Cavitation number, abbreviated \(Ca\) or \(\sigma\) (Greek symbol sugma), a dimensionless number, expresses the relationship between the difference of a local absolute pressure from the vapor pressure and the kinetic energy per volume.
Cavitation number formula |
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\( Ca \;=\; \dfrac{ p - p_v }{ \dfrac{1}{2} \cdot \rho \cdot v^2 }\) (Cavitation Number) \( p \;=\; \dfrac{1}{2} \cdot Ca \cdot \rho \cdot v^2 + p_v \) \( p_v \;=\; p - \dfrac{1}{2} \cdot Ca \cdot \rho \cdot v^2 \) \( \rho \;=\; \dfrac{ 2\cdot (p - p_v ) }{ Ca \cdot v^2 }\) \( v \;=\; \sqrt{ \dfrac{ 2\cdot (p - p_v ) }{ Ca \cdot \rho } }\) |
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| Symbol | English | Metric |
| \( Ca \) = Cavitation Number | \( dimensionless \) | \( dimensionless \) |
| \( p \) = Local Static Pressure | \(lbf \;/\; in^2\) | \(Pa\) |
| \( p_v \) = Fluid Vapor Pressure at a Given Temperature | \(lbf \;/\; in^2\) | \(Pa\) |
| \( \rho \) (Greek symbol rho) = Fluid Density | \(lb \;/\; ft^3\) | \(kg \;/\; m^3\) |
| \( U \) = Flow Velocity | \(ft \;/\; sec\) | \(m \;/\; s\) |
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.
Cavitation Number Interpretation
Physically, it expresses how close the local static pressure is to the liquid's vapor pressure, relative to the pressure drop the flow's own velocity/acceleration can produce.
High Ca - Large margin above vapor pressure relative to dynamic pressure, cavitation unlikely.
Low Ca (approaching a critical value) - Local pressure minima (e.g., over a hydrofoil suction side, at a valve vena contracta, at a propeller blade tip, in a pump impeller eye) can drop to or below vapor pressure, bubbles nucleate and grow, cavitation onset.
Ca \(\le\) 0 - In a strict sense is not physically meaningful under equilibrium assumptions, since pressure can't go below vapor pressure without the liquid flashing to vapor. Once cavitation is fully established, the cavitation number describing the cavity condition becomes closer to a fixed parameter dependent on cavity length/shape rather than a free-falling number.
Practical / Engineering Significance
Pump and Turbine Design: - Avoiding cavitation at the impeller/runner inlet to prevent efficiency loss, noise, vibration, and erosion damage (pitting) on blades.
Control Valves and Orifices - Predicting choked cavitating flow, which limits flow capacity and causes noise/vibration/material damage in valve trim.
Marine Propellers and Hydrofoils - Cavitation causes thrust breakdown, noise (relevant to submarine/naval acoustic signature), and blade erosion; some vehicles intentionally operate in supercavitation (very low Ca) to reduce drag.
Pipeline and Pump Suction System Design - Sizing suction piping and setting minimum submergence/NPSH margins to avoid cavitation in the field.
Ship Rudders, Pump Volutes, Injector Nozzles - Similar erosion/performance concerns.
Relation to Other Parameters
NPSH (Net Positive Suction Head) - Essentially Ca expressed in head units for pump suction analysis.
Pressure Coefficient (C_p) - Links cavitation number directly to the potential-flow pressure distribution around a body.
Reynolds Number (Re) - Viscous boundary-layer effects shift the actual minimum pressure location/magnitude from the inviscid prediction, so real cavitation inception depends on Re as well as Ca (scale effects between model tests and full-scale prototypes).
Froude Number (Fr) - Relevant for free-surface effects (e.g., propellers near the water surface, surface-piercing hydrofoils) alongside cavitation number.
Weber Number (We) - Relevant to bubble surface-tension effects and nuclei stability.
Strouhal Number (St) - Characterizes unsteady/cloud cavitation shedding frequency, relevant when cavitation is not steady but periodic (cavity growth-collapse cycles).
Thermodynamic Effect Parameter - Important for cryogenic or hot-liquid cavitation (e.g., rocket turbopumps), where local vaporization cools the liquid and suppresses further vapor pressure.
