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

The estimated evaporation is 51340 cubic meters.

Step-by-step 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\,(m^(3))/(s)`,
`\dot V_(out) = 1.25\,(m^(3))/(s)`,
`\Delta t = 2.592* 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.