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Homework Help: Axial velocity for fully developed flow in a pipe

  1. Apr 12, 2010 #1
    1. The problem statement, all variables and given/known data
    The book im 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?

    2. Relevant equations
    navier stokes?

    3. The attempt at a solution
  2. jcsd
  3. Apr 12, 2010 #2


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    Science Advisor

    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.
  4. Apr 12, 2010 #3
    Thanks, ill look up some stuff on Hagen-Poisoulle flows.

    Unfortunately i couldnt find any free pdfs of that book from google :(
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