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Problem 5.19 - Problem 5.19 Given Find Solution[Difficulty...

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Problem 5.19 [Difficulty: 2] Given: The list of velocity fields provided above Find: Which of these fields possibly represent incompressible flow Solution: We will check these flow fields against the continuity equation 0 1 1 t V z V r V r r r z r Governing Equations: (Continuity equation) Assumptions: (1) Incompressible flow ( ρ is constant) (2) Two dimensional flow (velocity is not a function of z) Based on the two assumptions listed above, the continuity equation reduces to: r r V r θ V θ 0 This is the criterion against which we will check all of the flow fields. a) V r r θ t ( ) K r V θ r θ t ( ) 0 r r V r r θ t ( ) 0 θ V θ r θ t ( ) 0 Hence r r V r
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