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Power output of a hydroelectric plant

  1. Feb 28, 2014 #1
    1. The problem statement, all variables and given/known data

    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?

    2. Relevant equations

    PE=mgy
    PE lost=KE gained

    3. 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!
     
  2. jcsd
  3. Feb 28, 2014 #2

    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.
     
  4. Feb 28, 2014 #3
    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!
     
  5. Feb 28, 2014 #4

    BvU

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    Yesss
     
  6. Feb 28, 2014 #5
    Great! Thank you! That was too easy for the last problem in a chapter. 0.o
     
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