EGM6812_HW7_questions

# EGM6812_HW7_questions - EGM 6812 Fluid Mechanics 1 Fall...

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EGM 6812 Fluid Mechanics 1 - Fall 2010 10/11/10, 7 th Homework 1/2 1. Given: An ideal irrotational vortex of strength 0 , 0 2 v r . Find: a. Using Stokes’ theorem (be careful regarding the limitations of using this theorem), determine the relationship between vorticity z and circulation in this flow as a function of radius. Please explicitly show the contour integral paths. What is the vorticity for 0 r ? What are the values of vorticity for 0 r ? Are these results consistent with calculating the vorticity by taking the curl of the velocity field? b. Now, the vortex is suddenly forced to have zero velocity at the origin at time 0, 0 v r t similar to Rayleigh’s impulsively started plate problem. Make appropriate assumptions about the character of the flow and simplify the -direction momentum equation and list the appropriate boundary and initial conditions. Make sure that you clearly list the appropriate assumption(s) needed to cancel each term of the equation. The resulting equation should be the radial diffusion equation.

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