Let's solve each problem step by step: --- ## **Question 14** **Given:** - Watershed area = 10.37 sq. miles - Curve Number (CN) = 75 - Rainfall (P) = 3.65 inches - Quarry area = 49 acres - Quarry depth = 30 feet (not limiting, just informational) - Quarry initially empty ### **Step 1: Calculate Runoff Depth (Q) Using NRCS Curve Number Method** #### **1.1 Calculate S (Potential Maximum Retention):** \[ S = \frac{100}{CN} - 10 \] \[ S = \frac{100}{75} - 10 = 13.33 - 10 = 3.33 \text{ in} \] #### **1.2 Calculate Initial Abstraction (Iₐ):** \[ I_a = .2S = .2 \times 3.33 = .67 \text{ in} \] #### **1.3 Calculate Runoff Depth (Q):** \[ Q = \frac{(P - I_a)^2}{(P - I_a) + S} \] \[ Q = \frac{(3.65 - .67)^2}{(3.65 - .67) + 3.33} \] \[ Q = \frac{(2.98)^2}{2.98 + 3.33} \] \[ Q = \frac{8.88}{6.31} = 1.41 \text{ in} \] ### **Step 2: Calculate Total Runoff Volume** #### **2.1 Area in Acres:** \[ 1 \text{ sq mile} = 640 \text{ acres} \] \[ 10.37 \text{ sq miles} = 10.37 \times 640 = 6,636.8 \text{ acres} \] #### **2.2 Volume in Acre-Inches:** \[ \text{Volume (acre-inches)} = \text{Area (acres)} \times \text{Runoff Depth (in)} \] \[ = 6,636.8 \times 1.41 = 9,363.9 \text{ acre-inches} \] #### **2.3 Convert to Acre-Feet:** \[ 1 \text{ acre-foot} = 12 \text{ acre-inches} \] \[ \text{Volume (acre-feet)} = \frac{9,363.9}{12} = 780.3 \text{ acre-feet} \] ### **Step 3: Find Water Depth in Quarry** \[ \text{Depth (ft)} = \frac{\text{Volume (acre-ft)}}{\text{Quarry Area (acres)}} \] \[ = \frac{780.3}{49} = 15.92 \text{ ft} \] --- **Final Answer for Q14:** \[ \boxed{15.9 \text{ feet}} \] (water depth in the quarry when runoff ends, rounded to one decimal place) --- ## **Question 15** **Given:** - Pond area = 25 acres - Initial depth = 7 ft - Evaporation = .2 in/day - Water pumped to vineyard (200 acres) = .5 in/day ### **Step 1: Calculate Total Daily Loss (in inches)** \[ \text{Total daily water removed} = \text{Evaporation from pond} + \text{Pumped to vineyard} \] #### **Evaporation Loss (in acre-inches/day):** \[ = 25 \text{ acres} \times .2 \text{ in} = 5 \text{ acre-inches/day} \] #### **Pumping Loss (in acre-inches/day):** \[ = 200 \text{ acres} \times .5 \text{ in} = 100 \text{ acre-inches/day} \] #### **Total Daily Loss:** \[ = 5 + 100 = 105 \text{ acre-inches/day} \] ### **Step 2: Calculate Initial Pond Water Volume** \[ \text{Initial volume (acre-feet)} = \text{Area} \times \text{Depth} = 25 \text{ acres} \times 7 \text{ ft} = 175 \text{ acre-feet} \] \[ 1 \text{ acre-foot} = 12 \text{ acre-inches} \] \[ \text{Initial volume (acre-inches)} = 175 \times 12 = 2,100 \text{ acre-inches} \] ### **Step 3: Calculate Days to Empty** \[ \text{Days} = \frac{\text{Initial volume (acre-inches)}}{\text{Daily loss (acre-inches/day)}} = \frac{2,100}{105} = 20 \text{ days} \] --- **Final Answer for Q15:** \[ \boxed{20 \text{ days}} \] --- ### **Summary Table** | Question | Final Answer | |----------|--------------| | 14 | 15.9 feet | | 15 | 20 days |