A tool for computing the cavitation number sigma, a dimensionless index of how close a flowing liquid is to vaporising. Adjust the local static pressure, vapour pressure and flow speed to see sigma update in real time from the dynamic pressure and pressure margin, and find out whether a hydrofoil, valve or pump is in the cavitation danger zone.
Parameters
Local static pressure (reference) p
kPa
Static pressure at the reference point around the body
Vapour pressure of the fluid p_v
kPa
The fluid vaporises once the pressure drops to this value
Fluid density rho
kg/m³
Flow speed V
m/s
Flow speed at the reference point
Inception cavitation number sigma_i
The value of sigma at which bubbles begin on this body
Results
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Cavitation number σ
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Dynamic pressure ½ρV² (kPa)
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Pressure margin p − p_v (kPa)
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Inception number σ_i
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σ / σ_i ratio
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Cavitation verdict
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Flow and body — cavitation visualization
Streamlines accelerate over the upper (suction) side of the body and form a low-pressure region. When σ falls below σ_i, a cloud of cavitation bubbles forms there and collapses downstream.
Cavitation number σ vs flow speed V
Cavitation number σ vs local static pressure p
Theory & Key Formulas
$$\sigma=\frac{p-p_v}{\tfrac12\rho V^2}$$
Cavitation number σ. p: local static pressure, p_v: vapour pressure, ρ: fluid density, V: flow speed. The numerator is the pressure margin against vaporising, the denominator is the dynamic pressure.
$$q=\tfrac12\rho V^2, \qquad \Delta p = p-p_v$$
Dynamic pressure q (proportional to the square of speed) and the pressure margin Δp above vapour pressure. Low pressure or high speed lowers σ.
Cavitation begins when σ falls to the body's inception value σ_i. σ_i is a characteristic value for each body.
What is the Cavitation Number?
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"Cavitation" is when "cavities" form around a pump or propeller, right? But why do bubbles appear inside water in the first place?
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Good question. It is really the same phenomenon as boiling. Water in a kettle boils when you raise the temperature, but a liquid also boils when you lower the pressure. When water races around a body in a flow, the pressure there drops sharply. If the pressure falls to the liquid's vapour pressure, even room-temperature water vaporises there and forms bubbles — cavities. That is cavitation.
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I see, it boils through pressure rather than temperature. So the "cavitation number" is a figure that measures how easily those bubbles form?
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Exactly. The cavitation number σ is a dimensionless number defined as σ = (p − p_v)/(½ρV²). The numerator (p − p_v) is "how much margin the current pressure has above vapour pressure", and the denominator ½ρV² is "the dynamic pressure of the flow". So σ is the pressure margin divided by the momentum of the flow. A large σ means plenty of margin and safety; a small σ means the flow is on the verge of forming bubbles.
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When I raise the "flow speed V" on the left, σ drops fast. Does that mean a faster flow is more dangerous?
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Yes, precisely. The dynamic pressure is ½ρV², so it depends on the square of V, and σ falls as 1/V². Look at the "σ vs flow speed" chart below — it has a steep curve at the low-speed side. A faster flow drops the surface pressure more easily. That is why running a propeller at high rpm, or throttling a valve to raise the local speed, makes cavitation more likely.
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A small σ means bubbles appear — but is there a clear "below this value it fails" threshold?
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That is the "inception cavitation number σ_i". A hydrofoil, a valve, a pump impeller — each shape has its own characteristic value of "once σ drops to this, bubbles start to appear". When the operating σ falls to σ_i it is inception, and σ < σ_i means full cavitation. Designers keep σ comfortably above σ_i. This tool also compares σ with σ_i and tells you whether you are safe, on the edge, or cavitating.
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Are bubbles really such a problem? A few bubbles sound harmless to me…
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That is exactly the trouble. Once a bubble is carried downstream into a higher-pressure region, it collapses in an instant. At the moment of collapse an extremely high pressure shock is generated locally, and it gradually chips away at the metal surface — this is cavitation erosion (pitting). It also causes vibration, noise and a drop in efficiency. You may have seen photos of a pump impeller riddled with holes like a sponge — that is all the work of cavitation.
Frequently Asked Questions
The cavitation number sigma is a dimensionless index of how close a flowing liquid is to vaporising (cavitating). It is defined as sigma = (p - p_v) / (1/2 rho V^2), where the numerator is the difference between the local static pressure p and the vapour pressure p_v (the pressure margin against cavitation) and the denominator is the dynamic pressure 1/2 rho V^2. A high sigma means a comfortable pressure margin and a safe flow; a low sigma (high speed or low pressure) means the flow is on the edge of vaporising.
The inception cavitation number sigma_i is the value of sigma at which cavitation begins on a particular body - a hydrofoil, valve trim, pump impeller or ship propeller. When the operating sigma falls to sigma_i, vapour bubbles start to form, and for sigma < sigma_i cavitation is occurring. sigma_i is a characteristic value set by the body shape and surface condition, and designers keep the operating sigma comfortably above it.
The dynamic pressure 1/2 rho V^2 is the denominator of the cavitation number sigma. As the flow speed V increases, the dynamic pressure grows with the square of V, so sigma falls as 1/V^2. Doubling the flow speed quadruples the dynamic pressure and cuts sigma to about a quarter. This is why faster flows drop the surface pressure more easily and are more prone to cavitation.
When vapour bubbles are carried into a higher-pressure region they collapse, and the collapse produces an intense, highly localised pressure shock that gradually erodes metal surfaces - cavitation pitting. It also causes vibration, noise and a loss of head and efficiency. Because this shortens the life of pumps, valves and propellers, the operating sigma must be kept safely above the inception value sigma_i.
Real-World Applications
Centrifugal pumps and NPSH: The impeller inlet of a pump is where the flow is fastest and the pressure lowest, making it the most cavitation-prone location. In practice the suction piping is designed so that the available NPSH exceeds the required NPSH — and the cavitation number concept is exactly what lies behind that. At operating points with low suction pressure, high flow rate or high head, σ drops and erosion progresses on the impeller.
Hydraulic turbines and ship propellers: Turbine runners and ship propellers cut through water at high speed, so they are classic cases where σ drops easily. On a propeller, sheet cavitation on the suction side of the blade or tip-vortex cavitation causes not only erosion but also noise and vibration. For naval submarines, hydrofoil designs that raise the cavitation inception speed are emphasised for the sake of stealth.
Control valves, orifices and throttling devices: When a valve throttles a flow, the local speed rises and the static pressure drops at the restriction. If the pressure falls close to the vapour pressure, cavitation occurs inside the valve and erodes the plug and seat. In process piping, σ is estimated from the differential pressure and downstream pressure to select multi-stage pressure-reducing trims or anti-cavitation valves.
CFD analysis and model testing: In cavitation-tunnel model tests and multiphase CFD analyses, the cavitation number is matched between the model and the full-scale machine as a similarity parameter. A quick estimate of σ like this tool helps set test conditions and serves as a sanity check on whether a CFD result is physically reasonable — for instance, whether the low-pressure region has dropped below the vapour pressure.
Common Misconceptions and Pitfalls
A common mistake is computing σ while being vague about where the reference point is. The local static pressure p and flow speed V in the definition of the cavitation number are values at one specific, agreed reference point. For the same machine, taking the reference point in the upstream tank or at the impeller inlet gives different p and V, and the numerical value of σ changes completely. When comparing against a literature value of σ_i, always check at which reference point that σ_i was defined. Comparing σ values defined on inconsistent references leads to badly wrong verdicts.
Next, assuming the vapour pressure p_v is constant. The vapour pressure of water is very sensitive to temperature: about 2.3 kPa at 20 °C, about 12 kPa at 50 °C and about 47 kPa at 80 °C. The warmer the liquid, the larger p_v, the smaller the pressure margin (p − p_v), and the lower σ. This is why cavitation can suddenly appear in summer or in a high-temperature process. Use the vapour-pressure slider in this tool to picture the effect of temperature. Cold does not automatically mean safe — it is important to use the p_v that corresponds to the operating temperature.
Finally, thinking that "as long as σ is even slightly above σ_i, it is absolutely safe". The inception cavitation number σ_i is itself an uncertain value that varies with surface roughness, tiny scratches, dissolved gas and turbulence intensity. There are also stages: exactly at σ_i there is "very weak inception", below it "developed cavitation", and erosion becomes serious only at still lower σ. In real designs a margin is kept so that σ stays roughly 1.2 to 2 times σ_i. This tool likewise warns of "near inception (caution)" when σ is within 1.2 times σ_i.
How to Use
Enter the local static pressure (kPa) at the point of interest in your flow system—typically measured downstream of a restriction or at a low-pressure zone in a pump.
Input the fluid's vapor pressure (kPa) and density (kg/m³); for water at 20°C use 2.3 kPa and 998 kg/m³.
Set the bulk flow velocity (m/s) past the critical location, then click Calculate to obtain cavitation number σ and pressure margin.
Compare σ against the reported inception number σ_i to assess cavitation risk; σ > σ_i indicates safe operation.
Worked Example
A centrifugal pump circulates water (ρ = 998 kg/m³, p_v = 2.3 kPa) at 3.5 m/s through an impeller eye where local pressure drops to 15 kPa. Reference pressure is atmospheric (101.3 kPa). Dynamic pressure is ½ × 998 × 3.5² ≈ 6.1 kPa. Cavitation number σ = (15 − 2.3) / 6.1 ≈ 2.11. If inception number σ_i = 1.8, the ratio σ/σ_i = 1.17 indicates marginal safety; velocity reduction to 3.0 m/s raises σ to 2.85, providing robust cavitation avoidance.
Practical Notes
In pump suction lines, measure local pressure with a piezometric tap; cavitation nucleates when σ falls below σ_i, causing erosion and noise within 24 hours.
For marine propellers operating near free surface, account for hydrostatic variations; a 2 m depth change alters local pressure by ~20 kPa, shifting σ significantly.
Valve cavitation (globe valves, control valves) requires σ_i values typically 1.5–3.0; maintain σ > 2.5 in throttling applications to prevent cavitation damage.
Fluid temperature affects vapor pressure exponentially; at 50°C, water p_v rises to 12.3 kPa, reducing σ by ~2.5× and accelerating cavitation onset.