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 about 0.01.
If the fluctuations in the density are indeed small, the equation of state may be approximated by the simpler:
It is quite common that the name "Tait equation of state" is improperly used for this EOS. This perhaps stems for the classic text by Cole calling this equation a "modified Tait equation" (p. 39).
- Robert H Cole "Underwater explosions", Princeton University Press, Princeton (1948)
- G. K. Batchelor "An introduction to ﬂuid mechanics", Cambridge University Press (1974) ISBN 0521663962
- Richard Courant "Supersonic flow and shock waves a manual on the mathematical theory of non-linear wave motion", Courant Institute of Mathematical Sciences, New York University, New York (1944)