#jsDisabledContent { display:none; } My Account |  Register |  Help

# Cauchy number

Article Id: WHEBN0015346623
Reproduction Date:

 Title: Cauchy number Author: World Heritage Encyclopedia Language: English Subject: Collection: Publisher: World Heritage Encyclopedia Publication Date:

### Cauchy number

The Cauchy number (Ca) is a dimensionless number in continuum mechanics used in the study of compressible flows. It is named after the French mathematician Augustin Louis Cauchy. When the compressibility is important the elastic forces must be considered along with inertial forces for dynamic similarity. Thus, the Cauchy Number is defined as the ratio between inertial and the compressibility force (elastic force) in a flow and can be expressed as

\mathrm{Ca} = \frac{\rho u^2}{K},

where

\rho = density of fluid, (SI units: kg/m3)
u = local flow velocity, (SI units: m/s)
K = bulk modulus of elasticity, (SI units: Pa)

## Relation between Cauchy number and Mach number

For isentropic processes, the Cauchy number may be expressed in terms of Mach number. The isentropic bulk modulus K_s = \gamma p, where \gamma is the specific heat capacity ratio and p is the fluid pressure. If the fluid obeys the ideal gas law, we have

K_s = \gamma p = \gamma \rho R T = \,\rho a^2,

where

a = \sqrt{\gamma RT} = speed of sound, (SI units: m/s)
R = characteristic gas constant, (SI units: J/(kg K) )
T = temperature, (SI units: K)

Substituting K (Ks) in the equation for Ca yields

\mathrm{Ca} = \frac{u^2}{a^2} = \mathrm{M}^2.

Thus, the Cauchy number is square of the Mach number for isentropic flow of a perfect gas.

## References

This article was sourced from Creative Commons Attribution-ShareAlike License; additional terms may apply. World Heritage Encyclopedia content is assembled from numerous content providers, Open Access Publishing, and in compliance with The Fair Access to Science and Technology Research Act (FASTR), Wikimedia Foundation, Inc., Public Library of Science, The Encyclopedia of Life, Open Book Publishers (OBP), PubMed, U.S. National Library of Medicine, National Center for Biotechnology Information, U.S. National Library of Medicine, National Institutes of Health (NIH), U.S. Department of Health & Human Services, and USA.gov, which sources content from all federal, state, local, tribal, and territorial government publication portals (.gov, .mil, .edu). Funding for USA.gov and content contributors is made possible from the U.S. Congress, E-Government Act of 2002.

Crowd sourced content that is contributed to World Heritage Encyclopedia is peer reviewed and edited by our editorial staff to ensure quality scholarly research articles.