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Problem 5.18 - Problem 5.18[Difficulty 2 The list of...

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Problem 5.18 [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) 0 V r rV r Based on the two assumptions listed above, the continuity equation reduces to: This is the criterion against which we will check all of the flow fields. 0 cos cos U U V r rV r (a) V r U cos θ ( ) V θ U sin θ ( ) This could be an incompressible flow field.
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