CFD Online Logo CFD Online URL
Home > Forums > General Forums > Main CFD Forum

Pipe flow analytical solution

Register Blogs Members List Search Today's Posts Mark Forums Read

Like Tree3Likes
  • 1 Post By sbaffini
  • 1 Post By FMDenaro
  • 1 Post By agd

LinkBack Thread Tools Search this Thread Display Modes
Old   February 2, 2020, 13:42
Default Pipe flow analytical solution
New Member
Join Date: Feb 2020
Location: Barcelona
Posts: 19
Rep Power: 6
cmoreno98 is on a distinguished road
Hello everybody, this is my first post in this forum

I am studying the flow of water along a tiny pipe (capillary tube). The data of the problem is the following:

- Length of the pipe: 10 mm
- Diameter of the pipe: 1 mm
- Inlet velocity: 0.5 m/s
- Outlet pressure: ambient pressure
- Reynolds number: 500 (laminar)
- No-slip condition at the wall

I ran a simulation using OpenFoam (SimpleFoam solver) and I got the next results:

This is the horizontal velocity distribution of the flow (cut in the XZ plane). As it can be seen, the inlet velocity (at the center of the pipe) is 0.5 m/s and the outlet velocity is approximately 0.88 m/s.
What I want to do is to compare the numerical solution with the analytical solution, that is, calculate the outlet velocity by hand. Is there a formula that provides the outlet velocity as a function of the length, the diameter, etc?

I also obtained the gauge pressure distribution:

I know that this is a classical fluid mechanics problem (Poiseuille flow) but when I studied it in class we considered that the pipe was infinitely long and the derivatives on the x axis were 0. Here I cannot assume that.

Can somebody help me? Thank you very much,

cmoreno98 is offline   Reply With Quote

Old   February 3, 2020, 04:42
Senior Member
sbaffini's Avatar
Paolo Lampitella
Join Date: Mar 2009
Location: Italy
Posts: 2,152
Blog Entries: 29
Rep Power: 39
sbaffini will become famous soon enoughsbaffini will become famous soon enough
Send a message via Skype™ to sbaffini
To the best of my knowledge there is no such analytical solution, only for the fully developed flow. There are, instead, formulas to estimates the length necessary to achieve the fully developed condition.

However, from your pressure distribution, the last 10%-20% of the pipe might be close enough to the fully developed condition (note that, if an analytical solution existed, it would tell you that the fully developed condition, for this case, would be reached only for x->Inf).

What you could do to double check this, besides actually comparing the outlet profile with the analytical, fully developed one, is to set up the case to use periodicity in the streamwise direction, so that you fully replicate the conditions underlying the analytical solution.

It really depends from what you want to do, testing OF on a case as similar as possible, or obtaining that very specific analytical solution (which I don't think it actually exists).
aero_head likes this.
sbaffini is offline   Reply With Quote

Old   February 3, 2020, 06:55
Senior Member
Filippo Maria Denaro
Join Date: Jul 2010
Posts: 6,765
Rep Power: 71
FMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura aboutFMDenaro has a spectacular aura about
In line of principle, if we start from the problem of two parallel flat plates, this 2D problem can be considered in the framework of two spatially evolving boundary layers (hence you know the analytical Blasius solution) that merge at a certain distance x=Xm producing the Poiseulle solution.
However, in the case of a pipe flow I think one could consider an extension of the theory for a boundary layer in (r,z) plane with axisymmetric condition. But I never tried to develop such a comparison.

I suppose that, given the Re number, you can also simply check you get a parabolic velocity profile after the merging lenght is reached.
aero_head likes this.
FMDenaro is online now   Reply With Quote

Old   February 3, 2020, 08:17
Senior Member
Join Date: Jul 2009
Posts: 351
Rep Power: 18
agd is on a distinguished road
While I agree with the recommendations of the previous posters, I would not worry about the velocity profile until you make sure that you are satisfying mass conservation. It may seem trivial, but it is one piece of the physics where you know the answer. I've seen lots of simulations over the years where the velocity profiles look reasonable but the user didn't conserve mass.
aero_head likes this.
agd is offline   Reply With Quote

Old   May 8, 2021, 13:10
New Member
Join Date: Apr 2021
Posts: 21
Rep Power: 5
carolee is on a distinguished road
Hello, I need your help
I'm new to openfoam, I'm doing my graduation project, I did the same as charlos, I made a tube with diameter 2.5cm and length 10cm, the flow must be laminar with velocity 0.5 m / s so I use the simpleFoam solver but the results look wrong, the velocity is almost the same in all tube positions (I put a picture), I have to get the same result as carlos and the speedprofile must be parabolic, I didn't understand where the problem is, please help me
carolee is offline   Reply With Quote


analytical solution, pipe flow, poiseuille flow

Thread Tools Search this Thread
Search this Thread:

Advanced Search
Display Modes

Posting Rules
You may not post new threads
You may not post replies
You may not post attachments
You may not edit your posts

BB code is On
Smilies are On
[IMG] code is On
HTML code is Off
Trackbacks are Off
Pingbacks are On
Refbacks are On

Similar Threads
Thread Thread Starter Forum Replies Last Post
Review: Reversed flow CRT FLUENT 1 May 7, 2018 05:36
High speed compressible flow through pipe Munni Main CFD Forum 6 December 7, 2015 11:33
Analytical Solution for a Free Surface Flow Ferreira, VG Main CFD Forum 0 February 25, 2007 04:56
Could anybody help me see this error and give help liugx212 OpenFOAM Running, Solving & CFD 3 January 4, 2006 18:07
Strange Solution for a simple pipe flow!! shekharc Main CFD Forum 4 May 9, 2005 09:21

All times are GMT -4. The time now is 06:59.