The mechanical energy of the river water per unit mass is 887.4 J/kg
The power generated is 452.574 MW.
Given:
Average velocity (v) = 3 m/s
Rate = 510 m³/s
Height (h) = 90 m
We know, that mechanical energy is the sum of potential energy and kinetic energy.
So,
E = ×m×v² + m×g×h
and energy per mass unit is
E/m = ×v² + g×h
E/m = ×3² + 9.81×90
E/m = 887.4 J/kg
So, mechanical energy per unit mass is 887.4 J/kg.
Power generated is expressed as;
Power generated = energy per unit mass ×rate×density
Density of water = 1000 kg/m³
Power generated = 887.4× 510× 1000
Power generated = 452574000 W
So, the power generated is 452.574 MW.
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