Chapter 5, Problem 66P

Consider a steady, laminar, fully developed, incompressible flow between two infinite plates, as shown. The flow is due to the motion of the left plate as well a pressure gradient that is applied in the y direction. Given the conditions that $\stackrel{\to }{V}\ne \stackrel{\to }{V}(z),w=0$, and that gravity points in the negative y direction, prove that u = 0 and that the pressure gradient in the y direction must be constant.

P5.66