At a hydroelectric power plant, the water pressure head is at a height of $300\; m$ and the water flow available is $100\; m ^{3} \,s ^{-1} .$ If the turbine generator efficiency is $60 \%,$ estimate the electric power available from the plant (in $MW$) $\left(g=9.8 \;m\,s ^{-2}\right)$
At a hydroelectric power plant, the water pressure head is at a height of $300\; m$ and the water flow available is $100\; m ^{3} \,s ^{-1} .$ If the turbine generator efficiency is $60 \%,$ estimate the electric power available from the plant (in $MW$) $\left(g=9.8 \;m\,s ^{-2}\right)$
Height of water pressure head, $h =300 \,m$
Volume of water flow per second, $V=100 \,m ^{3} / s$
Efficiency of turbine generator, $n =60 \%=0.6$
Acceleration due to gravity, $g=9.8 \,m / s ^{2}$
Density of water, $\rho=10^{3} \,kg / m ^{3}$
Electric power available from the plant $=\eta \times h \rho \,g\, V$
$=0.6 \times 300 \times 10^{3} \times 9.8 \times 100$
$=176.4 \times 10^{6} \,W$
$=176.4\, MW$
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