Cauchy number

The Cauchy number (Ca) is a dimensionless number in continuum mechanics used in the study of compressible flows. It is named after the French mathematician Augustin Louis Cauchy. When the compressibility is important the elastic forces must be considered along with inertial forces for dynamic similarity. Thus, the Cauchy Number is defined as the ratio between inertial and the compressibility force (elastic force) in a flow and can be expressed as
where
Relation between Cauchy number and Mach number.
For isentropic processes, the Cauchy number may be expressed in terms of Mach number. The isentropic bulk modulus formula_3, where formula_4 is the specific heat capacity ratio and "p" is the fluid pressure.
If the fluid obeys the ideal gas law, we have
where
Substituting "K" ("Ks") in the equation for Ca yields
Thus, the Cauchy number is square of the Mach number for isentropic flow of a perfect gas.