Chapter 5, Problem 68P

Consider a steady, laminar, fully developed incompressible flow between two infinite parallel plates as shown. The flow is due to a pressure gradient applied in the x direction. Given that ${\stackrel{\to }{V}}_1\stackrel{\to }{V}(z),w=0$ and that gravity points in the negative y direction, prove that υ = 0 and that the pressure gradients in the x and y directions are constant.