The water behind Hoover Dam is 206m higher than the Colorado river below it. At what rate must water pass through the hydraulic turbines of this dam to produce 100 MW of power if the turbines are 100 percent efficient?

m' = 4948.38 kg/s

Explanation:

For a case of 100% efficiency, the power produced must be equal to the rate of potential energy conversion

GIVEN THAT

Power = 100 MW

rate of Potential energy = (m') * g*h

100*10^6 = (m') * 9.81*206

m' = 4948.38 kg/s

49.484 m³ / s

Explanation:

Volume flow rate = Power in W / (efficiency * density * height * acceleration due to gravity)

Volume flow rate = 100 * 10⁶ / (1 * 1000 kg/m³ * 206 m * 9.81 m/s²)

V = 49.484 m³ / s