
New Member
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)

Elite Member
I have't seen one of these problems for a while.
If I remember correctly, [tex]\L\\\int_{a}^{b}{\rho}h(x)w(x)dx[/tex]
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.
[tex]\L\\2\int_{0}^{2}\underbrace{(8+y)}_{\text{h(y)}}\ underbrace{\sqrt{4y^{2}}}_{\text{w(y)}}dy[/tex]
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.

New Member
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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