Difference between revisions of "Cole equation of state"
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Revision as of 15:52, 23 August 2011
The Cole equation of state ^{[1]}^{[2]} can be written, when atmospheric pressure is negligible, has the form
 .
In it, is a reference density around which the density varies is an exponent 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
where is the largest velocity, and is the speed of sound (the ratio is Mach's number). The speed of sound can be seen to be
Therefore, if , the relative density fluctuations will be of about 0.01.