Cavitation Number

Overview

The cavitation number ($Ca$) predicts the onset of cavitation in fluid systems. When the local pressure drops below the vapor pressure, cavitation bubbles form.

Variables

Symbol	Description	Unit
$Ca$	Cavitation number	—
$P$	Local static pressure	Pa
$P_v$	Vapor pressure	Pa
$\rho$	Fluid density	kg/m³
$v$	Flow velocity	m/s

Formula

$Ca = \frac{P - P_v}{\frac{1}{2}\rho v^2}$

Calculator

Notes

• Results are approximate and should be verified for critical applications
• Input values should be within reasonable engineering ranges

Relationship to Euler Number

The Cavitation Number is a specialized form of the Euler Number (Eu), which is a dimensionless number used in fluid dynamics to describe the relationship between pressure forces and inertial forces.

Core Formula

The Cavitation Number (σ) is defined as:

$\sigma = \frac{p_r - p_v}{\frac{1}{2} \rho v^2}$

Where:

• $p_r$ = Reference pressure (Pa)
• $p_v$ = Vapor pressure of the fluid (Pa)
• $\rho$ = Density of the fluid (kg/m³)
• $v$ = Velocity of the fluid (m/s)

Practical Cavitation Prevention

To mitigate cavitation in a fluid system, the following engineering measures are commonly applied:

• Avoid low pressures and pressurize supply tanks if necessary.
• Reduce the fluid temperature.
• Use larger suction pipe diameters to reduce minor losses.
• Use cavitation-resistant materials or coatings.
• Introduce small amounts of air to the suction system to potentially reduce cavitation damage.
• Maintain the available Net Positive Suction Head (NPSH) well above the required NPSH.

Interpreting the Cavitation Number

The Cavitation Number (σ) indicates the proximity of a fluid system to cavitation conditions. The value serves as a key diagnostic parameter in hydraulic system design.

Condition	Interpretation
σ >> 0	System operating well above vapor pressure; cavitation unlikely
σ → 0	Local pressures approaching vapor pressure; cavitation risk increases
σ < 0	Local pressures below vapor pressure; cavitation is occurring

Physical Significance

The Cavitation Number compares the pressure margin above vapor pressure (numerator) to the dynamic pressure of the flowing fluid (denominator). A higher σ value indicates a larger safety margin against cavitation, while a lower value signals the system is closer to or within the cavitation regime.

When local static pressure drops below the fluid's vapor pressure ($p_v$), vapor bubbles form. These bubbles collapse violently upon entering higher-pressure regions downstream, causing erosion, noise, and performance degradation in pumps, propellers, and valves.

Typical Applications

• Pump design: Ensuring adequate inlet pressure to prevent suction-side cavitation
• Propeller analysis: Predicting cavitation onset on marine propellers at various speeds
• Valve sizing: Verifying that pressure drops across throttling valves do not trigger cavitation
• Hydraulic turbines: Maintaining appropriate draft tube pressures during operation

Cavitation Number Formula

The Cavitation Number (σ) is a dimensionless parameter used to predict the potential for cavitation in a flowing fluid. It is defined by the following relationship:

$$\sigma = \frac{p_r - p_v}{\frac{1}{2} \rho v^2}$$

Where:

• $p_r$ is the reference pressure (Pa)
• $p_v$ is the vapor pressure of the fluid (Pa)
• $\rho$ is the density of the fluid (kg/m³)
• $v$ is the velocity of the fluid (m/s)

Cavitation Prevention Strategies

To mitigate or prevent cavitation, consider the following engineering approaches:

• Pressurize supply tanks to avoid low-pressure conditions.
• Reduce the fluid temperature.
• Use larger suction pipe diameters to minimize minor losses.
• Employ cavitation-resistant materials or coatings.
• Introduce small amounts of air into the suction system, which may reduce cavitation damage.
• Ensure the available Net Positive Suction Head (NPSH) is well above the required NPSH.

References

• Original Source