p0522 - ) 1 r ( r sin ) ] k = ( 2) sin k Clearly, the flow...

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602 CHAPTER 5. MASS AND MOMENTUM PRINCIPLES 5.22 Chapter 5, Problem 22 Problem: A flowfield has the velocity vector u = Ξ r cos θ e r r sin θ e θ ,whe re Ξ is a constant and all quantities are dimensionless. Is there any value of Ξ for which this flow is irrotational? Is there any value of Ξ for which this flow is incompressible? Solution: For axisymmetric flow, the vorticity has only a z component and is as follows. ω = ^ 1 r r ( ru θ ) 1 r ∂θ ( u r ) ± k = ^ 1 r r p r 2 sin θ Q 1 r ∂θ ( Ξ r cos θ ) ± k = } 1 r ( 2 r sin
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Unformatted text preview: ) 1 r ( r sin ) ] k = ( 2) sin k Clearly, the flow is irrotational provided we choose = 2. The divergence of the velocity is u = 1 r r ( ru r ) + 1 r u = 1 r r p r 2 cos Q + 1 r ( r sin ) = 1 r (2 r cos ) + 1 r ( r cos ) = (2 1) cos Therefore, the flow is incompressible provided we select = 1/2....
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This note was uploaded on 02/09/2012 for the course AME 309 taught by Professor Phares during the Spring '06 term at USC.

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