Photos Attached: Consider the flow of a Newtonian fluid down an inclined plane a

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Consider the flow of a Newtonian fluid down an inclined plane as shown in the figure below. The eventual goal is to solve for the velocity field induced by the gravitational forces. Choose the reference frame as shown in the figure. The flow at the bottom of the channel so the liquid is in contact with the bottom wall. The top layer of the fluid is exposed to air. The appropriate boundary conditions are therefore: (i) no-slip at the bottom (y = 0) and (ii) stress-free at the top (so Txy,|y=h, = 0 dux/dy = 0). Making appropriate assumptions - which must be stated clearly - solve the Navier Stokes equations to obtain the exact analytical expression for steady flow down an inclined plane.

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