Question

.   The Helms Pumped Storage Plant near Fresno, CA helps to meet peak energy demand by pumping water at 25 °C from a lower to an upper reservoir during times of low electrical demand or high wind energy production, and releasing it for hydroelectric power generation during times of peak electrical demand. The vertical distance between the reservoir surfaces is 531 m. Reversible Francis pump/hydroturbine units – open continuous-flow systems – are used for both pumping and power generation. They move water uphill, like pumps, when supplied with an external power source. Then can also extract energy from water flowing downhill, like hydroturbines. Unlike the adiabatic steam turbines and compressors we have studied, these pump/hydroturbine units do not change the enthalpy of the water. Any frictional energy losses are rejected to the surroundings as heat. Kinetic energy changes in the water may be neglected.

Useful reading: Wikipedia articles on pumped storage hydropower, hydroelectricity, and Francis turbines.

a) When the Francis units are used as hydroturbines, each one accepts 84.95 m³/s of water and produces 404 MW. Find their efficiency: (desired output)/(required input) as hydroturbines. Hint: watch for the J to kJ conversion in the gz term, as you have done earlier for kinetic energy terms.

b) When the Francis units are used as pumps, their efficiency is 3 percentage points less than their efficiency as hydroturbines.   Find the overall efficiency for pumped storage in this system – that is, the ratio of energy output to energy input per unit mass of water making a round trip from the lower to the upper reservoir and back.

Answer 1

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404 96 (806o) Koo - 80 60 7. Overall Efficen 80.60%