A U-tube has vertical arms of radii 'r' and '2r', connected by a horizontal tube of length 'l' whose radius increases linearly from r to 2r. The U-tube contains liquid up to a height 'h' in each arm. The liquid is set oscillating, and at a given instant the liquid in the narrower arm is a distance 'y' above the equilibrium level.
Show that the potential energy of the liquid is given by...
U = (5/8)gρπ(r2)(y2)
'y' is the change in height.
So i have the potential energy of system like his is given by
U = gρπ(r2)(y2)
The Attempt at a Solution
Im not sure where this 5/8's comes from. Im pretty sure its from the fact that the raduis of the tube is changing from r to 2r. Any hints?