# Cauchy Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Cauchy number is a dimensionless number expressing the ratio of inertial force to compressibility force in a flow.

## FORMULA

$$Ca = \frac {v^2 \rho } { B }$$

Where:

$$Ca$$ = Cauchy number

$$v$$ = flow velocity

$$\rho$$ (Greek symbol rho) = density

$$B$$ = bulk modulus elasticity

Solve for:

$$v = \sqrt { \frac {Ca B}{\rho} }$$

$$\rho = \frac {Ca B} { v^2 }$$

$$B = \frac {v^2 \rho} { Ca }$$