Question

Clear Lake has a surface area of 70 ha. In April the inflow of the lake was 1.5 m3/sec. A dam regulated the outflow of the lake to be 1.25 m3/sec. If the precipitation recorded for the month of April was 7.62 cm and the storage volume increased by an estimated 650,000 m3. What is the estimated evaporation in cubic meters?

Answer 1

Answer:

The estimated evaporation is 51340 cubic meters.

Explanation:

Let suppose that precipitation is very small in comparison with depth of the Clear Lake. The monthly change in the volume of the lake ($\Delta V$), in cubic meters, is estimated by the following formula:

$\Delta V = A\cdot \Delta z + (\dot V_{in}-\dot V_{out})\cdot \Delta t -V_{evap}$ (1)

Where:

$A$ - Surface area of the lake, in square meters.

$\Delta z$ - Water precipitation, in meters.

$\dot V_{in}$ - Average water inflow, in cubic meters per second.

$\dot V_{out}$ - Average water outflow, in cubic meters per second.

$\Delta t$ - Monthly time, in seconds.

$V_{evap}$ - Evaporation, in cubic meters.

If we know that $A = 700000\,m^{2}$, $\Delta z = 0.0762\,m$, $\dot V_{in} = 1.5\,\frac{m^{3}}{s}$, $\dot V_{out} = 1.25\,\frac{m^{3}}{s}$, $\Delta t = 2.592\times 10^{6}\,s$ and $\Delta V = 650000\,m^{3}$, then the estimated evaporation is:

$650000 = 701340-V_{evap}$ (2)

$V_{evap} = 51340\,m^{3}$

The estimated evaporation is 51340 cubic meters.