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EML 5709 Homework 5 Spring 1995

1. Make question 7.1 in the book. Plot a typical velocity profile between the plates at an early time, an intermediate time, a long time and a very long time.
2. Make question 7.2 in the book. Are there conditions in which it is better to use an elliptical pipe to get the largest possible flow though the pipe?
3. Address the axial Stokes problem: initially the fluid inside a circular pipe of radius R is at rest, but at time t=0 the pipe is given a constant velocity U in the direction of it axis. What is the infinite time value of the flow in the pipe? If during the first 60 seconds, the differences from the infinite time flow velocity decrease to 2% of U, how much longer does it take to get within 1% of the initial value?
4. Make question 7.5 in the book. Is the torque on the smaller cylinder smaller? If not, what is the physical reason that it is not?
5. Make question 7.6 in the book. Is it possible for an inviscid potential flow to be the same as a solution of the viscous Navier-Stokes equations?
6. Make question 7.9 in the book, replacing ` for R=0' by ` for R=0'. Sketch the vorticity along a radial line for various times. Why does the book say that the maximum circulation around the vortex is the same for all times? I thought Kelvin's theorem does not apply to viscous flow?