Cavitation Number (σ)

Dimensionless margin against cavitation for a pump, valve, or hydrofoil operating point.

Inputσ = (p − pᵥ) / (½·ρ·V²)

Local static pressure (kPa)or enter psi — converts to kPaVapor pressure (kPa)or enter psi — converts to kPaFluid density (kg/m³)Reference velocity (m/s)or enter ft/s — converts to m/s

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The engineering

The cavitation number compares how far the local static pressure sits above the fluid's vapor pressure against the dynamic pressure of the flow. Reach for it when sizing pumps, throttling valves, or running propellers and hydrofoils: it non-dimensionalizes the operating point so lab data at one scale predicts cavitation onset at another. High σ means comfortable margin; as σ falls the flow approaches the inception value σᵢ where the first bubbles appear.

Watch the reference pair — p and V must be measured at the same station, and pᵥ is strongly temperature-dependent (water jumps from 2.3 kPa at 20 °C to over 12 kPa at 50 °C, quietly eroding your margin). Cavitation inception happens at a positive σᵢ, not at σ = 0, so σ dropping to zero already means you are well into vaporization; treat σᵢ from test data as the real limit.

Where this math comes from

Cavitation became an engineering problem the moment ships got fast: in 1893 the destroyer HMS Daring and later Charles Parsons' Turbinia lost thrust to vapor bubbles collapsing on their propellers. Parsons built the first cavitation tunnel in 1895 to see the phenomenon directly, and the dimensionless grouping of pressure margin over dynamic head fell out naturally as engineers tried to compare model and full-scale results.

Christopher Brennen's work, culminating in his 1995 text Cavitation and Bubble Dynamics, codified σ as the governing similarity parameter and cleanly separated the inception number σᵢ from the fully-developed condition — the framing this card uses.

1895Charles ParsonsBuilds the first cavitation tunnel to study propeller bubble collapse on Turbinia.
1917Lord RayleighDerives the collapse dynamics of a vapor bubble, grounding cavitation theory.
1948Robert KnappSystematic hydrodynamic cavitation experiments establish σᵢ scaling.
1995Christopher BrennenCavitation and Bubble Dynamics standardizes σ and the inception framework.

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