Section 4: Soil and Water Conservation Engineering
Watershed Management
Subtopic: Rainwater harvesting
Question Statement:
An excavated dugout farm pond has a mean water surface area of $A = 1200.0\text{ m}^2$ and an initial stored water volume of $V_0 = 3000.0\text{ m}^3$ at the end of the monsoon. Over a $30.0\text{-day}$ dry period with zero inflow, average evaporation loss is $6.0\text{ mm/day}$ and average seepage loss through the perimeter is $3.0\text{ mm/day}$. Assuming constant surface area, the remaining volume of water in the pond in $\text{m}^3$ at the end of the period is ________ (answer in integer).
```
Inflow Runoff Qi = 0 ───> |~~~~~~~~~~~~~~~~~~~~| ───> Overflow Qout = 0
| Initial V0 = 3000 | Evaporation E = 6 mm/d
|____________________|
| Seepage S = 3 mm/d
```
Answer Key:
2676
Step-by-Step Solution & Explanation
**Method 1: Total Depth Loss Integration**
1. Combined daily water loss rate:
$\text{Loss Rate} = E + S_p = 6.0\text{ mm/day} + 3.0\text{ mm/day} = 9.0\text{ mm/day} = 0.0090\text{ m/day}$
2. Total depth of water lost in $30.0\text{ days}$:
$\Delta d = 30.0 \times 0.0090\text{ m/day} = 0.270\text{ m}$
3. Total volume of water lost:
$V_{\text{loss}} = A \times \Delta d = 1200.0\text{ m}^2 \times 0.270\text{ m} = 324.0\text{ m}^3$
4. Remaining stored volume:
$V_{\text{remain}} = V_0 - V_{\text{loss}} = 3000.0 - 324.0 = 2676.0\text{ m}^3$
**Method 2: Daily Volumetric Step Balance**
$\text{Daily volumetric loss} = 1200.0 \times 0.009 = 10.8\text{ m}^3/\text{day}$
$V_{\text{loss}} = 30 \times 10.8 = 324.0\text{ m}^3$
$V_{\text{remain}} = 3000.0 - 324.0 = 2676\text{ m}^3$