# problem on Laminar flow in a pipe

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March 19, 2012, 14:44
problem on Laminar flow in a pipe
#1
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Goutam Saha
Join Date: Dec 2011
Location: UK
Posts: 131
Rep Power: 7
Since I have consider the same velocity (measured from the formula
Vc { 1 - (r/R)^2 } at the inlet and outlet Bcs, I am expecting a linear profile for velocity magnitude but I am getting a parabolic profile? Is this correct? Problem description is given below.

Fully developed Laminar flow in a pipe: (Solver: simpleFoam)

L = 1.2 m, R = 0.0295 m, D = 2R = 0.0519 m,
Re = 100, neu = 1.004 E -6 m^2/s.

Entrance length, Le = 0.3114 m, Avg Velocity, Vc = 0.001934 m/s.
At r = 0, Vmax = 2*Vc = 0.0038682 m/s.

Initial Condition: velocity = (0 0 0), Bcs: Inlet and outlet velocity, V = Vmax and wall velocity = (0 0 0).
Initial Condition for p = 0, Boundary condition for p: Inlet and Wall: Pressure gradient is zero, outlet : p = 0.

Thanks
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Last edited by Goutam; March 20, 2012 at 06:02.

 March 19, 2012, 18:58 #2 Senior Member     Kyle Mooney Join Date: Jul 2009 Location: Amherst, MA USA - San Diego, CA USA Posts: 321 Rep Power: 11 The steady state velocity profile for a laminar flow in a pipe is parabolic. Unless I'm confused it looks as though you are in fact getting the correct solution.

 March 20, 2012, 06:13 #3 Senior Member   Goutam Saha Join Date: Dec 2011 Location: UK Posts: 131 Rep Power: 7 Since, I have used parabolic velocity at the both ends (inlet and outlet) then the velocity profile should be a linear profile. Am I right?

March 20, 2012, 10:37
#4
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Kyle Mooney
Join Date: Jul 2009
Location: Amherst, MA USA - San Diego, CA USA
Posts: 321
Rep Power: 11
Quote:
 Originally Posted by Goutam Since, I have used parabolic velocity at the both ends (inlet and outlet) then the velocity profile should be a linear profile. Am I right?
What do you mean by "linear profile"? The pressure should decrease linearly from inlet to outlet if that's what you mean. Due to continuity, however, the velocity profile will not change.

 March 20, 2012, 11:13 #5 Senior Member   Goutam Saha Join Date: Dec 2011 Location: UK Posts: 131 Rep Power: 7 Sorry, I got the error. my result was correct but I want to use parabolic BC but I have used uniform BC. I want to use U(x) = 2U_0 [ 1- (x/r)^2 ]. This is the problem.

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