Cavitation Number
Cavitation Number
The cavitation number is the standard dimensionless parameter used across pumps, propellers, valves, and hydrofoils to judge how close a flow is to cavitating: it compares the available pressure margin above the fluid's vapor pressure to the dynamic pressure the flow itself generates, so a low cavitation number means the local pressure drops (which scale with dynamic pressure) are more likely to push the fluid down to its vapor pressure somewhere in the flow field. Because it is dimensionless, the cavitation number lets engineers compare cavitation risk across completely different scales and fluids — a scale-model propeller in a test tank versus a full-size ship propeller, for instance — which is exactly why it is the standard similarity parameter used in cavitation tunnel testing.
The cavitation number is sigma = (P - Pv)/(0.5·rho·v^2), the pressure margin above vapor pressure divided by the dynamic pressure. where P is the local (ambient) pressure, Pv is the fluid vapor pressure, rho is the fluid density, and v is the characteristic flow velocity.
Inputs
P_amb := 150000 Pa=150000 Pa
P_v3 := 2340 Pa=2340 Pa
rho_c := 1000 kg/m^3=1000 kg/m^3
v_c := 8 m/s=8 m/s
Dividing the pressure margin above vapor pressure by the flow's dynamic pressure gives a dimensionless number that expresses how much "headroom" the flow has before local low-pressure regions could drop to the vapor pressure and trigger cavitation.
sigma_cav := (P_amb - P_v3)/(0.5·rho_c·v_c^2)=4.61
Results
A cavitation number around 4.6 indicates a comfortable margin for most hydraulic machinery, since cavitation risk generally becomes a serious concern as sigma approaches and drops below roughly 1–2, depending on the specific geometry's pressure-drop characteristics. As velocity increases at fixed ambient pressure, sigma falls with the square of velocity, which is why cavitation is characteristically a high-speed-flow problem — propeller tips, pump impeller eyes, and valve throats, all places where local velocity spikes and pressure correspondingly dips. A design sigma value is normally compared against an experimentally determined incipient-cavitation sigma for the specific geometry in question rather than judged against a single universal threshold.
Assumptions & limitations
- Local pressure P assumed representative of the point of interest (not a bulk average).
- Incompressible flow assumed for the dynamic pressure term.
- Steady flow conditions; transient pressure spikes are not captured.
- Cavitation onset threshold is geometry-dependent and must be compared against test data, not a universal sigma value.