1 2 2 EQUATIONS FOR FLOW OPEN CHANNELS

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2 - EQUATIONS FOR FLOW OPEN CHANNELS AND PARTIALLY FILLED PIPES 3

The following table summarizes the equations used to calculate the primary parameters of interest for the flow in open channels and partially filled pipes. The subsequent sections cover each of the components used in the equations below. 4

It is frequently necessary to determine the velocity and depth of sewage in a pipe which is flowing only partially full. Use the following figure. 5

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3 - Design of Sewer Systems The steps in the design of a sewer system are as follows: 1 - Preliminary investigation 2 - The detailed survey 3 - The actual design 4 - Preparation of final map, plans, profiles and specifications which are to guide construction work. 5 - Correction of plans to conform to changes made during construction. When the design is completed, the sewer lines are shown as in the following figure: M. H. 17 Bore Hole 21 260 mm Bore Hole 20 Rock G. L 35. 4 I. L 33. 2 Dep. 2. 2 M. H. 18 250 mm 0. 01 M. H. 19 M. H. 20 Bore Hole 22 Bore Hole 23 0. 0076 250 mm 0. 0025 G. L 32. 7 I. L 31. 0 Dep. 1. 7 G. L 30. 4 I. L 27. 4 Dep. 3. 0 7 G. L 26. 6 I. L 24. 1 Dep. 2. 5

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M. H No. 1 2 3 4 5 6 7 8 9 Street El. 30. 88 31. 76 32. 11 32. 7 33. 3 34. 2 35. 55 34. 16 35. 07 M. H No. 10 11 12 13 14 15 16 17 18 Street El. 35. 8 34. 69 33. 63 35. 3 34. 12 33. 1 35. 48 34. 32 33. 2 9

7 1 6 2 8 5 13 14 1 To Treatment Plant 10 15 15 17 2 3 9 16 3 4 5 4 9 12 8 12 18 10 11 7 11 6 17 10 16

From Manhole To Manhole L, m 1 7 6 192 0. 352 2 6 5 143. 3 0. 021 3 9 8 118. 9 0. 05 4 8 5 117. 4 - 5 5 4 100. 6 0. 02 6 10 11 125 0. 04 7 11 12 122 0. 025 8 12 4 115. 9 0. 019 9 4 3 112. 8 - 10 16 17 115. 9 0. 02 11 17 18 122 0. 02 12 18 3 123. 5 0. 017 13 13 14 122 0. 053 14 14 15 115. 9 0. 021 15 15 3 125. 3 0. 039 16 3 2 70. 1 - 17 2 1 182. 9 - Pipe No. Total Area 11 0. 697

Pipe No. From Manhole To Manhole L, m 1 7 6 192 0. 352 - 4576 0. 053 2 6 5 143. 3 0. 021 0. 373 4849 0. 056 3 9 8 118. 9 0. 05 - 650 0. 008 4 8 5 117. 4 - 0. 05 650 0. 008 5 5 4 100. 6 0. 02 0. 443 5759 0. 07 6 10 11 125 0. 04 - 520 0. 006 7 11 12 122 0. 025 0. 065 845 0. 01 8 12 4 115. 9 0. 019 0. 084 1092 0. 013 9 4 3 112. 8 - 0. 527 6851 0. 079 1012 16 17 115. 9 0. 02 - 260 0. 003

Pipe No. From To Manhole L, m 11 17 18 122 0. 04 520 0. 006 12 18 3 123. 5 0. 017 0. 057 741 0. 009 13 13 14 122 0. 053 - 689 0. 008 14 14 15 115. 9 0. 021 0. 074 962 0. 011 15 15 3 125. 3 0. 039 0. 113 1469 0. 017 16 3 2 70. 1 - 0. 697 9061 0. 105 17 2 1 182. 9 - 0. 697 9061 0. 105 Note that : 1 - If a sewer changes direction in a manhole without change of size, a drop of 1 cm (or 0. 04 ft) is to be provided in a manhole. 2 - If the sewer changes size, the crowns of the inlet and outlet sewers are to be at the same elevation. 13

To 7 6 0. 053 0. 007 0. 256 0. 3 0. 081 0. 59 0. 177 1. 08 1. 24 6 5 0. 056 0. 0063 0. 266 0. 3 0. 077 0. 62 0. 186 1. 1 1. 2 9 8 0. 0077 0. 124 0. 2 0. 029 0. 37 0. 074 0. 85 0. 78 8 5 0. 008 0. 0073 0. 125 0. 2 0. 028 0. 38 0. 076 0. 85 0. 76 5 4 0. 07 0. 006 0. 292 0. 3 0. 075 0. 225 1. 15 1. 22 10 11 0. 006 0. 009 0. 108 0. 2 0. 031 0. 3 0. 06 0. 73 0. 72 11 12 0. 01 0. 0087 0. 131 0. 2 0. 031 0. 4 0. 08 0. 87 12 4 0. 013 0. 008 0. 147 0. 2 0. 029 0. 46 0. 09 0. 96 0. 89 4 3 0. 079 0. 0052 0. 314 0. 35 0. 105 0. 64 0. 224 1. 11 1. 21 16 17 0. 003 0. 01 0. 082 0. 033 0. 22 0. 044 0. 63 17 18 0. 006 0. 0092 0. 107 0. 2 0. 031 0. 3 0. 06 0. 74 0. 73 18 3 0. 009 0. 0088 0. 126 0. 2 0. 031 0. 38 0. 076 0. 85 0. 84 13 14 0. 008 0. 0097 0. 119 0. 2 0. 032 0. 34 0. 068 0. 81 14 15 0. 011 0. 0088 0. 136 0. 2 0. 031 0. 42 0. 084 0. 9 0. 89 15 3 0. 017 0. 0079 0. 163 0. 2 0. 029 0. 55 0. 11 1. 4 1. 29 3 2 0. 105 0. 005 0. 352 0. 4 0. 147 0. 62 0. 248 1. 1 1. 29 1 0. 105 0. 0048 0. 355 0. 4 0. 144 0. 63 0. 252 1. 11 1. 27 2 14 S Dia. Cal. Dia. Sel. V m/s From y

Example 4: Calculate the invert elevations of all pipes at manholes of above example if the minimum cover is 1. 5 m over the sewers. Pipe No. From To L S U/S Manhole Level D/S Manhole Level 1 7 6 192 0. 007 33. 75 32. 41 2 6 5 143. 3 0. 0063 32. 41 31. 51 3 9 8 118. 9 0. 0077 33. 37 32. 45 4 8 5 117. 4 0. 0073 32. 45 31. 59 5 5 4 100. 6 0. 006 31. 5 30. 9 6 10 11 125 0. 009 34. 1 32. 98 7 11 12 122 0. 0087 32. 97 31. 91 8 12 4 115. 9 0. 008 31. 91 30. 98 9 4 3 112. 8 0. 0052 30. 85 30. 26 10 16 17 115. 9 0. 01 33. 78 32. 62 11 17 18 122 0. 0092 32. 62 31. 5 12 18 3 123. 5 0. 0088 31. 5 30. 41 13 13 14 122 0. 0097 33. 6 32. 42 15

Pipe No. From To L S U/S Manhole Level 14 14 15 115. 9 0. 0088 32. 42 31. 4 15 15 3 125. 3 0. 0079 31. 4 30. 41 16 3 2 70. 1 0. 005 30. 21 29. 86 17 2 1 182. 9 0. 0048 29. 85 28. 97 16 D/S Manhole Level

4 17 16 3 15 2 14 1 13 22 17 23 18 24 19 20 5 9 12 11 8 10 7 9 6 8 18 21 22 23 19 20 10 7 17 11 6 12 5 13 4 14 3 15 2 25 16 21 24 1 25 A

M. H No. 1 2 3 4 5 6 7 8 9 Street 30. 82 31. 1 31. 3 31. 6 31. 9 32. 2 33. 5 33. 0 El. M. H No. 12 Street 32. 3 El. M. H No. 23 Street 32. 6 El. 18 13 34. 0 24 32. 1 14 15 16 17 18 19 20 10 11 32. 8 32. 5 21 22 33. 5 33. 1 32. 8 32. 6 32. 2 31. 9 31. 5 25 A 31. 8 30. 5 33. 1

19 From Manhole To Manhole L, m 1 2 20 0. 2 2 3 50 0. 4 3 4 50 0. 3 4 5 25 0. 25 5 6 60 0. 4 6 7 25 0. 15 8 9 20 0. 15 9 10 20 0. 15 10 11 25 0. 3 11 12 25 0. 2 13 14 20 0. 15 14 15 20 0. 15 15 16 25 0. 25 16 17 25 0. 15 17 12 50 - 12 7 50 - 18 19 30 0. 25

20 From Manhole To Manhole L, m 19 20 25 0. 2 20 21 20 0. 15 22 23 30 0. 25 23 24 25 0. 2 24 25 21 0. 2 25 21 50 - 21 1 50 - 1 A 40 -

Pipe No. From Manhole To Manhole L, m 1 13 14 20 0. 15 2100 0. 024 2 14 15 20 0. 15 0. 3 4200 0. 049 3 15 16 25 0. 55 7700 0. 089 4 16 17 25 0. 15 0. 7 9800 0. 113 5 17 12 50 - 0. 7 9800 0. 113 6 8 9 20 0. 15 2100 0. 024 7 9 10 20 0. 15 0. 3 4200 0. 049 8 10 11 25 0. 3 0. 6 8400 0. 097 9 11 12 25 0. 2 0. 8 11200 0. 13 10 12 7 50 - 1. 5 21000 0. 243 11 7 6 25 0. 15 1. 65 23100 0. 267 12 6 5 60 0. 4 2. 05 28700 0. 332 13 5 4 25 0. 25 2. 3 32200 0. 372 14 4 3 50 0. 3 2. 6 36400 0. 421 15 3 2 50 0. 4 3. 0 42000 0. 486 2 1 20 0. 2 3. 2 44800 0. 515 16 21

Pipe No. From Manhole To Manhole L, m 17 22 23 30 0. 25 3500 0. 041 18 23 24 25 0. 2 0. 45 6300 0. 073 19 24 25 21 0. 2 0. 65 9100 0. 105 20 25 21 50 - 0. 65 9100 0. 105 21 18 19 30 0. 25 3500 0. 041 22 19 20 25 0. 2 0. 45 6300 0. 073 23 20 21 20 0. 15 0. 6 8400 0. 097 24 21 1 50 - 1. 25 17500 0. 203 25 1 A 40 - 4. 45 62300 0. 721 22

Pipe From No. To S Dia. Cal. Dia. Sel. y V, m/s 1 13 14 0. 025 0. 15 0. 2 0. 052 0. 48 0. 096 0. 97 1. 61 2 14 15 0. 049 0. 02 0. 204 0. 25 0. 084 0. 55 0. 14 1. 05 1. 8 3 15 16 0. 089 0. 012 0. 281 0. 3 0. 106 0. 69 0. 21 1. 14 1. 71 4 16 17 0. 113 0. 008 0. 332 0. 35 0. 130 0. 7 0. 25 1. 14 1. 54 5 17 12 0. 113 0. 006 0. 35 0. 113 0. 79 0. 28 1. 16 1. 36 6 8 9 0. 024 0. 025 0. 15 0. 2 0. 052 0. 48 0. 096 0. 97 1. 61 7 9 10 0. 049 0. 01 0. 232 0. 25 0. 059 0. 7 0. 175 1. 14 1. 37 8 10 11 0. 097 0. 012 0. 29 0. 3 0. 106 0. 75 0. 225 1. 16 1. 74 9 11 12 0. 13 0. 008 0. 35 0. 13 0. 8 0. 28 1. 16 1. 57 10 12 7 0. 243 0. 002 0. 573 0. 6 0. 275 0. 72 0. 432 1. 14 1. 11 11 7 6 0. 267 0. 012, 0. 002 0. 424, 0. 59 0. 673, 0. 44, 0. 264, 0. 94, 0. 275 0. 78 0. 468 1. 16 2. 24, 1. 127 12 6 5 0. 332 0. 005 0. 54 0. 6 13 5 4 0. 372 0. 012, 0. 003 0. 48, 0. 62 0. 6, 0. 65 14 4 3 0. 421 0. 004 0. 62 0. 65 0. 434 0. 39 1. 12 1. 72 0. 673, 0. 53, 0. 318, 0. 416 0. 72 0. 47 1. 4, 1. 15 3. 34, 1. 44 1. 15 1. 67 0. 481 0. 65 0. 72 23 0. 468

Pipe From No. To S Dia. Cal. Dia. Sel. y V, m/s 15 3 2 0. 486 0. 0056 0. 61 0. 65 0. 569 0. 7 0. 455 1. 14 1. 95 16 2 1 0. 515 0. 001 0. 865 0. 9 0. 573 0. 74 0. 67 1. 15 1. 03 17 22 23 0. 041 0. 017 0. 197 0. 2 0. 043 0. 78 0. 156 1. 16 1. 58 18 23 24 0. 073 0. 02 0. 237 0. 25 0. 084 0. 73 0. 183 1. 15 1. 97 19 24 25 0. 105 0. 014 0. 29 0. 3 0. 114 0. 76 0. 228 1. 16 1. 88 20 25 21 0. 105 0. 006 0. 34 0. 35 0. 113 0. 75 0. 263 1. 16 1. 36 21 18 19 0. 041 0. 013 0. 207 0. 25 0. 068 0. 56 0. 14 1. 5 2. 07 22 19 20 0. 073 0. 012 0. 26 0. 3 0. 106 0. 61 0. 183 1. 1 1. 648 23 20 21 0. 097 0. 02 0. 264 0. 3 0. 137 0. 62 0. 186 1. 1 2. 13 24 21 1 0. 203 0. 014 0. 372 0. 4 0. 247 0. 28 1. 13 2. 22 25 1 A 0. 721 0. 0073, 0. 001 0. 67, 0. 98 0. 9, 1. 0 1. 568, 0. 48, 0. 76 0. 78 0. 43, 0. 78 0. 98, 1. 16 2. 42, 1. 12 24

Example: Calculate the invert elevations of all pipes at manholes of above example if the minimum cover is 1. 8 m over the sewers. 1 13 14 20 0. 025 U/S Manhole Level 32. 0 2 3 4 5 6 7 8 9 14 15 16 17 8 9 10 11 15 16 17 12 9 10 11 12 20 25 25 50 20 20 25 25 0. 02 0. 012 0. 008 0. 006 0. 025 0. 012 0. 008 31. 45 31. 00 30. 65 30. 44 31. 5 30. 95 30. 7 30. 35 Pipe From No. To L, m S 25 D/S Manhole Level 31. 5 31. 05 30. 7 30. 45 30. 14 31. 0 30. 75 30. 4 30. 15

10 12 7 50 0. 002 29. 89 D/S Manhole Level 29. 79 11 12 13 14 7 6 5 4 3 25 60 25 50 0. 002 0. 005 0. 003 0. 004 29. 78 29. 73 29. 38 29. 31 29. 73 29. 43 29. 31 29. 11 15 16 17 18 19 20 21 26 3 2 22 23 24 25 18 2 1 23 24 25 21 19 50 20 30 25 21 50 30 0. 0056 0. 001 0. 017 0. 02 0. 014 0. 006 0. 013 29. 11 28. 58 31. 1 30. 54 29. 99 29. 65 30. 55 28. 83 28. 56 30. 59 30. 04 29. 7 29. 35 30. 16 Pipe From To L, m No. S U/S Manhole Level

Pipe From No. 22 23 24 25 27 19 20 21 1 To L, m S 20 21 1 A 25 20 50 40 0. 012 0. 014 0. 001 U/S Manhole Level 30. 11 29. 81 29. 3 28. 46 D/S Manhole Level 29. 81 29. 41 28. 6 28. 42