Could you solve this problem The buffalo Bill Dam is a concrete dam on the Shosh

Question

Could you solve this problem The buffalo Bill Dam is a concrete dam on the Shoshone River in the state of Wyoming near Dr. Miller's childhood home. It is named after the famous Wild West figure William "Buffalo Bill" Cody, who founded the nearby town of Cody. According to Wikipedia, the electrical power generation system below this dam produces a total of 31.5 MW utilizing a vertical drop of 265 ft (81 m). Assuming 88% efficiency, how many cubic meters of water must flow from the top of the dam per second to produce this amount of power? (Each cubic meter of water has a mass of 1000 kg.)

Explanation / Answer

let X cubic meter of water is required per second to fall from the top of the dam to produce 31.5 MW energy

as effiicieny is 88%, energy required to be produced by the water flow=31.5/0.88=35.79545 MW

now, mass of X cubic meter of water=X*1000 kg

energy released when it drops 81 m=mass*9.8*height

=X*1000*9.8*81=7.938*X*10^5 J

so power produced in 1 seconds=7.983*X*10^5 W

given that power required=35.79545*10^6 W

==>7.983*X*10^5=35.79545*10^6

==>X=44.839

hence 44.839 cubic meter of water must flow from the top per second to produce this amount of power.

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