So I don't want to give the full details of the problem I'm working on, since I want to solve it myself. But I'm not sure which physical principles I'm supposed to use, since this is a Calc 2 question, and I'm not that familiar with Physics. Basically, I need to pump water out of a tank, which is shaped like a trapezoidal prism through a hole at the top. (The question is poorly written and doesn't tell me which side is the top, but I'll assume it's the short side of the parallel sides of the trapezoid.) Certainly I'll need the work formula $W = \int F(x)dx$ but will I also need some kind of fluid flow formula (didn't Bernoulli have something relevant here?). Thank you in advance.
asked Jul 19, 2014 at 15:34 1,229 2 2 gold badges 19 19 silver badges 27 27 bronze badgesMy assumption from hearing that problem is that you do not need to worry about fluid flow and the problem is only asking you to calculate how the mass of water is distributed.
If the tank were cylindrical or a right prism, you could simply assume that all the mass was at the midpoint of the height of the tank, and you have to raise it in the gravitational field to get it out of the tank. The work to empty the tank would be $\frac m g h$, where m is the total mass of water in the tank.
But this tank does not have the same cross section from top to bottom. You'll need to include the cross section at each height in your integration from the top of the tank to the bottom.
Is that enough information for you, or do you have some other clues in the problem that suggests that you do need to worry about fluid flow?