GATE AG 2007 • Q81 MCQ • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Hydrograph analysis, unit hydrograph theory and application

Question Statement:

A 4-h unit hydrograph (UH) is used to derive an S-hydrograph with the ordinates given above. The area of the watershed is:

Options:

  • (A) 215.98 km²
  • (B) 251.61 km²
  • (C) 547.15 km²
  • (D) 1006.47 km²

Official Answer Key:

D

Step-by-Step Solution & Explanation

For a D-hour unit hydrograph representing 1 cm of direct runoff, the equilibrium discharge relates to catchment area by $Q_{eq} = \frac{2.778 \times A}{t_r}$ ($Q_{eq}$ in m³/s, $A$ in km², $t_r$ in hours). $A = \frac{Q_{eq} \times t_r}{2.778} = \frac{699 \times 4}{2.778} \approx 1006.47\text{ km}^2$.

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