- #1
bermudianmango
- 4
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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.
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.