GATE 2024 CE (CE1) – Question 56
The ordinates of a 1-hour unit hydrograph (UH) are given below.
| Time (hours) | 0 | 1 | 2 | 3 | 4 | 5 |
|---|---|---|---|---|---|---|
| Ordinates of 1-hour UH (m$^3$/s) | 0 | 13 | 50 | 80 | 95 | 85 |
| Time (hours) | 6 | 7 | 8 | 9 | 10 | 11 |
|---|---|---|---|---|---|---|
| Ordinates of 1-hour UH (m$^3$/s) | 55 | 35 | 15 | 10 | 3 | 0 |
These ordinates are used to derive a 3-hour UH. The peak discharge (in m$^3$/s) for the derived 3-hour UH is _____________ (rounded off to the nearest integer).
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Correct answer: 87
Explanation
A 3-hour unit hydrograph is the average of three 1-hour unit hydrographs lagged by 0, 1 and 2 hours: $U_3(t) = \frac{U_1(t) + U_1(t - 1) + U_1(t - 2)}{3}$. The ordinates for $t = 1, \ldots, 8$ are 4.33, 21.0, 47.67, 75.0, 86.67, 78.33, 58.33 and 35.0 (m³/s). The largest is at $t = 5$ h: $\frac{85 + 95 + 80}{3} = 86.67 \approx 87$ m³/s.