A cylindrical tank, with base radius 9.4 meter, lies on its side and is partially filled with a liquid whose density is 1260 kilograms per cubic meter. The liquid fills the tank to a maximum depth of 14 meters. Determine the amount of force (in Newtons) exerted on a flat side of the tank.
October 1st 2009, 03:49 PM
Does any one know how to do this? I am having difficulty setting it up.
October 1st 2009, 04:05 PM
So far I have:
F= int (from -9.4 to 9.4) (14-y) 2(88.36-y^2)^(1/2)
Is that right?
October 1st 2009, 04:26 PM
Lol...ok whoever gave you this problem didn't like you a lot. Not only pgh changes with height but it doesn't change linearly because as you move further away from the center of your cylinder the submerged surface decreases so you cant just plug the submerged area as if the surface was a rectangle. Probably involves a cos(alpha x H) not sure though I don't have the time to do it right now.
There's an easier numerical method if you don't like integrals. Split the submerged portion into 3 parts and take an average heigth for each segment and calculate pgh for that height on that surface then when you have the 3 simply add them lol. The more segments you calculate the more precise your result is. If you calculate the integral it counts as infinite segments so the accuracy is 100%.