A 50% efficient hydroelectric power plant generates electricity from water falling a height of 110 m and at a rate of x kg/s.If the maximum possible power output of the plant was 27.0 MW,what is x?
A)25,000 kg/s
B)50,000 kg/s
C)100,000 kg/s
D)5100 kg/s
E)510,000 kg/s

Question

Quizplus · Accepted Answer

The maximum possible power output of a hydroelectric power plant can be calculated using the formula: Power = Efficiency × (Mass flow rate × g × Height), where g is the acceleration due to gravity (9.8 m/s^2). Given that the efficiency is 50% (or 0.5), the height is 110 m, and the desired power output is 27.0 MW (or 27,000,000 W), we can rearrange the formula to solve for the mass flow rate (x):$$27,000,000 = 0.5 \times (x \times 9.8 \times 110)$$$$27,000,000 = 0.5 \times x \times 1078$$$$27,000,000 = 539 \times x$$$$x = \frac{27,000,000}{539}$$$$x \approx 50,093 \, \text{kg/s}$$Rounding to the nearest option gives us 50,000 kg/s.

A 50% Efficient Hydroelectric Power Plant Generates Electricity from Water