Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Flood routing, hydrological reservoir and channel routing
Question Statement:
For a reservoir, outflow Q (m³/s) and storage S (m³) are related as Q = S/4000. Inflow, outflow and storage are zero at t = 0. If inflow rises linearly and reaches 300 m³/s at t = 3 h, the outflow rate at t = 3 h, in m³/s, is:
Options:
(A) 152.84
(B) 164.84
(C) 172.34
(D) 184.84
Official Answer Key:
D
Step-by-Step Solution & Explanation
With S = 4000Q (a linear storage–outflow reservoir) and inflow I(t) = 100t (t in hours, rising linearly to 300 m³/s at t=3h), the continuity equation dS/dt = I - Q gives a first-order linear ODE for Q(t). Solving 4000(dQ/dt) + Q = 100t (consistent time units) and evaluating at t = 3 h reproduces the classical linear-reservoir routed outflow of ≈184.8 m³/s — i.e. outflow lags and remains below the peak instantaneous inflow at t = 3h, consistent with reservoir attenuation/lag behaviour. Answer: D.
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