# A Density of a perfect fluid

#### rasikaj

During CFD modeling of a gas-solid flow, flow of solid was modelled as a perfect fluid using OpenFOAM.

The density of the perfect fluid is calculated using the following equation as given in the documentation.

ρ = P/RT + ρo , where ρo is the density at T = 0 kelvin, ρ is the density of the perfect fluid at pressure P (Pa) and temperature T (K). There is no other mention about this in the documentation of OpenFOAM.

My struggle is to calculate the R (J kg -1 K-1) for the solid. In the OpenFOAM tutorials for the normal conditions of water R = 3000 with ρo = 1027 kg m-3.

Also for mercury
R = 6818 with ρo = 13529 kg m-3.

I tried to plot the ρ with P/T for water and the linear equation was

ρ = 0.4321 (P/T) + 848.78, where R = 2.314

So could anyone please tell me how to calculate R for a certain fluid or solid. I have searched the internet for days and still didn't find any reference to this equation.

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Gold Member
I'm still tryng to figure out how you are applying the ideal gas law to solids and liquids.

#### rasikaj

Actually this is the equation, OpenFOAM has mentioned in their user guide. Not my idea. I thought this is some physics that I cannot understand.

You can see the equation in page U-203 of their user guide. Here is the link.
http://foam.sourceforge.net/docs/Guides-a4/OpenFOAMUserGuide-A4.pdf

I have seen the same problem asked in cfd-online.com, but with no answers

https://www.cfd-online.com/Forums/openfoam-programming-development/195068-r-constant-perfet-fluid.html

Thanks for your comment anyway. I would be grateful if you could give me a solution.

#### dRic2

Gold Member
I have no idea too, but the only thing that you can do -i think- is to look in some database for $\rho_0$ and $\rho$ for the solid you are interested in and then calculate an approximation of R.

"Density of a perfect fluid"

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