At a hydroelectric power plant, the water pressure head is at a height of 300 m and the water flow available is 100 `m^2 s^(-1)`. If the turbine generator efficiency is 60%, estimate the electric power available from the plant (g = 9.8 m `s^(-2)`?).

Explanation

Here height of water head h = 300 m, volume of water flow `V = 100 m^(3)s^(-1)`
`therefore `Mass of water flow m = V`rho = 100 xx 10^(3) = 10^(5) kg m^(-1)` [`therefore` Density of water `rho = 10^(3) kg m^(-3)`]
`therefore` Input power = Loss of potential energy per unit time = mgh
`=10^(3) xx 9.8 xx 300 = 2.94 xx 10^(8)`
As efficiency of turbine generator `eta = 60% = 60/100 = 0.6`
`therefore` Power output `= eta xx ` input power
`=0.6 xx 2.94 xx 10^(5) W = 176` MW.