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^7i 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 wras 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^-'f11
^ ^j^ -4---g g-:«)_-_-Jdr±iii 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_ fa]} jn fee^ of 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
<s
td
y
OQ
W
y
GO
dis-
charge
Mean ve
per seco
rg
S P-
la
S "S-
1 2,
Hi
o i
B §.
E?
03
C O
*H ^
is!
° s
M. °
slopes
of
Ft
> 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
&
*" <J
* S
': I
• S-
S- S.
: Is,
•r-
2- 1
' P*
1 2,
50
2.
24
4
15
2
44 i 164
1 tol
100
2.25
44
4| 144
4
5i
16
1 tol
250
2.5
15
5
134
134
54
14|
1 tol
500
2.75
274
54
13
25
6
14*
1 tol
1000
•
3.
50
6
13
45
6|
14*
1 tol
2000
3.25 774
7
13
70
7|
14*
14 tol
j
3000
3.5 95
8
12|
85
8*
14
14 to 1
4000
3.5
s&
12f
110
9*
14
14 tol
5000
3.67
1474
8|
124
130
9*
isi
14 to 1
6000
3.75
170
H
124
150
9|
134
14 to 1
While the dimensions given in the above table are,
doubtless, suitable for the locality mentioned,, still the
slopes assigned will not give the velocities stated in the
16 IRRIGATION CANALS AND
table. They are computed by a formula with a constant
co-efficient c =94.5. To prove this we have: —
substitute this value of / in Dwyer's formula and we
have: —
v = 0.92 ]/2 X 5280 X s X r
.-, v = 94.5 i/rs
It is now admitted that a formula with a constant co-
efficient, such as Dwyer's, is suitable for only a small
range of channels. It is, however, now generally ac-
cepted that Kutter's formula is applicable to a wide
range of channels, and that, of all the existing formulas,
it gives the closest approximation to the actual flow of
large open channels.
Assuming a value of n = .025 for the channels given
in table 2 below, we find the corresponding velocities.
These velocities show that Dwyer's formula used in
computing table 1 above, gives too high a velocity for
all the channels. This subject will be referred to at
length in the articles on the Flow of Water where the ap-
plication of Kutter's formula is fully discussed.
OTHER IRRIGATION WORKS. 17
TABLE 2. Giving velocities of Channels by Ku tier's formula with n— .025.
Breadth of chan-
nel at bottom
in feet.
Depth of water
with full
supply in feet.
Slope of surface
of water in inches
per mile.
Side slopes.
Velocity in foet
per second.
21
4
15
1 to 1
1.34
*l
4f
14|
1 to 1
1.61
15
5
13£
1 to 1
1.98
27|
5|
13
1 to 1
2.24
50
6
13
1 to 1
2.53
77i
M
/
13
l|to 1
2.87
95
8
12|
l|to 1
3.12
121J
8|
12|
l|to 1
3.30
147 &
8*
12|
l|to 1
3.30
170
8f
m
litol
3.39
Article 7. Side Slopes „
The side slopes usually adopted, on the water side, are
within the limits of J horizontal to 1 vertical, to 3 hori-
zontal to 1 vertical. For most soils a natter slope
than 2 to 1 will not be required, and it is very seldom
that as flat a slope as 3 to 1 is required.
The outer slopes in earthen soils may have an inclina-
tion regulated by the stability of the ground, and 1J to
1 is most common.
As every rule has an exception, so we find that Mr.
Walter EL Graves, C. E., states of the Grand River Canal
system of Colorado: —
"The soil of this locality is peculiar, a sort of argil-
laceous adobe, that when dry resembles ashes, and when
thoroughly wet becomes a slimy mud, that is almost iin-
2
18 IRRIGATION: CANALS AND
possible to control or maintain in a fixed position. In
the canal banks it has a tendency, when soaked with
water, to melt and flatten out, and to preserve in good
form and for good service the channel has proven a very
difficult and expensive matter."
Long experience on thousands of miles of large and
small channels in northern India has proved that, when
a flatter slope than J to 1 is adopted in construction, it
cannot be maintained with economy after the channel
has got into its working velocity.
With muddy water and on flat slopes, especially
where weeds grow, silt is deposited on the sides of the
channel and they eventually take a slope of about J to 1,
It is found advantageous to allow this slope to remain
and not to flatten it during the annual repairs.
The same thing has been observed in America, but,
in this country, the recorded observations are not so
full as in India.
Captain Edward L. Berthoud, of Golden, Colorado, in
a paper on Irrigation, published by the Denver Society
of Civil Engineers, is quoted as having stated: —
" I find that cuttings in our ditches should not be less
than 1 to 1. If flatter they will be more exposed to the
wash of sudden rains, and finally reduced to 1 to 1, or
even steeper slopes."
With reference to the inner side slopes of canals,
Major W. Jeffreys, R. E., in a note in the Professional
Papers on Indian Engineering, states: —
11 Opinions are divided as to the pitch with which
the inner slopes of distributaries should be made. In
the Punjab a slope of 1J to 1 is adopted, while in the
Northwest Provinces 1 to 1 is preferred, chiefly for eco-
nomical reasons. For very light soils the former of
these is, of course, the stronger construction, but an
OTHER IRRIGATION WORKS. 19
officer of irrigation experience is able to distinguish be-
tween a rajbuha (lateral or distributary) newly made, and
one that has settled down into an irrigating line. ^What-
ever slope is adopted in construction, it is found that
this cannot be advantageously maintained after the
channel has been in use for some time. A distributary
at the close of an irrigating season invariably assumes
the following shape, except when the soil is impregnated
with reh (alkali).
When the time for clearance comes round, the engi-
neer in charge, if he is wise, will not attempt to restore
the original section which is opposed to the form that
nature adopts. It is only waste of money to dig away
the long slopes which are soon recovered with silt, while
in theory it does not afford a maximum hydraulic depth
which it is the great object to attain in channels with
low velocities. The custom on the Ganges Canal Dis-
tributaries is to trim off the slope at J to 1, as shown by
thick dotted lines, a b, c dy in Figure 7; and this, in prac-
tice, is found to conform more closely to the average
working section than any other. To arrive, then, ap-
proximately, at anything like the working results, the
discharge tables employed by the rajbuha (distributary
or lateral) designer should be based on these conditions."
The following canals have the side slopes mentioned
opposite their names. More information relating to
these and other canals will be found in Article 10.
20 IRRIGATION CANALS AND
TABLE 3. Giving the inner side slopes of canals in earth and sandy loam.
Ganges Canal, India 1J (horizontal) to 1 (vertical).
Sone Canals, India 1 1 (horizontal) to 1 (vertical).
Sutlej Canal, India 1 (horizontal) to 1 (vertical).
Agra Canal, India 1 (horizontal) to 1 (vertical) .
Cavour Canal, Italy 1| (horizontal) to 1 (vertical).
Henares Canal, Spain 1 J (horizontal) to 1 (vertical).
Del Norte Canal, Colorado 3 (horizontal) to 1 (vertical).
Citizens Canal, Colorado 3 (horizontal) to 1 (vertical).
Turlock Canal, California 2 (horizontal) to 1 (vertical).
Central Canal, California 2 (horizontal) to 1 (vertical).
TABLE 4. Giving the natural slopes of materials with the horizontal line.
Degrees. Degrees.
Gravel, average 40 Shingle 39
Dry sand 38 Bubble 45
Sand 22 Clay, well drained 45
Vegetable earth 28 Clay, wet 16
Compact earth 50
Article 8. Grade or Slope of Bed of Canal.
The method of finding the grade of a channel of given
dimensions, in order that it may have a certain velocity
or discharge, is fully explained in the article on the
Floiv of Water, as well as the solution of all the other
problems relating to open channels, likely to occur in
practice.
The discharge of an irrigation canal is diminished
in proportion to the quantity of water expended for
irrigation from its head to its tail end. There are
three methods by which the diminution of the discharge
is regulated: —
1. By diminution of sectional area and an increase
of slope, so proportioned that, though the discharge is
reduced as required, still the velocity is not diminished
throughout the full length of the canal channels.
2. By keeping the same sectional area and diminish-
ing the longitudinal slopes or grades.
3. By maintaining the same grade and diminishing
the sectional area.
OTHER IRRIGATION WORKS. 21
An example of the first method is herewith given in
detail.
Where the fall of the country is tolerably uniform,
the slope of the bed of the main channel should be Tess
than that of the branches, which again should be less
than that of the minor channels and cuts. The object
of this is to secure, as far as possible, a uniform velocity
so that the alluvial matter held in suspension may be
carried on from the head, and deposited uniformly over
the lands irrigated.
There are two important reasons why the silt should
be carried on to the land, the first is that the annual silt
clearance from the canal may be lessened as much as
possible, and the second is, that the silt, if it has fertil-
izing qualities, is of great benefit to the land. The ben-
efit derived from this is fully explained in the article en-
titled Fertilizing Silt.
As to the actual fall which should be given to a main
canal, of say bed width 100 feet, and depth of water 6 to
10 feet, experience shows that about 6 inches to 1 foot in a
mile is ample, with a wetted border of average rough-
ness.
The List of Carnals, in Article 10, gives the grade of
the principal Irrigation Canals in existence.
Let us now assume that a canal having a capacity of
1,700 cubic feet per second is required to irrigate a certain
district. Experience on other canals in the district has
shown that a mean velocity of 2.5 feet per second will
prevent the deposition of silt, whilst at the same time it
will not erode the bed or banks. It is therefore deter-
mined to give the canal a bed-width of 100 feet, a depth
of water of 6.5 feet, and side slopes of 1 to 1. By Kutter's
formula, with n = .025, we find that a slope of 10 inches
per mile will give a velocity of 2.5 feet per second, and
that therefore the discharge is 1,730.6 cubic feet per
22 IRRIGATION CANALS AND
second which is near enough to the required discharge
for all practical purposes.
Let us now suppose that branches are drawn off to
supply water for irrigation, and that, after these sup-
plies are drawn off, the bed-width and depth of the chan-
nel are reduced, below the head of each branch. As
the mean velocity throughout is to be maintained at
what the channel had at starting, the grade of the canal
will have to be increased at each dimuiiition of dis-
charge. For example, at the tenth mile from the head-
work an irrigation channel takes off a supply of 550
cubic feet per second. This leaves a supply of 1,150
cubic feet per second in the main canal. Arranging
the dimensions required for this supply, we find that a
bed width of 80 feet, depth of water of 5.5 feet, side
slopes of 1 to 1, and a grade of 13 inches per mile, will,
by Kutter's formula, with n =• .025, give a discharge of
1,175.6 cubic feet per second, and a velocity of 2.50 feet
per second.
These agree near enough to the required velocity and
discharge for all practical requirements.
At the 10th mile a branch takes off 550 cubic feet per
second.
At the 19th mile a branch takes off 350 cubic feet per
second.
At the 31st mile a branch takes off 300 cubic feet per
second.
At the 40th mile a branch takes off 260 cubic feet per
second.
At the 54th mile a branch takes off 140 cubic feet per
second.
At the 60th mile a branch takes off 50 cubic feet per
second.
The channel at the tail of the canal has only 50 cubic
feet per second for ten miles.
OTHER IRRIGATION WORKS.
23
The table given below shows how the dimensions and
grades of the channels are arranged to give the dis-
charge required, which is shown in the sixth column.
It will be seen that the discharge by formula, given in
column seven of the table, differs a little from the re-
quired discharge in column six, but a slight difference of
this amount does not affect the work to any appreciable
extent.
TABLE 5. Giving full details of channels computed by Kutter's formula with
n = .025.
Bed,
Width in
Feet.
100
Depth
in Feet.
Side Slopes
Grade
per mile.
Computed
Mean Veloc-
ity in feet
per second.
Required
Discharge in
Cubic Feet
per second.
Computed
Discharge in
Cubic Feet
per second.
65
1 to 1
10 inches
2.50
1700
1730.6
80
5.5
ti
13 inches
2.50
1150
1175.6
60
5.0
«
15 inches
2.48
800
806.0 .
40
4.5
'<
19 inches
2.52
500
504.6
20
4.0
(C
2 feet
2.43
240
233.3
10
3.0
«
4 feet
2.64
100
103.0
6
2.5
5 feet
2.45
50
52.0
From the length of the different reaches of the canal
and the fall in feet per mile in each reach we find that
in the whole distance of 70 miles the total fall is 150 feet,
being an average fall of 2.2 feet, nearly, per mile. If
the fall of the country did not admit of so high an aver-
age, it might be easily reduced by maintaining a greater
depth in the channels and diminishing the width. A
greater depth would give a greater hydraulic mean depth,
and, according to the increase of the hydraulic mean
depth, the slope could be diminished.
24 IRRIGATION CANALS AND
The above will be sufficient to indicate the mode in
which the slope of the channel should be regulated, in
order to prevent accumulations of silt. In practice, a
canal is never perfectly aligned on this principle, but
every endeavor should be made to adhere to it, in de-
signing a system of irrigation works, so far as local pe-
culiarities and other circumstances will permit.
The accumulation of silt in channels, particularly in
the. main channel, is not only a serious impediment to
maintaining a supply of water till the crops are matured,
but the clearance may be enormously expensive. Even
if the silt cannot be carried on to the fields, as in a per-
fect canal, at least one step in advance is gained, if it is
prevented from accumulating in the main channel; for
the maintenance of the supply in it, is the most essen-
tial point, and if there are deposits in the branches
only, it may be possible to clear them in turn, without
cutting off the supply from the river. If this might not
be feasible with the branches, it would be so at all events
with the smaller irrigation channels; and it would not
only be advantageous to throw on the slit to them, and
to clear them in turn, without cutting off the supply of
water from the branches, but the clearance would evi-
dently be much less costly from them than it would be
from the larger channels, because the haul would be less.
When the fall of the country is so gentle as not to
allow of the fall of the channels being gradually in-
creased from ten inches a mile it would be necessary to
reduce the initial slope somewhat. A very slight reduc-
tion, would, as it affects the whole of the channel on-
wards, in the aggregate, amount to something consider-
able.
If, on the other hand, the fall of the country be too
great, the initial slope may be increased, with, if neces-
sary, a reduction in the depth of water; or, if the fall of
OTHER IRRIGATION WORKS. 25
country is rapid at first and afterwards more gentle, the
desired result may be obtained by constructing perpen-
dicular drops at intervals.
Any change of direction causes a certain loss of veloc-
ity, and the water thrown into branches and minor
channels would lose velocity in passing through head-
sluices, unless they possessed the full water-way of the
channel. Due allowance would have to be made for this
by adding somewhat to the slope at the heads of the
branches and channels. Where the water supply is
drawn from a river highly charged with silt, the princi-
ple above described of the necessity of keeping up the
velocity to the point of delivery of the water is very
often neglected, and as a result canals silt up, causing
additional expense to clear them out and a loss of irri-
gating capacity.
With reference to the second method it is sometimes
advisable, when there is little silt, to give a uniform rate
of fall to the canal, or at all events not to change it too.
often. It will be sometimes found preferable to reduce
the gradient instead of diminishing the cross-sectional
area in proportion to distribution of water along its
course, and as the requirements for carrying the volume
of water became lessened. An illustration of this is
found in the Quinto Sella Canal, in Italy, which main-
tains a constant section for about fifteen miles of its
length; and although in this distance about one-third
of its waters are drawn off for irrigation, its capacity
for the carriage of water is diminished solely by reduc-
tion of gradient, the slope of its channel being 1 in
1,000 at its derivation from the Cavour Canal, and
which is gradually reduced to 0.3 per 1,000 at the
end, according as its requirements become lessened.
An example of the third method is supplied by the
canal of the Central Irrigation District of California, of
which Mr. C. E. Grunsky is the Chief Engineer.
26 IRRIGATION CANALS AND
The main canal of this district has a constant slope
of 1 in 10,000, and a constant depth of six feet, and its
discharge is diminished by contracting the bed width
of the canal.
Sometimes the fall of the ground, that is, the profile
of the line, will determine the grade of the canal, after
which the bed width and depth are fixed.
Mr. T. Login, C. E., has stated with reference to the
water of the river Ganges, admitted into the head of
the Ganges Canal at Hurdwar, that it is nearly free from
silt from October to March; but as soon as the snow be-
'gins to melt in April, the water is highly charged with
silt. This silt is carried down the canal in the hot sea-
son, that is, from April to September, and is deposited
over the canal bed, to be again picked up and carried
forward in the cold season, that is, from October to
March, when the water becomes more pure. This in-
formation may be useful in other works, somewhat sim-
ilarly situated, as to the period during which the water
supply is highly charged with silt.
Article 9. Dimensions of Banks.
The top of the canal banks is generally from 6 to 10
feet in width, according to the material and depth of
water, and it is seldom less than 1J feet above the maxi-
mum level of the water. This, generally speaking, will
be sufficient, as irrigation canals, from their position,
are not subject to floods, and, as a rule, they 'do not re-
ceive much of the drainage of the country through
which they pass, and for this reason, the effect of a very
heavy rainfall would be imperceptible.
A roadway is sometimes made on one or both banks,
and, in this case, this determines the top width of the
banks.
The top width of the bank is made level, or slightly
OTHER IRRIGATION WORKS.
27
lower on the side furthest from the canal, to allow the
rain waters to run off in that direction as, were the con-
trary the case, during storms a considerable quantity of
earth, especially in light soils, might be washed inter the
canal.
In some cases the top of the bank is made a segment
of a circle with a slight rise in the center.
When the channel is partly in cut and partly in fill, a
berm of from 2 to 6 feet in width is left between the top
28 IRRIGATION CANALS AND
of the bank in cut and the bottom of the fill, and usually
the fill has a flatter slope than the cut.
In deep cutting, where the excavated material is run
to waste, a berm of at least 10 feet in width should be
left between the top of the cut and the bottom of the
slope of the waste bank, and the waste bank should be
dressed up uniformly along the line.
In side-hill ground an open drain should be made on
the high ground above the canal, and the intercepted
drainage water carried to the nearest water-course.
In some of the large canals in Colorado, the bed has a
slope from the sides to the center of from 1 to 3 feet,
and this is called the sub-grade. It is said to have a
tendency to keep the current in the center of the chan-
nel.
Another peculiarity of some canals in Colorado, is
mentioned by Captain E. L. Berthoud, already quoted.
He states: —
" When the open cutting of a ditch follows around a
mountain slope, I find that the transverse 'slope' of the
ditch bottom should be 0.40 to 0.70 of a foot lower than
the ' bank side ' of the ditch, thus throwing the wear-
ing force of the current near the mountain side, and
largely diminishing the tendency in bends to cut the
1 bank ; opposite the slope of cutting.
"This deepening of the transverse slope, practically
in a bend, has the same effect as the elevation of the
outer rail in a railroad curve."
OTHER IRRIGATION WORKS. 29
In silt carrying channels, this lowering of the bed
at sub-grade and at the inner slope in sidelong ground,
seems of doubtful utility. It is likely that,-ln__tiiue,
these channels would make a working section, in which
the low parts mentioned would not be very apparent nor
be very likely to have any very marked effect on the ve-
locity at these parts.
Article 10. A List of Irrigation Canals, Giving Di-
mensions, Grades, Etc.
The following list gives some details of irrigation
canals in the principal irrigating countries of the world.
These details refer to the greatest discharging part of
the canals mentioned, that is, the reach immediately
below the head works.
The dimensions of the main canal only are men-
tioned., The laterals or distributaries are not included.
For instance, the length of the Ganges Canal is given
as 456 miles. This is the length o'f the main canai
alone. It has in addition 2,599 miles of distributaries
or laterals and 895 miles of escapes and drainage chan-
nels, which makes its total length of drainage channel
3,950 miles.
Again, the Sutlej, also known as the Sirhind Canal,
has, including all its channels, a length of 4,950 miles,
but of this only 503 miles, the length of the main, canal,
is given in the list. There are thousands of miles of
irrigation canals, in the different countries mentioned,
not included in the above list. The Inundation canals
of the single province of Sind in India are over 5,000
miles in length.
The mean velocity of the canals varies from 2 feet per
second upwards to 7 feet, and the side slopes from 1 to 1
to 4 to 1. As a rule, however, the side slopes of irriga-
tion canals, when first constructed, vary from 1 to 1 to
30
IRRIGATION CANALS AND
2 to 1, but, it is generally found, that after being in use
for some time, and exposed to the action of the water,
they become steeper than they were originally con-
structed. The information about some of these canals
differs considerably. For instance, the discharge of the
Upper Ganges Canal, and the Lower Ganges Canal,
has been stated by some authorities to be 5,100 cubic
feet per second and by others as high as 7,000 cubic feet
per second. The best available information has, how-
ever, been taken with reference to the canals included
in the list.
TABLE 6. Giving a list of Irrigation Canals.
NAME OF CANAL.
COUNTRY.
Length in miles
~s
o S
3
i
5"
Depth in feet
Slope
Discharge in cubic
feet per second. . .
Upper Gauges..
India
456
531
170
216
120
190
70
180
180
90
113
174
174
20
20
20
13
131
27.7
53
8.23
10
8
5.5
6
10
9
9
8
LoisGi
20
10
17
10
12
6
11
4.9
liii 4224
1 in 10560
lin 4800
1 in 10560
1 in 10560
1 in 10560
liii 3520
1 in 16POO
1 in 15000
1 in 12000
lin. 20633
1 in 14000
1 in 25641
1 in 20000
lin 1860
lin 2000
1 in 3067
6000
6500
2372
1068
2500
3500
1100
4500
4500
3000
10846
3943
1138
906
981
114
1851
3250
700
1760
600
2175
738
177
89
on
Lower Ganges
Western Jumna
Eastern Jumna
Baree Doab
,
433
130
466
503
137
125
170
190
170
31
53
92
102
84
28
50
25
(
Sutlej or Sirhind
Agra
(
,
Sone, Western
Sone, Eastern
Soonkasela
,
,
<
Ibrahimia
Egypt . ,
Main Delta (Flood). ..
Main Delta (Summer).
Sirsawiah (Flood)
Nagar " ....
Sahel
Subk « ....
Grand Canal of Ticino
Cavour
<
(
,
<
Italy
Ivrea ..
' '.'.'.'.'.'.'.'.'.'.
Cigliano
Botto ...
Muzza
(
Martesana..
(
Henares.
Spain
Isabella II.
The Eoval Jucar . .
OTHEK IRRIGATION WORKS.
31
TABLE 6. — Continued.
g
NAME OF CANAL.
COTTNTBT.
Length in miles
«F
^
Si
5'
u
®
*d_
c?
5'
if
.<*
Slope
Discharge in cubic
feelt per second....
Marseilles .
France
52
9 84
7.87
lin 3333
424
Ourcq.. ....
11.48
4.92
1 in 9470
Crappone
<
33
26
6.5
500
Verdon
.
51
1 in 5000
212
Alpines
,
480
St. Julien
(
18
1 in 3333
165
Carpentaras
,
33
lin 4000
212
Del Norte
Colorado, U.S. A.
50
65
5 5
1 in 660
2400
Citizens .
45
40
5 5
1 in 1760
1000
Uncompahgre
S9
24
1 in 1560
725
Fort Morgan
<>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 0
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
0 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
0 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 Canaly
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 —
vb =v— 10.87 i/rs. In. which i;=mean
velocity in feet per second.
vmax — 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<W-i- 7.71
^"^max :"~TT(T28
The least velocity, or that of the particles in contact
with the bed, is almost as much less than the mean ve-
locity as the greatest velocity is greater than the mean.
Rankine also states that in ordinary cases the veloci-
ties may be taken as bearing to each other nearly the
proportions of 3, 4 and 5. In very slow currents they
are nearly as 2, 3 and 4.
The deductions of Dubuat are that the relation of the
velocity of the surface to that of the bottom is greatest
when the mean velocity is least: that the ratio is wholly
independent of the depth: the same velocity of surface
always corresponds to the same velocity of bed. He
42 IRRIGATION CANALS AND
observed, also, that the mean velocity is a mean pro-
portional between the velocity of the surface and that
of the bottom.
As the result of his experience on rivers of the largest
class, M. Revy arrived at the following conclusions: —
1. That, at a given inclination, surface currents are
governed by depths alone, and are proportional to the
latter.
2. That the current at the bottom of a river increases
more rapidly than that at the surface.
3. That for the same surface current the bottom cur-
rent will be greater with the greater depth.
4. That the mean current is the actual arithmetic
mean between that at the surface and that at the bottom.
5. That the greatest current is always at the surface,
and the smallest at the bottom; and that as the depth
increases, or the surface current becomes greater, they
become more equal, until, in great depths and strong
currents, they practically become substantially alike.
Article 14. Mean Velocities from Maximum Surface
Velocities.
Bazin has given a very useful formula for gauging
channels, by means of which the mean velocity can be
found from the hydraulic mean depth and the observed
maximum surface velocity. For measures in feet this
formula is: —
c X ^max
= c + 2^4
Now let ci = c and
c -H 2o.4
v = ci X vm&K
The following table will be found of great service in
saving time, when using this formula: —
v=Ci X vma,.
OTHER IRRIGATION WORKS.
TABLE 8. Giving values of cr
43
Value of cx.
Hydraulic
~ • — =.
mean depth in
For very even sur-
faces, fine plas-
For even sur-
faces, such as cut
For slightly un-
even surfaces,
For uneven sur-
feet r.
tered sides and
stone, brickwork,
such as rubble
faces, such as
bed, planed
unplaned plank-
masonry : —
planks, etc: —
ing, mortar, etc.: —
earth:—
0.5
.84 .81
.74
.58
0.75
.84 .82
.76
.63
1.0
.85
.82
.77
.65
1.5
.85
.82
.78
.69
2.0
.85
.83
.79
.71
2.5
.85
.83
.79
.72
3.0
.85
.83
.80
.73
3.5
.85
.83
.80
.74
4.C
.85
.83
.81
.75
5.0
.85
.83
.81
.76
6.0
.85
.84
.81
.77
7.0
.85
.84
.81
.78
8.0
.85
.84
.81
.78
9.0
.85
.84
.82
.78
10.
.85
.84
.82
.78
11.
.85
.84
.82
.78
12.
.85
.84
.82
.79
13.
.85
.84
.82
.79
14.
.85
.84
.82
.79
15.
.85
.84
.82
.79
16.
.85
.84
.82
.79
17.
.85
.84
.82
.79
18.
.85
.84
.82
.79
19.
.85
.84
.82
.79
20.
.85
.84
.82
.80
Article 15. Destructive Velocities.
Kutter (translation by Jackson) states: —
" The maximum velocities determined by Dubuat, as
suitable to channels in various descriptions of soil, are
taken from Morin's 'Aide Memoire de Mecanique Pra-
tique', page 63, 1864. The first column in the follow-
ing table gives the safe bottom velocity, and the second
the mean velocity of the cross-section; the formula by
which these are calculated is: —
v = y , -j- 10.87 i rs
44 IRRIGATION CANALS AND
TABLE 9. Giving safe bottom and mean velocities in channels.
Material of Channel.
Safe
Bottom velocity vb,
in feet per second.
Mean velocity v, in
feet per second.
Soft brown earth
Soft loam .
0.249
0 499
0.328
0.656
Sand . ...
1 000
1.312
Gravel
1.998
2.625
Pebbles
2 999
3.938
Broken stone, flint
4.003
5.579
Conglomerate soft slate
4.988
6 564
Stratified rock
6 006
8.204
Hard rock.
10.009
13.127
" We (Ganguillet and Kutter) are unable, for want of
observations, to judge how far these figures are trust-
worthy. The inclinations certainly have no influence
in this case, as the corresponding velocities are mutu-
ally interdependent, but the variation of the depth of
water is most probably of consequence, and in shallower
depths the soil of the bottom is possibly less easily and
rapidly damaged than in greater depths, under similar
conditions of soil and of inclination. Yet this effect is
not very large, while that of the actual velocity of the
water is of the highest importance. Hence, it appears
that these figures may be assumed to be rather dispro-
portionately small than too large, and we therefore rec-
ommend them more confidently."
Mr. John Neville, in his hydraulic tables, states that
for the materials given in the following table the mean
velocity per second should not exceed —
0.42 feet in soft alluvial deposits.
OTHER IRRIGATION WORKS.
0.67 feet in clayey beds.
1.0 feet in sandy and silty beds.
2.0 feet in gravelly earth.
3.0 feet in strong gravelly shingle.
- 4.0 feet in shingly.
5.0 feet in shingly and rocky.
6.67 feet and upwards in rocky and shingly.
The beds of rivers protected by aquatic plants, how-
ever, bear higher velocities than this table would as-
sign, up to 2 feet per second.
Water flowing at a high velocity and carrying large
quantities of silt, sand and gravel is very destructive to
channels, even when constructed of the best masonry.
The Deyrah Doon water-courses in India had chan-
nels of sections varying from 5x2 feet to 10 x 4 feet, and
with slopes varying from 50 feet to 80 feet per mile.
They were almost all of masonry, and had numerous
masonry falls from 5 to 6 feet in depth on them, and
they passed over numerous and long aqueducts. The
following table shows the mean velocity in these chan-
nels, computed by Kutter's formula with n =.015.
TABLE 10. Giving dimensions, grades and velocities of masonry channels.
DIMENSIONS OF CHANNEL.
Slope in feet
per rnile.
Velocity in feet
per second.
Width in Feet.
Depth in Feet.
5
2
50
10.3
5
2
80
13.0
10
4
50
16.5
10
4
80'
20.9
Before measures were taken to protect the channels
the water rushed down along their course with a tre-
46 IRRIGATION CANALS AND
meiidous velocity, and carrying large quantities of sand
and gravel, and the abrasion injured all the masonry
works on the line. The silt-laden water acted even more
injuriously, as, impelled by the great velocity, it cut
into the masonry with an action like that of emery
powder. Even to a bed laid with large bowlders, great
damage was caused: the mortar joints were washed out,
the bowlders lifted out of their places and then rolled
along; the bed to add to the mischief. But it is to brick-
o
work that the greatest damage was done. In fact, it re-
quires but time to make all brickwork disappear entirely
in the presence of such action. In some of the old canals
there was a flooring of brick on edge over the arches of
the aqueducts. On one of these aqueducts not only was
the foot in depth of the brick floor entirely cut through,
but deep ruts were formed in the arch itself. But it was
on the falls, which were all formerly built after the ogee
pattern, and of brick, that the damage was greatest, as
might be expected. Their surfaces were cut into deep
striae, and they were in constant need of repairs, which
were difficult to execute.
It was, therefore, important to keep the silt out, and
this was done by building silt traps on the line of the
canal. *
Except in storm sewers, which flow for only a short
period every year, the mean velocity in sewers is usually
kept below five feet per second.
Colonel Medley, R. E., had considerable opportuni-
ties of observing the abrading power of silt-laden water
on the Ganges Canal, India; and in the " Roorkee
Treatise on Civil Engineering " he writes thus: —
" Brickwork should not be used in contact with cur-
* Mr. R. E. Forrest, iii the first volume of the Professional Papers on.
Indian Engineering.
OTHER IRRIGATION WORKS.
47
rents with such high velocities (15 feet per second).
Even the very best brickwork cannot stand the Wear and
tear for any length of time, and stone should he— used
for all surfaces in contact with velocities exceeding, say,
10 feet per second."
Article 16. Velocity Increases with Increase of Depth
of Channel.
The following table is given in order to show that, in
the channels usually adopted for irrigation, the velocity
increases with the increase of depth. The channel 50
feet wide will, with a depth of two feet, deposit silt; at a
velocity of about 1.6 feet per second, but with a depth of
five feet and a velocity of about 2.9 feet per second, it
will keep itself clear of deposit.
N =.0275. Side slopes 1 to 1.
TABLE 11. Giving dimensions, grades and velocities of channels.
Bed Width 10 Feet.
Bed Width 50 Feet.
Bed Width 100 Feet.
Depth in Feet.
Slope 1 in 1000.
Slope 1 in 2500.
Slope 1 in 5000.
Velocity in Feet per
Second.
Velocity in Feet per
Second.
Velocity in Feet per
Second.
2.
2.173
1.582
1.136
3.
2.756
2.084
1 . 520
3.5
3.002
2.302
1.692
4.
3.221
2.511
1.856
4.5
3.440
2.701
2.007
5.
3.634
2.878
2.150
48 IRRIGATION CANALS AND
Article 17. Abrading and Transporting Power of Water.
Professor J. LeConte, in his "Elements of Geology/'
states: —
" The erosive power of water, or its power of overcom-
ing cohesion, varies as the square of the Velocity of the
current.
" The transporting power of a current varies as the
sixth power of the velocity. * * * If the velocity,
therefore, be increased ten times, the transporting power
is increased 1,000,000 times. A current running three
feet per second, or about two miles per hour, will move
fragments of stone of the size of a hen's egg, or about
three ounces weight. It follows from the above law that
a current of ten miles an hour will bear fragments of
one and a half tons, and a torrent of twenty miles an
hour will carry fragments of 100 tons. We can thus
easily understand the destructive effects of mountain
torrents when swollen by floods.
" The transporting power of water must not be con-
founded with its erosive power. The resistance to be
overcome in the one case is weight, in the other, cohe-
sion; the latter varies as the square; the former as the
sixth power of the velocity.
" In many cases of removal of slightly cohering mate-
rial, the resistance is a mixture of these two resistances,
and the power of removing material will vary at some
rate between v2 and v6."
Silt, sand, gravel and stones lose as much weight in
water as a volume of water having an equal cubic con-
tent, which is generally about equal to half their weight
in air. They are, therefore, easily moved, but, with the
exception of silt, their velocity is less than that of the
current, and the nearer their specific gravity approaches
that of water the nearer their velocity approaches that of
the current.
OTHER IRRIGATION WORKS.
49
The English Astronomer Royal, in a discussion at the
Institution of Civil Engineers, said that the formula for
the transporting power of water, was the only instance in
physical science, with which he was acquainted, in which
the sixth power came really into application.
Mr. T. Login, C. E., states as the result of his obser-
vations for several years, on the Ganges Canal and other
channels, that the abrading and transporting power of
water increases in some proportion as the velocity in-
creases, but decreases as the depth decreases.
Umpfenback gives the size of materials that will be
moved in the botton of small streams, at the following
figures: —
TABLE 12. Giving the transporting power of water.
Surface Velocity
in Metres.
Gravel, Diameter in
Metres.
Surface Velocity
in Feet.
Gravel, Diameter in
Feet.
0.942
0.026
3.091
0.085
1.569
0.052
5.148
0.170
Cubic Metres.
Cubic Feet.
2.197
0.00515
7.208
0.182
3.138
0.209
10.296
0.738
4.708
0.618
15.447
21.826
Chief Engineer Sainjon made observations in the
River Loire in France, with the following results: —
Velocity of feet per second, 1.64 3.28 4.92 6.56
Diameter of stone in feet, 0.034 0.134 0.325 0.56
In order to protect the foundations of the Ravi bridge,
in India, 15-inch concrete cubes (1.56 cubic feet), were
deposited around the piers. It was noted in one case,
that with a velocity of probably not less than 10 feet a
4
50 IRRIGATION CANALS AND
second, the blocks were moved from a sandy bottom on
to a level brick floor protecting the bridge. Although
exposed to a more violent current they were not moved
off the flooring. This evidence is somewhat in proof of
Smeaton's experience, that quarry stones of about half a
cubic foot, were not much deranged by a velocity of 11
feet per second, although the soil was washed from under
them.
Experiments made by Mr. T. E. Blackwell, C. E., for
the British Government, in the plan of the Main Drain-
age of London, show very clearly that the specific grav-
ity of materials has a marked effect upon the mean ve-
locities necessary to move bodies.
For example, coal of a specific gravity of 1.26, com-
menced to move in a current of from 1.25 to 1.50 feet
per second.
A second sample of coal, of specific gravity 1.33, did
not commence to move until the velocity was 1.50 to
1.75 feet per second.
A brickbat of specific gravity 2.0, and chalk of specific
gravity 2.05, required a velocity of 1.75 to 2 feet per
second to start them.
Oolite stone, specific gravity 2.17; brickbat, 2.12;
chalk, specific gravity 2.0; broken granite, specific grav-
ity 2.66, required a velocity of 2.0 to 2.25 feet per second
to start them.
Chalk, specific gravity 2.17; brickbats, specific gravity
2.18; limestone, specific gravity 1.46, required a veloc-
ity of from 2.25 to 2.50 feet per second to start them.
Oolite stone, specific gravity 2.32; flints, specific grav-
ity 2.66; limestone, specific gravity 3.00, required a ve-
locity of 2.5 to 2.75 to start them.
It was shown in these experiments that after the start
of the materials with the current, in no case did the ma-
terials to be transported travel at the same rate as the
OTHER IRRIGATION WORKS. 51
stream, but in every case their progress was considerably
less, as a rule, often more than 50 per cent, less than the
velocity of the current.
Mr. Baldwin Latham, C. E., in the course of his ex-
perience in sewerage matters, has found that in order to
prevent deposits of sewage silt in small sewers or drains,
such as those from 6 inches to 9 inches diameter, a mean
velocity of not less than 3 feet per second should be
produced. Sewers from 12 to 24 inches diameter should
have a velocity of not less than 2^ feet per second, and
in sewers of larger dimensions in no case should the
velocity be less than 2 feet per second.
Sir John Leslie gives the formula: —
v = 4 i/ a for finding the velocity required to move
rounded stones or shingle, in which
v = velocity of water in miles per hour, and
a = the length of the edge of a stone if a cube in feet,
or the mean diameter if a rounder stone or bowlder, also'
in feet.
This formula takes no note of specific gravity. Chailly
has supplied this omission, and he has derived the
following formula, which is just sufficient to set bodies
in motion: —
v = 5.67 i/ag, in which
a = average diameter of the body to be moved in feet,
g — its specific gravity, and
v = velocity in feet per second.
Experience on the irrigation canals in Northern India,
where rapids are in use, has proved that a bowlder
rapid, with a flooring composed of bowlders not less than
eighty pounds in weight each, well packed on end, and
at a slope of 1 in 15, will not stand a mean velocity of
17.4 feet per second.
52 IRRIGATION CANALS AND
Article 18. On Keeping Irrigation Canals clear of Silt.
BY E. B. BUCKLEY, C. E.
(Extracted from Proceedings of the Institution of Civil Engineers,
Volume LVIII.)
There are four methods by which it is possible to ex-
clude more then a desirable proportion of silt from en-
tering an irrigation system: —
1. By works in the river, which will clear the water
before it enters the canal.
2. By so constructing the head-sluice of the canal
that only water bearing the desired proportion of silt is
admitted.
3. By constructing a depositing basin near the head
of, and in the canal itself, to be cleared either by dredg-
ing or by hand labor; or, what is practically the same
thing, by making two supply canals from the river to
the canal, one to be used while the other is being cleansed.
4. By constructing a double row of sluices, with a
settling tank between, so arranged that the water is
drawn off from the lower row carrying the desired
amount of silt, and so designed that the deposit in the
tank can be flushed back again into the river.
These systems are, of course, applicable under differ-
ent circumstances. The first can be rarely used, and
only when the local conditions are suitable. As, for
example, when the bed of an inundation canal is per-
haps 8 feet or 10 feet above the level of the bed of the
river, and which canal is therefore only supplied when
the river is in flood. In such a case, if a position for
the head of the canal can be selected behind an island
covered with brushwood, the top of which is perhaps a
little below, or even slightly above the high flood level,
it may be well worth the cost to make an artificial con-
OTHER IRRIGATION WORKS. 53
nection between the head of the island and the main
land, so that all the water entering the canal will first
flow through the bay, found between the island anxLthe
main land, entering that bay from below. The velocity
of water in the bay will thus be diminished; the water
will deposit silt in the bay instead of carrying it into
the canal; and if the bay be a large one the canal may
work for many years without its bed silting up.
The same principles can be employed on large irriga-
tion schemes, by altering the methods now generally
adopted on these works. The almost invariable arrange-
ment is that the weir which stretches across the river,
at a height of from 8 feet to 15 feet above the bed, is
cut by two sets of under-sluices, which are purposely set
as close as possible to the head-sluices of the canal im-
mediately above the weir; the floors of the head-sluices
and of the under-sluices being at the same level. The
under-sluices are placed in this position so that silt may
not accumulate in front of the entrances to the canal,'
and thus impede the free entrance of boats to the lock,
and of water to the canal. This object is attained by
opening the under-sluices during floods, thus drawing
down a rapid stream immediately in front of the opening
to the canals, which scours the channel and removes
any deposit that may have accumulated. At the same
time that the action of the under-sluices clears the ap-
proaches to the canal, it causes the canal to be more
deeply silted, for the higher velocity produced by the
scour of the under-sluices removes an extra quantity of
silt from the bed of the river, and it is from this rapid
and silt-bearing stream, impinging directly on the head-
sluices, that the canal is supplied. But if the weir were
constructed with a double set of under-sluices at each
end, one set being in the line of the weir, and about 200
feet from the river bank, and the other set some dis-
54 IRRIGATION CANALS AND
tance lower down the river, but connected to the upper
set by a flank wall parallel to the river bank, and if the
off-take of the canal were placed immediately above the
lower set, the stream flowing to the upper set would not
pass in front of the off-take to the canal. The silt-bear-
ing water would pass through the upper set of under-
sluices with full velocity, while that portion of the river
destined for the canal would have its velocity checked,
immediately opposite the flank wall, and would deposit
its silt to a great extent before it reached the head-
sluices of the canal. To sweep away the silt, which
would be deposited between the weir and the head-
sluices, it would be necessary to close the upper under-
sluices and to work the lower ones. This plan would
be rendered most effective by closing the head of the
canal for a few hours every week, while the lower under-
sluices were opened, so that the channel might be kept
clean without allowing any silt-bearing water to have
access to the canal.
In almost all cases the head sluice of a canal is
formed by rows of single shutters, sliding in verti
grooves, so that water is always first admitted to the
canal from below the shutters, that is, at a level of the
sluice floor. If the sluices were constructed so that the
water was drawn from the top instead of from the bot-
tom of the river, much less silt would be carried into
the canal. In rivers which rise moderately it is best to
have a single opening in each vent, covered by three or
four shutters sliding in a vertical groove; and each of
these shutters should have independent opening gear.
In rivers liable to floods rising 30 feet it is necessary to
have in each vent of the sluices, several openings at dif-
ferent levels, each opening being fitted with an inde-
pendent shutter, so that water can be drawn off at dif-
ferent levels as the flood rises or falls. This way of
OTHER IRRIGATION WORKS. 55
dealing with the silt can at most be but partially effect-
ive, but there are some rivers, carrying a small amount
of silt, to which this system may be applied with- suffi-
cient effect to render the clearance of silt from the canal
unnecessary.
The third method is frequently adopted on Indian
canals. The first half mile of the canal is excavated
with a base sufficiently large to cause a great diminution
of velocity; the silt is deposited during floods, and ex-
cavated when the canal is closed during the summer,
or perhaps it is dredged out at a cost even more exces-
sive than that of excavating it by hand.
The fourth method is peculiarly suitable for rivers with
a rapid fall. It is also most desirable where a canal
runs alongside of the river for some distance before
branching off into the country. If this method be
adopted, the channel of the first half mile or so must be
of such capacity that the velocity of the water in it,
when carrying the full volume required for the canal,
shall not exceed that which will allow of the deposit of
the matter in suspension; so that the water, when it
reaches the end of this length, shall contain only that
proportion of silt which the channels below are arranged
to convey to the fields. At the end of this broad chan-
nel a sluice will have to be built to carry the full dis-
charge required in the canal with little or no head upon
it. The head sluice on the river bank must be designed
so that, with only a moderate flood in the river, a suffi-
cient quantity of water can be introduced into the canal
to generate a velocity of three to four feet per second in
the broad reach, the flushing sluices leading back from
this reach to the river being arranged to discharge a cor-
responding quantity, or even a larger quantity of water.
These sluices might be fitted with falling shutters. The
largest flushing sluice should be about 150 feet to 300
56 IRRIGATION CANALS AND
feet from the head sluice, for it is about this point that
the heavy sand is deposited and where the greatest scour
would be required. This system is the most effective and
the least expensive for large schemes. If the head sluice
on the river bank be constructed on the principle of tak-
ing water from the surface of the river, instead of from
below, the minimum amount of silt will enter the broad
reach, and that can under conditions, be cleared away by
closing the sluices at the extremity of the broad chan-
nel for a short time, and opening all the shutters of the
head sluice on the river bank and the various flushing
sluices.
Article 19. Fertilizing Silt.
The quality of the silt carried by water for irrigation
is a matter of great importance. Whilst in some locali-
ties it is of no use to the land as a fertilizer, still, in a
great number of places, it acts as a good manure.
It is well known that for ages the fertility of Egypt
has been preserved by the silt-laden waters of the Nile.
Every year the Nile deposits its load of rich slime on
the land, and, in consequence of this, the soil retains
the fertility for which it has been famous since the
earliest date of history. Such muddy water furnishes
not only moisture to bring the crop to perfection, but it
also brings manure to the land, and thus prevents it
from being exhausted. The silt annually deposited is
merely manure, which is consumed in. bringing the
crops to maturity. This is the reason that the land has,
for so many centuries, remained within reach of the
Nile flood.
In Upper Egypt large depositing basins, to retain the
Nile silt, have been in use from time immemorial, with
great success.
OTHER IRRIGATION WORKS. 57
Sir B. Baker, C. E., states, respecting the fertilizing
properties of the Nile water: —
" 1st. That the fertility of the Nile is due to thlTor-
ganic matter, and to the salts of potash and phosphoric
acid dissolved and suspended in it.
" 2d. That these constituents are most abundant in
the water during the months of August, September and
October, wThen the river is in flood; and that it is during
the period of inundation that the sedimentary matter,
or mud, deposited from the water, is most valuable as a
fertilizing agent."
In Lower Egypt these basins are not used. The land
is flooded, but the water flows off and deposits very
little of its silt.
This is known as the Improved System.
Mr. "W. Willcocks, C. E., in his account of Irrigation
in Lower Egypt, states on this subject: —
" In Upper Egypt, where the old Pharaonic system of '
basin irrigation exists, every acre of land is cultivated,
and pays revenue, while the soil is as rich to-day as it
was thousands of years ago. In Lower Egypt, on the
contrary, where the improved system of irrigation pre-
vails, and a triple crop is gathered, one-third of the area
is uncultivated, while the remaining two-thirds are in-
capable of paying a higher revenue than Upper Egypt.
The improved system, besides, has only lasted fifty years,
and yet there is a cry of deterioration of the soil and
produce from one end of the country to the other, a cry
which is re-echoed by English cotton-spinners. Nature
wants the slime of the Nile flood to be deposited on the
land; it is now forced into the sea; and though it is not
necessary to go to the full extent of Napoleon's state-
ment, that wrere he master of Egypt he would not allow
an ounce of slime to be wasted; yet it may be stated,
58 IRRIGATION CANALS AND
without fear of contradiction, that for every one pound
(five dollars) of profit resulting from the expenditure of
one thousand pounds (five thousand dollars) on the im-
provement of the existing irrigation system, ten pounds
(fifty dollars) would be the return on money spent in a
partial restoration of the basin system where the lands
are cultivated, and a complete restoration where the
lands are not under cultivation."
In respect to irrigation, there are four kinds of water:—
First, rain; this is almost pure, and supplies nothing
to the land but moisture. The land dependent upon it
must be continually renewed by manure.
Second, well water. This also is quite pure, being
filtered through the earth, or, what is worse, it is often
injured for irrigation by being mixed with injurious
minerals, especially at the end of the dry season.
Third, tank or reservoir water. This generally con-
tains a good deal of nourishment for plants in a state of
solution, which it has absorbed in the lands it has passed
over, but what it has held in suspension is almost all
deposited in the bed of the tank before the water is
drawn off for the fields.
Fourth, river water. This water is led direct from the
rivers by canals to the fields. It deposits in the chan-
nels only the coarser parts of the silt it has brought
down from the higher lands and forests, much of which
is only sand. A large quantity of its most fertilizing
silt is, however, conveyed to the land. 80 complete is
the effect of this fertilization, that lands so supplied
continue to bear one or two grain crops for hundreds of
years without other manure. Thus the district of Tan-
jore, in India, is believed to produce as large crops now
as it did 2,000 years ago.
Different rivers are more or less fertilizing according
OTHER IRRIGATION WORKS. 59
as they pass through different rocky strata. Thus the
Kistnah River, in India, which passes through a lime-
stone country, has a delta which was found to produce
crops 50 per cent, larger than the delta of the Godavery,
which passes chiefly through a granite country.
In Midnapore, in India, the rainfall is sometimes as
much as ten inches in twenty-four hours, but the culti-
vators are not satisfied with this. In order to gain the
advantage of the manure in the river water, they drain
off the rain water as quickly as possible and admit the
former water. Long experience has proved to them
that they get better crops by irrigating with the silt-
laden water of the river than by the rain water.
The water of the river Indus, in India, is preferred to
well water, owing to the fertilizing silt which it con-
tains.
The water of the river Durance, in France, has a high
reputation for irrigating purposes. In addition to the
sediment mechanically suspended, it also holds much
valuable agricultural matter in solution, which is con-
sidered the main cause of the waters of that river being
so valuable for irrigation.
Mr. Kilgour, C. E., in the Minutes of Proceedings I.
C. E., vol. 27, stated:—
" The silt in suspension in the waters of the Punjab
rivers in Northern India was invaluable as a manure in
the district, where, owing to the scarcity of timber, the
dung of the cattle was mixed with clay, sun-dried, and
employed as fuel."
Mr. George Gordon, C. E., in a paper on the storage
of water, published in Minutes of I. G. E., vol. 33, says: —
"Land irrigated from a river gives a better return
than that under a tank by, it is said, 25 per cent, in
these parts. Whether this is principally due to the
60 IRRIGATION CANALS AND
brackish quality of the water locally collected, or to the
insufficient supply from tanks, the author cannot say;
probably both causes contribute."
General Scott Moncrieff, R. E. , states that the price paid
for the water of the Po, in Italy, was three times the
amount paid for the water of the Dora Baltea, the extra
value of the water of the Po being due to the fact of its allu-
vial silt being considered highly fertilizing, while that of
the Dora Baltea is rather the reverse. He also refers to
the marked difference between the meadows irrigated with
the silt-bearing waters of the Durance Canals in France,
and those of the clear, cold Sorgues, so much so, that
cultivators prefer to pay for the former ten or twelve
times the price demanded for the latter.
Mr. J. H. Latham, C. E., states, as the result of his
observations in the Madras Presidency, in India, that
river channels are the most prized of all the sources of
supply for irrigation as they are stated to give 25 per
cent, more crop per acre than either wells or tanks.
Mr. Allan Wilson, C. E., refers to the great superior-
ity of river and tank or reservoir water for irrigation
purposes, as compared with well and spring water, as an
argument in favor of the formation of river and tank
reservoirs. He ascertained from observation, and the
experience of practical authorities in India, that sugar
cane watered from tanks and rivers yields a much heavier
crop than land watered from wells and springs, and the
molasses produced from the former realizes double the
price of the latter.
Mr. Walter H. Graves, C. E., of Denver, Colorado,
states that the very means of reclaiming the arid land
is a constant source of its fertilization. By irrigation
the pores of the most sterile soil can be filled and com-
pacted by the infiltration of the impalpable silt, and con-
OTHER IRRIGATION WORKS. 61
verted into a loam of prodigious fertility. Hence, as a
general statement, all lands that can be reached and
supplied .with water for irrigation are susceptible ol cul-
tivation.
Mr. A. D. Foote, C. E., in his Report on the Irrigating
and Reclaiming of Certain Desert Lands in Idaho, gives
full and interesting details of crops grown on lands irri-
gated by silt-laden water, and shows very plainly its
great value as a fertilizer. And in a discussion on irri-
gation at the American Society of Civil Engineers in
1887, Mr. Foote further states: —
"The fertilizing silt which swift running water usually
carries is eventually nearly as valuable as the water it-
self. Without it irrigation in this country would soon
be a failure. No land can stand continual production
without enriching, and it will be many years before our
Far West can afford the ordinary artificial manures. The
silt with which our western rivers is loaded in the spring
and summer is so valuable, that the land irrigated by it
improves even unto the heaviest cropping."
Mr. E. B. Dorsey, C. E., quotes an Idaho farmer as
having said: — " I would rather give two dollars an acre
for muddy water than one for clear."
Mr. C. L. Stevenson, C. E., Salt Lake City, states that: —
" The waters of irrigation from the mountains annually
carry with them fresh fertilizing material, so that prac-
tically it costs the average Utah farmer less to keep up
his ditches and apply his waters of irrigation than it
does the eastern farmer to manure his land. One field
near Farmingtoii, at first producing some sixty bushels
per acre, was kept in wheat for thirty years with no
other fertilizer than what was brought by the waters,
and there was after the second or third year a general
average yield of over forty bushels to the acre."
62 IRRIGATION CANALS AND
As every rule has an exception, so we find an exception
to the almost unanimous opinion as to the value of silt-
laden water for irrigation.
Major J. Browne, R. E., in the Transactions of the
Institution of Civil Engineers, volume 33, states as the
result of his observations in the Punjab, India, that: —
" He had always understood from such cultivators as he
had spoken to, that crops raised from well water were
of a better quality than those raised from canal water.
He could not say whether it was due to the higher tem-
perature of well water, or to any chemical difference in the
water itself, but canal-raised, were, he believed, generally
inferior to well-raised crops."
It is not unlikely that the cultivators through custom,
as has often been found in India, adhered to their old
method of well irrigation.
Article 20. Silt Carried by Rivers.
It is sometimes of importance to know not only the
quality of the silt carried in suspension by a river, with
reference to its utility as manure, but also its quantity.
This quantity varies greatly in different rivers, and also
at different stages of the flood in the same river. In
August the Nile conveyed three hundred times more
solids in suspension than in May, although during the
former month the volume of water discharged was only
ten times greater than in May, the weight of solids in
suspension to the weight of water being then -g-yro-j
whilst in August it rose to ^4r- Although the volume
of water discharged in August was one-quarter less than
in October, the suspended sedimentary matter was three
times greater. In August the weight of sediment at-
tained its maximum of 23,100,000 tons and in October
with the greatly increased discharge the sediment de-
OTHER IRRIGATION WORKS. 63
creased to 7,600,000 tons, the proportion of sediment to
water in August being ^T an(^ in October ^Vir-
The perennial flow of the Nile was due to the mag-
nificent lakes of Central Africa, which lay at its source;
while its annual inundation was caused by the flooding
of the Atbara and Blue Nile during the rainy season.
These two tributaries (although almost dried up from
the end of October to the beginning of May, when
mountainous Abyssinia was as rainless as Egypt,) were
mighty streams from the beginning of June to the end
of September, and the undoubted origin of the period-
ical inundations, the unfailing deposits, and the won-
derful fertility of Lower Egypt.
The Godavery and Mahanuddy in India have a pro-
portion about TTV m but this is much less than that in the
Kistiia and Indus, the quantity in the latter amounting
to nearly ^ of its bulk.
In the Durance in France, with a flood discharge of
210,000 cubic feet per second, the quantity of sediment
mechanically suspended increases with the flow of the
river. The ordinary maximum is about equal to ^ of
the water by weight. In exceptional cases, as in August,
1858, the proportion was as high as y1^- of the water by
weight. In extreme low water the proportion by weight
is about T-o-V(r- The average proportion for the nine
years, 1867—75, was about ^4o~. It is estimated that the
Durance transports annually to the sea seventeen mill-
ion tons of earthy matter. It is stated that in the
Vistula in floods the proportion is ^- in the Garonne in
France T^ Q-; in the Rhine in Holland T-J-g- ; and in the
P° S^TT- I*1 other rivers the proportion varies from that
given above as a maximum to TT^TTIT as a dry weather
flow.
Sir Charles Hartley, C. E., has given the following
64
IRRIGATION CANALS AND
table showing the principal characteristics of four of
the great rivers of the world: —
TABLE 13. Giving length, discharge, etc., of rivers.
KlVER.
Length
in
Drainage
area in
Annual
rainfall in
Mean
annual
discharge
Mean
Mean weight
of dry sedi-
ment to
miles.
square
miles.
cubic
miles.
in cubic
miles.
Ratio.
•weight of
water.
Nile . . .
3 300
1 293 000
892 1
oo 7
QO Q
i
l&Off
Ganges
1,680
588,000
548.8
43.2
12.7
Mississippi .
4,190
1,244,000
673.0
132.0
5.0
itW
Danube ....
1,750
316,000
198.0
44.3
4.5
WsTT
As the central and lower parts of the Nile flowed
through an exceptionally dry and sandy region, it dis-
charged, as shown on the table, ^¥ of the annual rain-
fall on its catchment basin, and as regarded ratio of
rainfall to discharge, compared with other rivers, it was
three, eight and nine times greater than the Ganges,
Mississippi and Danube respectively. Again, although
the Nile had about the same drainage area as the Mis-
sissippi, its annual rainfall was 30 per cent, greater,
whilst its annual discharge was six times less than that
of the " great Father of Waters." Compared with the
Danube, the annual discharge of the latter was double
that of the Nile, although the annual rainfall of the
Nile basin was four and a-half times that of the Danube.
An irrigation canal drawing its supply from a river,
which carries fertilizing silt in suspension, and which
has sufficient velocity to carry the silt on to the land
requiring irrigation, deposits an immense quantity of
good manure, in a few months, in a thin film, over the
land. For example: let a canal have a bed width of
OTHER IRRIGATION WORKS. 65
60 feet, a depth of 4 feet, and side slopes 1 to 1, and a
mean velocity of 2.5 feet per second. Let this canal
flow for four months, or 120 days, and during tnisTlime
let its supply be derived from a river which holds silt in
suspension to the extent of -g-J-j- of the bulk of water.
The discharge of the canal is 640 cubic feet per second.
There are 86,400 seconds in one day. We have there-
fore: —
640 X 86400 X 120
97 — =307,200 cubic yards of fertilizing
silt deposited by the canal on the land in 120 days.
From this a good idea can be formed of the great ad-
vantage of manurial silt in an irrigation supply.
Article 21. Improvement of Land by Silting Up, Warp-
ing or Colmatage.
Silting up of land, warping or colmatage, is here in-
tended to signify the improvement of land before this
of little, if any, use, by the deposition of silt. Warping
is usually applied to the artificial silting up of land on
the sea coast, in bays and estuaries, but it is here also
applied to the silting up by river water of land not
within the influence of the tides. Colmatage is a French
word also used in works written in English to express
the same thing as silting up.
When water containing fertilizing silt is not required
for irrigation it can be usefully employed in making
good land out of a sterile waste. There are, no doubt,
numerous localities in the United States where land can
be improved in this way. A description of the im-
provement of some land by this method is here given. *
Above Epinal in France the course of the river Mo-
selle is well defined and regular. Below that point it
>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 ay 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 (d—x)-\-(d—x) 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: —
x2 — 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
0 = angle of HP with horizon.
Then HE, = CR. cot o = (d—x) 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) —d2 cot ft— — cot 0
From this equation the value of x can be found.
Example: — Given ft = 0 = 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.
d2
Then B = ad -f -^ = 432
25 + 37
A = s X 6 = 186 .*. equation becomes
x2
-^ — 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
+ 0
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./
0
«\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 0 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 /0. 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 --10, 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
formedfof 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 TWtns 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. Per 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 <of
shutters similar to those used on the Mahaiiuddy Weir.f
*Mr. E. B. Buckley, C.E., on Movable Dams in Indian Weirs, in Trans-
actions of the Institution of Civil Engineers, Vol. 60.
t Professional Papers on Indian Engineering, Vol. 4, Second Series.
138 IRRIGATION CANALS AND
Let /> = 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
<e center of percussion " of the shutter, then
Tensile stress of each chain = 37, 794 Ibs.
In order to diminish the violent shock caused by the
rapid rising of the upper shutter, Mr. Fouracres, C. E.,
made important improvements in the method of work-
ing them. Figures 74, 75, 70 and 79, give four views of
the shutters of the Sone weir in different positions.
Figure 74 shows the sluice "all clear/' with both shut-
ters lying on the floor, the flood being supposed to be
running freely between the piers, which are eight feet
in height. When it becomes necessary to close the sluice
mid shut off the water flowing through it, a clutch worked
from a handle from the top of the pier is turned, which
frees the shutter from the floor, and it then floats par-
OTHER IRRIGATION WORKS.
139
tially up from its own buoyancy, when the stream, im-
pinging upon it, raises it to an upright position with
great force, .shutting up the sluice-wray, Figure 75.
Ml ON A PORE CANAL
Tumbler Regulating Gear for Distributaries.
o_a
aaaa
rzoa
— i — \
But if a shutter, twenty feet long and eight feet in
height, were allowed to come up with such velocity, it
would either carry away the piers or be carried away
itself. To destroy this sudden shock, Mr. Fouracres
fixed to the down-stream side of the upper shutters six
hydraulic buffers or rams, which also act as struts for
the shutters when in an upright position. These rams
are simply pipes with a large plunger inside, as shown
in longitudinal section, Figure 77, and cross-section,
Figure 78.
The pipes fill witli water when the shutter is laying
140
IRRIGATION CANALS AND
down, and when it commences to rise, the water has to
be forced out of them by the plunger in its descent, and,
as only a small orifice is provided for the escape of the
FOURACRES' SLUICES AT THE WEIR ON THE RIVER SOME.
water, the ascent of the shutter, forced up by the stream,
is slow and gentle, instead of being violent. The orifices
OTHER IRRIGATION WO11KS.
141
in the pipes are covered with india-rubber discs to pre-
vent them from being filled with sand or silt.
The water is now shut off effectually, as shown in Fig-
ure 75; but without other means being taken it would
'be impossible to open the sluice again, as it could not
^ 7?
SECTION Of HYDRAULIC BRAKE HEAD. SONE~WEIR.
be forced up-stream. The back shutter is therefore pro-
vided below it, as shown in this same view. This lower
or back shutter is so arranged that it can bo lifted up by
hand and placed upright, ties being placed to support it,
as shown in Figure 76. The water is then allowed to fill
the space between the two shutters, and the upper one
can then be thrown down on the floor again, but the
lower one is held up by ties which are hinged to it at
one-third of its height, and by this means it is " bal-
142
IRRIGATION CANALS AND
OTHER IRRIGATION WORKS. 143
anced," and resists the pressure on it until the water
rises to its top edge, when it loses its equilibrium and
falls over, thus opening the sluice again.
The sluices can be left to fall of themselves if the river
rises in the night; or, if it is thought not expedient,
they can be made fast by a clutch on the pier-head, as
shown in Figures 74, 75 and 76. By these expedients,
these large sluice-ways, twenty feet broad and eight feet
deep, can be shut off or opened as required, with the
greatest facility arid expedition, and the whole set of
twenty-five sluices can be opened in a few minutes, and
when opened they can pass through them anything that
the river brings down, without danger to the wier.*
Figure 79 shows the upper shutter as it is being raised
by the current through the sluice-way.
During the hot season, when it is of importance to
utilize all the available water, all leaks between the shut-
ters and piers are calked with hemp and straw, to pre-
vent loss of water by leakage.
It has been found in practice on the Soric Weir, that
the shutters can be safely lifted, without shock, against
a head of ten feet of water, and they haAre been fre-
quently worked under these conditions. The great-
est head against which other shutters on any other
weir have been lifted is believed to be about six feet
nine inches only. It is stated to be a sight worth see-
ing to watch a stream of water twenty feet broad
and eight or nine feet deep, flowing with a veloc-
ity of seventeen to twenty feet a second through the
sluices, with a difference of ten feet between the water
level above and below the sluices, to be suddenly closed
by a single gate twenty feet long by ten feet deep. The
water, when the shutter reaches the vertical, rises in a
i(/. September 10th, 1873.
144
IRRIGATION CANALS AND
wave one or two feet above the top of the shutters and
piers, and flows over for a few seconds before it sinks to
the mean level of the stream.
In the Transactions of the Institution of Civil En-
gineers, Vol. 60, Mr. F. M. G. Stoney, C. E., has given
a design for a large span lifting sluice, shown in Figures
80, 81, 82, 83 and 84. This is inserted here to show a
design that in certain circumstances it may be very ad-
vantageous to adopt, where it is necessary to have a
large opening.
The clear span was forty feet, and the depth of water
twelve feet. The gates were designed to be lifted twelve
feet. The up-stream face was vertical, and the gate
simply fitted at its ends against planed guides in the
pier faces, the contact being kept close by self-adjusting
slips, and the gate was free to press down fairly on a
level sill. The gate was simple. It was composed of two
main girders, placed equally at each side of the center
of pressure; cross vertical beams connected these gird-
ers, and carried the sheeting and the top of the gate.
The static pressure was eighty-one tons. The weight of
the gate was eighteen and one-half tons, and the mov-
ing load, including rollers, was roughly, twenty tons.
The whole was arranged to be lifted, by a pair of strong
right and left screws. These screws were placed liori-
OTHER IRRIGATION WORKS.
145
146
IRRIGATION CANALS AND
zontally 011 a foot bridge, and acted 011 large nuts travel-
ing in guides, each nut pulled chains which passed over
large pulleys down to the gate, where they were sym-
metrically grouped round its center of gravity. The
weight of this sluice-gate, foot bridge and all, was only
twenty-seven tons.
AND OTHER IRRIGATION WORKS. 147
Article 32. The Loss of Waiter by Percolation Under
a Weir.
While it is not practicable, by direct experiment, to
find the quantity of water lost by percolation through
a sandy bed under a weir, still an approximation can be
found 'to this loss by the method given below: —
By D'Arcy's experiments the discharge of a fourteen-
inch pipe filled at the bottom with sand, to a depth of
from two feet to six feet, was carefully ascertained under
heads ranging from three feet to forty-six feet. Dupuit,
in summarizing these and other experiments, states that
the discharge is directly proportional to the head, and
inversely proportional to the thickness of sand, and that
for one meter head and one meter thickness of filtering
material, the rate of percolation is twenty-six cubic
meters per day for coarse sand, and 4.5 cubic meters for
the finest sand. To check percolation, then, coarse
sand is required as a matrix to give stability, and fine
sand to fill up the interstices. With these materials, as
Brunei found at the Thames Tunnel, the water will run
through at first, but soon stop.
To give an instance of the application of D'Arcy's ex-
periments, let us find the loss by percolation under the
Godavery Anicut or Weir, Figure 44. A description of
this anicut has already been given in Article 28. This
ariicut rests upon a bed of coarse sand of unknown
depth, through which an incessant percolation takes
place, the water passing under the anicut, and rising to
the surface of the river again, below it. There is, at
the same time, a constant draught, by the three main
irrigation canals, of the greater part of the available
supply entering the pool above the anicut. Yet the
water only falls a foot or two below the crest, in the hot-
148 IRRIGATION CANALS AND
test weather. There is a certain area of the surface of
the bed of the river, above the dam, through which
leakage takes place. The leakage is greatest near the
dam, and gets less as the distance from the dam in-
creases up stream. We have no means of knowing to
what distance the appreciable leakage extends. Let us
assume one hundred feet as a reasonable distance, and,
as the total length of the anicut is 11,866 feet, we have
1,186,600 square feet of porous, sandy surface con-
stantly leaking under a head of twelve feet to fourteen
feet. Notwithstanding this immense area of porous
surface, the water level in the pool above the anicut
falls but little, though the total supply in the river may
be less than 3,000 cubic feet per second.'*
The mean distance the water would have to traverse
the sand, Figure 44, in order to pass from above to below
the anicut, upon the preceding hypothesis, would be
about eighty meters, and since the head of water is,
say, four meters, the velocity of filtration, by Dupuit's
formula, already stated, with a constant of fifteen cubic
meters, that is a mean of the coarse and fine sand,
would be: —
=f meter per day =—— feet per second.
80
Now this velocity multiplied by the area is: —
_ =338 cubic feet per second or about 11 per
cent, of 3,000 cubic feet per second, which is the ordi-
nary flow down the river in the dry season.
We thus see that the loss of water is not great, even
under the most favorable conditions for percolation,
* Engineering, April 28th, 1876.
OTHER IRRIGATION WORKS. 149
with a large area and clean sand. Under ordinary cir-
cumstances, however, the interstices of the sand, above
the weir, and near the surface of the bed of theTrlver,
get filled up with fine silt, and a layer of silt is formed
on the bed and banks of the river, thus materially pre-
venting the percolation.
Article 33. Bridges — Culverts.
Only a few brief remarks will be made with reference
to Bridges. There are several very good works published
treating very fully on this subject.
Ordinary highway bridges are required wherever roads
cross the canal, to accommodate the traffic of the court-
try.
In America, bridges 011 Irrigation Canals are usually
constructed of timber, but in India, Egypt and Italy,
they are as a rule constructed of masonry.
Bridges are sometimes combined with and form part
of Regulators and Falls. There is no difficulty about
the water-way of canal bridges, as the regulators and
escapes enable the high water in the canal to be always
kept within the limits of its intended full supply.
The Culverts for passing the drainage of the country
under the canal, are, in America, of the usual timber
box-culvert type.
The culvert should be amply large to pass away the
flood-water, without causing much heading up above its
top. Before fixing its size, it is advisable to have a rough
survey made of the area draining into the culvert, and
then, assuming a heavy rainfall, the number of cubic
feet of water per second reaching the culvert can be
found. Having fixed the grade of the culvert, we have
the grade and discharge from which the required area
can be found, as explained in the Flow of Water.
150 IRRIGATION CANALS AND
Myers has given a formula for finding approximately
the required area of the culvert. It is: —
<i ~c\/ Drainage area in acres.
where a — cross-sectional area of culvert in square feet,
and c is a variable co-efficient having the fol-
lowing values: —
c — 1.0 for slightly rolling prairie;
c == 1.5 for hilly ground;
c =- 4.0 for mountainous and rocky ground.
It may appear that this is going too much into com-
putations to design a simple culvert, but surely the
results from these are, as a rule, better than mere guess
work. The computations would take but a few minutes.
A defective culvert, causing a breach in a canal during
the irrigation season, would do a great deal of damage.
Article 34. Aqueducts — Flumes.
Aqueducts, usually called Flumes in America, are used
to carry a canal over a river or other obstruction. Before
adopting an aqueduct, it is advisable to investigate
whether, by altering the course of the river, the latter
can be made to run clear of the former. A very in-
structive example of this was the diversion of the Chuk-
kee torrent on the Baree Doab Canal, in India, for the
passage of which costly works were originally designed.
The Chukkee, at the time of the commencement of the
canal works, had two outlets. Just above the crossing
point of the canal, the main channel divided; one, the
larger branch, running into the river Beas, the other
into the river Eavee. This latter was embanked across
at the bifurcation by bowlder dams, and spurs of the
same material, protected at the extremity by masonry
OTHER IRRIGATION WORKS. 151
revetments. By these means the whole of the water was
forced to flow into the Beas, and the expense of the
works for the canal crossing saved.
When, however, a canal meets a river that cannot be
diverted, there are three cases under one of which it
may have to be crossed:
First. When the river is OH a lower level than the
canal.
Second. When the river is on the same level as the
canal.
Third. When the river is on a higher level than the
canal.
Ill the first case the canal is carried over the river by
an Aqueduct or Flume.
In the construction of an aqueduct there are two
things to attend to of vital importance. The first is that
the waterway, under the aqueduct, should be amply
large, in order to pass the greatest floods with safety,
and the second is that the junction of the aqueduct and
the earthen embankment at its ends, should be made
water-tight.
For want of ample provision for flood water the Kali
Xuddee Aqueduct on the Low^er Ganges Canal in India,
was destroyed on January 17th, 1885, causing a loss, not
only for its reconstruction, but also on account of the
stoppage of irrigation.
Every practical method should be employed to find
the flood discharge of the river, in order to have several
checks on the results, and sufficient waterway should be
provided to pass this flood wrater through the aqueduct,
without endangering its stability in any way. For in-
formation on this subject see the articles entitled Flow of
Water.
The embankments at the cuds of the masonry aque-
152
IRRIGATION CANALS AND
duct over the river Dora Baltea, on the line of the Ca-
vour Canal, in Italy, leaked very much at first. To
remedy this the embankment was dammed up at the
lower end and filled with water to a depth of about three
feet. Several boats were then employed, throwing in.
clay all over the bed. After a time the water was turned
off, and cattle driven into the muddy channel, which
was turned over and worked into puddle. Again it was
filled with water, and where filtration was observed, more
clay was thrown in, and the puddling process repeated;
and so on, till after nearly a year the filtration had en-
tirely ceased.
For purposes of economy a high velocity is usually
given to an aqueduct.
An aqueduct differs from a bridge in having to carry
a water channel over it, instead of a road or railway,
but, unlike the latter, it is not constantly subjected to
the jars of a suddenly applied load.
OTIIKR IRRIGATION WORKS. 153
Aqueducts are usually constructed of masonry, iron
or wood, or a combination of them. The Solani Aque-
duct in India, and the Dora Baltea Aqueduct in Itahr,
are two very fine specimens of masonry aqueducts.
A great deal of water is lost through the use of wooden
troughs in. flumes. When they are dry, the action of the
sun causes numerous cracks which it is afterwards im-
possible to keep water-tight.
Figures 85 and 86 show an elevation and section of a
flume on the Uiicompahgre Canal in Colorado. Figures
87 and 88 show plan and section of the Big Drop on tha
Grand Eiver Canal in Colorado. This drop shows anr
other peculiarity of American engineering. Before
reaching the drop the section of the channel is thirty
feet wide by four feet deep. At the drop it descends
thirty-five feet in 135 feet, and at the bottom the water
is discharged against a boom of solid timbers and thrown
backward in a penstock, whence it escapes over a riffled
floor.
Figure 89 is a view on the Platte Canal (High Line),,
showing the flume issuing from tunnel, and Figure 90
is a view of flume of Platte Canal (High Line, Colo-
rado), crossing Plum Creek at Acequia. Mr. P. O'Meara,
C. E., in Transactions of the Institution of Civil Engin-
eers, volume 73, describes flumes constructed in Colo-
rado. The North Poudre Canal is carried from the dam
154
IRKIGATIOX CANALS AND
to the mouth of the canon, through a series of tunnels
and flumes, these latter supported on shelves and gulch
bridges.
Platte River, with Platte Canal, Colorado,
The shelves are cut, for the most part, in the solid
rock, and are nine feet wide at the base. The flume
which rests on them, as on the bridges, is eight feet
OTHER IRRIGATION WORKS
155
156
IRRIGATION CANALS AND
wide by six feet deep in the clear, and projects a little
over the edge, a few running beams and upright props
being occasionally used to support it where fissures occur.
Lower down, where the canal crosses some creeks or riv-
ulets, the flumes are twelve feet wide by four feet three
inches deep in the clear, to accord better with the section
of the canal in the open plain, which is twenty feet wide
at the bottom and four feet three inches deep. Precau-
tions are taken to secure the sides of the canal for a
short distance from the ends of the flume against the
effects of increased speed in the water, and a slight al-
lowance is made at these points in. the general gradient.
Fig. 91. High Flume over Malad River, West Branch, Utah.
The whole of the flume work is carefully calked with
oakum. In. earthwork the ends of the flumes are raked
off to a slope one and one-half to one, and the spaces be-
tween the ties and posts, for about twelve feet back, are
filled with retentive clay. Where the flume terminates
in a rock cutting or tunnel, the side of the flume near the
end and the rock is built up with cement masonry, for
OTHER IRRIGATION WORKS. 1O<
three or four feet in length, or with two faces of masonry
filled between with clay.
Mr. O'Meara further stated that the soil was very stony
and pervious to water, and therefore, it was found
necessary to use wooden flumes instead of embankments
to carry the water. In one case about a quarter of a
mile of the North Poudre Canal was embanked, and
water let into it, and the consequence was that nearly all
of it was carried away, and a flume of wood had to be
inserted, and calked well to prevent the water from es-
caping. »
Fig. 92. Iron Flume over Malad River, Corlnne Branch, Utah.
Figure 91 shows the high iron flume over the Ma-
lad river at the ninth mile of the Bear River Canal
in Utah. This flume is 378 feet in length and eighty
feet in maximum height, supported on iron trestles, the
river span of which is seventy feet. The trough of this
flume is constructed of wood. It is twenty feet wide in
the clear and is intended to carry seven foot in depth of
158
IRRIGATION CANALS AND
OTHER IRRIGATION WORKS.
water,, and the approaches to the iron trestle are also
wooden flumes of similar dimensions, and 500 feet in
length.
Figure 92 shows the iron flume over the Malacl river
on the Corhme Branch of the Bear River Canal. This
(lume is founded on piles and iron cylinders filled with
concrete." This flume consists of three principal bents
from twenty-five to sixty feet in length, the peculiarity
of its construction being that the superstructure form-
ing the bridge itself is of iron plate girders and consti-
tutes the flume which carries the water.*
Probably the most celebrated aqueduct in existence is
the Solani Aqueduct, near lloorkee Civil Engineering
College, on the line of the Ganges Canal. A brief de-
scription of this work is herewith given.
The work by which the canal is carried across the
valley of the Solani river, consists of three parts.
Fi-wt. The embankment of earth and brickwork,
10,713 feet in length, from the high land on the up-
stream side of the canal to the Solani1 river. This is
shown in cross-section in Figure 94.
Second. The maxoiii't/ aqueduct over the Solani river,
9-20 feet in length.
Third. An embankment 2,723 feet in length, similar
to Figure 94.
The earthen embankment or platform is raised to an
average height of sixteen and a half feet above the coun-
try, having a base of 350 feet in width, and a breadth at
top of 290 feet. On this platform the banks of the canal
are formed, thirty feet in width at top, and twelve feet
in depth. These banks are protected from the action of
the water by lines of masonry retaining walls, formed in
*The views and descriptions of the two flumes on the Bear lliver
Canals are taken from the Irrigation Age of July ],• 1891.
160 IRRIGATION CANALS AND
steps, extending along their entire length, or for nearly
two and three-quarter miles.
The river itself is crossed by a masonry aqueduct,
which is not merely the largest work of the kind in In-
dia, but one of the most remarkable for its dimensions
in the world. The total length of the Solani Aqueduct is
920 feet. Its clear waterway is 750 feet, in fifteen arches
of fifty feet span each. The breadth of each arch is 192
feet. Its thickness is five feet; its form is that of a seg-
ment of a circle, with a rise of eight feet. The piers
rest upon blocks of masonry, sunk twenty feet deep in
the bed of the river, being cubes of twenty feet side,
pierced with four wells each, and under-sunk in the
usual manner. These foundations, throughout the whole
structure, are secured by every device that knowledge or
experience could suggest; and the quantity of masonry
.sunk beneath the surface is scarcely less than that visible
above it. The piers are ten feet thick at the springing
of the arches, and twelve and a half feet in height. The
total height of the structure above the valley of the river
is thirty-eight feet. It is not, therefore, an imposing
work when viewed from below, in consequence of this
deficiency of elevation; but when viewed from above,
and when its immense breadth is observed, with its line
of masonry channel, nearly three miles in length, the
effect is most striking.
The water-way of the masonry channel is formed in
two separate channels, each eighty-five feet in width;
the side walls are eight feet thick and twelve feet deep,
the depth of water at full supply being ten feet. A con-
tinuation of the earthen aqueduct, about three-quarters
of a mile in length, connects the masonry work with the
high bank at Roorkee, and brings the canal to the ter-
mination of the difficult portion of its course.
The aqueduct has carried over 7,000 cubic feet of
OTHP:R IRRIGATION WORKS.
161
water per second, but usually carries between 5,000 and
6,000 cubic feet per second.
Fig. 94. Cross-Section of Solan! Aqueduct Embankment.
Captain J. Crofton, R. E., in his Report on the Ganges
Canal, states that: " The aqueduct over the Solani tor-
rent has stood well. The state of the bed of the torrent
above and below shows that the waterway under the
aqueduct is just sufficient and no more; there is no hole
or retrogression of levels down stream, and little or no
silt has been deposited except under the side arches,
where a certain quantity would naturally be left on the
subsidence of floods. The flooring of the canal channel
above requires some waterproof covering; dripping still
continues through the arches, though less than at first,
the effect of which has been to loosen a considerable
surface of the outside plaster, and here and there bricks
of an inferior description (of which it is next to impos-
sible to prevent a few finding their way into so great a
mass of brickwork) may be seen slowly decomposing
from the same cause. It was at one time supposed that
the pores of the brickwork would gradually fill up and so
stop the percolation, but the fact is, that even the very
best of brickwork is of too absorbent a nature to be
proof by itself against the constant pressure of a head
of water even much less than that passing over this aque-
duct.
."A breach occurred some years since along a short
portion of the right bank revetment, Figure 94, from the
heeling over inwards, towards the channel of the wall,
A, from a point some four or five feet below the level of
the bed. The channel here had been considerably
11
162
IRRIGATION CANALS AND
deepened, and the accident occurred just after the canal
had been laid dry. The outer wall, B, was very little, if
at all affected.
Solan! Aqueduct, Ganges Canal.
" From the investigation made immediately after its
occurrence, it appears to have been caused by the pres-
OTHER IRRIGATION WORKS. 163
sure of the earth filling, between the waits, which had
become saturated by the percolation through the_ brick-
work. When the counteracting pressure of the water in
the canal was removed, the thin wall gave way, there
being no weep holes through it by which the drainage
from the backing could find an exit. The bed all along
between these revetments was to have been protected by
a layer of bowlders; this, however, has been deferred
from economical motives, the actual protecting work
now being confined to a sloping talus of bowlders and
brick kiln, rubbish, thrown down from time to time,
along the foot of the revetments."
11 The Henares Canal* is carried over the Majanar
Arroyo or torrent, in an iron aqueduct which is worthy of
admiration on account of its perfect fitness, both in de-
sign and construction, for the work it has to perform.
The discharge of the canal at full supply is 177 feet per
second. "
Full details are given in Figures 98, 99, 100, 101, 102,
103.
The iron trough is seventy feet long, with a clear bear-
ing of sixty-two feet. Its waterway is 10.17 feet wide,
the sides being composed of iron box-girders 6.2 feet
deep. The total weight of iron in the trough is 27.3
tons, and the weight of water when full is ninety tons.
Each girder is calculated to bear 200 tons, equally dis-
tributed, or the whole trough 400 tons. The aqueduct
is absolutely free from leakage, which was most inge-
niously prevented. The ends of the trough rest on
stone templates. Four inches from each end a pillow,
composed of long strips of felt carpet, about nine inches
wide, soaked in tallow, is let into the stone right across,
below the breadth of the trough, which pressing fully
* Lieut, (now General) C. C. Scott Moncrieff, R. E., Irrigation in South-
ern Europe.
164
IRRIGATION CANALS AND
on it, makes a water-tight joint without taking the bear-
ing off the stonework. Still further to make things se-
cure, a recess about one foot deep and four inches wide,
is cut in the stone all around the bottom and sides. In
this rests a lead flushing, riveted to the trough like a
fringe. Round this lead is poured in, a hot mixture of
pitch, gas tar, and fine sand, forming a water-tight joint,
and yet flexible enough to allow a slight play, as re-
quired by the expansion and contraction of the iron
trough. The result produced is perfect in preventing
the loss of water by leakage.
Article 35. Level Crossings.
The second case, mentioned at page 151, where a
canal crosses a river on the same level, is called a Level
Crossing. Small drainage channels carrying small quan-
tities of silt, may be passed into the canal without doing
OTHER IRRIGATION WORKS. 165
any material damage. If the river, or torrent, is of large
dimensions, and brings down a great volume of water at
a high velocity, the above method will not answer; as
Level Crossing, Ganges Canal.
the water loaded with silt would in some places choke
up the canal bed and cause the water to overflow its
bank, and in other places it would erode the banks and
cause breaches in them. Arrangements have, therefore,
to be made to pass the flood water across the canal,
which will be briefly explained, and will be understood
from the following description of a level crossing shown
in plan, in Figure 104: —
B is a regulating bridge across the canal, provided
with the usual sluice-gates. A is a dam across the chan-
nel of the torrent, provided with flood-gates. Under
ordinary circumstances, A is closed and B is open, so
that the canal water flows along its own channel as usual.
But when the torrent is in flood, then A must be open,
and B closed, so that the flood water may cross the canal
and run down its own channel. The quantity of water
flowing past the dam is likely to be, on some occasions,
equal to the flood discharge of the torrent, in addition to
the full supply of the canal.
The bed and banks of the canal and torrent, as far as
they are exposed to the erosive action of the water, must
be paved or otherwise protected, to prevent them from
being injured by the action of the water.
166
IRRIGATION CANALS AND
OTHER IRRIGATION WORKS.
167
A very good example of a level crossing is at Dhuno-
wree, on the Upper Ganges Canal, where the Rutmoo
torrent is passed. Figure 105 shows a view of tTielDrrdge
and dam at this crossing.
Fig. 106. Rutmoo Crossing, Ganges Canal.
Figure 106 shows the plan of the level crossing.
The dam itself consists of forty-seven sluices of ten
feet in width, some of which are shown in Figure 108,
with their sills flush with the canal bed, separated by
piers of three and a half feet in width. The above are
flanked on each side by five overfalls of the same width,
having the sills raised to a height of six feet, with inter-
mediate piers of the same dimensions as those in the
center sluices. On the extreme flanks are platforms
raised to a height of ten feet above the canal bed, and
corresponding in height with the rest of the piers.
These elevated platforms, which are seventeen feet in
168
IRRIGATION CANALS AND
length, are connected with the revetment esplanade by
inclined planes of masonry, carried through the flanks
of the dam.
_Lr~ W
H^l^b!ifialBH!tea*iU=A»aJ
The
Dhunowree Level Crossing, Ganges Canal,
amount of waterway, therefore, through the
sluices, up to a height of six feet, is equal to 470 feet in
width; to a height of from six to ten feet it is increased
to 570 feet, and when flood water passes over the full
expanse of the masonry, which is equal in width to 800
feet.
For the ten sluices in the flanks, the closing and open-
OTHER IRRIGATION WORKS. 169
ing is effected by sleeper planks, for which grooves are
fitted to the piers.
For the center openings drop gates are provide^,— a&
explained in Article 31, and Figures 67 and 68.
On the down-stream side of the dam a platform of box-
work, filled with river stone, extends to a width of forty-
three and a half feet from the masonry flooring. This
is held in position by double lines of twenty-feet piling,
strongly clamped together by sleepers fastened on to the
upper surface, the slope of which is two and a quarter
feet on an incline down-stream.
The regulating bridge has ten waterways each twenty
feet broad, and provided with gates to prevent any flood-
water passing down the canal. In addition to this, there
is a roadway bridge, and about a mile of revetment walls,
all resting on blocks of brick masonry, sunk to a depth
of twenty feet below the canal bed. The whole of this
work is protected by a forest of piles, and an enormous
number of bottomless boxes filled with bowlders.
The river, when not in flood, flows under the canal
by a double tunnel upwards of 500 feet long.
The great objection to this kind of work is, that it re-
quires a permanent establishment of men on the spot to
work it, and that, if they are careless or neglectful, a
sudden flood may do serious damage. On this account
level crossings are to be avoided whenever it is possible
to do so.*
Article 36. Superpassages.
The third case mentioned at page 151, where the tor-
rent crosses at a higher level than the canal, and, in this
case, the structure is called a superpassage , to distinguish
it from the first case, where the canal flows over a river
and is carried by an aqueduct. In America a superpas-
sage is usually called a flume.
'Roorkee Treatise on Civil Engineering.
170 IRRIGATION CANALS AND
Carrying a large body of water across and over a canal
is a very expensive and troublesome work, as a large
water channel has to be provided to carry any extraor-
dinary flood over the canal in safety, and, in navigable
canals, sufficient headway must be allowed under the
superpassage so as not to interrupt the navigation.
AVhen the grade of the country admits of it, as is almost
always the case, the canal can be dropped to the required
level by a masonry fall, a lock being provided for navi-
gation purposes, if required. The torrent will probably
require constant watching to prevent its shifting its
course and attacking the canal bank.
When not in flood a superpassage can be used as a
highway bridge.
The superpassage possesses the great advantage of
keeping the canal completely free from any influx of
flood-water from the torrent, which is always more or
less heavily charged with silt. It has the additional
recommendation of not requiring the maintenance of a
large establishment every rainy season, as in the case of
a level crossing, where the regulating apparatus must be
worked by manual labor. And lastly, the canal supply
can thus be kept up without interruption, there being-
no necessity to shut it off at the crossing to keep the silt-
laden flood-water out of the canal. The recommenda-
tions apply equally to a passage by aqueduct, and render
them both generally preferable to a level crossing, such
as that at Dhuiiowree, given in Article 35, when the
levels will admit of the substitution.
There are two fine examples of superpassages a few
miles below the headworks of the Upper Ganges Canal,
by which the Puttri and Ranipore torrents are carried
across the canal. These have a clear waterway between
the parapets of 200 and 300 feet, respectively, and when
OTHER IRRIGATION WORKS.
171
172 IRRIGATION CANALS AND
the torrents are not in flood, they are used as bridges of
communication.*"
Figure 110 gives a view of the Ranipore Superpassage.
It is taken from Irrigation in India, by Mr. H. M. Wil-
son, M. Am. Sec., C. E., in Transactions American So-
ciety of Civil Engineers, Volume 23.
The Seesooan Superpassage on the Sutlej Canalf is
shown in Figures 111, 112, 113 and 114.
Taking the catchment basin of the Seesooan to be
eight miles in length by three miles in Avidth, we obtain
an area of twenty-four square miles, which would give a
maximum rainfall, at the rate of half an inch per hour,
of 7, 752 cubic feet per second, agreeing very closely with
the discharge calculated from the area of the section at
the canal crossing, with the velocity due to a declivity of
1 in 791. To pass off this discharge, a water-way of 150
feet wide by six and a half feet in depth was given to
the masonry channel of the Superpassage. This would
require a mean velocity of about eight feet per second.
The dimensions given are more than ample for the re-
quired discharge, even with the worst description of
masonry surface. Major Croftoii, the designer of this
work, computed the velocity by one of the old formulae,
having a constant value of c, that is:
Computing the mean velocity through the masonry
channel, by Kutter's formula, and with different values
of n, suitable to masonry surfaces, we obtain the results
given in Table 16. The water channel is 150 feet wide,
with vertical sides six and a half feet deep, as shown in
Figure 114. The slope is 1 in 794. In round numbers,
*Koorkee Treatise on Civil Engineering.
t Report on the Sutlej Canal, by Major J. Crofton, E. E.
OTHER IRRIGATION WORKS.
173
is equal to 2.4 feet. For further information 011 this
subject, see Flow of Water.
174 IRRIGATION CANALS AND
TABLE 16. Giving velocities and discharges of channels with different
values of n.
Value of ] r
n in feet.
Slope 1 in 794
1«
1
i Mean velocity
j in feet per
second.
V
Discharpe in
cubic feet per
second.
Q
.013 2.4
.035489
12.6
12,285
.015 2.4
. 035489
11.0
10,725
.017 2.4
.035489
9.8
9,555
.020 2.4
. 035489
8.4
8,190
The difference of level between the beds of the canal
and the torrent is 21.93 feet, which is thus disposed of:
Feet.
Depth of water in canal 7.00
Head up to soffit of arch (for navigation) 10.00
Thickness of arch , 3 00
Brick-on-edge flooring 1.93
Total 21.93
The canal channel will be spanned by three central
arches of forty-five feet span each, and two at the sides
of thirty-two feet each; tow-paths, of seven and a half
feet wide in the clear, will be carried under each side
arch, leaving an aggregate water-way of 184 feet. The
mean water-way of the earthen channel of the canal is
only 177 feet. The addition is made to this work, in
consideration of the expense of increasing its dimensions
should the canal be required to carry a larger supply
hereafter. The water-way for the torrent above the canal
(Figure 114 shows one-half of this channel), is projected
in one channel 150 feet wide at the bottom, with side
walls (head walls of the work) ten feet in height, five
feet thick at the base, four feet at top; the flooring over
the arches to be formed of asphalt or some substance
OTHER IRRIGATION WORKS. 175
impervious to water, the upper surface being covered
with some hard material, probably a layer of kunkur
(nodular limestone) slabs. The backing of the abut-
ments will be of puddled clay, covered with a flooring of
kunkur, slag, or bowlders packed in cribs.
Article 37. Inverted Syphons.
An inverted syphon, sometimes called a syphon, is, in
some cases, used instead of an aqueduct or super-pas-
sage. The levels of the channels which cross each
other determine the work best suited for the locality.
The syphon is under pressure, and it is usual to give it
such a head, or fall of water surface, from its inlet to its
outlet, that it has a high velocity, and, therefore, its
current has sufficient scouring force to prevent the de-
position of silt and debris.
If the syphon has not sufficient velocity to keep itself
clear, not only of the silt held in suspension, but also of
the material rolled along its bed, it will in time, get
partly or entirely choked, and its waters, being thus
dammed, will cause floods, and very likely break the
canal banks and do material damage.
Probably the most interesting inverted syphon in ex-
istence is that under Stony Greek, on the line of the
Central Irrigation Canal, in Colusa County, California.
It serves four purposes, namely: —
1. As an inverted syphon or conduit under Stony
Creek.
2. As an escape-way for surplus canal water into the
creek.
3. As a secondary gate for checking the flow of
water in the canal above Stony Creek.
4. As an inlet from the creek in the lower portion of
the canal.
176 IRRIGATION CANALS AND
The following description of the work is given by the
designer, Mr. C. E. Grunsky, Chief Engineer of the
Central Irrigation District, and the drawings, descriptive
of the work, are reduced from drawings supplied by
him: —
" Central Irrigation District Canal has been planned
for the irrigation of 156,000 acres of land in the cen-
tral portion of the west side Sacramento Valley plain.
" The canal is cut out from Sacramento River on a
gradient of one in ten thousand (6| inches per mile).
It has a bottom width of 60 feet, and has been planned
to carry a maximum depth of six feet of water. Its
capacity is 730 cubic feet per second.
"In its southerly course, this canal crosses the creeks
which drain the eastern slope of the Coast Range. The
largest of the creeks thus crossed, is Stony Creek, which
has a drainage area of 760 square miles, and a maximum
flow of about 30,000 cubic feet per second.
"The grade of the bottom of the canal and the lowest
point of the creek bed at the point of crossing have the
same height. The width of the creek between firm
banks is about 600 feet. Its bed is clean gravel. Its
flow at the canal crossing generally ceases in June or
July.
" The conduit under the creek, shown in Figs. 115 to
119, consists of seven semi-circular wooden tubes, con-
structed of long staves and covered by a common hori-
zontal platform top. The wooden tubes are to be hung
under the platform by means of iron bands, whose ends
will project above longitudinal timbers on top of the
platform, serving to secure the same against upward
movement. The structure will be weighted with gravel
and anchored to the creek bed to prevent its floating out
of place.
" The conduit ends will rest on concrete in masonry
inlet and outlet chambers. Each of these will be so
OTHER IRRIGATION WORKS. 177
constructed that the space between masonry walls can be
opened or closed to the creek. The gates to accomplish
this will be arranged on the flash board principle, i. e.,
grooves along vertical posts will be provided to receive
and support the ends of loose horizontal boards ~
" The structure thus becomes an escape-way for canal
water to Stony Creek.
" It serves as a check- weir to the main canal and can
be used to regulate the volume of flow in the canal.
" It serves as an inlet for waters of Stony Creek,
thus enabling the creek to be used as a secondary source
of supply."
Figures 115, 116, 117, 118 and 119 show part plan
and sections of this work.
The line of the Agra Canal, India, crosses the Buriya
Torrent. The volume of the latter is 2,000 cubic feet per
second, and it flows over a steep and rocky channel. Its
passage under the canal is provided for by a partial sy-
phon having seven culverts, 6 feet wide and 4 feet deep,
the velocity of which, in high floods, will be 12 feet per
second. This velocity is sufficient to move ordinary
sized bowlders, and, therefore, sufficient to keep the
channel clear of any deposit that can reach it.
The culverts are covered by large stones bolted down
to the piers, and, for this purpose, bolts are built into the
latter. A strong breast wall on each side supports the
canal banks, and the ordinary earthen section of the
canal is carried over the syphon, culverts. The canal
flows over the syphon without any change in its wetted
cross-section or in its velocity. The syphon is provided
with a floor of massive rough ashlar, the entrance and
egress for the torrent being also built with large stone.
Figures 120, 121, 122 and 123 show the syphon carry-
ing the Hurroii Creek (Nullah) under the Sirhind or Sut-
lej Canal. This work is constructed of brick masonry.
12
178
IRRIGATION CANALS AND
OTHER IRRIGATION WORKS. 179
The Inverted Syphon carrying the Cavour Canal, Italy,
under the Sesia torrent, is one of the finest works of the
kind in existence. During extreme floods the Sesia car-
ries about 160,000 cubic feet per second.
The syphon is 863 feet in length. It consists of five
elliptically shaped conduits, or culverts, the horizontal
diameter at the entrance of each being 16 feet 5 inches,
and the vertical diameter of 7 feet 10 inches at the en-
trance, and 7 feet 6 inches at the exit. The area of the
five culverts at the entrance is about 483 square feet, and
the canal was designed to carry 3,883 cubic feet per sec-
ond. This would give a mean velocity, at the entrance,
of about 8 feet per second, and with a supply of 3,000
feet per second, it would give a mean velocity of about 6
feet per second, and, with these velocities, it is found
that no silting of the culverts takes place.
The arch is of brickwork 1 foot 9 inches in thickness.
On this is laid a thin layer of concrete and, again on
this, phmkiiig, the upper surface of which coincides with
the bed of the river.
The planks are laid in the direction of the general
flow of the current of the river. The total thickness of
brickwork, concrete and planking from the soffit of the
arch to the bed of the torrent is only 3 feet 2 inches.
The surface of the water in the canal, after passing
through the syphon, is 2 feet 3 inches above the bed of
the Sesia.
On the Verdoii Canal in France, there are several
wrought iron syphons; four of which are across deep
valleys. The most important is that at St. Paul, 890
feet long, constructed of two parallel wrought-iroii tubes,
each 5 feet 9 inches in internal diameter, with a max-
imum pressure equal to 116J feet head of water. The
capacity of this canal is equal to 212 cubic feet per sec-
ond, so that at full supply the mean velocity through
this syphon is equal to 8 feet per second.
180
IRRIGATION CANALS AND
OTHER IRRIGATION WORKS. 181
The horizontal portion of the syphon, laid at the bot-
tom of the valley, is 321.6 feet in length. The re-
mainder of its length, consisting of the two inclines, is
laid at a slope of about 2| to 1. The pipes are of
wrought-iron, and respectively 0.353 inch andTTT.315 inch
thick for the horizontal and inclined portions. They
are supported on, and fixed in, masonry at the junctions
of the horizontal and inclined portions. The remainder
of the lengths bear on. cast-iron rollers, resting on stone
blocks, placed about 31 feet apart. The arrangements
for the expansion and contraction consist in construct-
ing a short length of the tubes, in each of the horizon-
tal and inclined portions, of a gradually increasing di-
ameter from, and then increasing back to, the normal
diameter of the tube. The metal of the tubes at these
swellings is reduced to about J inch in thickness; in
order to obtain greater elasticity, and it is contended
that the bulging in and drawing out of the tube, at these
swellings, will respectively allow for expansion and con-
traction of the metals.
At the beginning of the works on this canal, the long
syphons, including that of St. Paul, above described,
were constructed through the natural rock, and lined
with masonry to prevent leakage, at a depth of 50 to 82
feet below the bottom of the valleys, the rock being in-
tended to resist the hydraulic pressure. After comple-
tion, not one of these tunnel syphons acted satisfactorily
when the water was let into them. Repairs were then
commenced, experimenting at first with those under the
least, and ending with those under the greatest head of
pressure. After much trouble and expense all were at
length caused to act satisfactorily, with the exception of
that of St. Paul, which had to be abandoned, and wrought
iron pipes substituted as above described.
182 IRRIGATION CANALS AND
On one of the branches of this canal, there is a syphon
443 feet long, under a head of pressure equal to 71J feet.
The Lozoya Canal, in Spain, with a discharge of 89
cubic feet per second, has six syphons, one of which
consists of four cast iron pipes, each 2.8 feet in diame-
ter, three of which carry the canal, the fourth being
used in case of accidents to any of the other three.
There are two- most interesting syphons on the Jucar
Canal, in Spain, under the barrancos or torrents of Carlet
and Alginet, the former 455 and the latter 524 feet long.
The Carlet syphon, situated about 14J miles below An-
tella, is a very old construction. Its discharge is 350
cubic feet per second. The canal is 19 feet wide just
above, but diminishes to 7.5 at the entrance of the
syphon, which is barred, first by an iron grating, and
again by a wooden one, the bars being about six inches
apart. Directly over the entrance stands the guard's
house. There are two masonry shafts built in the bed
of the torrent .down to the syphon. They, too, are pro-
tected by gratings. The mouth is closed in masonry
revetments, supported by arches, and the water-section
just below is 6.75 feet wide and 8 feet deep. The fall
through the syphon is 4.9 feet. M. Aymard questioned
some workmen who had once been in it, and they told
him the gallery was 5.9 feet wide and 6.5 feet high. He
hence calculated the velocity through it to be 10 feet per
second.
General Scott Moiicrieff* says that the Moors of Spain
have left many proofs of their skill in making tunnels
and syphons on their irrigation canals. The Mijares
Canal, which irrigates 9,800 acres of land, and close to
its prise, or headworks, enters a tunnel 1,300 feet long;
after which it is carried by a syphon 327 feet in length
under the Viuda ravine. The lowest point of this
* Irrigation in Southern Europe.
OTHER IRRIGATION WORKS. 183
syphon is about 180 feet below the mouth, and 90 feet
below the present bed of the torrent which crosses it.
There is a fall through it of 13 feet.
Article 38. Retrogression of Levels.
Retrogression of levels, or the lowering of the bed of
a channel by erosion, on long lines, is a serious evil in.
any irrigation channel, especially in a canal carrying a
large volume of water, say over 1,000 cubic feet per
second. Scour or erosion is usually referred to local
action of the water, while Retrogression of Levels is
usually applied to long reaches of a channel. It is
caused by giving too great a slope, and, therefore, too
great a velocity to the canal. For example, a canal is
constructed with a slope of two feet per mile, the bed of
which is shown by the line A B, Figure 124. The canal
Retrogression of Levels in Canals.
has a high mean velocity, over three feet per second. The
material through which the canal runs is sandy loam,
which cannot bear a higher mean velocity than 2.25
feet per second without erosion. In the course of a few
years the current in the canal scours the bed to such an
extent that retrogression of bed levels has taken place
from A B, with a grade of two feet per mile, and a mean
velocity of over three feet per second, to C B, with a grade
of one foot per mile, and a velocity of about 2.25 feet
per second. Retrogression of levels ceases at the line
184 IRRIGATION CANALS AND
C B, and on this grade line the canal has established its
regimen.
In another case, through the same material, the bed of
the canal, from A to E, Figure 125, was given a fall of
two feet per mile. At E was a vertical drop of four feet
to F, and then a grade of two feet per mile from F to R.
The fall E F was so badly constructed that it was
washed away and not rebuilt, thus practically adding
four feet to the fall of the bed from A to B. Retrogres-
sion of levels took place until all scour stopped at the
line C B at a ruling grade of one foot per mile.
Bad results generally follow the lowering of the bed,
of which a few are here mentioned.
The beds of the distributing channels taken from the
main channel between A and B were fixed with refer-
ence to the bed of the canal, A B, Figure 124, and any
lowering of this bed would diminish the depth of water
at, and, therefore, the supply entering their heads. For
example, midway between A and B, at E} a small chan-
nel is taken out with its bed three feet above the bed of
the main channel, but after some time, retrogression of
levels has lowered the bed of the main canal four feet
from E to F. The surface of water in the main chan-
nel, at full supply of six feet in depth, is, therefore, one
foot below the bed of the distributing channel at E. In.
order, therefore, to get water through the distributary,
a regulating gate would have to be constructed on the
main channel below E, so that, by closing this gate
as required, the level of the water could be raised.
Another plan would be to deepen the distributing chan-
nel for some distance from its head. This deepening of
the distributing channel would flatten its grade and
cause a diminution of its velocity and discharge. Fur-
thermore, the land on each side of the distributary, for
some distance from its head, would be too high above it
for irrigation by gravity.
OTHER IRRIGATION WORKS. 185
Another evil caused by lowering the canal bed would
be the lowering of the sub-surface water in the land on
each side of the canal, where in some cases such lower-
ing is not required.
Any one who has inspected the old Irrigation Chan-
nels in parts of California will have seen that retrogres-
sion of levels has taken place with bad results in
numerous cases. As a rule, too much grade has been
given to the old canals.
In the early days of the construction of large irriga-
tion canals, by the British Government, in India, this
mistake was made. The greatest canal engineer that
ever existed, General Sir Proby Cautley, the designer
and constructor of that magnificent work, the original
or Upper Ganges Canal, decided, after careful thought
and due regard to the experience gained on canals pre-
viously opened, that 15 inches per mile was required as
the grade of this canal. This slope was too great, and
probably six inches per mile would have been ample.
After the canal was in use for some years, retrogression
of levels took place to an alarming extent; deep holes
were scoured out below many of the falls and bridges,
thereby endangering their stability, and the bed of the
canal was in some places deepened, and in others
widened beyond the original cross-section.
When Cautley fixed the slope of the Ganges Canal,
nothing was then known of the experiments and inves-
tigations of Humphreys and Abbot, D'Arcy, Baziii,
Gordon, Kutter and Ganguillet and others. Cautley
fixed his slope in accordance with the formula of Du-
buat, a formula that was used for many years in India,
both before and after the opening of the Ganges Canal.
Neville's Hydraulics was then a standard work, in use
by the canal engineers of Northern India, and in the last
edition of this work, 1875, a table based on Dubuat's
186 IRRIGATION CANALS AND
formula is given for finding the Mean Velocity of Water
jioiuing in Pipes, Drains, Streams and Rivers.
No blame whatever can be attached to Cautley for de-
termining the slope of the Ganges Canal by this for-
mula, for it was generally used in India at the time, and
A\ras believed to be correct. It is now known to be very
inaccurate.
This mistake of the slope was the only radical defect
in the design of the Ganges Canal; and, with this excep-
tion, there has never been constructed a work of equal
magnitude, that showed so few mistakes, or that dis-
played more originality and boldness in design and
execution.
Notwithstanding all this, a set of carping critics made
the last years of the life of General Cautley miserable,
by direct and indirect, unjust attacks on his great work.
In 1864 a committee of five Royal Engineers — not a
single Civil Engineer was on it— recommended that Cap-
tain J. Crofton, another Royal Engineer, should report
on the remodelling of the Ganges Canal. Captain Crof-
ton did so report in 1866, and he estimated the cost of re-
modelling at $12,500,000.
One able Civil Engineer, Mr. Thomas Login, proved
conclusively that protective works, at a comparatively
small expense, would ensure the safety of the Canal. He
raised the crests of the falls in some places by planking,
and crib-work filled with bowlders was placed below
them in the bed of the canal. By these means water-
cushions were formed below the falls, which materially
reduced the destructive effect of the falling water. For
a detailed description of this work see the account given
by Mr. Thomas Login, C. E.*~ His only thanks was re-
moval to another work, and he was never again appointed
''Transactions of the Institution of Civil Engineers. Vol. XXVII.
1867-68.
OTHER IRRIGATION WORKS. 187
to the Ganges Canal. Mr. Login and the writer of this
work were intimate friends, and in justice to the former
this brief reference is made to his work on the Ganges
Canal, for which he did not get the credit that he de-
served.
In 1868 Mr. Login stated:* " Six years ago the Author
stood almost alone in maintaining the opinion that the
Ganges Canal needed only some protective work, and did
not require the radical alterations then proposed. The
Author will only add the expression of his firm convic-
tion, that the works may be placed out of danger by the
judicious use of wood and iron, at a less cost than if
stone be employed, without depriving the country of the
benefits of irrigation beyond a short time."
Time has fully justified Mr. Login's opinion, and a
few years since General C. E. Moncrieff, R. E., testified
to his sound judgment.! He states:
"Did they not remember how a committee of engi-
neers had pronounced Cautley's great Ganges Canal un-
sound, and how they would have spent fabulous sums
on it, had not Bro willow's common sense and attention
to details shown that the work was all right, as it has
triumphantly proved to be."
Had General Moncrieff given the credit of this success
to Login instead of Browiilow, his statement would be
more in accordance with the facts. It was mainly due
to Login's sound judgment, sturdy independence, and
having practically proved what could be done at com-
paratively small expense, that overtaxed India was saved
from the great expense that was proposed to be incurred
in remodelling the canal, and another serious matter,
the closing of the canal for one or two years.
* Transaction of the Institution of Civil Engineers, Vol. XXVII, 1867-
68.
t Irrigation in Egypt in Nineteenth Century. February, 1885.
188 IKKIGATION CANALS AND
Figures 126 and 127 are plan and profile of the orig-
inal Ganges Canal, through the Toghulpoor sand hill in
mile 37.* There was here more erosion in the width
than in the depth. The plan, Figure 126, shows the
widening, and the profile, Figure 127, shows that the
bed of the canal through this wide section is higher
than the narrow channel above and below that place.
..._---— — -— --
!
.
[ ^ y ^ j. • _L^T^V^» . »t. ^ •"* . ••^r"l»»* *^ * *• * >*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 .'. v2 = c2 X rs
substituting value of v2 we have: —
(C2 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 c2rs
^
X
m 2gh+ <?rs 2g h
X
OTHER IRRIGATION WORKS. 201
1
/N £/ ' \ C\ 1 •) /\ Cl 7 I 9
m V2(/ A -j- <r r -sy 5w « -T c r 8
.....
(2 1; /i + cr ra)*
Now, to find //, we have from equation above by-
squaring,
m
T*
Z2 ^ -f ^= a2 c2 r*
extract cube root
/ 2 72 v \x / 2gr/i + c?r s \ / 2 2 \
(ma r )3 X I- -- - j = (a2 c2 rs)
2g h + c2 r .s / ^c2j?-.s U
~~ ~ \ m1 P /
. = Ar
- \
m
rs .
"
Having thus got the value of h, deduct it from the depth
of water in the channel, and we have the height to
which the weir should be raised above the bed of the
canal, Figure 132, in order that the water in its ap-
proach to the weir may not have any increase of ve-
locity.
Example: — Let the bed width of the channel above
the weir be 60 feet, depth 9 feet, side slopes 1 to 1,
grade 6 inches per mile and n = .025. Also, let the
length of the crest of weir be 55 feet. Now, let us com-
pute to what depth the crest of the weir must be raised,
in order that the water approaching the weir may not
have a greater velocity than the mean velocity in the
open channel.
In the open channel we have: (see Flow of Water)
IRRIGATION CANALS AND
621
== 7,3295 and ,/r = 2.7 m = 3,
,
p 84. / 2b
and c == 86.4
,s == 6 inches per mile = .000094697;
substituting values of a, c, r, s, m, /, and </, in above
formula (A) we have
'621'2 S6.42 4- 7.3295 X .000094697
/62T_ - 86.42 -|- 7.3295 X . 000094697 \
= \ ~ 32 X 552 J
/86.42 X 7.3295 X .000094697x . y
\ 2 X32.2 ;
Now, as a check, let us compute the discharge over
\veir: —
Q = 3 X 55 X 4.1808 v/
= 1409 nearly, which is also the discharge in the
open channel, computed by Kutter's formula, with the
dimensions above given. Now 9 — 4.1808=4.8192 feet
is the height above crest of fall to which the weir must
be built. This raising of crest, however, is suited to only
one depth of water in the open channel. A much better
plan by which the crest of the weir can be adjusted to
any depth of water in the channel, is shown in Figures
152, 153 and 154.
Vertical Falls, with Grating*.
The result of experience seems to show that Vertical
Falls with Gratings, as used on the Baree Doab Canal,
and illustrated in Figures 142 to 151 inclusive, are the
best that have yet been adopted.
By referring to the drawings, it will be seen that, the
water is made to fall vertically through a grating laid at
aslope of about one in three, and that its action on the
surface below is thus spread over as large an area as may
be wished. Owing to the several filaments of water
OTHER IRRIGATION WORKS.
203
being separated by the bars, much air is carried down
with the water, and the action below is reduced to a
VERTICAL FALL WITH GRATING.
BAREfc DOA8 CANAL.
ElevaUon, 8cc,up Stream
^91 Th* tftton^of tht. Ji>usi«ta£lon 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 vmax
vb = 0.62 rM,~ (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,
vb == 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
0
3 . 0864
1
2 . 8909
« .<
2
2.6955
Center
3
2.5
Common difference 0.1955 nearly.
n «
4
2 . 3046
<c if
-
2.1091
Bottom
'j
1 .9136
What is required, then, is to shape the sides of a given
number of bars, placed in a given width of bay, so that
the above velocities may be maintained till the water
touches the grating, when, in consequence of the clear
fall, the velocity becomes considerably accelerated. This
accelerated velocity multiplied by the reduced area, of
space between the bars, should give the same discharge,
\vith the canal running full, as the product of the orig-
inal normal velocity and the original undiminished
space, the width of which is, of course, the distance be-
tween the centers of two contiguous burs.
208 IRRIGATION CANALS AND
Thus, taking the lowest film, along the bed of the
canal, whose normal velocity is 1.9136 feet per second,
and supposing 20 to be the number of bars in each bay,
then the uiidimmished space for each portion of the
stream will be half a foot, which multiplied by the above
velocity gives a product of 0.9568. Again, taking, the
same lowest film as it passes through the grating, with a
clear fall, and under a head of pressure of six feet, we find
its velocity to be 19.654 feet per second. Now, if we
called the required width of space between the bars at
this point xa, and assume the co-efficient of contraction
to be 0.6, we shall have:
0.9568
a;-= — =0.08 foot.
19.654 X 0.6
Similarly, taking the film on the level of the tops of
the bars, or 0.5 foot below the surface of the water, the
normal velocity of which is 2.9887, the uridiminished
space being, as before, 0.5 foot, we get a product of
1.4944; and as the velocity of the film falling through
the bars is 5.673 feet per second, we get: —
xs = L4944 =- 0.44 foot.
5.673 X 0.6
And lastly, taking the center film, the normal veloc-
ity of which is 2.5 feet per second, we have a product of
1.25, and as the velocity of the same film passing through
the grating is 13.89 feet per second, we get: — •
1 9Pi
ajt =- -0.15 foot.
13.89 X 0.6
Hence, it is seen that the sides of the bars should be
cut to a curve, as shown in Figure 149, convex towards
the open space; but in practice this nicety is scarcely re-
quisite, and they may be made as shown in Figure 150.
The above remarks have been limited to a consider-
ation of the effect caused by the grating on the channel
OTHER IRRIGATION WORKS.
209
above the fall. Its effect on the channel below the fall is
equally important. The velocity, eddies and consequent
erosion below the fall are much diminished by the grat-
ings. Fig. ,49.
Fig. 150. Plans of Bars of Grating.
Colonel Dyas, an engineer of great experience, when
in charge of the Baree Doab Canal wrote 011 this sub-
ject* :-
" In my opinion the Grating Fall is the best fall yet
known, and the next best is the Vertical Fall without
grating. We have but one Ogee Fall on the Baree Doab
Canal, and that one has given us more trouble in repair-
ing it than all the rest together. Indeed we have not
had to touch the others although we have had a flood
down the canal that submerged them. You can have 110
idea without seeing them how completely under control
the water is by their means. Divide and conquer is their
motto, and I think it is the true principle."
'Professional Papers on Indian Engineering, Volume 1.
14
First Series.
210
IRRIGATION CANALS AND
Figure 151 is a cross-section of a grating having hori-
zontal bars at right angles to the axis of the canal.
Section of Grating having Horizontal Bars.
Fall with Sliding Gate.
A Fall with a sliding gate, on the Sukkur Canal, in
India, is shown in Figures 152, 153 and 154.*
Above the fall the canal has a bottom width of 60 feet,
depth 9 feet, side slopes 1 to 1, and a fall of 6 inches
per mile. The mean velocity is 2.27 feet per second,
and the discharge 1,410 cubic feet per second. Kutter's
formula, with a value of n = .025, applied to this chan-
nel, will give the mean velocity mentioned of 2.27 feet
per second. See the Flow of Water.
The fall is divided into five bays of 11 feet each in
wTidth, by piers 4 feet thick. The plan of one of these
bays is shown in Figure 152. The difference of level
between the beds of the canal above and below the fall
is 7.55 feet, and of the high water lines 3.55 feet. The
crest of the masonry portion of the weir is nine inches
above the bed, Figure 153.
* Col. J. Le Mesm-ier, K. E., in Professional Papers on Indian Engineer-
ing, Vol. o, Second Series
OTHER IRRIGATION WORKri.
211
The thickness of the weir is two feet six inches. It
is in fact nothing more than a brickwork facing to the
rock, forming an even surface, on which the timbers are
fixed, against which the gates can slide.
Fall on the Sukkur Canal, India.
There is no cistern or basin to form a water-cushion
under the falling water, as the bed at this place is com-
212 IRRIGATION CANALS AND
posed of sound rock. The bed and banks, for a dis-
tance of 400 feet below the falls, are protected with
rough stone pitching, laid dry, about one foot six inches
or two feet thick.
The plan of using sliding gates to form the weir, in-
stead of building up a mass of masonry above the bed,
is believed to have been introduced for the first time
on the Sukkur Canal, to regulate the depth of fall to
actual discharge on a canal with a maximum capacity of
over 1,400 cubic feet per second.
The gate, Figures 153 and 154, is constructed of four-
inch teak plank, with a strip of 3J-inch angle-iron
along the top and bottom of the down-stream face.
The gate is strengthened, at front and back, by four
strips of three-eighths inch plate iron four inches wide,
and by two cross-pieces of Si-inch angle-iron at the
back. The gate, when lowered to the full extent, rests
on a piece of teak 11' 84" X 5" X 4-1", fastened to the
brickwork by bolts, and its top is then level with the
crest of the masonry, or nine inches above the bed of
the canal. It slides up and down against two vertical
straining pieces of teak scantling 5" X 4i", fastened by
lewis bolts to the piers, which are recessed for the pur-
pose; the thickness of the pier being four feet, and of
the upper cutwater three feet three and one-half inches.
When the full supply is going over the gate its top is
five feet above the level of the bed, or its bottom nine
inches below the crest of the masonry. The man in
charge of the falls has orders to keep the gauges at the
head regulator and at the falls, reading the same, and
when this is the case, the surface slope of the water is
six inches per mile. If less than nine feet is admitted
at the head, the gates at the falls are lowered until the
two gauges read the same. If at any time it is neces-
sary to admit a greater depth than nine feet, the gates
are raised.
OTHER IRRIGATION WORKS. 213
The apparatus for raising or lowering the gates is very
simple. Across the cutwaters, a teak beam nine inches
wide by twelve inches deep, is laid and bolted down to
the piers by a two-inch bolt. The screws which are
attached to the gates are of two-inch rod, cut to one-
quarter inch pitch; they pass through holes cut in the
teak beams, and are wound up and down by a brass nut,
turned by an iron handle. In the cold weather, when
the canal is dry, the wood and iron work of the gates are
well dressed with common fish oil, procured from the
fishermen on the river.
The gates are eleven feet eight inches long, and as the
opening in which they slide is eleven feet eight and one-
half inches, they have a play one-quarter inch at each
end. There is also a small play between the front of
the gate and the back of the masonry of the weir wall;
one-quarter inch is shown in Figure 153, but it is in
reality less than this. The four-inch strips of plate iron
are countersunk into the front of the gate, but not into
the back, and all the rivets and bolts as well, so that the
face of the gate is perfectly level and flush; and there is
no reason why more than one-sixteenth of an inch play
should be given. It was considered advisable, how-
ever, as the gates had to be made in Karachi, and sent
up to Sukkur ready to be put up, to allow for one-quarter
inch play when building the masonry.
One advantage of this kind of fall, and a very great
one, is that it suits a variable depth in the canal, as the
gate can be raised or lowered, according to the depth of
water admitted. Another advantage appears to be that,
the action of the water upon the bed and banks below
the fall is reduced to a minimum. The canal is merely
protected by a comparatively thin layer of rough stones,
procured from the excavation, and laid dry, and up to
the present time no repairs of any sort have been re-
214
IRRIGATION CANALS AND
quired. The bed and banks of the canal above the falls
are almost as clean as the day they were cut, as, what-
ever the depth of water is, the surface slope is kept fixed
at six inches a mile, and the mean velocity never exceeds
two and one-quarter feet per second, which is the velocity
with maximum supply.
Fall ^vith Plank Panels or Flash Boards,
Figure 155 shows a timber fall on the Galloway Canal,
California. Flash boards can be placed on the framing
of this fall to regulate the height of the water in the
upper reach of the canal. This is a very light structure,
and it is built on a somewhat similar plan to that of the
Kern River Weir, Figure 20.
Fig. 155. Timber Fall with Plank Panels or Flash Boards.
A good floor for the lower part of drops is sometimes
made in the following manner: A wooden box is con-
structed as large as the intended floor, and from one to
three feet in depth. If the material is sand or loam,
the joints of the boards are covered inside with thick
tarred brown paper, after which the box is filled with
sand or loam and the cover nailed on.
the box weight and stability.
The filling gives
OTHER IRRIGATION WORKS. 215
At the lower edge of the box a row of sheet piling is
sometimes fixed. The sheet piling should not be driven.
The best way to fix it is to excavate a trench and, if not
too large, to frame the sheet piling together and put it
into the trench framed in one piece, then fill in the ma-
terial on each side and tamp it in layers. A piece of tim-
ber can then be fixed and spiked to the top of the sheet
piling and the box.
On the Uncompahgre Canal in Colorado, carrying
725 cubic feet per second, the water drops 230 feet over
a precipitous rocky cliff into the bed of a dry wash.
Article 40. Rapids.
Instead of falls, and to accomplish the necessary
change of level, Rapids have been employed with suc-
cess 011 the Baree Doab Canal ,* that is, the fall is laid
out on a long slope of about 15 to 1, instead of by a sin-
gle drop. The slope is paved with bowlders, laid with
or without cement, and confined by walls of masonry in
cement, at intervals of 40 feet, both longitudinally and
across stream. The longer and flatter the slope, the
more gentle is, of course, ,the action of the water; but
the greater, also, is the quantity of masonry employed.
In general the choice between the two is a mere question
of expense and material available. On the Baree Doab
Canal, rapids were adopted wherever bowlders were pro-
curable at moderate cost. Figures 156, 157 and 158
show a rapid on the Baree Doab Canal.
Bowlders or quarry stone are the proper material for
the flooring of a rapid, and soft stone or ordinary brick
work should not be used in contact with currents of such
high velocities. Even the very best brick work cannot
^Professional Papers on Indian Engineering, Vol. 1, First Series, and
Hoorkee Treatise on Civil Engineering.
216
IRRIGATION CANALS AND
OTHER IRRIGATION WORKS. 217
stand the wear and tear, for any length of time, of water
at a high velocity and carrying sand and silt. Hard
stone should be used with all surfaces in contact with
velocities exceeding, say, ten feet per second.
The bowlders should generally be grouted in^witlrjroed
hydraulic mortar and small pebbles or shingle. Port-
land cement mortar, if available at moderate cost, would
be the best cementing material. Dry bowlder work is not
to be depended on for velocities higher than 15 feet per
second, even when they weigh as much
as 80 pounds each, and are laid at a
slope of 1 in 15. There should be no
F«g. '69. attempt made to bring the surface of
the bowlder work up smooth, by filling in the spaces
a, a, a, Figure 159.
All that is necessary is to lay the bowlders, and to pack
them, so that their tops are pretty well in line as b, c;
any further filling in would stand a good chance of being
washed out very soon, and if it remained, its effect
would be to increase the velocity of the current on the
rapid by diminishing the resistance presented to the
water by the rough bowlder work.
The Baree Doab Canal Rapids have tail walls of pe-
culiar construction, Figure 156, for the purpose of
destroying back eddies, and of protecting the canal
banks below the rapid from the direct action of the cur-
rent. These tail w^alls are intended to be so arranged
that the heaviest action of water at the foot of the rapid
shall take place in the widest part A A, the normal width
of the rapid being represented by B B, and they incline to-
wards each other from this point so as to direct the set of
the stream well to the center of the canal, thus protecting
the banks from the direct action of the current for a con-
siderable distance. At the same time, as may be seen from
the longitudinal section, Figure 158, the tail walls are not
218 IRRIGATION CANALS AND
kept at their full height throughout, hut beginning a
little helow where the curve ends, at the level of full
supply only, they gradually become lower and lower,
slope 1 in 20, till they vanish altogether, where they are
on the same level as the bed of the canal. The trian-
gular spaces. A C 1), behind the walls in plan, are filled
in with dry bowlders, to the level of the top of the slop-
ing tail wall. When the full supply is running, these
tail walls are submerged and invisible, the rapid appear-
ing to end just below A A. These tail walls do not
check the "lap-lap" or ceaseless wave-like undulation
of the water below the rapid. That is not their office,
and indeed it would be difficult to check that movement,
but they effectually do away with back eddies by keep-
ing the current always in onward motion, exposing 110
abruptly terminating projection behind which an eddy
can form, and at the same time they protect the banks
by making that motion moderate in the neighborhood
of the banks.
In case 110 such tail walls are given, experience has
shown that the banks of the canal when constructed of
ordinary loam, should be faced with bowlders or some
other protection for a length of 300 feet below the rapid
and on each side of the canal.
The maximum velocity of current which a bowlder
rapid will stand without injury cannot be exactly deter-
mined, but experience has proved that a rapid, such as
is shown in Figures 156, 157 and 158, with a flooring
composed of bowlders, weighing not less than eighty
pounds each, well packed on end, somewhat similar to
Figure 159, and at a slope of 1 in 15, will not stand a
mean velocity of 17.4 feet per second.
A good example of a wooden flume rapid has already
been illustrated in Figures 87 and 88, page 153.
OTHER 1 Rill NATION WO11KS,
210
Article 41. Inlets.
When a canal crosses a small drainage channel that
is filled only occasionally, in very heavy rains, and
whose duration of flood lasts but a short time, an Inlet
is provided in the canal embankment to allow the flood
220
IRRIGATION CANALS AND
water to pass into the canal. On the Indian and Italian
canals, this inlet is usually also a bridge to keep com-
munication open along the canal embankment.
Figures 160 to 164 show details of an inlet on a level,*
that is, the level of the bed of the drainage channel is
at, or nearly on, the same level as the bed of the canal.
There are usually no gates to an inlet. Sometimes per-
ennial streams, when they carry no debris or silt, are
admitted into the canal by an inlet.
An inlet differs from a level crossing, shown at page
167, in so far as that it has not an outlet on the opposite
side of the canal.
Figure 165 shows an inlet with 10 feet fall, from the
Section of Inlet.
bed of the torrent to the bed of the canal. To pass the
torrent over the canal by a Superpassage, Article 36, or
by an Inverted Syphon, Article 37, would be a very ex-
pensive work, therefore, an inlet was adopted as being
by far the least expensive.
For small streams, cement pipe or vitrified stoneware
pipe are very suitable as inlets.
Sone Canal Project, by Col. C. H. Dickens.
OTHER IRRIGATION WORKS.
221
Article 42. Heads of Branch Canals.
On the first-class Indian Canals it is usual to place a
Regulator, both on the main line and at the head of a
&A0rr-tJrz.g «%<? *?eZa£iese js>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 wras 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 wrater 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 Urcu,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 a1, a2, 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 61, 62, 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 d1, 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
1859—60, 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 are—quite
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. ) systenL
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 Az A3,
B B B3, 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 Az, 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 Bs, 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 A3 B3
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 wreek, 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. oO«T>
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.
Ql = 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 wrhich 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 twro 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
0
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 w7ell 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 0 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
Is
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
wrater 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
writh 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 wTater, 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.
<X 6 cd
a. 6 cm
Figure 205 is a diagram drawn to a scale of thirty feet
to the inch, showing the two channels on side-hill
ground. The slope of the ground is fourteen degrees.
This is about an average slope on the bad ground. The
cross-section a, /, g, k, adopted for the steep side-hill
ground in this report has an area in round numbers, of
151 square feet, and the cross-section of a, 6, c, d, with a
bed 50 feet wide, and side slopes of 2 to 1 has an area of
1,218 square feet, that is, in the latter, about eight times
as much material will have to be moved as in the former
section. If, again, the slope c, m, be made i to 1, then
the area a, b, c, m, is equal to 634 square feet, that is
more than four times as much as the section adopted.
The large section is not, under any circumstances, the
right one for steep side-hill ground, although it is, in
some cases, suitable for a canal in. the plains. An in-
OTHER IRRIGATION WORKS. 381
spection of the cross-sections in Figure 205, will make
this very evident.
In Figure 205, the cutting is made of such a depth that
the water is all in soil, that is, that the depth of cutting
is made equal to the depth of water in the channeT ~ If,
however, the canal, instead of being in cutting is in
embankment equal to or less than 3-> 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<fc 63
230
Duty of Water. . . .11, 251, 286, 289
to 293, 295, 298, 301, 302, 304, 313
341, 364, 365
Dwyer's Formula for Mean Ve-
locity 15
Dyas, Col. J. H. . . .39, 40, 200, 205
Earning, Annual, of a Cubic
Foot of Water per second . . . 338
339
Earthwork, Shrinkage of. . .75, 76
376-378
Eaton, Fred 294
Egypt.. 56, 57, 63, 82, 98, 99, 326
Egypt, Lower... .2, 97, 98, 99, 103
Elche, in Spain 364
Embankments, Breaches iii.69, 253
260, 274
Embankments, Kiver. ..66, 68, 69
• 70, 75, 97, 98, 106, 107, 113, 150
152, 157, 159, 160, 161, 190, 191
219, 241, 376
Engineer (London) 335
Engineering 143, 148
Engineering News 228, 312, 332
Epinal 65, 66
Equalizing, Cuttings and Em-
bankments 68-72
Erosion of Bed and Banks 13
36-40, 43-47, 80, 82, 83, 117, 121
165, 183, 188-191, 195, 199, 228
273, 274, 379
Escapes 29, 121, 124, 149, 175
177, 221, 226-229
Evaporation. 277, 288-291, 302, 310
316-320, 321, 366, 368-373
Excavation to Balance Embank-
ment . . 10
Page
Eytelwein's Formula for Open
Channels 172
Fahey, C. E 80
Failure of Dams rrrrn 377
Falls... 25, 33, 34, 36, 37, 46, 87
109, 120, 149, 184, 185, 189-215
241, 255, 256, 273
Fall, Timber 191, 196, 214
Fall, Vertical 87, 109, 119, 192
195, 197, 202, 209
Famine 335
Farmington 61
Fascines 88
Fernow, B. E 306
Fertilizing Silt 21, 56-62
Figari Bey 270, 271
Filtration (see Percolation).
Flanks of Dam. . . .84, 95, 101, 113
116. 117, 124
Flash Boards.. 89, 92, 176, 192, 214
Floats, Gauging 325
Flood, Discharge of River 151
Floods in Eivers . . .95, 98, 99, 101
105, 106, 110-113, 124
Flooding, Irrigation by. . .279, 283
333
Flooding, Size of Compartments
for 279
Flooring, Masonry . . 83, 84, 95, 96
101, 109, 114-116
Flooring, Plank 80
Flumes (see Aqueducts).
Flush Irrigation 285, 286, 358
Flynn, P. J 347
Foote, A. D..61, 229, 292, 341-344
Forestry and Irrigation 278
304-307
Forrest, E. E.46, 249, 251, 292, 304
Foundations 77-79, 82, 85, 90
99, 101, 102, 105, 106, 109, 111
112, 113, 114, 116, 120
Fouracres, C 138, 139, 142
Fouracres' Excavator 105, 140
392
INDEX.
Page
Franciscan Fathers 333
French Profile for Dams 119
French Weirs 135
Fresno 366
Furrow Irrigation. .. .279, 283, 285
286, 287, 288
Fyfe, Colonel 318
Ganges Kiver 64, 110
Ganguillet (see Kutter) 44
Garonne, Silt on River 63
Gates, Sliding 80, 84, 95, 96
128-146
Gauging Canal 325
Gauges on Canals 277
Gauge, Water 197
Geelong Dam 119
Ghooua Falls 37
Girders 159
Godavery Kiver 63
Godavery Anicut.87, 109, 115, 116
147
Godavery Headworks 135
Godavery River, Delta 59
Gordon, George 59
Gordon, E 185
Gophers 378
Grade of a Canal, Adjusting
the 20-26, 33, 34
Grade, Sub, of Canal 28, 29
Grade. Initial, Reduced 24
Grade, Too Great 36, 183-189
Grade, Adding to, at Head of
Distributaries 25
Grade, Reducing. 25
Grade or Slope of Bed of Canal. 20
21
Grade, Uniform 25
Graves, Walter H.... 3, 17, 60, 274
287, 316, 321, 344
Greaves, C 323
Grunsky, C. E 176
Gratings for Falls 202, 209
Gulch Bridge 154
Gwynne's Pnnips 115
Page
Haine River, Slope of 32
Hartley, Sir Charles 63
Heads of Branch Canals. . .221-226
Head of Canal. 9, 10, 108, 121, 122
125, 241
Head of Water 338
Head or Waterway 259
Headworks of Canal 73, 79-82
95, 98, 103, 134, 140, 275, 276
358-360
Health of Country. . . .69, 327, 328
332-336
Henares Canal Sluices 133
Higgin, G 344
Hilgard, Professor 332
Himalya Rivers 105
Hiuton, Col. R. J 262, 294
Horary Rotation.. 251, 302-304, 324
Horse-power 269, 270, 271
Humidity, mean, of Different
Countries 315
Humphreys and Abbot 40, 185
Hunter, Dr. W. W 335
Hurdwar 26, 319
Hurron Creek syphon 177, 180
Hyderabad, Evaporation in the
Deccan 318
Hyraulic Buffers or Rams 139
Hydraulic Miners 379
Ice Gorges 86
Idaho 61
Inclination of Canal (see grade)
Indus, River 2, 34, 59, 63, 81
Infiltration (see percolation).. .
Inlet 128, 175, 176, 219-220
Institution of Civil Engineers,
Proceedings of. 49, 52-56, 59, 62
80, 85, 94, 103, 137, 144 153, 186
187, 195, 197, 222, 249, 279, 304
305, 313, 317, 318, 323, 326, 328
336, 344
Inundation Canal 34, 52
Inverted Syphons (see syphons)
Irrigation Age. . . 159
INDEX.
393
Page
Irrigation Channels, Old Kiver
Beds as 6
Irrigation Canals, Works of . . . 77
Irrigation, From Kiver 7
Irrigation, Improved System,
Egypt 57, 103
Irrigation, Stoppage of 69
Irrigation, Limit 10
Jackson, L. D'A 43
Jaolee Falls 39
Jeffreys, Major W 110, 111
Jumna River 102, 106
Kali Nudee Aqueduct 151
Kaweah River, California. 231, 347
361, 366, 383
Kern County, California, Irri-
gation System 280
Kern River 88
Kern River Dam 83, 214
Kilgour, Mr 59
Kiiigsbridge, Tulare County,
California, Evaporation at ... 316
Kistna River, Delta 59, 63
Kunkur 110, 112, 175
Kurrachee 106, 213
Kutter 43, 200, 202, 210
Kutter's Formula.. 21, 45, 172, 379
Lago Maggiore 124
Lahore 224
Lang, Major A.M.... 105, 110, 115
La Gosse 66
Laterals (see Distributaries).
Latham, Baldwin 51
Latham, J. H 60
Le Conte, Professor J 48
Leakage (see Percolation).
Lamairesse, M 319
Leslie, Sir John 51
Levees, River 87
Level Crossing. . . 134, 151, 164-170
220
Lift Irrigation 285, 286
Page
Lifting Sluice 144
Limestone Country 59
Linant Pasha 320
Locks 1, 33, 53, 101, 104, 117
125, 170, 241,~24^T 277
Login, T..14, 26, 49, 186, 187, 195
197
Loire, River 49
Lozoya Dam, Spain 119
MacLean, L. F 222
Madhapore 224
Madras 95, 108
Madras Presidency 60, 82
Madras, System of Weirs. . 106, 109
Madrid Evaporation 317
Mahanuddy River 63
Mahanuddy Headworks. . . 135, 137
Mahewah Valley Ill
Mahmoodhoor Rajbuha (Dis-
tributary) 38
Maintenance and Operation of
Irrigation Canals 253, 257
273-278, 336
Majaiiar Torrent 163
Malad River, Corinne Branch,
Iron Flume '. 157, 159
Malad River. West Branch,
High Flume 156
Manure ....56, 58, 59, 61, 62, 64
Marcite Cultivation 298
Masonry 78, 83, 102, 105, 106
120, 375
Masonry Channels 14, 45
Measurement of Water, Mod-
ules, Meters 341-346, 385
Mediterranean 98
Medley, Colonel J. G 46
Merced Dam 375, 378
Methods of Irrigation.. . . . .279-289
Midnapore, Rainfall in 59
Mills.. ; 269
Mississippi 40, 64
Mississippi, Slope of 32
Miner's Inch of Water. . , . 361
394
INDEX.
Moncrieff, Gen'l Sir C. C. . .37,
65, 99, 101, 182, 187, 301,
Morin
Morton, Lieut. W. S 261,
Moors of Spain v
Moselle Kiver 65,
Mougul, M ,
Movable Dams. . . 104, 105, 128
Mud Sills
Mulching
Muskurra Eiver 37,
Myapore Dam. S3, 95,
Myapore Kegulating Bridge . . .
Myers
Page
60
320
364
43
262
182
66
99
-146
89
288
188
96
126
127
150
Nagpore, Evaporation in 318
Napoleon . , 57
Navigation Canals. 1, 11, 12,35, 36
103, 125, 170, 222, 240-243
Narora Weir. . .87, 95, 108, 109, 110
112
Needle Dams 132, 221-224, 226
Neva, Slope of 32
Neville's Hydraulics 40, 44, 185
Newarree Bridge 39
Newka, Slope of 32
Night, Use of Water at 293
Nile, Blue 63
Nile Eiver. . . .56, 57, 64, 98, 99, 101
102
Nile, Silt in 34, 62, 272
Nira Canal, India, Cross-sec-
tion of 27
North Poudre River, Weir 90
Nowgong Dam , 188
Nyashahur Bridge 37
Off-take of Canal 54
Ogee Falls 46, 87, 120, 192, 195
209
Ohio, Slope of 32
Okhla Weir.. . . 87, 95, 96, 102, 105
106, 108, 112, 113, 114, 125
O'Meara, P. . .94, 153, 157, 279, 313
322
Ontario Land Improvement Co. 234
Orissa 135
Orissa Canals, Cost of 339
Orme, Dr. H. S 333
Outfall into Eiver 331
Overfalls 167
Panel , 90
Paving 124, 379
Peculiarities of American En-
gineering 89, 105, 153
Penstock 153
Percolation.. . 10, 58, 60, 63, 68, 69
77, 94, 111, 112, 113, 120, 147, 148
149, 152, 161, 276, 277, 282, 291
302, 304, 321-326, 366, 368-373
Periar Eiver, India 233
Persia 305
Pharaonic System of Irrigation. 57
Phoenix, Arizona 87
Phosphoric Acid 57
Piers of Bridges 86
Piles 89, 115, 169
Piling, Sheet 89, 193, 199
Piles, Iron 159
Pipes... 139, 147, 181, 182, 186, 220
262
Pipe Inlet 128
Pipe Outlet, 253, 254
Pipe Irrigation 293-298, 333
Pipe Irrigation System, On-
tario, California 296
Plank Gate 129
Planking 87, 90
Planks on Weir 85, 260, 261
Plantations 278
Planting of Trees 304
Platform, Masonry.96, 101, 102, 103
Plaster 352
Plow 264, 272, 283, 289
Plunger 139
Plum Creek 153
Pondicherry 319
INDEX.
395
Pago
Po, Kiver 121
Po, River, Silt in 60, 63
Portland Cement 217
Posts on Weir 85
Potash, Salts of 57
Powell, Major 308
Professional Papers on Indian
Engineering... 105, 110, 115, 137
205, 209, 210, 215, 248, 280, 317
319
Prony 41
Prise or Headworks 182
Protecting Banks 84, 87
Public Works Department, In-
dia 105, 276
Puddle, Clay.... 110, 111, 115, 152
156, 175, 262, 323, 360, 374
Pumping 2, 115, 270, 271, 272
Punjab Eivers 59
Puttri Torrent 170
Rainfall.. 59, 64, 149, 172, 263, 290
305, 308-315, 320, 374, 383, 384
Rajhubas (see Distributaries)..
Ranipore Torrent 170, 171, 174
Rankiiie 41, 239
Rapids 51, 192, 215-218
Ratchets 134
Ravi Bridge 49
Ravi River 150, 224
Regimen of Rivers 83, 273
Regulator... 79, 80, 85, 89, 95, 96
101, 121, 124-137, 149, 165, 169
184, 191, 221, 222, 227, 243, 259
Regulating Bridge (see Regula-
tor).
Reh (see Alkali).
Relief Gates (see Escapes).
Revy, Mr 42
Repairs to Canals .. 69, 87, 273, 277
(see also Clearance of Canals) .
Reservoirs 58-60, 75, 81, 294
304, 305, 318, 351, 360-364, 366
374, 377, 384
Reservoir and Canal . . . 366-368
Page
Retaining Walls 238-240
Retrogression of Levels ... .36, 111
114, 161, 183-189
Revenue from Distributaries . . 259
Rhine, Silt in River ~~." .77. ~63
Rhine, Slope of River 32
Ribera 324
Rip Rap 360, 378
Ritso, G. F 197, 323
Rivers, Change of Course 6
Rivers, in Flood.. 52, 55, 62, 68, 81
84, 86
Rivers, North Poudre 90
Rivers, Raising Bed of 66
Rivers, Sandy Bed 79, 87
Rivers, Slope of 32
Rivers, Water for Irrigation . . 58-60
Roadway on Bank of Canal . .26, 274
Rock Cutting 156, 382
Roorkee 160, 318, 319
Roorkee Bridge 38,40
Roorkee Civil- Engineering Col-
lege 159
Roorkee Gauge 38
Roorkee Treatise on Civil En-
gineering 46,85, 96, 169, 260
277
Rosetta, branch of Nile.. 97, 98, 99
101, 102
Royal Engineers 186
Rubble 120, 381-383
Rubble, Dry 105, 106, 108
Rubble, Pitching 101, 109
Rutmoo River 167
Sacramento Valley 176
Sainjon, Chief Engineer. 49
Sakiyehs 271
Solaiii Aqueduct 38, 77, 153
158-163
Saluggia 268
San Antonia Tunnel, Cali-
fornia 234
San Bernardino Valley 235
San Gabriel . . . 295
396
INDEX.
Page
Sand Boxes (see Depositing
Basins).
Sand Dams 79
Sand, Quick 237
Sandstone 115
Saone, Slope of 32
Scougall, H 330
Scour.. 53, 56, 84, 86, 96, 108, 113
117, 135, 136, 140
Scouring Sluices (see Under
Sluices).
Scraper, Buck 265
Scraper, Iron 264
Scraper, V Shape 264
Sea, Level, Mean 106
Season for Irrigation . 278, 315, 362
Section, Constant Cross 25
Seesooan Superpassage 171, 173
Seine Kiver, Weirs on 135
Seine Kiver, Slope of 31
Senate Report U. S. ..262, 281, 283
Sesia Torrent, Italy. . *. 179
Sewers, Storm 46
Sewers, Velocity in 46,50, 51
Shadoofs 271
Shafts 182
Shafts, Tunnel 237, 263
Shahpur Inundation Canal. . . . 286
Sheet Piling 123
Streeviguntum Anicut.87, 108, 109
Shoals 86
Shrinkage of Earthwork 69, 72
75, 374, 376
Shutters for Weirs . . 54, 55, 56, 95
104, 105, 128-146, 359
Sidelong Ground, Canal on 28
73, 74, 352. 378-383
Side Slopes .... 17-20, 70, 257, 273
349, 360
Side Slopes, Protecting 341
Sidhnai Canal, India 222, 224
Sills 90, 96
Silt Carried by Kivers 62-65
Silt Fertilizing (see Fertilizing
Silt).
Page
Silt 5, 9, 18, 25, 26, 29, 33-35
37-39, 46-48, 52, 53, 57, 59-64
66, 67, 80-83, 115, 117, 124, 126
257, 260, 277
Silting up... 65-68, 81, 89, 93, 108
112, 121, 124, 125, 189, 190, 226
229, 257, 275
Silting Up, To Prevent 24, 104
Silt, On Keeping Irrigation
Canals Clean of 52-56
Silt Traps (see Depositing
Basins).
Sind, Inundation Canals in. 29, 81
Sirdhana 40
Skips 115
Slabs, Stone 79
Sleeper Planks 84, 130 169
Sliding Sluices 80, 134, 135
Slime, (see Silt 101
Slope of Bed of Canal (see
Grade).
Slope, Natural, of Materials . 20, 73
Slope of Canal Increases from
Head to Tail 21
Stoney, F. M. G 144
Sluices 98, 105, 128-146, 281
Sluices, Head.. 25, 52, 53, 56, 89
95, 96, 99, 104, 115, 117
Sluices, Under.. 53, 55, 77, 79, 80
83, 95, 96, 103-106, 108-110, 114
115, 117, 121, 124-127, 138
Smith, Colonel Baird 116, 317
Snow 26
Sorgues Kiver 60
Spain 120
Spoil Banks (see Waste Banks) . .
28, 35, 268
Spring Valley Water Company's
Dams, California 375, 378
Sprinkling Irrigation by 279
Spurs 150
Stand Pipes, for Irrigation . 298, 333
Stevenson, Col. C. L.. 61, 285, 301
Stony Creek 175-178
St. Paul Syphons 179, 181
INDEX.
397
Page
Stop-planks. 134
Stonework 101
Sub-soil Drainage 330, 331, 332
335
Sub-surface Irrigation by means
of Pipes 279, 333
Sugar Cane 60
Superpassage.. ..151, 169-175, 220
221
Superintendence of Canal 276
Super-saturation of Land (see
Water-logging).
Suranah . 225
Survey .241-252
Swamps, 69, 327, 328, 334, 336
Smeaton. 50
Syphons, Inverted 151, 175-183
220, 252, 255
Syphons, Kock 181
Tail of Apron 114, 116
Tail of Canal 81, 249, 255
Talus... 101, 103, 106, 107, 108, 109
110, 112, 114
Tambrapoorney Kiver 108
Tanjore .. 58
Tank (see Eeservoir)
Technical Society of the Pacific
Coast, Transactions of 75, 396
Telephone Service on Canals. . 274
Temperature at Eoorkee, India. 318
Temperature, Mean, of different
Countries 315
Thames Tunnel 147
Thompson, Dr. Henry 317
Ties 141
Tiber, Slope of 32
Timber, Decay of 277
Timber Falls (see Falls Timber).
Toghulpoor Sand Hill, Ganges
Canal 38, 188
Tower in Eeservoir 360, 378
Tow-paths on Navigation
Canals 174, 242
Training of Eivers 277
Page
Transporting Power of Water. . 43
-51, 62-65, 257
Trask, F. E 234, 296
Trautwine _ . . . 319
Trenails ~ "91
Trestle.... 89, 159
Trial Pits 69,348,349
Tropics 319
Tulare Irrigation District, Ee-
port on proposed Works of. . 347
Tumbler for Eegulating Distrib-
taries, Midnapore Caiia .... 139
Tunnels 147, 154. 156, 169, 181
182, 232-238, 267, 353-357, 360
378, 382
Tunnels to Develop Water. . .2, 232
233, 234, 235, 236, 237, 238
Tunnel Lining 235-238
Tuolumne Eiver 117
Turlock Weir. 87, 117
Umpfenbach 49
Utah 61, 90
Utah, Irrigation in , 285
Valencia in Spain 299
Velocity Allowable in Certain
Soils 14, 34, 35
43-47, 81
Velocity, Bottom 41-44, 113
Velocity, High 35, 44-47
Velocity, Destructive 43-47, 215
217, 218
Velocity too Great Better than
too Small 34
Velocity Increases with In-
crease of Depth 47
Velocity, Low mean 33, 34
Velocity, Maximum mean 34
Velocity, Maximum Surface.. . 37
38, 41, 42
Velocity, Mean 29, 35, 37-43
Velocities, Mean, Surface and
Bottom 41, 42, 207, 208
Velocity, Mean, Uniform 21
398
INDEX.
Page
Velocity, Minimum, in Canals
in America 34
Velocity, Minimum, in Canals
in Egypt. , 34
Velocity, Minimum, in Inunda-
tion Canals in Sind 34
Velocity, Minimum, in Indian
Canals 33
Velocity, Minimum, in Spanish
Canals 34
Vertical Drop of Dam 120
Vertical Falls (see Falls Verti-
cal).
Viga Valley Irrigation Project,
Madras 233
Viuda Kavine 182
Vrynwy Eeservoir Dam 119
Warping (see Colmatage) .
Waste Bank 28, 35, 69, 268
Waste Board 116
Waste Gates (see Escapes).
Waste Weir 360, 374, 378, 384
Water, Cost of and of Pump-
ing 270
Water Cushion.... 87, 96, 109, 120
137, 186, 197, 198
Water, Diverting the, from the
Eiver to the Land 5-11
Water, Duty of (see Duty of
Water).
Water, Economy of 113
Water, Kinds of 58
Water Logging of Lands... 69, 251
275, 289, 291, 304, 327, 328, 33 1*
366
Water Power of Irrigation Ca-
nals ;268, 269, 270
Water Spring 60
Water, Waste of, to Prevent. . . 385
Page
Waterings, Number and Depth
of 284, 298-302, 314, 324
Water, Quantity of Eequired
for Irrigation 11, 12
Watershed.. 244, 245, 248, 260, 328
Weeds.... 33, 38, 40, 189, 260, 273
327, 330
Weeping Holes 163, 243
Weirs.. 53, 77, 79, 80, 81-124, 125
134, 147-149, 277
Weirs, Cross Sections of . . 82, 105
106, 108, 115
Weirs, India, by Major A. M.
Lang 115
Weir, Curved on Plan 119, 122
Weir, Oblique , 85
Wells 2, 60, 62, 292
Wells, Artesian 2, 313
Wells, Foundation.. 77, 78, 79, 109
111, 114, 115, 116
Well Water , 58
Wilson, Allan 60, 305
Wilson, H. M...172, 197, 245, 246
Willcocks, W....57, 103, 319, 328
Windlasses 132, 134, 222
Wing Dam . , 87
Wing Walls 109
Wooden Flumes 153
Works of Irrigation Canals 77
Wrought Iron Syphon 179
Wutchumna Eeservoir 231, 232
Wutchumna Tunnel 231, 232
Yarpoor Falls 37
Zero of Canal for Measurement 95
243
j Zero for Levels 128, 132, 243
Zanjas or Open Ditches 333
FLOW OF
IRRIGATION CANALS,
DITCHES, FLUMES, PIPES, SEWERS,
CONDUITS, Etc.
WITH
TABLES
Simplifying and Facilitating the Application of the Formulae of
KUTTEE, D'AKCY AND BAZIN,
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," etc.
[ALL RIGHTS RESERVED.]
SAN FRANCISCO, CALIFORNIA.
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.
SAN FRANCISCO :
GEORGE SPAULDING & Co.,
PRINTERS AND ELECTROTYPERS.
TABLE OF CONTENTS.
ARTICLE 1 — Introduction rrrr-r-^- 1
Inaccuracy of old formulas, 1; Accuracy of the formulas of Kutter,
Bazin and D'Arcy, 1; Major Allen Cunningham's experiments
on the Ganges Canal, 2; Kutter's formula found to be correct, 3.
ARTICLE 2 — The Application of K niter's Formula simplified and facili-
tated by the use of the Tables in this ivork 5
Plan of Tables, 5; Example of their use, 6.
ARTICLE 3 — Formulae, for Mean Velocity in Open Channels 0
Nomenclature, 6; Value of g, 7. D'Aubisson's, Taylor's, Down-
ing's, Beardmore's, Leslie's, and Poles' formula for large and
rapid rivers, 8; Leslie's for small streams, 8; Stevenson for
streams over 2,000 cubic feet per minute, 8; Stevenson for
streams under 2,000 cubic feet per minute, 8; D'Aubisson, 8;
Beardmore, 8; Eytelwein, 8; Eytelwein, 9. Neville straight
rivers with velocity up to 1.5 feet per second, 9; Neville straight
rivers with velocities above 1.5 feet per second, 9; Neville, 9;
Dwyer, 9. Dupuit, 9; Young, 9; Dubuat, 9; Girard, 9; De
Prony, 9; De Prony with Eytelwein's co-efficient, 9; Weisbach,
10; St. Veuant, 10; Ellet, 10; Provis, 10; Hagen, 10; Schlicht-
ing's Hagen, 10; Fanning, 10; Humphreys and Abbot, 10;
Gauchler, 10. Table 1 — Giving the values of the co-efficients
to be employed in Gauchler's formula for canal and rivers, 11;
Molesworth, 11. Table .2— Giving the value of the co-efficients
in Molesworth's formula for canals and rivers, 11; Bazin, 11;
Brandreth's modification of Bazin, 12; Kutter, 12. Formulas
for Use in the Application of Tables, 13.
ARTICLE 4 — Remarks on the Formulae, 13
Old formulas have constant co-efficients, 13; Gauchler, Bazki,
Molesworth, Kutter, 13; value of c in Kutter varies with n, s,
and r, 13. Table 3 — Values of c for earthen channels by Kut
ter's formula, 14.
ARTICLE 5 — Bazin's Formula for Channels in Earth 15
Bazin's formula correct for small channels in earth, 15; Brandreth's
modification of Bazin, 16.
ARTICLE 6 — Comparing Kutter's and Bazin's Formulce. 10
Table 4 — Giving the Velocity and Discharge of earthen channels
according to the formulas of Bazin and also Kutter, 17.
ARTICLE 7 — Value of n 18
Table 5 — Giving value of n for different channels, 19. Table 6 —
Showing the effect of the co-efficient of roughness n on the
velocity in channels, 23.
IV TABLE OF CONTENTS.
Page
ARTICLE 8 — Side Slopes 24
In large channels change in side slopes makes little change in
velocity, 24. Table 7 — Showing the velocity and discharge of
channels having different side slopes, n = .025, 26.
AKTICLE 9 — Open Channels having the same velocity 27
ARTICLE 10 — Open Equivalent Discharging Channels 28
ARTICLE 1 1 — Interpolating 28
ARTICLE 12 — Preliminary Work 29
Fig. 1— Trapezoidal Channels, 30; Fig. 2 — Rectangular Channel,
30; Fig. 3— V-Flume.
ARTICLE 13 — Explanation and Use of the Tables 30
Example 1 — To find the mean velocity and discharge of a canal 31
Example 2 — Given the discharge, bottom width and depth, to find
the grade of channel 34
Example 3 — Given the discharge, bottom width and grade of canal,
to find the depth 36
Example 4 — Given the hydraulic mean depth and mean velocity of a
channel, to find the slope or grade 37
Example 5 — Given the discharge velocity and grade of a channel, to
find the bed width and depth 38
Example 6 — Gauging a stream to find its velocity and discharge, and
the number of acres it is capable of irrigating 40
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 42
Example 8 — Increased discharge of an earthen channel by clearing it
of grass and weeds 43
Example 9 — Increase of discharge by improving in smoothness the
masonry surface of a channel 44
Example 10 — To find the velocity and discharge of a channel having
bed width, depth and side slopes not given in the tables 45
Example 11 — Given the discharge, grade and ratio of bed width to
depth, to find bed width and depth 46
Example 12 — Diminution of discharge of channel by grass and weeds 47
Example 13 — Given discharge, velocity and ratio of bed width to
depth, to find slope or grade 48
Example 14 — Given the bed width, depth and grade of a channel not
given in the tables, to find the velocity and discharge 49
Example 15 — To find the value of c and n in an open channel 41
Example 16 — To find the velocity and discharge of a brick aqueduct
by Bazin's formula, the dimensions and grades having been given 52
Example 17 — Increase of discharge of a channel in rock-cutting by
plastering its surface 52
TABLE OF CONTENTS.
FLUMES. Example IS — To find the velocity and discharge of a rect-
angular flume ................................................ 54
Example 19 — To find the velocity and discharge of a V-flume ........ 55
Example 20 — Given bed width, depth and discharge of a flume, to
find its grade or slope ................................ 7. .T-TT— 56
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 = hy-
draulic mean depth in feet and also »J~r and a\fr .............. 57
Table 9 — Channels having a trapezoidal section with side slopes of •£
to 1. Values of the factors a, r, ^ and a*/r' ................ 73
Table 10— Sectional areas in square feet, of trapezoidal channels, with
side slopes of J to 1 .......................................... 82
Table 11 — Channels having a trapezoidal section of side slopes of 1^
to 1. Values of the factors a, r, \/f"and a\/r~ ................ 85
Table 1:2 — Sectional areas in square feet, of trapezoidal channels,
with side slopes of 1 \ to 1 .................................... 94
Table 13 — Channels having a rectangular cross-section. Values of the
factors a, r, \/r and a\/r .................................... 97
Table 14 — V-shaped flurne, right-angled cross-section, based on Kut-
ter's formula with n = .013, giving values of the factors a, r,
c-s/r and ac^/r" .............................................. 103
Table 15— Based 011 Kutter's formula with n — .009. Values of the
factors c and c\/r^ ........................................... 104
Table 16 — Based on Kutter's formula with n = .010. Values of the
factors c and c-^/r ........................................... 109
Table 17 — Based on Kutter's formula with « = .011. Values of the
factors c and c\/lr ............................................ 112
Table 18 — Based on Kutter's formula with n = .012. Values of the
factors c and c \/r .......................................... . 116
Table 19 — Based on Kutter's formula with n = .013. Values of the
factors c and c\/l- ........................................... 120
Table 20 — Based on Kutter's formula with n == .015. Values of the
factors c and c\/r ........................................... 124
Table 21 — Based on Kutter's formula with n = .017. Values of the
factors c and c\/7 . . ......................................... 128
Table 22 — Based on Kutter's formula with n = .020. Values of the
factors c and c^r ..................... . ..................... 133
Table 23 — Based on Kutter's formula with n — .0225. Values of the
factors c and c^/r ........................................... 138
VI TABLE OF CONTENTS,
Page
Table 24 — Based on Kutter's formula with n = .025. Values of the
factors c and c\/r 143
Table 2'5 — Based on Kutter's formula with n = .0275. Values of the
factors c and c^/r 148
Table 26 — Based on Kutter's formula with n = .030. Values of the
factors c and c\/r- 15,'}
Table 27 — Based on Kutter's formula with n = .035. Values of the
factors c and c\/r- 158
Table 28 — Value of c\/r to be used only in the application of the sec-
ond type of Baziii's formula for open channels, with an even lining
of cut stone, brickwork, or other material with surfaces of equal
roughness, exposed to the flow of water 163
Table 29 — Giving the length of two side slopes of a trapezoidal chan-
nel. The side slopes, plus the bed width, are equal to the perimeter 164
Table 30— Giving the velocities and discharges of trapezoidal chan-
nels in earth, according to Bazin's formula (37) for channels in
earth 165
Table 31 — Velocities and Discharges in Trapezoidal Channels based
on Kutter's formula with n = .025. Side slopes 1 horizontal to 1
vertical 169
Table 32 — Velocities and Discharges in Trapezoidal Channels based on
Kutter's formula with n = .03. Side slopes | horizontal to 1 ver-
tical 171
Table 33 — Giving fall in feet per mile; the distance or slope corres-
ponding to a fall of one foot, and the values of ,s- and v/-s 182
ARTICLE 14. — Formula* for mean velocity in Pipes, Sewers, Conduits, etc. 195
D'Arcy's formula for clean cast-iron pipes (51) 196
Flynn's modification of D'Arcy's formula (51) (52) 196
D'Arcy's formula for old cast-iron pipe (53) 196
Flynn's modification of D'Arcy's formula (5;>) (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£>r0^ 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 \/r—I.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.
vb = 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 sin2 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:<y= sra +(.0067 + 9114^ —.082 (14)
( r» ( B V)*
Youngs formula:,^ jS2+(j52) (
where A =
.0296
and 5 =
i
1,-hyp. log(±-}-1.6)
« /
.5
Young's formula: v==84.3v/r« ................... (16)
Dubuat's formula
88.49(^-0.03)
where hyp. log = 2.302585.
Girard's formula: v=(10567.8r8 + 2.67)s —1.64. ____ (18)
Girard's formula v = 103 T/^— 1.64 .............. (19)
De Prony's formula for canals: —
v=(0. 0556 + 10593rs)* —0.2357 .......... (20)
For canals and pipes :v=(Q. 0237 + 9966?\s)J— 0.1542 (21)
10 FLOW OF WATER IN
Weisbach's coefficient:v=(0. 00024 + 8675rs)*— 0.0154(22)
St. Venant's formula: v= 106. 068(rs)" ............ (23)
Ellet's formula :v=0. 64 ( A / )* + 0.04 A/ ...... (24)
where A=rnaxium depth of stream in feet.
Provis's formula :v=60 i/rs + 120 ^rsf. ......... (25)
Hagen's formula :v=4. 39 (r)* X(s)J .............. (26)
Schlichting's derivation of Hagen's formula: —
For large rivers and canals :i>=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 vl= 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, klf 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
XV// .......................... (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.
<tt = .015, second-class or rough-faced brickwork; well-
dressed stonework ; foul and slightly tubercu-
lated iron; cement and terra-cotta pipes, with im-
perfect joints and in bad order; and canvas lining
on wooden frames.
n =.017, brickwork, ashlar, and stoneware in an in-
ferior condition; tuberculated iron pipes; rubble
in cement or plaster in good order; fine gravel,
well rammed, J to f inches diameter; and, gener-
ally, the materials mentioned with n -= .013
when in bad order and condition.
20 FLOW OF WATER IN
n — .020, rubble in cement in an inferior condition;
coarse rubble, rough-set in a normal condition;
coarse rubble set dry; ruined brickwork and
masonry; coarse gravel, wrell rammed, from 1 to
1J 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; rectan-
gular wooden troughs, with battens on the inside
two inches apart; trimmed earth in perfect order.
n — .0225, canals in earth above the average in order
and regimen.
n == .025, canals and rivers in earth of tolerably uniform
cross-section, slope, and direction, in moderately
good order and regimen, and free from stones
and weeds.
n = .0275, canals and rivers in earth below the average
in order and regimen.
n =. .030, canals and rivers in earth in rather bad order
and regimen, having stones and weeds occasion-
ally, and obstructed by detritus.
n = .035, suitable for rivers and canals with earthen
beds in bad order and regimen, and having
stones and weeds in great quantities.
n = .05, torrents encumbered with detritus.
OPEN AND CLOSED CHANNELS.
21
TABLE 5 (continued). The following table, giving values of n for dif-
ferent surfaces exposed to the flow of water, is taken from Jackson's trans-
lation of Kutter. The dimensions are, however, changed from metrical to
feet measures.
r= hydraulic mean depth in feet.
s = sine of slope.
SERIES OF BAZIN.
T
in feet.
.
s
Breadth at
water sur-
face in feet
Depth
in
feet.
n
Xo.
28
29
24
2
25
26
9]
Carefully planed plank. . .
In cement — semi-circular.
" rectangular..
In cement, with one-third
sand — semi-circular . . .
Plank — semi-circular ....
trapezoidal
0.07
0.05
0.82
0.49
0.85
0.91
0 82
0.0048922
0.0152370
0.0014243
0.005060
0.0013802
0.0015227
0 0015213
0.328
0.328
3.28
5.9
3.28
3.6
4 6
0.14
0.079
1.47
0.59
1.61
1.61
1 24
0.0096
0.0087
0.01005
0.01040
0.01113
0.01195
0 01255
<>9
<«
0 65
0 0048751
4 36
0 98
0 01190
23
6
triangular 45°.. . .
rectangular
0.65
0.65
0.004655
0 0022136
4.36
6 5
1.87
0 85
0.0119
0 13
7
0 52
0 004889
6 5
0 6°
0 0119
8
0 46
0 0081629
6 5
0 52
0 0115
9
0 72
0 0014678
6 5
0 91
0 0129
10
0 46
0 0058744
6 5
0 55
0 0117
11
0 42
0 0083805
6 5
0 49
0 0114
18
19
0.65
0 49
0.0045988
0 0042731
3.9
2 6
0.91
0 82
0.0114.
0 0114
*>0
0 32
0 0059829
1 6
0 62
0 0114
27
RAMMED GRAVEL
f- to i inches thick — semi-
circular
0 75
0 0013639
3 28
1 34
0 0163
4
| to £ inches thick — rect-
angular
0.65
0 0049736
6 0
0 85
0 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
0 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
0.0149
0.0147
0.0149
0.0208
0.0211
0.0215
0 0133
3
39
Brickwork — rectangular . .
Ashlar
0.55
0 59
0.0050250
0 0081
3.0
3 9
0.65
0 85
0.0129
0 0129
32
RUBBLE,
Rather damaged — rectan-
gular..
0 52
0 10076
5 9
0 63
0 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 .
0 65
0 036856
5 9
0 88
0 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
0 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
0 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
0 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
0 00043
8.2
19.6
1.18
4.4
0.0230
0 . 0244
Jard Canal
I 97
0 . 0004
19.6
4.4
0.0255
Chesapeake Ohio Canal . .
Canal in England ..
3.7
2 43
0.000698
0 000063
22.6
17 7
7.9
3 9
0.033
0 0184
Lanter Canal, at Newbury
Pannerden Canal, in Hol-
land
1.81
10 2
0.000664
0 000224
29.5
558.
1.8
9.8
0.0262
0 . 0254
Canal of Marmels
2 31
0 0005
26 2
2 6
0 0301
Linth Canal
7 8
0.00034
123.
10.8
0.0222
Hiibengraben
0 6
0 0013
4 8
0 8
0 0237
Hockenbach
0 87
0 000787
11 1
1 1
0.0243
Speyerbach .
1 46
0 000667
16.4
1.9
0.0260
Mississippi. .
65 6
0 000667
2493.
16.4
0.0270
Bayou Plaquemine
16 8
0.00017
275.
25.6
0.0294
Bayou La Fourche
13 1
0 00004
220
23 o
0 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
0 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
0 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
0 000112
1440
9.7
0 026
Rhine at Germersheim
10.8
0 000247
748
0.0227
Rhine, at Basle
6.9
0.001218
660
9.1
0.03
Lech
3.1
0.00115
157
3.8
0 . 022
Saalach .
1 4
0 0011
68
2 1
0 027
Salzach..
4 1
0 0012
38
11 8
0 028
Issar
3.9
0 0025
164
4 4
0 0305
Escher Canal
4.0
0 003
72
4 9
0 03
Plessur
3.5
0 00965
42
4 6
0 027
Rhine, at Rhiuewald
.79
0 0142
14
.99
0 031
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 0
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
1°08 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
0 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/62+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=cXav/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, wrhich 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 : <? substitute values and
1323X72.32
60. 2s
Therefore the approximate slope is 1 in 1908.
Second method :
Finding by Table 32, as a first approximation, that
when -ft=.03'the slope to produce the given velocity is
1 in 1323, and we therefore know that when 7i=.025 the
slope must be flatter to give the same velocity. We
therefore look out in the next flatter slope, in Table 24,
with TI=. 025, which we find is 1 in 1666, and we find op-
posite \/r=l.Sl that cv/r = 131.11.
Substituting the value of c\/r and v in formula (43),
c yr
and we have
= ' °22888
«=. 022883
8=.0228832
and "^
But - =ratio of slope.
Now by logarithms:
From log 1 ............................. 0 . 0000000
deduct log .022883 = 2.3595130X2= ....... 4.7190260
3 . 2809740
which corresponds to 1910. As the computed slope 1 in
1910 has almost the same value of c as the assumed slope
1 in 1666, therefore the required slope is 1 in 1910.
36 FLOW OF WATER IN
Third method :
Find in the same way. as shown in Second Method, that
V/s=. 022883
Now, in Table 33 of slopes, look out the slope corre-
sponding to this \/8, and it will be found equal to 1 in
1910. This is the quickest method of finding the slope.
As a check on this work: by formula (45),
Substitute the values of a, c\/r and \/s, and we have:
Q=136X131.1X.02288S
=408 cubic feet per second.
EXAMPLE 3. — Given the discharge, bottom width and grade
of canal, to Jind the depth.
A main irrigation canal has a bed width of 100 feet,
side slopes of 1 to 1, and an inclination of 18 inches per
mile. At what depth, above the bed of the main canal,
must the sill of the head gate of a branch canal be placed,
so that the main canal will be flowing 1,000 cubic feet
per second, before any water flows into the branch canal;
Ti^.0225? By Table 33, 18 inches per mile=l in 3520,
and v/*=. 016854.
By formula (47),
Q 1000
Therefore, the product of the factors a\/r and c=59333.
All that is now required is to find in Table 8, and un-
der a bed width 100 feet, such a depth that the product
of the factors c (7i=.0225) and a\/r shall be=59333.
In Table 8, and under bed width 100 feet, look down
column a\/r, and also in Table 23, under slope 1 in 3333
(which is the nearest slope to 1 in 3520), look down col-
OPEN AND CLOSED CHANNELS. 37
umii c, and opposite the same or nearly the same value
of \/T in each column, until the product of the two fac-
tors is equal or nearly equal to 59333.
Thus, in Table 8, under a bed width of 100 feetTanct
depth 3.75, we find y'r= 1.875 and av/r— 729.5. In
Table 23, under a slope of 1 in 3333, we find opposite
V/r=1.8 that c=80.2
.-•'. v/^=0.075 that c= 1.2
.-. v/~ -1.875 that c=81.4
Now, 729.5 X 81.4=59381, being near enough, for all
practical purposes, to 59333.
The required depth is, therefore, 3.75 feet.
As a check on the above, let us compute the discharge
of the channel with the depth found. In Table 8, under
a bed width of 100 feet, and depth of 3.75 feet, the value
of av/r=729.5. In Table 23, under a slope of 1 in 3333,
we find by interpolation that when \/r= 1.875 that
c=81.4.
As before found, for 18 inches per mile y/.si=.016854.
Now substitute these values of av/r, c and \/s, in
formula (45): —
Q=a\/r XcX \/s and we have
Q=729.5 X 81.4 X .016854
= 1000 cubic feet per second.
EXAMPLE 4. — Given the hydraulic mean depth and mean
velocity of a channel, to find the slope or grade.
A canal has a hydraulic mean depth of 9.18 feet, and
a mean velocity of 5.5 feet per second. The canal is
trapezoidal in cross-section, but slightly rounded, and it
is free from detritus. Under these favorable conditions
38 FLOW OF WATER IN
the value of n is assumed =.0225. What is the slope of
the water surface of this canal ?
r being = 9.18 . •. \/r = 3.03.
We assume as an approximation that the slope is 1 in
1800.
We look out, in Table 23 (/i— .0225), and under slope
1 in 1666.6, which is nearest to 1 in 1800, and opposite
v/r = 3.03, we find the value of r = 94.3, and
.-.ci/r = 94.3 X 3.03 = 285.7.
v 5.5
Now, formula (43), v/a=-- ==-==. 019251.
Now look out, in Table 33, and the nearest value of
V/* to .019251 is .019245 opposite a slope of 1 in 2700.
We thus find a slope of 1 in 2700, but as the assumed
slope was 1 in 1800, we will compute again for a closer
approximation with the slope 1 in 2700.
In Table 23, and opposite y/r=3.03> 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 269.6—242.4=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, y7?'— 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=ciX«v//rX ]/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\/rt 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 \/st 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..55t 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[/rt 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 VT 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<x/V
Depth
in
Feet.
0.5
6.62
0.460
0.677
4.49
7.37
0.467
0.683
5.03
0.5
0.75
10.03
0.663
0.814
8.17
11.34
0.679
0.824
9.34
0.75
1 .
14.
0.884
0.940
13.10
15.
0.891
0.944
14.2
1.
1.25
17.81
1.077
1.038
18.5
19.06
.087
1.043
19.9
1.25
1.5
21.75
1.262
1 . 123
24.4
23.25
.275
1 . 129
26.2
1.5
1.75
25.81
1.439
1.200
31.
27.56
.454
1.206
33.2
1.75
2.
30.
1.608
1.268
38.
32.
.628
1.276
40.8
2
2^25
34.31
1.774
1 . 333
45.7
36.56
.795
1.340
49.
2*25
2.5
38.75
1.931
1 . 382
53.6
41.25
.958
1 . 398
57.7
2.5
2.75
43.31
2.085
1.444
62.5
46.06
2.115
1.454
67.
2.75
3.
48.
2.234
1 . 493
71.7
51.
2.268
1.506
76.8
3.
3.25
52.81
2.380
1.543
81.5
56.06
2.417
1.555
87.2
3.25
3.5
57.75
2.522
1.554
89.7
61.25
2.563
1.601
98.1
3.5
3 . 75
62.81
2.661
1.631
102.4
66.56
2.709
1.646
109.6
3.75
4.
68.
2.797
1.672
113.7
72.
2.845
1.687
121.5
4.
4.5
78.50
3.051
1.746
137.1
83.25
3.115
1.765
146.9
4.5
5.
90.
3.316
1.821
163.9
95.
3.376
1.810
171.9
5.
5.5
101.75
3.563
1.887
192.
107.25
3.630
1 . 905
204.3
5.5
6.
114.
3.804
1.950
222.3
120.
3.875
1.968
236 . 2
6.
BED 15 FEET.
BED 16 FEET.
Depth
Depth
in
Feet.
a
r
Vr
a\/r
a r \/r a\/r
in
Feet.
0.5
7.62
0.465
0.682
5.20
8.37 0.471
0.686 5.74
0.5
0.75
11.53
0.674
0.821
9.47
12.84 0.687
0.828' 10.63
0.75
1.
16.
0.897
0.947
15.2
17. 1 0.903
0.950 16.1
1.
1.25
20.31
1.096
1.047
21.3
21.56 1.104
1.051 22.6
1 . 25
1.5
24.75
1.286
1.134
28.1
26.25 1.297
1.139 29.9
1.5
1.75
29.31
1.469
1.212
35.5
31.06 1.482
1.217 37.8
1.75
2
34.
1.646
1.283
43.6
36.
1.662
1.289 46.4
2.
2.25
38.81
1.818
1.348
52.3
41.06
1.835
1.354: 55.6
2.25
2.5
43.75
1.982
1.408
61.6
46.25i 2 005
1.416 65.5
2.5
2.75
48.81
2.144
1.464
71.5
51.56 2.168
1.472 75.9
2.75
3.
54.
2.300
1.516
81.9
57.
2.328
1.526 87.
3.
3.25
59.31
2.452
1.566
92.9
62.56
2.484
1.576 98.6
3.25
3.5
64.75
2.601
1.612
104.4
68.25 2.635
1.623 110.8
3.5
3.75
70.31
2.746
1.657
116.5
74.06 2.783
1.668
123.5
3.75
4.
76.
2.888
1.700
129.2
80. 2.929
1.711
136.9
4.
4.5
87.75
3.165
1.779
156.1
92.25 3.211
1.792
165.3
4.5
5.
100.
3.431
1.852
185.2
105. 3.484
1.866
195.9
5.
5.5
112.75
3.690
1.921
216.6
118.25 3.748
1 . 936
228.9
5.5
6.
126.
3.941
1 . 985
250.1
132. 4.004
2.0011 264.1
6.
OPEN AND CLOSED CHANNELS.
61
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 formulae
v = c X VF'X V* and Q = c X a^/r X
BED 17 FEET.
BED 18 FEET.
Depth
i
Depth
IB
Feet.
a
r
N/F
a\/r a r
Vr
a\/r
in
Feet.
0.5
8.62
0.468
0 684
5.90
9.25
0.477
0.690
6.38
0.5
0.75
13.03
0.682
0.825
10.75
14.06
0.694
0.833
11.7
0.75
1.
18.
0.908
0.953
17.2
19.
0.912
0.955
18.1
1.
1.25
22.81
.111
1.052
24.
24.06
1.117
1.057
25.4
1.25
1.5
27.75
.306
1.143
31.7
29.25
1.315
1.147
33.5
1.5
1.75
32.81
.495
1.222
40.1
34.56
1.506
1.227
42.4
1.75
2.
38.
.677
1.295
49.2
40.
1.691
1.300
52.
2.
2.25
43.31
.853
1.361
58.9
45.56
1.870
1.367
62.3
2.25
2.5
48.75
2.025
1.423
69.4
51.25
2.044
1.430
73.3
2.5
2.75
54.31
2.193
1.481
80.4
57.06
2.213
1.487
84.8
2.75
3.
60.
2.354
1.534
92.
63.
2.379
1.542
97.1
3.
3.25
65.81
2.513
1.585
104.3
69.06
2.541
1.594
110.1
3.25
3.5
71 .75
2.667
1.633
117.2
75.25
2.697
1.642
123.6
3.5
3.75
77.81
2.819
1.679
130.6
81.56
2.851
1.688
137.7
3.75
4.
84.
2.967
1.722
144.6
88.
3.002
1.733
152.5
4.
4.5
96.75
3.255
1.804
174.5
101.25
3.296
1.810
183.8
4.5
5.
110.
3.532
1.880
206.8
115.
3.578
1.891
217.5
5.
5.5
123.75
3.801
1.950
241.3
129.25
3.852
1.962
253.6
5.5
6.
138.
4.062
2.015
278.1
144.
4.117
2.029
292.2
6.
7.
168.
4.565
2.137
359.
175.
4.630
2.152
376.6
7.
BED 19 FEET.
BED 20 FEET.
Depth '
j ! Depth
,&. • ' ^
a\/r
a
^ ! ^ | F&
1
0.5 9.62 0.471
0.686
6.60
10.25
0.479
0.692
7.09! 0.5
0.75 14.53 0.688
0.830
12.1
15.56
0.704
0.839
13.1
0.75
1. 20. 0.876
0.936
18.7
21.
0.920
0.959
20.1
1.
1.25
25.31
1.123
.060
26.8
26.56 1.129
1 . 063
28.2 1.25
1.5
30.75
1.323
.150
35.4
32.25 1.330
1.153
37.2
1.5
1.75 36.31
1.516
.231
44.7
38.06 1.525
1.235
47.
1.75
2. 42.
1.703
.305
54.8
44. 1.715
1.309
57.6
2.
2.25 47.81
1.886
.373
65.6
50.061 1.898
1.377
68.9
2.25
2.5
53.75
2.062
.436
77.2
56.25
2.078
1.442
81.1
2.5
2.75
59.81
2.234
.494
S9.4
62.56
2.252
1.501
93.9
2.75
3.
66.
2.401
.550
102.3
69.
2.422
1.556
107.4
3.
3.25 72.31
2.565
.601
115.8
75.56
2.589
1.609
121.6
3.25
3.5 ! 78.75
2.725
.651
130.
82.25
2.751
1.659
136.5
3.5
3.75 ! 88.31
2.882
.700
150.1
89.06
2.998
1.731
154.2
3.75
4. i 92.
3.035
.742
160.3
96.
3.066 1.751
168.1
4.
4.5 105.75
3.333
.825
193.
110.25! 3.369
1.835
202.3
4.5
5.
120.
3.621
.903
228.4
125. i 3.661
1.913
239.1
5.
5.5
134.75
3.899
.975| 266.1
140.25
3.944
1.986
278.5
5.5
6.
150.
4.170
2.042 306.3 156.
4.220
2.054
320.4
6.
7.
182.
4.691
2.166J 394.2 i 189. i 4.748
2.179
411.8
7.
8.
216.
5.189
2.2761 491.6 i 224. 5.255
2.292
513.4
8.
FLOW O¥ 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~fov use in the formulae
v — c X \/^~ X \A' and C* c X «\/V X \A
BED 25 FEET.
BED 30 FEET.
Depth
i
Depth
in
Feet.
a
r Vr
a\/r
a r vV
a\/r
in
Feet.
0.5
12.25
0.464
.681 8.34
15.25 0.486 .697
10.63
0.5
0.75
19.31
0.712
.844 16.3
23.06! 0.718 .847
19.5
0.75
1.
26.
0.934
.966j 25.1
31. 0.944 .976
30.3
1.
1.25
32.81
1.150
1.0721 35.2
39.06! 1.165 .079
42.1
1.25
1.5 39.75
1.359
1.166
46.3
47.25i 1.380 .175
55.5
1.5
1.75 46.81
1.563
1.250
58.5
55.56 1.592 .261
70.1
1.75
2. 54.
1.761
1.327 71.7
64. 1.795 .340
85.8
2.
2.25 61.31
1.954
1.397 85.6
72.56 1.995! .412
102.5
2.25
2.5 68.75 2.144 1.464 100.7
81.25 2.172 1.474
119.8
2.5
2.75 76.31 2:328i 1.526 116.4
90.06 2.384 1.544
139.1
'2. 75
3. 84.
2.509 1.584; 133.1
99.
2.573S 1.604
158.8
3.
3.25 91.81
2.684 1.639 150.5
108.06
2.758 1.661
179.5
3.25
3.5
99.75
2.858 1.691 168.7
117.25
2.939 1.711
200. G
3.5
3.75
107.81
3.028
1.7401 187.6
126.56
3.141 1.772
224.3
3.75
4.
116.
3.193
1.787
207.3
136.
3.291
1.814
246.7
4.
4^25 124.31
3.358
1.832
227.7
145.56
3.464
1.861
270.9
4.2f>
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
0
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
4.4731 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.
8.2731 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 ft
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 \/ir 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
Dr
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
</?
a\/r
Depth
in
Feet.
9.62
.478
.69
6.7
10.1
.478
.69
7
0.5
14.5
.701
.84
12.2
15.3
.706
.84
13
0.75
19.5
.918
.96
18.7
20.5
.922
.96
20
1.
24.5
1 . 124
.06
26.
25.8
1.132
1.06
27
1.25
29.6
1 . 324
.15
34.1
31.1
1.332
1.15
36
1.5
34.8
1.519
.23
42.9
36.5
1.527
1.23
45
1.75
40.
1.704
.31
52 2
42.
1.716
1.31
55
2.
45.3
1.885
.37
62.2
47.5
1.898
1.38
66
2.25
50.62
2.059
.43
72.6
52.6
2.056
1.44
77
2.5
56.
2.227
.49
83.6
58.8
2.249
1.5
88
2.75
61.5
2.392
.55
95.1
64.5
2.415
1.55
100
3.
67.
2.551
.6
107.1
70.3
2.578
1.6
113
3.25
72.6
2.707
.65
119.5
76.1
2.736
1.65
126
3.5
78.3
2.859
.7
132.4
82.
2:889
1.7
139
3.75
84.
3.006
.74
145.6
88.
3.04
1.74
153
4.
89.8
3.151
.78
159.3
94.
3.186
1.79
168
4.25
95.6
3.29
.81
173.5
100.1
3.36
1.83
183
4.5
107.5
3.629
.89
202.9
112.5
3.608
1.9
214
5.
119.6
3.963
.96
233.9
125.1
3.873
1.97
246
5.5
132.
4.294
2.02
266.4
138.
4.13
2.03
280
6.
157.5
4.545
2.13
335.8
164.5
4.614
2.15
353
7.
184.
4.988
2.23
410.9
192.
5.068
2.25
432
8.
78
FLOW OF WATER IN
TABLE 9.
Channels having a trapezoidal section, with side slopes of -J to 1. Values
of the factors a = area in sqiiare feet, and r = hydraulic mean depth in
feet, and also ^/r and a\/r for use in the formula
v = c X V'r X V^ and Q ~ c X a-^/r X -\A
JJ.CiJJ
^tj JJ .C
J-/JL.J-
' 9J\J A' JC.
Depth
Depth
in
Feet.
a
r
V'r
a\/r
a
r
V~
a\/r
in
Feet.
0.5
12.12
.464
.7
9
15.1
.485
.7
11
0.5
0.75
19.03
.713
.85
16
22.8
.72
.85
19
0.75
1.
25.5
.936
.97
25
30.5
.946
.97
30
1.
1.25
32.03
1.152
1.08
34
38.3
.168
.08
41
1.25
1.5
38.62
1 . 362
1.17
45
46.1
.382
.18
54
1.5
1.75
45.28
1.566
1.25
57
54.
.592
.26
68
1.75
2.
52.
1.764
1.33
69 1
62.
.798
.34
83
2.
2.25
58.78
1.957
.4
82 i
70.
.998
.41
91
2.25
2.5
65.62
2.145
.46
96
78.1
2.194
.48
116
2.5
2.75
72.53
2.329
.52
111
86.3
2.387
.54
133
2.75
3.
79.5
2.507
.58
126
94.5
2.574
.6
152
3.
3.25
86.53
2.681
.64
142
102.8
2.758
.66
171
3.25
3.5
93.62
2.853
.69
158
111.1
2.938
.71
190
3.5
3.75
100.78
3.019
.74
175
119.5
3.113
.76
211
3.75
4.
108.
3.182
.78
193
128.
3.287
.81
232
4.
4.25
115.28
3.341
.83
211
136.5
3.455
.86
254
4.25
4.5
122.62
3.497
.87
229
145.1
3.622
.9
276
4.5
4.75
130.03
3.654
.91
248
153.8
3.786
1.95
299
4.75
5.
137.5
3.8
.95
268
162.5
3.946
1.99
323
5.
5.25
145.03
3.948
.99
288
171.3
4.104
2.03
347
5.25
5.5
152.62
4.092
2.02
309
180.1
4.258
2.06
372
5.5
5.75
160.28
4.234
2.06
330
189.
4.41
2.1
397
5.75
6.
168.
4.373
2.09
351
198.
4.561
2.14
423
6.
6.25
175.78
4.510
2.12
373
207.
4.707
2.17
449
6.25
6.5
183.62
4.645
2.15
396
216.1
4.852
2.2
476
6.5
6.75
191.53
4.777
2.19
419
225.2
4.994
2.24
504
6.75
7.
199.5
4.908
2.22
442
234.5
5.137
2.27
531
7.
7.25
207.53
5.036
2^25
466
243.8
5.275
2.3
560
7.25
7.5
215.62
5.162
2.27
490
253.1
5.412
2.33
589
7.5
7.75
223.78
5.287
2.30
515
262.5
5.546
2.36
618
7.75
8.
232.
5.409
2.33
540
272.
5.68
2.38
648
8.
8.25
240.28
5.53
2.36
565
281.5
5.81
2.41
679
8.25
8.5
248.62
5.65
2.38
591
291.1
5.94
2.44
710
8.5
8.75
247.03
5.678
2.4
617
300.8
6.069
2.47
741
8.75
9.
235.5
5.844
2.43
644
310.5
6.195
2.49
773
9.
OPEN AND CLOSED CHANNELS.
79
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 v/r and a\/r for use in the formulae
v = c X Vr X V~s and Q = c X aVr X \A~
BED 35 FEET.
BED 40 FEET.
Depth
in
Feet.
a
r
Vr
a\/r
a
r
\/r i a^/r
Depth
in
Feet.
0.75
26.53 .723
.85
23
40.37
.727 .85
26
0.75
1.
35 . 25 . 947
.98
35
40.50
.959
.98
40
1.
1.25
44.53
1.178
1.09
48
50.78
1.187
.09
55
1.25
1.5
53.62
1.398
1.18
63
61.02
1.408
.19
73
1.5
1.75
62.78
1.613
1.27
80
71.58
1.630
.28
91
1.75
2.
72.00
1.824
1.35
97
82.
1.844
.36
111
2.
2.25
81.28
2.030
1.42
116
92.53
2.055
.43
133
2.25
2.5
90.62
2.233
1.49
135
103.2
2.264
.50
155
2.5
2.75
100.03
2.431
1.56
156
113.8
2.466
.57
179
2.75
3.
109 . 50
2.625
1.62
177
124.5
2.665 .63
203
3.
3.25
119.03
2.816
1.68
200
135.3
2.862
.69
229
3.25
3.5
128.62
3.004
1.73
223
146.1
3.055
.75
255
3.5
3.75
138.28
3.187
1.79
247
157.
3.245
.80
283
3.75
4.
148.00
3.368
1.84
272
168.
3.433 .85
311
4.
4.25
157.78
3.545
1.89
297
179.
3.617 1.90
340
4.25
4.5
167.62
3.720
1.93
323
190.1
3.797 1.95
371
4.5
4.75
177.53
3.891
1.97
350
201.3
3.977 2.00
401
4.75
5.
187.50
4.060
2.01
378
212.5
4.152 2.04
433
5.
5.25
197.53
4.226
2.05
406
223.8
4.326 2.08
465
5.25
5.5
207.62
4.390
2.10
435
235.1
4.495 2.12
499
5.5
5.75
217.78
4.551
2.14
465
246.5
4.664 2.16
532
5.75
6.
228.00
4.709
2.17
495
258.0
4.826 2.20
567
6.
6.25
238.28
4.865
2.21
526
269.5
4.993 2.24
602
6.25
6.5
248 . 62
5.019
2.24
557
281.1
5.155 2.27
638
6.5
6.75
259.03
5.171
2.28
589
292.8
5.315 2.31
675
6.75
7.
269.50
5.321
2.31
622
304.5
5.472 2.34
712
7.
7.25
280.03
5.468
2.34
655
316.3
5.627 2.37
750
7.25
7.5
290.62
5.614
2.37
689
328.1
5.779 2.40
789
7.5
7.75
301.28
5.756
2.40
723
340.
5.931; 2.44
828
7.75
8.
312.00
5.900
2.43
758
352.
6.081 2.47
868
8.
8.25
322.78
6.039
2.46
793
364.
6.228 2.50
908
8.25
8.5
333.62
6.177
2.49
829
376.1
6.376 2.52
950
8.5
8.75
344.53
6.314
2.52
866
388.3
6.519 2.55
991
8.75
9.
355.50
6.449
2.54
903
400.5
6.661
2.58
1034
9.
9.5
377.62
6.714
2.59
979
425.1
6.941 2.63
1120
9.5
10.
400.00
6.974
2.64
1056
450.
7.216
2.69
1209
10.
80
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 v"> 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
0 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 0 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
CVT
diff.
.01
$
diff.
.01
cVr
<Lff.
.01
.4
105.5
1.47
42.2
1.79
109.5
1.45
43.8
1.82
.4
.5
120.2
1.22
60.1
1.93
124.
1.20
62.
1.96
.5
.6
132.4
1.25
79.4
2.06
136.
1.01
81.6
2.07
.6
.7
142.9
.77
100.
2.15
146.1
.87
102.3
2.15
.7
.8
151.9
.90
121.5
2.22
154.8
.74
123.8
2.22
.8
.9
159.6
.69
143.7
2.28
162.2
.65
146.
2.27
.9
1.
166.5
.60
166.5
2.33
168.7
.57
168.7
2.32
1.1
172.5
.54
189.8
2.41
174.4
.51
191.9
2.35
: .1
1.2
177.9
.48
213.9
2.37
179.5
.45
215.4
2.39
.2
1.3
182.7
.44
237.6
2.43
184.
.41
239.3
2.40
.3
1.4
187.1
.39
261.9
2.46
188.1
.37
263.3
2.44
.4
1.5
191.
.36
286.5
2.49
191.8
.33
287.7
2.45
.5
1.6
194.6
.33
311.4
2.50
195.1
.31
312.2
2.47
.6
1.7
197.9
.30
336.4
2.52
198.2
.27
336.9
2.48
.7
1.8
200.9
.29
361.6
2.54
200.9
.26
361.7
2.49
.8
1.9
203.8
.24
387.
2.55
203.5
.23 i 386.6
2.51
.'9
2.
206.2
.24
412.5
2.56
205.8
.22 411.7
2.51
2.
2.1
208.6
.22
438.1
2.57
208.
.20 i 436.8
2.53
2.1
2.2
210.8
.21
463.8
2.58
210.
.19
462.1
2.53
2.2
2.3
212.9
.19
489.6
2.59
211.9
.18
487.4
2.54
2.3
2.4
214.8
.18
515.5
2.59
213.7
.16
512.8
2.55
2.4
2.5
216.6
.17
541.4
2.61
215.3
.15
538.3
2.55
2.5
2.6
218.3
.15
567.5
2.61
216.8
.15
563.8
2.56
2.6
2.7
219.8
.15
593.6
2.61
218.3 | .14
589.4
2.56
2.7
2.8
221.3
.14
619.7
2.63
219.7 ! .12
615.
2.57
2.8
2.9
222.7
.14
646.
2.66
220.9 S .12
640.7
2.57
2.9
3. 224.1
672.6
i
222.1 i
666.4
3.
100
FLOW OF WATER IN
TABLE 15.
Based on Kutter's formula, with n = .009. Values of the factors c and
for use in the formula}
v = c\/rs — c X V'?" X V s == C's/f X \A'
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
x/F
in feet
1 in 5000=1.056 ft. per mile
1 in 3333.3=1.584 ft. per mile
xA
in feet
s=.0002
a = .0003
diff.
diff.
diff.
diff.
c
.01
cVr
.01
c .01
c^/r
.0! 1
.4
114.1
1.42
45.6
1.86
117.5
1.40
47.
1.88
.4
.5
128.3
1.17
64.2
1.98
131.5
1.14
65.8
2.
.5
.6
140.
.97
84.
2.08
142.9
.95
85.8
2.08
.6
.7
149.7
.83
104.8
2.16
152.4
.79
106.6
2.16
.7
.8
158.
.70
126.4
2.21
160.3
.67
128.2
2.21
.8
.9
165.
.62
148.5
2.27
167.
.59
150.3
2.26
.9
1.
171.2
.53
171.2
2.30
172.9
.51
172.9
2.29
1.
1.1
176.5
.47
194.2
2.33
178.
.44
195.8
2.31
1.1
1.2
181.2
.42
217.5
2.36
182.4
.40
218.9
2.34
1.2
1.3
185.4
.38
241.1
2.38
186.4
.35
242.3
2.36
1.3
1.4
189.2
.34
264.9
2.40
189.9
.32
265.9
2.38
1.4
1.5
192.6
.30
288.9
2.41
193.1
.29
289.7
2.39
1.5
1.6
195.6
.28
313.
2.43
196.
.26
313.6
2.40
1.6
1.7
198.4
.26
337.3
2.44
198.6
.24
337.6
2.42
1.7
1.8
201.
.23
361.7
2.45
201.
.21
361.8
2.42
1.8
1.9
203.3
.21
386.2
2.47
203.1
.20
386.
2.43
1.9
2.
205.4
.20
410.9
2.46
205.1
.19
410.3
2.44
2.
2.1
207.4
.18
435.5
2.48
207.
.17
434.7
2.44
2.1
2.2
209.2
.17
460.3
2.49
208.7
.16
459.1
2.45
2.2
2.3
210.9
.16
485.2
2.49
210.3
.14
483.6
2.45
2.3
2.4
212.5
.15
510.1
2.49
211.7
.14
508.1
2.46
2.4
2.5
214.
.14
535.
2.50
213.1
.13
532.7
2.46
2.5
2.6
215.4
.13
560.
2.50
214.4
.12
557.3
2.47
2.6
2.7
216.7
.12
585.
2.51
215.6
.11
582.
2.47
2.7
2.8
217.9
.11
610.1
2.51
216.7
.11
600. 7
2.48
2.8
2.9
219.
.11
635.2
2.52
217.8
.09
631.5
2.47
2.9
3.
220.1
660.4
218.7
656.2
3.
OPEN AND CLOSED CHANNELS.
107
TABLE 15.
Based on Kutter's formula, with n = .009. Values of the -factors c and
c\/r for use in the formulae
v = c\/rs = c X \/f X \/a = v\/ 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 1000 = 5.28 ft. per mile
•s/r
in feet
s=.0004
5^.001
c
diff.
.01
cVr
diff.
.01
c
diff.
.01
cVr
diff.
.01
.4
119.3
1.39
47.7
1.89
122.8
1.37
49.1
1.91
.4
.5
133.2
1.13
66.6
1.99
136.5
1.09
68.2
2.02
.5
.6
144 . 5
.92
86.7
2.09
147.4
.89
88.4
2.10
.6
.7
153.7
.78
107.6
2.16
156.3
.75
109.4
2.16
.7
.8
161.5
.66
129.2
2.21
163.8
.62
131.
2.20
.8
.9
168.1
.57
151.3
2.25
170.
.54
153. 2.24
.9
1.
173.8
.49
173.8
2.28
175.4
.47
175.4
2 27
1.
1.1
178.7
.44
196.6
2.31
180.1
.41
198.1
2i29
1.1
1.2
183.1
.38
219.7
2.33
184.2
.36
221.
2.31
1.2
1.3
186.9
.34
243.
2.35
187.8
.32
244.1
2.33
1.3
1.4
190.3
.31
266.5
2.36
191.
.29
267.4
2.34
1.4
1.5
193.4
.28
290.1
2.38
193.9
.26
290.8
2.36
1.5
1.6
196.2
.25
313.9
2.39
196.5
.23
314.4
2.36
1.6
1.7
198.7
.23
337.8
2.40
198.8
.22
338.
2.38
1.7
1.8
201.
.21
361.8
2.40
201.
.19
361.8
2.37
1.8
1.9
203.1
.19
385.8
2.42
202.9
.18
385.5
2.39
1.9'
2.
205.
.18
410.
2.42
204.7
.16
409.4
2.33
2
2.1
206.8
.16
434.2
2.43
206.3
.15
433.2
2.40
2^1
2.2
208.4
.15
458.5
2.43
207.8
.14
457.2
2.40
2.2
2.3
209.9
.14
482.8
2.44
209.2
.13
481.2
2.40
2^3
2.4
211.3
.13
507.2
2.44
210.5
.13
505.2
2.42
2.4
2.5
212.6
.12
531.6
2.44
211.8
.11
529.4
2.41
2.5
2.6
213.8
.12
556.
2.45
212.9
.11
553.5
2.42
2.6
2.7
215.
.11
580.5
2.45
214.
.10
577.7
2.42
2.7
2.8
216.1
.10
605.
2.46
215.
.09
601.9
2.42
2.8
2.9
217.1
.09
629.6
2.45
215.9
.09
626.1
2.42
2.9
3.
218.
654.1
1
216.8
650.3
3.
108
FLOW OF "WATER IN
TABLE 16.
Based on Kutter's formula, with n=.Ql. Values of the factors c and
c\/r for use in the formulae
v = c\/rs — c X \/r X \A = c\/r X \/s~
All slopes greater than 1 in 1000 have the same co-emcieiit as 1 in 1000.
-v/r
in feet
1 in 20000=. 264 ft. per mile
1 in 15840=. 3333 ft. per mile
Vr
in feet
a = .00005
s=. 000063131
c
diff.
.01
cVr
diff.
.01
c
diff.
.01
cVr
diff.
.01
.4
81.
1.34
32.4
1.48
84.8
1.34
33.9
.52
.4
.5
94.4
1.16
47.2
1.64
98.2
1.15
49.1
.67
.5
.6
106.
1.03
63.6
1.78
109.7
1.01
65.8
.81
.6
.7
116.3
.92
81.4
1.90
119.8
.89
83.9
.91
.7
.8
125.5
.82
100.4
1.99
128.7
.79
103.
.99
.8
.9
133.7
.73
120.3
2.07
136.6
.70
122.9
2.07
.9
1.
141.
.66
141.
2.14
143.6
.63
143.6
2.13
1.
1.1
147.6
.61
162.4
2.20
149.9
.57
164.9
2.18
1.1
1.2
153.7
.55
184.4
2.25
155.6
.51
186.7
2.23
1.2
1.3
159.2
.50
206.9
2.30
160.7
.47
209.
2.26
1.3
1.4
164.2
.46
229.9
2.33
165.4
.44
231.6
2.30
1.4
1.5
168.8
.43
253.2
2.38
169.8
.39
254.6
2.33
1.5
1.6
173.1
.40
277.
2.40
173.7
.37
277.9
2.36
1.6
1.7
177.1
.36
301.
2.43
177.4
.33
301.5
2.38
1.7
1.8
180.7
.34
325.3
2.45
180.7
.32
325 . 3
2.41
1.8
1.9
184.1
.32
349.8
2.48
183.9
.29
349.4
2.42
1.9
2.
187.3
.30
374.6
2.50
186.8
.27
373.6
2.44
2
2.1
190.3
.28
399.6
2.52
189.5
.25
398.
2.45
2J
2.2
193.1
.26
424.8
2.53
192.
.24
422.5
2.47
2.2
2.3
195.7
.24
450.1
2.55
194.4
.22
447.2
2.48
2.3
2.4
198.1
.24
475.6
2.56
196.6
.22
472.
2.49
2.4
2.5
200.5
.22
501.2
2.57
198.8
.19
496.9
2.50
2.5
2.6
202.7
.20
526.9
2.59
200.7
.19
521.9
2.51
2.6
2.7
204.7
.20
552.8
2.60
202.6
.18
547.
2.52
2.7
2.8
206.7
.19
578.8
2.61
204.4
.16
572.2
2.53
2.8
2.9
208.6
.17
604.9
2.61
206.
.16
597.5
2.54
2.9
3.
210.3
631.
207.6
622.9
3.
OPEN AND CLOSED CHANNELS.
109
TABLE 16.
Based on Kutter's formula, with ?i — .01. Values of the factors c and
c\/r for use in the formulas
v — Cv/rs = c X \/-r X \A' — 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 10000^.528 ft. per mile
1 in 7500 = .704 ft. per mile
Vr
in feet
a — .0001
* == .000133333
c
diff.
.01
cVr
diff. I
.01
c
diff.
.01
cv/r
diff.
.01
.4
91.4
1.34
36.6
1:58
94.9
1.32
38.
1.61
.4
.5
104.8
1.12
52.4
1.72 !
108.1
1.11
54.1
1.74
.5
.6
116.
.97
69.6
1.84
119.2
.94
71.5
1.85
.6
.7
125.7
.83
88.
1.92
128.6
.80
90.
1.93
.7
.8
134.
.73
107.2
2.
136.6
.70
109.3
2.
.8
.9 i 141.3
.65
127.2
2.06 i
143.6
.02
129.3
2.05
.9
1.
147.8
.57
147.8
2.11 1
149.8
.54
149.8
2.10
1.
.1
153.5
.52
168.9
2.15
155 . 2
.49
170.8
2.13
1.1
.2
158.7
.46
190.4
2.18
160.1
.43
192.1
2.16
1.2
.3
163.3
.41
212 2
2 22
164.4
.39
213.7
2.19
1.3
.4
167.4
.38
234! 4
2^24
168.3
.36
235.6
2.22
1.4
.5
171.2
.35
256.8
2.27
171.9
.32
257.8
2.23
1.5
.6
174.7
.32
279.5
2.29
175.1
.29
280.1
2.26 1.6
.7
177.9
.29
302.4
2.30
178.
.27
302 . 7
2.26
1.7
.8
180.8
.27
325.4
2.32 ;
180.7
.25
325.3
2.28 1 8
.9
183.5
.25
348.6
2.34
183.2
.23
348.1
2.30 1.9 •
2
186.
.23
372.
2.34
185.5
.22
371.1
2 . 30 2
l'.\
188.3
.22
395.4
2.36
187.7
.20
394.1
2.31 2.1
2.2
190.5
.20
419.
2.37
189.7
.18
417.2
2.32 2 2
2.3
192.5
.19
442.7
2.37
191.5
.17
440.4
2.33 2 3
2.4
194.4
.17
466.4
2.39
193.2
.16
463.7
2.34 2.4
2.5
196.1
.17
490.3
2.39
194.8
.15
487.1 2.34 2 5
2.6
197.8
.15
514.2
2.40
196.3
.15
510.5 | 2.35 2.6
2.7
199.3
.15
538.2
2.41
197.8
.13
534.
2.35 i 2.7
2.8
200.8
.14
562.3
2.41
199.1
.13
557.5
3.36
2.8
2.9
202.2
.13
586.4
2.42
200.4
.12
581.1
2.36
2.9
3.
203.5
610.6
201.6
604.7
3.
110
FLOW OP WATER IN
TABLE 16.
Based on Kutter's formula, with ?? = .01. Values of the factors c and
c\/r for use in the formulae
v = c\/ra = 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 5000=1.056 ft. per mile
1 in 3333.3=1.584 ft. per mile
Vr
8= .0002
s=.0003
in feet
diff.
diff.
diff.
diff.
in feet
c
.01
cv/r
.01
c
.01
cx/r
.01
A 99.
1.30 i 39.8
1.64
102.
1.29
40.8
1.67
.4
.5 ! 112.
1.08
56.
1.77
114.9
1.06
37.5
1.78
.5
.6 ! 122.8
.91
73.7
1.86
125.5
.88
75.3
1.87
.6
.7 ! 131.9
.77
92.3
1.94
134.3
.75
94.
1.94 .7
.8
139.6
.67
111.7
2.
141.8
.64
113.4
1.99
.8
.9
146.3
.58
131.7
2.04
148.2
.55
133.3
2.04
.9
1.
152.1
.51
152.1
2.08
153.7
.51
153.7
2.10
1.1
157.2
.45
172.9
2. 12
158.8
.41
174.7
2.08 .1
1.2
161.7
.41
194.1
2.' 14
162.9
.38
195.5
2.12 .2
1.3
165.8
.36
215.5
2.17
166.7
.34
216.7
2.13 .3
1.4
169.4
.33
237.2
2.18
170.1
.31
238.
2.18 [ .4
1.5
172.7
.30
259.
2.20
173.2
.28
259.8
2.18
.5
1.6
175.7
.27
281.
2.22
176.
.25
281.6
2.19
1.6
1.7
178.4
.24
303.2
2~23
178.5
.24
303.5
2.20
1.7
1.8
180.8
.23
325.5
2.24
180.9
.21
325.5
2 22
1.8
1.9
183.1
.21
347.9
2.25
183.
.19
347.7
2.22
1.9
2.
185.2
.20
370.4
2.26
184.9
.18
369.9
2.23
2.
2.1
187.2
.18
393.
2.27
186.7
.17
392.2
2.23
2.1
2.2
189.
.16
415.7
2 27
188.4
.16
414.5
2.24
2.2
2.3
190.6
.16
438.4
2^28
190.
.14
436.9
2.25
2.3
2.4
192.2
.14
461.2
2.29
191.4
.14
459.4
2.25
2.4
2.5
193.6
.14
484.1
2.29
192.8
.12
481.9
2.26
2.5
2.6
195.
.13
507.
2.30
194.
.12
504.5
2.26
2.6
2.7
196.3
.12
530.
2.30
195.2
.11
527.1
2.26
2.7
2.8
197.5
.11
553.
2.30
196.3
.11
549.7
2.27
2.8
2.9
198.6
.11
576.
2.31
197.4
.10
572.4
2.27
2.9
3.
199.7
599.1
198.4
595.1
3.
OPEN AND CLOSED CHANNELS.
Ill
TABLE 16.
Based on Kutter's formula, with n— .01. Values of the factors c and
c\/r for use in the formulas
v = c^/rs =1 c X v/r X V*= <*\/r X
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 1000 = 5. 28 ft. per mile
v/r
in feet
0 =B .0004
*=.001
c
diff.
.01
<Vr
diff.
.01
c
diff.
.01
C\/r
diff.
.01
.4
103.7
1.28
41.5
1.67
106.9
1.26
42.7
1.70
.4
.5
116.5
1.04
58.2
1.79
119 5
1.01
59.7
1.80
.5
.6
126.9
.87
76.1
1.88
129.6
.84
77.7
1.89
.6
.7
135.6
.73
94.9
1.94
138.
.70
96.6
1.94
.7
.8
142.9
.62
114.3
1.99
145.
.60
116.
1.99
.8
.9
149.1
.55
134.2
2.04
151.
.52
135.9
2.03
.9
1.
154.6
.47
154.6
2.06
156.2
.45,
156.2
2.06
1.
1.1
159.3
.42
175.2
2.10
160.7
.39
176.8
2.07
1.1
1.2
163.5
.37
196.2
2.11
164.6
.35
197.5
2.10
1.2
.3
167.2
.33
217.3
2.14
168.1
.31
218.5
2.11
1.3
.4
170.5
.28
238.7
2.15
171.2
.28
239.6
2.14
1.4
.5
173.5
.27
260.2
2.17
174.
.25
261.
2.14
1.5
.6
176.2
.24
281.9
2.18
176.5
.23
282.4
2.16
1.6
.7
178.6
.23
303.7
2.19
178.8
.21
304.
2.16
1.7
.8
180.9
.20
325.6
2.19
180.9
.19
325.6
2.17
1.8
.9
182.9
.19
347.5
2.21
182.8
.17
347.3
2.17
1.9
2. j 184.8
.17
369.6
2.21
184.5
.16
369.
2.18
2
2.1
186.5
.16
391.7
2.22
186.1
.15
390.8
2.19
2!l
2.2
188.1
.15
413.9
2.23
187.6
.14
412.7
2.20
2.2
2.3
189.6
.14
436.2
2.22
189.
.13
434.7
2.20
2.3
2.4
191.
.13
458.4
2.24
190.3
.12
456.7
2.20
2.4
2.5
192.3
.12
480.8
2.24
191.5
.11
478.7
2.21
2.5
2.6
193.5
.12
503.2
2.24
192.6
.11
500.8
2.22
2.6
2.7
194.7
.10
525.6
2^25
193.7
.10
523.
2^21
2.7
2.8
195.7
.10
548.1
2.24
194.7
.09
545.1
2.21
2.8
2.9 '
196.7
.10
570.5
2.26
195.6
.08
567.2
2.20 2.9
3.
197.7
593.1
196.4
589.2
3.
112
FLOW OF WATER IN
TABLE 17.
Based on Kutter's formula, with n ~ .011. Values of the factors c and
c\/r for use in the formulas
v = c^/rs — c X \/r X \A = c\/r X v7*1
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 15S40=.3333 ft. per mile
Vr
in feet
8 = .00005
a=. 0000631 31
c
diff.
.01
. c\/r
cL'ff.
.01
c
diff.
.01
cx/r
cliff.
.01
.4
71.1
1.22
28.5
1.31
74.5
1.21
29.8
1.35
.4
.5
83.3
1.07
41.6
1.48
86.6
1.06
43.3
1.50
.5
.6
94.
.95
56.4
.60
97.2
.94
58.3
1.63
.6
.7
103.5
.84
72.4
.71
106.6
.82
74.6
1.72
.7
.8
111.9
.76
89.5
.81
114.8
.74
91.8
1.81
.8
.9
119.5
.69
107.6
.88
122 2
.66
109.9
1.89
.9
126.4
.63
126.4
.95
128^8
.59
128.8
1.94
1.
1
132.7
.57
145.9
2.02
134.7
.54
148.2
1.99
1.1
.2
138.4
.52
. 166.1
2.06
140.1
.50
168.1
2.05
1.2
.3
143.6
.48
186.7
2.11
145.1
.45
188.6
2.08
1.3
.4
148.4
.44
207.8
2.14
149.6
.41
209.4
2.11
1.4
.5 152.8
.41
229.2
2.19
153.7
.38
230.5
2.15
1.5
.6
156.9
.38
251.1
2.21
157.5
.35
252.
2.17
1.6
.7
160.7
.36
273.2
2.26
161.
.33
273.7
2.20
1.7
.8
164.3
.33
295.7
2 27
164.3
.30
295.7
2.22
1.8
.9
167.6
.30
.318.4 2.29
167.3
.29
317.9
2.24
1.9
2.
170.6
.29
341.3
2.31
170.2
.26
340.3
2.26
2
2.1
173.5
.28
364.4
2.34
172.8
.25
362.9
2.27
2.1
2.2
176.3
.25
387.8
2.34
175.3
.23
385.6
2.29
2.2
2.3
178.8
.24
411.2
2.37
177.6
.22
408.5
2.30
2!3
2.4
181.2
.23
434.9
2.39
179.8
•21
431.5
2.31
2.4
2.5
183.5
.21
458.7
2.38
181.9
.19
454.6
2.32
2.5
2.6
185.6
.20
482.6
2.41
183.8
.18
477.8
2.34
2.6
2.7
187.6
.20
506.7
2.41
185.6
.18
501.2
2.34
2.7
2 8
189.6
.18
530.8
2.43
187.4
.16
524.6
2.35
2.8
2.9
191.4
.18
555.1
2.45
189.
.16
548.1
2.36
2.9
3.
193.2
579.6
190.6
571.7
3.
OPEN AND CLOSED CHANNELS .
113
TABLE 17.
Based on Kutters formula, with n = .011. Values of the factors c and
c\/r for use in the fornrnlte
X \/!T ~ c\/r~ X
v — c-srs -— c X
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
v/r
1 in 10000=.52S ft. per mile
1 in 7500 ~ .704 ft. per mile
Vr
*=.0001
s ~ .000133333
in feet
diff.
diff.
diff.
diff.
in feet
c
.01
c*Jr
.01
c
.01
cvr
.01
.4
80.3
1.22
32.1
.41
83.5
1.21
33.4
1.44
.4
.5
92.5
1.04
46.2
.55
95.6
1.02
47.8
1.57
.5
.6
102.9
.89
61.7
.65
105.8
.87
63.5
1.66
.6
.7
111.8
.78
78.2
.74
114.5
.77
80.1
1.76
.7
.8
119.6
.69
95.6
.82
122.2
.65
97.7
1.81
.8
.9
126.5
.61
113.8
.88
128.7
.59
115.8
1.88
.9
1.
132.6
.55
132.6
.93
134.6
.51
134.6
1.91
1.
1.1
138.1
.49
151.9
.97
139.7
.47
153.7
1.96
1.1
1 2
143.
.44
171.6
2.
144.4
.41
173.3
1.97
1.2
i!s
147.4
.40
191.6
2.03
148.5
.38
193.
2.02
1.3
1.4
151.4
.37
211.9
2.07
152.3
.34
213.2
2.03
1.4
1.5
155.1
.33
232.6
2.08
155 . 7
.32
233.5
2.07
1.5
1.6
158.4
.31
253.4
2.11
158.9
.28
254.2
2.07
1.6
1.7
161.5
.28
274.5
2.12
161.7
.27
274.9
2.10
1.7
1.8
164.3
.27
295.7
2.16
164.4
.24
295.9
2.10
1.8
1.9
167.
.24
317.3
2.15
166.8
.22
316.9
2.11
1.9
2.
169.4
.23
338.8
2.18
169.
.21
338.
2.13
2.
2.1
171.7
.21
360.6
2.18
171.1
.20
359.3
2.15
2.1
2.2
173.8
.19
382.4 2.17
173.1
.18
380.8
2.15
2.2
2.3
175.7
.19
404.1
2.21
174.9
.17
402.3
2.15
2.3
2.4
177.6
.17
426.2
2.20
176.6
.16
423.8
2.17
2.4
2.5
179.3
.17
448.2
2.24
178.2
.15
445.5
2.17
2.5
2.6
181.
.15
470.6
2.21
179.7
.14
467.2
2.18
2.6
2.7
182.5
.15
492.7
2.25 It 181.1
.13
489.
2.17
2.7
2.8
i 184.
.13
515.2
2.22 1 182.4
.13
510.7
2.20
2.8
2.9
185.3
.13
537 . 4
2.24 | 183.7
.11
532.7
2.17
2.9
3.
186.6
: 559.8
184.8
554.4
3.
114
FLOW OP WATER IN
TABLE 17.
Based on Kutter's formula, with w = .011. Values of the factors c and
c\/r for use in the formulae
v = cx/rs = c X \/'~ X \A~— CvA7 X \/s~
All slopes greater than 1 in 1000 have the same co-efficient as 1- in 1000.
Vr
1 in 5000=1.056 ft. per mile
1 in 3333.3=1.584 ft. per mile
Vr
a = .0002
s = .0003
in feet
d iff.
diff.
diff.
diff.
in feet
c
.01
cVr
.01
c
.01
c^r
.01
.4
87-1
1.19
34.8
1.47
89.8
1.18
35.9
1.49
.4
.5
99.
1.
49.5
1.59
101.6
.99
50.8
.61
.5
.6
109.
.85
65.4
1.69
111.5
.82
66.9
.69
.6
.7
117.5
.73
82.3
1.75
119.7
.71
83.8
.76
.7
.8
124.8
.63
99.8
1.82
126.8
.61
101.4
.82
.8
.9
131.1
.55
118.
1.86
132.9
.53
119.6
.86
.9
1
136.6
.49
136.6
1.91
138.2
.46
138.2
.89
1.1
141.5
.44
155.7
1.93
142.8
.41
157.1
.92
.1
1.2
145.9
.39
175.
1.97
146.9
.37
176.3
.95
2
1.3
149.8
.35
194.7
1.99
150.6
.34
195.8
.97
.3
1.4
153.3
.31
214.6
2.01
154.
.29
215.5
.99
.4
1.5
156.4
.29
234.7
2.02
156.9
.28
235.4
2.01
.5
1.6
159.3
.27
254.9
2.04
159.7
.24
255.5
2.01
.6
1.7
162.
.24
275.3
2.06
162.1
.23
275.6
2.03
l^r
. /
1.8
164.4
.22
295.9
2.07
164.4
.21
295.9
2.04
.8
1.9
166.6
.21
316.6
2.07
166.5
.19
316.3
2.05
.9
2.
168.7
.19
337.3
2.09
168.4
.18
336.8
2.06
2.
2.1
170.6
.17
358.2
2.09
170.2
.16
357.4
2.06
2.1
2.2
172.3
.17
379.1
2.11
171.8
.16
378.
2.06
2.2
2.3
174.
.15
400.2
2.11
173.3
.15
398.7
2.07
2.3
2.4
175.5
.15
421.3
2.11
174.8
.13
419.5
2.08
2.4
2.5
177.
.13
442.4
2.12
176.1
.13
440.3
2.08
2.5
2.6
178.3
.13
463.6
2.13
177.4
.11
461.1
2.09
2.6
2.7
179.6
.12
484.9
2.12
178.5
.11
482.
2.10
2.7
2.8
180.8
.11
506.1
2.14
179.6
.11
503.
2.10
2.8
2.9
181.9
.11
527.5
2.14
180.7
.09
524.
2.09
2.9
3.
183.
548.9
181.6
544.9
3.
OPEN AND CLOSED CHANNELS.
115
TABLE 17.
Based on Kutter's formula, with n = .011. Values of the factors c and
c\/r for use in the formulae
v = c-v/rx — c X \/r~ X \/*~ = c-^/7~ X \/$~
All slopes greater than 1 in 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
Vr
s=.0004
* = .001
in feet
diff.
diff.
diff.
diff.
in feet
c
.01
c\/r
.01
c
.01
CN/F
.01
.4
91.3
1.18
36.5
1.50
94.1
1.16
37.6
1.52
.4
.5
103.1
.97
51.5
1.62
105.7
.95
52.8
1.63
.5
.6
112.8
.82
67.7
1.70
115.2
.79
69.1
1.71
.6
.7
121.
.69
84.7
1.76
123.1
.67
86.2
1.76
.7
.8
127.9
.59
102.3
1.81
129.8
.57
103.8 -
1.81
.8
.9
133.8
.52
120.4
1.86
135.5
.49
121.9
1.85
.9
1.
139.
.46
139.
1.89
140.4
.43
140.4
1.88
1.
1.1
143.6
.40
157.9
1.92
144.7
.39
159.2
1.91
1.1
1.2
147.6
.36
177.1
1.94
148.6
.34
178.3
1.93
1.2
1.3
151.2
.32
196.5
1.96
152.
.30
197.6
1.94
.3
1.4
154.4
.29
216.1
1.98
155.
.27
217.
1.95
.4
1.5
157.3
.26
235.9
2.
157.7
.25
236.5
1.98
.5
1.6
159 . 9
.24
255.9
2.
160.2
.22
256.3
1.98
.6
1.7
162.3
.22
275.9
2.02
162.4
.20
276.1
1.98
.7
1.8
164.5
.20
296.1
2.02
164.4
.19
295.9
2.01
1.8
1.9
166.5
.18
316.3
2.04
166.3
.17
316.
2.
1.9
2.
168.3
.18
336.7
2.04
168.
.16
336.
2.01
2.
2.1
170.1
.15
357.1
2.05
169.6
.15
356.1
2.03
2.1
2.2
171.6
.15
377.6
2.05
171.1
.13
376.4
2.01
2.2
2.3
173.1
.14
398.1
2.07
172.4
.13
396.5
2.04
3.3
2.4
174.5
.13
418.8
2.06
173.7
.12
416.9
2.03
2.4
2.5
175.8
.12
439.4
2.07
174.9
.11
437.2
2.04
2.5
2.6
177.
.11
460.1
2.07
176.
.10
457.6
2.04
2.6
2.7
178.1
.10
480.8
2.08
177.
.10
478.
2.04
2.7
2.8
179.1
.10
501.6
2.08
178.
.10
498.4
2.03
2.8
2.9
180.1
.10
522.4
2.08
178.9
.09
518.7
2.06
2.9
3.
181.1
543.2
179.8
539.3
3.
116
FLOW OF WATER IN
TABLE 18.
Based on Kutter's formula, with w=.012. Values of the factors c and
c\/r for use in the formula
•v = c^/rs = c X \/r X V* = c\/ X \/
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
Vr i
in feet
1 in 20000=. 264 ft. per mile
1 in 15840= .3333 ft. per mile
Vr
in feet
* = .00005
s=. 000063131
c
diff.
.01
cVr
diff.
.01
c
diff.
.01
c\/r
diff.
.01
.4
63.2
1.11
25.3
1.19
66.1
1.J2
26.4
1.22
.4
.5
74.3
.98
37.2
1.33
77.3
.98
38.6
1.36
.5
.6
84.1
.88
50.5
.45
87.1
.86
52.2
1.48
.6
.7
92.9
.79
65.
.57
95.7
.77
67.
1.57
.7
.8
100.8
.72
80.7
.65
103.4
.69
82.7
1.66
,8
.9
108.
.64
97.2
.72
110.3
.63
99.3
1.73
.9
114.4
.59
114.4
.80
116.6
.56
116.6
1.78
1.
.1
120.3
.54
132.4
.85
122.2 .52
134.4
1.85
1.1
.2
125.7
.50
150.9
.90
127.4
.47
152.9
1.88
.2
.3
130.7
.46
169.9
1.95
132.1
.43
171.7
1.92
.3
.4
135.3
.42
189.4
1.99
136.4
.39
190.9
1.95
.4
.5
139.5
.40
209.3
2.03
140.3
.37
210.4
2.
.5
.6
143.5
.36
229.6
2.05
144.
.34
230.4
2.02
.6
.7
147.1
.35
250.1
2.09
147.4
.32
250.6
2.05
1.7
1.8
150.6
.31
271.
2.11
150.6
.29
271.1
2.05
1.8
1.9
153.7
.30
292.1
2.14
153.5
.28
291.6
2.10
1.9
2.
156.7
.29
313.5
2.16
156.3
.27
312.6
2.13
2
2.1
159.6
.26
335.1
2.17
159.
.23
333.9
2.09
2^1
2.2
162.2
.25
356.8
2.20
161.3
.23
354.8
2.15
2.2
2.3
164.7
.23
378.8
2.21
163.6
22
376.3
2.16
2.3
2.4
167.
.23
400.9
2.22
165.8
.19
397.9
2.13
2.4
2.5
169.3
.21
423.1
2.25
167.7
.19
419.2
2.18
2.5
2.6
171.4
.20
445.6
2.25
169.6
.18
441.
2.18
2.6
2.7
173.4
.19
468.1
2.26
171.4
.17
462.8
2.19
2.7
2.8
175.3
.18
490.7
2.28
173.1
.17
484.7
2.22
2.8
2.9
177.1
.17
513.5
2.28
174.8
.15
506.9
2.20
2.9
3.
178.8
536.3
176.3
528.9
3.
OPEN AND CLOSED CHANNELS.
117
TABLE 18.
Based on Kutter's formula, with n = .012. Values of the factors c and
/T for use in the formulae
v — c^/rs = c X \/r~ X \/s~ = c\fr~ 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
,9 = .000133333
c
diff.
.01
cVr
diff.
.01
c
diff.
.01
cv/r
diff.
.01
.4
71.4
1.11
28.5
1.27
74.2
1.11
29.7
.29
.4
.5
82.5
.96
41.2
1.40
85 3
.95
42.6
.43
.5
.6
92.1
.84
55.2
1.51
94.8
.82
56.9
.52
.6
.7
100.5
.74
70.3
1.60
103.
.71
72.1
.60
.7
.8
107.9
.65
86.3
1.66
110.1
.63
88.1
.66
.8
.9
114.4
.57
102.9
1.72
116.4
.55
104.7
.72
.9
1.
120.1
.52
120.1
1.77
121.9
50
121.9
.77
1
1.1
125.3
.47
137.8
1.82
126.9
.44
139.6
.79
1.1
1.2
130.
.42
156.
1.85
131.3
.40
157.5
.84
1.2
1.3
134.2
.39
174.5
1.88
135.3
.36
175.9
.86
1.3
1.4
138.1
.35
193.3
1.91
138 9
.33
194 5
.88
1.4
1.5
141.6
.33
212.4
1.94
142.2
.31
213 3
.92
1.5
1.6
144.9
.30
231.8
1.96
145.3
.28
232.5
1.93
1.6
1.7
147.9
.27
251.4
1.97
148.1
.25
251.8
1.93
1.7
1.8
150.6
.26
271.1
2.
150.6
.24
271.1
1.96
1.8
1.9
153.2
.24
291.1
2.01
153.
22
290.7
1.97
1.9
2.
155.6
.22
311.2
2.02
155.2
]21
310.4
1.99
2.
2.1
157.8
.21
331.4
2.04
157.3
.19
330.3
1.99
2.1
2.2
159.9
.19
351.8
2.03
159 2
.18
350.2
2.01
2.2
2.3
161.8
.18
372.1
2.05
161.
.16
370.3
1.99
2.3
2.4
163.6
.17
392.6
2.06
162.6
.16
390 2
2.03
2.4
2.5
165.3
.16
413.2
2.07
164.2
.15
410 5
2.03
2.5
2.6
166.9
.15
433.9
2.08
165.7
.14
430.8
2.04
2.6
2.7
168.4
.15
454.7
2.10
167.1
.13
451.2
2.03
2.7
2.8
169.9
.13
475.7
2.08
168.4
.12
471.5
2.03
2.8
2.9
171.2
.13
496.5
2.10
169.6
.12
491.8
2.06
2.9
3.
172.5
517.5
170.8
512.4
3.
118
FLOW OF WATER IN
TABLE 18.
Based on Kutter's formula, with n — .012. Values of the factors c and
c\/r for use in the formulae
v = c-^/rs = c X V^ X \/s~~- c^/r' X \/T
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
s =.0003
c
diff.
.01
cv'r
diff.
.01
c
diff.
.01
cVr
diff.
.01
.4
77.4
1.10
30.9
1.33
79.8
1.10
31.9
1.35
.4
.5
88.4
.94
44.2
1.45
90.8
.92
45.4
1.46
.5
.6
97.8
.79
58.7
1.53
100.
.77
60.
1.54
.6
.7
105.7
.69
74.
1.61
107.7
.67
75.4
1.61
.7
.8
112.6
.60
90.1
1.66
114.4
.58
91.5
1.67
.8
.9
118.6
.53
106.7
1.72
120.2
.51
108.2
1.71
.9
1.
123.9
.46
123.9
1.74
125.3
.44
125.3
1.74
1.1
128.5
.42
141.3
1.79
129.7
.40
142.7
1.77
.1
1.2
132.7
.38
159.2
.82
133.7
.36
160.4
.81
.2
1.3
136.5
.34
177.4
.84
137.3
.32
178.5
.82
.3
1.4
139.9
.30
195.8
.85
140.5
.29
196.7
.84
.4
1.5
142.9
.28
214.3
.88
143.4
.27
215.1
.86
.5
1.6
145.7
.26
233.1
.90
146.1
.24
233.7
.87
.6
1.7
148.3
.24
252.1
.92
148.5
.22
252.4
.88
.7
1.8
150.7
.21
271.3
.90
150.7
.20
271.2
.89
.8
1.9
152.8
.21
290.3
.95
152.7
.19
290.1
.91
1.9
2.
154.9
.18
309.8
.93
154.6
.18
309.2
.92
2.
2.1
156.7
.18
329.1
.96
156.4
.16
328.4
.92
2.1
2.2
158.5
.16
348.7
.95
158.
.16
347.6
.95
2.2
2.3
160.1
.15
368.2
.96
159.6 .13
367.1
.90
2.3
2.4
161.6
.14
387.8
.97
160.9
.13
386.1
.94
2.4
2.5
163.
.14
407.5
.99
162.2
.12
405.5
.93
2.5
2.6
164.4
.12
427.4
.97
163.4
.12
424.8
.96
2.6
2.7
165.6
.12
447.1
.99
164.6
.11
444.4
1.96
2.7
2.8
166.8
.11
467.
.99
165.7
.10
464.
1.94
2.8
2.9
167.9
.11
486.9
2.01
166.7
.10
483.4
1.97
2.9
3.
169.
507.
167.7
503.1
3.
1
1
OPEN AND CLOSED CHANNELS.
119
TABLE IS.
Based on Kutter's formula, with n = .012. Values of the factors c and
c\/r for use in the formulae
v — c\/rs = c X \/r~ X \/s~= c>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
<v-
diff.
.01
4 69.4
1.03
27.8
1.20
71.6
1.02
28.6
.23
.4
.5
79.7
.87
39.8
1.32
81.8
.86
40.9
.34
.5
.6 88.4
.75
53.
1.41
90.4
.73
54 3
.41
.6
7 95.9
.65
67.1
1.48
97.7
.64
68.4
.49
.7
.8 ! 102.4
.57
81.9
1.54
104.1
.55
83.3
.45
.8
.9 i 108.1
.51
97.3
1.59
109.6
.48
97.8
.66
.9
113.2
.44
113.2
1.61
114.4
44
114.4
.63
1.
1
117.6
.40
129.3
1.66
118.8
.38
130.7
.64
1.1
2
121.6
.37
145.9
1.69
122.6
.35
147.1
.68
1.2
.3
125.3
.32
162.8
1.71
126.1
.31
163.9
1.70
1.3
.4
128.5
31
179.9
1.74
129.2
.28
180.9
1.71
1.4
.5
131.6
.27
197.3
1.75
132.
.26
198.
1.73
1.5
.6
134.3
.24
214.8
1.76
134.6
.23
215.3
1.74
1.6
.7
136.7
.24
232.4
1.79
136.9
.22
232.7
1.77
1.7
.8
139.1
.21
250.3
1.79
139.1
.20
250.4
1.76
1.8
.9
141.2
.19
268.2
1.81
141.1
.19
268.
1.80
1.9
2.
143.1
.20
286.3
1 83
143.
.16
286.
1.77
2.
2.1
145.1
.16
304.6
1 81
144.6
.17
303.7
1.81
2.1
2.2
146.7
.16
322.7
1.83
146.3
.14
321.8
1.80
2.2
2.3
148.3
.16
341.
1.86
147.7
.14
339.8
1.81
2.3
24
149.9
.13
359.6
1.85
149.1
.13
357.9
1.82
2.4
2.5
151.2
.14
378.1
1.85
150.4
.12
376.1
1.83
2.5
26
152.6
.12
396.6
1.85
151.7
.13
394.4
1.83
2.6
2.7
153.8
.12
415.1
1.88
152.9
.12
412.7
1.82
2.7
2.8
155.
.11
433 9
1.88
153.9
.10
430.9
1.85
2.8
2.9
156.1
.10
452.7
1.86
155.
.11
449.4
1.82
2.9
3. i 157.1
I
471.3
155.9
.09
467.6
3.
OPEN AND CLOSED CHANNELS
123
TABLE 19.
Based on Kutter's formula, with n — .013. Values of the factors c and
c\/r for Tise in the formulae
v -— c\/rs -—cX x//7 X V~ = Cx/r X \/s~
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
in feet
I in 2500 = 2.114 ft. per mile
1 in 1000 = 5.28 ft. per mile
in feet
s = .0004
8 = .001
c
diff.
.01
«VF
diff.
.01
c
diff.
.01
cvr
diff.
.01
.4
72.8
1.02
29.1
.24
75.2
1.01
30.1
.25
.4
.5
83.
.85
41.5
.34
85.3
.83
42.6
.46
.5
.6
91.5
.73
54.9
.42
93.6
.71
56.2
.43
.6
.7
98.8
.62
69.1
.49
100.7
.60
70.5
.49
.7
.8
105.
.54
84.
.54
106.7
.52
85.4
.53
.8
.9
110.4
.48
99.4
.58
111.9
.46
100.7
.57
.9
1.
115.2
.41
115.2
.61
116.5
.40
116.5
.60
1.
.1
119.3
.38
131.3
.64
120.5
.35
132.5
.63
1.1
.2
123.1
.34
147.7
.67
124.
.32
148.8
.66
1.2
.3
126.5
.29
164.4
.68
127.2
.29
165.4
.67
1.3
.4
129.4
.29
181.2
.72
130.1
.26
182.1
.69
1.4
.5
132.3
.24
198.4
.72
132.7
.23
199.
.70
1.5
.6
134.7
.23
215.6
.73
135.
.21
216.
.71
1.6
. 7
137.
.21
232.9
1.75
137.1
.20
233 . 1
.73
1.7
.8
139.1
.19
250.4
1.73
139.1
,18
250.4
.73
1.8
1.9
141.
.18
267.7
1.79
140.9
.17
267.7
1.75
1.9 •
2.
142.8
.18
285.6
1 80
142.6
.15
285.2
1.74
2.
2.1
144.6
.14
303.6
1.77
144.1
.14
302.6
1.75
2.1
2 2
146.
.14
321.3
1.77
145.5
.14
320.1
.78
2.2
2.3
147.4
.14
339.
.81
146.9
.12
337.9
.75
2.3
2.4
148.8
.12
357.1
.79
148.1
.11
355.4
77
2.4
2.5
150.
.12
375.
1.81
149.2
.11
373.1
78
2.5
2.6
151.2
.11
393.1
.81
150.3
.10
390.9
.77
2.6
2.7
152.3
.10
411 2
.80
151.3
.10
408.6
.79
2.7
2.8
153.3
.10
429.2
1.83
152.3
.09
426.5
1.79
2.8
2.9
154.3
.09
447.5
1.81
153.2
.09
444.4
1.80
2.9
3. 155.2
465.6
154.1
462.4
3.
124
FLOW OF WATER IN
TABLE 20.
Based 011 Kutter's formula, with n = .015. Values of the factors c and
c\/r for use in the formulae
v = CV/TS = c X xA7 X \/«~ = 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 20000 = .264 ft. per mile
1 in 15840=. 3333 ft. per mile
Vr
in feet
8 = .00005
s = .000063131
c
diff.
.01
cx/r
diff.
.01
c
diff.
.01
cV~
diff.
.01
.4
46.8
.87
18.7
.91
48.9
.88
19.6
.93
.4
. 5
55.5
.79
27.8
1.02
57.7
.79
28.9
1 05
.5
.6
63.4
.70
38.
1.13
65.6
.69
39.4
1.14
.6
.7
70.4
.67
49.3
1.24
72.5
.66
50.8
.25
M
. /
.8
77.1
.60
61.7
1.31
79.1
58
63.3
.31
.8
.9
83.1
.55
74.8
1.38
84.9
53
76.4
.38
.9
88.6
.50
88.6
1.44
90.2
49
90.2
.45
: !i
93.6
.47
103.
1.50
95.1
.45
104.7
.49
J
.2
98.3
.44
118.
.55
99.6
.42
119.6
.53
.2
.3
102.7
.40
133.5
.59
103.8
.38
134.9
.57
.3
.4
106.7
.38
149.4
.63
107.6
.36
150.6
.61
.4
.5
110.5
.35
165.7
.67
111.2
.33
166.7
.64
.5
.6
114.
.33
182.4
.70
114.5
.31
183 1
.68
.6
rr
. /
117.3
.31
199.4
.73
117.6
28
199.9
.68
.7
1.8
120.4
.29
216.7
1,76
120.4
.27
216.7
.72
.8
1.9
123.3
.28
234.3
1.78
123.1
.26
233.9
.74
.9
2.
126.1
.25
252 1
1.80
125.7
.24
251.3
-77
2.
2.1
128.6
.25
270.1
1.83
128.1
.22
269.
.77
2 1
2.2
131.1
.23
288.4
1.84
130.3
.21
286.7
.79
2.2
2.3
133.4
.22
306.8
1.87
132.4
.21
304.6
.82
2.3
2.4
135.6
.21
325.5
1.87
134.5
.18
322.8
.81
2.4
2.5
137.7
.20
344.2
1.91
136.3
.19
340.9
.83
2.5
2.6
139.7
.19
363.3
1.91
138.2
.17
359.2
.87
2.6
2.7
141.6
.18
382.4
1.91
139.9
.17
377.9
1.85
2.7
2.8
143.4
.17
401.5
1.93
141.6
.15
396.4
1.87
2.8
2.9
145.1
.16
420.8
1.94
143.1
.14
415 1
1.85
2.9
3.
146.7
440.2
144.5
433.6
3.
1
OPEN AND CLOSED CHANNELS.
125
TABLE 20.
Based on Kutter's formula, with n = .015, Values of the factors c and
c\/r for use in the formulae
v = c\/rs = c X \/r 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 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
cv/r
diff.
.01
.4
52.7
.89
21.1
.97
54.7
.90
21.9
.99
.4
.5
61.6
.78
30.8
.09
63.7
.78
31.8
1.11
.5
.6
69 4
.68
41.7
.17
71.5
.67
42.9
1.18
.6
.7
76.2
.63
53.4
.26
78.2
.61
54.7
1.28
.7
.8
82.5
.56
66.
.33
84.3
.54
67.5
1.32
.8
.9
88.1
.50
79.3
.38
89.7
.48
80.7
1.38
.9
1.
93.1
.46
93.1
.43
94.5
.44
94.5
1.43
1.
1.1
97.7
.41
107.4
.47
98.9
.39
108.8
1.46
1.1
1.2
103.8
.38
122.1
.51
102.8
.37
123.4
1.50
1.2
1.3
105.6
.34
137,2
.54
106.5
.32
138.4
1.52
1.3
1.4
109.
.32
152,6
.57
109.7
.30
153. G
1.55
1.4
1.5
112.2
.30
168.3
.60
112.7
.28
169.1
1.58
1.5
1.6
115.2
.27
184.3
.62
115.5
.26
184.9
1.59
1.6
1.7
117.9
.25
200.5
.63
118.1
.24
200.8
1.61
1.7
1.8
120.4
.25
216,8
.66
120.5
.22
216.9
1.62
1.8
1.9
122.9
.21
233.4
.67
122.7
.21
233. 1
1.65
1.9
2.
125.
.21
250.1
.69
124.8
.19
249.6
1.65
2.
21
127.1
.20
267.
.70
126.7
.18
266.1
1.66
2.1
2.2
129.1
.18
284.
.70
128.5
.17
282.7
1.68
2.2
2.3
130.9
.17
301.
.73
130.2
.16
299.5
1.68
2.3
2.4
132.6
.17
318.3
.74
131.8
.15
316.3
1.69
2.4
2.5
134.3
.15
335.7
.75
133.3
.14
333.2
1.70
2.5
26
135.8
.15
353 2
.75
134.7
.13
350.2
1.71
2.6
2.7
137.3
.14
370.7
.76
136.
.13
367.3
1.72
2.7
2.8
138.7
.13
388.3
.78
137.3
.12
384.5
1.72 2.8
2.9
140.
.12
406.1
.75
138.5
.12
401.7
1.69 2.9
3
141.2
423.6
139.7
558.6
3.
126
FLOW OF WATER IN
TABLE 20.
Based on Kutter's formula, with n = .015. Values of the factors c and
c\/V for use in the formulae
v = cvVs = c X \/r~ X \/s~ = c\/r~ X %A~
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
v~
in feet
1 in 5000=1.056 ft. per mile j 1 in 3333.3=1.584 ft. per mile
-v/r
in feet
s = .0002
s = .0003
c
diff.
.01
c\/r
diff.
.01
c
diff.
.01
c^r
diff.
.01
.4
57.1
.90
22.9
1.01
59.
.89
23.6
1.03
.4
.5
66.1
.77
33.
1.13
67.9
.76
33.9
.14
.5
.6
73.8
.65
44.3
1.19
75.5
.65
45.3
.21
.6
.7
80.3
.60
56 2
1.29
82.
.58
57.4
.28
.7
.8
86.3
.52
69.1
1.33
87.8
.50
70.2
.33
.8
.9
91.5
.46
82.4
1.37
92.8
.45
83.5
.38
.9
1.
96.1
.42
96.1
1.42
97.3
.40
97.3
.41
1.
1.1
100.3
.37
110.3
1.45
101.3
.36
111.4
.45
1.1
1.2
104.
.34
124.8
1.48
104.9
.32
125.9
.47
1.2
1.3
107.4
.31
139.6
1.51
108.1
.30
140.6
.49
1.3
1.4
110.5
.28
154.7
1.53
111.1
.26
155.5
.51
1.4
1.5
113.3
.26
170.
1.54
113.7
.25
170.6
1.53
1.5
1.6
115.9
.24
185.4
1.57
116.2
.22
185.9
1.54
1.6
1.7
118.3
22
201.1
1.58
118.4
.21
201.3
1.56
1.7
1.8
120.5
/21
216.9
1.60
120.5
.20
216.9
1.58
1.8
1.9
122.6
.19
232.9
1.60
122.5
.17
232.7
1.58
1.9
2.
124.5
.17
248.9
1.60
124.2
.17
248.5
1.58
2.
2.1
126.2
.17
264.9
1.65
125.9
.15
264.3
1.59
2.1
2.2
127.9
.15
281.4
1.62
127.4
.15
280.2
1.63
2.2
2.3
129.4
.14
297.6
1.64
128.9
.13
296.5
1 59
2.3
2.4
130.8
.14
314.
1.65
130.2
.13
312.4
1 63
2.4
2.5
132.2
.13
330.5
1.67
131.5
.12
328.7
1.63
2.5
2.6
133.5
.12
347.2
1.66
132.7
.11
345.
1.63
2.6
2.7
134.7
.12
363.8
1.67
133.8
.11
361.3
1.64
2.7
2.8
135.9
.10
380.5
1.66
134.9
.09
377.7
1.62
2.8
2.9
136.9
.11
397.1
1.69
135.8
.07
393 . 9
1.65
2.9
3.
138.
414.
136.8
410.4
3.
|
OPEN AND CLOSED CHANNELS.
127
TABLE 20.
Based on Kutter's formula, with n = .015. Values of the factors c and
c\/r for use in the formulae
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.
^
in feet
1 in 2500=2.114 ft. per mile
1 in 1000=5.28 ft. per mile
Vr
in feet
a — .0004
s=.001
c
diff.
.01
evT
diff.
.01
c
diff.
.01
c\/r
diff.
.01
.4
60.
.89
24.
1.04
62.
.88
24.8
1.06
.4
'.5
68.9
.75
34.4
1.15
70.8
.75
35.4
1.16
.5
.6
76.4
.64
45.9
1.21
78.3
.63
47.
.22
.6
.7
82.8
.58
58.
1.29
84.6
.55
59.2
.29
.7
.8
88.6
.50
70.9
1.33
90.1
.48
72.1
.33
.8
.9
93.6
.43
84.2
1.37
94 9
.42
85.4
.37
.9
1.
97.9
.39
97.9
1.41
99.1
.38
99.1
.41
1.
1.1
101.8
.35
112.
1.44
102.9
.33
113.2
.42
1.1
1.2
105.3
.32
126.4
1.46
106.2
.30
127.4
.46
1.2
1.3
108.5
.28
141.
1.49
109.2
.27
142.
.47
1.3
.4
111.3
.27
155.9
1.50
111.9
.25
156.7
.49
1.4
.5
114.
.23
170.9
1.52
114.4
.22
171.6
.50
1.5
.6
116.3
22
186.1
1.54
116.6
.20
186.6
.50
1.6
.7
118.5
.20
201.5
1.55
118.6
.19
201.6
.53
1.7
.8
120.5
.19
217.
1.55
120.5
.18
216.9
.55
1.8
.9
122.4
.17
232.5
1.56
122.3
.16
232.4
.54
1.9 '
2.
124.1
.16
248.1
1.59
123.9
.15
247.8
.55
2
2.1
125.7
.15
264.
1.59
125.4
.14
263 3
1.57
2^1
2.2
127.2
.14
279.9
1.59
126.8
.12
279.
1.54
2.2
2.3
128.6
.13
295.8
1.59
128.
.13
294.4
1.59
2.3
2.4
129.9
.12
311.7
1.60
129.3
.11
310.3
1.57
2.4
2.5
131.1
.12
327.7
1.43
130.4
.10
326.
1.56
2.5
2.6
132.3
.10
342.
1.80
131.4
.11
341.6
1.62
2.6
2.7
133.3
.11
360.
1.63
132.5
.09
357.8
1.57
2.7
2.8
134.4
.10
376.3
1.63
133.4
.09
373.5
1.60
2.8
2.9
135.4
.08
392.6
1.61
134.3
.08
389.5
1.58
2.9
3.
136.2
408.7
135.1
405.3
3.
128
FLOW OF WATER IN
TABLE 21.
Based on Kutter's formula, with n — .017. Values of the factors c and
for use in the fornmlee
v = c\/rs = c X \/r X \/s = c\/r~ X \/s~
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
Vr
«=. 00005
«=. 0000631 31
in feel
diff.
diff. !
diff.
diff.
in feet
c
.01
.01
c
.01
c\/r
.01
.4
39.6
.76
15.9
.77
41.3
.77
16.5
.80
.4
.5
47.2
.70
23.6
.89
49.
.70
24.5
.91
.5
.6
54.2
.63
32.5
.99
56.
.63
33.6
.6
.7
60.5
.59
42.4
.07
62.3
.58
43.6
.09
.7
.8
66.4
.54
53.1
.15
68.1
.52
54.5
.15
.8
.9
71.8
.49
64.6
.21
73.3
.49
66.
.22
.9
1.
76.7
.47
76.7
.28
78.2
.45
78.2
.27
1.
1.1
81.4
.43
89.5
.33
82.7
.41
90.9
.32
1.1
1.2
85.7
.40
102.8
.38
86.8
.38
104.1
.37
1.2
.3
89.7
.37
116.6
.42
90.6
.36
117.8
.40
1.3
.4
93.4
.35
130.8
.46
94.2
.33
131 . 8
.44
1.4
.5
96.9
.33
145.4
.49
97.5
.31
146.2
.47
1.5
.6
100.2
.31
160.3
1.53
100.6
.29
160.9
.51
1.6
.7
103.3
.29
175.6
1.56
103.5
.27
176.
.52
1.7
.8
106.2
.28
191.2
1.59
106.2
.26
191.2
.55
1.8
.9
109.
.26
207.1
1.61
108.8
.24
206.7
.58
1.9
2.
Ill 6
.24
223.2
1.63
111.2
.23
222 5
.59
2
2.1
114.
.24
239.5
1.65
113.5
.22
238.4
.61
2 1
2.2
116.4
.22
256.
1.68
115.7
.20
254.5
.62
2.'2
2.3
118.6
.21
272.8
1.69
117.7
.20
270.7
.65
2.3
2.4
120.7
.20
289.7
1.71
119.7
.18
287.2
.66
2.4
2.5
122.7
.19
306.8
1.73
121.5
.17
303.8
.66
2.5
2.6
124.6
.19
324.1
1.73
123.2
.17
320.4
.69
2.6
2.7
126.5
.17
341.4
1.76
124.9
.16
337 . 3
.69
2.7
2.8
128.2
.17
359.
1.76
126.5
.15-
354.2
.70
2.8
2.9
129 9
.16
376.6
1.78
128.
.15
371.2
.72
2.9
3.
131.5
.15
394.4
1.79
129.5
.14
388.4
.73
3.
3.1
133.
.15
412.3
.80
130.9
.13
405 . 7
.73
3.1
3.2
134.5
.14
430.3
.81
132.2
.12
423.
1.74
3.2
3.3
135.9
.13
448.4
.82
133.4
.13
440.4
1.75
3.3
3.4
137.2
.13
466.6
.83
134.7
.11
457.9
1.75
3.4
35
138.5
.13
484.9
.83
135.8
.12
475.4
1.76
3 5
3.6
139.8
.12
503.2
.84
137.
.10
493.
1.77
3.6
3.7
141.
.11
521.6
.85
138.
.11
510.7
1.77
3.7
3.8
142.1
.12
540.1
1.86
139.1
.10
528.4
1.79
3.8
3.9
143.3
.10
558.7
1.87
140.1
.9
546.3
1.78
3.9
4.
144.3
577.4
141.
564.1
4.
OPEN AND CLOSED CHANNELS.
129
TABLE 21.
Based on Kutter's formula, with n = .017. Values of the factors c and
/V for use in the formulae
v = cVrs — c X V~ X V~= c\/~ X ->/?
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
<VT
diff.
.01
c
diff.
.01
Cv/r
diff.
.01
.4
48.2
.79
19.3
.87
49.8
.78
19.9
.89
.4
.5
56 1
.68
28.
.98
57.6
.68
28.8
.98
.5
.6
62.9
.61
37.8
1.05
64.4
.60
38.6
1.07
.6
.7
69.
.53
48.3
l.U
70.4
.52
49.3
1.12
.7
.8
74.3
.48
59.4
1.18
75.6
.46
60.5
1.17
.8
.9
79.1
42
71.2
1.21
80.2
.42
72.2
1.22
.9
1.
83.3
.39
83.3
1 22
84.4
.37
84.4
1.25
1.
1.1
87.2
.35
95.9
1.29
88.1
.34
96.9
1.29
1.1
1.2
90.7
.32
108 8
1.32
91.5
.30
109.8
1.30
1.2
1.3
93.9
.29
122.
1.35
94.5
.28
122.8
1.34
1.3
1.4
96.8
.26
135.5
1.37
97.3
.25
136.2
1.35
1.4
1.5
99.4
.25
149.2
1.38
99.8
.24
149.7
1.38
1.5
1.6
101.9
.23
163.
1.41
102.2
.21
163.5
.38
1.6
1.7
104.2
.21
177.1
1.43
104.3
.20
177.3
.40
1.7
1.8
106.3
.20
191 4
1.43
106 3
.19
191.3
.43
1.8
1.9
108.3
.18
205.7
1.45
108.2
.17
205.6
.42
1.9
2.
110.1
.17
220.2
1.46
109.9
.16
219.8
.43
2.
2.1
111.7
.16
234.8
1.47
111.5
.15
234.1
.45
2.1
2.2
113.4
.15
249.5
1.48
113.
.14
248.6
.45
2.2
2.3
114.9
.14
264.3
1.49
114.4
.13
263.1
.46
2.3
2.4
116.3
.14
279.2
1.50
115 7
.13
277.7
.48
2.4
2.5
117.7
.12
294.2
.50
117.
.11
292.5
.46
2.5
2.6
118.9
.12
309.2
.51
118.1
.12
307.1
.50
2.6
2.7
120.1
.11
324.3
.51
119.3
.10
322.1
.47
2.7
2.8
121.2
.11
339.4
.52
120.3
.10
336.8
.50
2.8
2.9
122.3
.10
354.6
.53
121.3
.09
351.8
.48
2.9
3.
123.3
.10
369.9
.53
122.2
.09
366.6
.50
3.
3.1
124.3
.09
385.2
54
123.1
.08
381.6
.49
3.1
3.2
125.2
.09
400.6
1.54
123.9
.08
396.5
•50
3.2
3.3
126.1
.08
416.
1.54
124.7
.08
411.5
.52
3.3
3.4
126.9
.08
431.4
1.54
125.5
.07
426.7
.50
3.4
3.5
127.7
.08
446.8
1.58
126.2
.07
441.7
.51
3.5
3.6
128.5
.07
462.6
1.53
126.9
.07
456.8
.53
3.6
3.7
129.2
.06
477.9
1.55
127.6
.06
472.1
.51
3.7
3.8 .
129.8
.07
493.4
1.57
128.2
.07
487.2
.55
3.8
3.9
130.5
.07
509.1
1.55
128.9
.06
502.7
.55
3.9
4.
131.2
524.6
129.5
518.2
4.
OPEN AND CLOSED CHANNELS.
131
TABLE 21.
Based on Kutter's formula, with n = .017. Values of the factors c and
/r for use in the formulae
v = c^/rs = c X \/r X V —
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
Vr
in feel
1 in 2500 = 2.114 ft. per mile
1 in 1666.7=3.168 ft. per mile
Vr
in feet
s = .0004
s = .0006
c
diff.
.01
Cv/F
diff.
.01
c
diff.
.01
cVr
diff.
.01
.4
50.5
.78
20.2
.90
51.5
.79
20.6
.91
.4
.5
58.3
.68
29.2
.99
59.4
.67
29.7
1.00
.5
.6
65.1
.59
39.1
1.06
66.1
.58
39.7
1.07
.6
.7
71.
.52
49.7
1.12
71.9
.51
50.4
1.12
.7
.8
76.2
.45
60.9
.18
77.
.45
61.6
1.18
.8
.9
80.7
.41
72.7
.21
81 5
.40
73.4
1.21
.9
1.
84.8
.37
84.8
.25
85.5
.36
85.5
1.25
1.
1.1
88.5
.32
97.3
.28
89.1
.31
98.
1.27
1.1
1.2
91.7
.30
110.1
.30
92.2
.30
110.7
1.31
1.2
.3
94.7
.27
123.1
.33
95.2
.26
123.8
1.32
1.3
.4
97.4
.25
136.4
.35
97.8
.24
137.
1.33
1.4
.5
99.9
.23
149.9
.36
100.2
.22
150.3
1.36
1.5
.6
102.2
21
163.5
.38
102.4
.21
163.9
1.37
1.6
.. .7
104.3
.19
177.3
.39
104.5
.21
177.6
1.38
1.7
1.8
106.2
.18
191.2
.40
106.3
.18
191.4
1.39
1.8.
1.9
108.
.17
205.2
.42
108.1
.16
205.3
1.40
1.9
o
109.7
.15
219.4
.42
109.7
.15
219.3
1.42
2.
2.1
111.2
.15
233.6
.43
111.2
.14
233.5
1.41
2!l
2.2
112.7
.14
247.9
.44
112 6
.13
247.6
1.44
2.2
2.3
114.1
.12
262.3
.45
113.9
.12
262.
1.42
2.3
2.4
115.3
.12
276.8
.45
115.1
.11
276.2
1.44
2.4
2.5
116.5
.11
291.3
.46
116.2
.11
290.6
1.44
2.5
2.6
117.6
11
305.9
.46
117.3
.10
305.
1.45
2.6
2.7
118.7
.10
320.5
.47
118.3
.10
319.5
1.45
2.7
2.8
119.7
.10
335.2
.47
119.3
.09
334.
1.46
2.8
2.9
120.7
.09
349.9
.48
120.2
.09
348.6
1.46
2.9
3.
121.6
.08
364.7
.48
121.1
.08
363.2
1.46
3.
3.1
122.4
.08
379.5
.49
121.9
.08
377.8
.47
3.1
3 2
123.2
.08
394.4
.48
122.7
.07
392.5
.47
3.2
3 3
124.
.08
409.2
.51
123.4
.07
407.2
.47
3.3
3.4
124.8
.07
424.3
.48
124.1
.07
421.9
.48
3.4
3.5
125.5
.06
439.1
.50
124.8
.06
436.7
.48
3.5
3.6
126.1
.07
454.1
.51
125.4
.06
451.5
.47
3.6
3.7
126.8
.06
469.2
.52
126.
.06
466.2
.48
3.7
3.8
127.4
.06
484.4
.47
126.6
.06
481.
1.49
. 3.8
3.9
128.
.05
499.1
.50
127.2
.05
495.9
1.49
3.9
4.
128.5
514.1
127.7
510.8
4.
132
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 formulas
v = c^/rs = cX Vr X Vs SB c^r X V
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
Vr
1 in 1250 =4.224 ft. per mile
1 in 1000=5.28 ft. per mile
Vr
s = .0008
s = .001
in feet
diff.
diff.
diff.
diff.
in feet
c
.01
cVr
.01
c
.01
cVr
.01
.4
52.
.78
20.8
.91
52.3
.78
20.9
.91
.4
.5
59.8
.68
29.9
1.
60.1
.67
30.
1.01
.5
.6
66.6
.58
39.9
1.08
66.8
.58
40.1
1.07
.6
. 7
72.4
.50
50.7
1.12
72.6
.51
50.8
1.14
.7
.8
77.4
.45
61.9
1.18
77.7
.44
62.2
.17
.8
.9
81.9
.39
73.7
1.21
82.1
.39
73.9
.21
.9
1.
85.8
.34
85.8
1.23
86.
.35
86.
.24
1.
1.1
89.2
.33
98.1
1.29
89.5
.31
98.4
.27
1.1
1.2
92.5
.29
111.
1.30
92.6
.29
111.1
.30
1.2
1.3
95.4
.26
124.
1.32
95.5
.26
124.1
.32
1.3
1.4
98.
.23
137.2
1.33
98.1
.23
137.3
.33
1.4
1.5
100.3
.22
150.5
1.35
100.4
.21
150.6
.34
1.5
1.6
102.5
.20
164.
1.37
102.5
.20
104.
.36
1.6
1.7
104.5
.18
177.7
1.37
104.5
.18
177.6
.37
1.7
1.8
106.3
.17
191.4
1.39
106.3
.17
191.3
.39
1.8
1.9
108.
.16
205.3
1.39
108.
.16
205.2
.40
1.9
2.
109.6
.15
219.2
1.41
109.6
.14
219.2
.39
2
2.1
111.1
.13
233.3
1.41
111.
.14
233.1
.42
2.1
2.2
112.4
.13
247.4
1.42
112.4
.12
247.3
.40
2.2
2.3
113.7
.12
2G1.6
1.42
113.6
.12
261.3
.42
2.3
2.4
114.9
.11
275.8
1.43
114.8
.12
275.5
.48
2.4
2.5
116.
.11
290.1
1.44
116.1
.13
290.3
.40
2.5
2.6
117.1
.10
304.5
1.44
117.1
.10
304.3
1.46
2.6
2.7
118.1
.09
318.9
1.44
118.1
.10
318.9
1.43*
2.7
2.8
119.
.09
333.3
1.45
119.
.09
333.2
1.45
2.8
2.9
119.9
09
347.8
1.45
119.9
.09
347.7
1.44
2.0
3.
120.8
.08
362.3
1.46
120.7
.08
362.1
1.46
3.
3.1
121.6
.07
376.9
1.44
121 . 5
.08
376.7
1.43
3.1
3.2
122.3
.07
391 . 3
1.47
122.2
.07
391.
1.46
3.2
3.3
123.
.07
406.
1.47
122.9
.07
405.6
1.46
3.3
3.4
123.7
.07
420.7
1.47
123.6
.07
420.2
1.49
3.4
3.5
124.4
.06
435.4
1.46
124.3
.07
435.1
1 45
3.5
3 6
125.
.07
450.
1.51
124.9
.06
449.6
1.47
3.6
3.7
125.7
.05
465.1
1.44
125.5
.06
464.3
1.48
3.7
3.8
126.2
.05
479.5
1.47
126.1
.06
479.1
1.46
3.8
3.9
126.7
.05
494.2
1.48
126.6
.05
493.7
1.47
3.9
4.
127.2
509.
127.1
.05
508.4
4.
OPEN AND CLOSED CHANNELS.
133
TABLE 22.
Based on Kutter's formula, with n — .02. Values of the factors c and
/r for use in the formulas
v •= c\/rs = c X \/r X \A = c-v/r X -s/s
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
x/r
in feet
1 in 20000=. 264 ft. per mile
1 in 15840 = .3333 ft. per mile
Vr
in feet
s — .00005
s :-_= .000063131
c
diff.
.01
c^/r
diff.
.01
c
diff.
.01
cVT
diff.
.01
.4
32.
.63
12.8
.64
33.3
.65
13.3
.66
.4
.5
38.3
.59
19.2
.73
39.8
.58
19.9
.75
.5
.6
44.2
.54
26.5
.82
45.6
.55
27.4
.83
.6
.7
49.6
.51
34.7
.91
51.1
.49
35.7
.91
.7
.8
54.7
.47
43.8
.96
56.
.46
44.8
.98
.8
.9
59.4
.43
53.4
.03
60.6
.43
54.6
1.03
.9
63.7
.41
63.7
.09
64.9
.39
64.9
1.08
1.
.1
67.8
.38
74.6
.13
68.8
.38
75.7
1.14
1.1
.2
71.6
.36
85.9
.18
72.6
.34
87.1
1.17
1.2
.3
75.2
.34
97.7
.23
76.
.32
98.8
1.21
1.3
.4
78.6
.31
110.
.26
79.2
.30
110.9
1.25
1.4
.5
81.7
.31
122.6
.30
82.2
.29
123.4
1.28
1.5
.6
84.8
.28
135.6
.33
85.1
.27
136.2
1.30
1.6
.7
87.6
.26
148.9
.35
87.8
.25
149.2
1.33
1.7
.8
90.2
.26
162.4
.40
90.3
.24
162.5
1.36
1.8
.9
92.8
.24
176.4
.40
92.7
.22
176.1
1.38
1.9
2.
95.2
.23
190.4
.44
94.9
.22
189.9
1.39
2
2.1
97.5
.22
204.8
.44
97.1
.20
203.8
1.42
2^1
2.2
99.7
.21
219.4
.46
99.1
.19
218.
1.43
2.2
2.3
101 8
.20
234.2
.49
101.
.18
232.3
1.45
. 2.3
2.4
103.8
.19
249 1
.51
102.8
.18
246.8
1.47
2.4
2.5
105.7
.18
264.2
.53
104.6
.17
261.5
1.49
2.5
2.6
107.5
.18
279.5
.55
106.3
.16
276.4
1.48
2.6
2.7
109.3
.16
295.
.54
107.9
.15
291.2
1.51
2.7
2.8
110.9
.15
310.4
.57
109.4
.14
306.3
1.51
2.8
2.9
112.4
.16
326.1
.59
110.8
.14
321.4
1.53
2.9
3.
114.
.15
342.
.61
112.2
.14
336.7
1.55
3.
3.1
115 5
.14
358.1
.60
113.6
.13
352.2
1.55
3.1
3.2
116.9
.14
374.1
.59
114.9
.12
367.7
1.54
3 2
3.3
118.3
.13
390.
.66
116.1
.12
383.1
1.57
3.3
3.4
119.6
.12
406.6
.62
117.3
.11
398.8
1.56
3.4
3.5
120.8
.12
422.8
.64
118.4
.11
414.4
1.58
3.5
3.6
122.
.12
439.2
.66
119.5
.11
430.2
1.60
3.6
3.7
123.2
.11
455.8
.65
120. G
.10
446.2
1.59
3.7
3.8
124.3
.11
472.3
.68
121. G
.09
462.1
1.56
3.8
3.9
125.4
.11
489.1
1.69
122.5
.10
477.7
1.63
3.9
4.
126.5
5G6.
123.5
494.
4.
1
134
FLOW OF WATER IN
TABLE 22.
Based on Kntter's formula, with n -- .02. Values of the factors c and
c\/r for use in the formulae
v = c^/rs~ — c X \/r~ 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 10000^.528 ft. per mile.
1 in 7500 = .704 ft . per mile
Vr
in feet
a = .0001
s=. 000133333
c
diflf.
.01
cVT
diff.
.01
c
diff.
.01
CN/r
diff.
.01
.4
35.7
.66
14.3
.69
37.1
.66
14.8
.70
.4
.5
42.3
.59
21.2
.77
43.7
.59
21.8
.80
.5
.6
48.2
.54
28.9
.86
49.6
.53
29.8
.86
.6
.7
53.6
.48
37.5
.92
54.9
.48
38.4
.94
.7
.8
58.4
.45
46.7
.99
59.7
.43
47.8
.98
.8
.9
62.9
.40
56.6
1.03
64.
.40
57.6
1.04
.9
1.
66.9
.38
66.9
1.08
68.
.36
68.
1.08
1.1
70.7
34
77.7
1.13
71.6
.33
78.8
1.11
: .1
.2
74.1
.32
89.
1.15
74.9
.31
89.9
1.15
.2
.3
77.3
.30
100.5
1.19
78.
.28
101 4
1.18
.3
.4
80.3
.28
112.4
1.22
80.8
.27
113.2
1.20
.4
.5
83.1
.25
124.6
1.24
83.5
.24
125.2
1.23
1.5
.6
85.6
.24
137.
1.27
85.9
.23
137.5
1.24
1.6
.7
88.
.23
149.7
1.29
88.2
.21
149.9
1.27
1.7
.8
90.3
.21
162.6
.30
90.3
.20
162.6
1 28
1.8
1.9
92.4
.20
175.6
.33
92 3
.19
175.4
1.30
1.9
2.
94.4
.19
188.9
.33
94.2
.17
188.4
1.31
2
2.1
96.3
.18
202.2
.36
95.9
.17
201.5
1.32
2.1
2.2
98.1
.17
215 8
.37
97.6
.16
214.7
1.34
2.2
2.3
99.8
.16
229.5
.38
99.2
.15
228.1
1.25
2.3
2.4
101.4
.15
243.3
.39
100.7
.14
241.6
1.35
2.4
2.5
102.9
.14
257.2
.40
102.1
.13
255.1
1.37
2.5
2.6
104.3
.14
271.2
.41
103.4
.12
268.8
1.37
2.6
2.7
105.7
.13
285.3
.43
104.6
.12
282.5
1.39
2.7
2.8
107.
.12
299.6
.43
105.8
.12
296.4
1.38
2.8
2.9
108.2
.12
313.9
.43
107.
.11
310.2
1.40
2.9
3.
109.4
.11
328.2
.45
108.1
.10
324.2
1.40
3.
3.1
110.5
.11
342.7
.45
109.1
.10
338.2
1.41
3.1
3.2
111.6
.11
357.2
.46
110.1
.09
352.3
1.41
3.2
3.3
112.7
.10
371.8
.46
111.
.09
366.4
1.42
3.3
3.4
113.7
.09
386.4
.47
111.9
.09
380.6
1.43
3.4
3.5
114.6
.09
401.1
.47
112.8
.09
394.9
1.42
3.5
3.6
115.5
.09
415.8
.49
113.7
.08
409.1
1.46
3.6
3.7
116.4
.08
430.7
.47
114.5
.07
423.7
1.41
3.7
3.8
117.2
.08
445.4
1.48
115.2
.07
437.8
1.44
3.8
3.9
118.
.08
460.2
1.51
115.9
.08
452.2
1.45
3.9
4.
118.8
475.3
116.7
466.7
4.
OPEN AND CLOSED CHANNELS.
135
TABLE 22.
Based on Kutter's formula, with n = .02. Values of the factors c and
/r for use in the formulae
v = c-v/r* •= c X Vr~ X \/T — c *Jr~ X \A~
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
Vr
1 in 5000=1.056 ft. per mile
1 in 3333.3—1.584 ft. per mile
Vr
s = .0002
s == .0003
in feet
diff.
diff.
diff.
/ —
diff.
in feet
c
.01
Cv/r
.01
c
.01
c\/r
.01
.4
38.7
.66
15.5
.72
39.9
.67
16.
.73
.4
.5
45.3
.59
22.7
.80
46.6
.58
23 3
.82
.5
.6
51.2
.52
30.7
.88
52.4
.52
31 5
.88
.6
.7
56.4
.47
39.5
.94
57.6
.46
40.3
.95
.7
.8
61.1
.43
48.9
.99
62.2
.42
49.8
.99
.8
.9
65.4
.38
58.8
1.04
66.4
.37
59.7
1.04
.9
1.
69.2
.35
69.2
1.07
70.1
.33
70.1
1.07
1.
1.1
72.7
.31
79.9
1.11
73.4
.31
80.8
1.10
1.1
1.2
75.8
.30
91.
1.14
76.5
.28
91.8
1.13
1.2
1.3
78.8
.26
102.4
1.16
79.3
.26
103.1
1.16
1.3
1.4
81.4
.25
114.
1.19
81.9
.23
114.7
1.17
1.4
1.5
83.9
.23
125.9
1.21
84.2
.22
126.4
1.19
».«
1.6
86.2
.22
138.
1.22
86.4
.20
138.3
1.21
1.6
1.7
88.4
.19
150.2
.24
88.4
.20
150.4
1.23
1.7
1.8
90.3
.19
162.6
.26
90.4
.17
162.7
1.24
1.8.
1.9
92.2
.17
175.2
.27
92.1
.16
175.1
1.24
1.9
2.
93.9
.17
187.9
. .28
93.7
.16
187.5
.26
2.
2.1
95.6
.15
200.7
.29
95.3
.14
200.1
.27
2.1
2.2
97.1
.14
213.6
.30
96.7
.14
212.8
.28
2.2
2.3
98.5
.14
226.6
.31
98.1
.12
225.6
.27
2.3
2.4
99.9
.13
239.7
.32
99.3
.12
238.3
.30
2.4
2.0
101.2
.12
252.9
.33
100.5
.12
251.3
.30
2.5
2.6
102.4
.11
266.2
.33
101.7
.10
264.3
.30
2.6
2.7
103.5
.11
279.5
.34
102.7
.10
277.3
.32 ! 2.7
2.8
104.6
.10
292.9
.35
103.7
.10
290.5
.31
2.8
2.9
105.6
.10
306.4
.35
104.7
.09
303.6
.32
2.9
3.
106.6
.10
319.9
.36
105.6
.09
316.8
.33
3.
3.1
107.6
.09
333.5
.36
106.5
.08
330.1
.33
3.1
3.2
108.5
.08
347.1
.37
107.3
.08
343.4
.34
3.2
3.3
109.3
.08
360.8
.37
108.1
.68
356.8
.34
3.3
3.4
110.1
.08
374.5
.37
108.9
.07
370.2
.34
3.4
3.5
110.9
.08
388.2
.38
109.6
.07
383.6
.34
3.5
3.6
111.7
.07
402.
.39
110.3
.07
397.
1.35
3.6
3.7
112.4
.07
415.9
.39
111.
.06
410.5
1.35
3.7
3.8
113.1
.06
429.8
.43
111.6
.06
424.
1.35
3.8
3.9
113.7
.07
443.6
.39
112.2
.06
437.5
1.36
3.9
4.
114.4
457.5
112.8
451.1
4.
136
FLOW OP WATER IN
TABLE 22.
Based on. KutterV; formula, with n -~ .02. Values of the factors c and
c\/r for use in the formulae
v — c\/rs = c X x/r" X v/JT = CX/T 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. 112 ft. per mile il in 1666.7=3.168 ft. per mile]
a -•= .0004
* = .0006
Vr
in feet
c
diff.
.01
cx/r
diff.
.01
c
diff.
.01
<Vr~
diff.
.01
.4
40.6
.67
16.2
.74
41.3
.67
16.5
.75
.4
.5
47.3
.58
23.6
.83
48.
.58
24.
.83
.5
.6
53.1
.51
31.9
.89
53.8
.51
32.3
.90
.6
.7
58.2
.46
40.8
.95
58.9
.45
41.3
.94
.7
.8
62.8
.41
50.3
.99
63.4
.41
50.7
1.
.8
.9
66.9
.37
60.2
.04
67.5
.35
60.7
1.03
.9
1.
70.6
.32
70.6
.06
71.
.33
71.
1.07
1.
1.1
73.8
.31
81.2
.10
74.3
.30
81.7
1.10
1.1
1.2
76.9
.27
92.2
.13
77.3
.26
92.7
1.12
1.2
1.3
79.6
.25
103.5
.15
79.9
.25
103.9
1.14
1.3
.4
82.1
.23
115.
.17
82.4
.22
115.3
1.16
1.4
.5
84.4
.22
126.7
.18
84.6
.21
126.9
1.21
1.5
.6
86.6
.19
138.5
.20
86.7
.19
138.7
1.19
1.6
.7
88.5
.18
150.5
1.21
88.6
.18
150.6
1.21
1.7
.8
90.3
.17
162.6
1.23
90.4
.16
162.7
.21
1.8
.9
92.
.16
174.9
1.24
92.
.15
174 8
.23
1.9
2.
93.6
.15
187.3
1.25
93.5
.15
187.1
.23
'2.
2.1
95.1
.15
199.8
1.25
95.
.13
199.4
.24
2.1
2.2
96.6
.12
212.3
1.27
96.3
.13
211.8
.27
2.2
2.3
97.8
.12
225.
1.27
97.6
.11
224.5
.24
2.3
2.4
99.
.12
237.7
1.28
98 7
.12
236.9
.28
2.4
2.5
100.2
.11
250.5
1.29
99.9
.10
249.7
.27
2.5
2.6
101.3
.10
263.4
1.29
100.9
.10
262.4
1.27
2.6
2.7
102.3
.10
276.3
1.29
101.9
.09
275.1
1.28
2.7
2.8
103.3
.09
289.2
1.30
102.8
.09
287.9
1.29
2.8
2.9
104.2
.09
302.2
.31
103.7
.08
300.8
1.28
2.9
3.
105.1
.08
315.3
.31
104.5
.09
313.6
1.30
3.
8.1
105.9
.08
328.4
.31
105.4
.07
326.6
1.30
3.1
3.2
106.7
.08
341.5
.32
106.1
.08
339.6
1.30
3.2
3.3
107.5
.07
354.7
.32
106.9
.07
352 . 6
1.31
3.3
3.4
108.2
.07
367 . 9
.33
107.6
.06
365.7
1.30
3.4
3.5
108.9
.07
381.2
.32
108.2
.06
378.7
1.31
3.5
3.6
109.6
.06
394.4
.34
108.8
.07
391.8
1.32
3.6
3.7
110.2
.06
407.8
1.32
109.5
.05
405.
1.31
3.7
3.8
110.8
.06
421.
1.35
110.
.06
418.1
1.32
3.8
3.9
111.4
.06
434.5
1.33
110.6
.05
431.3
1.32
3.9
4.
112.
447.8
111.1
444.5
4.
OPEN AND CLOSED CHANNELS.
137
TABLE 22.
Based on Kutter's formula, with ?i — .02. Values of the factors c arid
c\/r for use in the formulae
v = c\/rs = c X \/r~ X %A — c\Jf X \A~
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
1
Vr
in feet
1 in 1250r=4.224 ft. per mile
1 in 1000 = 5.28 ft. per mile
Vr
in feet
s = .0008
» = .001
c
diff.
.01
CX/F
diff.
.01
c
diff.
.01
cvT
diff.
.01
.4
41.7
.67
16.7
.75
41.9
.67
16.8
.75
.4
.5
48.4
.58
24.2
.83
48.6
.58
24 3
.83
.5
.6
54.2
.51
32.5
.90
54.4
.51
32.6
.90
.6
.7
59.3
.45
41.5
.95
59.5
.45
41.6
.96
.7
.8
63.8
.40
51.
1.
64.
.40
51.2
1.00
.8
.9
67.8
.35
61.
1.03
68.
.35
61.2
.03
.9
1.
71.3
.32
71.3
1.07
71.5
.32
71.5
.08
1
1.1
74.5
.29
82.
1.09
74.7
.29
82.3
.08
1 1
.2
77.4
.27
92.9
1.12
77.6
.26
93.1
.12
1.2
.3
80.1
.24
104.1
1.14
80.2
.24
104.3
.13
1.3
.4
82.5
.22
115.5
1.16
82.6
22
115.6
.16
1.4
.5
84.7
.20
127.1
1.17
84.8
/20
127.2
.17
1.5
.6
86.7
.19
138.8
1.18
86.8
.18
138.9
1.17
1.6
.7
88.6
.18
150.6
.21
88.6
.18
150.6
1.21
1.7
.8
90.4
.16
162.7
.21
90.4
.16
162.7
1.21
1.8
.9
92.
.15
174.8
.22
92.
.15
174.8
1.22
1.9
2.
93.5
.14
187.
.22
93.5
.13
187.
1.21
2.
2.1
94.9
.13
199.2
.25
94.8
.13
199.1
1.23
2.1
2.2
96.2
.13
211.7
.25
96.1
.13
211.4
1.26
2.2
2.3
97.5
.11
224.2
.24
97.4
.11
224.
1.24
2.3
2.4
98.6
.11
236.6
.26
98.5
.11
236.4
1.26
2.4
2.5
99.7
.10
249.2
.27
99.6
.10
249.
1.25
2.5
2.6
100.7
.10
261.9
.27
100.6
.09
261.5
1.26
2.6
2.7
101.7
.09
274.6
.27
101.5
.09
274.1
1.26
2.7
2.8
102.6
•09
287.3
.28
102.4
.09
286.7
1.29
2.8
2.9
103.5
.08
300.1
.27
103.3
.08
299.6
.27
2.9
3.
104.3
.08
312.8
.30
104.1
.08
312.3
.29
3.
3.1
105.1
.07
325.8
.28
104.9
.07
325.2
.27
3.1
3.2
105.8
.07
338.6
.28
105.6
.07
337.9
.29
3.2
3.3
106.5
.07
351.4
.31
106.3
.07
350.8
.30
3.3
3.4
107.2
.07
364.5
.31
107.
.06
363.8
.28
3.4
3.5
107.9
.06
377.6
.30
107.6
.06
376.6
.29
3.5
3.6
108.5
.06
390.6
.31
108.2
.06
389.5
.31
3.6
3.7
109.1
.05
403.7
.28
108.8
.06
402.6
.31
3.7
3.8
109.6
.06
416.5
.33
109.4
.05
415.7
.29
3.8
3.9
110.2
.05
429.8
.30
109.9
.05
428.6
1.30
3.9
4.
110.7
442.8
110.4
441.6
4.
138
PLOW 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 formulae
v = c\/rs = c X \/~ X \/s~= 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
Vr
s == .00005
* == .000063131
in feet
diff.
diff.
diff.
c^— diff.
in feet
c
.01
(V>
.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. ihl 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 1000—5.28 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~ = cv/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
<vT
diff.
.01
.4
28.6
.53
11.4
.56
29.5
.53
11.8
.56
.4
.5
33.9
.47
17.
.62
34.8
.47
17.4
.63
.5
.6
38.6
.43
23.2
.68
39.5
.43
23.7
.70
.6
.7
42.9
.39
30.
.74
43.8
.38
30.7
.74
.7
.8
46.8
.35
37.4
.79
47.6
.35
38.1
.79
.8
.9
50.3
.33
45.3
.83
51.1
.32
46.
.83
.9
1.
53.6
.30
53.6
.87
54.3
.29
54.3
.86
1.
i.l
56.6
.29
62.3
.89
57.2
.27
62.9
.90
1.1
1.2
59.3
.26
71.2
.93
59.9
.24
71.9
.91
1.2
1.3
61.9
.24
80.5
.95
62.3
.23
81.
.94
1.3
1.4
64.3
.22
90.
.98
64.6
.21
90.4
.97
1.4
1.5
66.5
.20
99.8
.98
66.7
.20
100.1
.98
1.5
1.6
68.5
.19
109.6
.01
68.7
.18
109.9
1.
1.6
1.7
70.4
.19
119.7
.04
70.5
.18
119.9
.02
1.7
1.8
72.3
.16
130.1
.03
72.3
.17
130.1
.03
1.8
1.9
73.9
.17
140.4
.08
73.9
.15
140.4
.04
1.9'
2.
75.6
.15
151.2
.07
75.4
.14
150.8
.05
2.
2.1
77.1
.14
161.9
.08
76.8
.13
161.3
.05
2 1
2.2
78.5
.13
172.7
.08
78.1
.13
171.8
.08
2 2
2.3
79.8
.13
183.5
.11
79.4
.12
182.6
.08
2.'3
2.4
81.1
.12
194.6
.12
83.6
.11
193.4
.09
2.4
2.5
82.3
.12
205.8
.13
81.7
.11
204.3
.10
2.5
2.G
83.5
.10
217.1
.11
82.8
.10
215.3
.10
2.6
2.7
84.5
.11
228.2
.15
83.8
.10
226.3
.11
2.7
2.8
85.6
.10
239.7
.14
84.8
.09
237.4
.11
2.8
2.9
86.6
.09
251.1
.14
85.7
.09
248.5
.13
2.9
3.
87.5
.09
262.5
.15
86.6
.09
559.8
.15
3.
3.1
88.4
.09
274.
1.18
87.5
.08
271.3
.13
3.1
3.2
89.3
.08
285.8
1.15
88.3
.07
282.6
.11
3.2
3.3
90.1
.08
297.3
1.18
89.
.08
293.7
.16
3.3
3.4
90.9
.08
309.1
1.17
89.8
.07
305.3
.13
3.4
3.5
91.7
.07
320.8
1.18
90.5
.06
316.6
.15
3.5
3.6
92.4
.07
332.6
1.18
91.1
.07
328.1
.15
3.6
3.7
93.1
.07
344.4
1.19
91.8
.06
339.6
.16
3.7
3.8
93.8
.06
356.3
1.19
92.4
.06
351.2
.16
3.8
3.9
94.4
.06
368.2
1.19
93.
.06
362.8
1.1G
3.9
4.
95.
380.1
93.6
374.4
4.
10
146
FLOW OP WATER IN
TABLE 24.
Baaed on Kutter's formula, with n = .025. Values of the factors c and
c\/r for use iii the formula)
v — c\/rs = c X N/V X \A' = CX/F X \/~
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
•v/r
in feet
1 in 2500=2.112 ft. per mile
1 in 1666.7=3.168 ft. per mile
Vr
in feet
s = .0004
s = .0006
c
cliff.
.01
cVr
diflf.
.01
c
diff.
.01
CV/F
diff.
.01
.4
30.
.53
12.
.57
30.5
.53
12.2
.57
.4
.5
35,3
.47
17.7
.63
35.8
.47
17.9
.64
.5
.6
40.
.42
24.
.69
40.5
.42
24.3
.70
.6
.7
44.2
.38
30.9
.75
44.7
.38
31.3
.75
. /
.8
48.
.35
38.4
.80
48.5
.34
38.8
.79
.9
51.5
.31
46.4
.82
51.9
.31
46.7
.83
'.9
1.
54.6
.29
54.6
.87
55.
.29
55.
.87
1.
1.1
57.5
.26
63.3
.88
57.9
.25
63.7
.88
1.1
1 2
60.1
.25
72.1
.93
60.4
.24
72.5
.91
1.2
1.3
62.6
.22
81.4
.93
62.8
.22
81.6
.94
1.3
1.4
64.8
.21
90.7
.97
65.
.20
91.
.95
1.4
1.5
66.9
.19
100.4
.97
67.
.19
100.5
.97
1.5
1.6
68.8
.18
110.1
.99
68.9
.17
110.2
.98
l.G
1.7
70.6
.17
120.
1.01
70.6
.17
120.
1.01
1.7
1.8
72.3
.15
130.1
1.01
72.3
.15
130.1
1.01
1.8
1.9
73.8
.15
140.2
1.04
73.8
.14
140.2
1.C2
1.9
2
75.3
.14
150.6
1.05
75.2
.13
150.4
1.03
o
2^1
76.7
.13
161 1
1.05
76.5
.13
160.7
1.05
2.1
2.2
78.
.12
171.6
1.06
77.8
.12
171.2
1.05
2.2
2.3
79.2
.12
182.2
1.08
79.
.11
181.7
1.05
2.3
2.4
80.4
.11
193.
1.08
80.1
.11
192.2
1.08
2.4
2.5
81.5
.10
203.8
1.07
81.2
.10
203.
1.07
2.5
2.6
82.5
.10
214.5
1.10
82.2
.09
213.7
1.07
2.6
2.7
83.5
.09
225.5
1.08
83.1
.09
224.4
1.08
2.7
2.8
84.4
.09
236.3
1.11
84.
.09
235.2
1.10
2.8
2.9
85.3
.09
247.4
.12
84.9
.08
246.2
1.09
2.9
3.
86.2
.08
258.6
.11
85.7
.08
257.1
1.10
3.
3.1
87.
.07
269.7
.09
86.5
.07
268. 1
1.09
3.1
3.2
87.7
.08
280.6
.14
87.2
.07
279.
1.11
3.2
3.3
88.5
.07
292.
.13
87.9
.07
290.1
1.11
3.3
3.4
89.2
.07
303.3
.12
88.6
.06
301.3
1.11
3.4
3.5
89.9
.06
314.5
.13
89.2
.06
312.3
1.11
3.5
3.6
90.5
.06
325.8
.14
89.8
.06
323.4
1.12
3.6
3.7
91.1
.06
337.2
.13
90.4
.06
334.6
1.12
3.7
3.8
91.7
.06
348.5
.15
91.
.06
345.8
1.13
3.8
3.9
92.3
.05
360.
1.14
91.6
.05
357.1
1.12
3.9
4.
92.8
371.4
92.1
368.3
4..
OPEN AND CLOSED CHANNELS.
147
TABLE 24.
Based on Kutter's formula, with n= .025. Values of the factors c and
c\/r for use in the formula
= c X xA X \A = c^r X
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
1 in 1000=5.28 ft. per mile
Vr
in feet
s = .0008
*=.001
c
diff.
.01
cVr~
diff.
.01
c
diff.
.01
cx/F
diff.
.01
.4
30.8
.53
12.3
.58
30.9
.54
12.4
.58
.4
.5
36.1
.47
18.1
.64
36.3
.47
18.2
.64
.5
.6
40.8
.42
24.5
.70
41
.42
24.6
.70
.6
.7
45.
.38
31.5
.75
45.2
.37
31.6
.75
.7
.8
48.8
.34
39.
.80
48.9
.34
39.1
.80
.8
.9
52 2
.30
47.
.82
52.3
.31
47.1
.83
.9
55.2
.28
55.2
.86
55.4
.28
55.4
.86
1.
.1
58.
.26
63.8
.89
58.2
.25
64.
.88
1.1
.2
60.6
.23
72.7
.91
60.7
.23
72.8
.91
1.2
.3
62.9
22
81.8
.93
63.
.22
81.9
.94
.3
.4
65.1
.20
91.1
.96
65.2
.20
91.3
.95
.4
.5
67.1
.18
100.7
.95
67.2
.18
100.8
.96
.5
.6
68.9
.18
110.2
1.
69.
.17
110.4
.98
.6
.7
70.7
.16
120.2
.99
70.7
.16
120.2
.99
.7
.8
72.3
.15
130.1
1.01
72.3
.15
130.1
1.01
.8
.9
73.8
.14
140 2
.02
73.8
.13
140.2
1.
.9
2.
75.2
.13
150.4
.03
75.1
.13
150.2
1.02
2.
2.1
76.5
12
160.7
.02
76.4
.13
160.4
1.05
2.1
2.2
77.7
.12
170.9
.06 !
77.7
.11
170.9
.1.03
2.2
2.3
78.9
.11
181.5
.05
78.8
.11
181.2
1.06
2.3
2.4
80.
.10
192.
.05
79.9
.10
191.8
1.05
2.4
2.5
81.
10
202 5
.07
80.9
.10
202.3
1.06
2.5
2.6
82.
.09
213.2
.06
81.9
.09
212.9
1.07
2.6
2.7
82.9
.09
223.8
.08
82.8
.09
223.6
1.08
2.7
2.8
83.8
.08
234.6
.07
83.7
.08
234 .4
1.07
2.8
2.9
84.6
.08
245.3
.09
84.5
.08
245.1
1.08
2.9
3.
85.4
.08
256.2
.10
85.3
.07
255.9
1.07
3.
3.1
86.2
.07
267.2
.09
86.
.07
266.6
1.08
3.1
3.2
86.9
.07
278.1
.10
86.7
.07
277.4
1.07
3.2
3.3
87.6
.07
289.1
.11
87.4
.07
288.4
1.11
3.3
3.4
88.3
.06
300.2
.10
88.1
.06
299.5
1.10
3.4
3.5
88.9
.06
311.2
.10
88.7
.06
310.5
1.10
3.5
3.6
89.5
.06
322 2
.11
89.3
.06
321.5
1.10
3.6
3.7
90.1
.05
333.3
.12
89.9
.05
332.5
1.11
3.7
3.8
90.6
.06
344.5
.11
90.4
.06
343.6
1.11
3.8
3.9
91.2
.05
355.6
.12
91.
.05
354.7
1.11
3.9
4.
91.7
366.8
91.5
365.8
4.
148
FLOW OF WATER IN
TABLE 25.
Based on Emitter's formula, with n = .0275. Values of the factors c and
c\/r for use in the formulae
v = c^/rs = c X x/r" X \A~ = c\/r~ X \A~
All slopes greater thaii 1 in 1000 have the same co-efficient as 1 in 1000.
x/r
in feet
1 in 20000^.264 ft. per mile
1 in 15840=.3333 ft. per mile
Vr
in feet
8 = .00005
'a — . 000063 131
c
diflf.
.01
cVr
diff.
.01
C
^ *r
diff.
.01
4
21.2
.44
8.5
.43
22.
.45
8.8
.44
.4
.5
25.6
.42
12.8
.51
26.5
.42
13.2
.52
5
.6
29.8
.40
17.9
.58
30.7
40
18.4
.59
.6
.7
33.8
.37
23.7
.63
34.7
.37
24.3
.64
.7
8
37.5
.35
30.
.69
38.4
.35
30.7
.70
.8
.9
41
.34
36.9
.75
41.9
.32
37.7
.74
.9
44.4
.31
44.4
.78
45.1
.31
45.1
.79
•1
47.5
.30
52.2
.84
48.2
.29
53.
.83
.1
2
50.5
.28
60.6
.87
51.1
.28
61.3
.87
2
.3
53.3
.27
69.3
.91
53.9
.26
70.
.90
.3
4
56.
.26
78.4
.95
56.5
.24
79.
.94
.4
.5
58.6
.24
87.9
.98
58.9
.24
88.4
.96
.5
.6
61.
.24
97.7
.01
61.3
.22
98.
.00
.6
.7
63.4
.22
107.8
.05
63.5
.21
108.
.01
.7
.8
65.6
.22
118.3
.04
65.6
.20
118.1
.03
.8
.9
67.8
.20
128.7
.09
67.6 i .20
128.4
.06
1.9
2.
69.8
.19
139.6
.11
69.5
.19
139.
.10
2
2.1
71.7
.19
150.7
.13
71.4
.18
150.
.10
2.1
22
73.6
.18
162.
.15
73.2
.17
161.
.12
2.2
2.3
75.4
.18
173.5
.17
74.9
.16
172.2
.14
2.3
2.4
77.2
.16
185.2
.19
76.5
.15
183.6
.15
2.4
2 5
78.8
.16
197.1
.20
78.
.15
195.1
.17
2.5
2.6
80.4
.16
209.1
.22
79.5 j .15
206.8
.18
2.6
2.7
82 .15
221 3
.24
81. .13
218.6
.19
2.7
2.8
83.5 .14
233.7
.25
82.3 .14
230.5
.21
2.8
2.9
84.9 i .14
246.2
.27
83.7 .12 i 242.6
.22
2.9
3.
86.3
.13
258.9
.28
84.9 .12 254.8
.23
3.
3.1
87.6
.13
271.7
.28
86.1 1 .12 267.1
24
3.1
3.2
88.9
.13
284.5
.31
87.3 .12 i 279.5
.25
3.2
3.3
90.2
.12
297.6
.31
88.5 | .11 ! 292.
.25
3.3
3.4
91.4
.11
310.7
.32
89.6 j .10 ! 304.5
.27
3.4
3.5
92.5
.12
323.9
.33
90.6
.10 | 317.2
.28
3.5
3.6
93.7
11
337.2
.34
91.6
.11 330.
.28
3.6
3.7
94.8
.10
350.6
.35
92.7
.09 342.8
.29
3.7
3.8
95.8
.11
364.1
.37
93.6
.09 ! 355.7
.30
3.8
3.9
96.9
.10
377.8
.38
94.5
.09
368.7
.31
3.9
4.
97.9
391.6
.38 95.4
-
381.8
4.
OPEN AND CLOSED CHANNELS.
149
TABLE 25.
Based on Kutter's formula, with n = .0275. Values of the factors c and
c\/r for use in the formulas
v — c\/fi* = c X \/r X \A = 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 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 3333.3—1.584 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<v/r
diff.
.01
.4
23.5
.43
9.4
.45
23 9
.43
9.6
.45
.4
.5
27.8
.40
13.9
.52
28.2
.40
14.1
.52
.5
.6
31.8
.35
19.1
.56
32.2
.36
19.3
.58
.6
.7
35.3
.33
24.7
.62
35.8
.32
25.1
.61
.7
.8
38.6
.30
30.9
.65
39.
.29
31.2
.65
.8
.9
41.6
.27
37 4
.69
41.9
.28
37.7
.70
.9
1.
44.3
.25
44.3
.72
44.7
.24
44.7
.71
1.
1.1
46.8
.24
51.5
.75
47.1
.23
51.8
.75
1.1
1.2
49.2
.22
59.
.78
49.4
.22
59 3
.78
1.2
1.3
51.4
.20
66.8
.80
51.6
.19
67.1
.78
1.3
1.4
53.4
.18
74.8
.80
53.5
.19
74.9
.82
1.4
1.5
55.2
.18
82.8
.84
55 4
.17
83.1
.83
1.5
1.6
57.
.17
91.2
.86
57.1
.16
91.4
84
1.6
1.7
58.7
.15
99.8
.86
58.7
16
99.8
.86
1.7
1.8
60 2
.14
108.4
.86
60.2
.14
108.4
.86
1.8
1.9
61.6
.14
117.
.90
61.6
.13
117.
.88
1.9
2.
63.
.13
126.
.90
62.9
.13
125.8
.90
2.
2.1
64.3
.12
135.
.91
64.2
.12
134.8
.91
2.1
2.2
65.5
.12
144.1
.93
65.4
.11
143.9
.91
2.2
2.3
66.7
.11
153.4
.93
66.5
.11
153.
.94
2.3
2.4
67 8
.10
162.7
.93
67.6
.10
162.4
.91
2.4
2.5
68.8
.10
172.
.95
68.6
.09
171.5
.92
2.5
2.6
69.8
.10
181.5
.97
69.5
.09
180.7
.94
2.6
2.7
70.8
.09
191.2
.96
70.4
.09
190.1
.95
2.7
2.8
71.7
.08
200.8
,95
71.3
.08
199.6
.95
2.8
2.9
72.5
.08
210.3
.96
72.1
.08
209.1
.96
2.9
3.
73 3
.08
219.9
1.
72.9
.08
218.7
.98
3.
3.1
74.1
.08
229.9
.98
73.7
.07
228.5
.96
3.1
3.2
74.9
.07
239.7
.98
74.4
.07
238.1
.97
3.2
3.3
75.6
.07
249.5
.99
75.1
.06
247.8
.96
3.3
3.4
76.3
.06
259.4
.99
75.7
.07
257.4
.99
3.4
3.5
76.9
.07
269.3
.99
76.4
.06
267.3
.98
3.5
3.6
77.6
.06
279.2
1.01
77.
.06
277.1
.98
3.6
3.7
78.2
.06
289.3
1.
77.6
.05
286.9
.98
3.7
3.8
78.8
.06
299.3
1.01
78.1
.06
296.8
.99
3.8
3.9
79.3
.05
309 4
1.01
78.7
.05
306.7
.99
3.9
4.
79.9
.06
319.5
79.2
316.7
4.
OPEN AND CLOSED CHANNELS.
157
TABLE 26.
Based on Kutter's formula, with n = .030, Values of the factors c and
c\/r for use in the formula
v = c vV* = 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 1250=4.224 ft. per mile
1 in 1000=5.28 ft. per mile
Vr
a = .0008
«'= .001
in feet
diff.
,— diff.
diff.
diff.
in feet
c
.01
cvr | .01
c
.01
cVr
.01
.4
24.1
44
9.6
.47
24.2
.44
9.7 .46
.4
.5
28.5
.39
14.3
.53
28.6
.39
14.3
.52
.5
.6
32.4
.36
19.4
.58
32.5
.36
19.5
.58
.6
.7
36.
.32
25.2
.62
36.1 .32
25.3
.61
.7
.8
39.2
.29
31.4
.65
39.3 ! .29
31.4 .66
8
.9
42.1
.27
37.9
.69
42.2
.27
38. .69
.9
1.
44.8
25
44.8
.72
44.9
.25
44.9 .72
1.
1.1
47.3
.23
52.
.75
47.4 ! .23
52.1 .75
.1
1.2
49.6
21
59.5
.77
49.7
.21
59.6 .77
.2
1.3
51.7
.19
67.2
.78
51.8
.19
67.3
.79
.3
1.4
53 6
.18
75.
.81
53.7
.18
75.2
81
.4
1.5
55.4
.17
83.1
.83
55.5
.17
83.3
.82
.5
1.6
57.1
.16
91.4
.84
57.2
.15
91.5
.83
.6
1.7
58.7
.15
99.8
.86
58.7
.15
99.8 .86
.7
1.8
60.2
.14
108.4
.86
60.2
.14
108.4 .86
8
1.9
61.6
.13
117.
.88
61.6
.13
117. .88
.9 '
2.
62 9
.12
125.8
.88
62.9
.12
125.8 .88
2
2.1
64.1
.12
134.6
.91
64.1
.12
134.6 .89
2. 1
2.2
65.3
11
143.7
.90
65 3
.10
143.7 .88
2^2
2.3
66.4
10
152.7
.91
66.3
.11
152.5
.93
2.3
2.4
67.4
.10
161.8
.92
67.4
.09
161 8
.90
2.4
2.5
68.4
.10
171.
.94
68.3
.10
170.8
.94
2 5
2.6
69 4
.09
180.4
.94
69.3
.09
180.2
.93
2.6
2.7
70.3
08
189.8
.93
70.2
.08
189.5
.93
2.7
2.8
71 1
.08
199.1
.94
71.
.08
198.8
.94
2.8
2.9
71.9
.08
208.5
.96
71.8
.08
208.2
96
2.9
3.
72.7
.07
218.1
.94
72.6
.07
217.8
.94
3.
3.1
73.4
.07
227.5
.96
73.3
.07
227.2
.96
3.1
3.2
74.1
.07
237.1 ! .97
74.
.06
236.8
.94
3.2
3.3
74.8
.06
246.8 .96
74.6
.07
246.2
.98
3.3
3.4
75 4
07
256.4
.98
75.3
.06
256.
.97
3.4
3.5
76.1
.06
266.2
.98
75 9
.06
265.7
.96
3.5
3.6
76.7
.05
276.
.98
76 5
.05
275.3
.98
3.6
3.7
77.2
.06
285.8
.98
77.
.06
285.1
98
3.7
3.8
77.8
.05
295.6
.98
77.6
.05
294 8
.98
38
3.9
78.3
.05
305.4
.98
78.1
.05
304.6
.98
3.9
4.
78.8
.05
315.2
78.6
.05
314.4
4
158
FLOW" OF WATER IN
TABLE 27.
Based on Kutter's formula, with n = .035. Values of the factors c and
c\/r for use in the formulae
v = c^/rs = c X Vr~ 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 20000=. 264 ft. per mile
1 in 15840=. 3333 ft. per mile
Vr
in feet
s = .00005
s = .000063131
c
diff.
.01
cV'r
diff.
.01
c
diff.
.0!
cVr
diff.
.01
4
15.6
34
6.3
.32
16.2
.34
6.46
.34
.4
.5
19.
.33
9 5
.39
19.6
.33
9.8
.39
.5
.6
22.3
.31
13 4
.44
22.9
.31
13.7
.45
.6
.7
25.4
.29
17.8
.49
26.
.29
18.2
.49
.7
.8
28.3
.28
22.7
53
28.9
.28
23.1
.54
.8
.9
31.1
.27
28.
.58
31.7
.26 28.5
.58
.9
1.
33.8
.26
33 8
62
34.3
26
34.3
.63
1.
1.1
36.4
.24
40
.66
36.9
.24
40.6
.65
1.1
1.2
38.8
23
46 6
.69
39.3
.22
47.1
.69
1 2
1.3
41 1
23
53 5
.73
41.5
.22
54
.72
1.3
1 4
43.4
22
60.8
75
43.7
.21
61.2
.75
1.4
1 5
45 6
.20
68.3
.79
45 8
20
68.7
.78
1.5
1.6
47.6
.20
76.2
81
47.8
19
76.5
.80
1.6
1.7
49-6
19
84.3
84
49.7
19
84.5
.83
1.7
1.8
51.5
19
92.7
.87
51.6
.17
92.8
.85
1.8
1.9
53.4
17
101 4
.88
53.3
.17
101 3
87
1.9
2.
55 1
18
110 2
.92
55.
.16
110
.80
2.
2.1
56 9
.16
119.4
.93
56.6
16
118,9
.91
2.1
2 2
58.5
.16
128.7
.95
58.2
.15 i 128
.91
2.2
2.3
60.1
15
138.2
.97
59.7
.14 137.2
.92
2.3
2.4
61.6
.15
147 9
99
61.1
.14
146.7
.95
2.4
2.5
63.1
14
157.8
1.
62.5
.13
156.2
.95
2 5
2.6
64.5
.14
167.8
1.02
63.8
13 166 .98
2.6
2.7
65.9
.14
178.
.04
65 1
. 13 175 9 99
2.7
2.8
67.3
.13
188.4
.04
66.4
.12 185 9
2.8
2 9
68.6
.12
198.8
.06
67.6
.12 ! 196.
.01
2.9
3.
69.8
.12
209.4
.09
68 8
11
206.3
.03
3.
3.1
71.
.12
220.3
.09
69.9
11
216.7
.04
3.1
3.2
72.2
.12
231.2
10
71.
.10
227 2
05
3.2
3.3
73.4
.11
242 2
.11
72.
.11
237.8
.06
3.3
3 4
74 5
.11
253.3
.13
73.1
.10
248 5
.07
3.4
3.5
75.6
.10
264.6
.13
74.1
.09
259.2
.07
3.5
3.6
76.6
.11
275.9
15
75.
.10
270.1
.09
3.6
3.7
77.7
10
287.4
15
76.
.09
282.1
.10
3.7
3.8
78.7
.09
298 9
.17
76.9
.09
291.1
.10
3.8
3.9
79 6
.10
310.6
.18
77.8
.08
303 3
.12
3.9
4.
80.6
322.4
78.6
314.5
.12
4.
OPEN AND CLOSED CHANNELS.
159
TABLE 27.
Based on Kutter's formula, with n = .035. Values of the factors c and
c\/r for use in the formulae
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.
v'r
in feet
1 in 10000=0 52S ft. per mile
1 in 7500=0.704 ft. per mile
Vr
in feet
s = .0001
s=. 000133333.
c
diff.
.01
cVr
diff.
.01
c
diff.
.01
c\/r
diff.
.01
.4
17.1
.36
6.84
.36
17.6 .36 ,
7.04
.36
.4
.5
20.7
.83
10.4
.40
21.2
.34
10.6
.42
.5
.6
24.
.31
14.4
.46
24.6
.31
14.8
.46
.6
.7
27.1
.29
19.
.50
27.7
.29
19.4
51
. 7
.8
30.
.27
24.
.54
30.6
.27
24.5
55
.8
.9
32.7
.26
29.4
.59
33.3
.25
30.
58
.9
35.3
.24
35.3
.62
35.8
.24
35 8
62
I
37.7
.23
41.5
.65
38.2
23
42
66
!l
.2
40
.22
48.
.69
40.5
.21
48.6
68
.2
.3
42 2
.21
54.9
.71
42.6
.20
55 4
.70
.3
.4
44.3
.19
62.
.73
44.6
.19
62.4
74
.4
.5
46 2
.19
69.3
.77
46.5
.18
69.8
.75
1.5
.6
48.1
.18
77.
.78
48.3
17
77.3
.77
1.6
.7
49.9
.17
84.8
.81
50.
.16
85.
.79
1.7
.8
51.6
16
92 9
.82
51.6
15
92 9
80
1.8
1.9
53 2
.15
101.1
.83
53 1
15
100.9
.80
1.9 •
2.
54.7
.15
109.4
.86
54 6
14
109 2
.83
2.
2.1
56 2
.14
118.
.87
56.
.13
117.6
84
2.1
2.2
57.6
.13
126.7
.88
57.3
13
126 1
85
2.2
2.3
58.9
.13
135.5
.90
58 6
.12
134.8
87
2.3
2.4
60.2
.13
144 5
.93
59 8
.11
143.5
.87
2.4
2.5
61.5
.12
153.8
.92
60.9
.12
152 3
.88
2.5
2.6
62 7
.11
163.
.93
62 1
10
161 5
.89
2.6
2.7
63 8
.11
172.3
94
63 1
11
170 4
.94
2.7
2.8
64.9
.11
181.7
.97
64 2
.09
179.8
90
2.8
2.9
66.
10
191.4
.96
65.1
.10
188.8
.95
2.9
3.
67.
.10
201
.98
66 1
.09
198.3
.94
3.
3.1
68.
09
210 8
.97
67.
.09
207.7
.96
3.1
3.2
68 9
09
220 5
.98
67.9
.08
217.3
.94
3.2
3.3
69 8
.09
230 3
01
68.7
08
226 7
96
3.3
3.4
70.7
.99
240 4
.01
69 5
.09
236 3
.98
3.4
3.5
71.6
.08
250.5
.01
70.4
.07
246 1
.97
3.5
3.6
72 4
08
260.6
.02
71.1
.07
255.8
.99
3.6
3.7
73.2
.07
270.8
.02
71.8
.07
265 7
.98
3.7
3.8
74.
.07
281.
.04
72 5
.07
275.5
.99
3.8
3.9
74.7
.07
291.4
.03
73.2
.07
285.4
1.01
39
4.
75.4
301.7
73.9
295.5
4.
160
FLOW OF WATER IN
TABLE 27.
Based on Kutter's formula, with n — .035. Values of the factors c and
/F for use in the formulae
= c X \/ X \/*= cv" X
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
Vr
in feet
* = .0002
8 =. .
0003
Vr
in feet
c
diff. /— diff.
.01 c^r .01
C
diff.
.01
c\/r~
diff.
.01
.4
18.3
.36 7.32
.37
18.8
.37
7.52
38
.4
.5
21 9
.34 11. .42
22 5
.34
11.3
.42
.5
.6
25 3
.30
15.2
.40
25.9
.30
15.5
.47
.6
.7
28 3 . 30
19 8 .52 28.9
.29
20.2
.52
.7
.8
31.3 i .26
25. .55 31.8
.26
25.4
.56
.8
.9
33.9 .25
30.5
.59 ! 34.4
25
31
.59
.9
1.
36 4 .24
36.4
.63 36.9
.23
36 9
.62
1.
I
38.8
.21
42.7
64 39 2
.21
43.1
.65
1.1
2
40.9
.21
49.1
68 ! 41.3
.19
49.6
.67
1.2
.3
43.
.19
55 9 70 43.3
.19
56.3
.70
1.3
A
44.9
.18
62.9
72 45 2
.17
63.3
71
1.4
.5
46.7 .17
70.1
.73 i 46.9
.17
70.4
.74
1.5
.6
48.4 .17
77.4
.78
48.6
15
77.8
.74
1.6
.7
50 1 .15
85.2
.77
50 1
15
85 2
.77
1.7
.8
51 6 .14
92.9
.78
51.6
.14
92 9
78
1.8
.9
53
.14 100 7
81
53.
.13
100.7
.79
1.9
2.
54.4 .13 i 108.8
84
54.3 .12
108.6
.80
2.
2.1
55.7
13
117.
.84
55.5
.12
116.6
.81
2.1
2.2
57.
.12
125.4
.85 56.7
11
124.7
.82
2.2
2.3
58 2
.11
133.9
.84 57.8
.11
132.9
85
2.3
2.4
59 3
.11
142.3
.87 58.9
10
141.4
84
2.4
2.5
60 4
.10
151.
86 i 59.9
.10
149 8
85
2.5
2.6
61.4
10
159.6
89 60 9
.09
158.3
.86
2.6
2.7
62.4
.09
168 5
.87 61.8
.09
166.9
.87
2.7
2.8
63.3
.09
177.2
.90
62.7
,09
175.6
.88
2.8
2.9
64 2
.09
186.2
.91
63.6
.08
184.4
.88
2.9
3.
65 1
.09
195.3
.93
64.4
08
193 2
89
3.
3.1
66
.08
204 6
.92
65.2
.07
202 1
88
3.1
3.2
66.8
.07
213.8
90
65.9
.08
210.9
.92
3.2
3.3
67 5
.08
222.8
94
66.7
07
220.1
.91
3.3
3.4
68.3
.07
232 . 2
.93
67.4
.06
229.2
.89
3.4
3.5
69. .07
241.5
.94
68.
.07
238.1
.91
3.5
3.6 69 7 .07
250.9
.94
68.7
.06
247.2
.92
3.6
3.7
70 4 .06
260.3
.95
69 3
06
256 4
.92
3.7
3.8
71. .06
269.8
.95
69.9
.06
265 6
.92
3.8
3.9
71.6 .06
279.3
.96
70.5
.05
274.8
.93
3.9
4.
72.2
288.9
71.
284.1
4.
OPEN AND CLOSED CHANNELS.
161
TABLE 27.
Based on Kutter's formula, with % = .035. Values of the factors c and
/r for use in the formulse
= c X \/r X \A = c\/r X VV^-
All slopes greater than 1 in 1000 have the same co-efficient as 1 in 1000.
Vr
in feet
1 in 2500=2.112 ft. per mile
1 in 1666.7=3.168 ft. per mile
Vr
in feet
s — .0004
s =a .0006
c
diff.
.01
cvr
diff.
.01
c
diff.
.01
c^r
diff.
.01
.4
19.1 .37
7.6
.38
19 4
37
7.76
.39
.4
.5
22 8 ! .34
11.4
.43
23 1
.34
11.6
.43
.5
.6
26.2 j .30
15.7
.47
26.5
.31
15.9
48
.6
.7
29.2 ! .29
20 4
.53
29.6
.28
20 7
52
.7
.8
32.1 | .26
25.7
55
32.4
.26
25.9
56
.8
.9
34.7 .24
31.2
59
35.
.24
31.5
.59
.9
I.
37.1 .23
37.1
.62
37.4
.22
37 4
.61
1.
.1
39.4 .21
43.3
.65
39.6
21
43.5
.65
1.1
.2
41.5 .20
49.8
.68
41.7
.19
50.
.67
1.2
.3
43.5
.18
56.6
.68
43.6
18
56 7
.69
1.3
.4
45.3
.17
63 4
.71
45.4
17
63 6
.71
1.4
.5
47.
.16
70 5
.73
47.1
16
70.7
.72
1.5
.6
48.6
.15
77.8
.74
48.7
.15
77.9
.74
1.6
.7
50.1
.15
85 2
.77
50.2
.14
85.3
.76
1.7
1.8
51.6
.13
92 9
.76
51.6
.13
92.9
76
1.8
1.9
52.9
13
100.5
.79
52.9
.13
100 5
.79
1/9
o
54 2
12
108.4
.79
54 2
11
108.4
.77
2.
2*1
55 4
.12
116.3
.82
55 3
12
116.1
.82
2.1
2 2
56.6
.11
124 5
.82
56.5
10
124.3
.80
2.2
2*3
57.7
.10
132.7
.82
57.5
.10
132 3
.81
2.3
2.4
58.7
.10
140.9
.84
58.5
.10
140.4
.84
2.4
2.5
59.7
.10
149 3
85
59.5
.09
148.8
.82
2.5
2.6
60.7
.09
157.8
.85
60.4
.09
157
.85
2.6
2.7
61 6
.08
166.3
.84
61.3
.08
165.5
.84
2.7
2.8
62.4
.08
174.7
.86
62.1
08
173.9
.85
2.8
2.9
63.2
.08
183.3
.87
62.9
.08
182 4
.87
2.9
3.
64.
.08
192.
.89
63.7
.07
191 1
85
3.
3.1
64 8
07
200 9
.87
64.4
.07
199.6
.87
3.1
3.2
65.5
.07
209.6
.89
65 1
.06
208.3
.85
3.2
3.3
66 2
.07
218.5
.90
65 7
.07
216 8
.90
3.3
3.4
66.9
.06-
227.5
.89
66.4
.06
225 8
.87
3.4
3.5
67.5
.06
236 4
.89
67.
.06
234.5
.89
3.5
3.6
68 1
.06
245.3
.90
67.6
.06
243.4
.88
3.6
3.7
68.7
.06
254.3
.91
68.2
.05
252.2
.90
3.7
3.8
69 3
.06
263.4
.91
68.7
.06
261 2
.89
3.8
3.9
69.9
.05
272 5
.91
69.3
05
270 1
.90
3.9
4.
70.4
281.6
1
69.8
279.1
4.
11
162
FLOW OF WATER IN
TABLE 27.
Based ou Kutter's formula, with n = .035. Values of the factors c and
for use iu the formula
v ~ c^/r* = c X \/ X \/= ev' X \/s~
All slopes greater than 1 ia 1000 have the same co-efficient as 1 in 1000.
Vr
1 in 1250=4.224 ft. per mile
1 in 1000—5.28 ft. per mile
Vr
a = .0008
s = .001
in feet
diff. /—
diff.
diff.
diff.
in feet
c
.01 cVr
.01
c
.01
c\/r
.01
.4
19.6
.37
7.8
.39
19 7
.37
7.88
.39
.4
.5
23.3
.34
11.7
.43
23.4
.34
11.7
.44
.5
.6
26.7
.31
16.
.49
26.8
.31
16.1
.48
.6
.7
29.8
.28
20.9
.52
29.9
.28
20.9
.53
.7
.8
32.6
.26
26.1
.56
32.7
.26
26.2
.56
.8
.9
35.2
.24
31.7
.59
35.3
23
31.8
58
.9
37.6
.22
37.6
.62
37.6
.22
37.6
.62
.1
39.8
.20
43.8 64
39.8
.21
43.8
.65
.1
.2
41.8
.19
50,2
.66
41.9
.19
50.3
.66 .2
.3
43.7
.18
56.8
.69
43.8
.18
56.9
.69
.3
.4
45.5
.17
63.7
.71
45.6
.16
63.8
.70
.4
.5
47.2
.15
70 8
.71
47.2
.16
70.8
.73
.5
.6
48.7
.15
77 9
.74
48.8
.14
78.1
.72
1.6
.7
50.2
.14
85.3
.76
50.2
.14
85.3
.76
1.7
1.8
51.6
.13
92.9
.76
51.6
13
92.9
.76
1.8
1.9
52.9
.12
100.5
.77
52.9
.12
100.5
.77
1.9
2.
54.1
.12
108.2
.79
54.1
.11
108.2
.77
2.
2.1
55.3
.11
116 1
.80
55.2
.11
115.9
.80
2.1
2.2
56.4
.10
124.1
79
56.3
.11
123.9
81
2.2
2.3
57.4
.10
132
.82
57.4
.10
132.
.82
2.3
2.4
58.4
.10
140.2
.83
58.4
.09
140.2
.81
2.4
2.5
59.4
.09
148.5
.83
59.3
.09
148.3
.82
2.5
2.6
60.3
.08
156.8
.82
60.2
.08
156 5
.82
2.6
2.7
61.1
08
165.
.83
61.
.08
164.7
.83
2.7
2.8
61.9
08
173.3
.85
61 8
.08
173
.85
2.8
2.9
62.7
08
181.8
.87
62.6
.07
181.5
.84
2.9
3.
63.5
.07
190.5
85
63.3
.07
189 9
85
3.
3.1
64.2
.07
199.
.87
64.
.07
198 4
86
3.1
3.2
64.9
.06
207.7
.85
64.7
.07
207.
.88
3.2
3.3
65.5
.06
216.2
85
65.4
.06
215.8
.86
3.3
3.4
66.1
.06
224.7
.89
66.
.06
224 4
.86
3.4
3.5
66.7
.06
233.6
.88
66.6
.06
233.
.88
3.5
3.6
67.3
.06
242 4
.88
67.2
05
241 8
.87
3.6
3.7
67 9
.05
251.2
.88
67.7
.05
250.5
.88
3.7
3.8
68 4
.05
260.0
.89
68.2
.06
259.3
.90
3.8
3.9
68.9
.05
268.9
.89
68.8
.04
268.3
.87
3.9
4.
69.4
277 8
69.2
277.
4.
OPEN AND CLOSED CHANNELS.
163
TABLE 28.
Value of c\/F to be used only in the application of the second type
of Bazin's formula for open channels with au even lining of cut stone,
brickwork, or other material with surfaces of equal roughness, exposed to
the flow of water. This formula is: —
v = cx/r X -\/i"
where c = V 1 -r- .000013 f 4.354 4- _
~,^ w
s£ 5U
-"?£ g
-* ~. P 2
• P Ct
o
c\/r
^ w
g^BU
;p|
5
cVr
*h$
•:m
o'
c\/r
Hydraulic
mean
depth in
feet, r.
c^r
.104
23.710
.396
65.756
1.062
122.82
2.250
187.77
.125
27.617
.417
68.159
1.125
127.05
2.375
193.36
.146
31.284
.437
70.337
1.187
131.
2.500
198.83
.167
34.569
.458
72.615
1.250
135.03
2.750
209.31
.187
38.147
.479
74.764
1.312
138.93
3.
219.36
.208
41.327
.500
76.907
1 . 375
142.79
3.250
228.98
.229
44.484
.562
83.048
1.437
146.42
3.500
238.18
250
47 430
.625
88.772
1.500
149.90
3.750
246.96
.271
50.267
.687
94.315
1.625
156.83
4.
255.58
292
53.077
.750
99.573
1 . 750
163.46
4.250
263.81
.312
55.783
.812
104.53
1.875
169.80
4.500
271.87
.333
58.346
.875
109.35
2.
175.99
4.750
279.78
.354
60.898
.937
114.
2.125
182.02
5.
287.30
.375
63.336
1.
118.50
164
FLOW OF WATER IN
TABLE 29.
Giving the length of two side slopes of a trapezoidal channel,
side slopes plus the bed width are equal to the perimeter.
The
Depth
in
Feet
1 to 1
1 to 1
1J to 1
2 to 1
.5
1.118
1.414
1.803
2.236
.75
1.677
2.121
2.704
3.354
1.
2.236
2.828
3.606
4.472
1.25
2.795
3.535
4.507
5.590
1.5
3.354
4 . 242
5.408
6.708
1.75
3.913
4.949
6.310
7.826
2.
4.472
5.656
7 212
8.944
2.25
5.031
6.345
8.112
10.062
2.5
5.590
7.070
9.014
11.181
2.75
6.149
7.778
9.916
12.299
3
6.708
8.484
10.816
13.417
3.25
7.267
9.192
11.718
14 535
3.5
7.816
9.899
12.618
15.653
3.75
8.385
10.606
13.522
16.771
4.
8.944
11.312
14.422
17.889
4.25
9.503
12.021
15.324
19.006
4.5
10.062
12.728
16.226
20.124
4.75
10.621
13.435
17.126
21.242
5.
11.180
14.142
18.028
22.360
5.25
11.739
14.849
18.930
23.478
5.5
12.298
15.556
19.830
24.596
5.75
12.857
16.263
20.732
25.714
6.
13.416
16.970
21 634
26 833
6.25
13.975
17.678
22.536
27.951
6.5
14.534
18.385
23.436
29.069
6.75
15.093
19.092
24.338
30.187
7.
15.652
19.800
25.240
31.306
7.25
16.211
20.506
26.140
32.423
7.5
16.770
21.213
27.042
33.542
7.75
17.329
21.920
27.944
34.660
8,
17.888
22.627
28.844
35.778
8.25
18.447
23.334
29.746
36.896
8.5
19.006
24.042
30.648
38.014
8.75
19.565
24.749
31.550
39.132
9.
20.124
25.456
32.450
40 250
10.
22 360
28.284
36, 056
44.720
11.
24.596
31.112
39.662
49. 194
12.
26.832
33.941
43.268
53- 664
13.
29.068
36.769
46.872
58. 139
14.
31.304
39.598
50.748
62.611
15.
33.540
42.626
54.080
67.083
16.
35.776
45.254
57-690
71 555
OPEN AND CLOSED CHANNELS.
165
TABLE 30.
Giving velocities and discharges of trapezoidal channels in earth,
according to Bazin's formula (37), for channels in earth: —
» = \/t-*- .00035 (.2438 + -1 \
Side Slopes 1 to 1 . v — mean velocity in feet per second, and Q = dis-
charge in cubic feet per second.
(Professional Papers on Indian Engineering, Volume V, Second Series.)
Depth
in
feet.
Slope
lin
Bed width 3 ft.
Bed width 4 ft.
Bed width 5 ft.
Bed width 6 ft.
v Q v
Q
.
Q
v
Q
2500
.679 2.72 .721
3.61
.752
4.51
.776
5.43
,
2857
.635 2.54 .675
3.37
.704
4 22
.726
5.08
t
3333
.588 2.35 .625
3.12
.651
3.91
.672
4.70
4000
.537 2.15
.570
2.85
.595
3.57
.613
4.29
5000
.480 1.92
.510
2.55
.532
3.19
.549
3 84
6666
.416 1.66
.442
2.20
.461
2.76
.475
3.33
.5
2500
.899 6.07 1 .959
7 92
1.01
9.81
1.04
11.73
.5
2857
.841
5.68
.897
7 40
.941
9.17
.976
10:97
5
3333
.779
5.26
.831
6.85
.871
8.49
.903
10.16
.5
4000
.711 4.80
.758
6.26
.795
7.75
824
9.28
.5
5000
.636
4.29
.678
5.60
.711
6.93
.737
8.30
.5
G66G
.511
3.72
.588
4.85
616
6.01
.639
7-. 18
2
2500
1.09
10.91
1.16
13.96
1.22
17.11
1.27
20.32
2
2857
1.02
10.20
1.09
13.06 1
1.14
16.01
1.19
19.01
2.'
3333
.945
9.45
1.01
12.09 j
1.06
14.82
1.10
17.60
2.
4000
.862
8.62
.920
11.04
.966
13.53
1.
16.07
2.
5000
.771
7.71
.823
9 88
.864
12.10
.898
14.37
2.
6666
668
6.68
.713
8.55
.749
10.48
.778
12.44
2.5
2500
1.26
17.39
1.35
21.88
1 41
26.52
1.47
31.26
2.5
2857
1.18
16.27
1.26
20.47
1.32
24.80
1.38
29 23
2.5
3333
1.09
15.06
1 17
18.95
1.22
22.96
1.27
27.07
2.5
4000
1.
13.74
1.06
17.30
1.12
20.96
1.16
24 71
2.5
5000
.894
12.29
.952
15.47
1.
18.75
1.04
22.10
2.5
6666
.774
10.65
.825
13.40
.866
16.24
.901
19.14
3.
2500
1.43
25.65
1.51
31.79
1.59
38.13
1.65
44 60
3.
2857
1.35
23.99
1.42
29.74
1.40
35.67
1.55
41.72
3.
3333
1.23
22.21
1.31
27.54
1.38
33.02
1.43
38.64
3
4000
.13
20.27
.20
25.14
1.26
30.15
1.31
35 26
3.
5000
.01
18.13
.07
22.49
1.12
26.97
1.17
31.54
3.
6666
.873
15.71
.927
19.47
973
23.35
1..01
27.3-2
3.5
2500
.58
35.87
.67
43.86
1.75
52.08
1.82
60.51
3.5
2857
.47
33.50
.56
41.02
.64
48.72
1 70
56.60
3.5
3333
.37
31 07
.45
37.98
.52
45 11
1.58
52.40
3.5
4000
.25
28.36
.32
34.70
.38
41.18
1.44
47.83
3 5
5000
.12
25.37
.18
31.01
.24
36 83
1.29
42.79
3.5
6666
.966
21.97
.02
26.86
.07
31.89
1.11
37.05
166
FLOW OF WATER IN
TABLE 30.
Giving velocities and discharges of trapezoidal channels in earth,
according to Bazin's formula (37), for channels in earth: —
v = V 1-i- .00035
(.2438 + -!
Side Slopes 1 to 1. v — mean velocity in feet per second, and Q = dis-
charge in cubic feet per second. ,
Depth
in
feet.
Slope
lin
Bed width 7 ft.
Bed width 8 ft.
Bed width 9 ft.
Bed width 10 ft.
!
i "
Q
V
Q
V
Q
V
Q
2500
.795
6.36
.810
7.29
.823
8.23
.834
9.17
2857
.744
5.95
.758
6.82
.770
7.70
.780
8.58
3333
.688
5.51
.702
6.32
.713
7.13
.722
7.94
4000
.628
5.03
.641
5.77
.651
6.51
.659
7.25
't
5000
.562
4.50
.573
5.16
.582
5.82
.590
6.48
6666
.487
3.89
.496
4.47
.504
5.04
.511
5.62
.5
2500
1.07
13.68
1.10
15.65
1.12
17 63
1.14
19.63
.5
2857
1.
12.79
1.03
14.64
1.05
16.49
1.06
18.35
.5
3333
.929
11.85
.942
13.55
.970
15.27
.985
17.
.5
4000
.848
10.82
.869
12.37
885
13.93
.899
15.52
.5
5000
.759
9.68
.777
10.08
.792
12.47
.804
13.88
.5
6666
.657
8.38
.673
9.59
.686
10.80
.697
12.02
2.
2500
1.31
23.58
1.34
26.87
1 37
30.20
1.40
33.56
2.
2857
1.23
22.06
1.26
25 13
1.28
28.25
1.31
31.39
2.
3333
1.13
20.42
1.16
23.27
1.19
26 16
1.21
29.06
2.
4000
1.04
18.64
1.06
21.24
1.09
23.88
1.11
26 53
2
5000
.926
16.68
.950
19.01
.971
21.36
.989
23.73
2.
6666
.802
14.44
.823
16.46
.841
18.50
.856
20.55
2.5
2500
1.52
36.07
56
40.95
1.60
45.88
1.63
50.85
2.5
2857
1.42
33.74
.46 38.30
1.49
42.91
1.52
47.57
2.5
3333
1.32
31.24
.35 35 46
1 38
39.73
1.41
44.04
2.5
4000
1.20
28.51
.23
32.37
26
36.27
1.29
40.20
2.5
5000
1.07
25.51
.10
28.96
1.13
32.44
1.15
35.9(3
2.5
6666
.930
22.09
.955
25.08
.977
28.10
.997
31.14
3.
2500
1.71
51.21
.76
57.90
.80
64.66
.83
71.48
3.
2857
1.60
47.90
.64
54.15
.68
60.48
.71
06.86
3.
3333
1.48
44.35
.52
50.14
.56
55.99
.59
01.90
3.
4000
1.35
40.48
.39
45.77
.42
51.12
.45
56.51
3.
5000
1.21
36.21
.24
40.94
.27
45.72
.30
50.54
3.
6666
1 05
31.36
.07
35.45
.10
39.59
.12
43.77
3.5
2500
1.88
69.07
.93
77.77
1.98
86.57
.02
95.46
3.5
2857
1.76
64.61
.81
72.74
.85
80.97
.89
89.29
3.5
3333
1.63
59.82
.67
67.35
.71
74.79
.75
82.67
3.5
4000
1.49
54.60
.53
61.48
.56 68.44
.60
75.46
3.5
5000
1.33
48.84
.37
54.90
.40 61.21
.43
67.50
3.5
6666
1.15
42.30
.18
47.62
.21 i 53.01 j
.24
58.45
OPEN AND CLOSED CHANNELS.
167
TABLE 30.
Giving velocities and discharge^ of trapezoidal channels in earth,
according to Bazin's formula (37), for channels in earth: —
•o = ]l -T- .00035 .243
( .2438 +
Sides Slopes 1 to 1 . v = mean velocity in feet per second, and Q = dis-
charge in cubic feet per second.
II 1
Bed width 11 ft.
Bed width 12 ft. ! Bed width 13 ft.
Bed width 14 ft.
Depth
in
Slope
feet.
lin
V
Q
V Q
V
Q
V
Q
1.
•2500
.843
10.11
. 850
11.06
.858
12.01
.864
12.95
1.
2857
.788
9.46
.796
10.34
.802
11.23
.808
12.12
3333
.730
8.76
.737
9.58
.743
10.40
.748
1 1 . 22
4000
.666
8.
.673
8.74
.678
9.49
.683
10.24
5000
.596
7.15
.602
7.82
.606
8.49
.611
9.16
6666
.516
G.19
.521
6.77
.525
7.35
.529
7.93
5
2500
1.15
21 63
1.17
23.64
1.18
25.65
1.19
27.67
.5
2857
1.08
20.23
1.10
22.11
1.10
23.99
1.11
25.88
.5
3333
.999
18.73
1.01
20.47
1.02
22.21 ! 1.03
23.96
.5
4000
.912
17.10
.923
18.69
.932
20.28
.941
21.87
.5
5000
.816
15.29
.825
16.71
.834
18.14
842
19.57
.5
6666
.706
13.24
.715
14.47
.722
15.71
.729
16.94
2.
2500
1.42
36.92
1.44
40.31
1.46
43.71
1.47
47.12
2.
2857
1.33
34.54
1.35
37.70
1.36
40.88
1.38
44.07
2
3333
1.23
31.98
1.25
34.91
1.26
37.85
1.28
40.81
2.
4000
1.12
29.19
1.14
31.87
1.15
34.55
1.16
37.25
2
5000
1.
26.11
1.02
28.50
1.03
30 91
1.04
33.32
2
6666
.870
22.61
.882
24.68
.892
26.76
.902
28.85
2.5
2500
.65
55 . 84
1.68
60.89
1.70
65.95
1.72
71.03
2.5
2857
.55
52.24
.57
56.90
1.59
61 69
1.61
66 44
2.5
3333
.43
48.36
.45
52.73
1.47
57.11
1.49
61.51
2.5
4000
.31
44.15
.33
48.14
1.35
52.13
1.36
56.15
2.5
5000
.17
39.49
.19
43.06
1.20
46 63
1.22
50.23
2.5 6666
.01
34.20
.03
37.29
1.04
40.39
1.05
43.49
3.
2500
.87
78.36
.90
85.28
1.92
92.24
1.95
99.23
3.
2857
.75
73.29
.77
79.77
1.80
86.28
1.82
92.82
3.
3333
.62
67.86
.64
73.85
1.66
79.88
1.69
85.94
3.
4000
.48
61.95
.50
67.42
1.52
72.92
1.54
78.45
3.
5000
.32
55.41
.34
60.30
1.36
65.23
.38
70.17
3.
6666
.14
47.99
.16
52.22
1 18
56.49
.19
60.77
3.5
2500
.06
104.42
2.09
113.44
2.12
122.53
2.15
131.66
3.5
2S57
92
97.67
.96
106.11
1.98
114.61
2.01
123.15
3.5
3333
.78
90.43
.81
98.24
1.84
106.11
.86
114.01
3.5
4000
.63
82 . 55
.65
89.68
1.68
96.86
.70
104.08
3.5
5000
.45
73.84
.48
80 22.
1.50
86.64
.52
93.10
35
6666
.26
63.94
.28
69.47
1.30
75.03
.32
80.62
168
FLOW OF WATER IN
TABLE 30.
Giving velocities and discharges of trapezoidal channels in earth,
according to Baziii's formula (37), for channels in earth: —
V==Yl-*- .00035 ( .2438 -f _L \ X >/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
^ ftr
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/Tv41'6+^~)
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 +
vz
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
0 -
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
»*«
0
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 0
• p
|
• il
: II
: II
: p1
?
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+^i1) .
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 \v2
-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 v2
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?2s
I 700371 (12 d + 1)
but d2 = 16 r2 = 16 r X r = 4d X r substitute this value
for d2 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 d2
. . / 144 d2 s __ U
V0082 12 4- 1/
0082 (12 44- 1)
but d = 4r, and d2 = 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 belowr 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 0 .
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 wTe 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 discharget 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 = - -L56- = 71.5
.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
0 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: —
0 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 disr
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/77 for use in the formulas; —
v =-. c\/r X -\A~ aud 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
cv>
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/J7 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
<Vr
Fo'r dis-
charge
ac\/r
Diam-
eter in
ft. in.
a = area
in
square
feet.
For ve-
locity
c^/r
For dis-
charge
acv/F
4 7
16.499
170.5
2813.2
9 3
67.201
265.4
1783.9
4 8
17.104
172.6
2951.9
9 6
70.882
269.7
19118.
4 9
17.721
174.5
3091 . 8
9 9
74.662
274.
20157.
4 10
18.348
176.6
3238.7
10
78.540
278.3
21858.
4 11
18.986
178.6
3391 .
10 3
82.516
282.6
23320.
5
19.635
180.4
3543.
10 6
86.590
286.7
24823.
5 1
20.295
182.3
3699.6
10 9
90.763
290.7
26390.
5 2
20.966
184.3
3865.1
11
95.033
294.8
28020.
5 3
21.648
186.2
4031 . 1
11 3
99.402
298.9
29717.
5 4
22.340
188.1
4202.
11 6
103.87
303.1
31482
5 5
23.044
189.9
4377.5
11 9
108.43
306.9
33285.
5 6
23 758
191.8
4557.8
12
113.10
310.8
35156.
5 7
24.484
193.5
4738.1
12 3
117.86
314.7
37095.
5 8
25 . 220
195 4
4928.2
12 6
122.72
318.6
39104.
5 9
25.967
197.3
5123.5
12 9
127.68
322.3
41157.
5 10
26.725
199.2
5323.
13
132.73
326.3
43307.
5 11
27.494
200.8
5521.7
13 3
137.88
329.9
45493.
6
28.274
202.7
5731.5
13 6
143.14
333.6
47751.
0 3
30.680
207.9
6379.5
13 9
148.49
337.3
50085.
6 6
33.183
213.2
7075.2
14
153.94
341.
52491.
G 9
35.785
218.3
7812.7
14 6
165.13
348 2
57496.
7
38.485
223 3
8595.1
15
176.72
355.1
62748.
7 3
41.283
228.2
9420.3
15 6
188.69
362.
68313.
7 6
44.179
233.
10296.
16
201.06
369.
74191.
7 9
47.173
237.9
11225.
16 6
213.83
375.7
80342.
8
50.266
242.6
12196.
17
226.98
382.3
86769.
8 3
53.456
247.3
13219.
17 6
240.53
388.8
93528.
8 6
56.745
252.
14298.
18
254.47
395.4
100617.
8 9
60.132
256.5
15422.
19
283.53
408.3
115769.
9
63.617
261.
16604.
20
314.16
420.6
132133.
OPEN AND CLOSED CHANNELS.
257
TABLE 52.
Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter's
formula, with n •= .011.
Table 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 \/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 =.011, as for surfaces care-
fully plastered with cement with one-third sand, in good condition; also
for iron, cement and terra-cotta pipes, well jointed and in best order, and
also surfaces of other material equally rough.
d =-- di-
ameter
in
ft. in.
a = area
in
square
feet.
For ve-
locity
cVr
For
discharge
ac^/r
d = di-
ameter
in
ft. in.
a = area
in
square
feet.
For ve- For dis-
locity charge
c^/r ac\/r
5
.136
26.76
3.6398
2 11
6.681 113.5
758.16
6
.196
30.93
6.0627
3
7 068 115 7
817.50
7
.267
34.94
9.3294
3 1
7.466
117.9
880.03
8
.349
38.77
13 531
3 2
7.875
120.1
945.69
9
.442
42.40
18 742
3 3
8.295 122.1
1013.1
10
.545
45.83
24.976
3 4
8 726
124.3
1084.6
11
.660
49.46
32.644
3 5
9.169
126.3
1158. .
I
.785
52.85
41.487
3 6
9.621
128.3
1234 4
I . 1
.922
55.95
51.588
3 7
10 . 084
130.3
1314.1
I 2
1.069
59.13
63.210
3 8
10.559
132.3
1397.4
1 3
1.227
62.22
76.347
3 9
11 044
134.4
1484.2
I 4
1 . 396
65.21
91.037
3 10
11.541
136 4
1574.7
I 5
1.576
68.26
107.58
3 11
12.048
138.3
1666.5
I 6
1.767
71.08
125.60
4
12.566
140.4
1764.3
1 7
1.969
73 90
145 51
4 1
13 . 096
142.2
1862 7
I 8
2.182
76.76
167 50
4 2
13 635
144.3
1967.1
I 9
2.405
79.33
190.79
4 3
14.186 146 1
2072.7
1 10
2.640
82.11
216.76
4 4
14.748 148.
2182.5
I 11
2.885
84.75
244.50
4 5
15.321
149 9
2296.
2
3.142
87.36
274.50
4 6
15.904
151.7
2413 3
2 1
3 409
89 94
306.60
4 7
16.499
153.4
2531.7
2 2
3.687
92.38
340.59
4 8
17.104
155.3
2657 . 1
2 3
3.976
94 84
377.07
4 9
17.721
157 . 1
2783.4
2 4
4.276
97 . 33
416.16
4 10
18.348
159.
2917
2 5
4.587
99.66
457.13
4 11
18.986
160 9
3054.1
2 6
4.909
102.
500.78
5
19.635
162.6
3191 8
2 7
5.241
104 5
547 . 92
5 1
20 295
164 5
3337.5
2 8
5.585
106.8
596.70
5 2.
20.966
166.
3480.8
2 9
5 939
109.
647.18
5 3
21.648
167.9
3634.2
2 10
6.305
111.3
701.77
5 4
22.340
169.6
3789.
17
258
FLOW OF WATER IN
TABLE 52.
Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter's
formula with n = .011 for use in the formulae: —
v — cv/r X Vs and Q = ac\/r~ X \A~
d = di-
a = area
For ve-
For
d = di-
a — area
For ve-
For dis-
ameter
in
locity
discharge
ameter
in
locity
charge
in
square
c^/r
ac\/r
in
square
cVr
ac\/r
ft. in.
feet.
ft. in.
feet.
5 5
23.044
171.3
3944.4
10 9
90.763
264
23951
5 6
23.758
173.1
4111.9
11
95.033
567.7
25444
5 7
24.484
174 6
4275.4
11 3
99.402
271.5
26987
5 8
25.220
176.4
4448.
11 6
103.869
275.3
28593
5 9
25.967
178 1 i 4625.2
11 9
108.434
278.8
30235
5 10
26.725
179.8
4806.1
12
113.098
282.4
31937
5 11
27.494
181.4
4986.1
12 3
117.359
286.
33702
6
28.274
183.1
5176.3
12 6
122.719
289.5
35529
6 3
30.680
187.9
5764.
12 9
127.677
292.9
37399
6 6
33.183
192.7
6394 9
13
132.733
296.5
39358
6 9
35.785
197.2
7057.1
13 3
137.887
299.9
41352
7
38 485
202.
7774.3
13 6
143 139
303.3
43412
7 3
41.283
206.5
8522.9
13 9
148.490
306.7
45543
7 6
44.179
210.9
9318.3
14
153.938
310.1
47739
7 9
47.173
215.4
10162.
14 6
165.130
316.8
52308
8
50.266
219.7
11044
15
176.715
323.1
57103
8 3
53.456
224.
11978.
15 6
188.692
329.6
62186
8 6
56.745
228.3
12954.
16
201.062
336.
67557
8 9
60.132
232.4
13974.
16 6
213.825
342 2
73176
9
63 617
236.6
15049.
17
226.981
348.3
79050
9 3
67.201
240.7
16173.
17 6
240.529
354.3
85229
9 6
70.882
244.6
17338
18
254.470
360 4
91711
9 9
74.662
248.6
18558.
19
283.529
372.3
105570
10
78 540
252.5
19834.
20
314.159
383.8
120570
10 3
82.516
256.5
21166
10 6
86.590
260.2
22534
-
OPEN AND CLOSED CHANNELS.
250
TABLE 53.
Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter's
formula with n = .012.
Table giving the value of a, and also the values of the factors^Cy/F and
ac\/Ffor use in the formulae: —
v — cx/r" X \/s and Q = ac^/r X v^*"
These factors are to be used only where the value of n, that is the co-
efficient of roughness of lining of channel = .012 as for unplaned timber
when perfectly continuous on the inside and also flumes, and the surfaces
of other material equally rough.
d = di-
ameter
in
ft. in.
a = area
in
square
feet.
For ve-
locity
cv/F
For
discharge
ac\/r
1
d = di-
ameter
in
ft. in.
a = area
in
square
feet.
For ve-
locity
cv/r
For dis-
charge
ac\/r
5
.136
23.70
3.2234
2 4
4.276
87.81
375.46
6
.196
27.45
5.3800
2 5
4.587
89.94
412.54
7
.267
31.05
8.2911
2 6
4.909
92.09
452.07
8
.349
34 51
12.042
2 7
5.241
94.41
494.78
9
.442
37.80
16.708
2 8
5.585
96.52
539.07
10
.545
40 95
22.317
2 9
5 939
98.49
584.90
11
.666
44.22
29.183
2 10
6.305
100.6
634.46
1
.785
47.30
37.149
2 11
6.681
102.6
685.64
1 1
.922
50.11
46.19
3
7.068
104.6
739.59
1 2
1.069
52.99
56.64
3 1
7.466
106.7
796.38
1 3
1.227
55.78
68.44
3 2
7.875
108.7
856.12
1 4
1 . 396
58 50
81.66
3 3
8 295
110.6
917.41
1 5
J.576
61.26
96.54
3 4
8.726
112.6
982.39
1 6
1.767
63.83
112.79
3 5
9.169
114.4
1049.1
1 7
1.969
66.41
130.76
3 6
9.621
116.3
1118.6
1 8
2.182
69.03
150.61
3 7
10.084
118.1
1191.1
1 9
2.405
71.38
171.66
3 8
10.559
120.
1267.
1 10
2.640
73.92
195 14
3 9
11.044
121 9
1345.9
1 11
2.885
76.33
220.21
3 10
11.541
123.8
1428.3
2
3.142
78.72
247.33
3 11
12.048
125.7
1514.
2 1
3.409
81.07
276.38
4
12.566
127.4
1600.9
2 2
3.687
83.29
307 . 10
4 1
13.096
129.1
1690.7
2 3
3.976
85.54
340.10
4 2
13 635
131.
1785.8
260
FLOW OF WATER IN
TABLE 53.
Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter's
formula with n = .012 for use in the formulae: —
v = c\/r X \A and Q =
d = di-
a — area For ve-
For
d = di-
a = area
For ve-
For dis-
ameter
in
locity
discharge
ameter
in
locity
charge
in
square
cVr
ac\/r
in
square
cVr
ac\/r
ft. in.
feet.
ft. in.
feet.
4 3
14.186
132.7
1882 3
8 9
60.132
212.3
12766.
4 4
14.748
134.4
1982.3
9
63 617
216.2
13751.
4 5
15.321
136.2
2085.9
9 3
67.201
219.9
14780.
4 6
15.904
137.9
2193.
9 6
70.882
223.6
15847 .
4 7
16.499
139.5
2301.
9 9
74.662
227.2
16965.
4 8
17.104
141.2
2415.4
10
78 . 540
230.9
18134.
4 9
17.721
142 8
2530.8
10 3
82 516
234.6
19356.
4 10
18.348
144.6
2652.8
10 6
86.590
238.
20612.
4 11
18.986
146.3
2777.8
10 9
90.763
241.5
21921.
5
19.635
147.9
2903.6
11
95.033
245.
23285.
5 1
20.295
149.4
3032.9
11 3
99 402
248.5
24703.
5 2
20.966
151.2
3169.8
11 6
103 869
252.
26179.
5 3
21.648
152 8
3307.
11 9
108.434
255.4
27689.
5 4
22.340
154.4
3448 3
12
113.098
258.7
29254 .
5 5
23.044
155.9
3593.5
12 3
117.859
262.
30876.
5 6
23.758
157.5
3742.7
12 6
122.719
265.3
32558.
5 7
24.484
159.
3892.
12 9
127.677
268.5
34277.
5 8
25.220
160.6
4049.5
13
132 733
271.8
36077 .
5 9
25.967
162.2
4211.2
13 3
137.887
274.9
37909.
5 10
26.729
163.8
4376.4
13 6
143.139
278.1
39802.
5 11
27.494
165.1
4540 5
13 9
148.490
281 2
41755.
6
28.274
166.7
4713.9
14
153.938
284.4
43773.
G 3
30.680
171.1
5250.1
14 6
165.130
290.5
47969.
6 6
33.183
175.6
5825.9
15
176.715
296.4
52382.
6 9
35.785
179.9
6436.7
15 6
188.692
302.4
57061.
7
38.485
184.2
7087.
16
201.062
308 . 4
62008 .
7 3
41.283
188.3
7772.7
16 6
213.825
314.2
67183.
7 6
44.179
192 4
8501.8
17
226.981
319.8
72594.
7 9
47.173
196.6
9275.8
17 6
240.529
325.5
78289.
6
50.266
200.6
10083.
18
254.470
331 . 1
84247 .
8 3
53 456
204.5
10934.
19
282.529
342.1
96991 .
8 6
56.745
208.5
11832.
20
314.149
352.6
110905.
OPEN AND CLOSED CHANNELS.
261
TABLE 54.
Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter's
formula with n — .013.
Table giving the value of a, and also the values of the factors c\/r and
ae-v/^for use in the formulae: —
v = c^/7 X \/s~ an(l Q = acVr X \/*"
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 con-
dition, but not new, cement and terra cotta pipe not well jointed nor in
perfect order, plaster and planed wood in imperfect or inferior condition,
and also surfaces of other materials equally rough.
d = di-
ameter
in
ft. in.
a = area
in
square
feet
For ve-
locity
c-s/r
For
discharge
ac\/r
d = di-
ameter
in
ft. in.
a = area
in
square
feet
For
velocity
cVr
For dis-
charge
ac\/r
5
.136 21.20
2.8839
2 11
6.681
93.52
624.82
6
.196
24.60
4.8216
3
7.068
95.37
674.09
7
.267
27.87
7.4425
3 1
7.466
97.25
726.05
8
.349
31.
10.822
3 2
7.875
99.13
780.63
9
.442
34.
15.029
3 3
8.295
100.9
836.69
10
.545
36.87
20.095
3 4
8.726
102.8
896.27
11
.660
39.84
26.296
3 5
9.169
104.4
957 . 35
1
.785
42.65
33.497
3 6
9.621
106.1
1021 . 1
1
.922
45.22
41.692
3 7
10.084
107.9
1087.7
2
1.069
47.85
51.157
3 8
10.559
109.6
1157.2
3
1.227
50.42
61.867
3 9
11.044
111.3
1229.7
4
1.396
52.90
73.855
3 10
11.541
113.1
1305.3
5
1.576
55.44
87.376
3 11
12.048
114.9
1384.1
6
1.767
57.80
102.14
4
12.566
116.5
1463.9
7
1.969
60.17
118.47
4 1
13.096
118.1
1546.9
8
2.182
62.58
136.54
4 2
13.635
119.8
1633.5
9
2.405
64.73
155.68
4 3
14.186
121.4
1722.
10
2.640
67.07
177.07
4 4
14.748
123.
1813.8
1 11
2.885
69.29
199.90
4 5
15.321
124.6
1908.
2
3.142
71.49
224.63
4 6
15.904
126.2
2007.
2 i
3.409
73.66
251.10
4 7
16.499
127.7
2206.1
2 2
3.687
75.70
279.12
4 8
17.104
129.3
2211.1
2 3
3.976
77.77
309.23
4 9
17.721
130.7
2316.9
2 4
4.276
79.87
341.52
4 10
18.348
132.4
2429.1
2 5
4.587
81.83
375.37
4 11
18.986
134.
2543.9
2 6
4.909
83.82
411.27
5
19.635
135.4
2659.
2 7
5.241
85.95
450.49
5 1
20.205
136.9
2778.7
2 8
5.585
87.89
490.88
5 2
20.966
138.5
2903.5
2 9
5.939
89.71
532.76
5 3
21.648
139.9
3029.4
2 10
6.305
91.68
578.02
5 4
22.340
141.4
3159.
1 !
262
FLOW OF WATER IN
TABLE 54.
Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter's
formula with n = .013 for use in the formulae:—
v -— c\/r X
Q = ac\/r X \A
d = di-
a = area
For
For dis-
d = di-
a = area
For
For dis-
ameter
in
velocity
charge
ameter
in
velocity
charge
in
square
cVr
ac\/r \
in
square
cV
ac<)/r
ft. in.
feet
ft. in.
feet
5 5
23.044
142.9
3292
10 6
86 590
219.4
18996.
5 6
23.758
144.3
3429.
10 9
90.763
222.6
20205 .
5 7
24.484
145.6
3566.
11
95.033
225.9
21464.
5 8
25.220
147.1
3710.
11 3
99.402
229.1
22774.
5 9
25.967
148.6
3859.
11 6
103.869
232.4
24139.
5 10
26.729
150.1
4012.
11 9
108.434
235.4
25533.
5 11
27.494
151.4
4162.
12
113.098
238.6
26981.
6
28.274
152.9
4322.
12 3
117.859
241.7
28484.
6 3
30.680
157.
4816.
12 6
122.719
244 8
30041.
6 6
33.183
161.2
5339.
12 9
127.677
247 8
31633.
6 9
35.785
165.2
5911.
13
132.733
250.9
33301.
7
38.485
169.2
6510.
13 3
137.887
253.8
34998.
7 3
41.283
173.
7142.
13 6
143 139
256.8
36752.
7 6
44.179
176.9
7814.
13 9
148.490
259.7
38561.
7 9
47.173
180.8
8527.
14
153.938
262.6
40432
8
50.266
184.5
9272.
14 6
165.130
268.4
44322.
8 3
53.456
188.2
10059.
15
176.715
274.
48413.
8 6
56.745
19.1.9
10889.
15 6
188.692
279.6
52753.
8 9
60.132
195.4
11753.
16
201.062
285.2
57343.
9
63.617
199.1
12663.
16 6
213.825
290.6
62132.
9 3
67.201
202.6
13613.
17
226.981
295.8
67140.
9 6
70.882
205.9
14597.
17 6
240.529
301
72409.
9 9
74.662
209.3
15629.
18
254.470
306.3
77932.
10
78.540
212.8
16709.
19
282.529
316.6
89759.
10 3
82.516
216.2
17837.
20
314.159
326.5
102559
OPEN AND CLOSED CHANNELS.
263
TABLE 55.
Circular Pipes, Conduits, Sewers, etc., flowing full.
formula with n = .015.
Based on Kutter's
Tables giving the value of a, and also the values of the factors c\/r and
or use in the formulae: —
X \/8 and Q = ac^/r
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; canvas lining on wooden frames, and also the surfaces of other
channels equally rough.
d = di-
a = area
For ve-
For
d = di-
a = area
For
For dis-
ameter
in
locity
discharge
ameter
in
velocity
charge
in
ft. in.
square
feet.
cV~r
ac\/r
in
ft. in.
square
feet.
cVr
ac\/r
5
.136
17.36
2.3615
2 10
6.305
77.56
488.99
G
.196
20.21
3.9604
2 11
6.681
79.16
528.85
7
.267
22.95
6.1268
Q
7.068
80.77
570.90
8
.349
25.56
8.9194
3 1
7.4G6
82.39
615.14
9
.442
28.10
12.421
3 2
7.875
84.03
661.77
10
.545
30.52
16.633
3 3
8.295
85.54
709.56
11
.660
33.03
21.798
3 4
8.726
87 . 15
760.44
.785
35.40
27.803
3 5
9.169
88.61
812.38
1
.922
37.60
34.664
3 6
9.621
90.11
866.91'
2
!069
39.85
42.602
3 7
10 084
91.60
923.70
3
.227
42.05
51.600
3 8
10.559
93.11
983.11
4
.396
44.19
61.685
3 9
11.044
94.62
1045.
5
.576
46.36
73.066
3 10
11.541
96.15
1109.6
6
.767
48.38
85 . 496
3 11
12.048
97.55
1175.2
7
.969
50.40
99.242
4
12.566
99.10
1245.3
8
2 182
52.45
114.46
4 1
13.096
100.5
1315.8
1 9
2.405
54.29
130.58
4 2
13.635
102.
1390.8
1 0
2.640
56.29
148.61
4 3
14.186
103.4
1466.7
1 - 11 2.885
58.20
167.90
4 4
14.748
104.8
1545.7
2
3.142
60.08
188.77
4 5
15.321
106.2
1627.
2 1
3.409
61.95
211.20
4 6
15.904
107.6
1711.4
2 2
3.687
63.72
234.94
4 7
16.499
108.9
1796.5
2 3
3.976
65.51
260.47
4 8
17.104
110.3
1886.8
2 4
4.276
67.32
287.87
4 9
17.721
111.6
1977.7
2 5
4.587
69.02
316.59
4 10
18.348
113.
2074.1
2 6
4.909
70.74
347.28
4 11
18.986
114.4
2172.9
2 7
5.241
72.59
380.46
5
19.635
115.7
2272.7
2 8
5.585
74.27
414.81
5 1
20.295
117.1
2376.7
2 9
5.939
75.98
451.23
5 2
20.966
118.4
2482.
264
FLOW OF WATER IN
TABLE 55.
Circular Pipes, Conduits, Sewers, etc., flowing full. Based on Kutter's
formula with n = .015 for use in the formulae: —
v = c^/r X -\A~and Q = ac^/r X •>/*
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 = D2 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>aX 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 = D2 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 = Dl 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 \A7
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' 0
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' 0
"
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.
Bv . .
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, i«9^ 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.
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THIS BOOK IS DUE ON THE LAST DATE
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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
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36 37
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