Set up and calculate a definite integral giving the total force on the dam.

Question

If the width w=3620m, height h=110m, and base width b=3100 m, which are approximately the dimensions of the Aswan Dam in Egypt. Use density p=100kg/m^3 and g=9.8 m/s^2.

Answer 1

density should be 1000 kg/m³ for water. In math, they often ignore atmospheric pressure in the hydrostatic pressure equation P(z) = P₀ + ρgz with z = 0 at the top of the dam.

The Force can be obtained from the equation dF = PdA = (ρgz)w(z)dz where we have chosen P₀ to be 0 and w(z) is the width as you descend in z: w = 3620 - (3620-3100)(z/110) (a linear expression for w(z))

We can integrate in order to find the Force on the dam:

F = Integral from 0 to 110 of ((ρgz)(3620 - 4.7273z)dz)

I'll leave you to do the integral (Just power rule)