hw10 - Compare the results Does the solution make sense#3 A...

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HW #10 Read sections 4.4, 6.3, and Chapter 9. #1 Consider fully developed Couette flow —flow between two infinite parallel plates separated by distance h , with the top plate moving and the bottom plate stationary as illustrated in the figure below. The flow is steady, incompressible, and two-dimensional in the xy -plane. The velocity field is given by j i h y V v u V ˆ 0 ˆ ) 1 ( ) , ( + = = r . Generate an expression for the stream function, Ψ , as a function of the channel height y. What is the value of Ψ along the top wall? #2 Calculate the volume flow rate per unit depth into the page for problem #1 by a) Integrating the velocity field (integral conservation of mass) b) By using the streamlines at the top and bottom walls
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Unformatted text preview: Compare the results. Does the solution make sense? #3 A steady two-dimensional, incompressible flow field in the x-y plane has the following streamfunction: 2 2 cy bxy ax + + = Ψ Where a,b,c are constants. a) Find an expression for the u and v velocity components. b) Verify that the velocity field in a) is physically possible. h u=0 u=V wall x y #4 A general expression for the a steady two-dimensional velocity field is given by: j dy cx V i by ax U v u V ˆ ) ( ˆ ) ( ) , ( + + + + + = = r Where U,V, a,b,c, and d are constants. a) Calculate the x and y components of the acceleration field b) Find the two dimensional rate of strain tensor ε ij . #5...
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This homework help was uploaded on 04/07/2008 for the course ES 330 taught by Professor Bohl during the Spring '08 term at Clarkson University .

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hw10 - Compare the results Does the solution make sense#3 A...

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