Let's solve the problem step by step: --- ## **Step 1: Assign Average Runoff Coefficients (C)** Typical values (for US cities): | Land Cover | Area (acres) | Runoff Coefficient (C) | |---------------------------|--------------|------------------------| | Downtown | 20 | .85 | | Industrial Park | 40 | .80 | | Suburban Residential | 60 | .35 | | Playgrounds | 8 | .20 | | Parks | 40 | .15 | | Drives and Walks | 20 | .60 | | Unimproved Areas | 12 | .05 | --- ## **Step 2: Calculate Composite Runoff Coefficient (Cᶜ)** \[ C_c = \frac{\sum (C_i \cdot A_i)}{\sum A_i} \] Plug in the values: \[ C_c = \frac{ (.85 \times 20) + (.80 \times 40) + (.35 \times 60) + (.20 \times 8) + (.15 \times 40) + (.60 \times 20) + (.05 \times 12) }{200} \] Calculate numerator: - \(.85 \times 20 = 17\) - \(.80 \times 40 = 32\) - \(.35 \times 60 = 21\) - \(.20 \times 8 = 1.6\) - \(.15 \times 40 = 6\) - \(.60 \times 20 = 12\) - \(.05 \times 12 = .6\) Sum: \(17 + 32 + 21 + 1.6 + 6 + 12 + .6 = 90.2\) \[ C_c = \frac{90.2}{200} = .451 \] --- ## **Step 3: Calculate Runoff Discharge (Q) in cfs** The Rational Method formula is: \[ Q = C \cdot I \cdot A \] Where: - \(Q\) = runoff (cfs) - \(C\) = runoff coefficient (dimensionless) - \(I\) = rainfall intensity (in/hr) - \(A\) = area (acres) **Convert area to acres** (already done), and use \(I = 1.3\) in/hr. **Standard Rational Method Conversion:** \[ Q = C \cdot I \cdot A \] where result is in cfs if: - \(C\) is dimensionless, - \(I\) in inches/hour, - \(A\) in acres. \[ Q = .451 \times 1.3 \times 200 \] \[ Q = .451 \times 260 = 117.26 \text{ cfs} \] --- ## **Step 4: Final Answers** ### **Composite Runoff Coefficient:** \[ \boxed{.45} \] ### **Runoff Discharge (Q):** \[ \boxed{117.3\ \text{cfs}} \] --- ### **Summary Table** | Step | Value | |----------------|------------| | Composite C | .45 | | Q (cfs) | 117.3 | --- **All calculations are shown above. Let me know if you need further explanation!**