1 Definition and physical meaning

1.1 Basic concept

The cavitation number is a dimensionless quantity used to describe how close a liquid flow is to cavitating. It compares the pressure available in the flow to the vapor pressure of the liquid, usually in relation to a characteristic dynamic pressure. When the local pressure in a flowing liquid falls near or below vapor pressure, vapor cavities can form. The cavitation number therefore provides a practical measure of cavitation risk in moving fluids.

1.2 Interpretation in fluid systems

In a fluid system, a low cavitation number indicates that the pressure level is only slightly above the vapor pressure, so cavities are more likely to appear. A high value suggests that the flow has a larger pressure reserve and is less prone to cavitation. Engineers use this parameter to compare operating conditions across different devices, even when their size or geometry differs.

1.3 Relation to cavitation onset

Cavitation usually begins when the minimum pressure in a flow reaches the vapor pressure of the liquid. The cavitation number does not directly predict the exact moment of inception in every case, but it gives a useful threshold measure. As the number decreases, the probability of bubble formation increases, and below a critical value cavitation may become observable.

2 Mathematical formulation

2.1 Standard definition

A common form of the cavitation number is the ratio of the pressure margin above vapor pressure to the dynamic pressure of the flow. In symbolic form, it is often written as a difference between a reference pressure and vapor pressure divided by one-half the fluid density times the square of a characteristic velocity. This makes the quantity dimensionless and suited to flow comparison.

2.2 Alternative forms

Different engineering fields may use modified expressions for the cavitation number depending on which pressure or velocity scale is most relevant. Although the notation varies, the basic idea remains the same: a pressure difference normalized by a flow intensity measure. These alternative forms are often chosen to match the geometry or operating regime of a machine.

2.2.1 Velocity-based forms

In velocity-based formulations, the characteristic speed of the liquid is explicit in the denominator. This is common when analyzing flowing streams, jet systems, or rotating machinery where a representative velocity is easy to define. A higher velocity usually increases the dynamic pressure and may reduce the cavitation number, signaling greater cavitation susceptibility.

2.2.2 Pressure-based forms

Pressure-based forms may use inlet, ambient, or local system pressure as the reference quantity. These versions are useful when the pressure environment is more important than a single flow speed, such as in closed conduits or pressurized hydraulic equipment. The selected reference pressure strongly influences the reported value, so the definition must be stated clearly.

2.3 Dimensionless analysis

The cavitation number belongs to the family of dimensionless groups used in fluid mechanics. Such parameters allow comparison of flows under different scales, materials, and operating conditions. Because it combines pressure, density, and velocity into a unitless ratio, it helps identify similar cavitation behavior in both laboratory models and full-size machines.

3 Parameters in the cavitation number

3.1 Reference pressure

The reference pressure is the pressure level against which the flow is compared. It may represent upstream pressure, ambient pressure, or another system-specific value. Choosing this reference correctly is essential, because it determines how much pressure reserve is considered available before cavitation begins.

3.2 Vapor pressure

Vapor pressure is the pressure at which a liquid can coexist with its vapor at a given temperature. If local pressure drops to this level, vapor bubbles may form. Since vapor pressure rises with temperature, warmer liquids are often more susceptible to cavitation under the same flow conditions.

3.3 Flow velocity

Flow velocity appears in many cavitation number definitions because it sets the dynamic pressure scale. Faster motion typically means larger pressure fluctuations around surfaces, blades, or constrictions. As velocity increases, the cavitation number often decreases, reflecting the greater chance that pressure will fall to vapor pressure.

3.4 Characteristic pressure scale

A characteristic pressure scale is used to normalize the pressure difference in a way that matches the physical situation. In many cases, it is the dynamic pressure, but other relevant scales may be chosen for special flows. The selected scale must be consistent with the geometry and the intended comparison.

4 Cavitation number in different applications

4.1 Pumps

In pumps, the cavitation number helps assess whether the inlet pressure is sufficient to prevent vapor formation at the impeller eye or within internal passages. Cavitation can reduce discharge, create noise, and damage blades. Designers use the parameter to select safe operating conditions and to improve suction performance.

4.2 Hydraulic turbines

Hydraulic turbines rely on pressure drops and high-speed flow, making cavitation an important concern. The cavitation number is used to estimate whether low-pressure zones around runner blades or draft tubes may reach vapor pressure. Proper control of this parameter is important for preserving efficiency and avoiding surface damage.

4.3 Marine propellers

For marine propellers, cavitation occurs when pressure on the blade surface falls too low during rotation. The cavitation number helps evaluate whether the propeller will form cavities that reduce thrust or cause vibration. It is an important design and testing criterion for ship propulsion systems.

4.4 Nozzles and orifices

In nozzles and orifices, rapid acceleration can produce strong pressure drops. A low cavitation number may indicate that vapor bubbles will form in the jet or at the throat. This can alter flow rate, discharge behavior, and wear patterns, especially in high-pressure liquid delivery systems.

4.5 Aerodynamic and hydrodynamic devices

The cavitation number is also relevant in various hydraulic and hydrodynamic devices where local low-pressure regions occur. It may be applied to foils, underwater bodies, valves, and experimental test rigs. In each case, the parameter helps determine whether pressure conditions are likely to support stable liquid flow.

5 Cavitation inception and critical cavitation number

5.1 Threshold behavior

Cavitation inception refers to the first appearance of vapor cavities in a liquid flow. The critical cavitation number is the value at which this onset occurs under specified conditions. Because inception depends on geometry, surface condition, temperature, and dissolved gases, the critical value is not universal.

5.2 Experimental determination

Experimental determination of the critical cavitation number is usually done by gradually changing flow conditions until bubbles, streaks, or noise indicate the onset of cavitation. Visualization, acoustic monitoring, and pressure measurement may all be used. The resulting threshold is then associated with the tested system and operating state.

5.3 Dependence on flow conditions

The inception threshold changes with many flow variables, including velocity distribution, turbulence, liquid temperature, and surface roughness. Even small differences in nucleus content or pressure fluctuation can alter the observed onset. For that reason, cavitation data are often reported together with detailed test conditions.

6 Measurement and estimation

6.1 Experimental methods

Experimental methods include pressure sensing, high-speed imaging, stroboscopic observation, and acoustic detection. These techniques help identify low-pressure zones and visible vapor formation. In many cases, measurements are combined so that both the flow field and the resulting cavitation behavior can be evaluated.

6.2 Numerical simulation

Numerical simulation is widely used to estimate cavitation number effects before hardware is built. Computational fluid dynamics can model pressure fields, velocity distributions, and cavity development. Although simulation cannot capture every microscopic detail, it is useful for comparing designs and predicting regions of risk.

6.3 Empirical correlations

Empirical correlations relate cavitation behavior to measurable operating variables such as pressure, speed, geometry, and fluid properties. These relationships are especially valuable when exact analytical treatment is difficult. They are often derived from test data and are used for preliminary design and performance estimation.

6.3.1 Model testing

Model testing uses scaled-down prototypes to observe cavitation behavior under controlled conditions. The results can reveal how the cavitation number changes with speed and pressure. Careful similarity conditions are needed so the model reflects the behavior of the larger system as accurately as possible.

6.3.2 Prototype scaling

Prototype scaling translates model results to full-size equipment. Because cavitation is sensitive to pressure, speed, and size effects, direct scaling requires caution. Engineers use similarity laws and correction factors to estimate how a machine will perform in actual service.

7 Effects of cavitation

7.1 Performance degradation

Cavitation often reduces the performance of hydraulic equipment. In pumps and propellers, it can lower flow delivery, thrust, or pressure rise. The formation and collapse of vapor cavities disrupt the smooth transfer of energy between the device and the liquid.

7.2 Noise and vibration

The collapse of cavitation bubbles can generate strong noise and vibration. These effects may be audible as a rattling or crackling sound. In mechanical systems, repeated vibration can also shorten service life by stressing mounts, bearings, and nearby components.

7.3 Material erosion

When cavities collapse near solid surfaces, the resulting microjets and shock waves can damage material. Over time, this may produce pits, roughness, and metal loss. Cavitation erosion is a serious concern in blades, impellers, valve seats, and other exposed surfaces.

7.4 Efficiency losses

Cavitation reduces efficiency by disturbing smooth flow and dissipating energy. Some of the input power is lost to turbulence, vapor formation, and repeated collapse of cavities. In severe cases, the machine may also experience unstable operating behavior.

8 Engineering design considerations

8.1 Avoiding cavitation

Designers avoid cavitation by maintaining sufficient inlet pressure, reducing excessive speeds, and shaping passages to prevent sharp pressure drops. Surface finish and geometry can also be adjusted to reduce local low-pressure regions. The goal is to keep the cavitation number safely above the critical threshold.

8.2 Operating limits

Operating limits define the range of pressure, velocity, and temperature within which the system can function without unacceptable cavitation. These limits are often specified in equipment manuals or design standards. Staying within them helps preserve both performance and durability.

8.3 Safety margins

Because cavitation inception is influenced by many variables, engineers usually include a safety margin above the minimum acceptable cavitation number. This buffer helps account for uncertainty in measurement, aging of components, and variations in fluid properties. Larger margins are often used in critical or hard-to-access equipment.

8.4 Scaling and similarity laws

Scaling laws are important when applying test results from a model to a larger machine. Similarity requires matching relevant dimensionless numbers, including the cavitation number and often the Reynolds number. When this is done properly, the model can provide reliable guidance for full-scale design.

9.1 Reynolds number

The Reynolds number measures the relative importance of inertial and viscous forces in a flow. It affects turbulence, boundary layer behavior, and pressure distribution, all of which can influence cavitation. In many systems, cavitation performance depends on both Reynolds number and cavitation number.

9.2 Froude number

The Froude number compares inertial forces with gravity effects. It is especially relevant in free-surface and open-channel flows. While distinct from the cavitation number, it may be considered alongside it when pressure changes are tied to gravity-driven motion.

9.3 Thoma cavitation number

The Thoma cavitation number is a related parameter used especially in turbomachinery. It is often associated with suction performance and net positive suction head. Although the terminology differs, it serves a similar purpose in expressing resistance to cavitation.

9.4 Inlet cavitation number

The inlet cavitation number is a specific form that focuses on conditions at a machine entrance or suction side. It is frequently used in pumps and other flow devices where inlet pressure is the controlling factor. This version helps assess whether vapor formation will begin at the entry region.

10 History and usage

10.1 Development in fluid mechanics

The cavitation number emerged as fluid mechanics advanced toward more systematic analysis of high-speed liquid flow. As researchers studied bubble formation and collapse, they needed a concise way to compare operating conditions. The dimensionless parameter became a useful tool for organizing experimental and theoretical work.

10.2 Adoption in engineering practice

With the growth of pumps, turbines, marine propulsion, and hydraulic machinery, the cavitation number became a standard engineering measure. Its practical value lies in connecting flow conditions to the risk of damage and performance loss. Today it remains a common reference in design, testing, and troubleshooting of fluid equipment.