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 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