Calculate the change in storage (DS) of a lake or reservoir based on inflow, outflow, and rainfall using the equation Inflow - Outflow = DS.

Steps to Solve

1. Calculate the Inflow in $m^3$

The inflow rate is given as $6 , m^3/s$. We need to convert this to $m^3$ per month. There are 30 days in a month, 24 hours in a day, and 3600 seconds in an hour.

Inflow (from the source) $= 6 \frac{m^3}{s} \times 30 \frac{days}{month} \times 24 \frac{hours}{day} \times 3600 \frac{s}{hour}$ Inflow = $6 \times 30 \times 24 \times 3600 = 15552000 , m^3$

2. Calculate the Rainfall Volume in $m^3$

Rainfall is given as 145 mm, which needs to be converted to meters by dividing by 1000: $145 , mm = \frac{145}{1000} , m = 0.145 , m$ The area of the lake is $5000 \times 10000 , m^2 = 50000000 , m^2$. Rainfall Volume = Rainfall (in meters) x Area Rainfall Volume $= 0.145 , m \times 50000000 , m^2 = 7250000 , m^3$

3. Calculate the Total Inflow in $m^3$ Total Inflow = Inflow (from the source) + Rainfall Volume Total Inflow = $15552000 , m^3 + 7250000 , m^3 = 22802000 , m^3$

4. Calculate the Outflow in $m^3$

The outflow rate is given as $6.5 , m^3/s$. We convert this to $m^3$ per month.

Outflow = $6.5 \frac{m^3}{s} \times 30 \frac{days}{month} \times 24 \frac{hours}{day} \times 3600 \frac{s}{hour}$ Outflow = $6.5 \times 30 \times 24 \times 3600 = 16848000 , m^3$

5. Calculate the Water loss due to evaporation in $m^3$

Evaporation rate = $\frac{6}{100} m$ Area of the lake = $5000 \times 10000 , m^2 = 50000000 , m^2$ Volume loss due to evaporation = $\frac{6}{100} \times 50000000 = 3000000 , m^3$

6. Compute Total Outflow in $m^3$ Total Outflow= Outflow + Evaporation $Total Outflow = 16848000 + 3000000 = 19848000 , m^3$

7. Calculate the Change in Storage (DS) in $m^3$

Change in Storage (DS) = Total Inflow - Total Outflow

Change in Storage (DS) = $22802000 , m^3 - 19848000 , m^3 = 2954000 , m^3$