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Force exerted on Dam problem

  1. Aug 23, 2011 #1
    1. The problem statement, all variables and given/known data

    A vertical rectangular dam of width 25m contains water in a reservoir of depth 15m. What is the overall force exerted on the dam by the water?

    2. Relevant equations

    P=F/A .... F=PA
    P = pgh

    3. The attempt at a solution

    I'm really not sure about this one to be honest.

    I tried finding the Pressure (1000*9.807*15) and then multiplying that by area (15*25) but that doesn't give the right answer. Any tips would be much appreciated.
     
  2. jcsd
  3. Aug 23, 2011 #2

    Hootenanny

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    Welcome to Physics Forums.

    The reason that [itex]F = \rho\cdot A[/itex] does not give the correct answer is that the pressure varies with depth.

    Does that help nudge you in the right direction?
     
  4. Aug 23, 2011 #3
    Thanks for the reply, so I need to find the Pressure at each point along the Dam?

    Which would be (1000 * 9.807 * 1) + (1000 * 9.807 * 2) .... up to 15m?
     
  5. Aug 23, 2011 #4

    Hootenanny

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    You could do that, but it would be easier (and sufficient in this case) to find the average force on the damn.
     
  6. Aug 23, 2011 #5
    Would that be (1000 * 9.807 * 7.5) * (15 * 25)?

    Which gives 27,582kN
     
  7. Aug 23, 2011 #6

    Hootenanny

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    Yup :biggrin:
     
  8. Aug 23, 2011 #7
    Thanks for your help. Just looked at the answer that we were given for this question and it was 27,590kN.
     
  9. Aug 23, 2011 #8

    Hootenanny

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    No problem.

    You would have got exactly that answer if you'd have used [itex]g=9.81\;\text{m}\cdot\text{s}^{-2}[/itex].
     
  10. Aug 23, 2011 #9
    Ah yes, I thought that might be it. Bit odd considering we get told to use g = 9.807 and then the correct answer is through using it as 9.81!
     
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