1. **Problem Statement:** We have a 500 ha watershed with a Curve Number (CN) of 68 and initial abstraction ratio $I_a = 0.35$. We want to estimate runoff volume for two cases of rainfall considering antecedent moisture conditions. 2. **Formula and Important Rules:** Runoff depth $Q$ is estimated using the SCS-CN method: $$Q = \frac{(P - I_a S)^2}{P + (1 - I_a) S}$$ where: - $P$ = rainfall depth (mm) - $I_a = 0.35$ (initial abstraction ratio) - $S = \frac{25400}{CN} - 254$ (potential maximum retention in mm) Antecedent moisture condition affects CN: - Dormant season with 25 mm rainfall in past 5 days corresponds to AMC II (normal), so CN = 68 - If rainfall in past 5 days changes, CN adjusts accordingly (AMC I or AMC III), but here we keep CN = 68 for dormant season. 3. **Calculate $S$:** $$S = \frac{25400}{68} - 254 = 373.53 - 254 = 119.53 \text{ mm}$$ 4. **Calculate runoff for case (a):** - Rainfall $P = 80$ mm - $I_a S = 0.35 \times 119.53 = 41.84$ mm Check if $P > I_a S$: $$80 > 41.84 \Rightarrow \text{runoff occurs}$$ Calculate runoff depth $Q$: $$Q = \frac{(80 - 41.84)^2}{80 + (1 - 0.35) \times 119.53} = \frac{(38.16)^2}{80 + 0.65 \times 119.53} = \frac{1455.22}{80 + 77.70} = \frac{1455.22}{157.70} = 9.23 \text{ mm}$$ 5. **Calculate runoff volume for case (a):** - Watershed area = 500 ha = 5,000,000 m² - Runoff volume $V = Q \times \text{area} = 9.23 \text{ mm} \times 5,000,000 \text{ m}^2$ - Convert mm to meters: 9.23 mm = 0.00923 m $$V = 0.00923 \times 5,000,000 = 46,150 \text{ m}^3$$ 6. **Calculate runoff for case (b):** - Past 5 days rainfall = 35 mm (higher antecedent moisture) - Rainfall $P = 80$ mm Assuming CN remains 68 (dormant season), $S$ and $I_a S$ remain the same. Calculate runoff depth $Q$ again: $$Q = \frac{(80 - 41.84)^2}{80 + 0.65 \times 119.53} = 9.23 \text{ mm}$$ Runoff volume $V$ is the same as case (a): $$V = 46,150 \text{ m}^3$$ **Note:** If antecedent moisture changes CN, runoff would differ, but problem states CN = 68. **Final answers:** - (a) Runoff volume = 46,150 m³ - (b) Runoff volume = 46,150 m³