Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Hydrograph analysis, unit hydrograph theory and application
Question Statement:
For a catchment with an area of 400 km², the equivalent discharge of the S-curve obtained by summation of 4-h unit hydrograph in m³ s⁻¹ is
Options:
(A) 100
(B) 139
(C) 200
(D) 278
Official Answer Key:
D
Step-by-Step Solution & Explanation
The S-curve represents the outflow from a continuous series of unit hydrographs (each producing 1 cm of runoff over the duration t), and its equilibrium (constant) discharge equals the rate needed to deliver 1 cm depth of runoff, uniformly, over the entire catchment area, every t hours. Equilibrium discharge Qe = 2.78×A/t (A in km², t in hours, Qe in m³/s — this constant 2.78 converts 1 cm depth over 1 km² per hour into m³/s). Qe = 2.78×400/4 = 278 m³/s, matching option (D).
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