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## Homework Statement

This is not exactly a homework problem. I am trying to review material so that I can tutor it this semester. In the falling film problem, as described in this link: http://www.syvum.com/cgi/online/serve.cgi/eng/fluid/fluid204.html, I am confused why the velocity profile does not depend on z. I understand why there is dependence on the x direction, but do not understand why the fluid is not speeding up as it moves downward toward the earth due to gravity.

## Homework Equations

Final Velocity Profile: v

_{z}(x)=ρgδ

^{2}cosβ[1-(x/δ)

^{2}]/(2μ)

## The Attempt at a Solution

My thought that is perhaps since it is a steady state problem, the fluid shouldn't be speeding up over time, because {accumulation} = {in}-{out} but I am really not sure. I can do the calculations, I just don't understand why gravity does not affect the fluid speed.