Question Bank • QB_SWCE_ADV_126 NAT • 2 Marks

Section 4: Soil and Water Conservation Engineering

Hydrology

Subtopic: Runoff estimation

Question Statement:

A small agricultural watershed under antecedent moisture condition II (AMC-II) has a composite Curve Number of $CN = 80.0$. During an isolated storm event, total storm precipitation is $P = 75.0\text{ mm}$. Taking initial abstraction $I_a = 0.20 S$, the predicted direct storm runoff depth $Q$ in $\text{mm}$ using the SCS-CN method is ________ (round off to one decimal place).

Answer Key:

30.9

Step-by-Step Solution & Explanation

**Method 1: Direct SCS-CN Analytical Formulation** 1. Potential maximum retention $S$: $S = \frac{25400}{CN} - 254 = \frac{25400}{80.0} - 254 = 317.5 - 254.0 = 63.50\text{ mm}$ 2. Initial abstraction $I_a$: $I_a = 0.20 \times S = 0.20 \times 63.50 = 12.70\text{ mm}$ 3. Effective storm depth $(P - I_a)$: $P - I_a = 75.0 - 12.70 = 62.30\text{ mm}$ 4. Direct surface runoff $Q$: $Q = \frac{(P - I_a)^2}{P - I_a + S} = \frac{(62.30)^2}{62.30 + 63.50} = \frac{3881.29}{125.80} = 30.8528\text{ mm} \approx 30.9\text{ mm}$ **Method 2: Step-by-Step Normalized Ratio** $\frac{Q}{P - I_a} = \frac{P - I_a}{P - I_a + S} = \frac{62.30}{125.80} = 0.49523$ $Q = 0.49523 \times 62.30 = 30.85\text{ mm} \approx 30.9\text{ mm}$
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