I was unsure how the Fourier series would come into it as well.
How would you drop the assumption, allowing for the possiblity that it might be a cone, or cylinder or anything? By assuming it was a curve I was able to solve for the 1/4 power.
Our Fluid Mechanics professor gave us a challenge: to find the shape of a vessel with a hole at the bottom such that the water level in the vessel will change at a constant rate (i.e. if z is the height of the water in the tank dz/dt=constant).
I presented a solution assuming that the vessel...