Question Bank • QB_SWCE_GATE_003 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Hydrograph analysis, unit hydrograph theory and application

Question Statement:

A watershed has an SCS Curve Number $CN = 80$. A 24-hour storm yields a total rainfall $P = 100\text{ mm}$. Assuming initial abstraction $I_a = 0.2 S$, the depth of direct surface runoff $Q$ is ________ $\text{mm}$ (round off to 2 decimal places).

Answer Key:

50.54

Step-by-Step Solution & Explanation

SCS-CN Runoff Calculation: $S = \frac{25400}{80} - 254 = 63.5\text{ mm}$ $I_a = 0.2 \times 63.5 = 12.7\text{ mm}$ $Q = \frac{(100 - 12.7)^2}{100 - 12.7 + 63.5} = \frac{(87.3)^2}{150.8} = \frac{7621.29}{150.8} \approx 50.539\text{ mm}$ Rounding to 2 decimal places: **50.54** $\text{mm}$.
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