Problem 5.88

# Problem 5.88 - The angular deformations are x-y plane x v y...

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Problem 5.88 [Difficulty: 3] Given: Velocity field for pressure-driven flow between stationary parallel plates Find: (a) Rates of linear and angjular deformation for this flow (b) Expression for the vorticity vector (c) Location of maximum vorticity Solution: We will apply the definition of vorticity to the given velocity field. V Governing Equation: (Definition of vorticity) Assumptions: (1) Steady flow 0 z w y v x u V Rates of linear deformation in all three directions is zero. The volume dilation rate of the flow is:
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Unformatted text preview: The angular deformations are: x-y plane: x v y u u max 2 y b 2 y-z plane: y w z v z-x plane: z u x w angdef u max 2 y b 2 k b y u b y u z y x k j i V ˆ 2 1 ˆ ˆ ˆ 2 max 2 max k b y u ˆ 2 2 max The vorticity is: The vorticity is a maximum at y=b and y=-b...
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