Calculate Pressure on a dam

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Homework Statement



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.

Homework Equations





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:

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