# Hydrostatic force with a gate?

• Jun 24th 2008, 04:11 PM
elocin
Hydrostatic force with a gate?
THis is my last question, I promise!! Here is the problem: a vertical dam has a semicircular gate. Find the hydrostatic force against the gate. The picture is a square with a semicircle at the bottom in the middle. The diameter of that semicircle is 4 m. The height of the square dam thing is 12 m and the water level is 2m down. So I thought you integrate from 2 to 12, and then I don't know what to do next, I should be learning from these, but they're getting really hard! Would you find the area of the semicircle? and then the pressure against the gate. There's water and everything is in meters, so I think you use 1000 *9.8 times the depth for the pressure, but the depth varies on the gate. Help! THanks!! (Thinking)
• Jun 24th 2008, 04:39 PM
galactus
The horizontal length can be marked by 2x, but $x=\sqrt{4-y^{2}}$

So we have:

$2\int_{0}^{2}(8+y)\sqrt{4-y^{2}}dy$

EDIT: That should be 8+y on the diagram. You can multiply by your density. Since you are in meters, it is probably 9800.
• Jun 24th 2008, 04:42 PM
elocin
Hmm okay, let me wrap my mind around this. But, what about the density of water? Do you put that in front of the integral like the previous question? Thank you!
• Jun 24th 2008, 04:43 PM
elocin
OH I see your note. Never mind!! THank you, you are so smart!!!
• Jun 24th 2008, 04:46 PM
elocin
Well I got 544868 and it isn't right. I just integrated from 0 to 2 and then times that by 2 and then by 9800 right?
• Jun 24th 2008, 04:50 PM
galactus
Do you have to round to the hundredth?. I see nothing wrong with the integral.
• Jun 24th 2008, 04:53 PM
elocin
You have to round to the nearest whole number. Did you get 544868 too?
• Jun 24th 2008, 04:55 PM
galactus
Yes, I did. That and some change. 544868.39

Here is a link to a similar problem. Some advice: search the site for similar problems before you post. May save you some trouble.

http://www.mathhelpforum.com/math-he...uid-force.html
• Jun 24th 2008, 05:00 PM
elocin
Hmm okay! Yeah that problem does look similar! Thanks! I guess I'll keep trying!!
• Jun 24th 2008, 05:13 PM
elocin
ONE QUESTION!!!! Why did you integrate from 0 to 2?
• Jun 24th 2008, 05:33 PM
galactus
That is the radius of the gate, is it not?. It's diameter is 4, therefore, the radius is 2.