Problem 5.1 - Problem 5.1 [Difficulty: 1] The list of...

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Problem 5.1 [Difficulty: 1] Given: The list of velocity fields provided above Find: Which of these fields possibly represent two-dimensional, incompressible flow Solution: We will check these flow fields against the continuity equation  0 t w z v y u x 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: x u y v 0 This is the criterion against which we will check all of the flow fields. a) uxy t () 2 x 2 y 2 x 2 y vxy t x 3 xy 2 4y x t 4x 2x y y t x2y 4 Hence x u y v 0 INCOMPRESSIBLE b) t 2 x y x 2 y t 2 x y y 2 x 2 x t 2y y y t
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