I need some help in trying to understand why my "intuition" appears to have
misled me.
The problem my students bought me is:
A cylindrical tank is buried underground. It is 3m in radius and 12 m in
depth. It is half full of water, and the upper edge of the tank is at
ground level. What is the work required to pump the water out of the tank?
They had gotten this problem in Calculus class and wanted my help because
they thought it was more a Physics problem. The Calculus solution is:
W = integral from 0 to 6 { density*pi*3^2*g(12-y) dy}
which is 1.4978 x 10^7 if I didn't punch the wrong button on my calculator.
I thought this would be a simple potential energy problem. Move the CM of
the "block" of water from where it is to above the ground. So, I thought
it would be