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Unformatted text preview: MATH 505: Mathematical Fluid Dynamics Problem Set 3 due Friday, October 19, 2007 1. Consider the incompressible irrotational flow of a fluid which fills an open tank to an initial height h . The fluid is steadily escaping through a small hole at the bottom with speed U . By considering a streamline which runs from the upper surface to the surface at the hole, use Bernoullis equation to obtain a relation between U and the change in height of the fluid dh/dt . Under the assumption that the cross-sectional area of the hole is much smaller than any cross-section of the tank, obtain a simple approximate relation between U ( t ) and h ( t ) (Torricells Law). Does the fluid speed up or slow down as the tank drains? 2. Download the Mathematica .nb file from the webpage, and try out several values of the circulation G . Print out your results, and include them with your PS. Try including a pt vortex somewhere outside the cylinder - be careful about using Milne-Thompson!...
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This note was uploaded on 07/23/2008 for the course MATH 505 taught by Professor Belmonte,andrewl during the Fall '07 term at Pennsylvania State University, University Park.
- Fall '07