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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
For isentropic processes, the Cauchy number may be expressed in terms of Mach number. The isentropic bulk modulus K_s = \gamma p, where \gamma is the specific heat capacity ratio and p is the fluid pressure. If the fluid obeys the ideal gas law, we have
Substituting K (K_{s}) in the equation for Ca yields
Thus, the Cauchy number is square of the Mach number for isentropic flow of a perfect gas.
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