# A Density of a perfect fluid

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1. May 31, 2018

### 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.

2. May 31, 2018

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

3. May 31, 2018

### 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/o...velopment/195068-r-constant-perfet-fluid.html

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

4. Jun 1, 2018

### dRic2

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.