# Relationship between velocity and pressure drop

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 April 16, 2007, 18:44 Relationship between velocity and pressure drop #1 harry Guest   Posts: n/a Hi, guys Suppose that velocity field is available in a domain divided with polyhedral meshes, I want to calculate pressure drop in each polyhedron according the existing velocity profile. Is there any relation/formula available? I would appreciate your suggestion. Regards, Harry yuhehuan likes this.

 April 17, 2007, 02:36 Re: Relationship between velocity and pressure dro #2 Rami Guest   Posts: n/a Just a thought (I had never tried it myself). If the velocity field is known, you can isolate grad(p) in the Navier-Stokes equation and explicitly calculate it by numerical differentiation. In this way you may get the local value of grad(p) at any point. If then you wish to get a pressure drop in a certain direction, you can integrate grad(p) along a path.

 April 17, 2007, 02:39 Re: Relationship between velocity and pressure dro #3 Harry Guest   Posts: n/a I think this way costs too much calculations.

 April 17, 2007, 03:08 Re: Relationship between velocity and pressure dro #4 anon Guest   Posts: n/a I see 'Harry' is having fun again

 April 17, 2007, 04:19 Re: Relationship between velocity and pressure dro #5 Jonas Larsson Guest   Posts: n/a As long as you losses are not significant so that your total pressure can be assumed constant it should be a fairly simple operation to calculate grad(p) from a known velocity field. You will of course have to specify the absolute pressure in one point, but then the velocity field should give you the pressure in the whole field. If total pressure is not constant you need more information than just the velocity field to compute the static pressure.

 April 17, 2007, 06:36 Re: Relationship between velocity and pressure dro #6 Trinity Guest   Posts: n/a I have never tried this, but I think if you write the NS equations for a control volume, you can get the p at each point directly from the known velocity field. at worst you will have to invert a matrix for p. this way errors from differentiation and integration can be avoided. Also you ensure local conservation of momentum.

 April 17, 2007, 09:52 Re: Relationship between velocity and pressure dro #7 andy Guest   Posts: n/a If the flow is incompressible then if you know the velocity field you know the pressure field apart for the constant background pressure. Taking the divergence of the momentum equation and solving the resulting Poisson equation should give you something that is consistent with your differencing. If the flow is compressible then you would also need to know the other thermodynamic property and, probably, the value of pressure and/or the fluid state at the boundary.

 April 17, 2007, 18:19 Re: Relationship between velocity and pressure dro #8 Harry Guest   Posts: n/a Thanks. In fact, according to manuals of Fluent/CFX, I guess there should some formula to describe this matter. Here is the reason. Sometimes, pressure field is bad, but velocity seems normal. this inevitably happens in the solution of a transient multiphase flow. In such case, we'd better use velocity to calculate particle forces associated with pressure drop,or the robustness of code would be extremely week. You can check the related formation in Fluent/CFX in the part about DPM model (discrete particle model), especially pressure gradient force model. I would appreciate your further comment.

 April 19, 2007, 01:16 To andy #9 Harry Guest   Posts: n/a the possion equation preserves the same form in all situations for incompressible flow, is it right?

 April 19, 2007, 07:51 Re: To andy #10 andy Guest   Posts: n/a I do not understand your question but since you are performing multiphase simulations I am not sure it is answerable without understanding the details of what is being done.

 April 19, 2007, 18:06 Re: To andy #11 Harry Guest   Posts: n/a Hi,andy Is it possible for me to contact you by email as I need write some formula to elucidate this problem. Regards, Harry

 April 22, 2007, 10:57 Re: To andy #12 andy Guest   Posts: n/a Sorry but no. I am just chatting on a CFD forum when taking a break.

 April 22, 2007, 16:22 Re: To andy #13 Harry Guest   Posts: n/a it's ok. I have found the answer in a paper. It is a little complicated. the pressure drop can be related to fluid acceleration.

 May 8, 2007, 06:39 Re: Relationship between velocity and pressure dro #14 Harold Guest   Posts: n/a pls show a mathematical relationship between pressure and velocity

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