# Cauchy Number

## Introduction to 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 the *inertial force* and the *compressibility force* in a flow and can be expressed as

C = ρ v^{2}/ E (1)

where

C = Cauchy Number

ρ = density (kg/m^{3})

v = flow velocity (m/s)

E = bulk modulus elasticity (N/m^{2})

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

M^{2}= C (3)

where

M = Mach Number

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