Cannot figure out this calculus problem at all!
 

Okay...

A cylinder is given, laying on its side. It is 6 feet long, and has a 3 feet diameter. There is a pipe coming into the cylinder one foot above the top of it and extending to the bottom to pump out water. Given F = 9.8 * 1000, what is the work required to pump all of the water out?

Remember, its laying on its side... so the height is the diameter.

What I tried was the following:

Integral from 0 to 1.5: (2)(9800)(4-x)^2(pi)(6)dx
Which comes out to 9800(126pi)

This is incorrect. I have the answer which is supposed to come out to 9800(33.75pi)



Thanks for any help =)

What do you mean by "work" in this case? Where will the water end up? You should only need to figure out how much the centre of gravity of the body of water has been elevated, and how much the water weighs.

It doesn't matter where the water is going :) On the ground beside the cylinder if it helps I guess. =d

Well then, how do you define "work"? If the water is just going to the ground it will not require any actual work.

"There is a pipe coming into the cylinder one foot above the top of it and extending to the bottom to pump out water."

It doesn't take work to life the water over the 3 foot wall of the cylinder? ;)

I think for this problem, work is referring to the "physics work" or Force*Distance.

Now I have it set up like..

The integral from 0 to 3 of: 9.8*1000*6*(x+1)*(2*sqrt(2.25-x^2))

You can distribute the x+1 into two integrals but I cannot get this to solve correctly :/

Not if you set up a siphon, no. But I guess "work" here refers to getting all the water up to the exit... by the way, how does a pipe enter something one foot above it? Also, my old thermodynamics professor would tear you apart for not giving units, like F=9.8*1000 of what? Newton? Pounds per cubic foot?
At every lecture he'd mock some poor student who had made a stupid error on one of his exams. We all lived in mortal fear of becoming one of his examples.

Work is force x distance, if that's what you need to know. And yes, even with a siphon there is work being done - by the siphon. As for the hose comment, the pipe enters the cylinder from a height one foot above the top. Meaning it has to lift the water 1 extra foot past the top of the cylinder before it can exit.

But before we get too far off topic - let me just say that I figured this out.

I had to take the integral from -1.5 to 1.5 and use 2.5 - x for the height of the pipe for any who was wondering.