Cole equation of state: Difference between revisions

From SklogWiki
Jump to navigation Jump to search
m (minor syntax)
(Added ref and a link to Tait EOS)
Line 1: Line 1:
The '''Cole equation of state''' <ref>R. H. Cole "Underwater Explosions", Princeton University Press (1948) ISBN 9780691069227</ref><ref>
The '''Cole equation of state'''
G. K. Batchelor "An introduction to fluid mechanics", Cambridge University Press (1974) ISBN  0521663962</ref>
<ref>[http://www.archive.org/details/underwaterexplos00cole Robert H Cole "Underwater explosions", Princeton University Press, Princeton (1948)]</ref><ref>G. K. Batchelor "An introduction to fluid mechanics", Cambridge University Press (1974) ISBN  0521663962</ref><ref>[http://www.archive.org/details/supersonicflowsh00cour 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)]</ref>
has the form
has the form


Line 29: Line 29:
\frac{\rho-\rho_0}{\rho_0}
\frac{\rho-\rho_0}{\rho_0}
  \right]</math>
  \right]</math>
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).





Revision as of 11:55, 5 March 2015

The Cole equation of state [1][2][3] has the form

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

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 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).


References