# Thread: Find the hydrostatic force against the gate of vertical dam.

1. ## Find the hydrostatic force against the gate of vertical dam.

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)

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

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

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.

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

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.

3. 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!

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