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, where is the specific heat capacity ratio and is the fluid pressure. If the fluid obeys the ideal gas law, we have
- ,
where
- = speed of sound, (SI units: m/s)
- = characteristic gas constant, (SI units: J/(kg K) )
- = temperature, (SI units: K)
Substituting K (K_s) in the equation for yields
- .
Thus, the Cauchy number is square of the Mach number for isentropic flow of a perfect gas.
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