Find the rate with which falling water must supply energy to the turbine?

Question

Part 1:

A generator at Hoover Dam can supply 379 MW of electrical power. Assume that the turbine and the generator are 86.5 % efficient. The acceleration of gravity is 9.8 m/s2 :

Find the rate with which falling water must supply energy to the turbine. Answer in units of MW.

Part 2:

The energy of the water comes from the change of the potential energy, mgh. What is the needed change in potential energy each second? Answer in units of J/s.

Part 3:

If the water falls 17.2 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.

Answer 1

<< A generator at Hoover Dam can supply 379 MW of electrical power. Assume that the turbine and the generator are 86.5 % efficient. The acceleration of gravity is 9.8 m/s2 :

Find the rate with which falling water must supply energy to the turbine. Answer in units of MW. >>

Efficiency = output/input

Input = output/efficiency

Input = 379/0.865

Input = 438.15 MW

<< The energy of the water comes from the change of the potential energy, mgh. What is the needed change in potential energy each second? Answer in units of J/s. >>

Conversion factor : 1 watt = 1 joule/sec.

Therefore, if the input energy = 438.15 MW, this is equivalent to 438,150,000 watts which is numerically equal to 438,150,000 joules/sec.

  

<< If the water falls 17.2 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 >>

Energy = 438,150,000 = m(9.8)(17.2)

and solving for "m",

m = 438,150,000/(17.2 * 9.8)

m = 2,599,371.14 kg./sec.