1. Fluid flows in the negative y-direction between two infinite vertical plates as shown in the figure below. The plates are fixed and separated by some distance L. Assume incompressible, Newtonian steady, 1D, unidirectional, fully developed, laminar flow. Friction causes pressure loss in the direction of flow. Gravity acts in the negative y-direction.
a) Show that dP/dy is equal to a constant
b) Solve the Navier-Stokes equation to find the general solution of v(x)
c) Use boundary conditions to find the exact solutions of v(x) for the case where each of the plates are fixed.
d) Find the exact solution v(x) again, this time for the case where the left plate is moving at speed of U and the right plate is moving at speed of -U.
e) Show an accurate plot of the velocity profile across the plates for both cases c and d.
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