GATE CE 2023 Set 1 — Question 34
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Water Resources Engineering → Hydrographs & Groundwater → Unit Hydrographs
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Question
The ordinates of a one-hour unit hydrograph for a catchment are given below:
Using the principle of superposition, a -hour unit hydrograph for the catchment was derived from this one-hour unit hydrograph. The ordinates of the -hour unit hydrograph were obtained as at and at . The value of (in integer) is ________.
| t (hour) | 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 |
|---|---|---|---|---|---|---|---|---|
| Q () | 0 | 9 | 21 | 18 | 12 | 5 | 2 | 0 |
Correct answer
3 to 3
Solution
A -hour unit hydrograph (UH) can be derived from a 1-hour UH using the principle of superposition. The ordinate of a -hour UH at time , , is given by:where is the ordinate of the 1-hour UH.Given :Since , for , only the first term exists:Verification at :This matches the given value. Thus, .
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