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Effects of gravity in pipe - pressure distribution

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Old   June 29, 2001, 04:14
Default Effects of gravity in pipe - pressure distribution
Anthony Wachs
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Hi everybody,

I am currently simulating fluid-fluid displacement in pipes. As density ratio of the two fluids is a key parameter in this kind of situation (related to buoyancy forces), I first attempted to check how Fluent accounts for gravity.

Let's consider the flow of a single Newtonian fluid in a axisymmetric pipe. A velocity profile, corresponding to parabolic radial distribution is prescribed at the entry and constant radial pressure profile p=0 at the outlet. So it is the simplest problem you can imagine in Fluid Mechanics!! The goal is to obtain the right pressure gradient given by analytical solution.

If there is no gravity, the pressure gradient dp/dz is related to greatest axial velocity umax by :


mu stands for the viscosity, R the radius of the pipe

If gravity is taken into account, for the same flow rate, the pressure gradient dp'/dzis modified by the hydrostatic contribution, and we have :


ro is the density and g=9.81m/s2

What is surprising in Fluent is that the pressure gradient do not change wether gravity is considered or not.

I am now wondering how Fluent include gravity forces in conservation equations ? or how the post-processor plot pressure distribution ?

I studied this simple problem because for fluid-fluid displacement, the pressure distribution along the pipe in the axial direction is correct when viscosity differences between the two fluids is considered (no buoyancy forces), but seems unrealistic for density differences.

Any help or suggestion would be really appreciated

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Old   July 1, 2001, 18:51
Default Re: Effects of gravity in pipe - pressure distribu
Tamer Elsoukkary
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The problem is not from Fluent it is the finite volume method where the pressure and velocity coupling issue appear and the mass equation contain a pressure term (which is the dynamic pressure not the static). Refrence is to computational methods for fluid dynamics by Joel H. Ferziger and Milovan Peric' and to my thesis A finite volume model for the study of surface-Induced motions university of western ontario.

If you plug the gravity term it would be the highest order of magnitude in the momentum equation where everything else would be negligible with respect to gravity. To solve this problem gravity term is in cluded as deference effect between two levels instead of rho*g*h Also the time step have to be really small. I think in fluent these are taken care of automatically. Which should give the same solution if you looked at the dynamic pressure in your postprocessing not the totla pressure If you interested I can send you that section of my thesis discussing the issure let me know by e-mail
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Old   July 25, 2001, 07:07
Default Re: Effects of gravity in pipe - pressure distribu
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Dear Tamer

I am modeling the flow of molten steel in a tundish. It has a velocity inlet boundary condition (-y direction height) and pressure outlet again in (-y direction). Density of molten steel is 6997 kg/m3 at a temp of 1823 deg.K. The flow takes place due to gravity. Do I have to apecify the gravity direction. I found the message posted by you interesting. Could you please send me the section of thesis at my email add. Please see to it that the file is smaller than 2MB. I have a restriction on my mailbox. You can split the same and send it. Please send it at or at

Thanks for the same Regards Rajeev
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