# Power output of a hydroelectric plant

## Homework Statement

In a hydroelectric plant, water falls from a high elevation to a lower elevation,losing PE in the process/ In doing so, it turns turbines which generate electricity. In a particular hydroelectric plant, water flows at a rate of 400 kg/s. If 80% of the PE that the water loses gets converted to electricity, what is the power output of the dam, in watts?

## Homework Equations

PE=mgy
PE lost=KE gained

## The Attempt at a Solution

Known information:

m=400 kg/s (Right?)
g=9.8 m/s^2
y=30 meters

KE= .8(400 kg/s*9.8 m/s^2*30 m)=9408 Joules

That's easy enough, right? But don't a need a time to convert to Watts? Is the time just one second, so that my answer is 9408 Watts?

Thanks!

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BvU
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You want to do a dimensional check here. Perhaps you are ending up with one/s left over.... on the left hand side

Another thing you can do is calculate the amount of Joules in 100 seconds. Then divide by 100 to get the number of Joules/second, which is the power.

• 1 person
KE= .8(400 kg/s*9.8 m/s^2*30 m)=9408 Joules

I don't really understand the phrasing of your first sentence. Do you mean that I have three/s total, but only two cancel out, so my answer is 9408 J/S, which is 9408 Watts?

Thank you!

BvU
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