GATE 2019 CE (CE2) – Question 60
A 2-hour unit hydrograph for 1 cm effective rainfall has ordinates u (m³/s) at t = 0, 1, …, 12 hours: 0, 2, 8, 18, 32, 45, 30, 19, 12, 7, 3, 1, 0. A six-hour storm has effective rainfall 1 cm/h for hours 0–2, zero for 2–4 and 0.5 cm/h for 4–6. Base flow is constant at 5 m³/s. Find storm peak flow (m³/s), to one decimal place.
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Correct answer: 96.5 to 97.5
Explanation
The two effective rainfall blocks are 2 cm during hours 0–2 and 1 cm during 4–6. Superpose the 2-hour unit hydrograph: $Q_d(t)=2u(t)+u(t-4)$. The maximum occurs at hour 5: $2(45)+u(1)=92$ m³/s. Adding 5 m³/s base flow gives **97.0 m³/s**.