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Question 11.6: In the channel flow of a constant density, constant viscosity...

In the channel flow of a constant density, constant viscosity fluid shown in Figure 11.5, suppose the complete description of the flow is given in Cartesian coordinates by the velocity field u = {[h²(p1 − p2)]/2µL}[1−(y/h)²], v = 0, and w = 0, and the pressure field p(x) = p1 + [(p2 − p1)/L](x − x1). Here p1 and p2 are the pressures at the indicated locations, and the slight hydrostatic variation in pressure across the channel has been ignored. Show that this flow satisfies the constant density, constant viscosity Navier–Stokes equations in Cartesian coordinates, with the body force neglected.

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