 1.05 19.1 1.25 22.1 .273 1.13 25.0 1.5 26. .451 .2 31.4 1.75 30. .624 .27 38.2 2 34. .787 .33 45.5 2.25 38.1 .945 .39 53.2 2.5 42.3 2.099 .45 61.2 2.75 46.5 2.246 .5 69.7 3. 50.8 2.388 .55 78.5 3.25 55.1 2.526 .59 87.6 3.5 59.5 2.658 .63 97.1 3.75 64. 2.79 .67 106. 4. 73.1 3.038 .74 127.5 4.5 82.5 3.276 .81 149.3 5. 92.1 3.502 .87 172.4 5.5 102. 3.72 .93 196.7 6. BED 15 FEET. BED 16 FEET. Depth in Feet. a f Vr a\/r a r Vr a\/r Depth in Feet. 0.5 7.62 .473 .69 5.2 8.12 .474 .69 5.6 0.5 0.75 11.5 .689 .83 9.6 12.3 .696 .83 10.2 0.75 1. 15.5 .899 .95 14.7 16.5 .905 .95 15.7 1. 1.25 19.5 1.096 1.05 20.5 20.8 .161 .05 21.8 1.25 1.5 23.6 1.289 1.13 26.8 25.1 .297 .14 28.6 1.5 1.75 27.8 1.47 1.21 33.7 29.5 .482 .22 37. 1.75 2. 32. 1.643 1.28 41. 34. .661 .29 43.8 2. 2.25 36.3 1.812 1.34 49.2 38.5 .831 .35 52.6 2.25 2.5 40.6 1.972 1.4 57.1 43.1 .996 .41 60.9 2.5 2.75 45. 2.128 1.46 65.7 47.8 2.158 .47 70.2 2.75 3. 49.5 2.28 1.51 74.7 52.5 2.312 .52 79.8 3. 3.25 54. 2.425 1.56 84.2 57.3 2.463 .57 89.9 3.25 3.5 58.6 2.568 1.6 93.9 62.1 2.608 .61 100.3 3.5 3.75 63.3 2.707 1.65 104.1 67. 2.748 .66 111.1 3.75 4. 68. 2.84 1.69 114.6 72. 2.887 . 7 122.3 4. 4.5 77.6 3.096 1.76 136.3 82.1 3.15 .78 145.8 4.5 5. 87.5 3.342 1.83 160. 92.5 3.403 .84 170.6 5. 5.5 97.6 3.575 1.89 184.6 103.1 3.643 .91 196.9 5.5 6. 108. 3.801 1.95 210.5 114. 3.875 .97 224.4 6. OPEN AND CLOSED CHANNELS. 77 TABLE 9. Channels having a trapezoidal section, with side slopes of -J to 1. Values of the factors a = area in square feet, and r = hydraulic mean depth in feet, and also A/? 7 and a^/r for use in the formulae v = c X Vr X Vs and Q = c X a^/r X V* BED 17 FEET. BED 18 FEET. Depth in Feet. a r V~ a^/r a r x/r a\/r Depth in Feet. 0.75 13.031 .696 .84 10.9 13.8 .701 .84 11.5 0.75 1. 17.5 .915 .95 16.7 18.5 .914 .96 17.7 1. 1.25 22.031 .113 1.05 23.2 23.3 1.125 1.06 24.6 1.25 1.5 26.625 .308 1.14 30.4 28.1 1.316 1.15 32.3 1.5 1.75 31.281 .496 1.22 38.3 33. 1.506 1.23 40.6 1.75 2. 36. .677 1.29 46.6 38. 1.691 1.3 49.4 2. 2.25 40.8 .852 1.36 55.5 43. 1.867 1.37 58.8 2.25 2.5 45.6 2.019 1.42 64.8 48.1 2.039 1.43 68.7 2.5 2.75 50.5 2.182 1.48 74.7 53.3 2.207 1.49 79.1 2.75 3. 55.5 2.341 1.53 84.9 58.5 2.368 1.54 90. 3. 3.25 60.5 2.493 1.58 95.6 63.8 2.525 1.59 101.3 3.25 3.5 65.6 2.643 1.63 106.7 69.1 2.677 1.64 113.1 3.5 3.75 70.8 2.789 1.67 118.2 74.5 2.824 1.68 125.3 3.75 4. 76. 2.93 1.71 130.1 80. 2.969 1.72 137.9 4. 4.5 86.6 3.2 1.79 155. 91.1 3.246 1.80 164.2 4.5 5. 97.5 3.46 1.86 181.4 102.5 3.513 1.87 192.1 5. 5.5 108.6 3.707 1.93 209.2 114.1 3.766 1.94 221.5 5.5 6. 120. 3.945 1.99 238.3 126. 4.014 2 252.3 6. 7. 143.5 4.395 2.09 300. 150.5 4.472 2^11 318.3 7. BED 19 FEET. BED 20 FEET. Depth iu 0.5 0.75 1. 1.25 1.5 1.75 2. 2.25 2.5 2.75 3. 3.25 3.5 3.75 4. 4.25 4.5 5. 5.5 6. 7. 8. a T v/r a\/r a r and a*/r for use in the formulae v = c X \/r X <\/~ and Q = c X o\/r X \/?~ BED 45 FEET. BED 50 FEET. Depth in Feet. a r Vr a\/r a r Vr (i\/r Depth in Feet. 0.50 22.62 .490 .70 16 25.37! .490 .700 17.8 0.50 0.75 34.03 .729 .85 29 38.34 .728 .853 32.7 0.75 1. 45.50 .953 .98 45 51.50 .961 .980 50.5 1. 1.25 57.03 1.193 .09 62 64.84 1.190 1.091 70.7 1.25 1.50 68.62 1.419 .19 82 76.12 1.427 1.19 91. 1.50 1.75 80.28 1.641 .28 103 89.03 1.651 1.28 114. 1.75 2. 92.00 1.860 .36 125 102. 1.873 .37 140. 2. 2.25 103.78 2.074 .44 150 115. 2.090 .45 166. 2.25 2.5 115.62 2.285 .51 175 128.1 2.305 .52 194. 2.5 2.75 127.53 2.493 .58 201 141.3 2.517 .59 224. 2.75 3. 139.5 2.698 .64 229 154.5 2.723 .65 255. 3. 3.25 151.53 2.899 .70 258 167.8 2.930 .71 287. 3.25 3.5 163.62 3.098 .76 288 181.1 3.132 .77 320. 3.5 3.75 175.78 3.293 .82 319 194.5 3.331 .83 355. 3.75 4. 188. 3.485 .87 351 208. 3.529 .88 391. 4. 4.25 200.28 3.675 1.92 384 221.5 3.722 1.93 427. 4.2o 4.5 212.62 3.861 1.96 418 235.1 3.914 1.98 465. 45 4.75 225.03 4.046 2.01 453 248.8 4.104 2.03 504. 4.75 5. 237.50 4.228 2.06 488 262.5 4.291 2.07 544. 5. 5.25 250.03 4.407 2.10 525 276.3 4.475 2.12 585. 5.25 5.5 262.62 4.583 2.14 562 290.1 4.657 2.16 626. 5.5 5.75 275.28 4.758 2.18 600 304. 4.836 2.20 669. 5. 7o 6. 288. 4.930 2.22 639 318. 5.015 2.24 712. 6. 6.25 300.78 5.100 2.26 679 332. 5.190 2.28 756. 6.25 6.5 313.62 5.268 2.30 720 346.1 5.360 2.32 802. 6.5 6.75 326.53 5.434 2.34 761 360.3 5.535 2.36 848. 6.75 7. 339.50 5.598 2.37 803 374.5 5.704 2.39 894. 7. 7.25 352.53 5.759 2.40 725 388.8 5.872 2.43 942. 7.25 7.5 365.62 5.9H 2.43 890 403.1 6.037 2.46 990. 7.5 7.75 378.78 6.077 2.47 934 417.5 6.156 2.49 1040. 7.75 8. 392. 6.233 2.50 979 432. 6.363 2.52 1090. 8. 8.25 405.28 6.388 2.53 1024 446.5 6.523 2.55 1141. 8.25 8.5 418.62 6.540 2.56 1071 461.1 6.682 2.58 1192. 8.5 8.75 432.03 6.691 2.59 1118 475.8 6.840 2.61 1244. 8.75 9. 445.5 6.842 2.62 1165 490.5 6.995 2.64 1295. 9. 9.5 472.62 7.135 2.67 1262 520.1 7.300 2.70 1405. 9.5 10. 500. 7.423 2.72 1362 550. 7.601 2.76 1516. 10. 10.5 527.62 7.705 2.78 1465 580.1 7.809 2.81 1630. 10.5 11. 555.50 7.982 2.83 1569 610.5 8.184 2.86 1746. 11, OPEN AND CLOSED CHANNELS. 81 TABLE 9. Channels having a trapezoidal section, with side slopes of J to 1. Values of the factors a = area in square feet, and r hydraulic mean depth in feet, and also ^/r and a\/r for use in the formulae v = c X Vr X \/8 and Q = c X a^/r X \/a~ BED 60 FEET. Depth iu Feet. a r Vr a^/r 1. 60.50 .972 .99 60 1.5 91.12 1.438 1.20 109 1.75 106.53 1.667 1.29 137 2. 122. 1.892 1.38 168 2.25 137.53 2.115 1.46 200 2.5 153.12 2.334 1.53 234 2.75 168.78 2.552 1.60 270 3. 184.50 2.781 1.66 307 3.25 200.28 2.977 1.73 346 3-5 216.12 3.188 1.79 386 3.75 232.03 3.378 1.84 427 4. 248. 3.597 1.90 470 4.25 264 . 03 3.799 1.96 515 4.5 280.12 3.998 2. 560 4.75 296.28 4.195 2.05 607 5. 312.50 4.390 2.10 655 5.25 328.78 4.583 2.15 704 5.5 345.12 4.774 2.18 754 5 75 361.53 4.962 2.23 805 6. 378. 5.149 2.27 858 6.25 394.53 5.333 2.31 911 6.5 411.12 5.516 2.35 965 6.75 427 . 78 5.697 2.39 1021 7. 444.50 5.876 2 42 1077 7.25 461.28 6.053 2^46 1135 7.5 478.12 6.228 2.50 1193 7.75 495.03 6.363 2.53 1252 8. 512. 6.574 2.56 1313 8.25 529.03 6.744 2.59 1374 8.5 546.12 9.912 2.63 1436 8.75 563.28 7.079 2.66 1499 9. 580.50 7.245 2.69 1563 9.5 615.12 7.571 2.75 1693 10. 650. 7.892 2.81 1826 10.5 685.12 8.271 2.86 1963 11. 720.50 8.517 2.92 2103 82 FLOW OF WATER IN TABLE 10. Sectional areas, in square feet, of trapezoidal channels, with side slopes of Jto 1. Depth in Feet. BED WIDTH 70 feet 80 feet. 90 feet. 100 feet. 120 feet. 1. 70.50 80.50 90.50 100.50 120.50 1.5 106.12 121.12 136.12 151.12 181.12 2. 142. 162. 182. 202. 242. 2.25 160.03 182.53 205 . 03 227.53 272.r,:; 2.5 178.12 203.12 228.12 253.12 303.1-2 2.75 196.28 224.78 252.28 278.78 333.78 3. 214.50 244.50 274.50 304.50 364.50 3.25 232.78 265.28 297.78 330.28 395.28 3.5 251.12 286.12 321.12 356.12 426.12 3.75 269.53 307.03 344.53 382.03 457.03 4. 288. 328. 368. 408. 488. 4.25 306.53 349.03 391.53 43*. 03 519.03 4.5 325.12 370.12 415.12 460.12 550.12 4.75 343.78 391.28 438.78 486.28 581.28 5. 362.50 412.50 462.50 512.50 612.50 5.25 381.28 433.78 486.28 538.78 663.78 5.5 400.12 455.12 510.12 565.12 675.12 5.75 419.03 476.53 534.03 591.53 706.53 6. 438. 498. 558. 618. 738. 6.25 457.03 519.53 582.03 644.53 769.53 6.5 476.12 541 . 12 606.12 671.12 801.12 6.75 495.28 562.78 630.28 697.78 832.78 7. 514.50 584.50 654.50 724.50 864 . 50 7.25 533.78 606.28 678.78 751.28 896 . 28 7.5 553.12 628 . 12 703.12 778.12 928.12 7.75 572.53 650.03 727.53 805.03 960.03 8. 592. 672. 752. 832. 992. 8.25 611.53 694.03 776.53 859.03 1024.03 8.5 631.12 716.12 701 . 12 886.12 1056.12 8.75 650.78 738.28 825.78 913.28 1088.28 9. 670.50 760.50 850.50 940.50 1120.50 9.25 690.28 782.78 875.28 967.78 1152.78 9.5 710.12 805.12 900.12 995.12 1185.12 9.75 730.03 827.53 925.03 1022.53 1117.53 10. 750. 850. 950. 1050. 1250. 10.5 790.12 895.12 1000.12 1105.12 1315.12 11. 830.50 940.50 1050.50 1160.50 1380.50 11.5 871.12 986.12 1101.12 1216.12 1446.12 12. 912. 1032. 1152. 1272. 1512. OPEN AND CLOSED CHANNELS. 83 TABLE 10. Sectional areas, in square feet, of trapezoidal channels, with side slopes of } to 1. Depth BED WIDTH ill Feet. 140 feet. 160 feet. 180 feet. 200 feet. 220 feet. 1. 140.50 160.50 180.50 200.50 220.50 2. 282. 322. 362. 402. 442. 2.5 353.12 403.12 453.12 503. 10 553.12 2.75 388.78 443.78 498.78 553.78 608.78 3. 424.50 484.50 544.50 604.50 664.50 3.25 460.28 525 . 28 590.28 655.28 720.28 3.5 496.12 566.12 636.12 706.12 776.12 3.75 532.03 607.03 682.03 757.03 832.03 4. 568. 648. 728. . 808. 888.80 4.25 604.03 689.03 774.03 859.03 944.03 4.5 640.12 730.12 820.12 910.12 1000.12 4.75 676.28 771.28 866.28 961.28 1056.28 5. 712.50 812.50 912.50 1012.50 1112.50 5.25 748.78 853.78 958.78 1063.78 1168.78 5.5 785.12 895.12 1005.12 1115.12 1225.12 5.75 821.53 936.53 1051.53 1166.53 1281.53 6. 858. 978. 1098. 1218. 1338. 6.25 894.53 1019.53 1144.53 1269 53 1394.53 6.5 931.12 1061.12 1191.12 1321.12 1451.12 6.75 967.78 1102.78 1237.78 1372.78 1507.78 7. 1004.50 1144.50 1284.50 1424.50 1564.50 7.25 1041.28 1186.28 1331.28 1476.28 1621.28 7.5 1078.12 1228.12 1378.12 1528.12 1678.12 7.75 1115.03 1270.03 1425.03 1580.03 1735.03 8. 1152. 1312. 1472. 1632. 1792. 8.25 1189.03 1354.03 1519.03 1684.03 1849.03 8.5 1226.12 1396.12 1566.12 1736.12 1906.12 8.75 1263.28 1438.28 1613.28 1788.28 1963.28 9. 1300.50 1480.50 1660.50 1840.50 2020.50 9.25 1337.78 1522.78 1707.78 1892.78 2077.78 9.5 1375.12 1565.12 1755.12 1945.12 2135.12 9.75 1412.53 1607.53 1802.53 1997.53 2192.53 10. 1450. 1650. 1850. 2050. 2250. 10.5 1525.12 1735.12 1945.12 2155.12 2365.12 11. 1600.50 1820.50 2040.50 2260.50 2480.50 11.5 1676.12 1906.12 2136.12 2366.12 2596.12 12. 1752. 1992. 2232. 2472. 2712. 13. 1904.50 2164.50 2424.50 2684.50 2944.50 14. 2058. 2338. 2618. 2898. 3178. 15. 2212.50 2512.50 2812.50 3112.50 3412.50 16. 2368. 2688. 3008. 3328. 3648. 84 FLOW OF WATER IN TABLE 10. Sectional areas, in square feet, of trapezoidal channels, with side slopes of ito 1. Depth BED WIDTH 111 Feet. 240 feet. 260 feet. 280 feet. 300 feet. 1. 240.50 260.50 280.50 300.50 2. 482. 522. 562. 602. 2.5 603.12 653.12 703.12 753.12 2.75 663.78 718.78 773.78 828.78 3. 724.50 784.50 844.50 904 . 50 3.25 785.28 850.28 915.28 980.28 3.5 846.12 916.12 986.12 1056.12 3.75 907.03 982.03 1057.03 1132.03 4. 968. 1048. 1128. 1208. 4.25 1029.03 1114.03 1199.03 1284.03 4.5 1090.12 1180.12 1270.12 1360.12 4.75 1151.28 1246.28 1341.28 1436.28 5. 1212.50 13 J 2. 50 1412.50 1512.50 5.25 1273.78 1378.78 1483.78 1588.78 5.5 1335.12 1445.12 1555.12 1665.12 5.75 1396.53 1511.53 1626.53 1741.53 6. 1458. 1578. 1698. 1818. 6.25 1519.53 1644.53 1769.53 1894.53 6.5 1581.12 1711.12 1841.12 1971.12 6.75 1642.78 1777.78 1912.78 2047.78 7. 1704.50 1844.50 1984.50 2124.50 7.25 1766.28 1911.28 2056.28 2201.28 7.5 1828.12 1978.12 2128.12 2278.12 7.75 1890.03 2045.03 2200.03 2355 . 03 8. 1952. 2112. 2272. 2432. 8.25 2014.03 2179.03 2344.03 2509.03 8.5 2076.12 2246.12 2416.12 2586.12 8.75 2138.28 2313.28 2488.28 2663.28 9. 2200.50 2380.50 2560.50 2740.50 9.25 2262.78 2447.78 2632.78 2817.78 9.5 2325.12 2515.12 2705.12 2895.12 9.75 2387.53 2582.53 2777.53 2972.53 10. 2450. 2650. 2850. 3050. 10.5 2575.12 2785.12 2995.12 3205.12 11. 2700.50 2920.50 3140.50 3360.50 11.5 2826.12 3156.12 3486.12 3816.12 12. 2952. 3192. 3432. 3672. 13. 3204.50 3464.50 3724.50 3984.50 14. 3458. 3738. 4018. 4298. 15. 3712.50 4012.50 4312.50 4412.50 16. 3968. 4288. 4608. 4928. OPEN AND CLOSED CHANNELS. 85 TABLE 11. Channels having a trapezoidal section, with side slopes of 1| to 1. Values of the factors a area in square feet, and r = hydraulic mean depth in feet, and also \/r and a\/r for use in the formulae v = c X -\/r~ X -s/s" and also Q = c X a\/r X \A' BED 1 FOOT. BED 2 FEET. Depth Depth in Feet. a r Vr a\/r a r \/r a\/r in Feet. 0.5 .87 .312 .56 .49 1.375 .362 .60 .83 0.5 0.75 1.59 .452 .65 1.04 2.344 .499 .71 1.66 0.75 1. 2.5 .542 .74 1.84 3.5 .624 .79 2.76 1. 1.25 3.59 .652 .81 2.89 4.844 .744 .86 4.17 1.25 1.5 4.87 .761| .87 4.24 ! 6.37 .860 .93 5.93 1.5 1.75 6.34 .868 .93 5.9 8.09 .974 .99 8. 1.75 2. 8. .974 .99 7.9 10. 1.086 1.04 10.4 2. 2.25 9.84 1.081 1.04 10.2 12.09 1.196 1.09 13.2 2.25 2.5 11.87 1.186 1.09 12.9 14.37 1.294 1.14 16.4 2.5 2.75 14.09 1.280 1.14 16.1 16.84 1.414 1.19 20. 2.75 3. J6.5 1.397 1.18 19.5 19.50 1.521 1.23 24. 3. 3.25 22.34 1.629 1.28 28.5 3.25 3.5 25.37 1.736 1.32 33.4 3.5 3.75 28.6 1.842 1.36 38.8 3.75 4. 32. 1.949 1.39 44.4 4. BED 3 FEET. BED 4 FEET. Depth iu Feet. a r vT a\/r a i r ! vT" a^/r Depth in Feet. 0.5 1.875 .499 .63 1.17 2.37 .409 .64 1.51 0.5 0.75 3.094 .543 .73 2.29 3.84 .574 .76 2.92 0.75 1. 4.50 .681 .83 3.71 5.5 .723 .85 4.67 1. 1.25 6.09 .811 .90 5.48 7.34 .863i .93 6.83 1.25 1.5 7.87 .935 .97 7.62 9.37 .996 9.38 1.5 1.75 9.84 1.057 1.03 10.1 11.59 1.125 .06 12.3 1.75 2. 12. 1.175 1.08 13. 14. 1.248 .12 15.7 2. 2.25 14.34 1.291 1.14 16.4 16.59 1.370 .17 19.4 2.25 2.5 16.87 1.405 .19 20.1 19.37 1.489 .22 23.6 2.5 2.75 19.59 1.518 .23 24.1 22.34 1.607 .27 28.4 2.75 3. 22.50 1.628 .28 28.8 25.50 1.721 .31 33.4 3. 3.25 25.60 1.739 .32 33.8 28.84 1.835 .36 39.2 3.25 3.5 28.87 1.848 .36 39.3 32.37 1.947 .40 45.3 3.5 3.75 32.34 1.958 .40 45.3 36.09 2.060 .44 52. 3.75 4. 36. 2.067 .44 51.8 40. 2.171 .47 59. 4. 4.25 39.84 2.175 1.48 59. 44.09 2.282 1.51 66.6 4.25 4.5 43.87 2.283 1.51 66.3 48.37 2.392 1.55 75. 4.5 5. 52.5 2.497 1.58 83. 57.50 2.610 1.62 92.9 5. 86 FLOW OF WATER IN TABLE 11. Channels having a trapezoidal section, with side slopes of 1 J to 1. Values of the factors a = area in square feet, and r = hydraulic mean depth in feet, and also */r and a\/r for use in the formulae v -.= c X \/r X \/s and Q = c X a^/r X V* BED 5 FEET. BED 6 FKET. Depth Depth in Feet. a r VT a\/r a r Vr u\/r in Feet. 0.5 2.875 .423 .64 1.87 3.37 .433 .66 2.23 0.5 0.75 4.59 .597 .77 3.54 5.34 .614 .78 4.17 0.75 1. 6.5 .755 .87 5.64 7.5 .780 .89 6.62 1 . 1.25 8.59 .904 .95 8.17 9.84 .937 .97 9.55 1.25 1.5 10.87 1.045 1.02 11.09 12.37 1.084 1.04 12.9 1.5 1.75 13.34 1.179 1.09 14.54 15.09 1.226 1.11 16.8 1.75 2. 16. 1.310 1.15 18.24 18. 1.362 .17 21. 2. 2.25 18.84 1.437 1.20 22.61 21.09 1.495 .23 26. 2.25 2.5 21.87 1.560 1.25 27 . 33 24.37 1.623 .28 31.2 2.5 2.75 25.09 1.683 1.30 32.62 27.84 1.750 .33 37] 2.75 3. 28.5 1.802 1.34 38.20 31.5 1.873 .37 43.2 3. 3.25 32.09 1.919 1.39 44.61 35.34 1.995 .41 49.8 3.25 3.5 35.87 2.036 1.43 51.30 39.37 2.114 .45 57.1 3.5 3.75 39.84 2.153 1.47 58.57 43.59 2.233 .49 65. 3.75 4. 44. 2.266 1.51 66.40 48. 2.350 .53 73.6 4. 4.5 52.87 2.491 1.58 83.54 57.37 2.581 .60 91.8 4.5 5. 62.50 2.713 1.64 103. 67.50 2.808 1.67 113.1 5. 6. 84. 3.153 1.78 149.5 90. 3.256 1.81 162.9 6. BED 7 FEET. BED 8 FEET. Depth Depth in Feet. a r Vr a^T a r Vr aVr in Feet. 0.5 3.87 .440 .67 2.57 4.37 .446 .67 2.92 0.5 0.75 6.09 .623 .79 4.81 6.84 .640 .80 5.48 0.75 1. 8.5 .801 .89 7.61 9.5 .818 .90 8.58 1. 1.25 11.09 .965 .98 10.87 12.34 .987 .99 12.2 1.25 1.5 13.87 .119 1.06 14.71 15.37 1.146 .07 16.5 1.5 1.75 16.84 1.266 1.12 18.90 18.59 1.299 .14 21.2 1.75 2. 20. 1.407 1.18 23.70 22. 1.446 .20 26.5 2. 2.25 23.34 .545 1.24 29. 25.59 1.589 .26 32.3 2.25 2.5 26.87 .679 1.30 34.9 29.37 1.726 .31 38.5 2.5 2.75 30.59 .809 1.35 41.3 33.34 i.862 .36 45.4 2.75 3. 34.50 .936 1.39 48. 37.50 1.993 .41 52.9 3. 3.25 38.59 2.062 1.44 55.6 41.84 2.125 .46 61.1 3.25 3.5 42.87 2.184 1.48 63.4 46.37 2.248 .50 69.6 3.5 3.75 47.34 2.307 1.52 72. 51.09 2.374 .54 78.7 3.75 4. 52. 2.427 1.56 81.1 56. 2.497 .58 88.5 4. 4.5 61.87 2.664 1.63 100.9 66.37 2.739 .65 109.5 4.5 5. 72.50 2.897 1.70 123.3 77.50 2.976 .72 133.3 5. 6. 96. 3.353 1.83 175.8 102. 3.442 .85 189.2 6. OPEN AND CLOSED CHANNELS. 87 TABLE 11. Channels naving a trapezoidal section, with side slopes of 1 J to 1. Values of the factors a = area in square feet; r = hydraulic mean depth in feet, and alsa ^/r and a\/r for use in the formulae v = c X \/r X Vs and Q = c X a\/r X -s/s BED 9 FEET. BED 10 FEET. Depth Depth m Feet. a r N/r a\/r a r Vr a\/r in Feet. 0.5 4.875 .451 .68 3.28 5.375 .456 .68 3.63 0.5 0.75 7.59 .649 .81 6.15 8.344 .657 .81 6.15 0.75 1. 10.5 .833 .91 9.58 11.5 .845 .92 10.58 1. 1.25 13.594 1.006 13.6 14.844 1.023 .01 15. 1.25 1.5 16.875 1.170 !os 18.3 18.375 .192 .09 20. 1.5 1.75 20.344 1.329 .15 23.4 22.094 .355 .16 25.6 1.75 2. 24. 1.480 .22 29.3 26. .510 .23 32. 2. 2.25 27.844 1.623 .28 35.5 30.094 .662 .29 38.8 2.25 2.5 31.875 1.769 .33 42.4 34.375 .807 .34 46.2 2.5 2.75 36.094 1.909 .38 49.8 38.844 .951 .39 54. 2.75 3. 40.5 2.044 .43 57.9 43.5 2.090 .44 62.6 3. 3.25 45.094 2.176 .48 66.7 48 . 344 2.223 .49 72. 3.25 3.5 49.875 2.306 .52 75.8 53.375 2.358 .54 82.2 3.5 3.75 54.844 2.440 .56 85.6 58.594 2.491 .58 92.6 3.75 4. 60. 2.561 .60 96. 64. 2.620 .62 103.6 4. 4.25 65.344 2.687 .64 107.2 69.594 2.749 .66 115.5 4.25 4.5 70.875 2.810 .68 118.8 75.375 2.873 .70 128.1 4.5 - 5. 82.5 3.052 .75 144.4 87.5 3.121 .77 154.6 5. 6. 108. 3.525 .877 202.7 114. 3.604 .9 216.6 6. BED 11 FEET. BED 12 FEET. Depth Depth in Feet. a r VT a\/r a r Vr a\/r in Feet. 0.5 5.87 .459 .68 3.99 6.37 .462 .68 4.33 0.5 0.75 9.094 .664 .81 7.37 9.844 .670 .82 8.07 0.75 1. 12.5 .856 .93 11.63 13.5 .865 .93 12.55 1. 1.25 16.094 1.038 1.02 16.42 17 . 344 1.051 1.02 17.7 1.25 1.5 19.875 1.211 1.10 21.86 21.375 1.228 1.11 23.7 1.5 1.75 23 . 844 .377 1.17 27.90 25.594 1.398 1.18 30.2 1.75 2 28. .537 1.24 34.7 30. 1.561 1.25 37.5 2. 2^25 32.344 .693 1.30 42. 34.594 1.720 1.31 45.3 2.25 2.5 36.875 .842 1.36 50.2 39.375 1.874 1.37 53.9 2.5 2.75 41.594 .989 1.41 58.6 44.344 2.024 1.42 63. 2.75 3. 46.5 2.132 1.46 67.9 49.5 2.170 1.47 72.9 3. 3.25 51.594 2.271 1.51 77.9 54.844 2.312 1.52 83.4 3.25 3.5 56 . 875 2.407 1.55 88.2 60.375 2.452 1.57 94.8 3.5 3.75 62.344 2.543 1.59 99.1 66.094 2.590 1.61 106.4 3.75 4. 68. 2.675 1.64 111.5 72. 2.725 1.65 118.9 4. 4.5 79.875 2.933 1.71 136.6 84.375 2.990 1.73 146. 4.5 5. 92.5 3.186 1.78 164.6 97.5 3.247 1.80 175.5 5. 5.5 105.875 3.434 1.85 196.2 111.375 3.499 1.87 208.3 5.5 6. 120. 3.676 1.92 230.4 126. 3.746 1.94 244. 6. 88 FLOW OF WATER IN TABLE 11. Channels having a trapezoidal section, with side slopes of 1 to 1. Values of the factors a = area in square feet; r = hydraulic mean depth in feet, and also ^/r and a-^/r for use in the formulas v = c X Vr X V* and Q = c X a^/r X N/~ BED 13 FEET. BED 14 FEET. Depth Depth in Feet. a r Vr a\/r a r Vr a\/r in Feet. 0.5 6.87 0.464 0.681 4.68 7.37 0.467 0.68 5.03 0.5 0.75 10.594 0.675 0.82 8.69 11.34 0.679 0.82 9.30 0.75 1. 14.5 0.873 0.93 13.49 15.50 0.880 0.93 14.5 1. 1.25 18.594 1.061 1.03 19.15 19.84 1.072 .04 20.6 1.25 1.5 22.875 1.242 1.11 25.4 24.37 1.256 .12 27.3 1.5 1.75 27.344 1.416 1.19 32.5 29.09 1.433 .20 34.9 1.75 2. 32. 1.583 1.26 40.3 34. 1.602 .26 43. 2. 2.25 36.844 1.745 1.32 48.6 39.09 1.768 .33 52. 2.25 2.5 41.875 1.902 .38 57.8 44.37 1.928 .39 61.7 2.5 2.75 47.094 2.056 .43 67.3 49.84 2.085 .44 71.8 2.75 3. 52.5 2.204 .48 77.7 55.50 2.236 .50 83.3 3. 3.25 58.094 2.350 .53 89.0 61.34 2.382 .55 95.1 3.25 3.5 63.875 2.492 .58 100.9 67.37 2.530 .59 107.1 3.5 3.75 69.844 2.634 1.62 113.1 73.59 2.674 1.64 120.7 3.75 4. 76. 2.771 1.66 126.2 80. 2.814 1.68 134.3 4. 4.5 88.875 3.040 1.74 154.6 93.37 3.089 1.76 164.5 4.5 5. 102.5 3.303 1.82 186.6 107.5 3.356 1.83 196.7 5. 5.5 116.875 3.561 1.89 220.9 122.37 3.617 1.90 232.5 5.5 6. 132. 3.811 1.95 257.4 138. 3.872 1.97 271.9 6. BED 15 FEET. BED 16 FEET. Depth Depth in Feet. a r N/r a\/r a r ' \/r a\/r in Feet. 0.5 7.87 0.463 0.68 5.3 8.37 0.470 0.69 5.8 0.5 0.75 12.09 0.683 0.83 10. 12.84 0.687 0.83 10.7 0.75 1. 16.500 0.886 0.94 15.5 17.5 0.892; 0.94 16.5 1. 1.25 21.094 1.081 .04 22. 22.34 1.089: 1.04 23.2 1.25 1.5 25.875 1.267 .12 29.1 27.37 1.279 1.13 30.9 1.5 1.75 30.84 1.447 .20 37. 32.59 1.461 1.21 39.4 1.75 2 36. 1.620 .28 46.1 38. 1.637 1.28 48.6 2 2^25 41.344 1.789 .34 55.4 43.59 1.808 1.34 58.4 2 '.25 2.5 46.875 1.951 .39 65.6 49.37 1.974 1.40 69.1 2.5 2.75 52.594 2.111 .45 76.3 55.34 2 136 .46 80.8 2.75 3. 58.500 2.266 .51 88.3 61.50 2.293 .51 92.9 3. 3.25 64.594 2.417 1.56 100.8 67.84 2.447 .56 105.8 3.25 3.5 70.875 2.565 1.60 113.4 74.37 2.599 .61 119.7 3.5 3.75 77.344 2.711 1.65 127.3 81.09 2.747 .66 134.6 3.75 4. 84. 2.855 1.69 142. 88. 2.892 .70 149.6 4. 4.5 97.875 3.134 1.77 173.2 102.37 3.176 .78 182.2 4.5 5. 112.500 3.405 1.85 207.7 117.50 3.453 1.86 218.6 5. 5.5 127.875 3.677 1 . 92 245.5 133.37 3.722 1.93 257.4 5.5 6. 144. 3.930 1.98 285.1 150. 3.9811 2. 300. 6. OPEN AND CLOSED CHANNELS. 89 TABLE 11. Channels having a trapezodial section, with side slopes of 1J to 1. Values of the factors a --= area in square feet; r = hydraulic mean depth in. feet, and also ^/r and a^/'r for use in the formulae v = c X \/r X >/" and also Q = c X a^/7 X BED 17 FEET. BED 18 FEET. Depth Depth in Feet. a r V a\/r a r V? V* rlet. 0.75 13.59 .690 .83 11.3 14.34 .693 .83 11.9 0.75 1. 18.50 .897 .95 17.6 19.5 .902 .95 18.5 1. 1.25 23.59 1.097 .05 24.8 24.84 1.104 1.05 26.1 1.25 1.5 28.87 1.288 .13 32.6 30.37 1.297 1.14 34.6 1.5 1.75 34.34 1.473 .21 41.6 36.09 1.485 1.22 44. 1.75 2. 40. 1 1.652 .29 51.6 42. 1.665 1.29 54.2 2 2.25 45.84! 1.810 .35 61.9 48.09 1.842 1.36 65.3 2^25 2.5 51.87 1.993J .41 73.1 54.37 2.013 1.42 77.2 2.5 2.75 i 58.09; 2.159 1.47 85.4 60.84 2.180 1.48 90. 2.75 3. 64.50 2.318 1.52 98. 67.50 2.342| 1.53 106.3 3. 3.25 71.09 2.475 1.57 111.6 74.34 2.501 1.58 117.5 3.25 3.5 77.87 2.6281 1.62 126.2 81.37 2.658J 1.63 132.6 3.5 3.75 84.84 2.780 1.67 141.7 88.59 2.811J 1.68 148.8 3.75 4. 92. 2.927 1.71 157.3 96. 2.961i 1.72 165.2 4. 4.5 106.87 3.216 1.79 191. 111.37 3.254 1.80 200.8 4.5 5. 122.50 3.496 1.87 229. 127.50 3.539 1.88 239.7 5. 5.5 138.87 3.771! 1.94 269. 144.37 3.816 1.95 281.5 5.5 6. 156. 4.037 2.01 314. 182. 4.087 2.02 327.4 6. 7. 192. 50J 4.557! 2.135 411. 199.50 4.614 2.15 428 . 9 7. . BED 19 FEET. BED 20 FEET. Depth i Depth F^t.i - r \/r a\/r a r v~ a\/r in Feet . 0.75 15.09 0.695 0.834: 12.6 15.80 .698 . 835 13.2 0.75 1. 20.5 0.906 0.952 20.5 21.50 .910 .95 20.4 1 1.25 26.09 1.1 1.053 27.5 27.34 1.116 1.05 28.7 1^25 1 . o 31.87 1.305 1.142 36.3 33.37 1.313 .15 38.4 1.5 1.75 37.84 1.459 1.223; 46.3 39.59 1.505 .23 48.7 1.75 2. 44. 1 . 678 1.295 57. 46. 1.690 .30 59.8 2. 2.25 50.34 1.857 1.363 68.6 52.59 1.871 .37 72.1 2.25 2.5 56.87 2.03 1.425 81. 59.37 2.046 .43 85.5 2.5 2.75 63.59 2.199 1.4831 94.3 66.34 2.218 .49 98.9 2.75 3. 70.5 2.364 1.538] 108.4 73.50 2 386 .54 113.2 3. 3.25 77.59 2.526 1.589; 123.3 80.84 2.549 .60 129.4 3.25 3.5 84.87 2.683 1.64 139.2 88.37 2.708 1.65 145.8 3.5 3.75 92.34 2.839 1.685 155.6 96.09 2.867 1.69 162.4 3.75 4. 100. 2.992 1.709 170.9 104. 3.021 1.73 179.9 4. 4.25 107.84 3.142 1.772 191.1 112.09 3.174 1.78 199.5 4.25 4.5 115.87 3.289 1.813 210. 120.37 3.322 1.82 219.1 4.5 5. 132.5 3.577 1.892 250.5 137.5 3.615 1.90 261.7 5. 5.5 149.87 3.855 1.964 294.3 155.37 3.901 1.97 306. 5.5 6. 168. 4.134 2.033 341.5 174. 4.179 2.04 355. 6. 7. 1 206.5 4.668 2.16 446. 213.5 4.719 2.17 463.7 7 . 8. I 248. 5.183 2.277 564.7 256. 5.241 2.28 583.7 8. 90 FLOW OF WATER IN TABLE 11. Channels having a trapezoidal section, with side slopes of 1| to 1. Values of the factors a area in square feet; r hydraulic mean depth in feet, and also \/r and a\/r for use in the formulae v c X V> X Vs and Q = c X A/r X \A BED 25 FEET. BED 30 FEET. Depth Depth in Feet. a r Vr a^/r a r \/r a^/r in Feet. 0.5 12.87 .480 .693 8.92 15.37 .483 .695 10.69 0.5 0.75 19.59 .707 .841 16.5 23.34 .714 .845 19.7 0.75 1. 26.50 .926 .962 25.5 39.06 .937 .968 37.8 1. 1.25 33.59 1.138 1.067 35.8 47.81 1.132 1.064 50.9 1.25 1.5 40.87 1.344 1.16 47.4 48.37 1.366 1.17 56.3 1.5 1.75 48.34 1.544 1.24 60. 57.09 1 .572 1.25 71.4 1.75 2. 56. 1.733 1.32 73.9 66. 1.774 1.33 87.8 2. 2.25 63.844 1.922 1.39 88.7 75.09 1.970 1.40 105.1 2.25 2.5 71.875 2.107 1.45 104.3 84.37 2.167 1.47 124.3 2.5 2.75 80.094 2.294 1.51 120.9 93.84 2.351 1.53 143.6 2.75 3. 88.5 2.471 1.57 139. 103.59 2.536 1.59 165.2 3. 3.25 97.094 2.645 1.63 158. 113.34 2.717 .65 187. 3.25 3.5 105.875 2.814 1.68 177. 123.37 2.895 .70 209.7 3.5 3.75 114.844 2.982 1.73 199. 133.59 3.070 .75 233.8 3.75 4. 124. 3.146 1.78 221. 144. 3.242 .80 259.2 4. 4.25 133.344 3.307 1.82 243. 154.59 3.411 .85 286. 4.25 4.5 142.875 3.466 1.86 266. 165.37 3.578 .89 312.6 4.5 4.75 152.594 3.623 1.90 290. 176.34 3.743 .93 340.3 4.75 5. 162.5 3.776 1.94 315. 187.50 3.904 .97 371. 5. 5.25 172.594 3.929 1.98 342. 198.84 4.060 2.01 400. 5.25 5.5 182.875 4.079 2.02 369. 210.37 4.222 2.05 431. 5.5 5.75 193.3 4.228 2.06 398. 222. 4.377 2.09 460. 5.75 6. 204. 4.374 2.C9 426. 234. 4.532 2.13 498. 6. 6.25 214.8 4.519 2.126 457. 246.10 4.684 2.16 533. 6.25 6.5 225.9 4.663 2.109 490. 258.37 4.835 2.20 568. 6.5 6.75 237.1 4.806 2.192 520. 270.84 4.985 2.23 605. 6.75 7. 248.5 4.946 2.224 553. 283.50 5.132 2.27 641. 7. 7.25 260.1 5.086 2.255 587. 296.34 5.279 2.30 681. 7.25 7.5 271.9 5.224 2.285 621. 309.37 5.424 2.33 721. 7.5 7.75 283.4 5.354 2.314 656. 322.60 5.567 2.36 761. 7.75 8. 296. 5.497 2.344 694. 336. 5.710 2.39 803. 8. 8.25 307.3 5.614 2.369 728. 349.60 5.851 2.42 846. 8.25 8.5 320.9 5.776 2.403 771. 363.4 5.992 2.45 890. 8.5 8.75 333.6 5.899 2.429 810. 377.3 6.130 2.48 934. 8.75 9. 346.5 6.031 2.456 851. 391.5 6.269 2.50 980. 9. OPEN AND CLOSED CHANNELS. 91 TABLE 11. Channels having a trapezoidal section, with side slopes of H to 1 . Values of the factors a = area in square feet; r -- hydraulic mean depth in feet, and also \/r and a\/r for use in the formulae v = c X Vr X V* and Q = c X ci^/r X BED 35 FEET. BED 40 FEET. Depth in Feet. a r Vr a\/r a r Vr a\/r Depth in Feet. 0.75 27.09 .719 .847 22.95 30.84 .722 .85 26.2 0.75 1. 36.50 .945 .972 35.5 41.5 .952 .976 40.5 1. 1.25 46.11 1.167 1.080 49.8 52.3 1.176 1.084 56.7 1.25 1.5 55.87 1 . 383 1.176 65.7 63.4 1.396 1.181 74.9 1.5 1.75 65.844 1.594 1.26 83.4 76.34 1.648 1.28 97.7 1.75 2. 76. 1.801 1.34 101.8 86. 1.822 1.35 115. 2. 2.25 86.344 2.003 .41 121.7 97.59 2.029 1.42 138.6 2.25 2.5 96.875 2.201 .48 143.2 '' 109.37 2.232 1.49 163. 2.5 2.75 107.594 2.396 .55 166.8 121.34 2.431 1.56 189.3 2.75 3. 118.5 2.587 .61 190.8 133.50 2.627 1.62 216.3 3. 3.25 129.594 2.774 .67 216.4 145.84 2.839 1.68 245. 3.25 3.5 140.875 2.958 .72 242 . 4 158.37 3.010 1.73 274. 3.5 3.75 152.344 3.140 .77 269.6 171.09 3.197 1.79 306. 3.75 4. 164. 3.318 .82 298.5 184. 3.399 1.84 338. 4. 4.25 175.844 3.495 .87 329. 197.09 3.563 1.89 373. 4.25 4.5 187.875 3.668 .91 359. 210.37 3.742 1.93 406. 4.5 4.75 200.094 3.839 .96 392. 223.84 3.919 1.98 443. 4.75 5. 212.5 4.007 2. 425. 237.50 4.094 2.03 481. 5. 5.25 225.094 4.174 2.04 459. 251.34 4.265 2.07 520. 5.25 5.5 237.875 4.338 2.08 495. 265.37 4.435 2.11 560. 5.5 5.75 250.8 4.501 2.12 535.3 279.6 4.604 2.15 601. 5.75 6. 264. 4.661 2.16 570. 294. 4.770 2.18 641. 6. 6.25 277.3 4.820 2.19 608.7 308.6 4.935 2.22 685. 6.25 6.5 290.9 4.977 2.23 649. 323.4 5.097 2.26 ! 731. 6.5 6.75 304.6 5.133 2.26 689.9 338.3 5.259 2.29 ! 776. 6.75 7. 318.5 5.287 2.30 732.2 353.5 5.418 2.33 823. 7. 7.25 332.6 5.440 2.33 775.6 368.8 5.577 2.36 871. 7.25 7.5 346.9 5.591 2.36 820.4 384.4 5.733 2.39 920. 7.5 7.75 351.3 5.741 2.39 841.7 400.1 5.889 2.43 970. 7.75 8. 376. 5.889 2.42 912.2 416. 6.043 2.46 1023. 8, 8.25 390.8 6.037 2.45 960.2 432.1 6.195 2.49 i 1075. 8.25 8.5 405.9 6.183 2.48 1009. 448.4 6.347 2.52 1130. 8.5 8.75 421.1 6.327 2.51 1059. 464.8 6.497 2.55 1185. 8.75 9. 436.5 6.471 2.54 1110. 481.5 6.646 2.58 1241. 9. 9.5 467.9 6.756 2.60 1216. 515.4 6.941 2.64 1358. 9.5 10. 500. 7.037 2.65 1327. 550. 7.232 2.69 1479. JlO. 92 FLOW OF WATER IN TABLE 11. Channels having a trapezoidal section, with side slopes of 1 to 1. Values of the factors a = area in square feet; r = hydraulic mean depth in feet, and also \/r and a\/r for use in the formula v = c X V~r X\/s and Q = c X a^/r X \/~* BED 45 FEET. BED 50 FEET. Depth in Feet. a r i Vr a\/r a r x/r a\/r Depth in Feet. 0.5 22.87 .490 .700 16. 25.37 .490 .700! 17.8 0.5 0.75 34.59 .725 .852 29.5 38.34 .728 .85? 32.7 0.75 1. 46.50 .957 .977 45.4 51.50 .961 .980 50.5 1. 1.25 58.57 1.183 1.084 63.5 64.841 1.190 1.091 70.7 1.25 1.5 70.88 1.406 1.190 84.3 78.37 1.415 .190 93.3 1.5 1.75 83.34 1.624 1.274 106.2 92.09 1.635 .28 118. 1.75 2 96. 1.839 .356 130.2 106. 1.853 .36 138. 2. 2.25 108.8 2.049 .43 156. 120.09 2.067 .44 173. 2.25 2.5 121.9 2.257 .50 183. 134.37 2.277 .51 202. 2.5 2.75 135.1 2.460 .57 212. 148.84 2.484 .58 235. 2.75 3. 148.5 2.660 .63 242. 163.50 2.688 .64 268. 3. 3.25 162.1 2.858 .69 274. 178.34 2.890 .70 303. 3.25 3.5 175.9 3.052 .75 308. 193.37 3.088 .76 340. 3.5 3.75 189.8 3.244 .80 342. 208. 59j 3.284 .81 378. 3.75 4. 204. 3.433 .85 377. 224. 3.477 .86 417. 4. 4.25 218.3 3.620 1.90 415. 239.59 3.6681 .92 460. 4.25 4.5 232.9 3.804 1.95 454. 255.37 3.856 .96 501. 4.5 4.75 247.6 3.985 2. 495. 271.34 4.043 2.01 545. 4.75 5. 262.5 4.165 2.04 536. 287.50 4.226 2.05 591. 5. 5.25 277.6 4.342 2.08 577. 303.841 4.408 2.10 638. 5.25 5.5 292.88 4.518 2.13 624. 320.4 4.588 2.14 686. 5.5 5.75 308.34 4.683 2.16 667.2 337.1 4.766 2.18 735. 5.75 6. 324. 4.862 2.20 713. 354. 4.941 2.22 786. 6. 6.25 339.84 5.032 2.25 763.6 371.1 5.116 2.26 839. 6.25 6.5 355.99 5.200 2.28 811. 388.4 5.288 2.30 893. 6.5 6.75 372.1 5.366 2.31 861.8 405.8 5.461 2.33 948. 6.75 7. 388.5 5.531 2.35 913. 423.5 5.628 2.37 1005. 7. 7 25 405.7 5.703 2.39 968.8 441.3 5.799 2.40 1063. 7.25 7.5 421.9 5.856 2.42 1021. 459.4 5.9631 2.44 1122. 7.5 7.75 438.8 6.016 2.45 1076. 477.6 6.128 2.47 1182. 7.75 8. 456. 6.175 2.48 1133. 496. 6.291 2.50 1244. 8. 8.25 473.3 6.333 2.51 1191. 514.6 6.453 2.54 1307. 8.25 8.5 490.9 6.489 2.55 1250. 533.4 6.613 2.57 1371. 8.5 8.75 508.6 6.644 2.58 1311. 552.3 6.773 2.60 1437. 8.75 9. 526.5 6.798 2.61 1373. 571.5 6.931 2.63 1503. 9. 9.5 562.9 7.102! 2.66 11500. 610.4 7.244 2.69 1642. 9.5 10. 600. 7.414 2.72 '1633. 650. 7 . 5f>3 2.75 1786. 10. 10.5 637.9 7.869; 2.78 i!773. 690.4 7.858 2.80 1933. 10.5 11. 676.5 1 7.991! 2.83 11912. 731.5 8.158 2.86 209.2 11. OPEN AND CLOSED CHANNELS. 93 TABLE 11. Channels having a trapezoidal section, with side slopes of 1 J to 1. Values of the factors a = area in square feet; r = hydraulic mean depth in feet, and also ^/r and a\/r for use in the formulae r" X \AT and Q = c X a^/r X \A BED 60 FEET. BED 70 FEET. Depth - y Depth iu a r \/T a\/r a r -v//* a^/r in feet. feet. 1. 61.50 .951 .978 59.2 71.5 .9713 .98 70. 1. 1.5 91.12 1.393 .180 107.5 108.37 1.437 .J9 129. 1.5 1.75 109.59 1.647 .29 141.4 127.09 1.666 .29 164. 1.75 2. 126. 1.875 .37 172.6 146. 1.891 .37 200. 2. 2.25 142.60 2.094 .45 206.8 165.09 2.114 .45 239. 2.25 25 159.38 2.309 .52 242.3 184.37 2.334 .53 282. 2.5 2.75 176.34 2 522 59 280.4 203.84 2.551 .60 326. 2.75 3. 193.50 2.732 .65 320. 223.5 2.765 .66 371. 3. 3.25 210.84 2.940 1.71 360. 243 34 2.978 .73 421. 3.25 3.5 228.37 3.145 1.77 404. 263.37 3.188 .79 471. 3.5 3.75 246.09 3.347 1.83 450. 283.59 3.396 .84 522. 3.75 4. 264. 3.547 1.88 496. 304. 3.601 .90 578. 4. 4.25 282.09 3.745 1.94 547. 324.59 3.804 .95 633. 4 25 4.5 300.37 3.941 1.99 598. 345.38 4.006 2. 691. 4.5 4.75 318.84 4.134 2.03 647. 366.34 4.205 2.05 751. 4.75 5. 337.50 4.325 2.08 702. 387.5 4.402 2.10 814. 5. - 5.25 356.34 4.515 2.12 755. 408.8 4.597 2.14 875. 5.25 5.5 375.37 4.702 2.17 815. 430.4 4.791 2.19 943. 5.5 5.75 394.59 4.888 2.21 872. 452.09 4.983 2.23 1008. 5.75 6. 414. 5.071 2.25 932. 474. 5.172 2.27 1076. 6. 6.25 433.59 5.253 2 29 993. 496.09 5.361 2.32 1151. 6.25 6.5 453.37 5 434 2.33 1056. 518.4 5.548 2.36 1223. 6.5 6.75 473.34 5.612 2.37 1122. 540.84 5 733 2.39 1293. 6.75 7. 493.50 5.789 2.40 1188. 563.5 5.916 2.43 1369. 7. 7.25 513.84 5.965 2.44 1255. 586.34 6.099 2.47 1448. 7.25 7.5 534.37 6.139 2.47 1325. 609.4 6.279 2.51 1527. 7.5 7.75 555.09 6.312 2.51 1394. 632.59 6.459 2.54 1607. 7.75 8. 576. 6.483 2.54 1466. 656. 6.636 2.57 1686. 8. 8.25 597.09 6.605 2.58 1546. 679.59 6.813 2.61 1774. 8.25 8.5 618.37 6.822 2.61 1615. 703.4 6.988 2.64 1859. 8.5 8.75 639.84 6.989 2.64 1690. 727.34 7.162 2.68 1949. 8.75 9. 661.50 7.155 2.67 1770. 751.5 7.335 2.71 2036. 9. 9.5 705.37 7.484 2.73 1929. 800.4 7.677 2.77 2218. 9.5 10. 750. 7.808 2.79 2096. 850. 8.014 2.83 2406. 10. 10.5 795.37 8.128 2.85 2268. 900.4 8.347 2.90 2601. 10.5 11. 841.5 8.444 2.90 2445. 951.5 8.676 2.94 2802. 11. 94 FLOW OF WATER IN TABLE 12. Sectional areas, in square feet, of trapezoidal channels, with side slopes of 11 to 1. Depth in Feet. BED WIDTH 70 feet. 80 feet. 90 feet. 100 feet. 120 feet. 1. 71.50 81.50 91.50 101.50 121.50 1.5 108.37 123.37 138.37 153.37 183.37 2. 146. 166. 186. 206. 246. 2.25 165.09 187.59 210.09 232.59 277.59 2.5 184.37 209.37 234.37 259.37 309.37 2.75 203.84 231.34 258.84 286.34 313.84 3. 223.50 253.50 283.5 313.50 373.50 3.25 243.34 275.84 308.34 340.84 405.84 3.5 263.37 298.37 333 37 368.37 438 ,37 3.75 283.59 321.09 358.59 396.09 471.09 4. 304. 344. 384. 424. 504. 4.25 324.59 367.09 409.59 452.09 537 . 09 4.5 345.37 390.37 435.37 480.37 570.37 4.75 366.34 413.84 461.34 508 . 84 603.84 5. 387.50 437.50 487 . 50 537.50 637.50 5.25 408.84 461.34 513.84 566.34 671.34 5.5 430.37 485.37 540.37 595/37 705.37 5.75 452.09 509.59 567.09 624.59 739.59 6. 474. 534. 594. 654. 774. 6.25 496.09 558.59 621.09 683.59 808.59 6.5 518.37 583.37 648.37 713.37 843.37 6.75 540.84 608.34 675.84 743.34 878.34 7. 563 . 50 633.50 703.50 773.50 913.50 7.25 586.34 658.84 731.34 803.84 948.84 7.5 609.37 684.37 759.37 834.37 984.37 7.75 632.59 710.09 787.59 865.09 1020.09 8. 656. 736. 816. 896. 1056. 8.25 679.59 762.09 844.59 927.09 1092.09 8.5 703.37 788.37 873.37 958 . 37 1128.37 8.75 727.34 814.84 902.34 989.84 1164.84 9. 751.50 841.50 931.50 1021.50 1201.50 9.25 775.84 868.34 960.84 1053.34 1238.34 9.5 800.37 895.37 990.37 985.35 1275.35 9.75 825.09 922 . 59 1020.09 1117.59 1312.59 10. 850. 950. 1050. 1150. 1350. 10.5 900.37 1005.37 1110.37 1215.37 1425.37 11. 951.50 1061.50 1171.50 1281.50 1501.50 11.5 1003.37 1118.37 1233.37 1348.37 1578.37 12. 1056. 1176. 1296. 1416. 1656. OPEN AND CLOSED CHANNELS. 95 TABLE 12. Sectional areas, in square feet, of trapezoidal channels, with side slopes of Depth in Feet BED WIDTH 140 feet. 160 feet. 180 feet. 200 feet. 220 feet. 1. 141.50 161.50 181.50 201.50 221.50 2. 286. 326. 366. 406. 446. 2.5 359.37 409.37 459.37 509.37 559.37 2.75 368.84 423.84 478.84 533.84 588.84 3. 433.50 493.50 553.50 613.50 673.50 3.25 470.80 535.80 600.80 665.80 730.80 3.5 508.37 578.37 648.37 718.47 788.47 3.75 546.09 621.09 696.09 771.09 846.09 4. 584. 664. 744. 824. 904. 4.25 622 . 09 707.09 792.09 877.09 962.09 4.5 660.37 750.37 840.37 930.37 1020.37 4.75 698.84 793.84 888.84 983.84 1078.84 5. 737.50 837.50 937.50 1037.50 1137.50 5.25 776.34 881.34 986.34 1091.34 1196.34 5.5 815.37 925.37 1035.37 1145.37 1255.37 5.75 854.59 969.59 1084.59 1199.59 1314.59 6. 894. 1014. 1134. 1254. 1374. 6.25 933.59 1058.59 1183.59 1308.59 1433.59 6.5 973.37 1103.37 1233.37 1363.37 1493.37 6.75 1013.34 1148.34 1283.34 1418.34 1553.34 7. 1053.50 1193.50 1333.50 1473.50 1613.50 7.25 1093.84 1238.84 1383.84 1528.84 1673.84 7.5 1134.37 1284.37 1434.37 1584.37 1734.37 7.75 1175.09 1330.09 1485.09 1640.09 1795.09 8. 1216. 1376. 1536. 1696. 1856. 8.25 1257.09 1422.09 1587.09 1752.09 1917.09 8.5 1298.37 1468.37 1638.37 1808.37 1978.37 8.75 1339.84 1514.84 1689.84 1864.84 2039.84 9. 1381.50 1561.50 1741.50 1921.50 2101.50 9.25 1423.34 1608.34 1793.34 1978.34 2163.34 9.5 1465.35 1655.35 1845.35 2035.35 2225.35 9.75 1507.59 1702.59 1897.59 2092.59 2287.59 10. 1550. 1750. 1950. 2150. 2350. 10.5 1635.37 1845.37 2055.37 2265.37 2475.37 11. 1721.50 1941.50 2161.50 2381.50 2601.50 11.5 1808.37 2038.37 2268.37 2498.37 2728.37 12. 1896. 2136. 2376. 2616. 2856. 13. 2073.50 2333.50 2593.50 2853.50 3113.50 14. 2254. 2534. 2814. 3094. 3374. 15. 2437.50 2737.50 3037.50 3337.50 3637.50 16. 2624. 2944. 3264. 3584. 3904. i FLOW OF WATER IN TABLE 12. Sectional areas, in square feet, of trapezoidal channels, with side slopes of H to 1. Depth BED i VlDTH in Feet. 240 feet. 260 feet. 280 feet. 300 feet. 2 486. 526. 566. 606. 2.5 609 . 37 659.37 709.37 759.37 3. 733.50 793.50 853.50 913.50 3.25 795.80 860.80 925 . 80 990.80 3.5 858.47 928.47 998.47 1068.47 3.75 921.09 996.09 1071.09 1146.09 4. 984. 1064. 1144. 1224. 4.25 1047.09 1132.09 1217.09 1302.09 4.5 1110.37 1200.37 1290.37 1380.37 4.75 1173.84 1268 . 84 1363.84 1458.84 5. 1237.50 1337.50 1437.50 1537.50 5.25 1301.34 1406.34 1511.34 1616.34 5.5 1365.37 1475.37 1585.37 1695.37 5.75 1429.59 1544.59 1659.59 1774.59 6. 1494. 1614. 1734. 1854. 6.25 1558.59 1683.59 1808.59 1933.59 6.5 1623.37 1753.37 1883.37 2013.37 6.75 1688.34 1823.34 1958.34 2093.34 7. 1753.50 1893.50 2033.50 2173.50 7.25 1818.84 1963.84 2108.84 2253.84 7.5 1884.37 2034.37 2184.37 2334.37 7.75 1950.09 2105.09 2260.09 2415.09 8. 2016. 2176. 2336. 2496. 8.25 2181.09 2346.09 2511.09 2676.09 8.5 2148.37 2318.37 2488.37 2658.37 8.75 2214.84 2389.84 2564 . 84 2739.84 9. 2281.50 2461.50 2641.50 2821.50 9.25 2348.34 2533.34 2718.34 2903.34 9.5 2415.35 2605.35 2795.35 2985.35 9.75 2482.59 2677.59 2872.59 3067.59 10. 2550. 2750. 2950. 3150. 10.5 2685.37 2895.37 3105.37 3315.37 11.0 2821.50 3041.50 3261.50 3481.50 11.5 2958.37 3188.37 3418.37 3648 . 37 12. 3096. 3336. 3576. 3816. 13. 3373.50 3633.50 3893.50 3153.50 14. 3654. 3934. 4214. 4494. 15. 3937.50 4237.50 4537.50 4837.50 16. 4224. 4544. 4864. 5184. OPEN AND CLOSED CHANNELS. 97 TABLE 13. Channels having a rectangular cross-section. Values of the factors a = area in square feet; r = hydraulic mean depth in feet, and also ^/r and a\/r for use in the formulae 'o = c^Jrs and Q c X a\/r X BED 1 FOOT. BED 2 FEET. Depth in Feet. a r v~ a\/r a r VT a\/r Depth in Feet. 0.25 .25 .167 .408 .102 .5 .200 .447 .224 0.25 0.5 .5 .250 .500 .250 1. .333 .557 .557 0.5 0.75 .75 .300 .548 .411 1.5 .429 .655 .982 0.75 1. 1. .333 .577 .577 2. .500 .707 1.414 1. 1.25 1.25 .357 .598 .747 2.5 .555 .744 1.860 1.25 1.5 1.5 .375 .612 .918 3. .600 .775 2.325 1.5 1.75 3.5 .636 .798 2.793 1.75 2 4. .666 .816 3.264 2 2~25 4.5 .692 .832 3.744 2.25 2.5 5. .714 .843 4.215 2.5 2.75 5.5 .733 .856 4.708 2.75 3. 6. .750 .866 5.196 3. 3.25 6.5 .765 .874 5.681 3.25 3.5 7. .777 .882 6.174 3.5 BED 3 FEET. BED 4 FEET. Depth in Feet. a r v'r a\/ r a r \/r a\/r Depth in Feet. 0.25 .75 .214 .463 .347 1. .222 .471 .471 0.25 0.5 1.50 .375 .612 .918 2 .400 .632 1.264 0.5 0.75 2.25 .500 .707 1.591 3. .545 .738 2.214 0.75 1. 3. .600 .774 2.322 4. .666 .816 3.264 1. 1.25 3.75 .682 .825 3.094 5. .769 .877 4.385 1.25 1.5 4.50 .750 .866 3.897 6. .857 .926 5.556 1.5 1.75 5.25 .808 .899 4.720 7. .933 .965 6.755 1.75 2. 6. .857 .926 5.556 8. 1. 1. 8. 2. 2.25 6.75 .900 .948 6.399 9. 1.058 1.028 9.252 2.25 2.5 7.50 .937 .967 7.252 10. 1.111 1.054 10.540 2.5 2.75 8.25 .971 .989 8.159 11. 1.158 1.076 11.836 2.75 3. 9. 1. 1. 9. 12. 1.200 1.095 13.140 3. 3.5 10.5 1.05 1.024 10.752 14. 1.273 1.128 15.792 3.5 4. 4.5 12. 13.5 1.091 1.125 1.044 1.067 12.528 14.404 16. 18. 1.333 1.384 1.154 1.185 18.464 4. 21.330 4.5 5. 15. 1.154 1.074 16.110 20. 1.428 1.195 23.900 5. 98 FLOW OF WATER IN TABLE 13. Channels having a rectangular cross-section. Values of the factors a = area in square feet; r = hydraulic mean depth in feet, and also ^/r and a\/r for use in the formulae v = c\frs and Q c X BED 5 FEET. BED 6 FEET. Depth i Depth in Feet. a r Vr a\/r a r V> a\/r in Feet. 0.5 2.5 .416 .645 1.612 3. .428 .654 1.962 0.5 0.75 3.75 .577 .759 2.846 ! 4.5 .600 .775 3.487 0.75 1. 5. .714 .845 4.225 ! 6. .750 .866 5.196 1. 1.25 6.25 .833 .913 5.706 j 7.5 .882 .939 7.042 1.25 1.5 7.5 .937 .968 7.260 ! 9. 1. 9. 1.5 1.75 8.75 .029 1.014 8.872 10.5 !l06 1.051 11.035 1.75 2. 10. .111 1.054 10.540 12. 2 1.095 13.140 2. 2.25 11.25 .184 1.088 12.240 13.5 '.286 1.134 15.309 2.25 2.5 12.5 .250 1.118 13.975 15. .364 1.168 17.520 2.5 2.75 13.75 .309 1.144 15.730 16.5 .436 1.198 19.767 2.75 3. 15. .364 .168 17.520 18. 1.5 1.225 22.050 3. 3.25 16.25 .413 .187 19.289 19.5 1.56 1.250 24.375 3.25 3.5 17.5 .458 .208 21.140 21. 1.615 1.278 26.838 3.5 3.75 18.75 .500 .225 22.969 22.5 1.666 1.298 29.205 3.75 4. 20. 1.538 .241 24! 820 24. 1.714 1.309 31.416 4. 4.25 21.25 1.574 . .254 26.647 25.5 1.759 1.326 33.8 4.25 4.5 22.5 1.607 .268 28.530 27. 1.8 1.341 36.207 4.5 5. 25. 1.686 .290 32.250 30. 1.875 1.377 41.310 5 BED 7 FEET. BED 8 FEET. Depth Depth in Feet. a r Vr~ a\/r <& r VT a\Jr in Feet. 0.5 3.5 .438 .661 2.313 4. .444 .667 2.668 0.5 0.75 5.25 .618 .786 4.126 6. .632 .795 3.792 75 1. 7. .778 .882 6.174 8. .800 801 6.408 1. 1.25 8.75 .921 .960 8.400 10. .857 .826 8 260 1.25 1.5 10.50 .050 1.025 10.762 12. .091 1.044 12.528 1.5 1.75 12.25 .167 1.080 13.230 14. .218 1.104 15.456 1.75 2. 14. .273 1.128 15.792 16. .333 1.153 18.448 2. 2.25 15.75 .367 1.170 18.427 18. 440 1.200 21.600 2 25 2.5 17.50 .458 1.208 21.140 20. .538 1 240 24.800 2.5 2.75 19.25 .540 .241 23.889 22. .628 1.276 28.072 2.75 3. 21. .615 .271 26.691 24. .714 1.309 31.416 3. 3.25 22.75 .685 .298 29.5 26. .794 1.340 34.840 3.25 3.5 24.50 .750 .323 32.413 28. .866 1.366 38.248 3.5 3.75 26.25 .810 .345 35.3 30. .938 1 . 392 41.760 3.75 4. 28. .866 .366 38.2 32. 2. 1.414 45.248 4. 4.25 29.75 .919 .385 41.2 34. 2.061 1.436 48.824 4.25 4.5 31.50 1.969 .403 44.1 36. 2.117 1 . 455 52.380 4.5 4.75 33.25 2.015 .419 47.2 38. 2.171 1.473 55.974 4.75 5. 35. 2.059 .435 50.2 40. 2.222 1.490 59.600 6. OPEN AND CLOSED CHANNELS. 99 TABLE 13. Channels having a rectangular cross-section. Values of the factors a = area in square feet, and r = hydraulic mean depth in feet, and also x/Fand a\/r for use in the formulae v = c X Vr X Vs and Q = c X a^/r X V BED 10 FEET. BED 12 FEET. Depth 1 Depth in Feet. a r Vr a\/r a r x/r a\/r in Feet. 1. 10. .833 .913 9.130 12. .857 .926 11.112 1. 1.25 12.5 1. 1. 12.50 15. 1.035 1.017 15.255 1.25 1.5 15. 1.154 1.074 16.11 18. 1.2 1.095 19.710 1.5 1.75 17.5 1.295 1.138 19.91 21. 1.357 .165 24.465 1.75 2. 20. 1.429 1.195 23.90 24. 1.5 .224 29.376 2. 2.25 22.5 1.553 1.246 28.03 27. 1.636 .278 34.506 2.25 2.5 25. 1.666 1.290 32.25 30. 1.764 .328 39.840 2.5 2.75 27.5 1.777 1.333 36.66 33. 1.887 .374 45.342 2.75 3. 30. 1.875 1.369 41.07 36. 2. .414 50.904 3. 3 25 32.5 1.970 1.404 45.63 39. 2.106 .451 56.589 3.25 3.5 35. 2.058 .434 50.19 42. 2.209 .484 62.328 3.5 3.75 37.5 2.143 .463 54.86 45. 2.304 .517 68.265 3.75 4. 40. 2.222 .490 59 . 60 48. 2.4 .549 74.352 4. 4.25 42.5 2.297 515 64 4 51. 2.488 .578 80.5 4.25 4.5 45. 2.367 .538 69.21 54. 2.571 .603 86.562 4.5 4.75 47.5 2.436 .561: 74.1 57. 2.651 1.628 92.8 4.75 5. 50. 2.5 1.581! 79.05 60. 2.727 1.651 99.060 5. 6. 60. 2.727 1.651! 99.1 72. 3.000 1.732 124.7 6. ' BED 14 FEET. BED 16 FEET. Depth Depth in Feet r Vr a-\/r a r V'r a\/r in Feet. 1 14. .875 .935 13.090 16. .888 .942 15.072 1. 1.5 21. 1 . 244 1.115 23.415 24. 1.262 .123 26.952 1.5 1.75 24.5 1.397 1.182 28.959 28. 1.434 .197 33.516 1.75 2. 28. 1.555 1.246 34.888 32. 1.600 .265 40.480 2. 2.25 31.5 1.701 1.304 41.076 36. 1.757 .325 47.700 2.25 2.5 35. 1.841 1.357 47.495 40. 1.904 .379 55.160 2.5 2.75 38.5 1.971 1.404 54.054 44. 2.050 .432 63.008 2.75 3. 42. 2.1 1.450 60.900 48. 2.182 .455 69 840 3. 3.25 45 5 2.23 1.493 67.931 52. 2.311 .520 79.040 3.25 3.5 49. 2.333 1.527 74.823 56. 2.346 .532 85.792 3.5 3.75 52.5 2.447 1.564 82.110 60. 2.556 .599 95.940 3.75 4. 56 2.545 1.595 89.320 64. 2.666 .632 104.448 4. 4.25 59.5 2.644 1.626 96.747 68. 2.774 .665 113.220 4.25 4.5 63. 2.741 .655 104.265 72. 2.880 .697 122.184 4.5 4.75 66.5 2.833 .683 111.919 76. 2.979 .726 131.176 4.75 5. 70. 2.917 .708 119.560 80. 3.080 .755 140.400 5. 5.5 77.- 3.080 .755 135.135 88. 3.256 .804 158 752 5.5 6. 84. 3.230 .797 150.948 96. 3.429 .852 177.792 6. 6.5 91. 3.367 .835 166.985 104. 3.588 .894 196.976 6.5 7. 98. 3.500 .870J183.260 112. 3.733 .932 216.384 7. 100 FLOW OF WATER IN TABLE 13 Channels having a rectangular cross-section. Values of the factors a = area in square feet, and r = hydraulic mean depth in feet, and also vV"and a\fr for use in the formulae v = c X V~r X vT and Q = c X a^/r X V* BED 18 FEET. BED 20 FEET. Depth Depth in Feet. a r \/r a\/r a r v/r a-v/r in Feet. 0.5 9. .526 .725 6.525 10. .476 .690 6.9001 5 1. 18. .900 .948 17.064 20 .909 .953 19.060 1. 1.5 27. 1.286 1 . 134 30 . 620 30. 1.305 1.142 34.260 1.5 2. 36. 1.636 1.279 46.044 40. 1.666 1.290 51.600 2. 2.25 40.5 1.800 1 341 54.310 45. 1.836 .355 60.975 2 25 2.5 45. 1.953 1.397 62.865 50. 2. .414 70.700 2 5 2.75 49.5 2.109 1.452 71.874 55. 2.156 .468 80.740 2.75 3. 54. 2.250 1.500 81. 60. 2.307 .518 91.080 3. 3.25 58.5 2.387 1.545 90.382 65. 2.457 .567 101 . 855 3.25 3.5 63. 2.520 1.587 99.981 70. 2.590 .609 112 630 3.5 3.75 67.5 2.646 1.626 109.755 75. 2.727 .651 123.825 3 75 4. 72. 2.768 1.663 119.736 80. 2.857 .690 135.200 4. 4.25 76.5 2.892 1.700 130 050 85. 2.975 .725 146.625! 4.25 4.5 81. 3. 1 . 732 140.292 90. 3.105 .762 158.580 4.5 4.75 85.5 3.109 1.760 150.480 95. 3.211 .792 170.240 4.75 5. 90. 3.214 1.792 161.280 100. 3.333 .825 182 500 5. 5.5 99. 3.416 1.848 182.952 110. 3.553 .885 207 . 350 5.5 6. 108. 3.600 1.897 204.876 120. 3.750 .937 232.440 6. 6.5 117. 3.779 1.944 227 448 130. 3.939 1.984 257. 920J 6.5 7. 126. 3.938 1.984 249.984 140. 4.116 2 029 284.060J 7. BED 25 FEET. BED 30 FEET. Depth Depth in Feet. a r \/r ax/?* a r Vr a\Jr in Feet. 1. 25. .925 .961 24.025 30. .938 .968 29.040 1 1.5 37.5 1.338 1.156 43.350 35. 1.364 1.170 40.950 1.5 2. 50. 1.725 1.313 65 650 60. 1.764 .328 79.680 2. 2.25 56.25 1.901 .380 77.625 67.5 1.957 .391 93.892 2.25 2.5 62.5 2.083 .443 90.187 75. 2.143 .464 109.800 2.5 2.75 68.75 2.255 .500 103. 125 82.5 2.326 .525 125.812 2.75 3. 75. 2.422 .556 116.700 90. 2.500 .581 142.290 3. 3.25 81.25 2.579 .606 130.487 97.5 2.672 .634 159.315 3.25 3.5 87.5 2.734 .653 144.637 105. 2.835 .683 176.715 3.5 3.75 93.75 2.884 .699 159.281 112 5 3. .732 194.850 3.75 4. 100. 3.030 .746 174.600 120. 3.156 .776 213.120 4. 4.25 106.25 3.166 .779 189.019 127.5 3.312 .820 232.050 4.25 4.5 112.5 3.308 .818 204.525 135. 3.456 1.860 251.100 4.5 4.75 118.75 3 327 .824 216.600 142.5 3.608 1.899 270.607 4.75 5. 125. 3.571 .890 236.250 150. 3.750 1.936 290 400 5. 5.5 137 5 3.820 .954 268.675 165. 4.026 2.006 330.990 5.5 6. 150. 4.050 2.019 302.850 180. 4.286 2.072 372.960 6. 6.5 162.5 4.274 2.057 334.262 195. 4.544 2.131 415.545 6.5 7. 175. 4.480 2.117 370.475 210. 4.773 2.184 458.640 7. 7.5 187.5 4.687 2.165 405.937 225. 5. 2.235 502.875 7.5 8 200. 4.880 2.209 441 . 800 240. 5.22 2.284 548.160 8. OPEN AND CLOSED CHANNELS. 101 TABLE 13. Channels having a rectangular cross-section. Values of the factors a = area in square feet, and r= hydraulic mean depth in. feet, and also \/jr and a\/r for use in the formulae v = c X V~r X \/s and Q = c X a^/r X vT BED 35 FEET. BED 40 FEET. Depth in Feet. a r \/r a\/r a r V~ Depth *VF &. 1. 35. .945 .972 34. 40. .952 .975 39. 1. 1.5 52.5 1.382 1.176 61.7 60. 1.398 1.182 70.9 1.5 2. 70. 1 792 1.338 93.7 80. 1 818 1.348 107.8 2. 2.25 78.75 1.994 1.412 111 2 90. 2.023 1.422 128. 2 25 2.5 87.5 2.187 1.482 129.7 100. 2.222 1.490 149. 2.5 2.75 96.25 2.377 1 542 148.4 110. 2.418 1.555 171. 2.75 3. 105. 2.562 1.600 168. 120. 2.610 1.615 193.8 3. 3.25 113.75 2.741 1.655 188.3 130. 2.795 1.672 217.4 3.25 3.5 122.5 2.919 1.709 209.4 140. 2.982 1.727 241.8 3.5 3.75 131 25 3.071 1.752 229.9 150. 3.099 1.760 264. 3.75 4. 140. 3.162 1.778 248.9 160 3.333 1.826 292.2 4. 4.25 148.75 3.421 1.849 275. 170. 3.505 1.872 318.2 4.25 4.5 157.5 3.579 1.892 298 180. 3.672 1.916 344 . 9 4 5 4.75 166.25 3.737 1.933 321.4 190. 3.838 1.959 372.2 4.75 5. 175 3.944 1.986 347.6 200. 4. 2. 400. 5. 5.25 183.75 4 038 2.009 369.2 210. 4.158 2.039 428.2 5.25 5.5 192.5 4.177 2.044 389. 220. 4.314 2.077 456.9 5.5 5.75 201.25 4.328 2.080 418.6 230. 4.466 2.113 486. 5.75 6. 210. 4.468 2.114 444 1 240. 4.614 2.148 515.5 6. 6.25 218.75 4.605 2.146 469 4 250. 4.762 2 182 545.5 6.25 6.5 227 5 4.739 2.177 495.3 260. 4.906 2 215 575.9 6.5 6.75 236.25 4.871 2.203 520.5 270. 5.047 2.246 606 4 6.75 7. 245. 5. 2.236 547.8 280. 5.180 2.276 637.3 7. 7.25 253.75 5.126 2.264 574.5 290. 5.321 2.306 668.7 7.25 7.5 262.5 5 250 2.291 601.4 300. 5.455 2.335 700.5 7.5 7.75 271.25 5 372 2.318 628.8 310 5.586 2.360 731.6 7.75 8. 280 5 491 2.343 656. 320. 5 714 2.394 766.1 8. 9. 315. 5.943 2.438 768. 360. 6.207 2.491 896.8 9. 102 FLOW OF WATER IN TABLE 13 Channels having a rectangular section. Values of the factors a = urea in square feet, and r = hydraulic mean depth in feet, and also ^/r and for use in the formulae v = c X \/r X \A~ and Q = c X V> X \A' BED 50 FEET. BED 60 FEET. Depth in Feet. a T Vr a^/r a r \/r a\/r Depth in Feet. 1. 50. .962 .980 49. 60. .968! .984 59. 1. 2. 100. 1.852 1.360 136. 120. 1.875 1.369 164.3 2. 2.25 112.5 2 063 1.436 161.5 135. 2.093 1.446 195 2 2.25 2.5 125. 2.273 1.507 188.4 150. 2.3081 .519 227.8 2.5 2.75 137.5 2.477 1.574 216.4 165. 2.519 .587 261.8 2.75 3. 150. 2.679 1.637 245.5 180. 2.727 .651 297.2 3. 3.25 162.5 2.876 1.696 275.6 195. 2.932 .712 333.8 3.25 3.5 175. 3.069 1.751 306.4 210. 3.134 .770 371.7 3.5 3.75 187.5 3.261 1.806 338.6 225. 3.333 .825 410.6 3.75 4. 200. 3.448 1.857 371.4 240. 3.529 878 450.7 4. 4.25 212.5 3.632 1.906 405. 255. 3.722 .929 491.9 4.25 4.5 225. 3.814 1.953 439.4 270. 3.913 1.978 534.1 4.5 4.75 237.5 3.991 1.997 474.3 285. 4.101 2.025 577.1 4.75 5. 250. 4.167 2.041 510.2 300. 4.286 2.073 621.9 5. 5.25 262.5 4.339 2.083 546.8 315. 4.468 2.114 665.9 5.25 5.5 275. 4.507 2.123 583.8 330. 4.646 2.155 711.1 5.5 5.75 287.5 4.675 2.162 621.6 345. 4.825 2.196 757.6 5.75 6. 300. 4.839 2.200 660. 360. 5. 2.236 805 6. 6.25 312.5 5 2.236 698.7 375. 5.172 2.274 852 7 6.25 6.5 325. 5.158 2.271 738.1 390. 5.343 2.311 901.3 6.5 6.75 337.5 5.315 2.305 777.9 405. 5.510 2.347 950.5 6.75 7. 350. 5.470 2.339 818.6 420. 5.676 2.382 1000.4 7. 7.25 362.5 5.620 2.350 851.9 435. 5.839 2.416 1051. 7.25 7.5 375. 5.767 2.401 900.4 450. 6. 2.450 1102.5 7.5 7.75 387.5 5.916 2.432 942.4 465. 6.158 2.481 1153.7 7.75 8. 400. 6.060 2.461 984.4 480. 6.316 2.513 1206.2 8. 8.25 412.5 6.103 2.470 1018.9 495. 6.471 2.544 1259.3 8.25 8.5 425. 6.345 2.519 1070.6 510. 6.624 2.574 1312.7 8.5 8.75 437.5 6.481 2.546 1113.9 525. 6.775 2.603 1366.6 8.75 9. 450. 6.619 2.573 1157.8 540. 6.923 2 . 633 1421.8 9. 9.25 462.5 6.752 2.598 1201.6 555. 7.010 2.648 1475.7 9.25 9.5 475. 6.883 2.623 1245.9 570. 7.216 2.686 1531 . 9.5 9.75 487.5 7.014 2.648 1290.9 585. 7.358 2,712 1586.5 9.75 10. 500. 7.145 2.673 1336.5 600. 7.500 2.738 1642.8 10. 10.5 525. 7.394 2.719 1427 630. 7.7781 2.789 1757. 10.5 11. 550. 7.639 2.764 1520. 660. S.049i 2.837 1872.4 11. 12. 600. 8.108 2.847 1708. 720. 8.571i 2.927 2107 4 12. OPEN AND CLOSED CHANNELS. 103 TABLE 14. V-SHAPED FLUME, EIGHT-ANGLED CKOSS-SECTION. Based on Kutter's formula, with n .013. Giving values of a, r and c, and also the values of the factors c-y/r and ac\/r for use in the formulae v = c\/r X -\/s and Q ac\/r X \/s The constant factors c\/r and ac\/r given in table are substantially correct for all slopes up to 1 in 2640, or 2 feet per mile. These factors are to be used only where the value of n, that is the co- efficient of roughness of lining of channel = .013, as in ashlar and well- laid brickwork; ordinary metal; earthenware and stoneware pipe, in good condition but not new; cement and terra cotta pipe, not well jointed nor in perfect order, and also plaster and planed wood in imperfect or inferior condition, and generally the materials mentioned with n = .01 when in imperfect or inferior condition Depth of water in feet. a = area in square feet. r = hydraulic mean depth in feet. For velocity c^ For discharge ac\/r .40 .16 .141 27.07 4.33 .5 25 .177 32.54 8.14 .6 .36 .212 37.44 13.48 .7 .49 .247 42.16 20.66 .75 .56 .265 44.55 24.95 .8 .64 .283 46.76 29.92 .9 .81 .318 51.10 41.39 1. _ .354 55.63 55.63 ' 1.1 ]21 .389 59.47 72. 1.2 .44 .424 63.28 91.12 1.25 .56 .442 65.30 101.9 1.3 .69 .459 66.40 112 2 1.4 .96 .494 70.93 139. 1.5 2.25 .530 74.55 167.7 1.6 2.56 .566 78.06 199.8 1.7 2.89 .601 81.53 235.6 1.75 3.06 .618 83.24 254.7 1.8 3.24 .636 85.15 275.9 1.9 3.61 .672 90.47 326.6 2. 4. .707 91.50 366. 2.1 4.41 .743 94.73 417.8 2.2 4.84 .778 97.90 473.8 2.25 5.06 .795 99.46 503.3 2.3 5.29 .813 101.02 534.4 2.4 5.76 .849 104. 598.9 2.5 6.25 .884 106.9 668. 2.6 6.76 .919 109.9 742.9 2.7 7.29 .955 112.7 821.9 2.75 7.56 .972 114.2 863.2 2.8 7.84 .990 116.2 910.9 2.9 8.41 1.025 118.4 995.8 3. 9. 1.061 121.2 1091. 104 FLOW OF WATER IN TABLE 15. Based on Kutter's formula, with n = .009. Values of the factors c and c\/r for use in the formulas v = c^/rs = cX \/r~ X \/s~ = c^/r~ X \/s~ All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr in fcGt 1 in 20000=0.264 ft. per mile 1 in 15840=0.3333 ft. per mile Vr s = .00005 s = .000063131 diff. diff. diff. diff. in 1661 c .01 cVr .01 c .01 cV~ .01 .4 93.4 1.49 37.4 1.68 97.8 1.49 39.1 1.72 .4 .5 108.3 1.29 54.2 1.85 112.7 1.27 56.3 1.89 .5 .6 121.2 1.13 72.7 2. 125.4 1.10 75.2 2.03 .6 .7 132.5 .99 92.7 2.12 136.4 .95 95.5 2.13 .7 .8 142.4 .88 113.9 2.22 145.9 .85 116.8 2.21 .8 .9 151.2 .78 136.1 2.29 154.4 .75 138.9 2.30 .9 1. 159. .71 159. 2.37 161.9 .67 161.9 2.35 1. 1.1 166.1 .64 182.7 2.43 168.6 .60 185.4 2.41 1.1 1.2 172.5 .58 207. 2.48 174.6 .54 209.5 2.45 1.2 1.3 178.3 .53 231.8 2.52 180. .49 234. 2.49 1.3 1.4 183.6 .48 257. 2.57 184.9 .45 258.9 2.53 1.4 1.5 188.4 .45 282.7 2.59 189.4 .42 284.2 2.55 1.5 1.6 192.9 .41 308.6 2.63 193.6 .38 309.7 2.58 1.6 1.7 197. .38 334.9 2.66 197.4 .35 335.5 2.60 1.7 1.8 200.8 .35 361.5 2.68 200.9 .32 361.5 2.63 1.8 1.9 204.3 .33 388.3 2.70 204.1 .30 387.8 2.64 1.9 2. 207.6 .31 415.3 2.72 207.1 .28 414.2 2.65 2. 2.1 210.7 .29 442.5 2.74 209.9 .26 440.7 2.67 2.1 2.2 213.6 .27 469.9 2.75 212.5 .24 467.4 2.69 2.2 2.3 216.3 .25 497.4 2.77 214.9 .23 494.3 2.70 2.3 2.4 218.8 .24 525.1 2.78 217.2 .21 521.3 2.70 2.4 2.5 221.2 .22 552.9 2.79 219.3 .20 548.3 2.72 2.5 2.6 223.4 .21 580.8 2.81 221.3 .20 575.5 2.73 2.6 2.7 225.5 .20 608.9 2.81 223.3 .17 602.8 2.73 2.7 2.8 227.5 .19 637. 2.83 225. .17 630.1 2.75 2.8 2.9 229.4 .18 665.3 2.83 226.7 .16 657.6 2.74 2.9 3. 231.2 693.6 228.3 685. 3. OPKX AND CLOSED CHANNELS. 105 TABLE 15. Based 011 Kutter's formula, with n = .009. Values of the factors c and c\/r for use in the formulae v c\/rs .--- c X \//' X \A = c\/r X \A' All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr in feet 1 in 10000=0.528 ft. per mile 1 in 7500 = 0.704 ft. per mile \/r iia feet 8 = .0001 s = .000133,333 c diff. .01 CV T diff. .01 $ diff. .01 cVr Jr X \/s All slopes greater than 1 iu 1000 have the same co-efficient as 1 in 1000. N/r 1 in 2500=2.114 ft. per mile 1 in 1000 = 5.28 ft. per mile V'r s = .0004 s = .001 in feet diff. diff. diff. diff. in feet c .01 cVr .01 c .01 c\/r .01 .4 81.2 1.09 32.5 1.25 83.7 1.09 33.5 1.38 .4 .5 92.1 .91 46. 1.47 94.6 .88 47.3 1.47 .5 .6 101.2 .76 60.7 1.54 103.4 .75 62. 1.56 .6 .7 108.8 .66 76.1 1.62 110.9 .63 77.6 1.61 .7 .8 115.4 .57 92.3 1.67 117.2 .55 93.7 1.67 .8 .9 121.1 .49 109. 1.70 122.7 .47 110.4 1.70 .9 1. 126. .44 126. 1.74 127.4 .42 127.4 1.74 1 1.1 130.4 .39 143.4 1.77 131.6 .37 144.8 1.76 1.1 1.2 134.3 .34 161.1 .79 135.3 .32 162.4 .76 1.2 1.3 137.7 .31 179. .81 138.5 .30 180. .81 1.3 1.4 140.8 .29 197.1 .84 141.5 .26 198.1 .80 1.4 1.5 143.7 .25 215.5 .84 144.1 .24 216.1 .83 1.5 1.6 146.2 .23 233.9 .85 146.5 .22 234.4 .84 1.6 1.7 148.5 .22 252.4 1.89 148.7 .20 252.8 .84 1.7 1.8 150.7 .20 271.3 1.88 150.7 .18 271.2 .85 1.8 1.9 152.7 .18 290.1 1.89 152.5 .17 289.7 1.87 1:9 2. 154.5 .17 309. 1.90 154.2 .16 308.4 1.88 2 2.1 156.2 .15 328. 1.89 155.8 .14 327.2 1.86 2.1 2.2 157.7 .15 346.9 1.93 157.2 .14 345.8 .90 2.2 2.3 159.2 .13 366.2 1.90 158.6 .12 364.8 .87 2.3 2.4 160.5 .13 385.2 1.93 159.8 .12 383.5 .90 2.4 2.5 161.8 .12 404.5 1.93 161. .11 402.5 .89 2.5 2.6 163. .11 423.8 1.93 162.1 .10 421.4 .90 2.6 2.7 164.1 .10 443.1 1.92 163.1 .10 440.4 .91 2.7 2.8 165.1 .10 462.3 1.94 164.1 .09 459.5 .90 2.8 2.9 166.1 .09 481.7 1.93 165. .09 478.5 .92 2.9 3. 167. 501. 165.9 497.7 3. 120 FLOW OF WATER IN TABLE 19. Based on Kutter's formula, with n = .013. Values of the factors c and /F for use in the formula? v == c\/rs = c X \/r X \/~ = c\/r X \/s All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr in feet 1 in 20000=. 264 ft. per mile 1 in 15840=. 3333 ft. per mile 8 = .00005 a = .000063131 Vr in feet c diff. .01 c^r diff. .01 c diff. .01 cx/r diff. .01 .4 56.7 1.02 22.7 1.08 59.3 1.03 23.7 1.11 .4 .5 66.9 .91 33.5 .21 69.6 .90 34.8 1.24 .5 .6 76. .82 45.6 .33 78.6 .81 47.2 1.35 .6 .7 84.2 .74 58.9 .44 86.7 .73 60.7 1.45 .7 .8 91.6 .67 73.3 .51 94. .65 75.2 1.52 .8 .9 98.3 .61 88.4 .60 100.5 .59 90.4 1.60 .9 104.4 .56 104.4 .66 106.4 .53 106.4 1.65 1. il 110. .52 121. .72 111.7 .49 122.9 1.70 1.1 .2 115.2 .47 138.2 .76 116.6 .45 139.9 1.76 1.2 .3 119.9 .44 155.8 .82 121.1 .41 157.5 1.78 1.3 .4 124.3 .40 174. .85 125.2 .39 175.3 1.84 1.4 .5 128.3 .38 192.5 .89 129.1 .35 193.7 1.85 1.5 .6 132.1 .35 211.4 .92 132.6 .33 212.2 1.89 1.6 .7 135.6 .34 230.6 .96 135.9 .31 231 . 1 1.91 1.7 1.8 139. .31 250.2 .97 139. .29 250.2 1.93 1.8 1.9 142.1 .28 269.9 2. 141.9 .26 269.5 1.95 1.9 2. 144.9 .29 289.9 2.05 144.5 .25 289. 1.98 2. 2.1 147.8 .25 310.4 2.02 147. .24 308.8 1.98 2.1 2.2 150.3 .24 330.6 2.06 149.4 .22 328.6 2.01 2.2 2.3 152.7 .23 351.2 2.07 151.6 .22 348.7 2.04 2.3 2.4 155. .21 371.9 2.09 153.8 .19 369.1 2.01 2.4 2.5 157.1 .21 392.8 2.12 155.7 .18 389.2 2.03 2.5 2.6 159.2 .20 414. 2.12 157.5 .18 409.5 2.06 2.6 2.7 161.2 .19 435 . 2 2.14 159.3 .17 430.1 2 07 2.7 2 8 163.1 .18 456.6 2.16 161. .16 450.8 2.07 2.8 2.9 164.9 .16 478.2 2.14 162.6 .16 471.5 2.10 2.9 3. 166.5 499.6 164.2 492.5 3. OPEN AND CLOSED CHANNELS. 121 TABLE 19. Based on Kutter's formula, with n = .013. Values of the factors c and c\/r for use in the formulae v = c^/rs = c X \Sr~ X V*~ = c\/7~ X v^s All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr in feet 1 in 10000=.528 ft. per mile 1 in 7500=. 704 ft. per mile v/V in feet s = .0001 s = .000133333 c diff. .01 c\/r diff. .01 c diff. .01 c\/r diff. .01 .4 64. 1.03 25.6 .16 66.5 1.03 26.6 1.18 .4 .5 74.3 .90 37.2 .28 76.8 .89 38.4 .30 .5 .6 83.3 .78 50. .38 85.7 .76 51.4 .39 .6 .7 91.1 .69 63.8 .46 93.3 .67 65.3 .47 .7 .8 98. .61 78.4 53 100. .60 80. .54 .8 .9 104.1 .56 93.7 .60 106. .53 95.4 .59 .9 109.7 .49 109.7 .63 111.3 .47 111.3 .63 1 .1 114.6 .45 126. .69 116. .43 127.6 .68 11 .2 119.1 .41 142.9 .72 120.3 .39 144.4 .70 1 2 .3 123.2 .37 160.1 .76 124.2 .35 161.4 .74 1.3 .4 126.9 .34 177.7 .78 127.7 .32 178.8 .76 1.4 .5 130.3 .31 195 5 1.80 130.9 .30 196 4 .78 1.5 1.6 133.4 .29 213.5 1 83 133.9 .27 214.2 .80 1.6 1.7 136.3 .27 231.8 1.84 136.6 .24 232.2 .80 1.7 1.8 139. .25 250.2 .87 139. .24 250.2 .84 1.8 1.9 141.5 .23 268.9 .88 141.4 .22 268.6 .85 1.9 2 143.8 .23 287.7 .90 143.6 .18 287.1 .85 2 2.1 146.1 .19 306.7 .90 145 4 .20 305.6 .88 2.1 2.2 148. .19 325.7 .92 147.4 .18 324.4 .87 2.2 2.3 149.9 .18 344.9 .91 149.2 .15 343.1 .87 2.3 2.4 151.7 .17 364 .95 150.7 .16 361.8 .90 2.4 2.5 153.4 .15 383 5 .93 152.3 .15 380.8 .92 2.5 2.6 154.9 .15 402.8 .96 153.8 .13 400. .89 2.6 2.7 156.4 .15 422.4 .96 155 1 .14 418.9 .92 2.7 2.8 157.9 .14 442. 2. 156.5 .12 438.1 .92 2.8 2.9 159.3 .13 462. 1.98 157.7 .11 457.3 .91 2.9 3. 160.6 481.8 158.8 476.4 3. 122 FLOW OF WATER IN TABLE 19. Based on Kutter's formula, with n .013. Values of the factors c and c\/r for use in the formulae v = c\/rs = c X Vr~ X \/s~ = c^/r~ X \A~ All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. in feet 1 in 5000=1.056 ft. per mile ; 1 in 3333.3=1.584 ft. per mile in feet s = .0002 ! s = .0003 c diff. .01 cV'r diff. .01 c diff. .01 /? All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr 1 in 10000=. 528 ft. per mile 1 in 7500=704 ft. per mile Vr a = .0001 s = .000133333 in feet c diff. .01 cVF diff. .01 c diff. .01 c\A* diff. .01 in feet .4 44.5 .78 17.8 .83 46.2 .78 18.5 .85 .4 .5 52.3 .69 26.1 .94 54. .70 27.0 .96 .5 .6 59.2 .62 35.5 1.03 61. .61 36.6 .04 .6 .7 65.4 .57 45.8 1.11 67.1 .55 47.0 .11 .7 .8 71.1 .50 56.9 1.16 72.6 .49 58.1 .16 .8 .9 76.1 .46 68.5 1.22 77.5 .44 69.7 .22 .9 80.7 .41 80.7 1.26 81.9 .41 81.9 .27 .1 84.8 .39 93.3 1.31 86. .36 94.6 .29 ]l .2 88.7 .35 106.4 1.35 89.6 .34 107.5 .34 .2 .3 92.2 .32 119.9 1.37 93. .31 120.9 .36 .3 .4 95.4 .31 133.6 1.42 96.1 .28 134.5 .38 .4 .5 98.5 .27 147.8 1.41 98.9 .27 148.3 .42 .5 .6 101.2 .26 161.9 1.46 101 . 6 .24 162.5 .43 .6 K . / 103.8 .25 176.5 1.48 104. .23 176.8 .45 1.7 1.8 106.3 .22 191.3 1.48 106.3 .21 191.3 1.47 1.8- 1.9 108.5 .21 206.1 1.51 108.4 .20 206. 1.48 1.9 2. 110.6 .21 221.2 1,54 110.4 .18 220.8 1.48 2. 2.1 112.7 .18 236.6 .53 112.2 .18 235.6 1.52 2.1 2.2 114.5 .18 251.9 .56 114. .16 250.8 1.51 2.2 2.3 116.3 .17 267.5 .57 115.6 .16 265.9 .54 2.3 2.4 118. .16 283.2 .58 117.2 .14 281.3 .52 2.4 2.5 119.6 .15 299. .58 118.6 .14 296.5 .55 2.5 2.6 121.1 .14 314.8 .59 120. .13 312. .55 2.6 2.7 122.5 .13 330.7 .59 121.3 .13 327.5 .58 2.7 2.8 123.8 .13 346.6 1.62 122.6 .11 343.3 .54 2.8 2.9 125.1 .12 362.8 1.61 123.7 .12 358.7 1.60 2.9 3. 126.3 .12 378.9 1.66 124.9 .10 374.7 1.56 3. 3.1 127.5 .11 395.3 1.62 125.9 .10 390.3 1.58 3.1 3.2 128.6 .11 411.5 1.65 126.9 .10 406.1 1.60 3.2 3.3 129.7 .10 428. 1.64 127.9 .09 422.1 .58 3.3 3.4 130.7 .10 444.4 1.65 128.8 .09 437.9 .61 3.4 3.5 131.7 .09 460.9 1.65 129.7 .09 454. .62 3.5 3.6 132.6 .09 477.4 1.65 130.6 .08 470.2 .60 3.6 3.7 133.5 .08 493.9 1.64 131.4 .07 486.2 .58 3.7 3.8 134.3 .09 510.3 1.70 132.1 .08 502. .63 3.8 3.9 135.2 .08 527.3 1.65 132.9 .07 518.3 .61 3.9 4. 136. 543.8 133.6 534.4 ! 4. 130 FLOW OF WATER IN TABLE 21. Based on Kutter's formula, with n== .017. Values of the factors c and c\/r for use in the formulae v = Cv/Vs = c X \/r X \/s = c\/r X \/~ All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr in feet 1 in 5000=1.056 ft. per mile 1 in 3333.3=1.584 ft. per mile Vr in feet 8= .0002 a = .0003 c diff. .01 .01 c .01 .01 .4 27.4 .78 11. .50 28.5 .57 11.4 .57 .4 .5 33. .52 16.5 .64 34.2 .52 17.1 .65 .5 .6 38.2 .48 22.9 .72 39.4 .48 23.6 .74 .6 .7 43. .45 30.1 .79 44.2 .45 31. .79 .7 .8 47.5 .42 38. .85 48.7 .41 38.9 .87 .8 .9 51.7 .40 46.5 .92 52.8 .39 47.6 .91 .9 1. 55.7 .37 55.7 .96 56.7 .36 56.7 .96 I. I.I 59.4 .36 65.3 1.03 60.3 .34 66.3 .02 1.1 1.2 63. .32 75.6 1.05 63.7 .32 76.5 .05 1.2 1.3 66.2 .31 86.1 1.09 66.9 .30 87. .08 1.3 1.4 69.3 .30 97. 1.15 69.9 .28 97.8 .13 .4 1.5 72.3 .28 108.5 1.17 72.7 .27 109.1 .15 .5 1.6 75.1 .26 120.2 1.19 75.4 .25 120.6 .18 .6 1.7 77.7 .25 132.1 1.23 77.9 .23 132.4 .20 .7 1.8 80.2 .24 144.4 1.25 80.2 .23 144.4 .23 .8 1.9 82.6 .23 156.9 1.29 82.5 .21 156.7 .25 1.9 2 84.9 .22 169.8 .31 84.6 .21 169.2 .25 2. 2.1 87.1 .20 182.9 .31 86.7 .19 182. .28 2.1 2.2 89.1 .20 196. .35 88.6 .18 194.9 .31 2 "2 2.3 91.1 .19 209.5 .37 90.4 .18 208. .32 2.3 2.4 93. .18 223.2 .38 92.2 .17 221.2 .35 2.4 2.5 94.8 .18 237. .42 93.9 .16 234.7 .35 2.5 2.6 96.6 .16 251.2 .39 95.5 .15 248.2 .37 2.6 2.7 98.2 | .16 265.1 .43 97. .15 261.9 ! .38 2.7 2.8 99.8 .16 279.4 .47 98.5 .14 275.7 .39 2.8 2.9 101.4 .14 294.1 .43 99.9 .13 289.6 .41 2.9 3. 102.8 .15 308.4 .49 101.2 .13 303.7 .41 3. 3.1 104.3 .13 323.3 .46 102.5 .13 317.8 .42 3.1 3.2 105.6 .13 337.9 .52 103.8 .12 332. .44 3.2 3.3 106.9 .13 353.1 .49 105. .11 346.4 .44 3.3 3.4 108.2 .13 368. .51 106.1 .11 360.8 .45 3.4 3.5 109.5 .12 383.1 .53 107.2 .11 375.3 .46 3.5 3.6 110.7 .11 398.4 .53 108.3 .10 389.9 .47 3.6 3.7 111.8 .11 413.7 .53 109.3 .10 404.6 .47 3.7 3.8 112.9 .11 429. .55 110.3 10 419.3 1.48 3.8 3.9 114. .10 444.5 .56 111.3 .09 434.1 1.48 3.9 4. 115. 460.1 112.2 448.9 4. OPEN AND CLOSED CHANNELS. 139 TABLE 23. Based on Kntter's formula, with n = .0225. Values of the factors c and ^/r for use in the formulas v = c\/rs = c X \/r~ X \A' = c^/r X \A All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr_ 1 in 10000=.528 ft. per mile 1 in 7500 .704 ft. per mile Vr s=.0001 s = .000133333 in feet diff. _ diff. diff. __ diff. i hl feet c .01 c\/r .01 c .01 C^/T .01 .4 30.5 .58 12.2 .00 31.6 .59 12.6 .61 .4 .5 30. 3 .53 18.2 .08 37.5 .52 18.7 .69 .5 .6 41.6 .48 25 .75 42.7 .48 25.6 .77 .6 py . t 46.4 .43 32.5 .81 47.5 .43 33.3 .81 .7 .8 50.7 .41 40.6 .87 51.8 .40 41.4 .88 .8 .9 54.8 .37 49.3 .92 55.8 .36 50.2 .92 .9 1. 58.5 .34 58.5 .96 59.4 .33 59.4 .96 1. 1.1 61.9 .32 68.1 1. 62.7 .31 69. 1. 1.1 1.2 65.1 .30 78.1 1.04 65.8 .29 79. 1.03 1.2 1.3 68.1 .27 88.5 1.06 68.7 .26 89.3 1.05 1.3 1.4 70.8 .26 99.1 1.10 71.3 .25 99.8 1.09 1.4 1.5 73.4 .25 110.1 1.13 73.8 .23 110.7 1.11 1.5 1.6 75.9 .22 121.4 1.14 76.1 .22 121.8 1.13 1.6 1.7 78.1 .22 132.8 1.17 78.3 .20 133.1 1.14 1.7 1.8 80.3 .20 144.5 1.19 80.3 .18 144.5 1.17 1.8 1.9 82.3 .19 156.4 1.20 82.1 .16 156.2 1.18 1.9 2 84.2 .18 168.4 1.22 83.7 .16 168. 1.18 2. 2*1 86. .17 180.6 1.23 85.3 .15 179.8 1.20 2 1 2.2 87.7 .16 192.9 1.25 86.8 .13 191.8 1.24 2^2 2^3 89.3 .15 205.4 1.25 88.1 .14 204.2 1.23 3.3 2.4 90.8 .15 217.9 1.29 89.5 .12 216.5 1.23 2.4 2.5 92.3 .14 230.8 1 28 90.7 .12 228.8 1.25 2.5 2.6 93.7 .13 243.6 1.29 91.9 .11 241.3 1.25 2.6 2.7 95. .13 256.5 1.31 93. .11 253.8 1.28 2.7 2.8 96.3 .12 269.6 1.32 94.1 .10 266.6 1.27 2.8 2.9 97.5 .11 282 8 1.30 95.1 .10 279.3 1.29 2.9 3. 98.6 .11 295.8 1.33 96.1 .09 292.2 1.28 3. 3.1 99.7 .11 309.1 1.35 97. .09 305. 1.31 3.1 3.2 100.8 .10 322.6 1.33 97.9 .08 318.1 1.29 3.2 3.3 101.8 .10 335.9 1.36 98.7 .08 331. 1.31 3.3 3.4 102.8 .09 349.5 1.35 99.5 .08 344.1 1.29 3.4 3.5 103.7 .09 363. 1.36 100.3 .07 357. 1.31 3.5 3.6 104.6 .09 376.6 .38 101. .07 370.1 1.32 3.6 3.7 105.5 .08 390.4 .35 101.7 .07 383.3 1.34 3.7 3.8 106.3 .08 403.9 .38 102.4 .07 396.7 1.36 3.8 3.9 107.1 .08 417.7 .39 103.1 .06 410.3 1.37 3.9 4. 107.9 431.6 103.7 424. 4. 140 FLOW OF WATER IN TABLE 23 Based on Kutter's formula, with, n = .0225. Values of the factors c and c\/r for use in the formula} v = cx/ni = c X V^~ X V~~ c^/r~X V~ All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr in feet 1 in 5000=1.056 ft. per mile | 1 in 3333.3=1.584 ft. per mile Vr in feet s = .0002 * = .0003 c diff. .01 , diff. c ^ r .01 c diff. .01 . diff. c ^ r \ .01 i .4 33. .59 13.2 .62 34. .59 13.6 .64 .4 .5 38.8 .52 19.4 .71 39.9 .53 20. .71 .5 .6 44.1 .48 26.5 .77 45.2 .46 27.1 .78 .6 .7 48.9 .42 34.2 .83 49.8 .44 34.9 .85 .7 .8 53.1 .38 42.5 .87 54.2 .30 43.4 .86 .8 .9 56.9 .36 51.2 .93 57.8 .34 52. .92 .9 60.5 .32 60.5 .96 61.2 .32 61.2 .96 '.1 63.7 .29 70.1 .98 64.4 .23 70.8 .98 .1 .2 66.6 .27 79.9 1.02 67.2 .20 80.6 1.01 .2 .3 69.3 .26 90.1 1.06 69.8 .25 90.7 1.05 .3 !4 71.9 .23 100.7 1.06 72.3 .22 101.2 1.06 .4 .5 74.2 .22 111.3 1.09 74.5 .21 111.8 1.08 .5 .6 76.4 .20 122.2 1.11 76.6 .19 122.6 1.09 .6 1.7 78.4 .19 133.3 1.12 78.5 .17 133.5 1.09 1.7 1.8 80.3 .18 144.5 1.15 80.2 .17 144.4 1.12 1.8 1.9 82.1 .16 156. 1114 81.9 .16 155.6 1.14 1.9 o 83.7 .16 167.4 .17 83.5 .15 167. 1.15 2 2.1 85.3 .15 179.1 .19 85. .14 178.5 1.16. 2'.1 2.2 86.8 .13 191. .16 86.4 .13 190.1 1.16 2.2 2.3 88.1 .14 202.6 .22 87.7 .13 201.7 1.19 2.3 2.4 89.5 .12 214.8 .20 89. .11 213.6 1.17 2.4 2.5 90.7 .12 226.8 .21 90.1 .11 225.3 1.18 2.5 2.6 91.9 .11 238.9 1.22 91.2 .11 237.1 1.21 2.6 2.7 93. .11 251.1 1.24 92.3 .10 249.2 1.20 2.7 2.8 94.1 .10 263.5 1.23 93.3 .09 261.2 1.20 2.8 2.9 95.1 .10 275.8 1.25 94.2 .09 273.2 1.21 2.9 3. 96.1 .09 288.3 1.24 95.1 .09 285.3 1.23 3. 3.1 97. .09 300.7 1.26 96. .08 297.6 1.22 3.1 3.2 97.9 .08 313.3 1.24 96.8 .07 309.8 1.19 3.2 3.3 98.7 .08 j 325.7 1.26 97.5 .07 321.7 1.22 3.3 3.4 99.5 .08 i 338.3 1.27 98.2 .08 333.9 1.26 3.4 3.5 100.3 .07 351. 1.26 99. .07 346.5 1.24 3.5 3.6 101. .07 363.6 1.27 99.7 .07 358.9 1.26 3.6 3.7 101.7 .07 376.3 1.28 100.4 .06 371.5 1.23 3.7 3.8 102.4 .07 389.1 1.30 101. .06 383. 8 1.24 3.8 3.9 103.1 .06 402.1 1.27 101.6 .06 396.2 1.26 3.9 3. 103.7 414.8 102.2 408.8 4. OPEN AND CLOSED CHANNELS. 141 TABLE 23. Based on Kutter's formula, with n = .0225. Values of the factors c and c\/r for use in the formulae v = c\/rs = c X \/~r~ X \/#~ = c\/r~ X \/!T All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr 1 in 2500=2.112 ft. per mile 1 in 1666.6=3.168 ft. per mile Vr s .0004 s = .0006 in feet diff. diff. diff. diff. in feet c .01 cW .01 c .01 c^r .01 .4 34.6 .59 13.8 .65 35.2 .59 14.1 .65 .4 .5 40.5 .52 20.3 .71 41.1 .52 20.6 .75 .5 .6 45.7 .47 27.4 .79 46.3 .47 28.1 .76 .6 fj . I 50.4 .41 35.3 .83 51. .41 35.7 .84 .7 .8 54.5 .38 43.6 .89 55.1 .37 44.1 .88 .8 .9 58.3 .34 52.5 .92 58.8 .33 52.9 .92 .9 1. 61.7 .30 61.7 .95 62.1 .30 62.1 .95 1. 1.1 64.7 .28 71.2 .98 65.1 .28 71.6 .99 1.1 1.2 67.5 .26 81. 1.01 67.9 .25 81.5 1. 1.2 1.3 70.1 .24 91.1 .04 70.4 .23 91.5 1.03 1.3 1.4 72.5 .22 101.5 .04 72.7 .21 101.8 1.07 14 1.5 74.7 .20 111.9 .08 74.8 .20 112.5 1.05 1.5 16 76.7 .19 122.7 .09 76.8 .18 123. 1.08 1.6 1.7 78.6 .17 133.6 .09 78.6 .17 133.8 1.07 1.7 1.8 80.3 .16 144.5 .11 80.3 .16 144.5 1.11 1.8 1.9 81.9 .16 155.6 .14 81.9 .15 155.6 1.12 1.9 2 83.5 .14 167. 1.13 83.4 .13 166.8 1.09 2. 2 1 84.9 .13 178.3 1.13 84.7 .13 177.7 1.11 2.1 2.2 86.2 .13 189.6 1.17 86. .13 188.8 1.15 2.2 2.3 87.5 .12 201.3 1.16 87.3 .11 200.3 1.14 2.3 2.4 88.7 .11 212.9 1.16 88.4 .11 211.7 1.13 2.4 2.5 89.8 .11 224.5 1.18 89.5 .10 223. 1.15 2.5 2.6 90.9 .10 236.3 1.18 90.5 .10 234.5 1.17 2.6 2.7 91.9 .09 248.1 .17 91.5 .09 246.2 1.14 2.7 2.8 92.8 .09 259.8 .19 92.4 .09 257.6 1.18 2.8 2.9 93.7 .09 271.7 .21 93.3 .08 269.4 1.29 2.9 3 94.6 .08 283.8 .19 94.1 .08 282.3 1.19 3. 3.1 95.4 .08 295.7 .21 94.9 .07 294.2 1.04 3.1 3.2 96.2 .08 307.8 .23 95.6 .08 304.6 1.19 3.2 3.3 97. .07 320.1 1.21 96.4 .06 316.5 1.16 3.3 3.4 97.7 .07 332.2 1.22 97. .07 328.1 1.20 3.4 3.5 98.4 .06 344.4 1.20 97.7 .06 340.1 1.18 3.5 3.6 99. .06 356.4 1.23 98.3 .06 351.9 1.20 3.6 3.7 99.6 .06 368.7 1.23 98.9 .06 363.9 1.19 3.7 3.8 100.2 .06 381. 1.22 99.5 .06 375.8 1.19 3.8 3.9 100.8 .06 393.2 1.23 100.1 .05 387.7 1.20 3.9 4. 101.4 405.5 100.6 399.7 4. 142 FLOW OF WATER IN TABLE 23. Based on Kutter's formula, with n = .0225. Values of the factors c and c\/r for use in the formulas v = c\/rs = c X\/r X \A = c\/r X \A All slopes greater than 1 in lOOO'have the same co-efficient as 1 in 1000. iii feet 1 in 1250=4.224 ft. per mile 1 in 10005.28 ft. per mile in feet g == .0008 s = .001 c diff. .01 ^ diff. .01 c diff. .01 diff. .01 .4 35.5 .60 14.2 .65 35.7 .60 14.3 .65 .4 .5 41.5 .52 20.7 .73 41.7 .52 20.8 .73 .5 .6 46.7 .46 28. .79 46.9 .46 28.1 .80 .6 .7 51.3 .41 35.9 .84 51.5 .40 36.1 .83 .7 .8 55.4 .36 44.3 .88 55.5 .37 44.4 .89 .8 .9 59. .33 53.1 .92 59.2 .33 53.3 .92 .9 1. 62.3 .30 62.3 .95 62.5 .29 62.5 .94 1 1.1 65.3 .27 71.8 .98 65.4 .27 71.9 .98 1.1 1.2 68. .25 81.6 1.01 68.1 .25 81.7 1.01 1.2 1.3 70.5 .23 91.7 1 02 70.6 .23 91.8 1.03 1.3 1.4 72.8 .21 101.9 1.05 72.9 .21 102.1 1.04 1.4 1.5 74.9 .19 112.4 1.05 75. .19 112.5 1.05 1.5 1.6 76.8 .18 122.9 1.07 76.9 .18 123. 1.08 1.6 1.7 78.6 .17 133.6 1.09 78.7 .16 133.8 1.07 1.7 1.8 80.3 .16 144.5 1.11 80.3 .16 144.5 1.11 1.8 1.9 81.9 .14 155.6 1.10 81.9 .14 155.6 1.10 1.9 2, 83.3 .14 166.6 1.13 83.3 .13 166.6 1.11 2. 2.1 84.7 .12 177.9 1.11 84.6 .12 177.7 1.11 2.1 2.2 85.9 .12 189. 1.13 85.8 .13 188.8 1.15 2.2 2.3 87.1 .12 200.3 1.16 87.1 .11 200.3 1.14 2.3 2.4 88.3 .10 211.9 1.14 88.2 .10 211.7 1.13 2.4 2.5 89.3 .10 223.3 1.15 89.2 .10 223. 1.15 2.5 2.6 90.3 .10 234.8 1.17 90.2 .10 234.5 1.17 2.6 2.7 91.3 .09 246.5 1.17 91.2 .08 246.2 1.14 2.7 2.8 92.2 .08 258.2 1.15 92. .09 257.6 1.18 2.8 2.9 93. .08 269.7 1.17 92.9 .08 269.4 1.17 2.9 3. 93.8 .08 281.4 1.19 93.7 .08 281.1 1.19 3. 3.1 94.6 .08 293.3 1.20 94.5 .07 293. 1.16 3.1 3.2 95.4 .07 305.3 1.18 95.2 .07 304.6 1.19 3.2 3.3 96.1 .06 317.1 1.17 95.9 .06 316.5 1.16 3.3 3.4 96.7 .07 328.8 1.20 96.5 .07 328.1 1.20 3.4 3.5 97.4 .06 340.8 1.19 97.2 .06 340.1 1.18 3.5 3.6 98. .06 352.7 1.20 97.8 .05 351.9 1.20 3.6 3.7 98.6 .05 364.7 1.20 98.3 .06 363.9 1.19 3.7 3.8 99.1 .06 376.7 1.20 98.9 .05 375.8 1.19 3.8 3.9 99.7 .05 388.7 1.20 99.4 .05 387.7 1.20 3.9 4. 100.2 400.7 99.9 399.7 4. OPEN AND CLOSED CHANNELS. 143 TABLE 24. Based on Kutter's formula, with n = .025. Values of the factors c and /V for use in the formulae v = c^/rs = c X \Xr~X %/*""= c^/r~ X \A~ All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr 1 in 20000 = .264 ft. per mile 1 in 15840 = .3333 ft. per mile s = .00005 8 = .000063131 in feet diff. diff. diff. _ diff. in feet c .01 cVr .01 c .01 cVr .01 .4 23.9 .56 9.6 .48 24.8 .51 9.94 .50 .4 .5 28.9 .46 14.4 .57 29.9 .47 14.9 .57 .5 .6 .44 20.1 .64 34.6 .43 20.6 .66 .6 .7 37.9 .41 26.5 .71 38.9 .41 27.2 .72 .7 .8 42. .38 33.6 .76 43. .37 34.4 .77 .8 .9 45.8 .36 41.2 .82 46.7 .36 42.1 .82 .9 1. 49.4 .34 49.4 .87 50.3 .33 50.3 .87 1. 1.1 52.8 .32 58.1 .92 53.6 .32 59. .91 1.1 1.2 56. .31 67.3 .95 56.8 .29 68.1 .95 1.2 1.3 59.1 .29 76.8 59.7 .28 77.6 .99 1.3 1.4 62. .27 86.8 .03 62.5 .26 87.5 1.02 1.4 1.5 64.7 .26 97.1 !06 65.1 .25 97.7 1.05 1.5 1.6 67.3 .25 107.7 .10 67.6 .24 108.2 1.07 1.6 1.7 69.8 .24 118.7 .12 70. .22 118.9 .11 1.7 1.8 72.2 .22 129.9 .15 72.2 .21 130. .12 1.8 1.9 74.4 .22 141.4 .18 74.3 .21 141.2 .15 1.0 2. 76.6 .21 153.2 .20 76.4 .19 152.7 .17 2. 2.1 78.7 .19 165.2 .22 78.3 .18 164.4 .19 2.1 2.2 80.6 .19 177.4 .24 80.1 .18 176.3 .21 2.2 2.3 82.5 .18 189.8 .26 81.9 .17 188.4 .22 2.3 2.4 84.3 .18 202.4 .28 83.6 .16 200.6 .24 2.4 2.5 86.1 .16 215.2 1.29 85.2 .15 213. .25 2.5 2.6 87.7 .16 228 . 1 1.31 86.7 .15 225.5 .27 2.6 2.7 89.3 .16 241.2 1.33 88.2 .14 238.2 .28 2.7 2.8 90.9 .15 254.5 1.34 89.6 .14 251. .29 2.8 2.9 92.4 .14 267.9 1.35 91. .13 263.9 .30 2.9 3. 93.8 .14 281.4 .36 92.3 .13 276.9 .32 3. 3.1 95.2 .13 295. .38 93.6 .12 290.1 .32 3.1 3.2 96.5 .13 308.8 .39 94.8 .12 303.3 .33 3.2 3.3 97.8 .12 322.7 .40 96. .11 316.6 .35 3.3 3.4 99. .12 336.7 .41 97.1 .11 330.1 1.35 3.4 3.5 100.2 .12 350.8 .42 98.2 .10 343.6 1.36 3.5 3.6 101.4 .11 365. .43 99.2 .10 357.2 1.37 3.6 3.7 102.5 .11 379.3 .43 100.2 .10 370.9 1.37 3.7 3.8 103.6 .10 393.6 .45 101.2 .10 384.6 1.38 3.8 3.9 104.6 .11 408.1 .47 102.2 .09 398.4 1.39 3.9 4. 105.7 422.8 103.1 412.3 4. 144 FLOW OF WATEIl IN TABLE 24. Based on Kutter's formula, with n .025. Values of the factors c and c\/r for use in the formulae v = c\/rs =1 c X \/r X \/s~ = c v /F X \/ All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr in feet 1 in 10000= .528 ft. per mile 1 in 7500=. 704 ft. per mile Vr in feet s = .0001 s = .000133333 c diff. .01 c\/r diff. .01 c diff. .01 cVr diff. .01 .4 26.5 .52 10.6 .53 27.4 .52 11. .53 .4 .5 31.7 .47 15.9 .59 32.6 .47 16.3 .61 .5 .6 36.4 .43 21.8 .67 37.3 .43 22.4 .67 .6 .7 40.7 .40 28.5 .73 41.6 .40 29.1 .'74 , .7 .8 44.7 .37 35.8 .78 45.6 .36 36.5 .78 .8 .9 48.4 .34 43.6 .82 49.2 .34 44.3 .83 .9 51.8 .32 51.8 .87 52.6 .31 52.6 .87 1. !i 55. .30 60.5 .91 55.7 .28 61.3 .89 1.1 .2 58. .27 69.6 .93 58.5 .27 70.2 .94 1.2 .3 60.7 .26 78.9 .97 61.2 .25 79.6 .96 1.3 .4 63.3 .25 88.6 1.01 63.7 .24 89.2 1.4 .5 65.8 .22 98.7 1.01 66.1 .21 99.2 .99 1.5 .6 68. .22 108.8 1.05 68.2 .21 109.1 .04 1.6 .7 70.2 .22 119.3 1.07 70.3 .19 119.5 .05 1.7 .8 72.2 .19 130. 1.08 72.2 .19 130. .08 1.8 1.9 74.1 .19 U0.8 1.12 74.1 .17 140.8 .08 1.9 2. 76. .17 152. 1.12 75.8 .16 151.6 .09 2. 2.1 77.7 .16 163.2 1.13 77.4 .16 162.5 .13 2.1 2.2 79.3 .16 174.5 1.16 79. .14 173.8 .11 2.2 2.3 80.9 .15 186.1 1.17 80.4 .14 184.9 .14 2.3 2.4 82.4 .14 197.8 1.17 81.8 .13 196.3 .15 2.4 2.5 83.8 .13 209.5 1.18 83.1 .13 207.8 .16 2.5 2.6 85.1 .13 221.3 1.20 84.4 .12 219.4 .17 2.6 2.7 86.4 .12 233.3 1.20 85.6 .11 231.1 i .17 2.7 2.8 87.6 .12 245.3 1.22 86.7 .11 242.8 .18 2.8 2.9 88.8 .11 257.5 .22 87.8 .11 254.6 .21 2.9 3. 89.9 .11 269.7 .24 88.9 .10 266.7 .20 3. 3.1 91. .10 282.1 .23 89 9 .09 278.7 ! .19 3.1 3.2 92. .10 294.4 .25 90.8 .09 290.6 .20 3.2 3.3 83. .10 306.9 .27 91.7 .09 302.6 .19 3.3 3.4 94. .09 319.6 1.25 92.5 .09 314.5 .22 3.4 3.5 94.9 .09 332.1 1.27 93.3 .09 326.7 .23 3.5 3.6 95.8 .08 344.8 1.27 94.2 .07 339. 22 3.6 3.7 96.6 .09 357.5 1.28 94.9 .08 351.2 .'24 3.7 3.8 97.5 .07 370.3 1.29 95.7 .07 363.6 .24 3.8 3.9 98.2 .08 383.2 1.28 96.4 .07 376. .24 3.9 4. 99. 396. 97.1 388.4 4. OPEN AND CLOSED CHANNELS. 145 TABLE 24. Based on Kutter's formula, with n = .025. Values of the factors c and c\/r for use in the formulas v = c\/rs = c X X c ^/ r X All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr iii feet 1 in 5000=1.056 ft. per mile ||l in 3333.3=1.584 ft. per mile Vr in feet s = .0002 s = .0003 c diff. 01 c-v/F diff. .01 c diff. .01 /r X \/ s All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr in feet 1 in 10000=:. 528 ft. per mile 1 in 7500=. 704 ft. per mile Vr in feet s .0001 s = .000133333 c diff. .01 cV~ diff. .01 c diff. .01 /- diff. cVr .01 .4 23.4 .46 9.4 .46 24.2 .47 9.7 I .47 .4 .5 28. .4$ 14. .54 28 9 .43 14.4 .55 .5 .6 32.3 .40 19.4 .60 33.2 .39 19.9 .61 .6 .7 36.3 .36 I 25.4 .65 37.1 .36 28. .66 .7 .8 39.9 34 31.9 .71 40.7 .34 32.6 .71 .8 .9 43.2 .32 39. .75 44.1 .31 39.7 .75 .9 46.5 .29 46.5 .79 47.2 .29 47.2 .79 1. .1 49.4 .28 i 54.4 .82 50.1 .26 55.1 .82 1.1 .2 52.2 .26 62.6 .86 52.7 .25 63.3 .85 1.2 .3 54.8 .24 71.2 .89 55.2 .24 71.8 .88 1.3 .4 57.2 .23 80.1 .92 57.6 .22 80.6 .91 1.4 .5 59.5 .22 89.3 .94 59.8 .21 89.7 .93 1.5 .6 61.7 .20 98.7 .96 61.9 .19 99. .94 1.6 .7 63.7 .19 108.3 .99 63.8 .19 108.4 .98 1.7 .8 65.6 .19 118.2 1. 65.7 .17 118.2 .98 1..8 .9 67.5 .17 128.2 1 02 67.4 .16 128. .01 1.9 2. 69.2 .17 138.4 .04 69. .16 138.1 .01 2. 2.1 70.9 .15 148.8 .04 70.6 .15 148.2 .03 2.1 2.2 72.4 .15 159.4 .07 72.1 .14 158.5 .05 2.2 2.3 73.9 .15 170.1 ,08 73.5 .13 169. .05 2.3 2.4 75.4 .13 180.9 .09 74.8 .13 179.5 .07 2.4 2.5 76.7 .13 191.8 .10 76.1 .12 190.2 .08 2.5 2.6 78. .13 202.8 .12 77.3 .12 201. .10 2.6 2.7 79.3 .12 214. .13 78.5 .11 212. 1.08 2.7 2.8 80.5 .11 225.3 .14 79.6 .10 222.8 1.09 2.8 2.9 81.6 .11 236.7 .14 80.6 .10 233.7 1.12 2.9 3. 82.7 .11 248.1 .15 81 6 .10 244.9 1.12 3. 3.1 83.8 .10 259.6 . 17 82.6 .09 256.1 1.12 3.1 3.2 84.8 .10 271.3 .17 83.5 .09 267.3 1.14 3.2 3.3 85.8 .09 283. .17 84.4 .09 278.7 1.13 3.3 3.4 86.7 .09 294.7 .19 85.3 .08 290. 4.15 3.4 3.5 87.6 .09 306.6 .19 86.1 .08 301.5 1.14 3.5 3.6 88.5 .08 318.5 .19 86.9 .08 312.9 1.16 3.6 3.7 89.3 .08 330.4 .20 87.7 .07 224.5 1.16 3.7 3.8 90.1 .08 342.4 .21 88.4 .07 336.1 1.16 3.8 3.9 90.9 .07 354 5 .21 89.1 .07 347.7 1.17 3.9 4. 91.6 366.6 89.8 359.4 4. 150 FLOW OF WATER IN TABLE 25. Based on Kutter's formula, with n = .0275. Values of the factors c and /r for use in the formulae v = c\/rs = c X \/r~ X \f~s~ = c\/r X \A All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr in feet 1 in 5000=1.056 ft. per mile 1 in 3333.31.584 ft. per mile -v/r in feet s = .0002 s = .0003 c diff. .01 c\/r diff. .01 c diff. .01 c\A* diff. .01 .4 25.2 .47 10.1 . .49 25.9 .48 10.4 .50 .4 .5 29.9 .43 15. .55 30.7 .43 15.4 .56 5 .6 34.2 .39 20.5 .62 35. .39 21. .62 .6 .7 38.1 .36 26.7 .67 38.9 .35 27.2 .67 .7 .8 41.7 .33 33.4 .71 42.4 .33 33.9 .72 .8 .9 45. .30 40.5 .75 45.7 .29 41.1 .75 .9 1. 48. .28 48. .79 48.6 .28 48.6 .79 1.1 50.8 .26 55.9 .82 51.4 .25 56.5 .82 : i 1.2 53.4 .24 64.1 .84 53.9 .23 64.7 .84 .2 1.3 55.8 .22 72.5 .87 56.2 .22 73.1 .86 .3 1.4 58. .21 81.2 .90 58.4 .20 81.7 .89 .4 1.5 60.1 .20 90.2 .92 60.4 .19 90.6 .90 5 1.6 62.1 .18 99.4 .93 62.3 .17 99.6 .92 .6 1.7 63.9 .18 108.7 .95 64. .17 108.8 .94 7 1.8 65.7 .16 118.2 .97 65.7 .15 118.2 .95 .8 1.9 67.3 .15 127.9 .98 67.2 15 127.7 .97 .9 2 68.8 .15 137.7 .99 68.7 .14 137.4 .97 2 2.1 70.3 .13 147.6 1.00 70.1 .13 147.1 .99 2.1 2.2 71.6 .13 157.6 1.02 71.4 .12 157. .99 2.2 2.3 72.9 .13 167.8 1.03 72.6 .11 166.9 1.01 2.3 2.4 74.2 .12 178.1 1.03 73.7 .11 177. .01 2.4 2.5 75.4 .11 188.4 1.05 74.8 .11 187.1 .02 2.5 2.6 76.5 .10 198.9 1.05 75.9 .10 197.3 .03 2.6 2.7 77.5 .11 209.4 1.06 76.9 .10 207.6 .04 2.7 2.8 78.6 .09 220. 1.06 77.9 .09 218. .04 2.8 2.9 79.5 .09 230.6 1.08 78.8 .08 228.4 .05 2.9 3. 80.4 .09 241.4 1.08 79.6 .08 238.9 .05 3. 3.1 81.3 .09 252.2 1.08 80.4 .08 249.4 .06 3.1 3.2 82.2 .08 263. 1.09 81.2 .08 260. .06 3.2 3.3 83. .08 273.9 1.10 82. .07 270.6 .07 3.3 3.4 83.8 .07 284.9 1.10 82.7 .07 281.3 .07 3.4 3.5 84.5 .08 295.9 1.10 83.4 .07 292. .07 3.5 3.6 85.3 .06 306.9 1.11 84.1 .06 302.7 .08 3.6 3.7 85.9 .07 318. 1.11 84.7 .06 313.5 .08 3.7 3.8 86.6 .07 329.1 1.12 85.3 .06 324.3 .09 3.8 3.9 87.3 .06 340.3 1.12 85.9 .06 335.2 1.08 3.9 4. 87.9 351.5 86.5 346. 4. OPEN AND CLOSED CHANNELS. 151 TABLE 25. Based on Kutter's formula, with n - .0275. Values of the factors c and c\/r for use in the formulae v = c\/rs = c X \/r X \A = c\/r X \A' All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr in feet 1 in 2500=2.114 ft. per mile 1 in 1666.7=3.168 ft. per mile Vr in feet 8= .0004 s = .0006 c diff. .01 j-VC- diff - c ^ r .01 c diff. .01 cVr diff. .01 ,4 26.4 .48 10.5 .51 26.8 .48 10.7 .51 .4 .5 31.2 .43 15.6 .57 31.6 .43 15.8 .57 .5 .6 35.5 .38 21.3 .62 35.9 .39 21.5 .63 .6 .7 39.3 .35 27.5 .68 39.8 .35 27.8 .68 .7 .8 42.8 .32 34.3 .71 43.3 .31 34.6 .72 .8 .9 46. .30 41.4 .76 46.4 .29 41.8 .75 .9 1. 49. .27 49. .78 49.3 .27 49.3 .79 1. 1.1 51.7 .24 56.8 .81 52. .24 57.2 .81 1.1 1.2 54.1 .23 64.9 .85 54.4 .23 65.3 .84 1.2 1.3 56.4 .21 73.4 .86 56.7 .20 73.7 .85 1.3 1.4 58.5 .20 82. .88 58.7 .20 82.2 .88 1.4 1.5 60.5 .19 90.8 .90 60.7 .18 91. .89 1.5 1.6 62.4 .17 99. 8 .91 62.5 .16 99.9 .91 1.6 1.7 64.1 .16 108.9 .93 64.1 .16 109. .92 1.7 1.8 65.7 .15 118.2 .95 65.7 .15 118.2 .94 1.8 1.9 67.2 .14 127.7 .95 67.2 .13 127.6 .94 1.9 2. 68.6 .13 137.2 .97 68.5 .13 137. .96 2. 2.1 69.9 .12 146.9 .96 69.8 .12 146.6 .97 2.1 2.2 71.1 .13 156.5 1. 71. .12 156.3 .97 2.2 2.3 72.4 .12 166.5 1. 72.2 .11 166. .99 2.3 2.4 73.6 .10 176.5 1. 73.3 .10 175.9 .99 2.4 2.5 74.6 .10 186.5 1. 74.3 .10 185.8 .99 2.5 2.6 75.6 .10 196.5 1.02 75.3 .09 195.7 1.01 2.6 2.7 76.6 .10 206.7 1.04 76.2 .09 205.8 1.01 2.7 2.8 77.6 .08 217.1 1.03 77.1 .08 215.9 1.01 2.8 2.9 78.4 .08 227.4 1.02 77.9 .08 226. 1.02 2.9 3. 79.2 .08 237.6 1.03 78.7 .08 236.2 .02 3. 3.1 80. .07 247.9 1.05 79.5 .07 246.4 .03 3.1 3.2 80.7 08 258.4 1.04 80.2 .07 256.7 .03 3.2 3.3 31.5 .07 268.8 1.06 80.9 .07 267. .04 3.3 3.4 82.2 .06 279.4 1.05 81.6 .06 277.4 .04 3.4 3.5 82.8 .07 289.9 1.06 82.2 .06 287.8 .04 3.5 3.6 83.5 .06 300.5 1.06 82.8 .06 298.2 1.05 3.6 3.7 84.1 .06 311.1 1.07 83.4 .06 308.7 1.05 3.7 3.8 84.7 .05 321.8 1.07 84. .05 319.2 1.05 3.8 3.9 85.2 .06 332.5 1.07 84.5 .06 329.7 1.06 3.9 4. 85.8 343.2 85.1 340.3 4. 152 FLOW OF WATER IN TABLE 25. Based on Kutter's formula, with n = .0275 Values of the factors c and r.\/r for use in the formulas v c\/rs = c X \fr X -N/S" = c\/r X \/s All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. Vr in feet 1 in 1250=4.224 ft. per mile j 1 in 1000=5.28 ft. per mile Vr in. feet * == .0008 s = .001 c diff. .01 CV/F diff. .01 c i diff. .01 c\/r diff. .01 .4 27.1 48 10.8 .51 27.2 .48 10.9 .51 .4 .5 31.9 .43 15.9 .58 32. .43 16. .58 .5 .6 36.2 .38 21.7 .63 36.3 .39 21.8 .63 .6 .7 40. .35 28. .68 40.2 .34 28.1 .68 .7 .8 43.5 .32 34.8 .72 43 6 .32 34.9 .72 .8 .9 46.7 .28 42. .75 46.8 .28 42.1 .75 .9 1 49.5 .27 49.5 .78 49.6 .27 49.6 .79 1. 1.1 52.2 .24 57.3 .82 52.3 .23 57.5 .81 1.1 1.2 54.6 .22 65.5 .83 54.6 .23 65.6 .83 1.2 1.3 56.8 20 73.8 .86 56.9 .20 73.9 .85 1.3 .4 58.8 .19 82.4 .87 58.9 .19 82.4 .88 1.4 .5 60.7 18 91.1 .89 60.8 .17 91.2 .89 1.5 .6 62.5 .17 100. .91 62.5 .17 100.1 .90 1.6 m . 1 64 2 .15 109.1 .91 64.2 .15 109.1 .91 1.7 8 65 7 14 118.2 .94 65.7 .14 118.2 .93 1.8 .9 67.1 .14 127.6 .94 67.1 .14 127.5 .94 1.9 2 68.5 .13 137. .95 68.5 .12 136.9 .95 2. 21 69.8 .11 146.5 .96 69.7 .12 146.4 .96 2.1 2.2 70.9 .12 156.1 .97 70.9 .11 156. .96 2.2 2.3 72.1 .11 165.8 .98 72. .11 165.6 .98 2.3 2.4 73.2 .10 175.6 .98 73.1 .10 175.4 .98 2.4 25 74.2 .09 185.4 .99 74.1 .09 185.2 .99 2.5 2.6 75.1 .09 195.3 1. 75. .09 195.1 .99 2.6 2.7 76. 09 205.3 1. 75.9 .09 205. 1. 2.7 2.8 76.9 .08 215.3 1.01 76.8 .08 215. 1. 2.8 2.9 77.7 .08 225.4 .01 77.6 .08 225. 1.01 2.9 3. j 78.5 .07 235.5 .02 78.4 .07 235.1 1.01 3. 3 1 79.2 .07 245.5 02 79.1 .07 245.2 1.02 3.1 3.2 79.9 .08 255.9 .02 79.8 .07 255.4 1.02 3.2 33 80.7 .06 266.1 .03 80.5 .06 265.6 1.02 3.3 3.4 81.3 06 276.4 .03 81.1 .07 275.8 1.03 3.4 3.5 81.9 .06 286.7 .04 81.8 .05 286.1 1.03 3.5 3.6 82.5 06 297.1 .04 82.3 .06 296.4 1.04 3.6 3.7 83.1 .06 307 . 5 1.04 82.9 .05 306.8 1.03 3.7 3.8 83.7 .05 317.9 1.04 83.4 .06 317.1 1.04 3.8 3.9 84.2 .05 328.3 1.05 84. .05 327.5 1.04 3.9 4. 84.7 338.8 84.5 337.9 4. OPEN AND CLOSED CHANNELS. 153 TABLE 26. Based on Kutter's formula, with n = .030. Values of the factors c and c\/r for use in the formulae v = c \/rs c X \/r~ X \/s~ = c\/~ X \/*~~ All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. vV 1 in 20000=. 264 ft. per mile | 1 in 15840 = .3333 ft. per mile v/r s = .00005 5 = .0000631 31 in feet diff. y diff. diff. diff. in feet c .01 c\/r .01 c .01 Cv /r .01 .4 19. .40 7.59 .39 19.6 .42 7.86 .40 .4 .5 23. .38 11.5 .46 23 8 .38 11.9 .47 .5 .6 26.8 .37 16.1 .52 27.6 .36 16.6 .53 6 .7 30.5 .34 21.3 .58 31.2 .34 21.9 .58 . 7 .8 33.9 .32 27.1 .63 34.6 33 27.7 .64 8 .9 37.1 .31 33.4 .68 37.9 .30 34.1 .68 .9 1. 40.2 .29 40.2 .72 40.9 .28 40.9 .72 1. 1.1 43.1 .28 47.4 .77 43.7 .28 48.1 .77 1.1 1.2 45.9 .27 55.1 .80 46.5 .25 55.8 .80 1.2 1.3 48.6 .25 63.1 .84 49. .24 63.8 .82 1.3 1.4 51.1 .24 71.5 .88 51.4 .24 72. .87 1.4 1.5 53.5 .23 80.3 .90 53 8 .22 80.7 .89 1.5 1.6 55.8 .22 89.3 .93 56. .21 89.6 .92 1.6 1.7 58. .21 98.6 .96 58.1 .21 98.8 .95 1.7 1.8 60.1 .21 108.2 .99 60.2 .19 108.3 .96 1.8 1.9 62.2 .19 118.1 .01 62.1 .18 117.9 .99 1.9 2. 64.1 .19 128.2 .03 63.9 .18 127.8 1.01 2. 2.1 66. .18 138.5 .06 65.7 .17 137.9 .03 2.1 2.2 67.8 .17 149.1 .06 67.4 .16 148.2 05 2.2 2.3 69.5 .17 159.9 .08 69 .15 158.7 .06 23 2.4 71.2 .16 170.8 .11 70.5 .15 169.3 .10 24 2.5 72.8 .15 181.9 1.13 72. .16 180.3 .10 2.5 2.6 74.3 .14 193.2 1.12 73.6 .13 191.3 .08 2 6 2.7 75.7 .15 204.4 1.19 74 9 .13 202.1 .12 2.7 2.8, 77.2 .14 216.3 1.17 76.2 .13 213.3 .13 28 2.9 78.6 .14 228. 1.19 77.5 .12 224.6 .15 2.9 3. 80. .13 239.9 1.20 78.7 .12 236.1 .16 3. 3.1 81.3 .12 251.9 1.21 79.9 .11 247.7 .16 3.1 3.2 82.5 .12 264. 1.23 81. .12 ! 259 3 1.18 3.2 3.3 83.7 .12 276.3 1.24 82 2 .10 271.1 1.19 3.3 3.4 84.9 .11 288.7 1 24 83.2 .11 1 283. 1.20 3.4 3.5 86. .11 301.1 1.26 : 84.3 .1.0 (295. .20 3.5 3.6 87.1 .11 313 7 1.27 j 85.3 .10 i 307. .21 3.6 3.7 88.2 .11 326.4 1.28 86.3 .09 i 319.1 .22 3.7 3.8 89.3 .10 339.2 1.28 ! 87.2 09 331 . 3 23 3.8 3.9 90.3 .09 352. 1.30 88.1 .09 343.6 ]24 3.9 4. 91.2 365. 89. 356. 4. i 154 FLOW OP WATER IN TABLE 26. Based on Kutter's formula, with n = .030. Values of the factors c and c\/r for use in the formulae v = c\S7s c X -s/r" X \A~ = c\/r~ X -N/S~ All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. v/r in feet 1 in 10000=.528 ft. per mile 1 in 7500: .704 ft. per mile -v/r in feet s = .0001 * = .000133333 c diff, .01 c^/r diff. .01 c diff. .01 cy/r diff. .01 A 20.9 .42 8.4 .42 21.5 .43 8.6 .43 .4 .5 25.1 .39 12.6 .48 25.8 .39 12.9 .49 .5 .6 29. .36 17.4 .54 29.7 .36 17.8 .55 .6 .7 32.6 34 22.8 .60 33.3 .34 23.3 .61 .7 .8 36. .31 28.8 .64 36.7 .31 29.4 .64 .8 .9 39.1 .30 35.2 .69 39.8 .29 35.8 .69 .9 1. 42.1 .27 42.1 .72 42.7 .27 42.7 .72 1. .1 44.8 .26 49.3 .76 45.4 .25 49.9 .76 1.1 2 47.4 .25 56.9 .80 47.9 .24 57.5 .79 1.2 .3 49.9 .23 64.9 .82 50.3 .22 65.4 .81 1.3 .4 52.2 .21 73.1 .84 52.5 .21 73.5 .84 1.4 .5 54.3 .21 81.5 .87 54.6 .19 81.9 .85 1.5 .6 56.4 .19 90.2 .89 56.5 .19 90.4 .89 1.6 .7 58.3 .19 99.1 .93 58.4 .18 99.3 .91 1.7 1.8 60.2 .17 108 4 .92 60.2 .17 108.4 .92 1.8 1.9 61.9 .17 117.6 .96 61.9 .15 117.6 .92 1.9 2. 63.6 .16 127.2 .97 63.4 .15 126.8 .95 2 2.1 65.2 .15 136.9 .98 64.9 .15 136.3 .98 2.1 2.2 66.7 .14 146.7 .99 66.4 .13 146.1 .96 2 2 2.3 68.1 .14 156.6 1.02 67.7 .13 155.7 99 2.3 2.4 69.5 ! .13 166.8 1.02 69. .13 165.6 1.02 2.4 2.5 70.8 .13 177. 1.05 70.3 .12 175.8 1.01 2.5 2.6 72.1 1 .12 187.5 1.04 71.5 .11 185.9 1.01 2.6 2.7 73.3 | .12 197.9 1.07 72.6 .11 196. 1.04 2.7 2.8 74.5 .11 208.6 1.06 73.7 .10 206.4 1.02 2.8 2.9 75.6 .10 219.2 1.06 74.7 .10 216.6 1.05 2.9 3. 76 6 .11 229.8 1.11 75.7 .10 227.1 1.07 3. 3.1 77.7 .10 240.9 1.09 76.7 .09 237.8 1.05 3.1 3.2 78.7 .09 251.8 1.09 77.6 .08 248.3 1.04 3.2 3.3 79.6 .09 262.7 .10 78.4 .08 258.7 06 3.3 3.4 80.5 i .09 273.7 1.13 79.2 .08 269.3 .09 3.4 3.5 81.4 .09 285. .12 80. .08 280.2 .08 3.5 3.6 82.3 .08 296.2 .13 80.8 .08 291. .09 3.6 3.7 83.1 .08 307.5 .13 81.6 .07 301.9 .09 3.7 3.8 83.9 .08 318.8 .14 82.3 .07 312.8 .10 3.8 3.9 84.7 .07 330.2 .15 83. .07 323.8 .10 3.9 4. 85.4 341.7 83.7 334.8 4. OPEN AND CLOSED CHANNELS. 155 TABLE 26. Based on Kutter's formula, with n = .030. Values of the factors c and c\/r for use in the formulae v = c-s/fl = c X ^/r~ X \/s~ --~ All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000, -v/r in feet 1 in 5000 = 1.056 ft. per mile 1 in 3333. 3 = 1.584 ft. per mile Vr in feet 8 = .0002 s = .0003 c diff. .01 c\/r diff. .01 c diff. .01 c\/r diff. .01 .4 22.4 .43 8.96 .45 23.1 .43 9.24 .45 .4 .5 26.7 .42 13.4 .50 27.4 .40 13.7 .51 .5 .6 30.7 .36 18.4 .56 31.4 .36 18.8 .57 .6 .7 34.3 .33 24. .61 35. .32 24.5 .61 .7 .8 37.6 .30 30.1 .64 38.2 .30 30.6 .65 .8 .9 40.6 .29 36.5 .70 41.2 .28 37.1 .69 .9 43.5 .26 43.5 .72 44. .26 44. .73 1. .1 46.1 .24 50.7 .75 46.6 .24 51.3 .75 1.1 .2 48.5 .23 58.2 .78 49. .22 58.8 .78 1.2 .3 50.8 .21 66. .81 51.2 .20 66.6 .79 1.3 .4 52.9 .20 74.1 .83 53 2 .19 74.5 .82 1.4 .5 54.9 .19 82.4 .85 55.1 .18 82.7 .83 1.5 .6 56.8 .17 90.9 .86 56.9 .17 91. .86 1.6 .7 58.5 .17 99.5 .89 58.6 .16 99.6 .88 1.7 1.8 60.2 .16 108.4 .90 60.2 .15 108.4 .88 1.8 1.9 61.8 .14 117.4 .90 61.7 .14 117.2 .90 1.9 2 63.2 .14 126.4 .93 63.1 .13 126.2 .90 2. 2.1 64.6 14 135.7 .95 64.4 .13 135.2 .93 2.1 2.2 66 .12 145.2 .94 65.7 .12 144.5 .94 2.2 23 67.2 .12 154.6 .96 66.9 .11 153.9 .93 2.3 2.4 68.4 .12 164.2 .98 68. .11 163.2 .96 2.4 2.5 69.6 .11 174 .98 69 1 .10 172.8 .95 2.5 2.6 70.7 .10 183.8 .98 70.1 .10 182.3 .97 2.6 2.7 71.7 .10 193.6 1. 71.1 .09 192. .96 2.7 2.8 72.7 .09 203.6 .98 72. .09 201 6 .98 2.8 2.9 73.6 .09 213.4 1.01 72.9 .08 j 211.4 .97 2.9 3. 74.5 .09 223.5 1.02 73.7 .09 221.1 1.02 3. 3.1 75.4 .08 233.7 1.01 74.6 .09 231.3 .97 3.1 3.2 76.2 .08 243.8 1.03 75.3 .08 241. 1.01 3.2 3.3 77. .08 254.1 1.03 76.1 .07 251.1 1.01 3.3 3 4 77.8 .08 264.5 1.04 76.8 .07 261.1 1. 3.4 3.5 78.6 .07 274.9 1.04 77.5 .06 271.2 1.01 3.5 3.6 79.3 .06 285 3 1.05 78.1 .07 281.3 1.01 3.6 3.7 79.9 .07 295.8 1.05 78.8 .06 291.5 1.02 3.7 3.8 80.6 .06 308.3 1.05 79.4 .06 301.7 1.02 3.8 3.9 81.2 .07 316.8 1.06 80. .06 311.9 1.02 3.9 4. 81.9 327.4 80.6 322.2 4. 156 FLOW OF WATER IN TABLE 26- Based on Kutter's formula, with n = .030. Values of the factors c and c<\/r for use in the formulas v = c\/r~s c X A/r~ X \/~ = c^/r~ X \/~ All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000. 1 in 2500 = 2.114 ft per mile 1 in 1666.7=3.168 ft. per mile Vr in feet Vr in feet a = .0004 s = .0006 c diff. .01 c^/T diff. .01 c diff. .01 c/rs Side Slopes 1 to 1. v mean velocity in cubic feet per second, and Q discharge in cubic feet per second. Depth in feet. Slope 1 in Bed width 15 ft. Bed width 16 ft. : Bed width 18 ft. : Bed width 20 ft. V Q v Q V Q v Q 1.5 2500 1.20 29.69 1.21 31.72 1.22 35.78 1 . 24 39.85 1.5 2857 1 . 12 27.77 1.13 29.67 1.14 33.47 1.16 37.28 1.5 3333 1.04 25.71 1.05 27.47 1.06 30.99 1.07 34.52 1.5 4000 .948 23.47 .955 25.08 .967 28.29 .977 31.51 1.5 5000 .848 21. .854 22.43 .865 25.30 .874 28.18 1.5 6666 .735 18.18 .740 19.42 .749 21.91 .757 24.41 2. 2500 .49 50.54 1.50 53.96 1.52 60.84 1.54 67.74 2. 2857 .39 47.27 1 40 50.48 1.42 56.91 1.44 63.36 2. 3333 .29 43.77 1.30 46 74 1 . 32 52.69 1.33 58.66 2. 4000 .18 39.95 1.19 42.66 1.20 48.09 1.22 53.55 2. 5000 .05 35.74 1.06 38.16 1.08 43.02 1.09 47.90 2. 6666 .910 30.95 .918 33.04 .931 37.26 .943 41.48 2.5 2500 .74 76.13 1.76 81.24 .79 91.50 1.81 101.80 2.5 2857 .63 71.21 1.64 75.99 .67 85.58 1.69 95.22 25 3333 1.51 65.93 1.50 70.36 .55 79.24 1.57 88.16 2.5 4000 1.38 60.18 1.39 64 23 .41 72.33 1.43 80.48 2.5 5000 1.23 53.83 1.24 57.45 .26 64.70 1.28 71.98 2.5 6666 1.07 46.62 1.08 49.75 .09 56.03 1.11 62.34 3. 2500 1.97 106.26 1.99 113.30 .02 127.46 2.05 141.68 3. 2857 1.84 99.40 1.86 105.98 .89 119.22 1.92 132.53 3. 3333 1.70 92.02 1.72 98.12 .75 110.38 1.78 122.70 3. 4000 1.56 84. 1.57 89.57 .60 100.76 1.62 112.01 3. 5000 1.39 75.14 1.41 80.12 .43 90.13 1.45 100.19 3. 6666 1.21 65.07 1.22 69.38 1.24 78.05 1.26 86.76 3.5 2500 2.17 140.82 2.20 150.03 2.24 168.54 2.28 187.15 3.5 2857 2.03 131.72 2.06 140.34 2.09 157.64 2.13 175.05 3.5 3333 1.88 121.95 1.90 129.93 1.94 145.95 1.97 162.07 3.5 4000 1.72 1111.33 1.74 118.61 1.77 133.24 1.80 147.95 3.5 5000 1.54 99.58 1.55 106.09 1.58 119.17 1.61 132.33 3.5 6666 1.33 86.23 1.35 91.87 1.37 103.21 1.39 114.60 4. 2500 2.37 179.77 2.39 191.34 2 44 214.61 2.48 238.03 4. 2857 2.21 168.15 2 24 178.97 2.28 200.74 2.32 222.64 4. 3333 2 05 155.68 2.07 165.70 2.11 185.86 2.15 206.13 4. 4000 1.87 142.12 1.89 151.26 1.93 169.66 1.96 188.17 4. 5000 1.67 127.12 1.69 135.30 1.72 151 76 1.75 168.31 4. 6666 1.45 110.08 1.46 117.17 1.49 131.42 1.52 145.76 OPEN AND CLOSED CHANNEIS. 169 TABLE 31. Velocities and discharges in trapezoidal channels based on Kutter's formula with n= .025. Side slopes 1 horizontal to 1 vertical. BED WIDTH 30 FEET. BED WIDTH 40 FEET. Depth in feet. Slope lin Velocity in feet per Discharge in cubic feet Depth in feet. Slope lin Velocity In feet per Discharge in cubic feet second. per second. second. per second. 2 1500 2.203 141. 2 1500 2.242 188.3 2 2000 1.905 121.9 2 2000 1.941 163. 2 3000 1.539 98.5 2 3000 1.574 132.2 2 5000 1.231 78.8 2 5000 1.215 102.1 3 1500 2.856 282.7 3 1500 2.923 377. 3 2000 2.471 244 6 3 2000 2.535 327. 3 3000 2.013 199.3 3 3000 2.062 266. 3 5000 1.556 154. 3 5000 1.596 205.9 4 1500 3.396 461.8 4 1500 3.497 615.4 4 2000 2.936 399.3 4 2000 2.982 524.8 4 3000 2.401 326.6 4 3000 2.473 435.2 4 5000 1.858 252.7 4 5000 1.889 332.5 5 1500 3.859 675.3 5 1500 4.112 925.2 5 2000 3.334 585 2 5 2000 3.454 777.1 5 3000 2.736 478.8 5 3000 2.826 635.8 5 5000 2.123 371.5 5 5000 2.194 493.6 BED WIDTH 50 FEET. BED WIDTH 60 FEET. 2 1500 2.268 235.8 2 1500 2.294 284.4 2 2000 1.965 204.4 2 2000 1.979 245.4 2 3000 1.765 183.5 2 3000 1.611 199.7 2 5000 1.229 127.8 2 5000 1.238 153.5 3 1500 2.968 472. 3 1500 3 567. 3 2000 2.570 408.6 3 2000 2.600 491.4 3 3000 2.096 333.2 3 3000 2.127 402. 3 5000 1.618 257.3 3 5000 1.638 309.6 4 1500 3.559 768.7 4 1500 3.607 923.4 4 2000 3.085 666.3 4 2000 3.123 799.5 4 3000 2.537 548. 4 3000 2.553 653.5 4 5000 1 953 421.8 4 5000 1.980 506 . 9 5 1500 4.068 1118.7 5 1500 4.136 1344.2 5 2000 3.528 970.2 5 2000 3.582 1164.1 5 3000 2.887 793.9 5 3000 2.935 953.8 5 5000 2.243 616.8 5 5000 2.277 740. 170 FLOW OF WATER IN TABLE 31. Velocities and discharges in trapezoidal channels based on Kutter's formula with n =0.25. Side slopes 1 horizontal to 1 vertical. BED WIDTH 70 FEET. BED WIDTH 80 FEET. Depth in feet. Slope liu Velocity in feet per Discharge in cubic feet Depth in feet. Slope lin Velocity in feet per Discharge in cubic feet second per second. second. per second. 3 2000 2.622 574.2 3 2000 2.637 656.6 3 3500 1.976 432.7 3 3500 1.989 495.2 3 7500 1.344 294.3 3 7500 1.353 336.9 3 10000 1.163 254.7 3 10000 1.169 291.1 4 2000 3.152 933. 4 2000 3.175 1066.8 4 3500 2.387 706.5 4 3500 2.404 807.7 4 7500 1 . 635 483.9 4 7500 1.648 553.7 4 10000 1.418 419.7 4 10000 1.429 480.1 5 2000 3.621 1357.9 5 2000 3.653 1552.5 5 3500 2.746 1029.7 5 3500 2.77 1177.2 5 7500 1.89 708.7 5 7500 1.909 811.3 5 10000 1.643 616.1 5 10000 1.657 704.2 6 2000 4.040 1842.2 6 2000 4.080 2105.3 6 3500 3.066 1398.1 6 3500 3.099 1599. 6 7500 2.121 967.1 6 7500 2.144 1106.3 6 10000 1.848 842.7 6 10000 1.869 964.4 BED WIDTH 90 FEET. BED WIDTH 100 FEET. 3 2000 2.649 739.1 3 2000 2.657 821. 3 3500 1.998 557.4 3 3500 2.004 619.2 3 7500 1 . 359 379.1 3 7500 1.364 421.4 3 10000 1.175 327.8 3 10000 1.180 364.6 4 2000 3.196 1201.7 4 2000 3.208 1334.5 4 3500 2.419 909.5 4 3500 2.431 1011.3 4 7500 1.658 623.4 4 7500 1.667 693.4 4 10000 1.439 541.1 4 10000 1.446 601.5 5 2000 3.677 1746.6 5 2000 3.702 1943.5 5 3500 2.79 1325.2 5 3500 2.806 1473.1 5 7500 1 . 923 913.4 5 7500 1.935 1015.8 5 10000 1.670 793.2 5 10000 1.682 883. 6 2000 4.120 2373.1 6 2000 4.140 2633. 6 3500 3.122 1798.2 6 3500 3.143 1998.9 6 7500 2 161 1244.7 6 7500 2.176 1383.9 6 10000 1.888 1087.5 6 10000 1.898 1199.8 OPEN AND CLOSED CHANNELS. 171 TABLE 32. Velocities and discharges in trapezoidal channels based on Kutter's formula, with n = .03. Sides slopes \ horizontal to 1 vertical. BED WIDTH 1 FOOT. BED WIDTH 2 FEET. Depth in feet. Slope 1 iu Velocity iu feet per Discharge III cubic feet Depth in leet. Slope lin Velocity in feet per Discharge cubic feet second. per second. second per second. 1.5 266 j .625 .5 380 1 1.125 1.5 66 2 1.25 .5 95 2 2.25 1.5 30 3 1.875 .5 42 3 3.375 1.5 17 4 2.5 .5 24 4 4.5 542 1 1.5 1. 870 1 25 135 2 3. 1. 217 2 5. 60 3 4.5 1. 97 3 7-5 34 4 6. 1. 54 4 10, ^5 911 1 2.625 1.5 1340 1 4.125 .5 228 2 5.25 1.5 335 2 8.25 .5 101 3 7.875 1.5 149 3 12-375 1.5 57 4 10.5 1.5 84 4 16.5 2 1752 1 6. 2] 438 2 12. 2. 194 3 18. 2. 110 4 24. BED WIDTH 3 FEET. BED WIDTH 4 FEET. .5 448. 1 1.625 1. 1195 1 4.5 .5 112 2 3.25 1 . 300 2 9. .5 50 3 4.875 1. 133 3 13.5 .5 28 4 .6.5 1. 75 4 .18. 1. 1070 1 3.5 .25 1536 1 5.8 1. 268 2 7. 25 387 2 11.6 119 3 10.5 .25 172 3 17.3 67 4 14. .25 97 4 23.1 '5 1657 1 5.625 .5 1859 1 71 1.5 414 2 11.25 .5 473 2 14.2 1.5 184 3 16.875 1.5 210 3 21.4 1.5 104 4 22.5 1.5 118 4 28.5 2. 2216 1 8. 2. 2570 1 10. 2. 554 2 16. 2. 660 2 | 20. 2 246 3 24. 2. 293 3 30. 2. 138 4 32. 2 165 4 40. 2.5 2790 1 10.62 2^5 3188 1 13.1 2.5 698 2 21.25 2.5 822 2 26.3 2 5 310 3 31.88 2.5 365 3 39.4 2.5 174 4 42.5 2.5 206 4 52.5 172 FLOW OF WATER IN TABLE 32. Velocities and discharges in trapezoidal channels based on Kutter's formula, with n = .03. Side slopes J horizontal to 1 vertical. BED WIDTH 6 FEET. BED WIDTH 8 FEET. Depth in feet. Slope lin Velocity in feet per second. Discharge in cubic feet per second. Depth in feet. Slope lin Velocity in feet per second. Discharge in cubic feet per second. 1. 1380 1 6.5 1. 1459 1 8.5 1. 348 2 13. 1. 373 2 17. 1. 155 3 19.5 1. 166 3 25.5 1. 87 . 4 26. 1. 93 4 34. 1.25 1798 1 8.3 1.25 1984 1 10.8 1.25 457 2 16.6 1.25 504 2 21.6 1.25 203 3 24.8 1.25 224 3 32.3 .25 114 4 33.1 .25 126 4 43.1 .5 2230 1 10.1 .5 2433 1 13.1 .5 570 2 20.2 .5 624 2 26.3 .5 253 3 30.4 .5 277 3 39.4 .5 142 4 40.5 .5 156 4 52.5 .75 2671 1 12. .75 2947 1 15.5 .75 680 9 24. .75 758 2 31. .75 302 3 36.1 1.75 337 3 46.5 .75 170 4 48.1 1.75 190 4 62.1 2. 3101 1 14. 2. 3451 1 18. 2. 800 2 28. 2. 889 2 36. 2. 356 3 42. 2. 395 3 54. 2. 200 4 56. 2. 222 4 72. 2.25 3533 1 16. 2.25 3886 1 20.5 2 25 912 2 32. 2.25 1006 2 41. 2.25 405 3 48. 2.25 447 3 61.6 2.25 228 4 64.1 2.25 252 4 82.1 2.5 3895 1 18.1 2.5 4385 1 23.1 2.5 1006 2 36.2 2.5 1134 2 46.2 2.5 447 3 54.4 2.5 504 3 69.4 2.5 252 4 72.5 2.5 283 4 92.5 2.75 4292 1 20.3 2.75 4906 1 25.8 2.75 1107 2 40.6 2.75 1266 2 51.6 2.75 492 3 60.8 2.75 563 3 77.3 2.75 277 4 80.1 2.75 317 4 103.1 3. 4672 1 22.5 3. 5348 1 28.5 3. 1213 2 45. 3. 1382 2 57. 3. 539 3 67 5 3. 615 3 85.5 3. 303 4 90. 3. 346 4 114. OPEN AND CLOSED CHANNELS. 173 TABLE 32. Velocities and discharges in trapezoidal channels based on Kutter's formula, with n = .03. Side slopes J horizontal to 1 vertical. BED WIDTH 10 FEET. BED WIDTH 12 FEET. Depth in S'ope Velocity in Discharge in Depth in Slope Velocity in Discharge in feet. lin feet per cubic feet feet. lin feet pet- cubic feet second. per second. second. per second. ' \ 1.0 2651 1 16.1 .5 2803 1 19.1 1.5 680 2 32.3 .5 718 2 38.3 1.5 302 3 48.4 .5 319 3 57.4 1.5 170 4 64.5 .5 180 4 76.5 1.75 3190 1 19. .75 3368 1 22.5 1.75 822 2 58 .75 866 2 45.1 1.75 365 3 57.1 .75 385 3 67.6 1.75 206 4 76.1 .75 217 4 90.1 2. 3731 1 22. 2 3953 1 26. 2. 958 2 44. 2. 1030 2 52. 2. 426 3 66. 2. 458 3 78. 2. 239 4 88. 2. 258 4 104. 2.25 4275 1 25. 2.25 4586 1 29.5 2.25 1107 2 50. 2.25 1186 2 59.1 2.25 492 3 75.1 2.25 528 3 88.6 2.25 277 4 100.1 2.25 297 4 118.1 2.5 4826 1 28.1 2.5 5128 1 33.1 . 2.5 1237 2 56.3 2.5 1323 2 66.2 2.5 551 3 84.4 2.5 588 3 99.4 2.5 310 4 112.5 2.5 331 4 132.5 2.75 5352 1 31.3 2.75 5728 1 36.8 2.75 1383 2 62.6 2.75 1467 2 73.6 2.75 615 3 93.8 2.75 655 3 110.3 2.75 346 4 125.1 2.75 368 4 147.1 3. 5945 1 34.5 3. 6328 1 40.5 3. 1528 2 69. 3. 1625 2 81. 3. 682 3 103.5 3. 725 3 121.5 3. 384 4 138. 3. 408 4 162. 3.25 6503 ** 1 37.8 3.25 7023 1 44.3 2.25 1658 2 75.6 3.25 1794 2 88.6 3.25 740 3 113.3 3.25 800 3 132.8 3.25 416 4 151.1 3.25 450 4 177.1 3.5 6992 1 41.1 3.5 7577 1 48.1 35 1793 2 82.2 3.5 1930 2 96.2 3.5 800 3 123.4 3.5 864 3 144 4 3.5 450 4 164.5 3.5 486 4 192.5 174 FLOW OF VvATER IN TABLE 32. Velocities and discharges in trapezoidal channels based on Kutter's formula, with n .03. Side slopes \ horizontal to 1 vertical. BED WIDTH 14 FEET. BED WIDTH 16 FEET. Depth in Slope Velocity in Discharge in Depth in Slope Velocity in Discharge in feet. lin feet per cubic feet feet. lin f^et per cubic feet second. per second. second. per second. 1.5 2859 1 21.1 .5 2948 1 25.1 1.5 738 2 44.2 .5 758 2 50.2 1.5 328 3 66.3 .5 337 3 75.3 1.5 185 4 88.5 .5 189 4 100.5 1.75 3472 1 26. .75 3623 1 29.5 1.75 889 2 52. 1.75 935 2 59. 1.75 395 3 78. .75 415 3 88,5 1.75 222 4 104. 1,75 234 4 118.1 2. 4120 1 30. 2. 4293 1 34. 2. 1060 2 60. 2. 1110 2 68. 2. 470 3 90. 2. 492 3 102. 2. 264 4 120. 2. 277 4 136. 2.25 4678 1 34. 2^25 4898 1 38.5 2.25 1210 2 68. 2.25 1266 2 77. 2.25 539 3 102. 2.25 563 3 115.5 2.25 303 4 136.1 2.25 317 4 154.1 2.5 5364 1 38.1 2.5 5552 1 43.1 2.5 1383 2 76.2 2.5 1433 2 86.2 2.5 615 3 114.3 2.5 637 3 129.3 2.5 346 4 152.5 2.5 359 4 172.5 2.75 6064 1 42.3 2.75 6325 1 47. S 2.75 1559 2 84.6 2.75 1622 2 95.6 2.75 696 3 126.8 2.75 726 3 143 3 2.75 392 4 169.1 2.75 408 4 191.1 3. 6732 1 46.5 3. 7023 1 52.5 3 1723 2 93. S. 1794 2 105. 3. 770 3 139.5 3. 800 3 157.5 3. 433 4 186. 3. 450 4 210. 3.25 7427 1 50.8 3.25 7730 1 57.3 3.25 1896 2 101.6 3.25 1964 2 114.6 3.25 848 3 152.3 3 . 25 880 3 171.8 3.25 477 4 203.1 3.25 495 4 229.1 3.5 8013 I 55.1 3.5 8331 1 62.1 3.5 2045 2 110.2 3.5 2120 2 124.2 3.5 914 3 165.3 3.5 949 3 186. 3 3.5 514 4 220.5 3.5 534 4 248.5 OPEN AND CLOSED CHANNELS. 175 TABLE 32. Yelocities and discharges in trapezoidal channel.; based on Kutter's formula, with n = .03. Side slopes horizontal to 1 vertical. BED WIDTH 18 FEET. BED WIDTH 20 FEET. Depth in feet. Slope 1 in Velocity in feet per second. Discharge in cubic feet per second. Depth in feet. Slope 1 in Velocity in feet per second. Discharge in cubic feet per second. 1.5 3124 1 28.1 1.5 3022 1 31.1 1.5 779 2 56.2 1.5 779 2 62.3 1.5 348 3 84.4 1.5 346 3 93.3 1.5 195 4 112.5 1.5 195 4 124.5 1.75 3713 1 33. 1.75 3713 1 36.5 1.75 958 2 66. 1.75 958 2 73. 1.75 426 3 99.1 1.75 426 3 109.6 1.75 240 4 132.1 1.75 240 4 146.1 2. 4385 1 38. 2. 4492 1 42 2 1130 2 76. 2. 1157 2 84. 2 504 3 114. 2. 515 3 126. 2 284 4 152. 2. 290 4 168. 2^25 5114 1 43. 2.25 5245 1 47.5 2.25 1320 2 86. 2.25 1352 2 95. 2.25 589 3 129.1 2.25 602 3 142.6 2.25 331 4 172.1 2.25 338 4 190. 2.5 5825 1 48.1 2.5 5935 1 53.1 2.5 1500 2 96.2 2.5 1528 2 106.2 2.5 668 3 144.4 2.5 682 3 159.3 2.5 376 4 192.5 2.5 384 4 212.5 2.75 6585 1 53.3 2.75 6737 1 58.8 2.75 1692 2 106.6 2.75 1726 2 117.6 2.75 755 3 159.8 2.75 770 3 176.3 2.75 425 4 213.1 2.75 433 4 235.1 3. 7285 1 58.5 3. 7427 1 64.5 3. 1862 2 117. 3. 1897 2 129. 3. 832 3 175.5 3. 848 3 193. 3. 468 4 234. 3. 477 4 258. 3.25 8028 1 63.8 3.25 8163 1 70.3 3.25 2056 2 127.6 3.25 2083 2 140.6 3.25 914 3 191.3 3.25 931 3 210.8 3.25 514 4 255.1 3 25 524 4 281.1 3.5 8807 1 69.1 3.5 8966 1 76.1 3.5 2251 2 138.2 3.5 2282 2 152.2 3.5 1000 3 207.4 3.5 1018 3 228.3 3.5 563 4 276.5 3.5 573 4 304.5 176 FLOW OP WATER IN TABLE 32. Velocities and discharges in trapezoidal channels based on Kutter's formula, with ?i = .03. Side slopes -J horizontal to 1 vertical. tfED WIDTH 2> 1'EET. 13ED WIDTH 3U JttEET. Depth in feet. Slopo 1m Velocity iu feet per Discharge in cubic feet Depth in feet. Slopo 1 iu Velocity in feet per Discharge in cubic feet second. per second. second. per second. 2. 4697 ' 1 52. 2. 4797 1 62. 2. 1212 2 104. 2. 1237 2 124. 2. 541 3 156. 2. 551 3 186. 2. 304 4 208. 2. 310 4 248. 2.25 5489 1 58.8 2.25 5589 1 70. 2.25 1408 2 117.6 2.25 1435 2 140. 2.25 628 3 176.3 2.25 641 3 210. 2 25 353 4 235.1 2.25 361 4 280. 2.5 6197 1 65.6 2.5 6448 1 78.1 2.5 1586 2 131.2 2.5 1657 2 156.2 2.5 711 3 196.8 2.5 740 3 234 3 2.5 400 4 262.5 2.5 416 4 312.5 2.75 6992 1 72.5 2.75 7310 1 86.3 2.75 1792 2 145. 2.75 1866 2 172.6 2.75 800 3 217.6 2.75 832 3 258.8 2.75 450 4 290.1 2.75 468 4 345.1 3. 7878 1 79.5 3. 8108 1 94.5 3. 2008 2 159. 3. 2084 2 189. 3. 897 3 238.5 3. 931 3 283.5 3. 504 4 318. 3. 523 4 378. 3.5 9651 1 93.6 3.5 10007 1 111.1 3.5 2450 2 187.2 3.5 2531 2 222.2 3.5 1091 3 280.9 3.5 1127 3 333.3 3.5 614 4 374.5 3.5 634 4 444.5 4. 11308 i 108. 4. 11952 1 128. 4. 2840 2 216. 4. 2958 2 256. 4. 1263 3 324. 4. 1323 3 384. 4. 708 4 432. 4. 745 4 512. 4.5 13185 1 122 6 4.5 13831 1 145.1 4.5 3285 2 245.2 4.5 3436 2 290.2 4.5 1454 3 367.9 4.5 1522 3 435.3 4.5 818 4 490.5 4.5 856 4 580.5 OPEN AND CLOSED CHANNELS. 177 TABLE 32. Velocities and discharges in trapezoidal channels based on Kutter's formula, with n = .03. Side slopes horizontal to 1 vertical. BED WIDTH 35 FEET. BED WIDTH 40 FEETT Depth in feet. Slope lin Velocity in feet per Discharge in cubic feet Depth in feet. Slope lin Velocity in feet per Discharge in cubic feet second. per second. second. per second. 2. 4886 1 72. 2. 5012 1 82. 2. 1266 2 144. 2. 1294 2 164. 2. 563 3 216. 2. 576 3 246. 2. 317 4 288. 2. 324 4 328. 2.25 5706 1 81.3 2.25 5853 1 92.5 2.25 1465 2 162.6 2.25 1504 2 185. 2.25 655 3 243.8 2.25 668 3 277.6 2.25 368 4 325.1 2.25 376 4 370.1 2.5 6601 1 90.6 2.5 6732 1 103.1 2.5 1691 2 181.2 2.5 1725 2 206.3 2.5 754 3 271.9 2.5 770 3 309.4 2.5 425 4 362.5 2.5 433 4 412.5 2.75 7261 1 100. 2.75 7725 1 113.8 2.75 1935 2 200. 2.75 1969 2 227.6 2.75 864 3 300. 2.75 880 3 341.3 2.75 486 4 400. 2.75 495 ! 4 455.1 3. 8479 1 109.5 3. 8642 1 124.5 3. 2158 2 219. 3. 2199 2 249. . 3. 965 3 328.5 3. 982 3 373.5 3. 543 4 438. 3. 552 4 498. 3.5 10381 1 128.6 3.5 10751 1 146.1 3.5 2630 2 257.2 3.5 2705 2 292.2 3.5 1164 3 385.8 3.5 1203 3 438.3 3.5 654 4 514.4 3.5 677 4 584.5 4. 12515 1 148. 4. 12776 1 168. 4. 3125 2 296. 4. 3163 2 336. 4. 1380 3 444. 4. 1406 3 504. 4. 782 4 592. 4. 791 4 672. 4.5 14505 1 167.6 4.5 14997 1 190.1 4.5 3591 2 335.2 4.5 3701 2 380.3 4.5 1591 3 502.9 4.5 1640 3 570.4 4.5 895 4 670.5 4.5 922 4 760.5 12 178 FLOW OF WATER IN TABLE 32. Velocities and discharges in trapezoidal channels based on Kutter's formula, with n = .03. Side slopes J horizontal to 1 vertical. BED WIDTH 45 FEET. BED WIDTH 50 FEET. Depth in feet. Slope 1 in Velocity in feet per Discharge in cubic feet Depth in feet. Slope 1 m Velocity in feet per Discharge in cubic feet second. per second. second. per second. 2. 5013 1 92. 2. 5128 1 102. 2. 1294 2 184. 2. 1322 2 204. 2. 576 3 276. 2 589 3 306. 2. 324 4 368. 2 331 4 408. 2.25 5951 1 103.8 2 25 6086 1 115. 2.25 1527 2 207.6 2.25 1557 2 230. 2.25 682 3 311.3 2.25 697 3 345. 2.25 384 4 415.1 2.25 392 4 460. 2.5 6864 1 115.6 2.5 6999 1 128.1 2.5 1759 2 231.3 2.5 1794 2 2.36.3 2.5 785 3 346.9 2.5 800 3 384.4 2.5 442 4 462 5 2.5 450 4 512.5 2.75 7886 1 127.5 2.75 8039 1 141.3 2 75 2012 2 255. 2.75 2034 2 282.6 2.75 897 3 382.6 2.75 914 3 423.9 2.75 504 4 510.1 2.75 514 4 565.1 3. 8800 1 139.5 3. 8969 1 154 . 5 3. 2239 2 279. 3. 2275 2 309. 3. 998 3 418.5 3. 1018 3 463.5 3. 562 4 558. 3. 573 4 618. 3.5 10930 1 163.6 3.5 14130 1 181.1 3.5 2751 2 327.3 3.5 2796 2 362.2 3.5 1223 3 490.9 3.5 1243 3 543.4 3.5 688 4 654.5 3.5 699 4 724.5 4. 13180 i 188. 4. 13410 1 208. 4. 3272 2 376. 4. 3331 2 416. 4. 1454 3 564. 4. 1477 3 624. 4. 821 4 752. 4. 830 4 832. 4.5 15230 1 212.6 4.5 15707 1 235.1 4.5 3751 2 425.3 4.5 3866 2 470.2 4.5 1661 3 637.9 4.5 1707 3 705.4 45 935 4 850.5 4.5 960 4 940.5 OPEN AND CLOSED CHANNELS. 179 TABLE 32. Velocities and discharges in trapezoidal channels based on Kutter's formula, with n = .03. Side slopes -J horizontal to 1 vertical. BED WIDTH 60 FEET. BED WIDTH 70 FEET. Depth in feet. Slope 1 in Velocity in feet per Discharge in cubic feet Depth in feet. Slope liu Velocity in feet per Discharge in cubic feet _ second. per second. second. per second. 3. 2317 2 369. 3. 2356 2 429. 3. 1035 3 553.5 3. 1050 3 643.5 3. 583 4 738. 3. 593 4 858. 3. 373 5 922.5 3. 378 5 1072.5 3.25 2623 2 400,6 3.25 2661 2 465.6 3.25 1163 3 600.8 3.25 1183 3 698.4 3.25 654 4 801.1 - 3.25 665 4 931.1 3.25 419 5 1001.4 3.25 426 5 1163.9 3.5 2893 2 432.3 3.5 2949 2 502.3 3.5 1286 3 648.4 3.5 1305 3 753.4 3.5 723 4 864.5 3.5 734 4 1004.5 3.5 464 5 1080.6 3.5 470 5 1255.6 4. 3435 2 496. 4. 3488 2 576. 4. 1522 3 744. 4. 1544 3 864. 4. 856 4 992. 4. 869 4 1152. 4. 548 5 1240. 4. 556 5 1440. 4.5 3988 2 560.3 4.5 4094 2 650.3 4.5 1759 3 840.4 4.5 1807 3 975.4 4.5 989 4 1120.5 4.5 1017 4 1300.5 4.5 633 5 1400.6 4.5 651 5 1625.6 5. 4602 2 625. 5. 4653 2 725. 5. 2020 3 937.5 5. 2045 3 1087.5 5. 1133 4 1250. 5. 1148 4 1450. 5. 723 5 1562 . 5 5. 734 5 1812.5 6. 5785 2 756. 6. 5963 2 876. 6. 2538 3 1134. 6. 2584 3 1314. 6. 1406 4 1512. 6. 1440 4 1752. 6. 900 5 1890. 6. 922 5 2190. 180 FLOW OF WATER IN TABLE 32. Velocities and discharges in trapezoidal channels, based on Kutter's formula, with n .03. Side slopes \ horizontal to 1 vertical. BED WIDTH 80 FEET. BED WIDTH 90 FEET. Depth in Slope Velocity in Discharge in Depth in Slope Velocity in Discharge in feet. lin feet per cubie feet feet. lin feet per cubic feet second. per second. (second. per second. 3. 2404 2 489. 3. 2403 2 549. 3. 1070 3 733.5 3. 1074 3 823.5 3. 603 4 978. 3. 603 4 1098. 3. 386 5 1222.5 3. 386 5 1372.5 3.25 2661 2 530.6 3.25 2704 2 595.6 3 25 1183 3 795.8 3.25 1203 3 893.3 3.25 665 4 1061.1 3.25 677 4 1191.1 3.25 426 5 1326.4 3.25 433 5 1488.9 3.5 2946 2 572.3 3.5 2982 2 642.3 3.5 1305 3 858.4 3.5 1326 3 963.4 3.5 734 4 1144.5 3.5 746 4 1284.5 3.5 470 5 1430.6 3.5 477 5 1605.6 4. 3541 2 656. 4. 3596 2 736. 4. 1567 3 984. 4. 1590 3 1104. 4. 882 4 1312. 4. 895 4 1472. 4. 564 5 1640. 4. 573 5 1840. 4.5 4167 2 740.3 4.5 4221 2 830.3 4.5 1835 3 1110.4 4.5 1859 3 1245.4 4.5 1030 4 1480.5 4.5 1045 4 1660.5 4.5 660 5 1850.6 4.5 668 5 2075.6 5. 4792 2 825. 5. 4833 2 925. 5. 2104 3 1237.5 5. 2139 3 1387.5 5. 1178 4 1650. 5. 1194 4 1850. 5. 754 5 2062.5 5. 764 5 2312.5 6. 6079 2 996. 6. 6175 2 1116. 6. 2649 3 1494. 6. 2682 3 1674. 6. 1477 4 1992. 6. 1488 4 2232. 6. 943 5 2490. 6. 952 5 2790. OPEN AND CLOSED CHANNELS. 181 TABLE 32. Velocities and discharges in trapezoidal channels, based on Kutter's formula, with n .03. Side slopes J horizontal to 1 vertical. BED WIDTH 100 FEET. BED WIDTH 120 FEET. Depth in feet. Slope liii Velocity in feet per second. Discharge in cubic feet per second. Depth in feet. Slope 1 in Velocity in feet per second. Discharge in cubic feet per second. 3. 2443 2 609. 6. 6462 2 1476. 3. 1090 3 913.5 6. 2796 3 2214. 3. 614 4 1218. 6. 1554 4 2952. 3. 393 5 1522.5 6. 986 5 3690. 3.25 2748 2 660.6 7. 7914 2 1729. 3.25 1223 3 990.8 7. 3389 3 2593.5 3.25 688 4 1321.1 7. 1879 4 3458. 3.25 440 5 1651.4 7. 1195 5 4322.5 3.5 3029 2 712.3 8. 9595 2 1984. 3.5 1346 3 1068.4 8. 4034 3 2976. 3.5 757 4 1424.5 8. 2231 4 3968. 3.5 485 5 1780.6 | 8. 1412 5 4960. 4. 3650 2 816. 4. 1614 3 1224. BED WIDTH 140 FEET. 4. 908 4 1632. 4. 581 5 2040. 4. 3701 2 1136. 4. 4221 2 920.3 4. 1640 3 1704. 4. 1859 3 1380.4 4. 921 4 2272. ' 4. 1045 4 1840.5 4. 589 5 2840. 4. 668 5 2300.6 5 5051 2 1425. 5. 4913 2 1025. 5. 2217 3 2137.5 5. 2161 3 1537.5 5. 1241 4 2850. 5. 1210 4 2050. 5. 794 5 3562.5 5. 774 5 2562 . 5 6. 6533 2 1716. 6. 6231 2 1236. 6. 2811 3 2574. 6. 2714 3 1854. 6. 1568 4 3432. 6. 1512 4 2472. 6. 997 5 4290 6. 963 5 3090. 7. 8109 2 2009. BED WIDTH 120 FEET. 7. 7. 7- 3462 1925 1001 3 4 3013.5 4018. 4. 3652 2 976. . 8. i^ZL 9795 2 5022 . 5 2304. 4. 1612 3 1464. 8. 4116 3 3456. 4. 906 4 1952. 8. 2278 4 4608. 4. 580 5 2440. 8. 1443 5 5760. 5. 4989 2 1225. 9. 11453 2 2601. 5. 2190 3 1837.5 9. 4822 3 3901.5 5. 1224 4 2450. 9. 2632 4 5202. 5. 784 5 3062.5 9. 1633 5 6502.5 182 FLOW OP WATER IN TABLE 33. Giving fall in feet per mile; the distance on slope corresponding to a fall of one foot, and also the values of s and s/^ s= =siiie of slope fall of water surface (h), in any distance (I), 6 divided by that distance. Fall in iuches per mile. Slope 1 in s V Fall in feet per mile. Slope 1 in s 3 \/s 2 31680 .000031565 .005618 .25 21120 .000047349 .006881 2* 25344 .000039457 .006281 .50 10560 .000094697 .009731 31 18103 .000055240 .007432 .75 7040 .000142045 .011918 4 15840 .000063131 .007945 1. 5280 .000189393 .013762 4| 14080 .000071023 .008427 1.25 4224 .000236742 .015386 5 12672 .000078913 .008883 1.5 3520 .000284091 .016854 5| 11520 .000086805 .009317 1.75 3017 .000331439 .018205 6| 9748 .000102588 .010129 2. 2640 .000378788 019463 7 9051 .000110479 ,010511 2^25 2347 . 000426076 .020641 71 8448 .000118371 .010880 2.5 2112 .000473485 .021760 8 7920 .000126261 .011237 2.75 1920 .000520833 .022822 8* 7454 .000134154 .011583 3. 1760 .000568182 .023837 9-i 6670 .000149937 .012245 3.25 1625 .000615384 .024807 10 6336 .000157828 .012563 3.5 1508 .000663130 .025751 10| 6034 .000165720 .012873 3.75 1408 .000710227 .026650 11 5760 .000173598 .013176 4. 1320 .000757576 . 027524 HI 5510 .000181502 .013472 5. 1056 .000946970 .030773 12 5280 .000189393 .013762 : 6. 880. .001136364 .03371 12| 5069 .000197285 .014016 7. 754.3 .001325732 .036416 12| 4969 .000201231 .014185 8. 660. .001515152 .038925 13 4874 .000205182 .014324 9. 586.6 .001704445 .041286 13| 4693 . 000213068 .014597 10. 528. .001893939 .043519 13| 4608 .000217014 .014732 11. 443.6 .002083333 . 045643 14 4526 . 000220960 .014865 12. 440. .002272727 .047673 141 4425 . 000225989 .015033 13. 406,1 .002462121 . 04962 14| 4370 .000228851 .015128 14. 377.1 .002651515 .051493 14| 4271 .000234137 .015301 15. 352. .002840909 .0533 15| 4088 .000244634 .015641 16. 330. .003030303 .055048 16 3960 000252525 .015891 17. 310.6 .003219696 .056742 161 3840 .000260411 .016137 18. 293.3 .003409090 .058388 17 3727 .000268308 .016381 19. 277.9 .003598484 .059988 17| 3621 .000276199 .016619 20. 264. .003787878 .061546 18| 3425 .000291982 .017087 21. 251.4 .003977272 .063066 19 3335 .000299874 .017317 22. 240. .004166667 .064549 19* 3249 .000307765 .017543 23. 229.6 .004356060 .066 20 3168 .000315656 .017767 24. 220. .004545454 .067419 20 1 3091 .000323548 .017987 25. 211.2 .004734848 .06881 21| 2947 .000339331 .018421 26. 203.1 . 004924242 .070173 22 2880 .000347222 .018634 27. 195.2 .005113636 .07151 22J 2816 .000355114 .018844 28. 188.6 .005303030 .072822 23 2755 .000363005 .019052 29. 182.1 .005492424 .074111 23 1 2696 .000370896 .019259 30. 176. .005681818 .075373 OPEN AND CLOSED CHANNELS. 183 TABLE 33. SLOPES. Slope 1 in Fall in feet per s Slope 1 in Fall in feet per milo Vs Q1110* 4 1320. .25 .5 51 103.5 .019607843 . 140028 5 1056. .2 .447214 52 101.5 .019230769 . 138676 6 880. . 166666666 .408248 I 53 99.62 .018867925 .137361 7 754.3 .142857143 .377978 54 97.78 .018518519 . 136085 8 660. .125 . 353553 55 96. .018181818 . 134839 9 586.7 .111111111 . 333333 56 94.29 .017850143 . 133630 10 528. .1 .316228 57 92.65 .017543860 . 132453 11 480 .090909090 .301511 58 91.03 .017241379 .131305 12 440. .083333333 .288675 59 89.49 .016949153 . 130189 13 406.2 .076923077 .277350 60 88. .016666667 . 129100 14 377.1 .071428571 .267261 61 86.56 .016393443 . 128037 15 352. .066666667 .258199 62 85.16 .016129032 . 127000 16 330. .0625 .25 63 83.81 .015873010 . 125988 17 310.6 .058823529 . 242536 64 82.50 .015625 .125 18 293.3 .055555555 .235702 65 81 23 .015384615 . 124035 19 277.9 .052631579 .229416 66 80. .015151515 . 123091 20 264. .05 .223607 67 78.81 .014925353 .122169 21 251.4 .047619048 .218218 68 77.65 .014705882 . 121286 22 240. . 045454545 .213200 60 76.52 .014492754 . 120386 23 229.6 .043478261 .208514 70 75.43 .014285714 .119524 24" 220. .041066667 .204124 71 74.36 .014084507 .118678 25 211.2 .04 .2 72 73.33 .013888889 .117851 26 203.1 .038461538 .196116 73 7 2 33 .013688630 .117041 27 195.6 . 037037037 . 192450 74 7l!36 .013513514 .116248 28 188.6 .035714286 . 188982 75 70.40 .013333333 .115470 29 182.1 . 034452759 . 185695 76 69.47 .013157895 .114708 30 176. . 033333333 . 182574 77 68.57 .012987013 .113961 31 170.3 .032258065 . 179605 78 67.69 .012820513 .113228 32 165. .03125 .176777 70 06.84 .012658228 .112509 33 160. .030303030 . 174077 80 66. .0125 .111803 34 155.3 .029411765 .171499 81 65.18 .012345679 .111111 35 150.9 .028571429 . 169031 82 04.39 .012195122 .110431 36 146.7 .027777778 . 166667 83 63.62 .012048193 . 109764 37 142.7 .027027027 . 164399 84 62.80 .011904762 . 109109 38 138.9 .026315789 . 1G2221 85 62.12 .011764706 . 108465 39 135.4 .025641028 . 160125 86 61.40 .011627907 .107833 40 132. .025 .158114 87 60.69 .011494253 107211 41 128.8 . 024390244 . 156174 88 60. .011363636 . 106600 42 125.7 . 023809524 . 154303 89 59.32 .011235955 . 106000 43 122.8 .0232,55814 . 152490 90 58.66 .011111111 . 105409 44 120. .022727273 . 15075G 91 58.02 .010989011 . 104828 45 117.3 .022222222 . 149071 92 57.39 . 010869565 . 104257 46 114.8 .021739130 . 147444 93 56.78 .010752688 . 103695 47 112.3 .021276600 .U5865 94 56.17 .010638298 . 103142 48 110. .020833333 .144337 ! 95 55.58 .010526316 . 102598 49 107.8 .020408163 .142857 1 96 55. .010416667 . 102062 50 105.6 .02 .141421 97 4.43 .010309278 . 101535 184 FLOW OF WATER IN TABLE 33. SLOPES. Fall in Fall in Slope 1 in feet per mile. s V* Slope ; 1 in feet per mile. s v~ 98 53.88 .010204082 .101015 145 36.41 .006896552 .083046 99 53.34 .010101010 . 100504 146 36.16 .006849315 .OS2760 100 52.8 .010 .1 147 35.92 .006802721 .082479 101 52.28 . 009900990 .099504 148 35.68 . 006756757 .082199 102 51.76 .009803922 .099015 149 35.44 .006711409 .081923 103 51.26 .009708738 .098533 150 35.20 .006666667 .081650 104 50.77 .009615385 .098058 151 34.97 .006622517 .081379 105 50.29 .009523810 . 097590 152 34.74 .006578947 .081111 106 49.81 .009433962 .097129 153 34.51 . 006535948 .080845 107 49.35 .009345794 . 096674 154 34.29 . 006493506 .080582 108 48.89 . 009259259 .096225 155 34.06 .006451613 .08)0322 109 48.44 .009174312 .095783 156 33.85 .006410256 .080065 110 48. .009090909 .095346 157 33.63 .006369427 .079809 111 47.57 .009009009 .094916 158 33.42 .006329114 .079556 112 47.14 .008928571 .094491 159 33.21 . 006289308 . 079305 113 46.72 .008849558 .094072 160 33. .00625 .079057 114 46.31 .008771930 .093659 161 32.8 .006211180 .078811 115 45.91 .008695692 .093250 162 32.59 .006172840 .078568 116 45.52 . 008620690 .092848 163 32.39 .006134969 .078326 117 45.13 .008547009 .092450 164 32.20 .006097561 .078087 118 44.75 .008474576 .092057 165 32. . 006060606 . 077850 119 44.37 .008403361 .091669 166 31.81 .006024096 .077615 120 44. .008333333 .091287 167 31.62 .005988024 .077382 121 43.64 .008264463 .090909 168 31.43 .005952381 .077152 122 43.28 .008196721 .090536 169 31.24 .005917160 .076923 123 42.93 .008130081 .090167 170 31.06 .005882353 .076697 124 42.58 .008064516 . 089803 171 30.88 . 005847953 .076472 125 42.24 .008 . 089442 172 30.7 .005813953 . 076249 126 41.91 .007836508 .089087 173 30.52 . 005780347 . 076029 127 41.58 . 007874016 .088736 174 30.34 .005747126 .075810 128 41.25 .0078125 .088388 175 30.17 .005714286 .075593 129 40.93 .007751938 .088045 176 30. .005681818 .075378 130 40.62 .007692308 .087706 177 29.83 .005649718 .075164 131 40.31 .007633588 .087370 178 29.66 .005617978 .074953 132 40. .007575758 .087039 179 29.50 .005586592 .074744 133 39.70 .007518797 .086711 180 29.33 .005555556 .074536 134 39.40 .007462687 . 086387 181 29.17 .005524862 .074329 135 39.11 .007407407 .086066 182 29.01 .005494505 .074125 136 38.82 .007352941 .085749 183 28.85 . 005464481 .073922 137 38.54 .007299270 .085436 184 28.70 . 005434783 .073721 138 38.26 .007246377 .085126 185 28.54 . 005405405 .073521 139 37.98 .007194245 .084819 186 28 . 39 . 005376344 .073324 140 37.71 .007142857 .084516 187 28.24 .005347594 .073127 141 37.45 .007092199 .084215 188 28.09 .005319149 .072932 142 37.18 . 007042254 .083918 189 27.94 .005291005 .072739 113 36.92 .006993007 .083624 190 27.79 .005263158 .072548 144 36.67 .006944444 .083333 191 27.64 .005235602 .072357 OPEN AND CLOSED CHANNELS. 185 TABLE 33. SLOPES. Slope 1 iii Fall in feet pel- mile. s \/s Slope 1 in Fall in feet per mile. s x/a 192 27.50 .005208333 .072169 395 13.37 .002531646 .050315 193 27.36 .005181347 .071982 . 400 13.20 .002500000 .050000 194 27.22 .005154639 .071796 405 13.04 .002469136 .049690 195 27.08 .005128205 .071612 410 12 88 . 002439024 .049387 196 26.94 .005102041 .071429 415 12.72 .002409639 .049088 197 26.80 .005076142 .071247 420 12.57 .002380952 .048795 198 26.67 .005050505 .071067 425 12.42 .002352941 .048507 199 26.53 .005025126 .070888 430 12.28 .002325581 .048224 200 26.40 .005 .070710 435 12.14 .002298851 .047946 205 25.76 .004878049 .069843 440 12. .002272727 .047673 210 25.14 .004761905 .069007 445 11.87 .002247191 .047404 215 24.56 .004651163 .068199 450 11.73 .002222222 .047140 220 24. 004545454 .067419 455 11.60 .002197802 .046880 225 23.47 .004444444 .066667 460 11.48 .002173913 .046625 230 22.96 .004347826 .065938 465 11.35 .002150538 .046374 235 22.48 .004255319 .065233 470 11.24 .002127660 .046126 240 22. .004166667 .064549 475 11.12 .002105263 .045883 245 21.55 .004081623 .063885 480 11. .002083333 .045644 250 21.12 .004000000 .063246 . 485 10.89 .002061856 .045407 255 20.71 .003921569 .062620 490 10.78 .002040816 .045175 260 20.31 .003846154 .062018 495 10.67 .002020202 .044947 265 19.92 .003773585 .061430 500 10.56 .002000000 .044721 270 19.56 .003703704 .060858 505 10.46 .001980198 .044499 275 19.20 . 003633634 . 060302 510 10.35 .001960784 .044281 280 18.86 .003571429 .059761 515 10.25 .001941748 .044065 285 18 53 .003508772 .059235 520 10.15 .001923077 .043853 290 18.20 .003448276 .058722 525 10.06 .001904763 .043644 295 17.90 .003389831 . 058222 530 9.962 .001886792 .043437 300 17.60 . 003333333 .057735 535 9.870 .001869159 .043234 305 17.31 . 003278689 .057260 540 9.778 .001851852 .043033 310 17.03 .003225806 .056796 545 9.688 .001834862 .042835 315 16.76 .003174603 056344 550 9.600 .001818182 .042640 320 16.50 .003125000 .055902 555 9.513 .001801802 .042448 325 16.25 . 003076923 .055470 560 9.428 .001785714 . 042258 330 16. .003030303 .055048 565 9.345 .001769912 .042070 335 15.76 .002985075 .054636 570 9.263 .001754386 .041885 340 15.53 .002941176 .054232 575 9.182 .001739130 .041703 345 15.30 .002898551 .053838 580 9.103 .001724138 .041523 350 15.09 .002857143 .053452 585 9.026 .001709420 .041345 355 14.87 .002816901 .053074 590 8.949 .001694915 .041169 360 14.67 .062777778 .052705 595 8.874 .001680672 .040996 365 14.47 1.002739726 .052342 600 8.800 .001666667 .040825 370 14.27 .002702703 .051988 605 8.727 .001652893 .040656 375 14.08 i. 002666667 .051640 610 8.656 .001639344 .040489 380 13.90 . 002631579 .051299 615 8.585 .001626016 .040324 385 13.71 .002597403 .050965 620 8.516 .001612903 .040161 390 13.54 .002504103 .050637 625 8.448 .001600000 .040000 186 FLOW OF WATER IN TABLE 33. SLOPES. Slope 1 in Fall in feet per mile. s V~ Slope 1 in Fall in feet per mile. s %/ 630 8.381 .001587302 .039841 , 865 6.104 .001156069 .034001 635 8.317 .001574803 .039684 870 6.069 .001149425 . 033903 640 8.250 .001562500 . 039528 875 6.034 .001142857 . 033800 645 8.186 .001550388 .039375 880 6. .001136364 .033710 650 8.123 .001538462 .039223 885 5.966 .001129944 .033614 655 8.061 .001526718 .039073 890 5.932 i. 001 123597 .033520 660 8. .001515152 1.038925 895 5.900 1.001117318 .033426 665 7.940 .001503759 .038778 900 5.867 .0011,11111 .033333 670 7.881 .001492537 ; 038633 905 5.834 .001104972 ! 033241 675 7.822 .001481481 .038490 910 5.802 .001100110 .033108 680 7.765 .001470588 .038348 915 5.770 .001093896 .033059 685 7.708 .001459854 .038208 920 5.739 .001086957 .032969 690 7.652 .001449275 .038069 ! 925 5.708 .001081081 .032879 695 7.597 .001438849 .037932 I 930 5.677 .001075269 .032791 700 7.543 .001428571 .037796 i 935 5.648 .001069519 . 032703 705 7.490 .001418440 .037662 ! 940 5.617 .001063830 .032616 710 7.437 .001408451 .037529 945 5.587 .001058201 .032530 715 7.385 .001398601 .037398 950 5.558 .001052632 .032444 720 7.333 . 001388889 .037268 955 5.528 .001047120 . 032359 725 7.283 .001379310 .037139 960 5.500 .001041667 . 032275 730 7.233 001369863 .037012 965 5.472 .001036269 .032191 735 7.184 .001360544 .036885 970 5.434 .001030928 .032108 740 7.135 .001351351 .036761 975 5.415 .001025641 .032026 745 7.087 .001342282 .036637 980 5.388 .001020408 .031944 750 7.040 .001333333 . 036515 985 5.360 .001015228 .031863 755 G.993 .001324503 .036394 990 5.333 .001010101 .031782 760 6.948 .001315789 .036274 995 5.306 .001005025 .031702 765 6.902 .001307190 036155 1000 5.280 .001000000 .031623 770 6.857 .001298701 .036038 1005 5.253 .000985025 .031544 775 6.812 .001290323 .035921 1010 5.228 .00099099 .031466 780 6.769 .001282051 .035806 1015 5.202 . 000985222 .031388 785 6.726 .001273885 .035691 1020 5.176 .000980392 .031311 790 6.684 .001265823 . 035578 1025 5.151 .000975610 .031235 795 6.642 . 001257862 .035466 1030 5.126 .000970873 .031159 800 6.600 .001250000 .035355 1035 5.101 .000966184 .031083 805 6.559 .001242236 .035245 1040 5.077 .000961538 .031009 810 6.518 .001234568 .035136 1045 5.053 .000956938 .030934 815 6.478 .001226994 .035028 1050 5.029 .000952381 .030861 820 6.439 .001219512 . 034922 1055 5.005 .000947867 . 030787 825 6.400 .001212121 .034816 1060 4.981 .000943396 .030715 830 6.362 .001204819 .034710 1065 4.958 .000938967 .030643 835 6.324 .001197605 .034606 1070 4.935 .000934579 .030571 840 6.2S6 .001190476 .034503 1075 4.912 . 000930233 .030499 845 6.248 .001183432 .034401 1080 4.889 .000925926 .030429 850 6.212 .001176471 .034300 1085 4.866 .000921659 .030359 855 0.175 .001169591 .034199 1090 4.844 .000917431 .030289 860 6.140 .001162791 .034099 1095 4.822 .000913242 .030220 OPEN AND CLOSED CHANNELS. 187 TABLE 33. SLOPES. Slope 1 in Fall in feet per mile. s r | Slope Vt) 1 in Fall in feet per mile. s N/r 1100 4.800 .000909090 .030151 [I 1335 3.955 .000749064 . 027369 1105 4.778 .000904159 . 030069 i 1340 3.940 .000746268 .027318 1110 4.757 . 000900900 .030015 1345 3.926 .000743420 .027267 1115 4.735 .000896861 .029948 1350 3.911 .000740741 .027217 1120 4.714 .000892857 .029881 1355 3.897 .000738007 .027166 1125 4.693 . 000888888 .029814 1360 3.882 .000735294 .027116 1130 4.673 .000884956 .029748 1365 3.868 .000732601 .027067 1135 4.652 . 000881057 .029683 1370 8.854 .000729927 .027017 1140 4.632 .000877193 .029617 1375 3.840 .000727273 .026968 1145 4.611 .000873365 .029553 1380 3.826 . 000724638 .026919 1150 4.591 .000869566 .029488 1385 3.812 . 000722022 .026870 1155 4.571 .000865801 .029425 1390 3.799 .000719424 .026822 1160 4.552 .000862069 .029361 1395 3.785 .000716846 .026774 1165 4.532 .000858370 .029298 1400 3.771 .000714286 . 026726 1170 4.513 .000854701 .029235 1405 3.758 .000711744 .026679 1175 4.494 .000851064 .029173 1410 3.745 .000709220 .026631 1180 4.475 .000847458 .029111 1415 3.731 .000706714 .026584 1185 4.456 .000843882 .029049 1420 3.718 . 000704225 .026537 1190 4.437 .000840336 .028988 1425 3.705 .000701754 .026491 1195 4.418 .000836820 .028928 1430 3.692 .000699300 .026444 1200 4.400 .000833333 .028868 1435 3.680 .000696864 .026398 1205 4.382 .000829875 .028808 1440 3.667 .000694444 .026352 1210 4.364 .000826446 .028748 1445 3.654 .000692042 .026307 1215 4.346 .000823045 .028689 1450 3.641 . 000689655 .026261 1220 4.328 .000819672 .028630 1455 3.629 .000687285 .026216 1225 4.310 .000816326 .028571 1460 3.617 . 000684931 .026171 1230 4.293 .000813008 .028513 1465 3.604 .000682594 .026126 1235 4.275 .000809717 .028455 1470 3.592 .000680272 .026082 1240 4.258 .000806452 .028398 1475 3.580 .000677966 .026038 1245 4.241 .000803213 .028341 1480 3.568 .000675676 .025994 1250 4.224 .000800000 .028284 1485 3.556 .000673401 . 025950 1255 4.207 .000796813 .028228 1490 3.544 .000671141 .025907 1260 4.190 .000793651 .028172 1495 3.532 .000668896 .025803 1265 4.174 .000790514 .028116 1500 3.520 .000666666 .025820 1270 4.157 000787402 .028061 1505 3.508 .000664452 .025777 1275 4.141 000784314 .028006 1510 3.497 ,000662252 .025734 1280 4.125 000781250 .027951 1515 3.485 .000660066 .025691 1285 4.109 000778210 .027896 1520 3.474 .000657895 . 025649 1290 4.093 000775116 027841 1525 3.462 .000655737 .025607 1295 4.077 000772201 027789 1530 3.451 .000653595 . Q25566 1300 4.062 000769231 027735 1535 3.440 .000652117 .025524 1305 4.046 000766283 027682 1540 3.429 .000649351 025482 1310 4.031 000763359 027629 1545 3.417 .000647275 025441 1315 4.015 000760456 027576 1550 3.407 .000645161 .025400 1320 4. 000757576 027524 1555 3.396 .000643087 025359 1325 3.985 000754717 027472 1560 . 3.385 .000641025 025318 1330 3.970 000751880 . 027420 1565 3.374 .000638978 025278 188 FLOW OF WATER IN TABLE 33. SLOPES. Slope 1 iii Fall in feet per mile. s S/.S Slope 1 in Fall in feet per mile. s v/ 1570 3.363 .000636943 .025238 1805 2.925 .000554017 .023538 1575 3.352 .000634921 .025198 1810 2.917 .000552486 . 023505 1580 3.342 . 0006329 1J .025158 1815 2.909 .000550964 .023473 1585 3.331 .000630915 .025118 1820 2.901 .000549451 .023440 1590 3.321 .000628931 .025078 1825 2.893 . 000547945 .023408 1595 3.310 .000626959 . 025039 1830 2.885 .000546448 .023376 1600 3.300 .000625000 . 025000 1835 2.877 .000544949 .023344 1605 3.290 . 000623053 .024961 1840 2.870 .000543478 .023313 1610 3.280 .000621118 .024922 1845 2.862 .000542005 .023281 1615 ] 3.269 .000619195 .024884 1850 2.854 .000540541 .023250 1620 3.259 .000617284 . 024845 1855 2.847 .000539084 .023218 1625 3 249 .000615384 .024807 1860 2.839 .000537633 .023187 1600 3.239 .000613497 . 024769 1865 2.831 .000536193 .023156 1635 3.229 .000611621 . 024731 1870 2.824 .000534759 .023125 1640 3.220 .000699756 .024693 1875 2.816 .000533333 . 023094 1645 3.210 .000607900 .024656 1880 2.809 .000531915 .023063 1650 3.200 .000606060 .024618 1885 2.801 .000530504 .023033 1655 3.190 . 000604230 .024581 1890 2.794 .000529101 .023002 1660 3.181 000602409 .024544 1895 2.786 .000527705 .022972 1665 3.171 .000600601 . 024507 1900 2.779 .000526316 .022942 1670 3.162 .000598802 .024470 1905 2.772 .000524934 .022911 1675 3.152 .000597015 . 024434 1910 2.764 .000523500 .022881 1680 3.143 .000595238 .024398 1915 2.757 .000522193 . 022852 1685 3.134 .000593102 . 024354 1920 2.750 .000520833 .022822 1690 3.124 .000591717 .024325 1925 2.743 .000519481 .022792 1695 3.115 .000589971 .024290 1930 2.736 .000518135 .022763 1700 3 106 .000588235 . 024254 1935 2.729 .000516796 .022733 1705 3.097 .009586510 .024218 1940 2.722 .000515464 -.022704 1710 3.088 . 000584795 .024183 1945 2.715 .000514139 . 022G75 1715 3.079 . 000583090 .024147 1950 2.708 .000512821 .022646 1720 3.070 .000581395 .024112 1955 2.701 .000511509 .022616 1725 3.061 .000579710 .024077 1960 2.694 .000510204 .022588 1730 3.052 .000578035 . 024042 19G5 2.687 .000508906 .022559 1735 3.042 .000576369 .024008 1970 2.680 .000507614 .022530 1740 3.035 .000574712 .023973 1975 2.673 . OC0506329 . 022502 1745 3.026 . 000573066 .023939 1980 2.667 .000505051 .022473 1750 3.017 .000571429 .023905 1985 2.660 .000503778 . 022445 1755 3.009 .000569801 .023871 1990 2.653 .000502513 .022417 1760 3. .000568182 .023837 1995 2.647 .000501253 .022388 1755 2.992 .000566572 .023803 2000 2.640 .000500000 .022301 1770 2.983 .000564972 . 023769 2005 2.633 .000498753 .022333 1775 2.975 . 000563380 .023736 2010 2.627 .000497512 . 022305 1780 2.966 .000561798 .023702 2015 2.620 .000496278 .022277 1785 2.958 .000560224 .023669 2020 2.614 . 000495050 .022250 1790 2.950 .000558659 .023636 2025 2.607 .000493827 022222 1795 2.942 .000557103 .023603 2030 2.601 .000492611 .022195 1800 2.933 .000555555 |. 023570 2035 2.595 . 000491400 .022168 OPEN AND CLOSED CHANNELS. 189 TABLE 33. SLOPES. Slope 1 in Fall in feet per mile. s v/s \ Slope 1 in Fall in feet per mile. s Vs 2040 2.588 .000490196 .022140 2265 2.331 .000441501 '. 021012 2045 2.582 .000488998 .022113 2270 2.326 .000440529 .020989 2050 2 576 .000487805 .022086 2275 2.321 .000439560 .010966 2055 2.569 .000486618 .022059 2280 2.316 i. 000438597 .020943 2060 2.563 . 000485437 .022033 2285 2.311 .000437637 . 020920 2065 2.557 .000484213 . 022005 2290 2.306 .000436681 .020897 2070 2.551 .000483093 .021979 2295 2.301 . 000435730 . 020874 2075 2 . 545 .000481928 .021953 2300 2.296 .000434783 .020853 2080 2 538 . 000480769 .021926 2305 2.291 . 000433839 .020829 2085 2.532 .000479616 .021900 2310 2.286 .000432900 . 020806 2090 2.526 . 000478469 .021874 2315 2.281 .000431965 .020784 2095 2.520 .000477327 .021848 2320 2.276 000431034 .020761 2100 2.514 .000476190 .021822 2325 2.271 .000430108 .020740 2105 2.508 .000475059 .021796 2330 2.266 .000429185 .020717 2110 2.502 .000473934 .021770 2335 2.261 .000428266 . 020694 2115 2.496 .000472813 .021744 2340 2.256 .000427350 .020672 2120 2.491 .000471698 .021719 2345 2 252 .000426439 .020650 2125 2.485 . 000470588 .021693 2350 2.247 .000425532 .020628 2130 2.479 . 000469484 .021668 2355 2.242 .000424629 .020607 2135 2.473 .000468384 .021642 2360 2.237 .000423729 .020585 2140 2.467 .000467290 .021617 2365 2.233 .000422833 .020563 2145 2.462 .000466200 .021592 2370 2.228 1.000421941 .020541 2150 2.456 .000465116 .021567 2375 2.223 j. 00042 1053 .020520 2155 2.450 .000464037 .021542 2380 2.219 j.000420168 .020498 2160 2.444 .000462963 .021517 2385 2.214 1.000419287 .020477 2165 2.439 i. 00046 1894 .021492 2390 2.209 000418410 .020455 2170 2.433 .000460829 .021467 2395 2.205 .000417534 .020434 2175 2.428 . 000459770 .021442 2400 2.200 .000416667 .020412 2180 2.422 .000458716 .021418 2405 2.195 .000415801 .020391 2185 2.416 .000457666 .021393 2410 2.191 !. 0004 14938 .020370 2190 2.411 .000456621 .021369 2415 2.186 .000414079 .020349 2195 2.405 .000455581 .021344 2420 2.182 .000413223 .020328 2200 2.400 .000454545 .021320 2425 2.177 .000412371 . 020307 2205 2 . 395 .000453515 .021296 2430 2.173 .000411523 .020286 2210 2.389 . 000452489 .021272 2435 2.168 .000410678 .020265 2215 2.384 .000451467 .021248 2440 2.164 .000409836 .020244 2220 2.378 .000450450 .021224 2445 2.160 .500408998 .020224 2225 2.373 .000449438 .021200 2450 2.155 .000408163 .020203 2230 2.368 .000448430 .021176 2455 2.151 .000407332 .020182 2235 2.362 .000447427 .021152 2460 2.146 .000406504 .020162 2240 2.357 .000446429 .021129 2465 2.142 .000405680 .020141 2245 2.352 .000445434 .021105 2470 2.138 .000404858 .020121 2250 2.347 .000444444 .021082 2475 2.133 . 000404040 .020101 2255 2.341 .000443459 .021058 2480 2.129 .000403226 .020080 2260 2.336 .000442478 .021035 2485 2.125 .000402414 .020060 190 FLOW OF WATER IN TABLE 33. SLOPES. Slope 1 in Fall in feet per mile. s vA" Slope 1 in Fall in feet per mile. s V* 2490 2.120 .000401606 . 020040 2715 1.945 . 000368324 .019192 2495 2.116 .000400802 . 020020 ! 2720 1.941 . 000367647 .019174 2500 2.112 . 000400000 .020000 2725 .938 .000366972 .019156 2505 2.108 .000399202 .019980 2730 .934 .000366300 .019139 2510 2.104 .000398406 .019960 2735 .931 .000365631 .019121 2515 2.099 .000397614 .019940 2740 .927 .000364964 .019104 2520 2.095 .000396825 .019920 2745 .923 .000364299 .019086 2525 2.091 . 000396039 .019901 2750 .920 .000363636 .019069 2530 2.087 .000395257 .019881 2755 .916 .000362972 .019052 2535 2.083 .000394477 .019861 2760 .913 .000362319 .019035 2540 2.079 .000393701 .019842 ! 2765 .910 .000361664 .019017 2545 2.075 .000392927 .019822 2770 1.906 .000361011 .019000 2550 2.071 .000392157 .019803 2775 1.903 .000360360 .018983 2555 2.066 .000391389 .019784 i 2780 1.900 .000359712 .018966 2560 2.063 . 000390625 .019764 2785 1.896 .000359066 .018949 2565 2.058 .000389864 .019745 1 2790 1.892 . 000358423 .018932 2570 2.054 .000389105 .019726 2795 1.889 . 000357782 .018915 2575 2.050 .000388349 .019706 2800 .886 .000357143 .018898 2580 2.047 .000387697 .019687 2805 .882 .000356506 .018881 2585 2.042 .000o86847 .019668 2810 .879 .000355871 .018865 2590 2.039 .000386100 .019649 2815 .875 .000355279 .018848 2595 2.035 .000385357 .019630 2820 .872 .000354610 .018831 2600 2.031 .000384615 .019612 2825 .869 . 000353982 .018814 2605 2.027 .000383877 .019593 2830 .866 . 000353357 .018797 2610 2.023 .000383142 .019574 2835 .862 .000352733 .018781 2615 2.019 .000382410 .019555 2840 1.859 .000352113 .018764 2620 2.015 .000381679 .019536 2845 1.856 .000351423 .018746 2025 2.011 .000380952 .019518 2850 1.852 . 000350877 .018731 2630 2.008 .000380228 . 019499 2855 1.849 .000350877 .018715 2635 2.004 .000379507 .019481 2860 1.846 . 000349650 .018699 2640 2. .000378787 .019462 2865 1.843 . 000349040 .018682 2645 1.996 .000378072 .019444 2870 .839 .000348432 .018666 2650 1.992 .000377359 .019426 2875 .836 .000347827 .018650 2655 1.989 .000376648 .019407 2880 .833 .000347222 .018634 2660 1.985 .000375940 .019389 2885 .830 .000346662 .018617 2665 1.981 .000375235 .019371 2890 .827 .000346021 .018602 2670 1.977 .000374532 .019353 2895 .824 . 000345427 .018585 2675 1.974 .000373832 .019334 2900 .820 . 000344827 .018569 2680 1.970 .000373134 .019316 2905 .817 .000344234 .018554 2685 1.966 .000372437 .019298 2910 .814 .000343643 018537 2690 1.963 .000371747 .019281 2915 .811 .000343057 .018521 2695 1.959 .000371058 .019263 2920 .808 . 000342456 .018506 2700 1.956 . 000370370 .019245 2925 .805 .900341880 018490 2705 1.952 . 000369686 .019228 2930 1.802 .000341297 .018474 2710 1.949 .000369004 .019209 2935 1.799 .000340716 018456 OPEN AND CLOSED CHANNELS. 191 TABLE 33. SLOPES. Slope 1 in Fall in feet per mile. s jr Slope 1 in Fall in feet per mile. s V~ 2940 1.796 . 000340136 .018442 3460 1.526 .000289017 .017000 2945 1.793 . 000339559 .018427 3480 1.517 .000287356 .016951 2950 .790 .000338983 .018414 3500 1.509 000285714 .016903 2955 .787 .000338409 .018396 3520 1.500 .000284091 .016855 2960 .784 . 000337838 .018380 3540 1.491 .000282486 .016807 2965 .781 .000337268 .018264 3560 1.483 .000280899 .016760 2970 .778 .000336700 .018349 35SO 1.475 .000279329 .016713 2975 .775 .000336134 .018334 3600 1.467 .000277778 .016667 2980 .772 .000335571 .018319 3620 .459 .000276243 .016620 2985 .769 .060335008 .018303 3640 .450 .000274725 .016575 2990 .766 . 000334482 .018288 3660 .442 .000273224 .016530 2995 .763 . 000333890 .018272 3680 .435 .000271739 .016484 3000 .760 .000333333 .018257 3700 .427 .000270270 .016440 3010 .754 .000332226 .018227 3720 .420 .000268817 .016395 3020 .748 .000331129 .018197 3740 .412 .000267380 .016352 3030 .742 .000330033 .018667 3760 1.404 .000265958 .016308 3040 .737 . 000328947 .018137 3780 1 . 397 .000264550 .016265 3050 1.731 .000327869 .018107 3800 1.390 .000263158 .016222 3060 1.725 .000326797 .018077 3820 1.382 .000261780 .016180 3070 1.720 .000325733 .018048 3840 1.375 .000260417 .016138 3080 1.715 .000324675 .018019 3860 1.368 .000259067 .016095 3090 1.709 .OOC323625 .017989 3880 .361 000257732 .016054 3100 1.703 .000322581 017960 3900 .354 .000256410 .016013 3110 1.698 .000321543 .017932 3920 .347 .000255102 .015972 3120 1.692 .000320513 .017903 3940 .340 .000253807 .015931' 3130 1.687 000319489 .017874 3960 .333 .000252525 .015891 3140 1.682 .000318471 .017845 3980 1.327 .000251256 .015851 3150 1.676 .000317460 .017817 4000 1.320 000250000 015811 3160 1.671 .000316456 .017789 4020 1.313 .000248756 .015772 3170 1.666 .000315457 .017761 4040 1.307 .000247525 .015733 3180 1.660 .000314465 .017733 4060 1.300 .000246306 .015694 3190 1.655 .000313480 .017705 4080 .294 .000245098 .015655 3200 .650 . 000312500 .017677 4100 .288 .000243903 .015617 3220 .640 000310559 .017622 4120 .282 .000242718 .015580 3240 .629 .000308641 .017568 4140 .275 .000241546 .015542 3260 .620 .000306748 .017514 4160 .269 .000240382 .015505 3280 .610 .000304878 .017461 4180 .263 .000239235 .015467 3300 .600 .000303030 .017408 4200 1.257 . 000238095 .015430 3320 .590 .000301205 .017355 4220 1.251 .000236967 .015394 3340 .581 .000299401 .017303 4240 1.245 .000235849 .015358 3360 .571 .000297619 .017251 4260 1.239 . 000234742 .015322 3380 .562 .000295858 .017200 4280 1.234 .000233645 . 015286 3400 1.553 .000294113 .017150 4300 1.228 . 000232558 .015250 3420 1.544 . 000292398 .017100 4320 1.222 .000231482 .015215 3440 1.535 . 000290688 .017050 4340 1.217 .000230415 .015180 192 FLOW OF WATER IN TABLE 33. SLOPES. Slope 1 in Fall in feet per mile. s \/s Slope 1 in Fall in feet per mile. s V^ 4360 1.211 .000229716 .015145 6000 .880 .000166667 .012910 4380 .205 .000228311 .015110 6080 .868 .000164474 .012820 4400 .200 .000227273 .015076 61CO .857 .000162338 .012741 4420 .194 .000226244 .015041 6240 .846 .000160256 .012659 4440 .189 .000225225 .015007 6320 .836 .000158228 .012579 4460 .184 .000224215 .014974 6400 .825 .000156250 .012500 4480 .179 .000223214 .014940 6480 .815 .000154321 .012422 4500 .173 .000222222 .014907 6560 .805 .000152439 .012347 4520 .J68 .000221239 .014874 6640 .795 .000150602 .012272 4540 .163 .000220264 .014841 6720 .786 .000148810 .012199 4560 .158 .000219298 .014808 6800 .777 .000147059 .012127 4580 .153 .000218341 .014776 6880 .767 .000145349 .012056 4600 .148 .000217391 .014744 1 6960 .759 .000143678 .011986 4620 .143 .000216450 .014712 7000 .754 .000142857 .011952 4640 .138 .000215517 .014681 7040 .750 .000142045 .011919 46GO .133 .000214592 .014649 7120 .742 .000140449 .011851 4680 1.128 .000213675 .014617 7200 .733 .000138889 .011785 4700 1.124 .000212766 .014586 7280 .725 .000137363 .011720 4720 1.119 .000211864 .014557 7360 .718 .000135869 .011656 4740 1.114 .000210970 .014524 7440 .710 .000134408 .011594 4760 1.109 .000210084 .014492 7500 .704 .000133333 .011547 4780 1.104 . 000209205 .014464 7520 .702 .000132979 .011532 4800 1.100 .000208333 .014434 7600 .695 .000131579 .011471 4820 .096 . 000207469 .014404 7680 .687 .000130208 .011411 4840 .091 .000206612 .014374 7760 .680 .000128866 .011352 4860 .0^7 .000205761 .014344 7840 .673 .000127551 .011293 4880 .082 .000204918 .014315 7920 .667 .000126263 .011237 4900 .078 .000204081 .014285 8000 .660 .000125000 .011180 4920 .073 . 000203252 .014256 8080 .653 .000123763 .011125 4940 .069 . 000202429 .014227 8160 .647 .000122549 .011070 4960 .065 .000201613 .014199 8240 .64.1 .000121359 .011016 4980 .060 .000200803 .014170 8320 .635 .000120192 .010963 5000 .056 . 000200000 .014142 8400 .629 .000119048 .010911 5040 .048 .000198570 .014086 8480 .623 .000117925 .010860 5120 .031 .000195313 .013975 8560 .617 .000116823 .010809 5200 .015 .000192308 .013888 8640 .611 .000115741 .010759 5280 1. .000189394 .013862 8720 .605 .000114679 .010709 5360 .985 .000186567 .013659 8800 .600 .000113636 .010660 5440 .971 .000183824 .013558 8880 .595 .000112613 .010612 5520 .957 .000181160 .013460 8960 .585 .000111607 .010565 5600 .943 .000178572 .013363 9000 .587 .000111111 .010541 5680 .930 .000176056 .013268 9040 .584 .000110620 .010518 5760 .917 000173611 .013176 9120 .579 .000108649 .010472 5840 .904 .000171233 .013085 9200 .574 .000108696 ' .010427 5920 .892 .000168919 .012997 9280 .569 .000107759 .010380 OPEN AND CLOSED CHANNELS. 193 TABLE 33. SLOPES. Q1 Fall in ^r-r s vA Slope 1 in Fall in feet per mile. s \ Vs' 9360 .564 .000106838 .010336 12880 .410 1.000077640 .008811 9440 .559 .000105932 1.010293 12960 .407 |. 00007 7 160 .008784 9520 .555 .000105042 1. 010249 13000 .406 . 000076923 .008771 9600 .550 .000104167 ,010206 13040 .405 . 000076687 .008757 9680 .545 .000103306 .010164 13120 .402 .000076220 .008730 9760 .541 000102459 .010122 13200 .400 .000075758 .008704 9840 .537 .000101626 .010081 13280 .398 .000075301 .008678 9920 .532 .000100807 .010040 13360 .395 . 000074850 .008651 10000 .528 .000100000 .010000 13440 .393 .000074405 .008625 10080 .524 .000099206 .009960 13520 .390 .000073965 .008600 10160 .520 .000098425 .009921 13600 .388 .000073530 .008575 10240 .516 .000097656 .009882 13680 .386 .000073100 .008550 10320 .512 . 000096924 . 009844 13750 .384 . 000072675 .008525 10400 .508 .000096154 .009806 13840 .382 .000072254 .008500 10480 .504 .000095420 .009768 13920 .379 .000071839 .008476 10560 .500 .000094697 .009731 14000 .377 .000071429 .008452 10640 .496 .000093985 .009695 14080 .375 .000071023 .008428 10720 .492 .000093284 . 009658 14160 .373 .000070622 .008404 10800 .489 . 000092593 .009623 14240 .371 . 000070225 .008380 10880 .485 .000091912 .009587 14320 .369 . 000069832 .008357 10960 .482 .000091241 .009552 14400 .367 . 000069445 .008334 11000 .480 .000090909 .009534 14480 .365 .000069061 .008310 11040 .478 .000090580 .009518 14560 .363 . 000068681 .008288 11120 .475 .000089928 .009483 14640 .361 .000068306 .008265 11200 .471 .000089286 . 009449 14720 .359 .000067935 .008242 11280 .468 . 000088653 .009416 14800 .357 .000067568 . 008220 11360 .465 . 000088028 . 009382 14880 .355 . 000067204 .008198 11440 .462 .000087412 .009350 14960 .353 . 000066848 .008176 11520 .458 .000086806 .009317 15000 .352 . 000066667 .OOG165 11600 .455 .000086207 . 009285 15040 .351 .000066490 .008154 11680 .452 .000085617 .009253 15120 .349 .000066138 .008133 11760 .449 j . 000085034 .009221 15200 .347 . 000065790 .008111 11840 .446 .000084459 .009190 15280 .346 . 000065445 .008090 11920 .443 .000083893 .009160 15360 .344 .000065104 .008069 12000 .440 . 000083333 .009129 15440 .342 1.000064767 . 008048 12080 .437 .000082782 .009099 i 15520 . 340 . 000064433 .008027 12160 .434 . 000082237 .009069 i 15600 .339 .000064103 .008007 12240 .431 .000081699 .009039 15680 .337 1.000063776 .007986 12320 .429 .000081169 .009010 i 15760 .335 .000063452 .007966 12400 .426 .000080645 .008980 15840 .333 .000063131 .007946 12480 .423 .000080128 .008951 15920 1 .332 .000062814 .007926 12560 .420 .000079618 .008923 16000 .330 :. 000062500 007906 12640 I .418 .000079114 . 008895 ' 16080 .328 .000062189 .007886 12720 j .415 .000078616 .008867 16160 .327 .000061881 .007867 12800 ! .413 .000078125 .008839 1 16240 j .325 .000061577 1.007847 13 194 FLOW OF WATER IN TABLE 33. SLOPES. Fall in ^ f tr s N/T 1 Slope 1 in Fall in feet per mile. s V* 16320 i .324 .000061275 .007828 18800 .281 .000053191 .007293 16400 . 322 . 000060976 .007809 18880 .280 .000052966 .007278 16480 .320 .000060680 .007790 18960 .279 .000052742 . 007262 16560 .319 .000060387 .007771 19000 .280 . 000052632 .007255 16640 .317 .000060096 .007753 I 19040 .277 .000052521 .007246 16720 .316 .000059809 . 007734 1 19120 .276 .000052301 .007232 16800 .314 . 000059524 .007715 I 19200 .275 . 000052083 .007217 16880 .313 . 000059242 .007697 ! 19280 .274 000051867 .007202 16960 .311 .000058962 007679 19360 .273 .000051653 .007187 17000 .311 . 000058824 .007670 j 19440 .272 .000051440 .007172 17040 .310 .000058686 .007661 19520 .271 .000051229 .007157 17120 .308 .000058411 . 007643 S 19600 .269 .000051020 .007142 17200 .307 .000058140 . 007625 ! 19680 268 000050813 .007128 17280 .306 .000058146 . 007608 19760 .267 . 000050607 .007114 17360 .304 . 000057604 . 007590 19840 .266 . 000050403 .007100 17440 .303 1.000057429 .007573 19920 .265 .000050201 .007085 17520 .301 1.000057078 . 007555 ! 20000 .264 .000050000 .007071 17600 .300 j. 0000568 18 .007538 i 20080 .263 .000049800 .007057 17680 .299 .000056561 .007520 20160 .262 . 000049603 . OC7043 17760 .297 i . 000056306 . 007504 20240 .261 . 000049407 . 007029 17840 .296 .000056054 .007487 i 20320 .260 .000049212 .007015 17920 .295 1.000055804 . 007470 20400 .259 . 000049020 .007001 18000 .293 ;. 000055555 . 007454 \ 20480 .258 .000048828 . 006987 18080 .292 .000055310 . 007437 i 20560 .257 .000048638 .006974 18160 .291 .000055066 .007421 20640 .256 .000048447 . 006960 18240 .289 .000054825 .007404 i 20720 .255 .000048263 .006947 18320 .288 .000054585 .007388 20800 .254 .000048077 .006934 18400 .287 i. 000054348 .007372 ! 20880 .253 . 000047893 . 006920 18480 .286 .000054112 .007356 20960 .252 .000047710 .006907 18560 .285 .000053879 .007340 ! 21040 .251 j. 000047529 .006894 18640 .283 .000053648 .007324 21120 250 .000047348 .00688) 18720 .282 .000053419 .007308 OPEN AND CLOSED CHANNELS. 195 Article 14. Formulae for Mean Velocity in Pipes, Sewers, Conduits, etc. In continuation of the formulae for mean velocity in open channels, given at page 8, the following collection of formulae is given for finding the mean velocity in pipes, sewers, conduits, etc. As already stated, it is believed that such a collection will be useful, not only for reference, but also for comparison with the most modern and accurate formulae. This list contains al- most all the formula) in use in different countries, in modern times, and it is the most complete collection of formulae, relating to the Flow of Water in Open and Closed Channels, ever before gathered together in a sin- gle work. Some of the formulae for open channels, already given, have also been used for pipes, sewers, conduits, etc. These will not be reproduced here. They will, how- ever, be denoted by the numbers already given to them. The same symbols are used here as already given at page 6. We have also, in addition: d = diameter of pipe in feet, if not otherwise stated. The formulae already used for open channels, and which have also been used for pipes, sewers conduits, etc., are: D'Aubisson's, Taylor's, Downing's, Beardmore's, Les- lie's, Pole's, formula (1); D'Aubisson's (5); Beardmore's (7); Eytelwein's (8); Neville's (12); Dwyer's (13); Young's (16); Dubuat's (17); De Prony's (21); St. Ve- nant's (23); Provis's (25); Fanning's (28); Kutter's (40). The following formulae are also applicable to pipes, sewers and conduits: 196 FLOW OF WATER IN D'Arcy's formula for clean iron pipes under pressure is: ( rs Y v = --) M61)7726 + ..OOOOOT62 > ............. (51) ( r ) Flynn's modification of D'Arcy's formula is: 155256 D'Arcy's formula as given by J. B. Francis, C. E., for old cast-iron pipe, lined with deposit, and under pres- sure is: 144 (53) Flynn's modification of D'Arcy's formula for old cast- iron pipe is: 70243. 9 Molesworth's modification of Kutter's formula (40) with n = .013 is: 181 + = 026 , 00281 \ X ^ V8 (55) 1+ v/Tv 41 ' 6+ ^~) Flynii's modification of Kutter's formula is (see Article 20, in which are given values of K and \/r ): = 1 + (44.41 X - \ | Lampe's formula is: X \/TS (56) (57) OPEN AND CLOSED CHANNELS. 197 Weisbach's formula is: i (58) .016921 : j 1.505 +CX--J where c = .01439 + v z Prony's formula is: v = 97 v/^ .08 nearly (59) Eytelwein's formula is: v= 108 v/r -13 nearly (60) Another formula of Eytelwein is: )* (6D D'Aubisson's formula is: v= 98i/rs .1 ........................... (62) Hawksley's formula is: o = 48.05( ^* \* .................... (63) V * + 64 a / Poncelet's formula is: .................... (64) Blackwell's formula is: v = 47.913 (^_V ....................... (65) Neville's formula is: (h r \i /r*n\ _ i ................ (66) .0234/-H-- 0001085 l) Hughes' modification of Eytelwein's formula (61) is: -_ 2.112 198 FLOW OP WATER IN BlackwelFs modification of Eytelwein's formula (61) Kirkwood's formula for tuberculated pipes is: v = 80 v/rs ................................ (69 Article 15. Remarks on the Formulae. For the purpose of comparison, the formula of D'Arcy and Lampe, for the diameters given in Table 34, have been changed into the form: and the values of c are given in Table 34. For the same purpose of comparison the formulae of Kutter (40), is given in the same table. Kirkwood's formula (69), also given, is modern, but it has a, constant co-efficient. Also three of the old formulae are given, namely, BlackwelPs (65), Pronv's (59), and Downing's (i). Almost all the old formulae have constant co-efficients. It was well known to many engineers, that these co- efficients gave too high a velocity for small channels, and too low a velocity for large channels. To remedy this, Leslie (see page 8), gave a co-efficient of 100, formula (1), for large and rapid rivers, and a co-efficient of 68, formula (2), for small streams. In the same way Stevenson gave a co-efficient of 96, formula (3), for streams discharging over 2,000 cubic feet per minute, and 69, formula (4), for streams discharging under 2,000 cubic feet per minute. There was no easy curve from one co-efficient to another. It was a sudden in- crease. It is evident that this cannot be correct. An inspection of the old formulas will show that their co- OPEN AND CLOSED CHANNELS. 199 efficients were constant, arid, according to the different authorities, varied from 92.3 to 100. The modern and more accurate formulae have varying co-efficients, whose value increases with the me^ease of the hydraulic mean depth, r. The value of the co-efficient in D'Arcy's formula (51), depends on the hydraulic mean depth, r, and is not affected by the slope; and it is the same with Lampe's formula (57). In Kutter's formula (40), the co-efficient depends not only on the hydraulic mean depth, r, but also, to a less extent, on the slope, s. The co-efficients of the modern formulae increase very much from the small diameters to the large ones, where- as, the old formulae have the same co-efficients for all diameters, being too high for diameters under one foot, and too low for diameters exceeding one foot. For diameters larger than 6 feet there is very little change in D'Arcy's co-efficient, and for very large pipes it does not exceed 113.8. For diameters greater that 10 feet D'Arcy's co-efficient is almost constant. It increases very little more than 113.5, even for a diameter of 16 feet or more, but Kut- ter's co-efficient continues to increase until such a diameter is reached as is never likely to be required in practice. Now, the experiments on which D'Arcy's formula is based were made 011 clean pipes, of the diameters us- ually adopted in practice, flowing under pressure, and under conditions somewhat similar to pipes in actual use, and, therefore, as the experiments were conducted with great accuracy, the results are entitled to the con- fidence of engineers. D'Arcy's experiments did not, however, include pipes of a very large hydraulic mean radius. In one respect he differs from most of the mod- 200 FLOW OF WATER IN ern authorities, inasmuch as the slope has 110 effect 011 the value of the co-efficient of his formula. Kutter ; s formula is derived, not only from experi- ments made on channels with small hydraulic radius, but also on channels with large hydraulic radius, and his co-efficients for very large pipes are, therefore, more likely to agree with the actual discharge than D'Arcy's constant co-efficient of 113.5 for very large pipes. But again, Kutter's formula is open to the objection that it is based 011 experiments made on open channels. I may here remark, although it is only remotely connected with pipe discharge, that Major Allan Cunningham states, as the result of his extensive experiments for four years on the Ganges Canal, that Kutter's formula alone, of all those tried by him, was found generally applica- ble to all conditions of discharge, and that it gave nearer results to the actual velocity than any of the other formula) tried by him. It gave results with a dif- ference from the actual velocity seldom exceeding 5 per cent., and usually much less than that. When we con- trast the wide divergence of the old formulae under varying flow from the actual velocity, with the results obtained by Kutter's formula, it will be seen that the latter is the most accurate formula for channels with large hydraulic mean radius. With reference to D'Arcy's co-efficients not being af- fected by the slope, Neville states: " As long as the diameter of a long pipe continues constant, the velocity (by D'Arcy's formula) is always represented by a given fixed multiple of }/rs, 110 mat- ter how small or great the declivity of the pipe may be. For an inch pipe this multiplier for feet measures is 80.3. ****** " In the excerpt proceedings of the Institution of Civil Engineers, p. 4, 6th Feb., 1855, James Simpson, Presi- OPEN AND CLOSED CHANNELS. 201 dent, in the chair, there is given for the " Colinton pipe " 16 inches diameter, eight or nine years in use, three observations. First, 29,580 feet long, a head of 420 feet, an^ardis- charge of 571 cubic feet per minute. These give v = 6.816 feet = 99.2 i/rJTnearly. Secondly, a length of 25,765 feet, a head of 184 feet, and a discharge of 440 cubic feet per minute; these give v --= 5.252 feet = 96.3 \/rs. And thirdly, a length of 3.815 feet, a head of 184 feet, and a discharge of 1.215 cubic feet per minute; these give v == 14.5 feet = 115 \/rs nearly. In these three examples the diameter, castings and age of the pipes, are the same. Yet it is seen, clearly, that the in- clination affects the multiplier of \/rs which increases with the inclination, s, although M. D'Arcy's formula would make the multiplier the same in each case, and for all inclinations, viz.: v = 110 \/r8." In the formulae of Lampe and Kutter the co-efficients have a steady increase with the increase of the diameter'. K utter' s formula has the great advantage of being easily adapted to a change in the surface of the pipe exposed to the flow of water, by a change in the value of n. It will be seen that the co-efficients of Lampe agree somewhat with Kutter with n = .011. Now, very few engineers, even with the smoothest pipe, use Kutter with n = .011. It is more usual to use n = .013, to provide for the future deterioration of the surface ex- posed to the flow of water. The 48-inch Glasgow water pipes mentioned at page 218 gave at first a discharge more than that given by the old formula), but it gradually diminished, though the pipes still continued to discharge more than the quan- tity given by the old formulae. An inspection of Table 34 will show that for all 202 FLOW OF WATER IN diameters greater than 1 foot 6 inches, Lampe's co- efficients are very much greater than D'Arcy's, for clean pipes, and than Kutter with n = .013. It is, therefore, evident that, for old pipe, Lampe's formula gives too high a discharge. The 48-inch pipe given as an example at page 234 has, by D'Arcy's formula for clean pipes (52), a co-effi- cient = 112.6, and in Table 34 we find that for this pipe, Kutter, with n = .013, has a co-efficient of 116.5. As the pipe gradually deteriorated D'Arcy's co-efficient 112.6, represented the maximum flow. For this pipe Lampe gives a co-efficient = 139.0, being sixteen per cent, in excess of the maximum co-efficient found by experiment. Comparing D'Arcy's and Kirkwood's formulae for tuberculated pipe, the co-efficients of the latter are the greater for all the diameters given. As in the case of clean pipe, D'Arcy's co-efficient for tuberculated pipe increases very little for the large diameters. OPEN AND CLOSED CHANNELS. 203 TABLE 34. Giving the value of c iu the formula v = c^/rs in ten dif- ferent formulas: VALUE OF CO-EFFICIENT c. s y H . W . W . W _ w S b Tuberculated p" 1 fjf 5! II 8| 8-| II 3 - 1 fa, - 05 ! o " H -o Hf ^ o"* <-s 1 cc" CfQ Sgf g-g; 3' B p II ii g I II jf t-j B GO l-h o 'So * STb ^2 ^b H^ O d | 00* ^& 'tr 2. ,S 0* M 4*- -"'"' 7- co "gjo | O5 Hj 1 1 1 VI s ft. in. i p | il : II : II : p 1 ? p" : ? 1 80.3 65.1 47.l! 95.8 97. 100. 54.1 80. 2 92.9 74.8 61.5 95.8 97. 100. 62.5 80. 4 101.7 85.4 77.4: 95.8 97. 100. 68. 4 80. 6 105.3 92.8 87.4: 77.5 69.5 95.8 97. 100. 70.8 80. 1 109.3 106.2 105. 7! 94.6 85.3 95.8 97. 100. 73.5 80. 1 6 110.7 115. 116.1! 104.3 94.4 95.8 97. 100. 74.5 80. 2 111 5 128.5 123.6 111.3 101.1 95.8 97. 100. 74.9 80. 3 112.2 133.2 133.6 120.8 110.1 95.8 97. 100. 75.5 80. 4 112.6 139. 140.4 127.4 116.5 95.8 97. 100. 75.7 80. 5 112.8 145.2 145.4 132.3 121 . 1 95 8 97. 100. 75.9 80. 6 113. 150.4 149.4 136.1 124.8 95.8 97. 100. 76. 80. 7 113.1 155. 152.7 139.2 127.9 95.8 97. 100. 76.1 80. 8 113.2 159.1 155.4 141.9 130.4 95.8 97. 100 76.1 80. 9 113.2 162.7 157.7 144.1 132.7 95.8 97. 100. 76.2 80. 10 113.3 166.1 159.7 146. 134.5 95.8 97. 100. 76.2 80. 11 113.3 169.2 161.5 147.8 136. 2i 95.8 97. 100. 76.2 80. 12 113.3 172.1 163. 149 3 137.7 95.8 97. 100. 76.2 80. 14 113.4 177.3 165.8 152 140.4 95.8 97. 100. 76.3 80. 16 113.4 182.9 168. 154 2 142.1 95.8 97. 100. 76.3 80. 18 113.5 186.1 169.9 156.1 144.4 95.8 97. 100. 76.3 80. 20 113.5; 190. 171 61 157.7 146. 95.8 97. 100. 76.4 80. i i 204 FLOW OP WATER IN Article 16. Values of c and c \/r for Circular Channels Flowing Full. Slopes Greater than i in 2640. According to Kutter's formula, the value of c, the co-efficient of discharge, is the same for all slopes greater than 1 in 1000, that is, within these limits, c is constant. We further find that up to a slope of 1 in 2640 the value of c is, for all practical purposes, constant, and even up to a slope of 1 in 5000 the difference in the value of c is very little. This is well exemplified in Table 35, which is compiled from Table 19. TABLE 35. Giving the value of c for different values of \/r and s in Kutter's formula, with n = .013 SLOPES. 1 iu 1000 1 in 2500 1 in 3333. 3 1 in 5000 c c c c .6 93.6 91.5 90.4 8S. 4 1. 116.5 115.2 113.2 113. C 2. 142.6 142.8 141.1 141.2 An inspection of the values of c in Tables 15 to 27, will show the slight difference in the value of c up to a slope of 1 in 5000. In Kutter's formula the value of c is found from an equation involving the values of r, n and s } so that any change in the value of s would cause a change in the value of c, but as the influence of s on the value of c, as shown above, is not very marked in such slopes as are usually adopted for pipes, sewers and conduits, the value of the co-efficient c has been computed for one slope, that is 1 in 1000, or s = .001. The value of the OPEN AND CLOSED CHANNELS. 205 co-efficient for all channels, open and closed, is practically constant for all values of s with a steeper slope than 1 in 1000. For natter slopes than 1 in 1000, up to even 2 feet per mile, or 1 in 2640, the tables give results show- ing a maximum error in the case of a sewer 2 feet in diameter, and n .015, of less than two per cent., and in the case of a sewer 8 feet in diameter, less than one- half per cent.; therefore, for all practical purposes, the tables are sufficiently accurate. Article 17. Construction of Tables for Circular Chan- nels. The plan on which these tables are constructed will be briefly stated here, and their use will be fully explained in Article 26, page 231. The author has computed the value of c for different sizes of channels and different values of n, from his sim- plified form of Kutter's formula (73). By this means the complicated form of Kutter's formula (40) is re- duced to the Chezy form of formula: v = c \/r X v/ 8 In a similar way, the author has reduced the compli- cated formulae of D'Arcy (51) and (53), to forms better adapted to computations, formulae (52) and (54) and by the latter formulae, the values of c have been com- puted. The values of r and a being given, and the values of c computed, the values of the factors c yr and ac\/r are computed and tabulated from Table 48 to Table 69, inclusive. These tables are all that is neces- sary for the rapid solution of all problems relating to pipes, sewers and conduits, by the formulae of Kutter and D'Arcy. The author was the first to use the v/s as 20G FLOW OF WATER IN a separate factor , and its use has simplified the application of the other factors very much. We have: v c \/r X v/ 6 ' and, therefore, Q = ac-\/r X i/s By selecting the proper factors and using the required formula (41) to formula (50), any problem relating to pipes, sewers and conduits, can be solved rapidly. Article 18. The Tables as a Labor Saving Machine. In order to show the utility of these tables as a labor saving machine, and also their correctness, an instance is given of the computation of discharge from sewers. A few years since a report was published on the sew- erage of Washington, D. C., by Captain F. V. Greene, U. S. Engineers. In this report a table is given show- ing the discharge of circular and egg-shaped sewers with n = .013, computed by Kutter's formula. Table 36 given below shows about half of the table given in Captain Greene's report, and in parallel columns is also given the discharge as computed by the tables in this work. The discrepancies are caused by Captain Greene having used 41.66 instead of 41.6 on the right hand side of formula (40). It will be seen that the results by the tables in this book are practically the same as those obtained by the use of Kutter's formula (40). It is not an exaggeration to assert, that in the computation of similar tables to these in Captain Greene's report, as much work could be done in one hour by the use of the tables in this book as could be done in twelve or more hours by the use of Kutter's formula (40). OPEN AND CLOSED CHANNELS. 207 TABLE 36. Giving discharge in cubic feet per second of circular and jgg-shaped sewers, based on Kutter's formula, with n = .013. DISCHARGE ix CUBIC FEET PER SECOND Dimensions of Slope 1 in 100 Slope 1 in 200 Slope 1 in 300 - By Kut- ter's form- ula. By Flynn's Tables. By Kut- ter's formula By Flynn s Tables. By Kut- ter's formula By Flynn's Tables. 1' 0" circular. 3.39 3.35 2.40 2.37 1 96 1.93 V 3" 6.25 6.19 4 42 4.37 3.61 3.57 1' 6" 10.35 10.21 7.32 7.22 5.97 5.9 r 9" 15.78 15.57 11.16 11.01 9.10 8.99 2 / 0" 22.68 22.46 16.04 15.88 13.08 12.97 10' 0" 1673.7 1670.9 1183.3 1181.5 965.7 964.7 20' 0" 10240. 10256 . 7240. 7252. 5909. 5921. EGG-SHAPED. 2 / 0"x3 / 0"... 36.69 36.49 25.94 25.8 21.17 21.06 2' 6" x 3' 9". . . 65 85 66.8 46.56 47.23 39.99 38.57 3' 0" x 4' 6". . . 109.84 109.2 77.66 77.21 63.38 63.04 3' 6" x 5' 3". . . 167.3 165.4 118.3 117. 96.5 95.5 4' 0" x 6' 0" ... 240. 236.6 169.7 167.4 138.5 136.8 4'6"x6' 9"... 325. 324. 229.8 229.1 187.5 187.1 5'0"x7 / 6"... 429.2 429.1 303.5 303.4 247.7 247.7 In Table 37, with n = .011, the same accordance is shown by the use of Kutter's formula (40) and Flynn's tables. TABLE 37, Giving the velocity in feet per second in pipes, sewers, con- duits, by Kutter's formula, with n = .011. Diame- ter in feet Slope 1 in Velocity by Kut- ter's formula (40) Velocity by Flynn's Tables Diame- ; ter in feet Slope 1 in Velocity by Kut- ter's formula (40) Velocity by Flynn's Tables. 1 66 5.34 5.25 4 66 ' 14.44 14.34 1 2640 .81 .83 4 2640 2.24 2.27 2 66 8.91 8.8 6 66 18.91 18.82 2 2040 1.36 1.39 6 2640 2.94 2.98 208 FLOW OF WATER IN It will be seen that the results as given by the rapid method of the tables may, for all practicable purposes, be taken as identical to those given by the use of the troublesome and tedious formula (40). Should the engineer, however, prefer to use the for- mula (40), even then the tables will give a ready means of checking the computations. Article 19. Discussion on Kutter 's Formula. The following notes by the Author on Kutter's formula (40), with reference to Molesworth's Kutter, were pub- lished in the Transactions of the Technical Society of the Pacific Coast of January, 188G. They are inserted here as they contain some useful information on Kut- ter's formula (40). In that admirable and useful work, "Moles worth's Pocket Book of Engineering Formulae," (21st edition), a modified form of Kutter's formula for pipe discharge is given, in which the value of .00281 18.1 -f - .(70) c z / .00281 1 + .026(41.6 + -^ For facility of reference I will call this formula Moles- worth's Kutter (70). No mention is made by Molesworth of the value of n, that is, as to whether the formula is intended to apply to pipes having a rough or a smooth inner surface. An in- vestigation will, however, show that his formula is accurately applicable to only one diameter, that is, to a diameter of one foot and with the value of -M .013. The value of the term ^ in formula (40), is given Vr OPEN AND CLOSED CHANNELS. 209 by Molesworth in. formula (70), as a constant quantity, and =.026, whereas, in fact, it is a variable quantity, its value -with the same value of n changing with every change in the hydraulic mean radius or^ diameter of pipe. Now, assuming the value of n taken by Molesworth to be =.013 and substituting this value for n in Kutter's formula (40), we have: 1.811 00281 c = 181 + / .00281 but by Molesworth's Kutter (70) \/r ?'=.25, and as the hydraulic mean depth of a pipe is one-fourth of the diameter, If we substitute in formula (71) for \/r its value 0.5, we have: 181 + _;..0281 s 1 + .026(41 .6+^i 1 ) . which is Molesworth's Kutter (70). It is therefore apparent that, no matter what the value of n may be, Molesworth's Kutter (70), does not give 14 210 FLOW OF WATER IN the same results as Kutter's formula (40), as it gives a constant co-efficient of velocity, c, for all diameters hav- ing the same slope and the same value of n. Kutter's formula (40), has certain peculiarities which are wanting in Molesworth's Kutter, and an investiga- tion will show that Molesworth's Kutter differs materially from Kutter's formula (40), and that its application, ex- cept to one diameter, is sure to lead to serious error. I will briefly explain: 1. By Kutter's formula (40), the value of c, or the velocity, changes with every change in the value of r, s, or n, and with the same slope and the same value of n, the value of c increases with the increase of r, that is, with the increase in diameter. It is on this variability of its co-efficient to suit the different changes of slope, diameter and lining of channel, that the accuracy of Kutter's formula depends. By Molesworth's Kutter a change in the diameter, other things remaining the same, does not affect the value of c. With the same slope the value of c is constant for all diameters. As an instance, with a slope of 1 in 1000: FORMULAE. 6 inches diameter. 20 feet diameter. c = By Kutter's formula (40) Molesworth's Kutter (70) 69.5 85.3 146. 85 3 It will thus be seen that the value of c by Kutter's formula (40), when s = .001, has a large range, from 69.5 to 146.0, showing an increase of 111 per cent, from a diameter of 6 inches to a diameter of 20 feet. It will be further found that Molesworth's formula gives the value of c, and therefore the value of the velocity and discharge, too high for diameters less than OPEN AND CLOSED CHANNELS. 211 one foot, and too low for diameters above one foot, and the more the diameter differs from one foot the greater is the error. In these respects it follows the errors of the old formulae. 2. According to Kutter's formula (40) the value of c increases with the increase of slope for all diameters whose hydraulic mean depth is less than 3.281 feet one metre and with a hydraulic mean depth greater than 3.281 feet, an increase of slope gives a diminution in the value of c. The small table, herewith given, shows this: TABLE 38. Giving the co-efficients of discharge, c, in circular pipes of different diameters and different grades with n = .013. FORMULA. 12 feet diameter. 20 feet diameter. 1 in 1000 . 1 in 40. i 1 in 1000. Iin40. Molesworth's Kutter c =.. . Kutter's formula c . 85.3 137.7 86.9 137.9 85.3 146. 86.9. 145.7 It will thus be seen that by Kutter's formula (40), when r ~ 3 feet, that is, less than 3.281 feet, an increase in the slope from 1 to 1000 to 1 in 40, causes a slight increase in the co-efficient, but when r is 5 feet, that is, more than 3.281 feet, the same increase in the slope causes a slight diminution in the value of c. By Molesworth's Kutter formula (70), when r = 3 feet, an increase in the slope from 1 in 1000 to 1 in 40 causes a greater proportional increase in the co-efficient than Kutter gives, and when r = 5 feet the value of the co-efficient does not diminish with the increase of slope, but, 011 the contrary, it increases with the increase in slope, and its value is the same as when r = 3 feet. 212 FLOW OF WATER IN 3. By Kutter's formula (40), when the hydraulic mean depth is equal to 3.281 feet, one metre, the value 1 811 of c is constant for all slopes, and is = , which in n -j o-i i this case = 1 ' 011 = 139.31 . .013 Let r -=3.281 feet, and, therefore, i/r = v/3.281 = 1.811, substitute this value in Kutter's formula (40), and we have c = 71.811 1 Q1 1 and . . c = ' , and when n == .013, c = 139.31. This is the only instance, I believe, where Kutter's formula (40) gives a constant co-efficient with a change of slope. By Molesworth's Kutter (70), on the contrary, the value of c changes with every change of slope when r = 3.281. It is evident that Molesworth's Kutter was adopted in order to simplify the application of Kutter's formula (40), but its simplification is of no practical use, as it gives very inaccurate results. As shown above, with the exception of its application to one diameter, the formula is not Kutter's, although in appearance bearing a resemblance to it. However, a modification of Kutter's formula can be made simpler in form than even Molesworth's Kutter (70), and giving results near enough for all practical purposes to those obtained by the use of the more com- plicated Kutter formula (40). OPEN AND CLOSED CHANNELS. 213 The value of c in Kutter's formula (40), with a slope of 1 in 1000, and n =.013 is thus expressed: c .013 ' .001 1 (4 .00281\ .013 i r i \ - 1-^4 .001 Jyf 183.72 1 I / .013\ 1 1 A A A 1 \/ .(72) The following table will show the value of the co- efficient c for several slopes and diameters according to formula (70), (40) and (72). TABLE 39. Giving values of c, the co-efficient of discharge, according to different modifications of Kutter's formula with n = .013. Moles- worth's Kut- ter (70) Kutter's formula (40) c = Flynn's Kutter (72) c = c = 6 inch diameter, slope 1 in 40.... 86.9 71.5 69.5 6 inch diameter, slope 1 in 1000.. 85.3 69.5 69.5 4 feet diameter, slope 1 in 400 ... 87.2 117. 116.5 4 feet diameter, slope 1 in 1000... 85.3 116.5 116.5 8 feet diameter, slope 1 in 700 ... 85.8 130.5 130.5 8 feet.diameter, slope 1 in 2600... 82.9 129.8 130.5 This table shows the close agreement of formula (72) with Kutter's formula (40), and it also shows the inac- curate results obtained by the use of Molesworth's Kut- ter. The first column of this table shows that a formula with a constant value of c = 85, that is: v = 85 \/TS 214 FLOW OP WATER IN will give results differing in an extreme case only 2J per cent, from Molesworth's Kutter, and in the greater num- ber of cases differing only about one per cent. The second column of the table shows the wide range of the co-efficient c by Kutter's formula (40) from 69.5 to 130.5, to suit the different changes in the hydraulic mean depth and slope. The objection to the old formulae was that they gave velocities too high for small pipes and channels, and too low for large pipes and channels. The following table will show that the same inaccurate results are obtained by the use of Molesworth's Kutter (70). TABLE 40. Giving the mean velocity, in feet per second, of pipes of different diameters and grades, with n= .013. Velocity in Feet per Second. Moles- worth (70). Kutter (40). Flynn's Kut- ter (72). 6 inches diameter, slope 1 in 40.. 4.86 4. 3.89 6 inches diameter, slope 1 in 1000 .95 .78 .78 4 feet diameter, slope 1 in 400. . . 4.36 5.85 5.83 4 feet diameter, slope 1 in 1000.. 2.70 3.68 3.68 8 feet diameter, slope 1 in 700... 4.59 6.97 6.97 8 feet diameter, slope 1 in 2600. . 2.30 3.60 3.62 This table shows that there is a wide difference be- tween the velocities obtained by Molesworth's Kutter (70) and Kutter's formula (40), and it further shows that for the slopes usually adopted in practice for pipes, sewers, conduits, etc., that is, for slopes not natter than 2 feet per mile, or 1 in 2640, formula (72) will give velocities that, for all practical purposes, may be consid- OPEN AND CLOSED CHANNELS 215 ered as. almost identical with the velocities obtained by Kutter's formula (40). In Vau Nostraud's Engineering Magazine for September, 1886, is a let- ter on this subject from Mr. Guildford Molesworth, the author ~uf the Pocket Book, of which the following is a copy: To the Editor of Van NostraiuVs Magazine: Mr. Flynn's criticism of my modification of Kutter's formula for pipes has just reached me. Mr. Flynii is quite correct. The formula as it stands in page 25 of the twenty-first edition of my pocket book has an omission of ^/d. As I originally framed it, it stood thus: 181 + Unfortunately, the omission of ^/d escaped my observation in correcting the proofs of this twenty-first edition. Taking the side cases which Mr. Flynn has worked out, a comparison of Kutter's formula and my modification of it for pipes, as corrected, stands thus : Diameter of Pipe. Slope 1 in Kutter. 1 Molesworth. 6 inches 40 71.50 71.48 6 inches 1000 69.50 69.79 4 feet 400 117. 117. 4 feet 1000 116.5 116.55 8 feet 700 130.5 130.68 8 feet 2600 129 8 129.93 The two formulae are thus far substantially identical in results, though differing slightly in form. GUILDFORD MOLESWORTH. Simla. India, May 17, 1886. Article 20. Flynn's Modification of Kutter's Formula. The author has reduced Kutter's formula for slopes up to 1 in 2640, into the simplified form given in for- mula (73). Referring to the simplified form of Kutter's formula 216 FLOW OF WATER IN (72), if we call the numerator on the right hand side of the equation K, for any value of n we have: K and v = -{ i (44.41 X^- .(73) In the following table the value of K is given for the several values of n. TABLE 41. Giving the value of K for use in Flynn's modification of Kutter's formula: n R | n K N K I | n K n K .009 245.63 .012 195.33 .015 165.14 Lois 145.03 .021 130.65 .010 225.51 .013 183.72 .01G 157.6 .019 139.73 .022 126.73 .011 209.05 j.014 137.77 1.017 150.94 .020 134.96 .0225 124.9 To further simplify formula (73), the value of y/V for a large range of diameters will be found in Table (42). If, therefore, in the application of formula (73), with- in the limits of n as given in the table, we substitute for n, K, and \/r, their values, we have a simplified form of Kutter's formula (40). For instance, when ?i = .011, and d = 3 feet, we have: 209.05 44.41 X - .011 .866 \ x Ol'EN AND CLOSED CHANNELS. 217 TABLE 42. Giving values of \/r for circular pipes, sewers and conduits of different diameters: Diamet'r Ft. Ins. Vr in Feet Diamet'r Ft. Ins. x/V in Feet. Diamet'r Ft. Ins. ! Vr in Feet Diamet'r Ft. Ins. -v*- in Feet 5 .323 2 9 .829 5 1 1.127 10 1.581 6 .354 2 10 .842 5 2 1.137 10 3 1.601 7 .382 2 11 .854 5 3 .146 10 6 1.620 8 .408 3 .866 5 4 .155 10 9 1.639 9 .433 3 1 .878 5 5 .164 11 1.658 10 .456 3 2 .890 5 6 .173 11 3 1.677 11 .479 3 3 .901 5 7 .181 11 6 1.696 1 .500 3 4 .913 5 8 .190 11 9 1.714 1 1 .520 3 5 .924 5 9 .199 12 .732 1 2 .540 3 6 .935 5 10 .208 12 3 .750 1 3 .559 3 7 .946 5 11 .216 12 6 .768 1 4 .577 3 8 .957 6 .225 12 9 .785 1 5 .595 3 9 .968 6 3 .250 13 .803 1 6 .612 3 10 .979 6 6 .275 13 3 .820 1 7 .629 3 11 .990 6 9 .299 13 6 .837 1 8 .646 4 . 7 .323 13 9 .854 1 9 .661 4 1 .010 7 3 .346 14 1.871 1 10 .677 4 2 .021 7 6 .369 14 6 1.904 1 11 .692 4 3 .031 7 9 .392 15 1.936 2 .707 4 4 .041 8 .414 15 6 1.968 2 1 .722 4 5 .051 8 3 .436 16 2 2 2 .736 4 6 .061 8 6 .458 16 6 2^031 2 3 .750 4 7 .070 8 9 .479 17 2.061 2 4 .764 4 8 .080 9 .500 17 6 2.091 2 5 .777 4 9 .089 9 3 .521 18 2.121 2 6 .790 4 10 1.099 9 6 1.541 19 2.180 2 7 .804 4 11 1.109 9 9 1.561 20 2.236 2 8 .817 5 1.118 Article 21. D'Arcy's Formulae. M. H. D'Arcy's experiments on the flow of water in new and old cast-iron pipes are the most thorough and elaborate investigations of the kind which have ever been carried out. He demonstrated that the degree of roughness of the wetted surface has an important effect on the discharge of the pipe. M. D'Arcy had observed, in the course of his ex- perience on waterworks, that in proportion to the smoothness of the inner surface of the pipe, so was its 218 FLOW OF WATER IN discharge increased. He had at his disposal ample means to carry out experiments to prove this. He was an engineer eminently fitted to carry out such experi- ments, on account of his great scientific attainments, and his practical experience gained whilst in charge of City Waterworks, and the results of his observations fully justified the confidence placed in his ability. It is to be regretted that his experiments did not ex- tend to large pipes. He made experiments with 22 pipes of cast and wrought iron, sheet iron covered with bitu- men, and lead and glass, but none of them were of large dimensions. His experiments on pipes fully justified his former experience, and Bazin's observations on small open channels gave further testimony to the same effect. The experiments of D'Arcy and Bazin. * were after- wards of great value to Kutter in his hydraulic investi- gations. After the publication of the results of D'Arcy's ob- servations in the French, Mr. J. B. Francis, M. Am. Soc. C. E.f presented his formula) in a form suitable to feet measures. Mr. J. W. Adams, M. Am. Soc. C. E., in Engineering News of March 10th, 1883, writes: "When the Loch Katrine Water Works for Glasgow were being extended some years since, a portion of the distance was carried over low grounds by a cast-iron trough 6| feet deep and 8 feet in width, supported on masonry piers, and giving good opportunity to deter- mine the daily flow. By this and other means it was found that the cast-iron pipes, 4 feet in diameter, which with a fall of 1 in 1056 on the rest of the line, had been computed to carry 21,000,000 gallons, were really dis- * Recherches Hydrauliques. t Transactions American Society of Civil Engineers. Vol. II. OPEN AND CLOSED CHANNELS. 219 charging daily 23,430,000 gallons. The engineer, Mr. Gale, brought the matter to Professor Rankine's atten- tion; who, in a paper and subsequent discussion before the Institution of Engineers of Scotland, Marcli~17th, 1869, uses this language: ' It might be interesting to the Institution to know that there was a formula which agreed exactly with the results of Mr. Gale's experi- ments. Suppose that before these four-feet pipes were laid, the probable discharge had been calculated by D'Arcy's formula, the result would have differed by one jxirt in a thousand, from the actual discharge, which was 23,430,000 gallons daily. This went to show that they now possessed a general formula for the flow of water in pipes, and the resistance to that flow, which applied to large as well as small pipes (it applied to pipes of an inch in diameter), and from Mr. Gale's experiments they would see that it also applied to pipes four feet in diameter.' The Glasgow pipes had been coated with Dr. Smith's process, and were treated as clean pipes and calculated by the formula (for clean pipes). I think that D'Arcy's experiments conducted as they were under circumstances which contributed in every way to inspire confidence. Mr. Francis' labors in presenting this formula to us in English dress, with the prestige grow- ing out of his well-known capacity for careful investiga- tion and computation, and Professor Rankine's indorse- ment of its applicability to all conditions of pipe discharge up to four feet diameter, must be considered as estab- lishing the practical value of this special formula for the flow through iron pipes." Mr. W. Humber, C. E., in his work on "Water Sup- ply/' states: " That which is known as D'Arcy's formula, in pipes of large diameter, appears to approach in its results nearer to the actual discharge than any other, and it was 220 FLOW OF WATER IN the opinion of Professor Rankine, that the resistance decreases to a greater extent in pipes of larger diameter than has been previously supposed. The experiments were made with, and the formula of D'Arcy deduced from, pipes which had been long in use without offering any impediment from incrustation." Example 23 is an illustration of the accuracy of D'Arcy's formula, where the actual discharge from a 48- inch pipe was found to be the same as that given by computing by D'Arcy's formula. It was found, however, that after some time the dis- charge gradually fell off, and, though in the first instance, the amount was 50 per cent, larger than that given by the old formula, still it gradually diminished, though the pipes still continued to discharge more than the amount gained by the old formula. The degree of roughness of the pipe was a measure of its discharging capacity. In a paper presented to the Technical Society of the Pacific Coast, on February 6, 1885, the author simplified D'Arcy's formula (51), into the form of formula (52): /1 55256 d\J 12 This was done in order to obtain a formula adapted to the preparation of a table facilitating the use of D'Arcy's formula. In a similar way the author has simplified D'Arcy's formula (53), for old cast-iron pipe lined with deposit, into the form given in formula (54). Table 48 is for clean cast-iron pipe, and table 49, for old cast-iron pipe lined with deposit. D' Arcy's formula for finding the mean velocity in clean cast-iron pipes. For feet measures D'Arcy's formula for mean velocity in clean cast-iron pipes is: OPEN AND CLOSED CHANNELS. 221 .000001B2 I .00007726 + - and from this we have: . 00000162 \v 2 -I .00007726 + r ) r In order to simplify, substitute for r in feet the diameter d in inches, arid we have / .00000162 X 48\48 v 2 8 = ( 00007726 + j- J j- .-. s = f. 00370848 d+. 00373248 \-^- As the change will riot materially affect the result, Mr. J. B. Francis, C. E., simplifies this into the form 8 = .00371 (d+ 1 \-- (A) \ / d v ( Sc1 * V \ .00371 (d+~l) ) In order, however, to further simplify the equation into the Chezy form of formula, which is the form re- quired for the preparation and use of the tables adopted by the writer, and given in this book, let equation (A) be transformed into one with the diameter d in feet, and it becomes: (\ *,2 12 d + 1 Therefore, for clean iron pipes f 144c? 2 s I 700371 (12 d + 1) but d 2 = 16 r 2 = 16 r X r = 4d X r substitute this value for d 2 in the last equation, and v __ / 144 X 4d X r X s\ { .00371(12^ + 1) J 222 FLOW OF WATER IN Therefore, for feet measures, D'Arcy's formula for ve- locity is simplified into / 155256 - ^ /" X \/rs and putting the first factor on. the right-hand side of the equation = c, we have v == c\/rs c\/r X ]/* 1)' Arcy' s formula for finding the mean velocity in old cast- iron pipes. Mr. J. B. Francis, M. Am. Soc. C. E., has given D'Arcy's formula for the Flow of Water through old cast- iron pipes lined with deposit as: ....................... (B) where s and v have the same values as given at pages 6 and 7, and d = diameter in inches. In order, however, to further simplify the equation into the Chezy form of formula, which is the form re- quired for the preparation and use of the tables, as already stated, let formula (B), be transformed into one with the diameter d in feet, and it becomes: --=.0082 l2d / 144 d 2 . . / 144 d 2 s __ U V0082 12 4- 1/ 0082 (12 44- 1) but d = 4r, and d 2 = d X 4 r, substitute these values in formula (C) for c/ 2 , and: _ / 144 d X 4rs \* ~\.0082(12cM-l)/ and therefore, for feet measures D'Arcy's formula for OPEN AND CLOSED CHANNELS. 223 the mean velocity in old cast-iron pipes lined with de- posit is simplified into the form: /70243.9r/V Viixrr) (1/ and putting the first factor in parenthesis on the right hand side of the equation = c, we have: V C\/TS Article 22. Comparison of the Co-efficients for Small Diameters of the Formulae of D'Arcy, Kutter, Jack- son and Fanning. v = c\/r X \/s In tables 48 to 57 inclusive, the values of the factors of Kutter's formula are not given for diameters less than 5 inches. Mr. L. D'A. Jackson, C. E., in his Hydraulic Manual, states: " For the present, and until further experiments have thrown more light on the subject, it may be assumed that the co-efficient of discharge for all full cylindrical pipes, having a diameter less than 0.4 feet, will be the same as those of that diameter." Although Mr. Jackson's opinion is entitled to great weight, still the facts all tend to prove that the co- efficients of diameters below 5 inches should diminish with the diminution of diameter. The smaller the diameter the more effect will the roughness of the sur- face have in diminishing the discharge. Table 43 shows that Kutter's co-efficient for 5 inches diameter with ??, .011 is 82.9, and therefore, according to Mr. Jack- son, all the diameters from 5 inches to | inch should have a co-efficient of 82.9. This is contrary to the principle of Kutter's formula, the accuracy of which is due to the- fact that, other things being equal, its co- 224 FLOW OF WATER IN efficients vary with the diameter. The following proofs are given in support of the opinion that co-efficients of diameters below r 5 inches should diminish according to the diminution of diameter. TABLE 43. Of co-efficieiits (c) from the formulae of D'Arcy, Kutter, Jackson and Fanning, for small pipes below 5 inches in diameter, v = c\/rs (c) (c) (c) (c) Kutter's co-em- jKutter's co-effi- Fanning's co- Diameter in D'Arcy's co- cient from for- cient recom- efficient for inches. efficient for mula mended by L. clean iron clean pipes. = .on D'A. Jackson. pipes. 8 = .001 1 59 4 32. 82.9 1 65.7 36.1 82.9 1 74.5 42.6 82 9 I 80.4 47.4 82.9 80.4 u 84.8 51.9 82.9 11 88.1 55.4 82.9 88. If 90.7 58 8 82.9 92.5 2 92.9 61.5 82.9 94.8 2J 96.1 66. 82.9 3 91.5 70.1 82.9 96.6 4 101.7 77.4 82.9 103.4 5 103.8 82.9 82.9 1. In Table 43 the co-efficients of Darcy's formula are seen to diminish with the diminution of diameter. At 5 inches diameter the co-efficient is 103.8, and at f inch diameter 59.4. 2. In Table 43 the co-efficients of Farming's formula diminish from 4 inches diameter with a co-efficient of 103.4, to 1 inch diameter with a co-efficient of 80.4. These co-efficients are derived from the mean velo- cities in clean pipes with a slope of 1 in 125 given in Fanning's tables. 3. In Table 43 the co-efficients, as found by Kutter's formula with a slope of 1 in 1000, and n = .011, are for 5 inches diameter, 82.9, and for f inch diameter, 32.0. OPEN AND CLOSED CHANNELS. 225 The facts, therefore, show that the co-efficients dimin- ish from a diameter of 5 inches to smaller diameters, and it is a safer plan to adopt co-efficients varying with the diameter than a constant co-efficient. No- opinion is advanced as to what co-efficients should be used with Kutter's formula for small diameters. The facts are simply stated, giving the results of well-known authors. As the co-efficients of D'Arcy's formula vary only with the diameter, the values of the factors c\/r and ac\/r given in Tables 48 and 49 for D'Arcy's formula, are practically the exact values for all diameters and slopes given, and the results found by the use of the tables will be the same as the results found by using the formula. In Tables 50 to 67, the values of c\/r and ac\/r for Kutter's formula sometimes differ, when the slope is natter than 1 in 1000, by a small quantity from the actual values as found by the use of formula (40). These values by Kutter's formula depend not only on r, but also on n and s, so that a change in any of these three quantities causes a change in the values of c\/r and ac\/r. It is found, however, that the slope of 1 in. 1000 will give co-efficients which practically differ very little from the co-efficients derived from the slopes usually given to lines of pipes, sewers and con- duits. The values of the factors c\/r and ac\/r, from Kutter's formula given in the tables 50 to 67, have been computed for a slope of 1 in. 1000, and they give values of c\/r and ac\/r near enough for practical work. 15 226 FLOW OF WATER IN Article 23. Pipes, Sewers, Conduits, etc., Having the Same Velocity. The columns c\/r in Tables 48 to 57, inclusive, for circular channels, and Tables 59 to 67, inclusive, for egg-shaped sewers, can be used to compare velocities, as, other things being equal, the velocities are proportional to c\/r. The formula: v c^/r X \/.s, is proof of this-. For example, a circular pipe or sewer 4 feet in diame- ter flowing full, with a value of n == .013, and a slope of 1 in 1500, has a mean velocity of 2.988 feet, that is, prac- tically, 3 feet per second. In Table 54 we find that this channel has c\/r 116.5. Now all pipes, under different values of n, of different diameters, having the same grade and the same value of c\/r, will have the same velocity. Again, the slope being equal, we can find, merely by inspection, the dimensions of an egg-shaped sewer, of a different value of n, flowing full, two-thirds full, or one- third full, that will have the same velocity as a circular sewer with a different value of n flowing full. Thus, taking the circular sewer mentioned above of 4 feet in diameter and n = .013, and we want to find the dimensions of an egg-shaped sewer flowing two-thirds full, that, with n .015, and the same grade, will have the same velocity. In Table 66 of egg-shaped sewers flowing two-thirds full and with n =.015, we find opposite a sewer having the dimensions of 4'x6', that c\/r = 116.5, therefore a circular sewer 4 feet in diameter with n = .013, will, with the same slope, have the same velocity as an egg-shaped sewer 4'x6' with n = .015, and flowing two-thirds full. Table 47, giving the values of the hydraulic mean OPEN AND CLOSED CHANNELS. 227 depth, r, of circular pipes, etc., and Table 58, giving the values of r for egg-shaped sewers, can be used with great advantage in a variety of problems in. comparing the velocities in pipes, sewers and conduits. In the following table, given to illustrate what has been just stated, the nearest values of c\/r given in the working tables are inserted: TABLE 44. Circular Pipes, Sewers and Conduits having the same mean velocity and the same grade, but with different diameters and different values of n, based on Kutter's formula: No. of Table Value of n Diameter, Ft. Ins. cVr Slope 1 in 1500 %A Velocity in feet per second. Remarks. 50 .009 2 2 117. .02582 3.021 Circular. 51 .01 2 7 116.8 .02582 3.016 Circular. 52 .011 3 1 117.9 .02582 3.044 Circular. 53 .012 3 6 116.3 .02582 3.003 Circular. 54 .013 4 116.5 .02582 2.988 Circular. . 55 .015 5 1 117.1 . 02582 3.023 Circular. 56 .017 6 3 117.6 .02582 3.036 Circular. 57 .020 8 117.2 .02582 3.026 Circular. The mean velocity of egg-shaped sewers can be com- pared in the same way, or can be compared with circular sewers. Thus, let us find the dimensions of egg-shaped sewers having the same velocity and the same grade as the circular sewers in Table 44, but with different values of n. 228 FLOW OF WATER IN TABLE 45. Egg-shaped sewers having the same velocity and the same grade, but with different dimensions and different values of n : No. of Table Value of n Dimen- sions cV Slope 1 in 1500 vT Velocity in feet per sec- ond. Kemarks. 59 .011 2' 8" x 4' 0" 118. .02582 3.047 Full depth. 60 .011 2' 6" x 3' 9" 119.9 .02582 3.096 f full depth. 61 .011 3' 8" x 5' 6" 116.4 .02582 3.005 i full depth. 62 63 .013 .013 3' 6" x 5' 3" 3' 2" x 4' 9" 117.6 116.5 .02582 .02582 3.036 3.008 Full depth, f full depth. 64 65 .013 .015 4' 10" x 7'3" 4' 4" x 6' 6" 116.5 116. .02582 .02582 3.008 2.995 I full depth. Full depth. 66 .015 4' 0" x 6' 0" 116.5 .02582 3.008 f full depth. 67 .015 6' 2" x 9' 3" 117.3 .02582 3.028 I full depth. Article 24. Pipes, Sewers and Conduits Having the Same Discharge. By an exactly similar method to that adopted for velocities in Article 23, we can use the columns of ac\/r for finding equivalent discharging pipes, sewers and conduits. We can also find the dimensions of a single sewer having a discharge equivalent to that of several other sewers. For example, three circular sewers have, at different times, been constructed to an outfall on a river. The sewers are, respectively, 10, 12 and 18 inches in diameter. The grade is 1 in 300, and their value of n = .013. What must be the dimensions of an egg-shaped sewer that, flowing two-thirds full depth, with the same value of n and the same grade, will have a discharge double that of the three circular sewers mentioned? OPEN AND CLOSED CHANNELS. 229 In Table 54, of circular sewers with n = .013, we find a 10 inch sewer has ac\/r = 20.095 12 inch sewer has ac\/r = 33.497 18 inch sewer has ac\/r = 102.140 Therefore, the three circular sewers ac\/r = 155.732 Now 155.732 X 2 = 311.464, which is the value of ac\/r of the water section of the new sewer. In Table 63 of egg-shaped sewers flowing two-thirds full depth with n = .013, we find opposite a sewer 2' 2" X 3' 3" that aci/r = 317.19, therefore the required sewer is 2' 2" X.3' 3". In order to further illustrate this subject, Table 46 is given. This table further shows the effect of the value of n ; for a pipe 2 feet 2 inches diameter with a value of n = .009, has practically the same discharge as a 2 foot 9 inch pipe with a value of n = .015. TABLE 46. Pipes, Sewers and Conduits, having the same grade and the same or nearly the same discharge, but with different diameters and differ- ent values of n. No. of Table. Value of n. DIAMETER. ac^/r Slope 1 in 1500 v^ Discharge in cubic ft. per second Kemarks. Feet. Inches. 50 .009 2 2 431.5 .02582 11.14 Circular. 51 .01 2 3 421.9 .02582 10.89 Circular. 52 .011 2 5 457.1 . 02582 11.8 Circular. 53 .012 2 6 452.1 .02582 11.67 Circular. 54 .013 2 7 450.5 .02582 11.63 Circular. 55 .015 2 9 451.2 .02582 11.65 Circular. 230 FLOW OF WATER IN In the same manner the discharge of egg-shaped sewers can be compared. The discharge is not exactly the same for each pipe, for the reason that the exact value of ac\/r = 431.5 could not be found opposite the diameters in tables, and, therefore, the nearest value to 431.5 was taken. What has been shown in this and the foregoing articles is sufficient to demonstrate to the practical engineer the rapidity with which problems relating to pipes, sewers and conduits can be solved by the tables in this work. Article 25. Egg-Shaped Sewers. Where the volume of sewage fluctuates, the oval form of sewer is the best adapted with a small discharge, to give a velocity sufficient to prevent the deposit of silt, as its hydraulic mean depth is greater for small volumes of flow than the circular sewer. Fig. 4. Egg-shaped Sewer. The egg-shaped sewer treated of in this work has its depth, or vertical diameter, equal to 3.5 times its greatest OPEN AND CLOSED CHANNELS. 231 transverse diameter, that is, the diameter of top or arch. This form of cross-section of sewer is illustrated in Figure 4. D == AB greatest transverse diameter, that is, the 2 // diameter of top or arch = - o H = CD = depth of sewer or vertical diameter = 1.5 D. TT B = ED = radius of bottom or invert = 6 R AF = radius of sides = H. By reference to Table 69, it will be seen that the value of the velocity of an egg-shaped sewer flowing two-thirds full depth, is always greater than that of the mean ve- locity of the same sewer flowing full depth. The dis- charge, however, is always greater in the sewer flowing full depth. Article 26. Explanation and Use of the Tables. Pipes, Sewers and Conduits. EXAMPLE 21. Given the diameter, length, fall and value of n of a pipe, to find its mean velocity and discharge. An inverted syphon, B, G, D, E, F, measured along the line of pipe, is five miles in length, and its outlet at F is 40 feet below the surface of the reservoir at A. The Fig. 5. Inverted Syphon. pipe is 2 feet in diameter. It is made of sheet-iron, double riveted, dipped in hot asphaltum. This dip 232 FLOW OF WATER IN gives a very smooth surface at first, but to allow for the deterioration of that surface the value of n is taken =.013. What is its mean velocity in feet per second, and the discharge in cubic feet per second? It is well to remember that at no part of its length should the pipe rise above the hydraulic grade line A F. A fall of 40 feet in five miles is equivalent to 8 feet per mile, or 1 in 660. In Table 33, opposite a slope of 1 in 660, we find i/s = .038925. In Table 54, for circular pipes with n =.013, we find a = 3.142, cv/r = 71.49 and ac^/r = 224. 63. Now, to find mean velocity, substitute the values of C]/T and \/s in formula (41), and we have: v = 71.49 X .038925 = 2.783 feet per second. Again, to find the discharge, substitute the values of ac\/r and \/s in formula (45), and we have: Q = 224.63 X .038925 = 8.744 cubic feet per second. As a check on the above we have by formula (45): Q = av substitute the values of a and v above found and we have: Q = 3.142 X 2.783 = 8.744 cubic feet per second, which is the same as the discharge before found. EXAMPLE 22. Given the discharge and cross-sectional dimensions of a rectangular, masonry, Inverted Syphon, to find its grade or fall from surface of water at inlet to its outlet. At page 177 of Irrigation Canals and other Irrigation Works, there is a description of an inverted syphon un- der the Agra Canal, India. The syphon is capable of discharging 2,000 cubic feet per second. It has seven culverts each 6 feet wide and 4 feet deep. The syphon is provided with a floor of massive rough ashlar, the entrance and egress for the torrent being also built of OPEN AND CLOSED CHANNELS. 233 large stone. The culverts are covered with large stones bolted down to the piers. The length of the syphon is assumed at 200 feet. From the description given of the surface of the syphon exposed to the flow of water, we may assume its value of n .017 (see page 19). The total discharge being 2,000 cubic feet per second, therefore, each of the seven syphons has to discharge 286 cubic feet per second. The area of one culvert = 6' X 4' == 24 square feet. Q 286 1 . v = - = = 12 feet per second nearly. CL LtQ. r = = 1.2 .-.^ = 1/0= 1.1 nearly. Under a slope of 1 in 1000 and opposite \/r = 1.1 in Table 21, page 132, we find c\/r = 98.4. Now substitute this value of CI/T and also the value of v in formula (43), and we have: The nearest value to this, in Table 33, is .122169 opposite a slope of 1 in 67, but as the total length is 200 feet .*. _ = 3 feet nearly, being the head required to generate a velocity of 12 feet per second. This head of three feet can be given to the culvert in three ways: 1st. The culvert having a level floor, the water will head up three feet on the upper side, the pipe being under pressure. 2d. A fall of three feet is given to the floor of the culvert in its length of 200 feet. 3d. A less fall than three feet is given to the floor in its length of 200 feet, and, in addition to this, sufficient heading takes place on the upper side to give the re- quired velocity. 234 FLOW OF WATER IN In so short a channel, an addition should be made to the head to generate such a high velocity as twelve feet per second, but as the flood water of the torrent arrives at the inlet of the syphon with a high velocity, a few inches additional to the head will suffice for this. There is even a quicker method than that given above for finding the head approximately. For the same area of channel, a circle has the greatest hydraulic mean depth, and, therefore, requires the least head to give the same velocity. The culvert 6'x4' has a cross-sectional area of twenty-four square feet, and a circular channel of the same area, will require less head to produce the same velocity. We will use Table 56 for circular channels, with n =.017, to find the required head. In Table 56 the nearest area to twenty-four square feet is 23.758 square feet, having a diameter of five feet six inches. In the same line we find c\/r = 107.6. Let us now substitute the value of c\/r and v in for- mula (43). ,/=*= 12 .111524 c\/ r 107 . 6 Now, n Table 33 the nearest value of \/s to this is .111803 opposite a slope of 1 in 80. As the length of the culvert is 200 feet, the head required for a circular chan- nel is 2.5 feet, while that required for the rectangular channel 6'x4' already found, is three feet. EXAMPLE 23. Given the diameter and grade of a Pipe to find the mean velocity and discharge by D' Arcy' s formula (51), for clean cast-iron pipes. Humber, in his work on Water Supply, states: 11 With a 48-inch cast-iron pipe in the Lock Katrine Water Works, having an inclination of 1 in 1056, or five OPEN AND CLOSED CHANNELS. 235 feet per mile, the actual velocity was found to be 3.46 feet per second, and D'Arcy's formula gives practically the same results." Compute the velocity by the tables. In Table 48, computed by D'Arcy's formula for clean pipes, we find opposite 4 feet diameter, that a = 12.566, cv/r = H2.6, and ac^/r = 1414.7. We also find in Table 33 that opposite a grade of five feet per mile \/s = .030773. Let us now substitute value of c\/r and \/s in formula (41), and we have: v == 112.6X- 030773 = 3.46 feet per second, being the same as the actual velocity, and also the same as the velocity obtained by computing by the longer method of D'Arcy's formula (51). Now Q = av = 12.566X3.46 = 43.478 cubic feet per second. As a check on this, let us substitute the value of ac\/r and \/s in formula (45) and we have: Q= 1414.7 X. 030773 =43.535 cubic feet per second-, being practically the same as that found before. EXAMPLE 24. Given the grade, mean velocity and value of n, of a Circular Sewer to find its diameter. The grade of a circular sewer is to be 1 in 480, its mean velocity 4 feet per second, and its value of n = .015. What is the required diameter? In Table 33 we find opposite a slope of 1 in 480 that V/ = .045644 substitute this and the value of v, already given in formula (42). and we have Vs cyr = _ - = 87 . 63 .045644 236 FLOW OF WATER IN Now look out in Table 55 for the nearest value of c\/r to this, which we find to be 87.15 opposite three feet four inches in diameter, which is the diameter required. EXAMPLE 25. Given the discharge, grade and value of n of a Circular Sewer to find its diameter. A circular brick sewer, with a value of n = .015, is to discharge 9 cubic feet per second and to have a grade of 1 in 200. What must its internal diameter be? In Table 33, opposite a slope of 1 in 200, we find \/s = .07071. Now substitute this value and also the value of Q already given in formula (47): ac^/r = ^L.- and we have Vs = 127.28 .07071 In Table 55, with a value of n = .015, the value of ac\/r, nearest to this we find to be 130.58 opposite to which is the diameter of 1 foot and 9 inches which is the diameter required. EXAMPLE 26. Given the diameter, the value of n and the mean velocity in a Pipe, to find its inclination or grade. A sheet-iron, double riveted pipe, 18 inches diameter, with a very smooth interior, and laid in an almost straight line, is to have a velocity of 3 feet per second. Under the above favorable conditions its value of n is assumed equal to .011. What should its slope or grade be by Kutter's formula? In Table 52, with a value of n = .011 the value of c\/r opposite a diameter of 1 foot 6 inches is 71.08. Substitute this value, and also the value of v already given, in formula (43): OPEN AND CLOSED CHANNELS. 237 V/s = - =. and we have cv/r ^= -708- = - 042206 Look out the nearest value of \/s to this in Table 33, and we find it to be .042258 opposite a slope of 1 in 560. This is near enough for all practical purposes. If, how- ever, a greater degree of accuracy is required, we have: l/s = .042206 squaring each side s === .001781346436, and =561. Therefore the slope is 1 in 561. S EXAMPLE 27. Given the diameter, discharge and value of n of a Circular Conduit flowing full to jind the slope or grade. A circular conduit flowing full is to have a diameter of 6 feet, and its value of n is assumed as equal to .017. What must be its slope or grade in order that its dis- charge may be 180 cubic feet per second? In Table 56, with n .017, we find opposite 6 feet in diameter that ac\/r == 3232.5. Substitute this value and also the value of Q in formula (48), and w T e have: V"7= Q = 18Q = .055684 ac]/ T 3232.5 In Table 33 the nearest value of \/s to this is .055470 opposite a slope of 1 in 325. The required slope is, therefore, 1 in 325. EXAMPLE 28. To Jind the diameter in three sections of an Intercepting Seicer, with increasing discharge t the grade or inclination being the same throughout, and the value of n being given. A circular brick sewer has, for 500 feet of its length to 238 FLOW OF WATER IN discharge, flowing full, 10 cubic feet per second, then for 600 feet more it has to discharge 12 cubic feet per second, and again, for 700 feet further, it has to discharge 15 cubic feet per second. The total fall available is 5 feet. Its value of n = .015. What is the required di- ameter and fall of each section? In the total length of 1,800 feet there is a fall of 5 feet, that is at the rate of 1 in 360. In Table 33, opposite a fall of 1 in 360, we find / == .052705. V 8 In this equation substitute the values of Q and s for each section and compute the corresponding values of ac\/r. Now, in the first column of Table 55, with n = .015, and opposite these values of ac\/r we shall find the diameters required. For example: 10 By formula (47): ac\/^ = acy r = .052705 12 .052705 JL5 7052705 = 189.7 = 227.7 1 8 o> 1 a O diam. 2' 0" diam. 2' 2" diam. 2' 4" Now s = ---.'. h = si, therefore, the Fall of first section = d = .002777 X 500. . . . = 1.39 ft. Fall of second section = si = .002777 X 600. . . = 1.67 ft. Fall of third section = ttl .002777 X 700 .'. .= 1.95 ft, Total fall 5.00 ft. We have, therefore, 1st section, diameter 2' 0", fall 1.39 ft. 2d section, diameter 2' 2", fall 1.67 ft. 3d section, diameter 2' 4", fall 1.94 ft. OPEN AND CLOSED CHANNELS. 239 EXAMPLE 29. To find the value of c and n of a Pipe. A tuber culated pipe originally twenty-four inches in diameter, but reduced by tuberculation to a mean diam- eter in the clear of twenty-three inches, and ha\dng_a^ slope of 1 in 1000, is found to discharge 4.5 cubic feet per second. What is its value of c and n? 4 ' 5 = 1.56 feet per second. a 2.885 In Table 33 it will be found that a slope of 1 in 1000 has \/s = .031623, and in Table 47 opposite, a diameter of twenty-three inches the value of r= .479, therefore j/V = .69. Substitute values of v, \/H and \/r in for- mula (50). c = /== ----- and we have Vr X Vs c = - -L 56 - = 7 1.5 .69 X .031623 Now let us look in the tables of the values of c and c\/r, and under a slope of 1 in 1000, and opposite \/r =.7 (which is the nearest given to .69), until we find, in Table 21, under a value of n = .017 that c = 72.6, but by the column of difference it should be .51 less, there- fore, the value of c = 72.09 and n .017. Now, as a check on this, let us find in Table 56 with n= .017, and opposite a diameter 1 foot 11 inches, that ac\/r == 144. Substitute this value and also the value of \/s given above, in formula (45), and we have: Q = ac\/r X \/s = 144X .031623 = 4.55 cubic feet per second, being near enough for all practical purposes. 240 FLOW OF WATER IN EXAMPLE 30. Given the diameter of an old pipe to find the diameter of a neiu pipe to discharge double that of the old pipe. An old cast-iron pipe 3 feet 6 inches in diameter, whose natural co-efficient is assumed = .013, is to be re- placed by a new sheet-iron pipe capable of discharging double that of the old pipe, the slope remaining un- changed. What is the diameter by Kutter's formula of the new pipe? It is to bo dipped in hot asphalt, and its natural co-efficient is assumed .011 Find by inspection in Table 54, with n = .013, the value of ac]/i' opposite 3 feet 6 inches diameter, and it is found to be 1021.1. Then 1021.1 X 2= 2042.2. As the value of n for the new pipe = 011, look out in Table 52 the value of ac\/r nearest to 2042.2 and it is found to be 2072.7 opposite a diameter of 4 feet 3 inches, which is the diameter required. EXAMPLE 31. Given the discharges and grades of a System of Pipes to find the diameters. A system of pipes consisting of one main and two branches, is required to discharge by one branch 15, and by another 24 cubic feet of water per minute, and, there- fore, the main is to discharge 39 cubic feet of water per minute. The levels show the main pipe to have an in- clination of 4 feet in 1000 feet, the first branch 3 feet in 600 feet, and the second branch 1 foot in 200 feet. What should be the diameters of the pipe? The pipe being clean cast-iron pipe, Table 48, derived from D'Arcy's formula (51), will be used in the solution of the problem. The main is to discharge 39 cubic feet per minute, equivalent to 0.65 cubic feet per second, with a grade of 1 in 250. One branch is to discharge 15 cubic feet per OPEN AND CLOSED CHANNELS. 241 minute, equivalent to 0.25 cubic feet per second, with a grade of 1 in 200, and the other branch 24 cubic feet per minute, equivalent to 0.4 cubic feet per second, with a grade of 1 in 200. By inspection, we find in Table 33, that with a grade of 1 in 250 the \/s == .063246 and a slope of 1 in 200 has ^/s =.07071. Now, by formula (47): /- Q acyr = 7=. ' - for main pipe Vs nearest value of ac\/r to this, in Table 48, is 10.852, opposite to which is the diameter, 7 inches. In the same way for the first branch 25 ac\/r = - - = 3.535, and the nearest value f of ac\/r to this is 4.561, corresponding to diameter of 5 inches. For the second branch: 4 ac\/V = -- = 5.657, and the .07071 nearest value of acj/r to this, in Table 48, is 7.3 opposite a diameter of 6 inches. The required diameters are, therefore, for the main pipe 7 inches, for the first branch 5 inches, and for the second branch 6 inches. Although the explanation of this example in the use of the tables may appear somewhat long, still the actual work can be done very rapidly and with little trouble. If a comparison is made of the work required for the solution of this example, as given above, with the work required for its solution by the method of approximation as given in Weisbach's Mechanics of Engineering, from 16 242 FLOW OF WATER IN which the example is extracted, it will be seen that there is a great saving of labor effected by the use of the tables. EXAMPLE 32. To find the dimensions of an Egg-shaped Sewer to replace a Circular Sewer. A circular sewer 5 feet in diameter and 4,800 feet in length has a fall of 16 feet. It is to be removed and re- placed by an egg-shaped sewer with a fall of 8 feet, whose discharge flowing full shall equal that of the circular sewer flowing full, the value of n in each sewer being assumed = .015. A grade of 16 in. 4800 == 1 in 300, and in Table 33 the \/8 corresponding to this is, .057735. In Table 55, opposite 5 feet diameter, the value of ac\/r = 2272.7. Substitute this value and also the value of ]/s in formula (45), and we have: Q = 2272.7 X .057735 = 131.21 cubic feet per second, the discharge of the circular sewer. The egg-shaped sewer is to have a grade of 8 in 4800 = 1 in 600, and in. Table 33 the \/H corresponding to this =.040825. Sub- stitute this value and also the value of \/ A just found in formula (47), and we have: /- Q 131.21 acyr = 3*-. = . . = 3213.9 1/7 .040825 In Table 65 the nearest value of ac\/r to this is 3353, opposite an egg-shaped sewer having the dimensions of 4' 10" X 7' 3", therefore, with a value of n = .015 for both sewers. A circular sewer of 5 feet in diameter, and having a grade of 1 in 300, has the same discharging capacity as an egg-shaped sewer 4' 10" X 7' 3", having a grade of 1 in 600. OPEN AND CLOSED CHANNELS. 243 EXAMPLE 33. To find the diameter of a Circular Seiuer whose discharge flowing full depth shall equal that of an Egg-shaped Sewer flowing one-third full depth. Find the diameter of a circular sewer, with ~n -=^7013, whose discharge flowing full shall equal that of the egg- shaped sewer in. last example, flowing one-third full with n = .015, the slope being the same in each. In Table 67 with n = .015 and ^ full depth and oppo- site the size 4' 10" X 7' 3" we find acy/r = 657.53. Also in Table 54 circular n = .013, the nearest value of ac\/r to this is found to be 674.09 opposite a diameter of 3 feet, which is the diameter of the circular sewer required. EXAMPLE 34. In the same way as in Example 33 , we can find the diameter of a Circular Sewer whose velocity flowing full shall equal the velocity of an Egg-shaped Sewer flowing one-third full depth. EXAMPLE 35. To find the dimensions and grade of an Egg-shaped Sewer flowing full, the mean velocity and dis r charge being given. An egg-shaped sewer flowing full is to have a mean velocity not greater than five feet per second, and is to discharge 108 cubic feet per second. Its value of n is .015. What are its dimensions and grade? By formula (46). a = J?_ = -. = 21.6 square feet. v 5 In column two of Table 65, the nearest area to this is 21.566 square feet opposite the dimensions 4' 4" X 6' 6". In the same line we find the value of c\/r= 116.0, and ac\/r = 2501.4. Substitute this latter value and the value of Q in formula 48, and we have: 1/s = ^= = *, 8 , - .043176, and in table 33. acv/> 2501.4 244 FLOW OF WATER IN the nearest to this, is .043234 opposite a slope of 1 in 535. The sewer required is therefore 4' 4" X 6' 6", and has a slope of 1 in 535. As a check on this work by formula 45, and by substi- tuting the values of a, c\/r and \/s already found, we have : Q = a X c]/r X i/s = 21.6X 116 X .043234 = 108.3 cubic feet per second, being near enough for all practical purposes. EXAMPLE 36. The diameter and grade of a Circular Seiver being given, to find the dimensions and grade of an Egg-shaped Sewer, whose discharge floiuing tico-thirds full depth shall equal that of the Circular Sewer flowing full depth, and ivhose mean velocity at the same depth shall not exceed a certain rate. A circular sewer 6 feet in diameter and with a slope of 1 in 600 is to be removed and to be replaced by an egg- shaped sewer whose discharge flowing at two-thirds of its full depth, shall be equal to that of the circular sewer flowing full depth, and whose mean velocity at the same two-thirds depth shall not exceed five feet per second, the value n in each being = .015. Give the dimensions and slope of the egg-shaped sewer. In Table 55 for circular channels with n .015 and 6 feet in diameter, the value of ac\/r = 37 02 .3 , and in Table 33 opposite 1 in 600, the value of v/s = .040825. Substitute these values in formula (45). C] ac\/r X 1/8 and we get Q = 3702 . 3 X .040825 = 151.15 cubic feet per second as the discharge of the circular sewer. Now OPEN AND CLOSED CHANNELS. 245 substitute this discharge and the velocity given, five feet per second, in formula (46). a = and we get a = = 30 . 23 square feet, the 5 area at two-thirds full depth of the egg-shaped sewer. In Table 66, of egg-shaped sewers flowing two-thirds full depth with n = .015, we find the nearest value of a to this is 30.317 square feet opposite a sewer having the dimensions of 6 feet 4 inches by 9 feet 6 inches. At the same time take out the value of aci/r in the same line and we find it equal to 4811.9. Substitute this value of ac\/r, and also the value of Q, already found in for- mula (48), \/s = Su- and we get ac = - - 031412 - Look out in Table 33, and by interpolation we find the nearest slope to this is 1 in 1015. The egg-shaped sewer required is, therefore, Q' 4" X 9' 6" and the grade 1 in 1015. EXAMPLE 37. To find the dimensions and grade of an Egg-shaped Sewer to have a certain discharge when flowing full, and whose mean velocity shall not exceed a certain rate when flowing two-thirds full depth. An egg-shaped sewer is to discharge 110 cubic feet per second flowing full, and its mean velocity flowing two- thirds full depth is not to exceed 5 feet per second. Find its dimensions and slope, the value of n being taken = .015. 246 FLOW OF WATER IN In an egg-shaped sewer the velocity flowing full is always less than the velocity flowing two-thirds full, therefore, as a first approximation let us assume the ve- locity flowing full at 5 feet per second. a = ^ = - ~ = 22 square feet, the area of the v 5 assumed egg-shaped sewer flowing full, and in Table 65 the nearest size sewer to this is 4' 4" X 6' 6". Now with these dimensions the value of c\/r full depth = 116.0 and Table 66 the value of c\/r two-thirds full depth == 123.1; therefore, we may assume that the velocity of the sewer of the given dimensions flowing full is about six per cent, less than when flowing two-thirds full depth, that is, assuming the velocity at two-thirds full depth = 5 feet per second the velocity at full depth will be about 4.7 feet per second. Substituting this velocity and also the given discharge in formula (46), a = = 23.4 square feet, the area of egg-shaped sewer flowing full. In Table 65, the near- est size opposite to this area is 4' 6" X 6' 9" which is the diameter required for the egg-shaped sewer. At the same time that this size of sewer is found, its value of ae\/r will be found on the same line == 2770. Substi- tute this value and also the value of Q in formula (48), and we have: = .039711. 2770 Look out in Table 33 and the nearest \/s to this is .039684 opposite a slope of 1 in 635. Therefore, the size of the sewer is 4' 6" X 6' 9", and its grade 1 in 635. As a check on the above work by substituting the factors already found, we can find the discharge of the sewer OPEN AND CLOSED CHANNELS. 247 flowing full depth, and also find the mean velocity of the same sewer flowing two-thirds full depth. Q = ac^/r X v/s = 2770 X .039684 == 109.9 cubic feet per second, that is, practically, 110 cubic feet peiLsecond which was required, and v = c\/r X v/s = 126 - 3 X .039684 5.01 feet per sec- ond, that is, practically 5 feet per second, which was re- quired. 248 FLOW OF WATER IN TABLE 47. Giving the value of the hydraulic mean depth r, for Circular Pipes, Con- duits and Sewers. The hydraulic mean depth is equal to one-fourth the diameter of a circular channel. Diam- eter, ft. in. r in feet. Diam- eter, ft. in. r in feet. Diam- eter, ft. in. r in feet. Diam- eter, ft. in. r in feet. I .0078 2 1 .521 4 7 .146 9 3 2.312 .0104 2 2 .542 4 8 .167 9 6 2.375 1 .0156 2 3 .562 4 9 .187 9 9 2.437 1 .0208 2 4 .583 4 10 .208 10 2.5 li .0260 2 5 .604 4 11 .229 10 3 2.562 H .0312 2 6 .625 5 .25 10 6 2.625 It .0364 2 7 .646 5 1 .271 10 9 2.687 2 .0417 2 8 .667 5 2 .292 11 2.750 2* .052 2 9 .687 5 3 1.312 11 3 2.812 3 .063 2 10 .708 ! 5 4 1.333 11 6 2.875 4 .084 2 11 .729 5 5 1.354 11 9 2.937 5 .104 3 .75 5 6 1.375 12 3. 6 .125 3 1 .771 5 7 1 . 396 12 3 3.062 7 .146 3 2 .792 5 8 1.417 12 6 3.125 8 .167 3 3 .812 5 9 1.437 12 9 3.187 9 .187 3 4 .833 5 10 1.558 13 3.25 10 .208 3 5 .854 5 11 1.479 13 3 3.312 11 .229 3 6 .875 6 1.5 13 6 3.375 .250 3 7 .896 6 3 1.562 13 9 3.437 1 .271 3 8 .917 6 6 1.625 14 3.5 2 .292 3 9 .937 6 9 1.687 14 6 3.625 3 .313 3 10 .958 7 1.75 15 3.75 4 .333 3 11 .979 7 3 1.812 15 6 3.875 5 .354 4 1. 7 6 1.879 16 4. 6 .375 4 1 1.021 7 9 1.937 16 6 4.125 7 .396 | 4 2 1.042 8 2. 17 4.250 8 .417 4 3 1.062 8 3 2.062 17 6 4.375 9 .437 4 4 1.083 8 6 2.125 18 4.5 10 .458 4 5 1.104 8 9 2.187 19 4.75 11 .479 4 6 1 . 125 9 2.25 20 5. 2 .5 1 OPEN AND CLOSED CHANNELS. 249 TABLE 48. Circular Pipes, Conduits, etc., flowing under pressure. Based 011 D'Arcy's formula for the flow of water through clean cast-iron pipes. Table giving the value of a, and also the values of the factors c\/r and ac-s/7 7 for use in the formulas; v =-. c\/r X -\A~ au d Q ac\/r X \/s These factors are to be used only for clean cast-iron pipes, flowing under pressure, and also for other pipes or conduits having surfaces of other material equally rough. d = di- ameter in ft. in. a = area in square feet. For ve- locity cVr For dis- charge ac\/r d = di- ameter in ft. in. a = area in square feet. For ve- locity cv/r For dis- charge ac\/r .00077 5.251 .00403 1 10 2 640 75.32 198.83 | .00136 6.702 .00914 1 11 2.885 77.05 222.30 1 .00307 9.309 .02855 j 2 3.142 78.80 247.57 1 . 00545 11.61 .06334 2 1 3.409 80.53 274.53 li .00852 13.68 .11659 i 2 2 3.687 82.15 302.90 H .01227 15.58 .19115 2 3 3.976 83.77 333.07 if .01670 17.32 .28936 | 2 4 4.276 85.39 365.14 2 .02182 18.96 .41357 2 5 4.587 86.89 398.57 2i .0341 21.94 .74786 2 6 4.909 88.39 433.92 3 .0491 24.63 1.2089 2 7 5.241 90.01 471.73 4 .0873 29.37 2.5630 2 8 5.585 91.51 511.10 5 .136 33.54 4.5610 2 9 5.939 92.90 551/72 6 .196 37.28 7.3068 2 10 6.305 94.40 595.17 7 .267 40.65 10.852 2 11 6.681 95.78 639.88 8 .349 43.75 15.270 3 7.068 97.17 686.76 9 .442 46.73 20.652 3 1 7.466 98.55 735.75 10 .545 49.45 26.952 3 2 7.875 99.93 786.94 11 .660 52.16 34.428 3 3 8.295 101 2 839.38 1 .785 54.65 42.918 3 4 8.726 102.6 895.07 1 1 .922 57. 52.551 3 5 9.169 103.8 952.10 1 2 1.069 59.34 63.435 3 6 9.621 105.1 1011.2 1 3 1.227 61 56 75.537 3 7 10.084 106.4 1072.6 1 4 1.396 63.67 88.886 3 8 10.559 107.6 1136.5 1 5 1.576 65.77 103.66 3 9 11.044 108.9 1202.7 1 6 1.767 67.75 119.72 3 10 11.541 110.2 1271.4 1 7 1.969 69.74 137.31 3 11 12.048 111.4 1342.4 1 8 2.182 71.71 156.46 4 12.566 112 6 1414.7 1 9 ! 2.405 73.46 176.66 4 1 13.096 113.7 1489.4 250 FLOW OF WATER IN TABLE 48. Circular Pipes, Conduits, etc., flowing under pressure. Based on D'Arcy's formula for the flow of water through clean cast-iron pipes, for use in the formulae: V and Q = ac^/r X \A d = di- ameter in ft. in. a = area in square feet. For ve- locity Cv/f For dis- charge ac\/r d = di- ameter in ft. in. a = area in square feet. For ve- locity cVr For dis- charge ac\/r 4 2 13.635 115. 1567.8 8 6 56.745 165. 9364.7 3 14.186 116.1 1647.6 8 9 60.132 167.4 10068. 4 14 748 117.3 1729.8 9 63.617 169.8 10804. 5 15.321 118.4 1814.6 9 3 67.201 172 2 11575. 6 15.904 119.6 1901.9 9 6 70.882 174.5 12370. 7 16.499 120.6 1990.1 9 9 74.662 176.8 13200. 8 17 104 121.8 2082.6 10 78.540 179.1 14066. 9 17.721 122.8 2176.1 10 3 82.516 181.4 14967 . 4 10 18.348 124. 2274.1 10 6 86.590 183.6 15893. 4 11 18.986 125.1 2374.8 10 9 90.763 185.7 16856. 5 19.635 126.1 2476.4 11 95.033 187.9 17855. 5 1 20.295 127.2 2580.5 11 3 99.402 190.1 18892. 5 2 20.966 128.3 2689.9 11 6 103.869 192.2 19966. 5 3 21.648 129.3 2799.7 11 9 108.434 194.3 21065. 5 4 22.340 130.4 2912.4 12 113.098 196.3 22204. 5 5 23.044 131.4 3027.8 12 3 117.859 198.4 23379. 5 6 23.758 132.4 3146.3 12 6 122.719 200.4 24598 . 5 7 24.484 133.4 3264.9 12 9 127.677 202.4 25840. 5 8 25 . 220 134.4 3388.9 13 132.733 204.4 27134. 5 9 25.967 135.4 3516. 13 3 137.887 206.4 28456. 5 10 26.725 136.4 3646.1 13 6 143.139 208.3 29818. 5 11 27.494 137.4 3776.2 13 9 148.490 210.2 31219. 6 28.274 138.4 3912.8 14 153.938 212.2 32664. 6 3 30.680 141.3 4333.6 14 6 165.130 216. 35660. 6 6 33.183 144.1 4782.1 15 176.715 219.6 38807. 6 9 35.785 146.9 5255.1 15 6 188.692 223.3 42125. 7 38.485 149.6 5757.5 16 201.062 226.9 45621. 7 3 41.283 152 . 2 6284.6 16 6 213.825 230.4 49273. 7 6 44.179 154.9 6841.6 17 226.981 233.9 53082. 7 9 47.173 157.5 7429.3 17 6 240.529 237 . 3 57074. 8 50.266 160. 8043. 18 254.470 240.7 61249. 8 3 53.456 162.5 8688. 19 283.529 247.4 70154. 20 314.159 253.8 79736. OPEN AND CLOSED CHANNELS. 251 TABLE 49. Circular Pipes, Conduits, etc., flowing under pressure. Based on D Arcy's formula for the flow of water through old cast-iron pipes lined with deposit. Table giving the value of a, and also the values of the factors-rj-v^" and ac\/r for use in the formulae: v = c\/r X -s/^aiid Q = ac\/r X \/s These factors are to be used only for old cast-iron pipes flowing under pressure, and also for other pipes or conduits having surfaces of other material equally rough. Diam- eter in ft. in. a = area in square feet. For ve- locity c^r For discharge ac\/r Diam- eter in ft. in. a = area in square feet. For ve- locity cVr For dis- charge ac\/r 1 . 00077 3.532 .00272 1 9 2.405 49.410 118.83 1 .00136 4.507 .00613 1 10 2.640 50.658 133.74 4 .00307 6.261 .01922 1 11 2.885 51.829 149.53 1 . 00545 7.811 .04257 2 3.142 52.961 166.41 11 .00852 9 255 .07885 2 1 3.409 54.166 184.65 H .01227 10.48 . 12855 2 2 3.687 55.258 203.74 if .01670 11.65 . 19462 2 3 3.976 56 . 348 224.04 2 .02182 12.75 .27824 2 4 4.276 57.436 245 . 60 2i .0341 14.76 .50321 2 5 4.587 58.448 268.10 3 .0491 16.56 .81333 2 6 4.909 59.455 291.87 4 .0873 19.75 1.7246 2 7 5.241 60.544 317.31 5 .136 22 56 3.0681 2 8 5 . 585 61.55 343.8 6 .196 25.07 4.9147 2 9 5.939 62.49 371.1 7 .267 27.34 7 . 2995 2 10 6.305 63.49 400.3 8 .349 29.43 10.271 2 11 6.681 64.42 430.4 9 .442 31.42 13.891 3 7.068 65.35 461.9 10 .545 33.26 18.129 3 1 7.466 66.29 494.9 11 .660 35.09 23 . 158 3 2 7.875 67.21 529.3 1 .785 36.75 28.867 3 3 8.295 68.09 564.6 1 1 .922 38.33 35.345 3 4 8.726 69. 602. 2 1.069 39.91 42.668 3 5 9.169 69.85 640.4 3 1.227 41.41 50.811 3 6 9.621 70.70 680.2 4 1 . 396 42.83 59.788 3 7 10.084 71.55 721.5 5 1.576 44.24 69.723 3 8 10.559 72.40 764.5 6 1.767 45.57 80.531 3 9 11.044 73.25 809. 7 1 . 969 46.90 93.357 3 10 11.541 74.10 855.2 8 2.182 48.34 105.25 3 11 12.048 74.95 903. 252 FLOW OF \YATER IN TABLE 49. Circular Pipes, Conduits, Sewers, etc., flowing under pressure. Based on D'Arcy's formula for the flow of water through old cast-iron pipes lined with deposit, for use in the formulae v = c*/r X \A~ and Q = ac\/r X Vs Diam- eter in ft. in a = area in square feet. For ve- locity c\/r For dis- charge ac^/'T Diam- eter in ft. in. a = area in square feet. For ve- locity c\/r For dis- charge ac\/r 4 12.566 75.73 951.6 8 6 56.745 111. 6299.1 4 1 13.096 76.50 1000.8 8 9 60. 132 112.6 6772.2 4 2 13.635 77.35 1054.6 9 63.617 114.2 7267.3 4 3 14.186 78.12 1108.2 9 3 67 . 201 115.8 7785.2 4 4 14.748 78.89 1163.5 9 6 70.882 117.4 8320.6 4 5 15.321 79.66 1220.5 9 9 74.6G2 118.9 8879. 4 6 15.904 80.43 1279.2 10 78.540 120.4 9460 9 4 7 16.499 81.13 1338.6 10 3 82.516 122. 10CC7. 4 8 17.104 81.90 1400.8 10 6 86.590 123.4 10GCO. 4 9 17.721 82.20 1456.8 10 9 90.763 124.9 11338. 4 10 18.348 83.37 1529.6 11 95.033 126.3 12010. 4 11 18.986 84.14 1597.5 11 3 99.402 127.8 127C7. 5 19.635 84.83 1665.7 11 6 103.869 129.3 13429. 5 1 20.295 85.54 1735.8 11' 9 108.434 130.6 141G9. 5 2 20 . 966 86.30 1809.3 12 113.098 132. 14935 . 5 3 21.648 86.99 1883.2 12 3 117.859 133.4 15727. 5 4 22.340 87.69 1958.9 12 6 122.719 134.8 16545. 5 5 23.044 88.38 2036.6 12 9 127.677 136.1 17380. 5 6 23.758 89.07 2116.2 13 132.733 137.5 1825-2. 5 7 24.484 89.69 2191.5 13 3 137.887 138.8 19140. 5 8 25 . 220 90.38 2279.5 13 6 143.139 140.1 2005G. 5 9 25 967 91.08 2365. 13 9 148.490 141.4 20999. 5 10 26.725 91.77 2452.9 14 153.938 142.7 21971 5 11 27.494 92.39 2540.1 14 6 165.130 145.2 23986. 6 28.274 93.08 2631.7 15 176.715 147.7 26103. 6 3 30.680 95. 2914.8 15 6 188.692 150.1 28335. 6 6 33.183 96.93 3216.4 16 201.062 152.6 30686. 6 9 35.785 98.78 3534.7 16 6 213.825 155. 33144. 7 38.485 100.61 3872.5 17 226.981 157.3 35704. 7 3 41.283 102.41 4227.1 17 6 240.529 159.6 38389. 7 6 44.179 104.11 4601.9 18 254.470 161.9 41199 7 9 | 47.173 105.91 4997.2 19 283.529 166.4 47186. 8 50.266 107.61 5409.9 20 314.159 170.7 53633. 8 3 53.456 109.31 5843.6 1 OPEN AND CLOSED CHANNELS. 253 TABLE 50. Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter's formula, with n .009. Table giving the values of a, and also the values of the factors c\/r and ac\/v" for use in the formulae: v = c\/r X Vs and Q = ac\/r X -^/s These factors are to be used only when the value of n, that is the co- efficient of roughness of lining of channel = .09, as for well-planed tim- ber in perfect order and alignment; otherwise, perhaps .01 would be suit- able. It is also suitable for other channels having surfaces equally rough. Diam- eter in ft. in. a = area in square feet. For ve- locity c\/r For dis- charge ac^r Diam- eter in ft. in. a = area in square feet. For ve- locity CV/F For dis- charge acv/V" 5 .136 35.31 4.803 2 6 4.909 128.8 622.3 6 .196 40.62 7.962 2 7 5.241 131.9 691.3 7 .267 45.70 12.20 2 8 5.585 134.7 752.2 8 .349 50.55 17.64 2 9 5.939 137.3 815.3 9 .442 55.13 24.37 2 10 6.305 140 1 883.4 10 .545 59.49 32.42 2 11 6.681 142.7 953.7 11 .660 64. 42.24 3 7.068 145.4 1027.6 1 .785 68.25 53.60 3 1 7.466 148.1 1105.5 1 1 .922 72.11 66.49 3 2 7.875 150.7 1187.1 1 2 .069 76.06 81.31 3 3 8.295 153.2 1270.9 1 3 .227 79.90 98.03 3 4 8.726 155.8 1359.9 1 4 .396 83.60 116:7 3 5 9.169 158.3 1451 3 1 5 .576 87.38 137.7 3 6 9.621 160.7 1546.3 1 6 .767 90.86 J60.5 3 7 10.084 163.2 1645.4 1 7 .969 94.34 185.7 3 8 10.559 165.6 1749. 1 8 2.182 97.86 213.5 ! 3 9 11.044 168.1 1856.6 1 9 2.405 101. 242.9 1 3 10 11.541 170.6 1969. 1 10 2.640 104.4 275.7 1 3 11 12.048 173.1 2085.6 1 11 2.885 107.7 310.6 4 12.566 175.4 2204.1 2 3.142 110.9 348.4 4 1 13.096 177.6 2326.2 2 1 3.409 U4. 388.7 4 2 13.635 180.1 2455.6 2 2 3.687 117. 431.5 4 3 14.186 182.3 2586.7 2 3 3.976 120. 477.3 4 4 14.748 184.6 2722.5 2 4 4.276 123.1 526.3 4 5 15.321 186.9 2863. 2 5 4.587 125.9 577.7 4 6 15.904 189.1 3008.2 254 FLOW OF WATER IN TABLE 50. Circular Pipes, Conduits, Sewers, etc., flowing full. formula, with n = .009, for use in the formulae: X V~s and Q = ac^/r X Based on Kutter's Diam- eter in ft. in. a = area in square feet. For re- locity c v > For dis- charge ac\/r Diam- eter in ft. in. a = area in square feet. For ve- locity cVr For dis- charge ac^/r 4 7 16.499 191.2 3154.6 9 3 67.201 295.7 19875 4 8 17.104 193.5 3309.5 9 6 70.882 300.4 21296 4 9 17.721 195.5 3465.6 9 9 74.562 305.1 22784 4 10 18.348 197.9 3630.6 10 78.540 309.9 24339 4 11 18.986 200.1 3799.9 10 3 82.516 314.6 25962 5 19.635 202.2 3969.8 10 6 86.590 319.1 27630 5 1 20.295 204.2 4144.7 10 9 90.763 323.5 29365 5 2 20.966 206.5 4329.5 11 95.033 328. 31171 5 3 21.648 208.5 4514.9 11 3 99.402 332.5 33051 5 4 22.340 210.6 4705 4 11 6 103.869 337. 35005 5 5 23.044 212.7 4901 . 1 11 9 108.434 341.3 37006 5 6 23.758 214.7 5102.4 12 113.098 345.5 39079 5 7 24.484 216.6 5303.7 12 3 117.859 349.8 41230 5 8 25.220 218.7 5515.9 12 6 122.719 354.1 43459 5 9 25.967 220.8 5733.7 12 9 127.677 358.2 45733 5 10 26.725 222.8 5956. 13 132.733 362.5 48117 5 11 27.494 224.7 6177.7 13 3 137.887 366.5 50537 6 28.274 226.7 6411.1 13 6 143.139 370.5 53036 6 3 30.680 232.5 7133.1 13 9 148.490 374.5 55619 6 6 33.183 238.3 790.7 14 153.938 378.6 58280 6 9 35.785 243.9 8728. 14 6 165.130 386.4 63805 7 38.485 249.4 9599.6 15 176.715 394.1 69639 7 3 41.283 254.7 10517. 15 6 188.692 401.7 75799 7 6 44.179 260.1 11492. 16 201.062 409.4 82315 7 9 47.173 265.5 12525. 16 6 213.825 416.7 89114 8 50.266 i 270.6 13605. 17 226.981 423.9 96219 8 3 53.456 275.8 14741. 17 6 240.529 431 . 1 103687 8 ,6 56.745 i 280.9 15941. 18 254.470 438.2 111519 8 9 60.132 285.9 17190. 19 283.529 452.3 128254 9 63.617 290.8 18503. 20 314.159 465.7 146322 OPEN AND CLOSED CHANNELS. 255 TABLE 51. Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter s formula, with n = .010. Table giving the values of a, and also the values of the factors c\/r and acv/J 7 for use in the formulas: v = c\/r X \/s and Q = ac-^/r X \/s~ These factors are to be used only where the value of n, that is the co- efficient of roughness of lining of channel = .010, as for plaster in pure cement; planed timber; glazed, coated or enamelled stoneware and iron pipes; glazed surfaces of every sort in perfect order, and also surfaces of other material equally rough. Diam- eter in ft. in. a = area in square feet. For ve- locity cVr For dis- charge ac^/r Diameter in ft. in. a area in square feet. For ve- locity cVr For dis- charge ac^/r 5 .136 30.54 4.154 2 6 4.909 114. 559.6 6 .196 35.23 6.906 2 7 5.241 116.8 612. 7 .267 39.73 10.61 2 8 5.585 119.3 668.3 8 .349 44.02 15.36 2 9 5.939 121.6 722.4 9 .442 48.09 21.25 2 10 6.305 124.2 783.1 10 .545 51.96 28.32 2 11 6.681 126.6 845.8 11 .660 55.97 36.94 3 7.068 129. 911.8 1 .785 59.75 46.93 3 1 7.4(36 131.4 981.2 1 1 .922 63.19 58.26 3 2 7.875 133.8 1054.1 1 2 1.069 66.71 71.31 3 3 8.295 136.1 1128.9 1 3 1.227 70.13 86.05 3 4 8.726 138.5 1208.4 1 4 1.396 73.44 102.5 3 5 9.169 140.7 1289.9 1 5 1.576 76.81 121. 3 6 9.621 142.9 1374.7 1 6 1.767 79.93 141.2 3 7 10.084 145.1 1463.3 1 7 1 969 83.05 163.5 3 8 10.559 147.3 1555.8 1 8 2.182 86.21 188.1 3 9 11.044 149.6 1652.1 1 9 2.405 89.05 214.1 3 10 11.541 151.8 1752.5 1 10 2.640 92.19 243.3 3 11 12.048 154 1 1856.9 1 11 2.885 95.03 274.2 4 12.566 156.2 1962.8 2 3.142 97.91 307.6 4 1 13.096 158.2 2072. 2 1 3.409 100.7 343.4 4 2 13.635 160.4 2187.7 2 2 3.687 103.4 381.3 4 3 14.186 162.5 2305. 2 3 3.976 106.1 421.9 4 4 14.748 164.5 2426.5 2 4 4 276 108.8 465.4 4 5 15.321 166.6 2552 . 2 2 5 4.587 111.41 511. 4 6 15 . 904 168.6 2682.1 256 FLOW OF WATER IN TABLE 51. Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter s formula, with n = .010, for use in the formulae: v c^/r X \/~ and Q == ac^/r X \A~ Diam- eter in ft. in. a = area in square feet. For ve- locity /* d = di- ameter in ft. in. a = area in square feet. For ve- locity cVr For dis- charge ac\/r d = di- ameter in ft. in. a = area in square feet For ve- locity cx/r For dis- charge ac\/r 5 3 21.648 119.7 2590.5 12 113.10 206.5 23352. 5 4 22.340 121. 2702.1 12 3 117.86 209.2 24658 5 5 23.044 122.2 2816.7 i 12 6 122.72 212. 26012. 5 6 23.758 123.5 2934.8 12 9 127.68 214.6 27399. 5 7 24.484 124.8 3056.4 13 132.73 217.4 28850. 5 8 25.220 126. 3177.3 13 3 137.88 220. 30330. 5 9 25.967 127.3 3305.6 13 6 143.14 222.6 31860. 5 10 26.725 128.6 3436.3 13 9 148.49 225.2 33441 . 5 11 27.494 129.7 3566.6 14 153.94 227.8 35073. 6 28.274 131. 3702 . 3 14 3 159.48 230. 36736. 6 3 30.680 134.6 4130.3 14 6 165.13 232.9 38454. 6 6 33.183 138.3 4588 . 3 14 9 170.87 235.4 40221 . 6 9 35.785 141.8 5074.7 15 176.72 237.9 42040. 7 38.485 145.3 5591.6 15 3 182.65 240.5 43931 . 7 3 41.283 148.7 6136.8 | 15 6 188.69 242.8 45820. 7 6 44.179 152. 6717. | 15 9 194.83 245.3 47792. 7 9 47.173 155.5 7333.5 16 201.06 247.8 49823. 8 50.266 158.7 7978.3 1 16 3 207.40 250.3 51904. 8 3 53.456 162. 8658.8 16 6 213.83 252.7 54056 . 8 6 56.745 165.3 9377.9 16 9 220.35 254.9 56171. 8 9 60.132 168.4 10128. 17 226.98 257.2 58387 . 9 63.617 171.6 10917. 17 3 233.71 259.7 60700. 9 3 67.201 174.7 11740. 17 6 240.53 261.9 62999. 9 6 70.882 177.7 12594. 17 9 247.45 264.4 65428. 9 9 74.662 180.7 13489. 18 254.47 266.6 67839. 10 78.540 183.7 14426. || 18 3 261.59 268.9 70346 . 10 3 82.516 186.7 15406. 18 6 268 . 80 271.3 72916. 10 6 86.590 189.5 16412. 18 9 276.12 273.5 75507 . 10 9 90.763 192.4 17462. 19 283.53 275.8 78201 . 11 95.033 195.2 18555. 19 3 291.04 278. 80216. 11 3 99.402 198 1 19694. 19 6 298.65 280.2 83686 11 6 103.87 201. 20879. 19 9 306.36 282.4 86526. 11 9 108.43 203.7 22093. 20 314.16 284.6 I 89423. OPEN AND CLOSED CHANNELS., 265 TABLE 56. Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter's formula with n = .017. Tables giving the value of a, and also the values of the factors Cv/r and use in the formulae: X Q = acv/r X >/" These factors are to be used only where the value of n, that is the co- efficient of roughness of lining of channel = .017, as for brickwork, ashlar and stoneware in an inferior condition; tuberculated iron pipes; rubble in cement or plaster in good order; fine gravel, well rammed, to f inches diameter; and generally the materials mentioned with n = .013 when in bad order and condition, and the surfaces of other channels equally rough. Diameter in ft. in. a = area in sqiiare feet. For velocity q/r For 1 discharge acj/r Diameter ,in ft. in. a area in square feet. For velocity cy7 For discharge acf/r 5 .136 14.55 1.979 6 6 33.183 120.8 4010. 6 .196 16.98 3.329 6 9 35.785 124. 4437.9 7 .267 19.33 5.162 7 38.485 127.1 4893. 8 .349 21.59 7.535 7 3 41.283 130.1 5373.3 9 .442 23.76 10.50 j 7 6 44.179 133.2 5884.2 10 .545 25.84 14.08 7 9 47.173 136.2 6427 . 9 11 .660 28. 18.48 8 50.266 139.2 6995.3 1 .785 30.05 23.60 8 3 53 . 456 142. 7594.1 1 1 .922 31.95 29.46 8 6 56.745 145. 8226 . 3 1 2 1.069 33.90 36.24 8 9 60.132 147. S 8886.4 1 3 1.227 35.80 43.93 9 63.617 150.6 9580 7 1 4 1.396 37.65 52.56 9 3 67.201 153.4 10307. 1 5 1.576 39.55 62.33 9 6 70.882 156. 11061.' 6 1.767 41.31 72.99 9 9 74.662 158.7 11851. 7 1.969 43.07 84.81 10 78.540 161.4 12678. 8 2.182 44.88 97.92 10 3 82.516 164.1 13544. 9 2.405 46.49 111.8 10 6 86.590 166.7 14434. 10 2.640 48.25 127.3 10 9 90.763 169.3 15364. 1 11 2.885 49.92 144. 11 95.033 171.9 16333 2 3.142 51.57 164. 11 3 99.402 174.5 17343. 2 3 3.976 56.32 223.9 11 6 103.869 177 1 18395 2 G 4.909 60.98 299.3 11 9 108.434 179.5 19468. 2 9. 5.939 65.47 388.8 12 113.098 182. 20584. 3 7.068 69.80 493.3 12 6 122.719 186.9 22938. 3 3 8.295 74. 613.9 13 132.733 191.7 25451. 3 6 9.621 78.04 750.8 13 6 143.139 196.4 28117. 3 9 11.044 82.04 906. 14 153.938 201.1 30965. 4 12.566 86. 1080.7 14 6 165.130 205.7 33975. 4 3 14.186 89.79 1273.8 15 176.715 210 2 37147. 4 C 15.904 93.51 1487.3 15 6 188.692 214.7 40510. 4 9 17.721 97.05 1719.9 16 201.062 219.2 44073. 5 19.635 100.6 1977. 16 6 213.825 223.5 47784. 5 3 21.648 104.2 2255 . 8 17 226.981 227.6 51669. 5 6 23.758 107.6 2557 . 2 17 6 240.529 231.8 55762. 5 9 25.967 111. 2882 1 18 254.470 236. 60067. 6 28.274 114.3 3232.5 19 282.529 244.4 69301 6 3 30.680 117.5 3606.8 20 314.159 252 3 79259. 266 FLOW OF WATER IN TABLE 57. Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter's formula with n = .020. Table giving the values of a and r, and also the values of factors c\/r and ac-^/r for use in the formulae: v = c\/r- X \/s~ and Q = ac\/r X %/s" These factors are to be used only where the value of n = .020, as in rub- ble in cement in an inferior condition; coarse rubble rough set in a nor- mal condition; coarse rubble set dry; ruined brickwork and masonry; coarse gravel well rammed, from 1 to 1 inch diameter; canals with beds and banks of very firm, regular gravel, carefully trimmed and rammed in defective places; rough rubble, with bed partially covered with silt and mud; rectangular wooden troughs, with battens on the inside two inches apart; trimmed earth in perfect order, and surfaces of other materials equally rough. diam- a = area For ve- For diam- a = area For ve- For dis- eter in locity discharge eter in locity charge in square cVr acy/r in square cV'r ac\/r ft. in. feet. ft. in. feet. 6 .196 13.56 2.658 6 28.274 95.85 2710.2 9 .442 19.10 8.442 6 6 33.183 101.4 3365 . 6 1 .785 24.30 19.07 7 38.485 106.8 4111.4 1 3 1.227 29.08 35.68 7 6 44.179 112.1 4951. 1 6 1.767 33 66 59.49 8 50.266 117.2 , 5891.5 1 9 2.405 38.01 91.42 9 63 617 127.2 8092.1 2 3.142 42.29 132.9 10 78.540 136.6 10731. 2 3 3.976 46.31 184.1 11 95.033 145.8 13856. 2 6 4.909 50.20 246.4 12 113.098 154.5 17479. 2 9 5.939 54.01 320.8 13 132.733 163. 21639. 3 7.068 57.71 407.9 14 153.938 171.3 20365. 3 3 8.295 61.23 507.9 15 176.715 179 1 31660. 3 6 9.621 64.72 622 7 16 201.062 186.9 37583. 3 9 11.044 68.13 752.4 17 226.981 194 4 44119. 4 12.566 71.50 898.5 18 254.470 201 . 6 51312. 4 6 15 904 77.93 1239.4 19 283.529 208.9 59238. 5 19.635 84.10 1651.2 20 314.159 215.9 67837. 5 6 23.758 90.12 | 2140.8 OPEN AND CLOSED CHANNELS. 267 TABLE 58. Giving the value of the hydraulic mean depth r, for egg-shaped sewers flowing full depth, two-thirds full depth and one-third full depth. Let D = transverse diameter, that is, diameter of top of sewer, then Hydraulic mean depth of sewer flowing full depth D X (L2897._ Hydraulic mean depth of sewer flowing f full depth D X 0.3157. Hydraulic mean depth of sewer flowing full depth = D X 0.2066. r = hydraulic mean r = hydraulic mean depth in feet depth in feet Size Size of Sewer ; i of Sewer 1 Full ! | Full % Full Full f Full i Full Depth ' (jepth ; Depth Depth Depth j Depth ft. in. ft. in. ft. in. ft. in. .1 1 XI 6 .2897 .316 | .207 5 2X 7 9 1.497 1.631 .068 1 2X1 9 .3380 .368 ' .241 5 4X 8 1 545 1.684 .102 1 4X2 .3864 .421 .276 5 6X 8 3 1.593 1.736 .136 1 6X2 3 .4345 .474 .310 5 8X 8 6 1.642 i 1.789 .171 I 8X2 6 .4828 .526 .344 5 10X 8 9 1.690 1.842 .205 1 10X2 9 .5311 .579 .379 6 X 9 1.738 1.894 .240 2 X3 .5794 .631 .413 6 2X 9 3 1.787 1.947 .274 2 2X3 3 .6277 .684 .448 6 4X 9 6 1.835 1.999 .309 2 4X3 6 .6760 .737 .482 6 6X 9 9 1.883 2.052 .343 2 6X3 9 .7242 .789 .517 6 8X10 1.931 2.095 .377 2 8X4 .7725 .842 .551 6 10X10 3 1.980 2.157 .412 2 10X4 3 . 8208 .894 .585 7 X10 6 2.028 2.210 .446 3 X4 6 .8691 .947 .620 7 4X11 2.124 2.315 515- 3 2X4 9 .9174 1.000 .654 7 8X11 6 2.221 2.420 .584 3 4X5 .9657 1.052 .689 8 X12 2.318 2 526 .653 3 6X5 3 1.014 1.105 .723 8 4X12 6 2.414 2.631 .722 3 8X5 6 1 062 1.158 .758 8 8X13 2.511 2.736 .791 3 10X5 9 .111 1.210 .792 9 X13 6 2.607 2 841 .859 4 X6 .159 1 . 263 .826 9 4X14 2.704 2.947 .928 4 2X6 3 .207 1.315 .861 9 8X14 6 2.800 3 052 .997 4 4X6 6 .255 1.368 .895 10 X15 2.897 3.157 2.066 4 6X6 9 .304 1.421 ! .930 10 6X15 9 3.042 3.315 2.169 4 8x7 .352 ! 1.473 .964 11 X16 6 3.187 3.473 2.273 4 10x7 3 .400 1.526 .999 12 XlS 3.476 3.788 2.479 5 X7 6 .449 1.579 1.033 268 FLOW OF WATER IN TABLE 59. Egg-shaped Sewers flowing full depth. = .011. Based on Kutter's formula with Giving the value of a, and also the values of the factors c\/r and ac\/'r for use in the formulae: X Q These factors are to be used only when the value of n = .011 as in plaster in cement with one-third sand in good condition; also for iron, cement, and terra cotta pipes, well jointed and in best order, and also the surfaces of other materials equally rough. The egg-shaped sewer referred to has a vertical diameter equal to 1.5 times the greatest transverse diameter D, that is, the diameter of the top of sewer. Area of egg-shaped sewer flowing full depth = D 2 X 1.148525. Perimeter of egg-shaped sewer flowing full dep'th = D X 3.9649. Hydraulic mean depth of egg-shaped sewer flowing full depth = D X 0.2897. Size of sewer ft. in. ft. in. a = area in square feet For ve- locity c^/r For dis- charge ac\/r Size of sewer ft. in. ft. in a = area in square feet For ve- Fordis- locity ! charge c\/r i ac-v/r 1 XI 6 1 . 1485 58.8 67.5 5 2X 7 9 30.660 182.7 5602 . 1 2X1 9 1.5632 65.9 102.9 5 4X 8 32.669 186.5 6093 5 1 4X2 2.0417 72.7 148.4 5 6X 8 3 34.743 190.2 6607.5 1 6X2 3 2.5841 78.9 204. 5 8X 8 6 36.880 193.8 7150.2 1 8X2 6 3.1903 85.2 272. 5 10X 8 9 39.081 197.6 7722.4 1 10X2 9 3.8602 91.1 351.7 6 X 9 41.347 201. 8312.7 2 X3 4.5941 96.8 444.7 6 2X 9 3 43.676 204.7 8940.8 2 2X3 3 5.3914 102.3 551.7 6 4X 9 6 46 . 068 208. 9582.1 2 4x3 6 6.2529! 107.7 673.3 6 6X 9 9 48.525 211.5 10263. 2 6X3 9 7.1783 112.9 810.6 6 8X10 51.046 215. 10976. 2 8X4 8.1674 118. 964.1 6 10X10 3 53.629 218.3 11709. 2 10X4 3 9.2198 123. 1134.3 7 X10 6 56.278 221.6 12473. 3 X4 6 10.377 127.7 J1325.1 7 4x11 61.764 228.1 14087. 3 2X4 9 11.517 132.5 11526. 7 8X11 6 67.508 234.6 15835. 3 4X5 12.761 137.1 1749.9 8 X12 73.506 240.8 17704. 3 6X5 3 14.069 141.7 1993.3 8 4X12 6 79.758 247.1 19713. 3 8X5 6 15.442 146.1 2255.9 8 8x13 86.268 253.3 21853. 3 10X5 9 16.877 150.4 2538.4 9 X13 6 93.031 259.2 24119 4 X6 18.376 154.7 2843.9 9 4X14 100.049 264.9 26509. 4 2X6 3 19.940 159. 3170.9 9 8X14 6 107.324 270 7 29051 . 4 4X6 6 21.566 162.9 3514.4 10 X15 114.853 276.5 31754. 4 6x6 9 23.258 167. 3885.8 10 6x15 9 126.625 284.7 36058. 4 8x7 25.013 171. 4279.1 11 X16 6 138.972 292.9 40707. 4 10x7 3 26.830 174.9 4694.3 12 X18 165.388 308.7 51051. 5 X7 6 28.713 179. 5140.6 OFKN AND CLOSED CHANNELS. 269 TABLE 60. Egg-shaped Sewers flowing two-thirds full depth. Based on Ktitter's formula with n = .011. Giving the value of a, and also the values of the factors c\/r" and ac\/r for use iii the formulae: v = c\/r X \A and Q = ac\/r X \S& The egg-shaped sewer referred to has a vertical diameter 1.5 times the greatest transverse diameter, Z>, that is, the diameter of the top of sewer. A.rea of egg-shaped sewer flowing two-thirds full depth Z> 2 X 0.755825. Perimeter of egg-shaped sewer flowing two-thirds full depth = D X 2.3941. Hydraulic mean depth of egg-shaped sewer flowing two-thirds full depth = D X 0.3157. 1 1 a area For ve- Fordis- a=area For ve- For dis- Size Size of Sewer m 1 locity 1 charge of Sewer in locity charge square Cv/r j ac\/r square ^- ac\/r ft. in. ft. in. feet \ \ ft. in. ft. in. feet 1 Xl 6 .7558 62.71 47.40! 5 2x 7 9 20.176 193.1 3896.2 1 2X1 9 1.0287 70.26 72.27 5 4X 8 21.498 197.2 4239.5 1 4X2 1 . 3436 77.27 103.8 5 6X 8 3 22.864 201. 4596.7 1 6X2 3 1.7005 84 04 142.9 5 SX 8 6 24.269 204.9 4972.8 1 8X2 6 2.0994 90.63 190.3 5 10X 8 9 25.718 208.6 5364.3 1 10X2 9 2.5402 96.79 245.9 6 X 9 27.210 212.3 5776.3 2 X3 3.0232 102.9 311.2 6 2X 9 3 28.742 216. 6208.8 2 2x3 3 3.5480 108.6 385.4 6 4X 9 6 30.317 219.7 6660.6 2 4x3 6 4.1149 114.2 469.9 6 6X 9 9 31.933 223.4 7133.6 2 6X3 9 4.7237 119.9 566.6 6 8X10 33.592 226.9 7622.3 2 8X4 5.3746 125.2 672.9 6 10X10 3 35.292 230.4 8132.3 2 10X4 3 6.0674 130.3 790.6 7 X10 6 37.035 234. 8670.0 3 X4 6 6.8022 135.3 920.5 I 7 4X11 40 . 646 240.8 9789.8 3 2X4 9 7.5790 140.4 1064.1 7 8X11 6 44.426 247.5 10988. 3 4X5 8.3970 145.2 1219.3 8 X12 48.372 254.1 12293. 3 6X5 3 9.2585 149.8 1387.5 8 4X12 6 52.487 260.6 13679. 3 8X5 6 10.161 154.6 1570.8 8 8X13 56.771 266.9 15154. 3 10X5 9 11.106 159.2 1767.7 9 X13 6 61.222 273.3 16731. 4 X6 12.093 163.7 1979.6 9 4X14 65.840 279.4 18397. 4 2X6 3 13.122 168.1 2205.5 9 8X14 6 70.628 285.3 20154. 4 4X6 6 14.192 172.5 2448. 10 X15 75.582 291.3 22018. 4 6X6 9 15.305 176.7 2705.3 10 6X15 9 83.330 300.1 25007. 4 8X7 16.460 181.1 2981.6 ! 11 X16 6 91.455 308.7 28233. 4 10X7 3 17.656 185. 3266.2 |12 X18 108.838 325.1 35387. 5 X7 6 18.895 189. 3571.8 270 FLOW OF WATER IN TABLE 61. Egg-shaped Sewers flowing one-third full depth. Based on Kutter's formula with n = .011. Giving the value of a, and also the values of the factors c\/r and ac\/r for use in the formulae: v c\/r X %/" and Q = ac^/r X \/s~ The egg-shaped sewer referred to has a vertical diameter 1 .5 the greatest transverse diameter, Z), that is, the diameter of the top of the sewer. Area of egg-shaped sewer flowing one-third full depth = >' 2 X 0.284. Perimeter of egg shaped sewer flowing one-third full depth =D X 1 .3747. Hydraulic mean depth of egg-shaped sewer flowing one-third full depth = D X 0.2066. Size of Sewer ft. in. ft. in. a = area in square feet For ve- locity cVr i For dis- charge ac\/r Size of Sewer ft. in. ft. in. a area in square feet. For ve- locity C% /7 For dis- charge ac\/r XI 6 .2840 45.72 12.98 5 2X 7 9 7.5812 146.5 1110.6 2X1 9 .3865 51.39 19.89 5 4X 8 8.0782 149 7 1209.1 4X2 .5049 56.74 28.65 5 6X 8 3 8.5910 152.7 1311.8 6X2 3 .6390 61.89 39.55 5 Sx 8 6 9.1196 155.7 1420.3 8X2 6 .7889 66.90 52.78 5 10X 8 9 9.6639 158.8 1534.4 10X2 9 .9545 71.58 68.36 6 X 9 10.224 161.6 1652.4 2 X3 1 . 1360 76.26 86.63 62x9 3 10.800 164.6 1778.1 2 2x3 3 1.3332 80.71 107.6 6 4X 9 G 11.391 167.5 1908.1 2 4X3 6 1.5462 85.28 131.8 ! 6 6X 9 9 1 1 . 999 170.4 2044.3 2 6X3 9 1.7750 89.42 158.7 6 8X10 12.622 173.3 2187. 2 8X4 2.0195 93.42 188.7 6 10X10 3 13.261 176. 2334.7 2 10X4 3 2.2799 97.50 222.3 7 X10 6 13 916 178.9 2489.4 3 X4 G 2.5560 101.6 259.8 7 4x11 15.273 184.2 2813.5 3 2X4 9 2.8479 105.4 300.2 7 8X11 C> 16.693 189.4 3161 9 3 4X5 3.1556 109.1 344.5 8 X12 18.176 194.8 3541.7 3 6X5 3 3.4790 112.7 392.3 8 4X12 6 l'J.722 199.9 3942.3 3 8X5 6 3.8182 116.4 444.4 | 8 8X13 21.331 204.9 4370.8 3 10X5 9 4.1732 120.1 501.1 ! 9 X13 6 23.004 209.9 4829.6 4 X6 4 . 5440 123.6 561 5 i 9 4X14 24.739 214.8 5314 8 4 2X6 3 4.9306 127. 626.3 9 8X146 26 538 219.5 5825 3 4 4X6 6 5.3329 130.3 694.9 10 X15 28.400 224.2 6366.4 4 6X6 9 5.7510 133.6 768.6 10 6x15 9 31.311 231.2 7239.6 4 8X7 6.1849 137. 847.4 1 11 X16 6 34.364 237 . 9 8176. 4 10X7 3 6.6346 140.4 931.5 12 X1S 40.892 251.3 10277. 5 X7 6 7.100 143 3 1017.8 OPEN AND CLOSED CHANNELS. 271 TABLE 62. Egg-shaped Sewers flowing full depth. Based on Kutter's formula with n = .013. Giving the value of a, and also the values of the factors c\/3" and ac\/r for use in the formulae: v = c\/r X -N/S and Q = ac\/r X \A The factors are to be used only where the value of n, that is the co-effi- cient of roughness of lining of channel = .013 as in ashlar and well laid brickwork; ordinary metal; earthenware and stoneware pipe, in good con- dition but not new; cement and terra cotta pipe not well jointed nor in perfect order, and also plaster and planed wood in imperfect or inferior condition and generally the materials mentioned with n = .010 when in imperfect or inferior condition and also the surfaces of other materials equally rough. The egg-shaped sewer referred to has a vertical diameter equal to 1.5 times the greatest transverse diameter, D, that is, the diameter of the top of sewer. Area of egg-shaped sewer flowing full depth = 7> a X 1.148525. Perimeter of egg-shaped sewer flowing two-thirds full depth = D x 3.9649. Hydraulic mean depth of egg-shaped sewer flowing one-third full depth = D X 0.2897. a=area For ve- For dis- a=area For For dis- Size of Size of Sewer. in square locity c^/r charge ac-^/r Sewer. in square ve- locity charge ac\/r ft. in. ft. in. feet. ft. in. ft. in feet. cVr 1 XI 6 1.148J 47.58 54.653 5 2X 7 9 30.66 152.5 4677.4 1 2X1 9 1.563 53.46 83.585 5 4x 8 32.669 155.8 5091.4 1 4x2 2.041 59.19 120.83 5 6X 8 3 I 34.743 159. 5523.7 1 6X2 3 2.584 64.44 166.53 5 8X 8 6 i 36.88 162.1 5980.5 1 8x2 6 3.19 69.74 222 .48 5 10X 8 9 39.081 165.3 64G2.4 1 10X2 9 3.86 74.68 288.27 6X91 41.347 168.3 6960.1 2 X3 4.594 79.42 364.85 6 2X 9 3 43.676 171.5 7490.3 2 2X3 3 5.391 84.12 453.56 6 4X 9 6 46.068 174.3 8032.2 2 4X3 6 6.253 88.64 554.29 6 6X 9 9 48.525 177.4 8607.6 2 6X3 9 7.178 93.06 667.99 6 SxiO 51.046 180.4 9210.5 2 8X4 8.167 97.40 795.52 6 10X10 3 53.629 183.3 9830.4 2 10X4 3 9.22 101 6 937.06 7 XlO 6 56.278 186.1 10476. 3 X4 6 10.337 105.6 1092.2 7 4X11 61.764 191.7 11841. 3 2X4 9 11.517 109.7 1264.1 7 8X11 6 67.508 197.3 13322. 3 4X5 12.761 113.7 1451.6 8 X12 73.506 202.7 14903. 3 6X5 3 14.069 117.6 1654.5 8 4X12 6 79.758 208.1 16601. 3 8X5 6 15.442 121 4 1874.5 8 8X13 86.268 213.4 18413. 3 10X5 9 16.877 125.1 2110.8 9 X13 6 93.03 218.5 20331 . 4 X6 18.376 128.8 2366.6 j 9 4X14 100.049 223.4 22356. 4 2X6 3 19.94 132.4 2639.8 9 8X14 6 107.324 228.4 24514. 4 4X6 6 21.566 135.7 2927.5 10 X15 114.853 223.4 26808. 4 6X6 9 23 258 139.3 3239.6 10 6X15 9 126.625 240.6 30471. 4 8X7 25.013 142.7 3569.6 11 X16 6 138.972 247.7 34431. 4 10X7 3 26.83 146. 3917 12 X18 IG5.388 261.4 i3237. 5 X7 6 28.713 149.4 4291.2 272 FLOW OF WATER IN TABLE 63. Egg-shaped Sewers flowing two-thirds full. Based ou Kutter's formula with n = . 013. Giving the value of a, and also the values of the factors c\/r and ac\/r for use in the formulae: v = c-v/r X s/Fand Q = ac^/r X \/s The egg-shaped sewer referred to has a vertical diameter 1.5 times the greatest transverse diameter, Z>, that is, the diameter of the top of sewer. Area of egg-shaped sewer flowing, two-thirds full depth = D 2 X 0.755825. Perimeter of egg-shaped sewer flowing two-thirds full depth = D X2.3941. Hydraulic mean depth of egg-shaped sewer flowing two-thirds full depth = Z> X 0.3157. Size of sewer. ft. in. ft. in. a=area in square feet. For ve- locity cVr For dis- ! i charge ac-^/r Size of sewer. ft. in. ft, in. a=area in square feet. For ve- locity c\/r For dis- charge ac\/r 1 XI 6 .756 50.83 38.42 5 2X 7 9 20.177 161 5 3258.4 1 2X1 9 1.029 57.12 58.76 5 4X 8 21.498 165. 3547 . 8 1 4X2 1.344 63. 84.65 5 6X 8 3 22.863 168.3 3848.8 1 6X2 3 1.701 68.7 116.82 5 8X 8 6 24.270 171.7 4166.3 1 8X2 6 2.099 74.24 155.86 5 10X 8 9 25.718 174.8 4496 . 8 1 10X2 9 2.540 79.42i 201.74 6 X 9 27.21 178. 4844 . 9 2 X3 3.023 84.59 255.73 6 2X 9 3 28.743 181.3 5210.9 2 2X3 3 3.548 89.4 317.19 6 4X 9 6 30.317 184.5 5603.7 2 4X3 6 4.115 94.14 387.38 6 6X 9 9 31.933 187.7 5992.9 2 6X3 9 4.724 98.97 467.52 6 8X10 33.592 190.7 6406.4 2 8X4 5.375 103.5 556.2 6 10X10 3 35.292 193.7 6837.9 2 10X4 3 6.067 107.8 654.45 7 X10 6 37 . 035 196.8 7289.2 3 X4 6 6.802 112.1 762.85 7 4X11 40.646 202.7 8240.8 3 2X4 9 7.579 116.5 882.95 7 8X11 6 44.426 208.5 9262.3 3 4X5 8.398 120.6 1012 7 8 X12 48.373 214.1 10358. 3 6X5 3 9.259 124 6 1153.4 8 4X12 6 52.487 219.7 11532. 3 8X5 6 10.161 128.6 1307. 8 8X13 56.771 225.1 12783. 3 10X5 9 11.106 132.5 1472.1 9 X13 6 61 222 230.6 14122. 4 X6 12.093 136.4 1649.3 9 4X14 65.84 236. 15537. 4 2X6 3 13.123 140.1 1838.5 9 8X14 6 70.628 241.1 17032. 4 4X6 6 14.192 143.8 2041 5 10 X15 75.583 246.3 18621 . 4 6X6 9 15 305 147.5 2257.1 10 6X15 9 83.33 254. 21165. 4 8X7 16.46 151.1 2486.8 11 X16 6 91.455 261.4 23909. 4 10X7 3 17.656 154.5 2728.3 12 X18 108.84 275.730008. 5 X7 6 18.895 158. 2985.4 OPEN AND CLOSED CHANNELS. 273 TABLE 64. Egg-shaped Sewers flowing one-third full depth. Based on Kutter's formula with n = .013. Giving the value of a, and also the values of the factors c^/r and ac^/r for use in the formulae : v = c-v/r" X >/ and ac^/7 X \A~ The egg-shaped sewer referred to has a vertical diameter 1.5 times the greatest transverse diameter, Z>, that is, the diameter of the top of the sewer. Area of egg-shaped sewer flowing one-third full depth = Z> 2 X .284. Perimeter of egg-shaped sewer flowing one-third full depth =D X 1.3747. Hydraulic mean depth of egg-shaped sewer flowing one-third full depth = Z> X .2066. a = area For ve- For dis- a area For For dis- Size of Size of in locity charge in ve- charge sewer. square cVr ac\/r sewer. square locity acv'r ft. in. ft. in. feet. ft. in ft. in. feet. cV~r 1 XI 6 .284 36.74 10.436 5 2X 7 9 7.581 121.7 922.69 1 2X1 9 .387 41.43 16.015 5 4X 8 8.078 124.4 1005.1 1 4X2 .505 45.87 23.162 5 6X 8 3 8.591 127. 1091.1 1 6X2 3 .639 50.14 32.044 5 8X 8 6 9.120 129.6 1181.9 1 8X2 6 .789 54.31 42 . 845 5 10X 8 9 9.664 132.2 1277.8 I 10X2 9 .955 58.22 55 . 573 6 X 9 10.224 134.6 1376.4 2 X3 1.136 62.14 70.598 6 2X 9 3 10.8 137.2 1481.7 2 2X3 3 1 . 333 65.89 87 853 6 4X 9 6 11.391 139.6 1590.3 2 4X3 6 1.546 69.74 107.84 6 6X 9 9 12.999 142. 1704.6 2 6X3 9 ! 1.776 73.22 129.97 6 8X10 12.622 144.5 1824. 2 8X4 ! 2.020 76.59 154.67 6 10X10 3 13.261 147. 1S49.2 2 10X4 3 2.280 80.02 182.44 7 XlO 6 13.916 149.3 2077.6 3 X4 6 2.556 83.51 213.46 7 4X11 15.273 153.8 2349.9 3 2X4 9 2.848 86.70 246.91 7 8X11 6 16.693 158.3 2643. 3 4X5 3.156 89.85 283.55 8 X12 18.176 163. 2962.7 3 6X5 3 3.479 92.90 323.22 8 4X12 6 19 722 167.3 3300.4 3 8X5 6 3.818 96. 366.53 8 8X13 21.332 171.7 3662. 3 10X5 9 4.173 99.13 413.68 9 X13 6 23.004 176. 4049.6 4 X6 4.544 102 1 463.9 9 4X14 24.739 180.2 4459.6 4 2X6 3 4.931 105. 517.91 9 8X14 6 26.538 184.3 4891.3 4 4X6 6 5.333 107.8 575.22 10 X15 28.4 188.3 5348.7 4 6X6 9 5.751 110.7 636.6 10 6X15 9 31.311 194.4 6088. 4 8X7 6.189 113.6 702.5 11 X16 6 34.364 200.2 6880.4 4 10X7 3 6.635 116.5 772.9 12 X18 40.892 211.7 8658. 5 X7 6 7.100 119. 845. 18 274 FLOW OF WATER IN TABLE 65. Egg-shaped Sewer flowing full depth. Based on Kutter's formula with n = ,015. Giving the value of a, and also the values of the factors c\/r and ac^/r for use in the formulae: v c\/r X \A and Q ac\/r X \A These factors are to be used only where the -value of n, that is the co- efficient of roughness of lining of channel = .015, as in second-class or rough faced brickwork; well-dressed stonework; foul and slightly tuber- culated iron; cement and terra cotta pipes, with imperfect joints and in bad order, and canvas lining on wooden frames, and also the surfaces of other materials equally rough. The egg-shaped sewer referred to has a vertical diameter equal to 1.5 times the greatest transverse diameter, D, that is, the diameter of the top of sewer. Area of egg-shaped sewer flowing full depth = Z> 2 X 1.148525. Perimeter of egg-shaped sewer flowing full depth D X 3.9649. Hydraulic mean depth of egg-shaped sewer flowing full depth = D X 0.2897. Size of sewer, ft. in. ft. in. a = area in square feet. For ve- locity cVr For dis- charge ac\/r Size of sewer, ft. in. ft. in. a=area in square feet. For ve- locity cVr For dis- charge ac\/r 1 XI 6 1.148 39.62 45.528 5 2X 7 9 30.660 130.7 4007.9 1 2X1 9 1.563 44.66 69 804 5 4X 8 32.669 133.6 4364.9 1 4X2 2.041 49.57 101.17 5 6X 8 3 34.743 136.4 4738. 1 6X2 3 2.584 54.08 139.74 5 8X 8 6 36.880 139.2 5131.7 1 8X2 6 3.190 58.64 187.06 5 10X 8 9 39.081 142. 5548. 1 10X2 9 3.860 62.83 242 . 52 6 X 9 41.347 144.6 5980 3 2 X3 4.594 66.93 307.48 62X93 43.676 147.3 6435.1 2 2X3 3 5.391 71.01 382.81 6 4x 9 6 46.068 149 8 6902 6 2 4X3 6 6.253 74.93 468.54 66X99 48 . 525 152.5 7399 3 2 6X3 9 7.178 78.76 565.34 6 8X10 51.046 155.2 7920.6 2 8X4 8.167 82.44 673.29 6 10X10 3 53.629 157.7 8547.1 2 10X4 3 9.220 86.21 794.86 7 X10 6 56.278 160.2 9015.7 3 X4 6 10.337 89.70 927 23 7 4X11 61.764 165. 10192 3 2X4 9 11.517 93.25 1074. 7 8X11 6 67 . 508 170.1 11482. 3 4X5 12.761 96.73 1234.4 8 X12 73 506 174.8 12852. 3 6X5 3 14.069 100.1 1407 . 6 8 4X12 6 79.758 179.6 14327 3 8X5 6 15 442 103.4 1596.7 8 8X13 86.268 184.3 15898. 3 10X5 9 16.877 106.6 1799.1 9 X136 93.030 188.8 17563. 4 X6 18.376 109.9 2019.5 9 4X14 100.049 193.1 19323. 4 2X6 3 19.940 113. 2254. 9 8X14 6 107.324 197.5 21198. 4 4X6 6 21.566 116. 2501.4 10 X15 114.853 201.9 23191. 4 6X6 9 23 . 258 119.1 2770. 10 6X15 9 126.625 208 . 3 26376. 4 8X7 25.013 122.1 3053 8 11 X16 6 138.972 214 6 29822. 4 10X7 3 26.830 125. 3353. 12 X18 165.388 226.8 37502. 5 X7 6 28.713 128. 3675.6 OPEN AND CLOSED CHANNELS. 275 TABLE 66. Egg-shaped Sewers flowing two-thirds full depth. Based on Kutter's formula with n = .015. Giving the value of a, and also the values of the factors c\/r and ac\/r for use in the formulae: v = c\/r X \A' and Q = ac^/r X \A The egg-shaped sewer referred to has a vertical diameter 1.5 times the greatest transverse diameter, 7), that is, the diameter of the top of sewer. Area of egg-shaped sewer flowing two-thirds full depth = D l X 0.755825. Perimeter of egg-shaped sewer flowing two-thirds full depth = D X 2.3941. Hydraulic mean depth of egg-shaped sewer flowing two-thirds full depth = DX .03157. Size of sewer ft. in. ft. in. a=area in square feet. For ve- locity C-v/f For dis- charge ac-^/r Size of sewer ft. in. ft. in \ a = area in square feet. For ve- locity c\/r For dis- charge ac\/r 1 Xl 6 .756 42.40 32.048 5 2X 7 9 20.177 138.6 2795.9 1 2X1 9 1.029 47.80 49.181 5 4X 8 21.498 141.7 3045.5 1 4X2 1 . 344 52.82 70.993 5 6X 8 3 22.863 144.6 3305 . 3 1 6X2 3 1.701 57.68 98.115 5 8X 8 6 24.270 147.5 3578.9 1 8X2 6 2.099 62.46 131.10 5 10X 8 9 25.718 150.3 3864.8 1 10X2 9 2.540 66.94 170.02 6 X 9 27.210 153.1 4165.3 2 X3 3.023 71.42 216.54 6 2X 9 3 28.743 155.9 4481.6 2 2X3 3 3.548 75.59 268.19 6 4X 9 6 30 317 158.7 4811.9 2 4X3 6 4.115 79.69 327.93 6 6X 9 9 31.933 161.5 5158.5 2 6X3 9 4.724 83.90 396.32 6 8X10 33.592 164.2 5516 6 2 8X4 5.375 87.82 472.01 6 10X10 3 35.292 166.9 5891. 2 10X4 3 6 067 91.60 555.74 7 X10 6 37.035 169.6 6283.5 3 X4 6 6.802 95 . 33 648.40 7 4X11 40.646 174.8 7106.8 3 2X4 9 7.579 99.10 751.08 7 8X11 6 44.426 179.9 7993. 3 4X5 8.398 102.7 862.41 8 X12 48.373 184.9 8944. 3 6X5 3 9.259 106.2 983.24 8 4X12 6 52.487 189.8 9964.1 3 8X5 6 10.161 109.7 1115.1 8 8X13 56.771 194.6 11050. 3 10X5 9 11.106 113.2 1256.1 9 X1S 6 61.222 199.5 12213. 4 X6 12.093 116.5 1409.4 9 4X14 65 . 840 204.2 13444. 4 2X6 3 13.123 119.8 1572.1 9 8X14 6 70 628 208.7 14743. 4 4X6 6 14.192 123.1 1746.9 10 X15 75.583 213.3 16125. 4 6X6 9 15.305 126.3 1932.7 10 6X15 9 83.330 220.1 18342. 4 8X7 16.460 129.4 2130.5 II X16 ( 91.455 226.8 20738. 4 10X7 3 17.656 132.5 2338.6 12 X18 108.84 239.4 26060. 5 X7 6 18.895 135.5 2560.3 276 FLOW OF WATER IN TABLE 67. Egg-shaped Sewers flowing one-third full depth. Based 011 Kutter's formula with n = .015. Giving the value of a, and also the values of the factors c\/r and ac^/r for use in the formula: v = c\/r X \/s and Q = ac\/r X \A 7 The egg-shaped sewer referred to has a vertical diameter 1 .5 times the greatest transverse diameter, D, that is, the diameter of the top of the sewer. Area of egg-shaped sewer flowing one-third full depth = D' 2 X .284. Perimeter of egg-shaped sewer flowing one-third full depth = D X 1.3747. Hydraulic mean depth of egg-shaped sewer flowing one-third full depth = D X .2066. Size of sewer ft. in. ft. in. a=area in square feet. For ve- locity c^/r For dis- charge ac\/r Size of sewer ft. in. ft. in. a=area in square feet. For ve- locity cVr For dis- charge ac\/r 1 Xl 6 .284 30.41 8.637 5 2X 7 9 7.581 103.7 785.86 1 2X1 9 .387 34.38 13.303 5 4X 8 8.078 106.1 856.67 1 4X2 .505 38.16 19.269 5 6X 8 3 8.591 108.3 930.54 1 6X2 3 .639 42.23 26.986 5 8X 8 6 9.120 110.6 1008 7 1 8X2 6 .789 45.39 35.815 5 10X 8 9 9.664 112.9 1091 . 1 10X2 9 .955 48.74 46.546 6 X 9 10.224 115. 1175.8 2 X3 1 136 52.09 59. 173 6 2X 9 3 10.800 117.3 1266.4 2 2X3 3 1.333 55.29 73.696 6 4X 9 6 11.391 119.4 1359.8 2 4x3 6 1.546 58.58 90.568 6 6X 9 9 12.999 121.5 1458.1 2 6X3 9 1.776 61.58 109.37 6 8X10 12.622 123.7 1561. 2 8X4 2.020 64.49 130.26 6 10X10 3 13.261 125.8 1668.8 2 10X4 3 2.280 67.46 153.80 7 X10 6 13.916 127.9 1779.4 3 X4 6 2.556 70.48 180.14 7 4X11 15.273 131.9 2014.1 3 2X4 9 2 . 848 73.24 208.98 7 8X11 6 16.693 135.8 \ 2266.7 3 4X5 3.156 75.98 239.79 8 X12 18.176 139.9 2542.7 3 6X5 3 3.479 78.63 273.54 8 4X12 6 19.722 143.7 2833.8 3 8X5 6 3.818 81.31 310.44 8 8X13 21.332 147 . 5 3146.2 3 10X5 9 4.173 84.03 350.67 9 X13 6 23.004 151.3 3480.7 4 X6 4.544 86.61 393.55 9 4X14 24.739 155. 3834.7 4 2X6 3 4.931 88.98 438.75 9 8X146 26.538 158.6 4208.4 4 4X6 6 5.333 91.60 488.50 10 X15 28.400 162.1 4604.7 3 6X6 9 5.751 94.08 541.04 10 6X15 9 31.311 167.5 5245.3 4 8X7 6.189 I 96.57 597.29 11 X16 6 34.364 172.6 5932.1 4 10X7 3 6.635 99.10 657.53 12 X18 40.892 183.1 7489. 5 X7 6 7.100 101 3 719.27 OPEN AND CLOSED CHANNELS. 277 TABLE 68. Giving velocities and discharges of Circular Pipes, Sewers and Conduits, iled on Kutter's formula, with n .013. (I = diameter. v =-mean velocity in feet per second. Q discharge in cubic feet per second. d = = 5" d = = 6" d* = 7" d = r 8" d = 9" Slope lia V Q V Q V Q V Q V Q 40 3.35 .456 3.89 .762 4.40 1.17 4.90 1.71 5.37 2 37 70 2.53 .344 2.94 .576 3.33 .889 3.7 1.29 4.06 1.79 100 2 12 .288 2 46 .482 2.79 .744 3.1 1.08 3.40 1.50 2CO 1.50 .204 .74 .341 1.97 .526 2.19 .765 2 4 1.06 300 1.22 .166 .42 .278 .61 .430 1.79 .624 1.96 .868 400 1.06 .144 .23 .241 1 39 .372 1.55 .54 1.7 .75 500 1.01 .137 .17 .230 33 . 355 1.48 .516 1.62 .717 GOO .865 .118 . .197 .14 .304 1.26 .441 1.39 .613 d = 10" d = : 11" d = r o" d = r r d = r 2" 60 4.76 2.59 5.14 3.39 5.5 4 32 5.84 5.38 6.18 6.6 80 4.12 2.24 4 45 2.94 4.77 3.74 5 05 4 66 5 35 5.72 100 3.68 1. 3.98 2.63 4.26 3.35 4.52 4.16 4.78 5 15 200 2.61 1.42 2.82 1.86 3.01 2.37 32 2.95 3.38 3.62 3CO 2.13 1.16 2.3 1.52 2.46 1.93 2.61 2.4 2 76 2.95 400 1.84 .5 1.99 1.31 2.13 1.67 2 26 2.08 2.39 2.57 500 1.65 .9 1.78 1.17 1.91 1.5 2.02 1.86 2.14 2 29. 600 1.5 .82 1.62 1.07 1.74 1.37 1.84 1.70 1.95 2.09 d == r 3" d = r 4" d = r 6" d = i' 8" d = 1' 10" 100 5.04 6.18 5.29 7.38 5.78 10 21 6.25 13.65 6 70 17.71 200 3.56 4.37 3.74 5.22 4.09 7 22 4.43 9.65 4.74 12.52 300 2.91 3.57 3.05 4.26 3.34 5.89 3.61 7.88 3 87 10.22 400 2.52 3.09 2.64 3.69 2.89 5.10 3.12 6.82 3.35 8.85 500 2.25 2.77 2.36 3 30 2 58 4.56 2.8 6.1 3. 7.92 000 2.06 2.52 2.16 3.01 2.36 4.17 2 56 5.57 2.74 7.23 700 1 90 2.34 2. 2.79 2.18 3.86 2 37 5.16 2 53 6.69 800 1.78 2.19 1.87 2.61 2.04 3.61 2.21 4.83 2.37 6.26 d = 2' 0" d = 2' 2" d = I' 4" d = I' 6" d = 2' 8" 200 5.05 15.88 5.35 19.73 5.65 24.15 5.92 29.08 6.21 34.71 400 3.57 11.23 3.78 13.96 3 . 99 17.07 4.19 20.56 4.39 24 54 600 2.92 9.17 3.09 11.39 3.26 13.94 3.42 16.79 3 59 20.04 800 2 53 7.94 2.67 9.87 2.82 12.07 2 96 14.54 3.11 17.35 1000 2.26 7.1 2.39 8.82 2 52 10.8 2.65 13. 2 78 15.52 1250 2.02 6.35 2.14 7.89 2.26 9 66 2 37 11.63 2.48 13.88 1500 1.84 5.8 1.95 7.2 2.06 8.82 2 16 10.62 2.27 12.67 1800 1.68 5.29 1.78 6.58 1.88 8.05 1.97 9.69 2.07 11.57 278 FLOW OF WATEK IN TABLE G8. Giving velocities and discharges of Circular Pipes, Sewers and Conduits, based on Kutter's formula, with n .013. d diameter. v = mean velocity in feet per second. Q = discharge in cubic feet per second. d -.- 2' 10" d = 3' 0" d = 3' 2" d = 3' 4" d = 3' 6" Slope 1 in V Q V Q V Q V Q Q 500 4.10 25.84 4 26 30.14 4.43 34.90 4.59 40.08 4.74 45.66 750 3.34 21.10 3.48 24.61 3.61 28.50 3.75 32.72 3 87 37.28 1000 2.89 18-27 3.01 21.31 3.13 24.68 3.25 28.34 3.35 32.28 1250 2.59 16.34 2.69 19.06 2.80 22.07 2.90 25.35 3. 28.87 1500 2.36 14.92 2.46 17.40 2.55 20.15 2.65 23.14 2.73 26.36 1750 2.19 13.81 1 2.28 16.11 2.36 18.66 2.45 21.42 2.53 24.40 2000 2.05 12.92 2.13 15.07 2.21 17.45 2.29 20.04 2.37 22.83 2640 1.78 11.24 1.85 13.12 1.92 15.19 2. 17.44 2.06 19.87 d = 3' 8" d = 3' 10" d = 4' 0" d = 4' 6" d = 5' 0" 500 4.90 51.74 5.06 58.36 5.21 65.47 5.64 89.75 6.05 118.9 750 4. 42.52 4.13 47.65 4.25 53.46 4.61 73.28 4.94 97.09 1000 3.4C 36.59 3.58 41.27 3.68 46.3 3.99 63.47 4.28 84.08 1250 3.1 32.72 3.2 36.91 3.29 41.41 3.57 56.76 3.83 75.21 1500 2.83 29 87 2.92 33.69 3.01 37.8 3.26 51.82 3.49 68.65 1750 2.62 27.66 2.7 31.2 2.78 34.5 3.01 47.97 3.24 63.56 2000 2.45 25.87 2.53 29.18 2.61 32.74 2.82 44.88 3.02 59.46 2640 2.13 22 59 2.2 25.4 2.27 28.49 2.46 39.06 2.63 51.75 d ~ 5' 6" d = 6' 0" d== 6' 6" d = 7' 0" d = 7' 6" 750 5.27 125.2 5.58 157.8 5.88 195. 6 18 237.7 6.46 285.3 1000 4.56 108.4 4.83 136.7 5.1 168.8 5.35 205.9 5.59 247.1 1500 3.72 88.54 3.95 111.6 4.16 137.9 4.37 168.1 4.57 201.7 2000 3 22 76.67 3.42 96.66 3.60 119.4 3.78 145.6 3.95 174.7 2500 2.88 68.58 3.06 86.45 3 22 106.8 3.38 130.2 3.53 156.3 3000 2.63 62.6 2.79 78.92 2.94 97.49 3.09 118.8 3.23 142.6 3500 2.44 57.96 2.58 73.07 2.72 90.26 2.86 110. 2.99 132.1 4000 2.28 54.21 2.42 68.35 2.55 84.43 2.67 102.9 2.8 123.5 d = 8' 0" d = S' 6" d = 9' 0" d = 9' 6" d 10' 0" 1500 4.76 239.4 4.95 281.1 5.14 327. 5.31 376.9 5.49 431.4 2000 4 12 207.3 4.29 243.5 4.45 283.1 4 6 326.4 4.76 373.6 2500 3.69 195.4 3.84 217.8 3.98 253.3 4.12 291.9 4.25 334.1 3000 3.37 169.3 3.50 198.8 3.63 r>31 2 3.76 266.5 3.88 305. 3500 3.12 156 7 3.24 184. 3.36 214. 3.48 246.7 3.6 282.4 4000 2.92 146.6 3.03 172 2 3.15 200.2 3.25 230.8 3 36 264.2 4500 2.75 138.2 2.86 162.3 2 97 188.7 3.07 217.6 3.17 249.1 5000 2.61 131.1 2.71 154. 2.81 179.1 2.91 206.4 3.01 236.3 OPEN AND CLOSED CHANNELS. 279 TABLE 69. Giving velocities and discharges of Egg-Shaped Sewers, based on Kut- ter's formula, with n = .013. Flowing full depth. Flowing f full depth. Flowing i full depth. v =.meaii velocity in feet per second. Q = discharge in cubic feet per second. Size of Sewer 2' 9" x 3' 0" Slope liii Full 1 )epth i Fr.ll Depth i Full : Depth V Q V Q V Q 100 7.94 36.48 8.46 25.57 6.21 7.06 200 5.61 25.8 5.98 18.08 4.39 4.09 300 4.58 21.06 4.88 14.76 3.59 4.07 500 3.55 16.31 3.78 11.43 2.78 3.16 700 3. 13.79 3.2 9.66 2.35 2.67 1000 1200 2.51 2.29 11.54 10.53 2.67 2.44 8.08 7.38 1.96 1.79 2.23 2.04 1500 2.05 9.42 2.18 6.6 1.6 1.82 Siz e of Sewer 2' 2" x 3' 3 100 8 41 45.35 8.94 31.72 6.59 8.78 200 5.95 32.07 6.32 22.43 4.66 6.21 300 4.85 26.19 5.16 18 31 3.80 5.07 500 4.01 21.64 4.26 15.14 3.14 4.19 700 3.18 17.14 3.38 11.99 2.49 3.32 1000 2 66 14 . 34 2.83 10.03 2.08 2.78 1200 2.43 13.09 2.58 9.15 1.9 2.53 1500 2.17 12.71 2.31 8.19 1.7 2 26 Siz e of Sewer 2' 4" x 3' 6 150 7.24 45.26 7.68 31.63 5.69 8.8 300 5.12 32. 5.43 22.37 4.02 6.22 600 3.62 22.63 3.84 15.81 2.84 4.4 1000 2.8 17.53 2.97 12.25 2.2 3.41 1250 2.51 15.68 2.66 10.96 1.97 3.05 1500 2.29 14.31 2.43 10. 1.8 2.78 1750 2.12 13 25 2.25 9.26 1.67 2.58 2000 1 98 12.39 2.1 8.66 1.56 2.41 Siz a of Sewer 2' 6" x 3' 9 " 300 5 37 38.57 5.71 26.99 4.2 7.5 600 3.8 27.27 4.04 19.08 2.98 5.31 1000 2.94 21.12 3.13 14.78 2.31 4.11 1250 2.63 18.89 2 8 13.22 2.06 3.68 1500 2.4 17.25 2.55 12.07 1.88 3.36 1750 2 22 15.97 2 37 11.17 1.74 3.11 2000 2.08 14.94 2.21 10.45 1 63 2.91 2640 1 81 13. 1.93 9.1 1.42 2 53 280 FLOW OF WATER IN TABLE 69. Giving velocities and discharges of Egg-Shaped Sewers, based on Kut- ter's formula, with n = .013. Flowing full depth. Mowing f full depth. Flowing ^ full depth. v velocity in feet per second. Q = discharge in cubic feet per second. Slope 1 in Size of Sewer 2' 8" x 4' 0" Full Depth f Full Depth 4 Full Depth V Q V Q V Q 500 750 1000 1250 1500 1750 2000 2640 4.35 3.55 3 08 2.75 2.51 2.32 2.17 1.89 35.57 29.04 25.15 22.49 20.53 19.01 17.78 15.48 4.62 3.77 3.27 2.92 2.67 2.47 2.31 2.01 24.87 20.30 17.58 15.73 14.36 13.29 12 43 10.82 3.42 2.79 2.42 2.16 1.97 1.83 1.71 1.49 6.91 5.64 4 89 4.37 3.99 3.69 3.45 3.01 Siz< 3 of Sewer 2' 10" x 4' 3" 500 4.54 41.90 4.82 29.26 3.57 8.15 750 3.70 34.21 3.93 23 89 2.92 6.66 1000 3.21 29.63 3.41 20.69 2.52 5.76 1250 2.87 26.50 3.05 18.50 2.26 5.15 1500 2.62 24.19 2.78 16.89 2.06 4.70 1750 2.42 22 39 2.57 15.64 1.91 4 36 2000 2.27 20.95 2.41 14 63 1.78 4.07 2640 1.97 18.23 2.10 12.73 1.55 3.55 Siz e of Sewer 3' 0" x 4' 6 500 4.72 48.83 5.01 34.11 3.73 9.54 750 3.85 39.87 4.09 27.85 3.04 7.79 1000 3.33 34.53 3.54 24.12 2.64 6.74 1250 2.98 30.88 3.17 21.57 2.36 6.03 1500 2.72 28.19 2.89 19.69 2.15 5.50 1750 2.52 26.10 2.67 18.23 1.99 5.10 2000 2.36 24.41 2.50 17.05 1.86 4.77 2640 2.05 21.25 2.18 14.84 1.62 4.15 Siz e of Sewer 3' 2" x 4' 8 " 500 4.90 56.52 5.20 39.48 3.87 11.04 750 4. 46.15 4.25 32.24 3.16 9.01 1000 3.46 39 97 3 68 27 92 2.74 7.80 1250 3.10 35.75 3.29 24.97 2.45 6.98 1500 2.83 32.63 3. 22.79 2.23 6.37 1750 2.62 30.21 2.78 21.10 2.07 5.90 2000 2.45 28.26 2.60 19.74 1 93 5.52 2640 2.13 24.60 2.26 17.18 1.68 4.80 OPEN AND CLOSED CHANNELS. 281 TABLE 69. Giving velocities and discharges of Egg-Shaped Sewers, based on Kut- ter's formula, with n = .013. Flowing full depth. Flowing $ full depth. Flowing % full depth. v = mean velocity in feet per second. Q = discharge in cubic feet per second. Siz e of Sewer 3' 4" x 5' Slope 1 in Full . Depth f Full Depth i Full ] Depth v Q V Q V Q 500 750 1000 1250 1500 1750 2000 2640 5.08 4.15 3.59 3.21 2.93 2.72 2.54 2.21 64.89 52.98 45.88 4i. 37.46 34.68 32.44 28.24 5.39 4.40 3.81 3.41 3.11 2.88 2.69 2 34 45 25 36 . 95 32. 28.62 26.13 24.19 22.63 19 69 4.01 3.27 2.83 2.53 2.32 2.14 2.01 1.74 12.67 10.35 8.96 8.01 7.32 6.77 6.34 5.51 Si? e of Sewer 3' 6" x 5' 3 500 750 1000 ] 250 1 500 1750 2000 2640 5.26 4.29 3.72 3.32 3.03 2.81 2.63 2.29 73.97 60.39 52 . 30 46.78 42.70 39.53 36.98 32.19 5.57 4 55 3.94 3.52 3.21 2.98 2.78 2.42 51.56 42.10 36.46 32.61 29.77 27.56 25.78 22.44 4.15 3.39 2.94 2.62 2.40 2.22 2^08 1.81 14.45 11.80 10.22 9.14 8 34 7.72 7.22 6 29 Siz e of Sewer 3' 8" x 5' 6 500 750 1000 1250 1500 1750 2000 2640 5.43 4.43 3 84 3 43 3.13 2.9 2 71 2.36 83.81 68 43 59.26 53. 48.39 44.8 41 9 36.47 5.75 4.69 4.07 3.64 3.32 3.07 2.87 2.50 58.45 47.72 41.33 36.97 33.74 31.24 29.22 25.44 4.29 3.50 3.03 2.71 2.48 2.29 2.14 1.87 16.39 13.38 11.59 10.37 9.46 8.76 8.19 7.13 Siz e of Sewer 3' 10" x 5' 9" 750 1000 1250 1500 1750 2000 2640 3000 4 56 3 95 3 53 3 23 2.99 2.79 2.43 2.28 77.08 66.76 59.71 54.51 50.46 47.2 41.09 38.54 4.84 4.19 4.03 3.42 3.17 2.96 2.58 2.42 53.75 46.55 41.63 38. 35.19 32.91 28 65 26 87 3.62 3.13 2.8 2 56 2.37 2.22 1.93 1.81 15.11 13.08 11.7 10.68 9.89 9.25 8.05 7.55 282 FLOW OF WATER IN TABLE 69. Giving velocities and discharges of Egg-Shaped Sewers, based on Kut- ter's formula, with n = .013. Flowing full depth. Flowing f full depth. Flowing full depth. v mean velocity in feet per second. Q = discharge in cubic feet per second. Slope 1 in Size of Sewer 4' 0" x Q' 0" Full Depth f Full Depth i Full Depth V Q V Q V Q 1000 1250 1500 1750 2000 2640 3000 3500 1000 1250 1500 1750 2000 2640 3000 3500 1250 1500 1750 2000 2640 3000 3500 4000 1250 1500 1750 2000 2640 3000 3500 4000 4.07 3.64 3.32 3.07 2 88 2.50 2.35 2.17 74.82 66 91 61.09 56.66 52.90 46.04 43.19 39.99 4.31 3.85 3.52 3.26 3.05 2.65 2.49 2.30 52.14 46.64 42.57 39.41 36.87 32.09 30.10 27.87 3.22 2.88 2.63 2.44 2.28 1.98 1.86 1.72 14.66 13.12 11.97 11.08 10.37 9.02 8.46 7.84 Size of Sewer 4' 2" x 6' 3" 4.18 3.74 3.41 3.16 2 96 2.57 2.41 2.29 83.48 74.66 68.16 63.10 59.03 51.38 48.19 44.62 4.43 3.96 3.61 3.34 3.13 2.72 2.55 2.36 58.12 51.98 47.45 43.93 41.09 35.77 33.55 31.06 3.32 2.96 2.71 2.51 2.34 2.04 1.91 1.77 16.37 14.64 13.37 12.38 11.58 10.07 9.45 8.75 Size of Sewer 4' 4" x 6' 6" 3.84 3.5 3.24 3.03 2.64 2.48 2.29 2.14 82.79 75.57 69.97 65.45 56.97 53.44 49.47 46.28 4.07 3.71 3.44 3.21 2.8 2.62 2.43 2.27 57.73 52.7 48.79 45.64 39.72 37.26 34.5 32.27 3.05 2.78 2.58 2.41 21 1.97 1.82 1.7 16.27 14.85 13.45 12.86 11 19 10.5 9.72 9.09 Size of Sewer 4' 6" x 6' 9" 3.94 3 6 3.33 3.11 2.71 2.54 2.35 22 91.61 83 63 77.43 72.42 63.04 59.13 54.75 51.21 4.17 3.81 3.52 3.3 2.87 2.69 2.49 2.33 63.84 58.27 53 95 50.47 43.93 41.21 38.15 35.68 3.13 2.85 2.65 2.47 2.15 2.02 1.87 1.75 18.01 16.44 15.22 14.24 12.39 11.62 10.76 10.07 OPEN AND CLOSED CHANNELS. 288 TABLE 69. Giving velocities and discharges of Egg-Shaped Sewers, based on Kut- ter's formula, with n = .013. Flowing full depth. Flowing f full depth. Flowing full depth. v = mean velocity in feet per second. Q discharge in cubic feet per second. Si; :e of Sewer 4' 8" x 7' C 1" Slope 1 in Full Depth } Full Depth i Full Depth V Q V Q V Q 1250 1500 1750 2000 2640 3000 3500 4000 4.04 3.68 3.41 3.19 2.78 2.60 2.41 2.26 101. 92.17 85 . 34 79.82 69.48 65.18 60.34 56.44 4.27 3.9 3.61 3.38 2 94 2.76 2.55 2.39 70.34 64.21 59.45 55.61 48.4 45.4 42.04 39.31 3.21 2.93 2 71 2.54 2.21 2.07 1.92 1.79 19.87 18.14 16.79 15.7 13.67 12.83 11.87 11.11 Siz e of Sewer 4' 10" x 7' 3" 1250 1500 1750 2000 2640 3000 3500 4000 4.13 3 77 3.49 3.26 2.84 2.66 2.47 2.31 110.8 101.1 93.63 87.59 76.24 71.51 66.21 61.93 4.37 3.99 3.69 3.45 3.01 2.82 2.61 2.44 77 16 70.43 65.21 61. 53.09 49.8 46.11 43.13 3.29 3.01 2.78 2.60 2 27 2.13 1.97 1 .84 21.86 J9.96 18.48 . 17.28 15.04 14.11 13.06 12.22 Siz e of Sewer 5' 0" x 7' 6 " 1500 1750 2000 2640 3000 3500 4000 5000 3.86 3.57 3.34 2.91 2.73 2 . 52 2.36 2.11 110.8 102.6 95.95 83.51 78.34 72.53 67.84 60.68 4.08 3.78 3.53 3.07 2.88 2.67 2.5 2.23 77.07 71.35 66.75 58.1 54.5 50.45* 47.2 42.21 3.07 2.84 2.66 2.32 2.17 2.01 1.88 1.68 21.82 20.2 18.9 16.45 15.43 14.28 13.36 11.95 Siz e of Sewer 5' 4" x 8' " 1500 1750 2000 2640 3000 3500 4000 5000 4.02 3.72 3.48 3.03 2.84 2.63 2.46 2.2 131.4 121.7 113.8 99.1 92.95 86.05 80 49 72. 4 26 3.94 3.69 3.21 3.01 2.79 2.61 2.33 91.61 84.81 79.33 69.05 64.77 60. 56.1 50.18 3.21 2.97 2.78 2.42 2.27 2.1 1 97 1 76 25.95 24 . 02 22.47 19.56 18.35 17. 15 89 14.21 ]P. J. ( M. AM. Soc. C. E.) CIVIL AND HYDRAULIC ENGINEER, BOX 917, STATION C, LOS ANGELES, CALIFORNIA. CONSULTING BNGINJBBR For Irrigation, Water Works, Sewerage, Canals, Ditches, Pipe Lines, Reservoirs, Dams, Land Drainage and River Embankments. The Discharge of Rivers, Streams. Ditches and Canals Measured. Hydraulic Investigations a Specialty. IRRIGATION CA.NA.LS AND Other Irrigation W^oris, AND THE FLOW OF WATER IN IRRIGATION CANALS DITCHES, FLUMES, PIPES, SEWERS, CONDUITS, ETC., WITH Simplifying and Facilitating the Application of the Formulae of KUTTEK, D'AKCY AND BAZIN, BY P. J. FLYNN, C. E., Member of the American Society of Civil Engineers; Member of the Technical Society of the Pacific Coast; Late Executive Engineer, Public Works Department, Punjab, India. Author of " Hydraulic Tables based on Kutter's Formula," " Flow of Water in Open Channels," &c. TWO VOLUMES BOUND TOGETHER. 711 pages, 92 tables, 211 illustrations. B v . . Box 917, Station C, LOS ANGELES, CAL. CALIFORNIA ASPHALT. OIL BURNING AND SUPPLY CO. furnish the finest and purest grades of Refined California Asphalts for Reservoirs, Irrigation Channels, Aqueducts, Wooden Flumes, for all purposes to economize water, and for all other purposes wherein a preservative against decay is required. We recom- mend our "A. G." brand 85$ to 90% pure. Contractors and dealers supplied in quantities to suit on short notice. Samples on application. We are also prepared to make contracts and do all kinds of work in this line. Estimates furnished. Address, THE OIL BURNING AND SUPPLY COMPANY, 8 & 9 BURDICK BLOCK, Co'. Spring and Second Sts. LOS ANGELES, CALIFORNIA, Established in New York 1834, Established in San Francisco 1855, JOSKPH C. SALA, Successor to JOHN ROACH, MAKER OF Surveyors', Nautical and Mathematical INSTRUMENTS. 4:29 Montgomery St. S. W. Cor. Sacramento St. SAN FRANCISCO. Instruments Examined, Repaired ^ Carefully Adjusted. Materials for Office Work Supplied. J. McMuLLEN, President. H. KRUSI, Chief Engineer. J. M. TAYLOR. Sec'y and Treas. H. S. WOOD. ) . GEO. W. CATT, C. E., Vice President. J. B. C. LOCKWOOD, ' r San Francisco Bridge Company Established 1877. Capital (paid up), $25O,OOO. Incorporated 1883. ENGINEERS AND CONTRACTORS. 42 Market St., San Francisco, Oal, '' Occidental Block, Seattle, Wash. CONTRACTORS FOR STEAM EXCAVATION AND DREDGING FOR THE IMPROVEMENT OF NAVIGATION AND RECLAMATION OF LANDS. Special Machinery for the Economical Excavation of Large Canals. STEAM SHOVEL AND ROCK EXCAVATION. (See Cut, page 266.) Designers and Builders of Railroad and Highway Bridges, Sub. and Superstructure, Pile Driving, Dock and Pier Building and Flume Construction. During the current year we have constructed works to the value of over a million and a-half dollars, and which required the handling of two and one- half million cubic yards of material, and consumed twenty-two million feet of lumb- r, twenty thousand piles, and three and a-half million pounds of steel and iron. Built fifteen linear miles of railroad trestle bridges in 1890, and one mile of railroad truss bridges. With a plant that represents an in- vestment of over one hundred and fifty thousand dollars, and a corps of experienced engineers and superintendents, and thirteen years' experience, we have facilities and equipment for the execution of this kind of work with the greatest skill, thoroughness and economy. Plans and Estimates Furnished. Correspondence Solicited. A U O . M AY E R , Civil and Sanitary and Contracting Engineer, Room 12, Burdiek Block, Cor. Spring and Second Sts. P. O. Box 995, Station C, LOS ANGELES, CAL. WILL FURNISH PLANS, SPECIFICATIONS AND ESTIMATES FOR Sewerage of Cities; the Disposal and Utilization of Sewage of Country Houses; Waterworks, Irrigation, Etc., Etc. WORK EXAMINED AND SUPERINTENDED. BUFF & BERGER, IMPROVED engineering and Surveying Instruments, No. 9 Province Court, Boston, Mass. They aim to secure in their instruments: Accuracy of division; Sim- plicity in manipulation; Lightness combined with strength; Achromatic telescope, with high power; Steadiness of Adjustment* under varying temperatures; Stiff- ness to avoid any tremor, even in a strong wind, and thorough workmanship in every part. Their instruments are in general use by the U. S. Government Engineers, Geologists, and Surveyors, and the range of instruments, as made by them for River, Harbor, City, Bridge, Tunnel, Railroad and Mining Engineering, sis well as those made for Triangulation or Topographical Work and Land Surveying, etc., is larger than that of any other firm in the country. Illustrated Manual and Catalogue sent on Application. THE PACIFIC FLUSH TANK CO. Los ANGELES, MANUFACTURERS OF The Miller and Cosmos Automatic Siphons FOR FLUSHING SEWERS, Housedpains, Water Closets, Urinals, Etc. Well adapted for Intermittent Sub-Soil Irrigation. Our Siphons stand unequaled ; they are the simplest and most efficient in the world ; they act promptly when fed by the smallest supply of water or sewage, and cannot get out of order. They are durable and very easily set. They consist of only two solid castings and have 120 moving parts. Satisfaction guaranteed. Sold and delivered at Eastern prices. Send for pamphlet. PACIFIC FLUSH TANK CO. "... It (the MILLER) is uiuiuestiouably a very simple and reliable apparatus." THE J. L. MOTT IRON WORKS, N. Y. "... Both the MILLHR and COSMOS deserve the first place among automatic flushing svices for sewers." P. J. FLYNN, C. E. LACY MANUFACTURING CO. CALIFORNIA IRRIGATION HYDRANT, (Patented March 31, 1891.) MANUFACTURERS OF Steel Iron Pipe, Irrigation Supplies. Hydrants, Gates, etc, Office, i9^ West First Street. 1,08 ANGEI/ES, CAI,. Spreckels Bros. Commercial Co. j J. D. Spreckels & Bros. SOLE IMPORTERS, SOLE IMPORTERS, San Diego, Cal. San Francisco, Cal. Made of Samples taken from 5O,OOO Bbls. "GILLINGHAM" im- ported in 189O for the Spring Valley Water Works. [51.OOO Bbls. used in construction of their dam at San Mateo.] Tests made by HERMANN SCHUSSLER, Chief Engineer, under the following conditions. Briquettes made of pure cement, mixed with water, with a cross section of one square inch, kept in the molds for 24 hours after mixing, being covered with a damp cloth and during rest of the term kept immersed in water. Average breaking strain \ Average breaking strain Age. in pounds per sq. inch. Age. in pounds per sq. inch. 1 Day 4O4 9 Days 642 2 " 447 14 " 7O5 3 " 541 42 " 8O1 4 " 588 No other London Portland Cement can show such a remarkable result: Tlie Cement manufactured by the " GILLINGHAM " Company is noted for its Uniform Quality and Great Strength. PARTIAL LIST OF NOTABLE STRUCTURES ON WHICH "GILLINGHAM" CEMENT HAS BEEN USED. California Sugar Refinery, Leland Stanford University, D. N. & E. Walters' Building, Lachmaii & Jacobi, Wine Vaults, New City Hall, San Francisco, Sea Wall Construction, Corralitos Water Works, Western Beet Sugar Factory, Hibernia Bank, Donahue Building, Doyle Building, H. J. Crocker Building, Eureka Court House, Pacific Rolling Mills, U. O. Mills Building, Jas. G. Fair Building, Mercantile Library Building, Farmers Union Flour Mill, Piedmont Cable Rail Road, Golden Feather Channel Dam, Laurel Hill Cemetery Association, Weinstock & Lubin Wine Vault, Los Angeles Cable Railway, Los Angeles City Water Co. Los Angeles Public Sewers, Stowell Cement Pipe Co. Frink Bros. Cement Pipe Co. Los Angeles Court House, Bear Valley Irrigation Co. East Whitter Land and Water Co. Drarta Mount. Irrigation and Canal Co. Sweet water Dam, Dealers aiid Irrigating Co's throughout Southern Caliiornia, Hotel del Coronada. And numerous other prominent con- structions throughout the Pacific Coast. 8*e>x*re>r* JPi*3e> Oo. MANUFACTURERS OF Salt-Glazed Vitrified Iron Stone SEWER * WHTER PIPE Irrigation Pipe, Culvert Pipe, Well Tubing, Drain Tile, Fire Brick, Fire Clay. TElftR COTTfl CHWflEY PIPE flflD TOPS. Office and Yard, No. 248 BROADWAY, Cor. THIRD. LOS ANQELES, CAL. FACTORY, LOS ANGELES, CAL. California Sewer Pipe Company Standard Patterns of Sewer Pipe and Fittings. OFFICE, SEWER PIPE 248 BROADWAY, near THIRD, Los Angeles, Cal. RRIGATION AT HOME AND ABROAD. Were you aware, my friend, that in these piping times of industrial progress and devel- opment we were making his- tory very fast and history of _^ a mighty interesting kind, too? Such is the fact; and in no section of the country are the guide-posts of prosperity being located faster than through- out that vast domain which reaches from the plains to the Pacific Coast. IRRIGATION has given the impetus, and irrigation will build a future for the West, grand and magnificent. The history of irrigation development is being made every day, and the historian is The Irrigation. Age ( Pioneer journal of its kind in the world.) ENGINEERS Do you want to keep posted on news of construction work? INVESTORS Do you want to keep close watch upon the irrigation bond as a means of investment? CAPITALISTS Do you want to know where lie the lands that are easily brought under water? FARMERS Do you want to know how to obtain the biggest returns from the soil ? Of course you do, and The Irrigation Age will tell you all you want to know. SALT LAKE, 26 W. Third South. DENVER, SAN FRANCISCO, 1115 Sixteenth St. Chronicle Bldg Paper DO tl^e Rest. Which means that you send us your subscription and take advertising space. we believe the people of the country know a good thing when they see it, and that's why we want them to see The Irrigation Age (Pioneer Journal of its kind in the world. 1 ) CHAPTER I. ADVERTISING. The Kilbourne Jacobs Manufacturing Co., of Columbus, Ohio, says: Referring to our '"ad" which we placed with you for six months, we desire to say that we are well pleased, for it has brought us many in- quiries. We shall continue it six months longer. The F. C. Austin Manufacturing Co., of Chicago, says: We are pleased with your paper. So far as our " ad " is concerned, we have reason to attach direct good to your efforts. Lord & Thomas, Chicago, say: Your paper cannot but be of great interest to those who are engaged in irrigation enterprises, and we believe you have a field which you can fill to the advantage of investor and those on the other side. The Irrigation Machinery Co., of Denver, Colo., says: We have obtained better results from our ad- vertising in THE IRRIGATION AGE than from any other publication. It reaches the irrigation interests of the United States very generally. It is a splendid medium. CHAPTER II. SUBSCRIPTION. Col. R. J. Hinton says: On my recent tour I encountered THE AGE at every turn . I found it in the hands of engin- eers, business men and farmers. Its circula- tion for a new journal is marvelous. The Denver Times says: THE AGE should be supported for the work it is doing. It is a public benefactor. James Kirkpatrick, of Dillon, Mont., says: No farmer who irrigates can afford to be with- out THE AGE any more than lie can be without head-gates in his ditches. L. Bradford Prince, Governor of New Mexico, says: THE AGE is valuable to the West. It is ad- mirable in make-up and general appearance. 5. J. Gilmore, President of the Colorado Irriga- tion Society, says: Allow me to congratulate you on the general character and soundness of the articles in your paper. S. W. Winn, Secretary of the Syndicate Land and Irrigation Co. , Kansas City, says: I believe the public interest in irrigation will be greatly improved by the vigorous, intelligent way you are conducting THE AGE. We umnt you* Subscription and me uiant your Advertising patronage AGE TUB IRRIGATION ( BY THE SMYTHE, BRITTON & POORE CO.) DENVER, 1115 Sixteenth St. SALT LAKE, 26 W. Third South. SAN FRANCISCO, Chronicle Bldg. THIS BOOK IS DUE ON THE LAST DATE STAMPED BELOW AN INITIAL FINE OF 25 CENTS WILL BE ASSESSED FOR FAILURE TO RETURN THIS BOOK ON THE DATE DUE. THE PENALTY WILL INCREASE TO 5O CENTS ON THE FOURTH DAY AND TO $1.OO ON THE SEVENTH DAY OVERDUE. OCT APR 5 1968 i W i v c. MAR 2 2 '68 -8 AM LOAM LD 'Jl-o 36 37 UNIVERSITY OF CALIFORNIA LIBRARY