Fluid force on the surface of a dam.

Question

The figure to the right shows the shape and dimensions of a small dam. Assuming the water level is at the top of the​ dam, find the total force on the face of the dam. Use 1000 kg/m3 for the density of water and 9.8 m/s2 for the acceleration due to gravity.

Here's the image for the dam.

I know the formula for the integral for fluid force but I just can't figure out a width for any y on the trapezoid. Please help.

Answer 1

The width depends linearly on the height $h$. At the top ($h=36$) it's 48, and at the bottom ($h=0$) it's 24. So the width is $w-w_0=m(h-h_0)$, where $m=(48-24) / (36-0)$ and you can take $w_0=24$, $h_0=0$. Plugging these numbers in gives $w=\frac{2}{3}h+24$.