The Equation of State

The equation of state gives a relationship between the pressure, density and temperature. It can take several different forms depending of the situation being modelled. For example, when considering a uniform incompressible fluid it is simply

$$\rho = \hbox{ constant}.$$ (2.10)

For a perfect gas, it is

$$p = \rho {R} T,$$ (2.11)

where ${R} = 8.3 \times 10^{3}$ is the gas constant, so that the pressure proportional to both the density and temperature. The temperature must then be given by an energy equation (or specified as a constant).