# Cauchy Number

Written by Jerry Ratzlaff on . Posted in Dimensionless Numbers

Cauchy number, abbreviated as Ca, a dimensionless number, is 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:

 Units English Metric $$\large{ Ca }$$ = Cauchy number $$\large{dimensionless}$$ $$\large{ B }$$ = bulk modulus elasticity $$\large{\frac{lbm}{in^2}}$$ $$\large{Pa}$$ $$\large{ \rho }$$  (Greek symbol rho) = density $$\large{\frac{lbm}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$ $$\large{ v }$$ = velocity of flow $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$