p0508 - 5.8 CHAPTER 5 PROBLEM 8 457 5.8 Chapter 5 Problem 8...

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5.8. CHAPTER 5, PROBLEM 8 457 5.8 Chapter 5, Problem 8 The flow is incompressible if the divergence of the velocity vanishes. To check: · u = X i x + j y + k z ~ · X x 3 z y 2 i 3 x 2 z y j 3 x 2 z 2 y 2 k ~ = x X x 3 z y 2 ~ + y X 3 x 2 z y ~ + z X 3 x 2 z 2 y 2 ~ = 3 x 2 z y 2 + 3 x 2 z y 2 6 x 2 z y 2 =0 Therefore this velocity vector does correspond to an incompressible flow. The flow is irrotational if the curl of the velocity is zero. To check: ω = e e e e e e e e e e e e e ij k x y z x 3 z y 2 3 x 2 z y 3 x 2 z 2 y 2 e e e e e e e e e e e e e = ^ y X 3 x 2 z 2 y 2 ~ z X 3 x 2 z y i + ^ z X x 3 z y 2 ~
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This note was uploaded on 10/12/2009 for the course AME 309 at USC.

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