Cauchy Number

An introduction to and a definition of the Cauchy Number

The Cauchy Number is a dimensionless value useful for analyzing fluid flow dynamics problems where compressibility is a significant factor.

The Cauchy Number is the ratio between inertial and the compressibility force in a flow and can be expressed as

C = ρ v² / E (1)

where

C = Cauchy Number

ρ = density (kg/m³)

v = flow velocity (m/s)

E = bulk modulus elasticity (N/m²)

The bulk modulus elasticity has the dimension pressure and is commonly used to characterize the compressibility of a fluid.

The Cauchy Number is the square of the Mach Number

M² = C (3)

where

M = Mach Number