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The catchment surrounding a reservoir has a plan area of A (km2). In a month (30 days), the measured water level dropped from X (m) to Y (m). Assume that water is abstracted from the reservoir for drinking water supply at the rate of Q x 106 litres per day, that the plan area of the reservoir is B (km2), the monthly rainfall is R (mm) and the measured evaporation from the reservoir is E (mm). 
By undertaking a water balance on the reservoir, determine for the 30-day month:
Volume of water between the upper and lower water levels;
Volume of rainfall directly onto the reservoir;
Volume of water abstracted from the reservoir;
Volume of water evaporated from the reservoir;
Volume of runoff from the catchment to the reservoir.
The percentage of rainfall falling on the catchment 
that is converted to runoff to the reservoir.
State any simplifying assumptions implied in your calculations.

Water balance for reservoir:
 		
Volume out              -                  Volume in                =            Volume change in reservoir

[ Abstraction              -             [Runoff                          =            Volume change in reservoir  
+ Evaporation]                           + Rainfall on reservoir]   

A= 380 km square

B= 34 km square
R= 31 mm
E= 200 mm
X=186.1m
Y = 185.7 m
Q= 460 L/day 
Solve the problem 

To solve this problem, we'll use the given water balance equation for the reservoir and compute the required volumes step by step. Let's list the variables provided and the steps we'll follow.

### Given dataTo solve this problem, we'll use the given water balance equation for the reservoir and compute the required volumes step by step. Let's list the variables provided and the steps we'll follow.

### Given 
- \( A = 380 \, \text{km}^2 \) (Catchment area around the reservoir)
- \( B = 34 \, \text{km}^2 \) (Plan area of the reservoir)
- \( R = 31 \, \text{mm} \) (Monthly rainfall)
- \( E = 200 \, \text{mm} \) (Measured evaporation)
- \( X = 186.1 \, \text{m} \) (Initial water level)
- \( Y = 185.7 \, \text{m} \) (Final water level)
- \( Q = 460 \times 10^6 \, \text{litres/day} = 0.46 \, \text{MCM/day} \) (Abstraction rate from the reservoir)
- Time duration: \( t = 30 \, \text{days} \)

### Step-by-Step Solution:

1. **Volume change in the reservoir:**
   The change in water level in the reservoir over 30 days can be calculated as:
   \[
   \Delta h = X - Y = 186.1 - 185.7 = 0.4 \, \text{m}
   \]
   The corresponding change in volume for the reservoir is the plan area \( B \) multiplied by this height difference \( \Delta h \):
   \[
   V_{\text{change}} = B \times \Delta h = 34 \, \text{km}^2 \times 0.4 \, \text{m} = 34 \times 10^6 \, \text{m}^2 \times 0.4 \, \text{m} = 13.6 \, \text{MCM}
   \]
   (Note: 1 km² = \( 10^6 \, \text{m}^2 \), and MCM = million cubic meters.)

2. **Volume of rainfall directly onto the reservoir:**
   The volume of rainfall on the reservoir is calculated as the plan area of the reservoir \( B \) multiplied by the rainfall depth \( R \) (converted to meters):
   \[
   V_{\text{rainfall}} = B \times \left( \frac{R}{1000} \right) = 34 \, \text{km}^2 \times \left( \frac{31}{1000} \, \text{m} \right) = 34 \times 10^6 \, \text{m}^2 \times 0.031 \, \text{m} = 1.054 \, \text{MCM}
   \]

3. **Volume of water abstracted from the reservoir:**
   The total volume of water abstracted over the 30-day period is:
   \[
   V_{\text{abstraction}} = Q

The catchment surrounding a reservoir has a plan area of A (km2). In a month (30 days), the measured water level dropped from X (m) to Y (m). Assume that water is abstracted from the reservoir for drinking water supply at the rate of Q x 106 litres per day, that the plan area of the reservoir is B (km2), the monthly rainfall is R (mm) and the measured evaporation from the reservoir is E (mm). By undertaking a water balance on the reservoir, determine for the 30-day month: Volume of water between the upper and lower water levels; Volume of rainfall directly onto the reservoir; Volume of water abstracted from the reservoir; Volume of water evaporated from the reservoir; Volume of runoff from the catchment to the reservoir. The percentage of rainfall falling on the catchment that is converted to runoff to the reservoir. State any simplifying assumptions implied in your calculations.

Learn how to perform a water balance calculation for a reservoir, including determining changes in water volume, rainfall, abstraction, and evaporation. This problem involves key mathematical concepts such as volume calculation, unit conversion, and the principle of conservation of mass. Suitable for students in Grades 11-12.

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