A 65-MW hydroelectric power plant uses a turbine-generator located at the bottom

Question

A 65-MW hydroelectric power plant uses a turbine-generator located at the bottom of a 120-m deep dam. During the power plant operation, water flows into the turbine at the rate of 75 m^3/sec and the generator operates at an average efficiency of 91%. Neglect any losses in the piping system. Evaluate
a) the overall efficiency of the power generation system
b) the turbine efficiency
c) the power delivered to the generator by the turbine

Provide (sketch) and steps of the problem configuration.
Do not forget units & dimensions. Thanks

Explanation / Answer

Input power to turbine = gQH = 1000*9.81*75*120 = 88290000 W = 88.29 MW

c) Output power from turbine = Input power to generator = 65/0.91 = 71.43 MW

b) Turbine eff = Output/Input = 71.43/88.29 = 0.809 = 80.9 %

a) Overall efficiency = 0.809*0.91 = 0.736 = 73.6 %

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