A lake had a water surface elevation of 102.91 m above datum at the beginning of the month. The average lake surface area can be taken as 5000 ha.

Given,

1. Inflow volume = 16 Mm³

2. Outflow volume = 16 Mm³

3. Input due to precipitation = 7.5 Mm³

4, Outflow due to evaporation = 3 Mm³

Find out the net water surface elevation at the end of the month. 

Concept:

Water - Budget Equation:

The Water - Budget equation is based on conservation of mass in a closed system and states that any water entering a system, must be transferred into either evaporation, surface runoff, or stored in the ground.

A general water balance equation is

Mass inflow - Mass outflow = Change in storage

or

P = R + E + ΔS

where

P is precipitation (gain)

E is evapotranspiration (loss)

R is streamflow (loss)

ΔS is the change in storage 

As per Water Budget Equation,

Calculation:

Given,

Water surface level at the beginning of the month = 102.91 m

Area = 5000 ha

Inflow volume = 16 Mm³, Outflow volume = 16 Mm³

Inflow due to precipitation = 7.5 Mm³, Outflow due to precipitation = 3 Mm³

∵ ΔS = Σ Incoming - Σ Outgoing

ΔS = (16 + 7.5) - (16 + 3) = 4.5 Mm³

Convert this change in storage in terms of depth, ΔS = \(\frac{4.5\ \times 10^6}{5000\ \times 10^4}\) 

ΔS = 0.09 m

Net water surface elevation at the end of the month = 102.91 + 0.09 = 103.0 m