Question

Find the amount of work done in emptying a cylindrical tank completely filled with kerosene. Assume that the radius of the cylindrical tank is 3 m, height is 6 m, and the density of kerosene is 817.15 kg/m3.

Answer 1

I can't say that I know how to do this off the top of my head. I would try Googling your question. I found another OpenStudy thread that might be of use
http://openstudy.com/study#/updates/4e3d53a10b8bfc76a3f6bc64

Here are also some similar questions that might be of use to you
http://sites.csn.edu/gcohen/182/07_work.pdf

Best of luck!

Answer 2

If you know calculus, you can build an integral. Model it as if you are lifting small cylinders of thickness dz out of the cylinder.


I am on mobile right now or I'd draw something to help more.

Answer 3

note, we are using a z axis, with z = 0 at the bottom of the cylinder, and z = 6 at the top

so you can see that the mass of that small element is \(dm = \rho \, dV = \rho \pi R^2 dz\)

if it is lifted to the top of the cylinder, which is what you have to do to get it out of the cylinder, then its increase in potential energy is \(dU = dm \,g \, \Delta h = \rho \pi R^2 dz \, g \, (6-z) \) and that is the work done on that element

\(dW = \rho \pi R^2 \, g \, (6-z) \, dz \)

and then, if you can see that, you can integrate in interval \(0 \lt z \lt 6\) as we re doing that for every single small element in the cylinder....