How much power is theoretically available from a mass flow of 1000 kg/s of water that falls a vertical distance of 50 m?
A) 980 kW
B) 98 kW
C) 4900 W
D) 490 kW

Question

Quizplus · Accepted Answer

The formula for potential energy is given by PE = mgh, where m is the mass, g is acceleration due to gravity, and h is the height. Therefore, the potential energy of the given mass of water falling a vertical distance of 50 m is PE = 1000 kg/s x 9.81 m/s² x 50 m = 490,500 W or 490.5 kW. However, not all of this potential energy can be converted to useful work due to losses in the system. Generally, the efficiency of hydroelectric power plants ranges from 80% to 90%. Therefore, the theoretical power available would be lower, around 392 kW to 441 kW. The closest answer to these values is D) 490 kW.

How Much Power Is Theoretically Available from a Mass Flow