Compute the cavitation number σ (also called cavitation index) – the key dimensionless parameter to predict cavitation inception in hydraulic systems. Enter flow conditions, and the tool will assess cavitation risk and visualize bubble intensity.
In fluid dynamics, the cavitation number (σ) – also called the cavitation index – is a dimensionless quantity that characterizes the tendency of a flow to cavitate. It is defined as:
σ = (p - pv) / (½ ρ V2)
where p = reference absolute pressure, pv = liquid vapor pressure, ρ = density, V = characteristic velocity.
Low values of σ (typically below 1) indicate that the local pressure may drop below vapor pressure, leading to the formation of vapor bubbles – cavitation. Cavitation can cause erosion, noise, vibration, and performance loss in pumps, turbines, propellers, and marine vessels.
The systematic study of cavitation began in the late 19th century with the investigation of rapid propeller erosion on steam ships. Lord Rayleigh (1917) published the first mathematical analysis of a spherical bubble collapse, predicting the enormous pressures generated during collapse. The cavitation number was introduced as a similarity parameter to scale model tests to full-scale prototypes. Today it is indispensable in hydraulic engineering, naval architecture, and biomedical ultrasound.
The cavitation number derives from the Bernoulli equation along a streamline. At a point where the velocity increases, pressure drops. If the pressure falls below pv, cavitation occurs. By rearranging Bernoulli: p + ½ρV² = constant. The minimum pressure coefficient Cp,min is related to σ. Typically, incipient cavitation corresponds to σ = –Cp,min for the body. This tool uses the basic definition; for engineering applications, one often compares σ with the cavitation inception index of a specific geometry.
Values below are indicative; actual σ depends on flow speed and pressure.
| Scenario | p (Pa) | pv (Pa) | ρ (kg/m³) | V (m/s) | σ | Cavitation risk |
|---|---|---|---|---|---|---|
| Water 20°C, 10 m/s, 1 atm | 101325 | 2340 | 998 | 10 | 1.98 | Low (no cavitation) |
| Seawater 30°C, 15 m/s (propeller) | 150000 (≈15m depth) | 4240 | 1025 | 15 | 1.32 | Moderate, possible tip cavitation |
| Pump inlet (low pressure) | 30000 | 2340 | 998 | 5 | 2.21 | Low, but NPSH must be checked |
| Cavitating flow (high speed) | 101325 | 2340 | 998 | 25 | 0.32 | Very high – full cavitation |
| High‑speed torpedo | 200000 (depth) | 2340 | 998 | 40 | 0.22 | Supercavitation likely |
A large container vessel operates with a propeller at 10 m depth (p ≈ 200,000 Pa). Water temperature 25°C (pv ≈ 3,170 Pa), ρ = 997 kg/m³, blade tip velocity V = 30 m/s. Cavitation number σ = (200000 – 3170) / (0.5*997*900) = 196830 / 448650 ≈ 0.44. This low σ indicates strong likelihood of cavitation. The shipowner may need to adopt a skewed propeller design or increase immersion depth to avoid erosion and noise. Our calculator instantly provides this insight.
In pump engineering, cavitation is often expressed through NPSH available (NPSHa) and required (NPSHr). The relation with cavitation number is: NPSH = (p – pv) / (ρ g). Therefore σ = NPSH * 2g / V². This tool can be used to convert between these parameters.
function cavitationNumber(p, pv, rho, V) {
if (rho <= 0 || V === 0) return NaN;
let q = 0.5 * rho * V * V; // dynamic pressure
let dp = p - pv; // net pressure
let sigma = dp / q;
return { sigma, q, dp };
}