Cauchy Number

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The Cauchy number (Ca) is a dimensionless parameter used in fluid mechanics to characterize the relative importance of inertial forces to hydrostatic forces in a fluid flow situation. It’s named after the French mathematician Augustin-Louis Cauchy.

Cauchy number is proportional to { (inertial force) / (compressibility force) } and is used in momentum transfer in general and compressible flow calculations in particular. It is normally defined in the following form above

Where:
Eb	=	bulk modulus of fluid
gc	=	Dimensional constant
rho	=	Density
V	=	Velocity

The Cauchy number helps determine whether inertial effects or pressure effects dominate the behavior of the fluid flow. Depending on the value of the Cauchy number, different flow regimes can be identified:

If Ca ≪ 1, hydrostatic forces dominate over inertial forces, and the flow behavior is primarily determined by pressure gradients. This typically occurs in situations where the fluid velocity is low relative to the pressure changes, such as in slow-moving or quiescent flows.
If Ca ≫ 1, inertial forces dominate over hydrostatic forces, and the flow behavior is primarily determined by the fluid velocity. This typically occurs in situations where the fluid velocity is high relative to the pressure changes, such as in high-speed flows or turbulent flows.

The Cauchy number is commonly used in the analysis of fluid flow problems, particularly in the study of multiphase flows, free-surface flows, and fluid-structure interactions. It helps engineers and scientists understand and predict the behavior of fluids under different flow conditions.