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# 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 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

## Related Topics

• ### Fluid Mechanics

The study of fluids - liquids and gases. Involving velocity, pressure, density and temperature as functions of space and time.

## Related Documents

• ### Bulk Modulus and Fluid Elasticities

Introduction to - and definition of - Bulk Modulus Elasticity commonly used to characterize the compressibility of fluids.
• ### Density vs. Specific Weight and Specific Gravity

An introduction to density, specific weight and specific gravity.
• ### Mach Number

An introduction to the Mach Number.

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## Citation

• The Engineering ToolBox (2004). Cauchy Number. [online] Available at: https://www.engineeringtoolbox.com/cauchy-number-d_580.html [Accessed Day Month Year].

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10.2.10