In: Civil Engineering
Question 1 The storage - outflow relationship for a small dam is given in Table 1. The inflow hydrograph for the uncontrolled spillway of this dam is tabulated in Table 2. Determine:
Hint: Use Table 1 values to obtain S=f(Q).
Table 1
Q (m³/s) |
50 |
100 |
150 |
200 |
250 |
2S/Δt (m³/s) |
300 |
450 |
600 |
750 |
900 |
Table 2
t |
Inflow |
|
0 |
45 |
|
2 |
175 |
|
4 |
370 |
|
6 |
540 |
|
8 |
390 |
|
10 |
280 |
|
12 |
215 |
|
14 |
175 |
|
16 |
135 |
|
18 |
100 |
|
20 |
70 |
|
22 |
45 |
TABLE 1
O (m3/s) | 2S/dt | (2S/dt)+O |
50.0 | 300.00 | 350.00 |
100.0 | 450.00 | 550.00 |
150.0 | 600.00 | 750.00 |
200.0 | 750.00 | 950.00 |
250.0 | 900.00 | 1150.00 |
TABLE 2
assume initial outflow 50m3/s
Time (h) | Inflow (m3/s) | Ij+Ij+1(m3/s) | (2Sj/dt)-Oj | (2Sj+1/dt)+Oj+1 | Outflow(m3/s) |
0.0 | 45.0 | 250.00 | 50.00 | ||
2.0 | 175.0 | 220.00 | 310.00 | 470.00 | 80.00 |
4.0 | 370.0 | 545.00 | 502.50 | 855.00 | 176.25 |
6.0 | 540.0 | 910.00 | 781.26 | 1412.50 | 315.62 |
8.0 | 390.0 | 930.00 | 930.62 | 1711.26 | 390.32 |
10.0 | 280.0 | 670.00 | 875.30 | 1600.62 | 362.66 |
12.0 | 215.0 | 495.00 | 760.28 | 1370.30 | 305.01 |
14.0 | 175.0 | 390.00 | 650.14 | 1150.28 | 250.07 |
16.0 | 135.0 | 310.00 | 555.44 | 960.14 | 202.35 |
18.0 | 100.0 | 235.00 | 470.22 | 790.44 | 160.11 |
20.0 | 70.0 | 170.00 | 395.12 | 640.22 | 122.55 |
22.0 | 45.0 | 115.00 | 330.06 | 510.12 | 90.03 |
PEAK DISCHARGE = 390.32 m3/s
d. at this point inflow and outflow are equal.