Cauchy Number

The Cauchy Number calculator computes the Cauchy Number based on the density of fluid, velocity of flow and the bulk modulus of elasticity.

INSTRUCTIONS: Choose units and enter the following:

• (ρ) Density 

• (V) Flow Velocity 

• (E) Bulk modulus elasticity

Cauchy Number (C): The value is returned as a real number.

The Math / Science

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        

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

C  =M²

where

M = Mach Number