Contents preface (VII) introduction 1—37
(A) Computation of Unit Hydrograph ordinates (Example 2.7)
- Bu səhifədəki naviqasiya:
- (B) Computation of S-hydrographs for deciding duration of UH (Example 2.7)
| (A) Computation of Unit Hydrograph ordinates (Example 2.7)
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Time |
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Runoff |
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Base flow |
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DRH |
UH |
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Adjusted UH | ||
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(hr) |
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(cumecs) |
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(cumecs) |
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(cumecs) |
(cumecs) |
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(cumecs) | |
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(1) |
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(2) |
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(3) |
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(4) |
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(5) |
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(6) |
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0 |
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0 |
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0 |
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0 |
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0.00 |
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0 |
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2 |
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171 |
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1.43 |
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169.57 |
20.41 |
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20 | |
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4 |
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393 |
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2.86 |
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390.14 |
46.95 |
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47 | |
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6 |
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522 |
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4.29 |
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517.71 |
62.30 |
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62 | |
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8 |
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297 |
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5.71 |
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291.29 |
35.05 |
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35 | |
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10 |
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133 |
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7.14 |
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125.86 |
15.15 |
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15 | |
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12 |
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51 |
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8.57 |
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42.43 |
5.11 |
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5 | |
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14 |
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10 |
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10 |
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0 |
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0.00 |
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0 |
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16 |
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10 |
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10 |
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18 |
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10 |
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10 |
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Total |
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1537 |
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184.96 |
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184 |
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Measured runoff volume |
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= (2 × 3600) [0 + 169.57 + 390.14 + 517.71 + 291.29 + 125.86 + 42.43 + 0] | ||||||||||
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= 2 × 3600 × 1537 |
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= 11066400 m3 |
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∴ |
Runoff depth = |
Runoff volume |
= |
11066400 |
= 0.0831 m |
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catchment area |
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133.1 × 106 |
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= 83.1 mm = 8.31 cm.
Therefore, the ordinates of the unit hydrograph (for 1 cm rainfall) (Col. 5 of Table A) would be obtained by dividing the DRH values with 8.31. These values have been rounded off suitably (Col. 6 to Table A).
Runoff volume for UH = (2 × 3600) [0 + 20 + 47 + 62 + 35 + 15 + 5 + 0]
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(2 × 3600) (184)
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1324800 m3
∴ Runoff depth from UH = 1324800/(133.1 × 106)
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9.95 × 10–3 m -
0.995 cm.
This runoff depth of 0.995 cm for the unit hydrograph is close to 1.0 cm and is, therefore, accepted without any more adjustment. The UH so obtained is shown plotted in Fig. 2.27 (b). To determine the duration of the derived UH, one needs to derive effective rainfall intensity hyetograph for which knowledge of φ-index is required.
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Total rainfall depth
= 21.90 + 43.10 + 30.90
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95.90 mm
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9.59 cm
∴ Losses due to abstractions = 95.90 – 83.10
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12.80 mm
80
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Discharge(cumecs) |
IRRIGATION AND WATER RESOURCES ENGINEERING
70
60
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50 |
2 - hr UH |
40
30
20
10
0
0 5 10 15 Time (hrs)
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Fig. 2.27 (b) 2-hour Unit hydrograph (Example 2.7)
∴
φ-index =
12.80
6
= 2.13 mm/hr.
Ordinates of the effective rainfall hyetograph (i.e., plot of effective rainfall intensity versus time) have been worked out as follows :
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Time |
Rainfall depth |
Rainfall intensity |
φ-index |
Effective rainfall |
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(hr) |
(mm) |
(mm/hr) |
(mm/hr) |
intensity (mm/hr) |
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0-2 |
21.90 |
10.95 |
2.13 |
8.82 |
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2-4 |
43.10 |
21.55 |
2.13 |
19.42 |
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4-6 |
30.90 |
15.45 |
2.13 |
13.32 |
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Effective rainfall hyetograph so obtained is shown in Fig. 2.27 (c).
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depth(mm) Rainfall |
40
20
0
0 2 4 6
Time (hr)
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Rainfall |
intensity (mm/hr) |
20
10
0 0
f - Index
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2 |
4 |
6 |
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Time (hr) |
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intensity(mm/hr) |
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Effectiverainfall |
20
10
0
0 2 4 6
Time (hr)
Fig. 2. 27 (c) Derivation of effective rainfall hyetograph (Example 2.7)
The duration of the unit hydrograph is expected to be between tpk/3 and tpk/5. Since tpk (i.e., time to peak) for the present problem is 6 hrs, the duration of the UH is expected to be tetween 1.2 to 2 hrs. To decide on the duration of the UH, one should draw S-hydrographs of
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HYDROLOGY |
81 |
different durations around the expected range of the duration. S-curve of duration shorter than that of the unit hydrograph would be very smooth while that of longer duration would be a wavy curve. This observation combined with the expected range between tpk/3 and tpk/5 enables one to choose suitable value for the duration of the unit hydrograph. For the present problem, three S-hydrographs for the durations of 1-hr, 2-hr and 3-hr are drawn. The ordinate values are listed in Cols. 3, 4 and 5 of Table B and the S-curves are as shown in Fig. 2.27 (d) . One may adopt 2 hour as the duration of the UH.
(B) Computation of S-hydrographs for deciding duration of UH (Example 2.7)
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Time
UH
S-Hydrographs (cumecs)
(hour)
(cumecs)
1-hr
2-hr
3-hr
(1)
(2)
(3)
(4)
(5)
0
0
0
0
0
1
10
10
10
10
2
20
30
20
20
3
33
63
43
33
4
47
110
67
57
5
55
165
98
75
6
62
227
129
95
7
48
275
146
105
8
35
310
164
110
9
25
335
171
120
10
15
350
179
120
11
10
360
181
120
12
5
365
184
125
13
2
367
183
122
14
0
367
184
120
367
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400 |
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1 hour |
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(cumecs) |
300 |
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200 |
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2 hour |
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Discharge |
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3 hour |
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100 |
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0 |
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8 |
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14 |
16 |
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2 |
4 |
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Time (hrs)
Fig. 2. 27 (d) S-hydrographs considering different durations of unit hydrograph (Example 2.7)
82 IRRIGATION AND WATER RESOURCES ENGINEERING
Time of concentration = Base of DRH – Duration of effective rainfall = 14 – 2 = 12 hrs.
For obtaining UH of 2T i.e., 4-hr unit duration, one may use method of superposition. For 4-hr UH, one would require to superpose two 2-hr UH’s separated from each other by 2 hrs. The ordinates of the second UH (separated from the previous one by 2 hrs) are listed in Col. 3 of Table C. By adding the values of Cols. 2 and 3, one can obtain the ordinates of DRH of 2 cm rainfall in a duration of 4 hrs. (Col. 4 of Table C). Thus, the ordiantes of 4-hr unit hydrograph (Col. 5) would be obtained by dividing the values of Col. 4 of Table C by 2. The 4-hr unit hydrograph is shown in Fig. 2.27 (e).
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