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Calculate Pressure on a dam

  1. Oct 26, 2011 #1
    1. The problem statement, all variables and given/known data

    Set up and calculate a definite integral giving the total pressure on the dam shown in the figure, which is about the size of the Aswan Dam in Egypt.

    The figure is a trapezoid, top 3600m, bottom 3000m, height of 100m.

    2. Relevant equations



    3. The attempt at a solution

    First, I will make horizontal slices since the pressure of the water in a horizontal slice is constant when the depth of the slice approaches 0.

    Next, I want the area of a slice. To do this, I essentially broke it into three shapes. The two outer triangles, and the inner square. These make up the width, while delta y is the height.

    The width of the inner square is a constant 3000. The triangles mimic the line x = 6y, and there are two of them, so I define the area of a slice to be:

    (3000+12y)Δy

    The pressure on a given slice varies with depth. The force on a given slice is the pressure multiplied by area.

    1000gy(3000+12y)Δy

    Now I add up all slices with integration, over a depth of 100 meters:

    [itex]\int^{100}_{0} 9800y(3000+12y)dy[/itex]

    For a final answer of 1.862x10^11 Newtons.

    This is incorrect. Where did I go wrong?

    Thank you.


    EDIT: Is it because the direction of increasing pressure and of "larger width" of the slices don't match? Must be it, how to correct? -12y?


    Making that change, I get 1.07x10^11 N. I only have one attempt left, look good?
     
    Last edited: Oct 26, 2011
  2. jcsd
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