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Parabolic velocity profile in a rectangular channel

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Old   October 26, 2013, 10:12
Default Parabolic velocity profile in a rectangular channel
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Nithish
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We are trying to obtain a parabolic velocity profile in a rectangular channel subjected to laminar flow,but we are unable to obtain the desired velocity variation instead we are getting a maximum value through out the y axis except the edges instead of obtaining the maximum value at the centre with the variations along the axis.Attached are the files for velocity and pressure.we request help regarding the check for the boundary conditions and clarifications on them.And also please check the velocity plotted along the y axis.





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Old   October 27, 2013, 17:31
Default Test or BC
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nithishgupta,

Are you seeking the duct solution as an Open FOAM test or to serve as an inlet BC in a different problem? If it's the latter, note there's a closed-form solution (though it's an infinite series solution) for fully-developed laminar flow. I don't have it with me, but can provide it in a day or two.

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Old   October 28, 2013, 17:35
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That would be really helpful for me if you could post it.
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Old   October 30, 2013, 06:39
Default Analytical solution for rectangular ducts...and more...
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nithishgupta,

I was unhappy to learn that some of the CD-ROMs I had burned prior to leaving graduate school are no longer readable. My loss is not necessarily yours, though. I was able to find the closed-form solution posted on the internet at the following link.

http://www.engineering.uiowa.edu/~me...t1-updated.pdf

Expressions for velocity profile and flow rate in rectangular ducts can be found on page 13, eqns (3-48) and (3-49), respectively. You can use (3-49) in conjunction with your desired flow rate to determine the required pressure gradient to use in (3-48) and compute the velocity profile.

I hope this helps.

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