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 would be a 3D curve: http://imgur.com/2RhMCgD This was correct but apparently not good enough. He responded: "You have to show how you come up with the 1/4 power mathematically and rigorously from first principle. For instance, start with a Fourier series with a set of orthogonal functions, and take it from here." Does anyone have any idea where to begin? Thanks in advance.