Axial velocity for fully developed flow in a pipe

[Quadruple Bypass]

Homework Statement

The book I am reading just randomly states that the axial velocity for a fully developed laminar flow in a pipe is vx=2*u*(1-r^2/ro^2). i am not sure where this comes from. does come from the navier stokes equations?

also, is there a book that lists other types of axial velocities for flows in a duct with different width and height ratios?

Homework Equations

navier stokes?

The Attempt at a Solution

 

[minger]

I think you would be wise to do a google search Hagen-Poisoulle flows. Flows like these are pressure driven, essentially reducing to pipe flow.

That equation looks like the velocity at a certain radius, given the maximum velocity u. That is, when the radius is ro, you get 1-(ro/ro) or 0 -> no flow on the pipe wall.

Also, yes there are analytic solutions for different geometries. I have "Viscous Flow Flow" by White which I believe lists solutions for different geometries.

 

[Quadruple Bypass]

Thanks, ill look up some stuff on Hagen-Poisoulle flows.

Unfortunately i couldn't find any free pdfs of that book from google :(