u* = y* + P*y*(y* – 1) и* h dP и y* y p* %3D µV dx и3D V х u = 0
Consider dimensionless velocity distribution in Couette flow (which is also called generalized Couette flow) with an applied pressure gradient which is obtained in the following form as attached, where u, V, ∂P/∂x, and h represent fluid velocity, upper plate velocity, pressure gradient, and distance between parallel plates, respectively. Also, u* , y* , and P* represent dimensionless velocity, dimensionless distance between the plates, and dimensionless pressure gradient, respectively. (a) Explain why the velocity distribution is a superposition of Couette flow with a linear velocity distribution and Poiseuille flow with a parabolic velocity distribution. (b) Show that if P*>2, backflow begins at the lower wall and it never occurs at the upper wall. Plot u* versus y* for this situation. (c) Find the position and magnitude of maximum dimensionless velocity.
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