Problem 5.2 - Problem 5.2[Difficulty 2 Given Velocity...

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Problem 5.2 [Difficulty: 2] Given: Velocity fields Find: Which are 3D incompressible Solution: We will check these flow fields against the continuity equation  0 t w z v y u x Governing Equation: (Continuity equation) Assumption: Incompressible flow ( ρ is constant) Based on the assumption, the continuity equation reduces to: x u y v z w 0 This is the criterion against which we will check all of the flow fields. a) uxy z t () 2 y 2 2x z vxy z t 2 y z 6x 2 y z wxy z t 3 x 2 z 2 x 3 y 4 x z t 2z y z t 2 z z z t 2 z Hence x u y v z w 0 NOT INCOMPRESSIBLE b) z t x y z t z t x y z t 2 z t z 2 xt 2 yt x z t ty z y z t t 2 x z
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