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Cauchy Number

Introduction to the Cauchy Number.

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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 v2 / E                        (1)


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)


M = Mach Number

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