In a hydroelectric power plant, 65 m3/s of water flows from an elevation of 90 m to a turbine, where electric poweris generated. The overall efficiency of the turbine–generator is84 percent. Disregarding frictional losses in piping, estimate the electric power output of this plant.

Electric power output of this plant is .

Explanation:

From First Law of Thermodynamics we understand that hydroelectric power plant transforms mechanical energy from fluid into electric energy. The power output of this plant (), measured in watts, is determined by this expression, which is derived from definition of mechanical energy and energy efficiency:

(1)

Where:

- Energy efficiency, no unit.

- Density, measured in kilograms per cubic meter.

- Gravitational acceleration, measured in meters per square second.

- Fluid column, measured in meters.

- Volume flow, measured in cubic meters per second.

If we know that , , , and , then the estimated electric power output of this plant is:

Electric power output of this plant is .

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