Find the hydrostatic force against the gate of vertical dam.

[SUhottie10]

A vertical dam has a semicircular gate as shown in the figure. Find the hydrostatic force against the gate. (the picture shows 12 m height, water level is 2 m below the top of the dam, and the semicircular gate at the bottom in the center of the dam is 4 m wide)

 

[galactus]

I have't seen one of these problems for a while.

If I remember correctly, \(\displaystyle \L\\\int_{a}^{b}{\rho}h(x)w(x)dx\)

The gate is 4' wide at the bottom, therefore a radius of 2'

The water level is 2' below the top of the dam which is 12' high.

It is 8 feet deep from the top of the gate to water level.

\(\displaystyle \L\\2\int_{0}^{2}\underbrace{(8+y)}_{\text{h(y)}}\underbrace{\sqrt{4-y^{2}}}_{\text{w(y)}}dy\)

Don't forget to multiply by your weight density.

I hope I am on the right track. Check it out. Maybe someone else will either confirm or deny.

 

[SUhottie10]

Thanks, I went to the math center at my school before I got your message and I handed in my assignment today so I dont remember exactly how I did it but I am pretty sure that is right. Thanks for the reply!