A generator at Hoover Dam can supply 388 MW of electrical power. Assume that the

Question

A generator at Hoover Dam can supply 388 MW of electrical power. Assume that the turbine and the generator are 83% efficient-therefore falling water must supply energy at a rate of 467.5 MW. The acceleration due to gravity is 9.8 m/s^2 .

A) The energy of the water comes from the change of the potential energy (mgh). What is the needed change in potential energy each second?

B) If the water falls 24.9 m, what is the mass of the water that must pass through the turbine each second to supply this power? Answer in units of kg/s.

(Please provide work!)

Explanation / Answer

A generator at Hoover Dam can supply 396 MW of electrical power. Assume that the turbine and the generator are 83.1% effi- cient. Find the rate with which falling water must supply energy to the turbine. The accelera- tion due to gravity is 9.8 m/s2 . Answer 476.53 Part 2 If the water falls 21.3 m, what is the mass of the water that must pass through the turbine each second to supply this power? Answer in units of kg/s   

total energy supplied = 396* 100 / 83.1= 476.53 MW

power required to pump water = ( M G H ) / time = (M/time).G.H

M/time = power/ G.H =396/(21.3*9.8)= 1.897 * 10^3 kg/sec

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