# Cavitation Number

on . Posted in Dimensionless Numbers

Cavitation number, abbreviated Ca, a dimensionless number, expresses the relationship between the difference of a local absolute pressure from the vapor pressure and the kinetic energy per volume.

The cavitation number is used in fluid dynamics to characterize the potential for cavitation to occur in a flowing fluid.  Cavitation refers to the formation and subsequent collapse of vapor bubbles in a liquid due to a decrease in pressure below the vapor pressure of the liquid.   The cavitation number represents the ratio of the pressure drop to the kinetic energy in the fluid flow.  It provides a measure of the relative importance of the pressure change compared to the fluid's kinetic energy.  When the cavitation number is less than 1, the fluid flow is considered to be at risk of cavitation.

If the cavitation number is close to or below 1, the fluid pressure can drop below the vapor pressure, causing the formation of vapor bubbles.  These bubbles can subsequently collapse violently, leading to damage to equipment and undesirable effects such as noise, erosion, and loss of efficiency in hydraulic systems, pumps, propellers, and other fluid flow applications.

By analyzing the cavitation number, engineers and researchers can assess and design systems to minimize the occurrence and impact of cavitation, ensuring the safe and efficient operation of fluid flow devices.

## Cavitation number formula

$$\large{ Ca = \frac{ 2\; \left(p \;-\;p_v \right) }{\rho\; U^2} }$$

### Cavitation Number - Solve for Ca

$$\large{ Ca = \frac{ 2\; \left(p \;-\;p_v \right) }{\rho \; U^2} }$$

 pressure, p vapor pressure, pv density, ρ characteristic velocity, U

### Cavitation Number - Solve for p

$$\large{ p = \frac{ Ca \; \rho \; U^2 }{ 2 } \; + p_v }$$

 cavitation number, Ca density, ρ characteristic velocity, U vapor pressure, pv

### Cavitation Number - Solve for pv

$$\large{ p_v = p - \; \frac{ Ca \; \rho \; U^2 }{ 2 } }$$

 pressure, p cavitation number, Ca density, ρ characteristic velocity, U

### Cavitation Number - Solve for ρ

$$\large{ \rho = \frac{ 2\; \left(p \;-\;p_v \right) }{ Ca \; U^2} }$$

 pressure, p vapor pressure, pv cavitation number, Ca characteristic velocity, U

### Cavitation Number - Solve for U

$$\large{ U = \sqrt{ \frac{ 2\; \left(p \;-\;p_v \right) }{ Ca \; \rho} } }$$

 pressure, p vapor pressure, pv cavitation number, Ca density, ρ

Symbol English Metric
$$\large{ Ca }$$ = Cavitation number $$\large{ dimensionless }$$
$$\large{ p }$$ = local pressure $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ p_v }$$ = vapor pressure of the fluid $$\large{\frac{lbf}{in^2}}$$ $$\large{Pa}$$
$$\large{ \rho }$$  (Greek symbol rho) = density of the fluid $$\large{\frac{lb}{ft^3}}$$ $$\large{\frac{kg}{m^3}}$$
$$\large{ U }$$ = characteristic velocity of the flow $$\large{\frac{ft}{sec}}$$ $$\large{\frac{m}{s}}$$ 