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

${\displaystyle \mathrm {Ca} ={\frac {\rho u^{2}}{K}}}$,

where

${\displaystyle \rho }$ = density of fluid, (SI units: kg/m³)

u = local flow velocity, (SI units: m/s)

K = bulk modulus of elasticity, (SI units: Pa)