Cole equation of state
In it, is a reference density around which the density varies is the adiabatic index and is a pressure parameter.
Usually, the equation is used to model a nearly incompressible system. In this case, the exponent is often set to a value of 7, and is large, in the following sense. The fluctuations of the density are related to the speed of sound as
Therefore, if , the relative density fluctuations will be of about 0.01.
If the fluctuations in the density are indeed small, the equation of state may be approximated by the simpler: