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Unformatted text preview: v , show that these are equivalent to the vector conservation law ( ~u ) t + div( ~u ~u ) = ~ f int + ~ f ext where ( ~u ~u ) ij = u i u j is the tensor product. Remember that for each quantity q we assume an advective ux ~ F = q~u . 4. Using Bernoullis equation for steady incompressible irrotational ow, calculate the pressure eld for the ow past a cylinder described in Problem 2, with = 0. 5. The only unphysical aspect of a Point Vortex is that the velocity eld approaches inn-ity at its center (!!). So consider the Rankine Vortex, a ow eld given in cylindrical coordinates by ~u = (0 , v ( r ) , 0), with v ( r ) = r if r a a 2 /r if r > a , (a) Let C b be a circle of radius b centered on the origin, and calculate the circulation integrated around that curve, as a function of b . (b) Calculate the vorticity for the Rankine Vortex....
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This note was uploaded on 07/23/2008 for the course MATH 505 taught by Professor Belmonte,andrewl during the Fall '07 term at Pennsylvania State University, University Park.
- Fall '07