PS3 - MATH 505 Mathematical Fluid Dynamics Problem Set 3...

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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 Bernoulli’s 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 ) (Torricell’s 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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