hw7 - 2.011 Homework#7 Spring 2006 Out 25 April 2006 Due 2...

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2.011 Homework #7 Spring 2006 Out 25 April 2006 Due 2 May 2006 1. For the flow of an incompressible fluid the velocity component in the x -direction is: 2 u = ax 2 + bxy + cy , and the velocity component in the z direction is zero. Find the velocity component v in the y-direction. To evaluate arbitrary functions that might appear in the integration, assume that v = 0 at y = 0. 2. Given the following description of a flow field, 2 u K = 2 y i ˆ + xt ˆ j + xy k ˆ m/sec find the total acceleration of a fluid particle. 3. Flow between two flat plates, spaced a distance h apart with the top plate moving at speed U , is considered a special case of Couette flow . It is typically assumed that these plates are very, very long in the x direction, so that there is no variation in any variable in the x direction (to the right). Also, there is no flow in the y direction (into the page) and nothing varies in the y direction. Note that the solution given below, u (z) = Uz/h , has the property that there is no slippage between the fluid and the plates, i.e., the fluid in contact with the plates has the

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