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Homework Help: Hydrostatic Forces

  1. Nov 30, 2007 #1
    [SOLVED] Hydrostatic Forces

    Any Help would be GREATLY appreciated. My grade depends on me understanding this.

    1. The problem statement, all variables and given/known data

    A tank contains freshwater. The end of a tank containing water is vertical and has the indicated shape. Explain how to approximate the hydrostatic force against the end of the tank by a Riemann sum. Then express the force as an integral and evaluate it.

    calculus.jpg

    2. Relevant equations

    F=pgAd
    A=wdx
    3. The attempt at a solution

    F= int 0->5 1000(9.8)2sqrt(100-y^2)(5)
    98000*int 0->5 sqrt(100-y^2)
    u=100-y^2
    -1/2*du=dy
    98000*int 75->100 u^(.5)
    98000{(2/3)u^(3/2)} 75->100
    64171414.85 N
     
    Last edited: Nov 30, 2007
  2. jcsd
  3. Nov 30, 2007 #2
    I figured it out finally.....
    The right answer should be 2.29x10^6. I actually did it right another way the first time.

    F=(1000)(9.8)*int 0->5 (100-x^2)^.5(-2x)dx
    =-9800{(2/3)(75^(2/3)-1000}0->5

    U substitution works too... that's what I did hours ago, but I doubted my answer.


    F=(1000)(9.8)(2)(5)*int 0->5 (100-x^2)^.5
    =98000 int 0->5 sqrt(100-x^2)
    u=100-x^2
    -2dx=du
    dx=-.5du
    98000 int 75->100 u^.5
    98000{(2/3)u^(3/2)}75->100
     
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