I am trying to solve the well known problem of identifying the velocity profile of a fluid on an inclined plane. The assumptions we know are that the flow is Newtonian, incompressible, with a low reynolds number. I have been following my professor's notes on the problem, but ran into an assumption that I do not understand.
In evaluating Navier Stokes along an axis in line with the incline, we assume that the change in pressure along the incline $$\cfrac{\partial P}{\partial z}$$ is 0, since the flow is gravity driven. I do not understand why it is reasonable for us to make this assumption.
By evaluating the continuity equation, and Navier stokes along the other two axes, we discover that the velocity along the incline does not change (no acceleration). In addition, there is no pressure change out of the page and perpendicular to the incline axis (duh). However, I don't see any mathematical expression that leads to this conclusion.
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