# How the pressure of a system changes in terms of density?

I am modeling a closed natural circulation loop, filled with water. Some parts of the loop are heated, some are cooled and other are assumed adiabatic. As an effect of heating and cooling the density of water changes and so does the total pressure in the loop. My question is as follows:

Is there a way to calculate the total pressure of the system in terms of, for example, mean density, mean temperature and total volume of the system? For air, the ideal gas equation should be a nice approximation, but it is not applicable for liquids. The problem becomes more complex when the water starts to boil at some point, then it is a two-phase fluid.

I have seen answer to this question What equation of state is needed for liquid states? but it does not help in my case.

• How are you modeling it (i.e., what equations are you using)? – Kyle Kanos Feb 17 '14 at 14:40
• I am using a method described here in the section 'numerical sulution'. – Wojciech Feb 17 '14 at 14:50
• Hmm. A stiffened equation of state (e.g., $p=\left(\gamma-1\right)\rho\varepsilon - \gamma\pi$ with $\pi$ a characteristic parameter of the fluid) may work for this. However, you may also want to investigate multi-fluid models for more information (I am only vaguely familiar with what that is, and not at all knowledgeable about how it works). – Kyle Kanos Feb 17 '14 at 15:20
• @KyleKanos thanks a lot. I'll try to investigate this further in the evening, and if I manage to find trustworthy information, I'll post it here. – Wojciech Feb 17 '14 at 15:24