# Cauchy Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Cauchy number, abbreviated as Ca, a dimensionless number expressing the ratio of inertial force to compressibility force in a flow.  When the compressibility is important the elastic forces must be considered along with inertial forces.

### Cauchy Number FORMULA

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

Where:

$$\large{ Ca }$$ = Cauchy number

$$\large{ B }$$ = bulk modulus elasticity

$$\large{ \rho }$$  (Greek symbol rho) = density

$$\large{ v }$$ = velocity of the flow

Solve for:

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

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

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

## Cauchy Number CALCULATOR

Tags: Equations for Force