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 \(\vec{V} eq \vec{V}(z), w=0\), 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.

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N Vo x P5.66