0

I've established a relationship between the upper horizontal boundary layer $U$ and pressure gradient $G$ where $\mu$ is dynamic viscosity and h is the height of the pipe the fluid is travelling through

$$U=\frac {Gh^2} {6\mu}$$

And I'm now asked to sketch the velocity profile... apparently its a parabola from $y=0$ to $y=h$ but h is a constant, so $U$ is a constant, so I don't understand why it varies depending on $y$

If anyone could clear up why the velocity profile for this is what it is, I'd be very grateful.

Thank in a advance

John Doe
  • 14,545
Doug
  • 77
  • If your expression doesn't vary with $y$ then it is incorrect, you might have to add some more details. – David Nov 09 '15 at 00:32
  • 1
    What is your physical case? Because i dont understand what you mean by 'upper horizontal boundary layer $U$'. Do you have a fluid in a pipe with a pressure gradient applied between in- & outlet (Hagen-Poiseuille flow? Or is there also a velocity at one (or both) walls (Couette flow)? How did you determine your relationship if you 'apparently' don't know it's a parabola? It seems to me this is required knowledge to derive your relationship. – nluigi Nov 09 '15 at 10:59
  • A constant pressure gradient G, drives a viscous fluid through a pipe, with the upper boundary of the pipe at $y=h$ moving at velocity $U$ in the x-direcrion. The lower boundary at $y=0$ is fixed. $\mu$ is dynamic viscosity in my relationship. – Doug Nov 09 '15 at 11:02

0 Answers0