Consider the flow of an incompressible, Newtonian fluid between two long, horizontal parallel plates having infinite width as illustrated below. The bottom plate is fixed, the top plate moves to the right with constant speed U, and the plates are separated by a vertical distance H. Determine the velocity profile u(y) of the fluid between the two plates for zero pressure gradient, i.e. ?p/?x = 0, which is called Couchette flow.

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