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Unformatted text preview: , show that the velocity must be zero everywhere inside the box. Note that you may show this at least two ways: either by explicitly solving for the incompressible irrotational velocity eld, or by invoking certain theorems for solutions to particular partial dierential equations. 5. Beginning with Eulers equation for an incompressible uid, take the curl and thus obtain an equation for the vorticity = ~u . Under what conditions will be conserved in the Lagrangian frame? 6. Make an estimate of the Reynolds number characterizing the ow for: a) Your car travelling at 55 mph. b) The water coming out of your kitchen faucet. c) A red blood cell (diameter 1 m) moving through your artery at 2 cm/s, assuming that blood is a Newtonian (NavierStokes) uid. Version 1.1...
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 Fall '07
 BELMONTE,ANDREWL
 Math

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