1. **Problem Statement:** Estimate the runoff volume for a 400 ha watershed with initial abstraction $I_a = 0.1S$ and Curve Number (CN) II value of 73, given rainfall of 65 mm on Day 1 and 80 mm on Day 2. 2. **Formula and Important Rules:** The runoff depth $Q$ is estimated using the SCS-CN method: $$Q = \frac{(P - I_a)^2}{P - I_a + S}$$ where: - $P$ = rainfall (mm) - $I_a = 0.1S$ (initial abstraction) - $S = \frac{25400}{CN} - 254$ (potential maximum retention in mm) 3. **Calculate $S$:** $$S = \frac{25400}{73} - 254 = 347.945 - 254 = 93.945 \text{ mm}$$ 4. **Calculate $I_a$:** $$I_a = 0.1 \times 93.945 = 9.3945 \text{ mm}$$ 5. **Calculate runoff for Day 1 ($P=65$ mm):** Check if $P > I_a$: $$65 > 9.3945 \Rightarrow \text{runoff occurs}$$ Calculate $Q_1$: $$Q_1 = \frac{(65 - 9.3945)^2}{65 - 9.3945 + 93.945} = \frac{(55.6055)^2}{149.5505} = \frac{3093.9}{149.5505} = 20.69 \text{ mm}$$ 6. **Calculate runoff for Day 2 ($P=80$ mm):** Check if $P > I_a$: $$80 > 9.3945 \Rightarrow \text{runoff occurs}$$ Calculate $Q_2$: $$Q_2 = \frac{(80 - 9.3945)^2}{80 - 9.3945 + 93.945} = \frac{(70.6055)^2}{164.5505} = \frac{4985.1}{164.5505} = 30.29 \text{ mm}$$ 7. **Calculate total runoff depth:** $$Q_{total} = Q_1 + Q_2 = 20.69 + 30.29 = 50.98 \text{ mm}$$ 8. **Convert runoff depth to volume:** Watershed area = 400 ha = 4,000,000 m² Runoff depth in meters: $$50.98 \text{ mm} = 0.05098 \text{ m}$$ Runoff volume: $$V = \text{area} \times \text{depth} = 4,000,000 \times 0.05098 = 203,920 \text{ m}^3$$ **Final answer:** The estimated runoff volume for the two days is approximately **203,920 cubic meters**.