Question Bank • QB_SWCE_008 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Runoff estimation

Question Statement:

A watershed has an SCS runoff curve number $CN = 80$. A total storm rainfall of $100\text{ mm}$ occurs over the catchment. The direct runoff depth generated from the storm in $\text{mm}$ (using the standard SCS-CN equation with initial abstraction $I_a = 0.2 S$) is ________ (round off to 1 decimal place).

Answer Key:

50.5

Step-by-Step Solution & Explanation

1. Potential maximum watershed retention ($S$): $S = \frac{25400}{CN} - 254 = \frac{25400}{80} - 254 = 317.5 - 254 = 63.5\text{ mm}$ 2. Initial abstraction ($I_a$): $I_a = 0.2 S = 0.2 \times 63.5 = 12.7\text{ mm}$ 3. Direct runoff depth ($Q$): $Q = \frac{(P - I_a)^2}{P - I_a + S} = \frac{(P - 0.2S)^2}{P + 0.8S}$ $Q = \frac{(100 - 12.7)^2}{100 + 0.8(63.5)} = \frac{(87.3)^2}{100 + 50.8} = \frac{7621.29}{150.8} = 50.539\text{ mm} \approx 50.5\text{ mm}$
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