Cavitation Number (σ): Dimensionless Indicator of Vapor Bubble Formation
The cavitation number σ (Greek letter sigma) compares the difference between local static pressure and vapor pressure with the dynamic pressure of a flowing liquid. Expressed as σ = (p − p_v)/(0.5 ρ v²), where p is static pressure, p_v is vapor pressure, ρ is density, and v is flow velocity, the dimensionless parameter indicates how close a system is to cavitation. When σ falls below critical thresholds, vapor bubbles form, collapse, and can erode surfaces or induce vibration. Designers use σ to assess pumps, propellers, spillways, and water jets across scales.
This article defines the cavitation number, reviews its historical development, explores conceptual foundations, demonstrates engineering applications, and emphasises its importance for reliability and efficiency. Pair σ analysis with the hydrostatic pressure calculator and pump specific speed guide to design cavitation-resistant systems.
Definition and Measurement
Deriving σ from Bernoulli’s equation
Cavitation risk emerges when static pressure drops toward the liquid’s vapor pressure. Starting from Bernoulli’s equation, p + 0.5 ρ v² + ρ g z = constant, subtracting the vapor pressure and normalising by dynamic pressure yields the cavitation number. Engineers often evaluate σ at pump inlets, hydrofoil minima, or nozzle throats where pressure dips. Because σ is dimensionless, it supports similarity analysis between laboratory models and full-scale prototypes.
Measuring inputs
Accurate σ estimation requires reliable pressure and velocity measurements. Static pressure taps or transducers capture p, while vapor pressure p_v depends on fluid temperature. Velocity derives from flow meters or computational fluid dynamics (CFD). Uncertainty analyses incorporate instrument accuracy, temperature fluctuations, and turbulence intensity to ensure σ predictions reflect operating variability.
Historical Development
Early cavitation research
Cavitation gained attention in the late 19th century when ship propellers suffered pitting and noise. Researchers like Osborne Reynolds and Lord Rayleigh described bubble dynamics, while Parsons and Froude conducted towing tank tests. By the 1930s, aeronautical laboratories adopted cavitation tunnels to test hydrofoils and torpedoes. The cavitation number emerged as a convenient scaling parameter, formalised by the US Navy’s David Taylor Model Basin and other hydrodynamic research centres.
Modern computational advances
Today, CFD codes incorporate cavitation models (Rayleigh–Plesset or Zwart–Gerber–Belamri formulations) to predict σ distributions and bubble structures. High-speed imaging and laser diagnostics validate simulations, while machine learning helps classify cavitation regimes from sensor data. Standards from the Hydraulic Institute and ISO 9906 reference σ when specifying allowable cavitation margins for pumps and turbines.
Concepts and Design Considerations
σ and net positive suction head (NPSH)
For pumps, the cavitation number relates closely to net positive suction head (NPSH). Maintaining σ above critical values ensures that NPSH available exceeds NPSH required. Designers raise suction pressure, reduce pump speed, or adjust impeller geometry to preserve σ. Plotting σ alongside NPSH curves aids in selecting operating points that minimise cavitation without sacrificing efficiency.
Scale effects and similarity
Model testing requires matching cavitation number between scale models and prototypes. However, surface roughness, dissolved gas content, and nuclei population can introduce scale effects. Testing facilities degas water or seed nuclei to align cavitation inception with full-scale conditions. Combining σ with Reynolds and Froude numbers helps ensure comprehensive similarity.
Applications and Importance
Marine and turbomachinery design
Naval architects evaluate σ for propellers and water jets to avoid noise, vibration, and efficiency loss. Turbine designers use σ to prevent cavitation at runner blades and draft tubes, which can erode surfaces and excite structural modes. Pump manufacturers publish σ-based suction specific speed limits to guide selection and maintain warranty compliance.
Infrastructure and process systems
Spillways, valves, and high-head penstocks experience rapid pressure changes that can trigger cavitation. Engineers deploy aeration slots, surface treatments, or pressure-sustaining valves to maintain σ. Process industries managing cryogenic fluids or liquefied gases monitor σ as vapor pressure shifts dramatically with temperature. Operational dashboards integrate σ with sump pump runtime planning and compression cost models to safeguard assets.
Key Takeaways
The cavitation number condenses pressure, velocity, and vapor pressure relationships into a practical indicator of cavitation risk. Mastering σ helps engineers design quieter, longer-lasting hydraulic machines and infrastructure. Integrating σ analysis with pressure calculations, similarity parameters, and operational monitoring supports resilient, efficient fluid systems.