Hi, I've been thinking about the Navier-Stokes equations and trying to build skill in implementing it in various situations. In a particular situation, if I have a fluid flowing down an inclined surface such that it forms a film of finite height which is smaller than the length of flow, there is no applied pressure. So am I allowed to cross off the pressure term in the momentum conservation equation along the direction of flow? In a detailed solution to this problem, our instructor non-dimensionalizes the equation to show that the pressure term goes away. However, I'm wondering, since there is no applied pressure, can't I just cross it off (like Couette flow)? Also, in another problem (the situation is that oil is flowing up an inclined surface submerged in water) the instructor replaces the pressure gradient by the buoyancy force . So in the inclined flow case, am I not allowed to simply replace the pressure term by the hysdrostatic pressure? I think my question boils down to whether the pressure term in the NS equation is an external force or internal property of the fluid.