GATE 2023 CE (CE1) – Question 34
The ordinates of a one-hour unit hydrograph for a catchment are given below.
| t (hour) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| Q (m$^3$/s) | 0 | 9 | 21 | 18 | 12 | 5 | 2 | 0 |
Using the principle of superposition, a D-hour unit hydrograph for the catchment was derived from this one-hour unit hydrograph. The ordinates of the D-hour unit hydrograph were obtained as 3 m$^3$/s at t = 1 hour and 10 m$^3$/s at t = 2 hour. The value of D (in integer) is ________________________.
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Correct answer: 3
Explanation
A D-hour unit hydrograph is the average of D one-hour hydrographs lagged by 0, 1, ..., D − 1 hours. At $t = 1$ only the unlagged one contributes: $\frac{9}{D} = 3$, so $D = 3$. Check at $t = 2$: $\frac{21 + 9}{3} = 10$, which matches.