# Cauchy Number

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.

The Cauchy number provides a measure of the importance of viscous effects compared to inertial effects in a fluid flow.  It helps determine the behavior of the flow, such as whether it is dominated by viscous forces (low Cauchy number) or inertial forces (high Cauchy number).

## Cauchy Number formula

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

### Cauchy Number - Solve for Ca

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

 velocity, v density, p bulk modulus elasticity, B

### Cauchy Number - Solve for v

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

 Cauchy Number, Ca bulk modulus elasticity, B density, p

### Cauchy Number - Solve for p

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

 Cauchy Number, Ca bulk modulus elasticity, B velocity, v

### Cauchy Number - Solve for B

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

 velocity, v density, p Cauchy Number, Ca

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