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Advanced energy: Flow rate example questions

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What is the flow rate in GPM (gallon per minute) for the water to run through each of the reversible turbine generator (6 of them} in Ludigton's hydro pumped system, assuming the average height at 300 ft and 312 MW power rating for each generator. How long will it take to drain the entire reservoir with a capacity of 27 billion gallons?

a. What is the energy generated (or stored} per second? {E = PT)?
b. What is the meter equivalence to the 300 ft height (h)?
c. What is the potential energy of 1 liter (one kg} of water stored in the reservoir (P.E. = mgh), g = 9.8 m/sec^2?
d. How many liters of water is needed to generated (or stored) the amount of energy in part (a)?
e. What is the gallon equivalence of answer from part (d)?
f. What is the flow rate in gallon per second?
g. What is the flow rate in gallon per minutes?
h. What is the flow rate in gallon per hour?
i. What is the result by dividing the capacity of the reservoir by the answer you get from part (h)?

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Solution:
a) Energy generated (or stored) per second by each turbine generator (E) = Power (P) x Time (t)
E = 312 x 106 x 1 = 312 x 106 Joule/sec
Energy generated by 6 turbine generators per second = 6 x 312 x 106 Joule = 1872 x 106 Joule/sec
b) 1 ft = 0.3048 m. Hence, 300 ft = 300 x 0.3048 = 91.44 m.
c) Potential energy (PE) of a mass m placed at a height h above ...

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