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.
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:
The pressure on a given slice varies with depth. The force on a given slice is the pressure multiplied by area.
Now I add up all slices with integration, over a depth of 100 meters:
For a final answer of 1.862x10^11 Newtons.
This is incorrect. Where did I go wrong?
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?