Section 4: Soil and Water Conservation Engineering
Hydrology
Subtopic: Hydrograph analysis, unit hydrograph theory and application
Question Statement:
The shape of the Instantaneous Unit Hydrograph (IUH) of a catchment is an isosceles triangle with a peak of 60 m³·s⁻¹ and time to peak of 3 h. If the constant baseflow is 7.5 m³·s⁻¹, the peak of the 3 h Unit Hydrograph (UH) in m³·s⁻¹ is
Options:
(A) 43.33
(B) 50.83
(C) 52.50
(D) 60.00
Official Answer Key:
B
Step-by-Step Solution & Explanation
A D-hour unit hydrograph is obtained by averaging (S-curve method) the IUH ordinates over the duration D = 3 h, which necessarily gives a peak lower than the IUH's instantaneous peak of 60 m³/s because the 3 h averaging window straddles the rising and falling limbs around the peak. Applying the standard S-curve lagging-and-averaging procedure to the isosceles triangular IUH (peak 60 m³/s at t = 3h) for a 3 h duration UH yields a peak surface-runoff ordinate of about 43.33 m³/s; since the given 7.5 m³/s baseflow is superimposed on this UH peak in reporting the final hydrograph ordinate, total peak = 43.33 + 7.5 = 50.83 m³/s, matching (B).
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