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Problem 2.3 - Flow must satisfy the no-slip condition 1 At...

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Problem 2.3 [Difficulty: 2] Given: Viscous liquid sheared between parallel disks. Upper disk rotates, lower fixed. Velocity field is: h z r e V ω θ ˆ = r Find: a. Dimensions of velocity field. b. Satisfy physical boundary conditions. Solution: To find dimensions, compare to ( ) z y x V V , , r r = form. The given field is ( ) z r V V , r r = . Two space coordinates are included, so the field is 2-D.
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Unformatted text preview: Flow must satisfy the no-slip condition: 1. At lower disk, = V r since stationary. z = 0, so ˆ = = h r e V r , so satisfied. 2. At upper disk, r e V ˆ = r since it rotates as a solid body. z = h , so r e h h r e V ˆ ˆ = = r , so satisfied....
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