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 crosssectional area of the hole is much smaller than any crosssection 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 MilneThompson!...
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 Fall '07
 BELMONTE,ANDREWL
 Math, Fluid Dynamics, complex potential, incompressible irrotational flow, Zhukovsky

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