Abstract

A centrifugal pump converts shaft work into fluid head through a rotating impeller and stationary casing or diffuser. The most familiar cavitation location is the impeller eye and blade leading edge, where relative velocity is high and pressure is low. Other forms occur in tip leakage vortices, balance passages, wear ring clearances, inlet recirculation, discharge recirculation, blade wake interactions, and diffuser or volute regions. These mechanisms have different operating point dependencies and therefore require different remedies [1], [2].

Chapter 4. Cavitation in Hydraulic Machinery, Valves, Piping, and Marine Systems

4.1 Cavitation in Pumps and Impellers

4.1.1 Locations and Mechanisms

A centrifugal pump converts shaft work into fluid head through a rotating impeller and stationary casing or diffuser. The most familiar cavitation location is the impeller eye and blade leading edge, where relative velocity is high and pressure is low. Other forms occur in tip leakage vortices, balance passages, wear ring clearances, inlet recirculation, discharge recirculation, blade wake interactions, and diffuser or volute regions. These mechanisms have different operating point dependencies and therefore require different remedies [1], [2].

Table 4.1. Pump cavitation locations and characteristic signatures. [3]

Location or mechanism	Common operating condition	Typical evidence	Priority response
Impeller eye and leading edge	Insufficient suction head, high temperature, excessive speed, high flow, or inlet prewhirl.	Vapor at blade inlet, crackling noise, head loss as severity increases.	Increase suction pressure, reduce losses or speed, correct inlet geometry.
Inlet recirculation	Operation well below best efficiency flow.	Intermittent low frequency pressure fluctuations, vapor near inlet and suction pipe.	Move operating point, use minimum flow control, review impeller and suction design.
Discharge recirculation	Very low flow and high internal recirculation.	Noise and erosion near blade discharge or cutwater, heat rise.	Avoid prolonged low flow, provide bypass, revise impeller or casing geometry.
Tip or clearance vortex	Open impeller, inducer, axial machine, or large clearance.	Vortex core vapor and localized erosion away from the nominal leading edge.	Reduce clearance, weaken vortex, relocate collapse, improve surface resistance.
Diffuser or volute interaction	Off design incidence or strong blade wake.	Pressure pulsation at blade passing frequency and local vapor pockets.	Correct operating point, vane geometry, spacing, or cutwater clearance.
Internal seals and balance devices	High pressure drop through small clearance.	Pitting, unstable axial thrust, leakage change.	Stage pressure drop, change clearance geometry, raise local backpressure.

4.1.2 Net Positive Suction Head

Net positive suction head available, $NPS{H}_A$, is the total absolute suction head at the pump datum above the vapor pressure head. One common form is where $p_s$ and $V_s$ are suction pressure and velocity at the stated reference section. For an open suction vessel, a useful system form is:

$$NPS{H}_A=\frac{p_s}{\rho g}+\frac{V_s^2}{2g}-\frac{p_v}{\rho g}$$

(4.1)

$$NPS{H}_A=\frac{p_{surface}-p_v}{\rho g}+z_s-h_{f,s}$$

(4.2)

where $p_{surface}$ is the absolute pressure above the liquid surface, $z_s$ is the static elevation of that surface relative to the pump datum, and $h_{f,s}$ is suction line loss. Signs must be assigned consistently. $NPS{H}_A$ varies with flow, liquid level, vessel pressure, temperature, fouling, valve position, and transient acceleration [1,3,4].

Figure 4.1. Pump suction system and NPSH concepts.

Net positive suction head required, $NPS{H}_R$, is a pump characteristic determined by test at specified speed, flow, liquid, and criterion. $NPS{H}_3$ commonly denotes the value at which pump total head has fallen by 3 percent relative to a noncavitating reference. Cavitation usually begins before that point, and noise or erosion can occur at larger NPSH values. Manufacturer curves must therefore be interpreted with the test definition and the application consequence in mind [1,3,4].

Figure 4.2. Illustrative NPSH3 test curve. The 3 percent head drop criterion is a repeatable pump test point, not a universal inception or damage threshold [1], [3], [4].

Two simple margin measures are where M is absolute margin and $M_R$ is a ratio. Current guidance treats the required margin as application specific because pump type, speed, energy density, operating region, liquid, duty criticality, and acceptable degradation differ [3], [3]. A single percentage cannot represent all services.

$$M=NPS{H}_A-NPS{H}_R{M}_R=\frac{NPS{H}_A}{NPS{H}_R}$$

(4.3)

Suction specific speed is often used as a comparative indicator where n is rotational speed and Q is flow under a stated unit convention. The numerical value depends on units and pump definition, so it should be used only with a declared convention. High suction specific speed may indicate aggressive inlet loading and a narrower stable low flow range, but it is not a standalone cavitation criterion [1],

$$N_{ss}=\frac{n\sqrt{Q}}{NPS{H}_R^{3/4}}$$

(4.4)

Hydraulic power and pump efficiency are

$$P_h=\rho gQH\eta =\frac{P_h}{P_{shaft}}$$

(4.5)

A falling head, unstable power, efficiency loss, and flow limitation can therefore provide indirect evidence of developed cavitation. Incipient cavitation often produces acoustic and pressure signatures before a measurable efficiency change.

4.1.3 Damage Patterns and Operational Symptoms

Operators often describe pump cavitation as gravel, crackling, or marbles in the casing. Sound alone is not conclusive because entrained air, bearing faults, solids, and recirculation can produce similar symptoms. More reliable interpretation combines the operating state, performance trends, and inspection. Erosion near the impeller inlet typically appears as rough, scalloped pitting and can progress to loss of blade profile, imbalance, crack initiation, and leakage [5], [5], [1], [1].

Figure 4.3. Cavitation damage on a centrifugal pump impeller. Photograph by Jean Jacques Milan [6].

4.1.4 Prevention Priorities for Pumps

Verify absolute suction pressure, temperature, vapor pressure, liquid level, and flow on a consistent basis. A relative pressure value without barometric correction can misstate $NPS{H}_A$.

• Reduce suction line loss by enlarging pipe, shortening the run, opening or removing restrictive fittings, cleaning strainers, and preventing air pockets. Keep adequate straight approach flow where the pump design requires it.

• Raise the liquid level or vessel pressure, lower the pump, lower liquid temperature where the process allows, or install a booster pump or inducer.

• Reduce rotational speed or move operation toward the preferred operating region. Do not treat throttling on the suction side as a routine flow control method.

• Evaluate inlet recirculation and discharge recirculation separately from low NPSH cavitation. A large NPSH margin cannot correct an unstable off design flow pattern.

• After a design change, verify the result by pressure, performance, vibration or acoustic trend, and inspection rather than by sound alone.

4.2 Cavitation in Valves and Piping Systems

4.2.1 Vena Contracta and Pressure Recovery

When liquid accelerates through a throttling element, the jet continues to contract downstream of the minimum geometric area. Static pressure reaches its minimum near this vena contracta and then partially recovers as the jet expands and mixes. Cavitation begins when the minimum pressure falls below vapor pressure and cavities subsequently enter a region of higher pressure. A trim with strong pressure recovery can therefore cavitate even when both upstream and downstream pipe pressures are well above vapor pressure [7–9].

Figure 4.4. Pressure profiles through a throttling restriction. Cavitation requires pressure recovery above vapor pressure, flashing persists when downstream pressure remains below vapor pressure [7–9].

4.2.2 Cavitation Indices and Recovery Factor

A common valve cavitation index is ${\sigma }_v$ where $p_1$ is upstream pressure and $p_2$ is downstream pressure. Index conventions vary among industries, and some definitions use the inverse ratio or a different reference pressure. Published incipient, constant, or damage thresholds must therefore be used only with the matching definition, valve style, size, travel, and test method [7–9].

$${\sigma }_v=\frac{p_1-p_v}{p_1-p_2}$$

(4.6)

The liquid pressure recovery factor$F_L$ can be expressed as where $p_{vc}$ is pressure at the vena contracta. A smaller recovery factor indicates that the minimum internal pressure is much lower than the measured downstream pressure. Valve sizing methods incorporate recovery and a critical pressure ratio to predict liquid choking. Detailed selection should follow a recognized sizing standard and manufacturer data [7], [8].

$$F_L=\sqrt{\frac{p_1-p_2}{p_1-p_{vc}}}$$

(4.7)

4.2.3 Cavitation, Choking, and Flashing

Table 4.2. Pressure states in valves and restrictions. [2]

State	Pressure relationship	Downstream behavior	Primary risk
Single phase liquid	Minimum pressure remains above vapor pressure.	No vapor generated by pressure reduction.	Turbulence, vibration, or erosion may still occur for other reasons.
Incipient cavitation	Small regions intermittently fall below vapor pressure.	Cavities collapse after pressure recovery.	High frequency noise; little performance change; possible early pitting.
Developed cavitation	A substantial vapor region forms near the vena contracta.	Repeated collapse in trim, body, or downstream pipe.	Noise, vibration, erosion, and reduced capacity.
Choked cavitating flow	Increasing pressure drop no longer produces the expected increase in liquid flow.	Vapor volume controls effective flow area.	Capacity limitation and severe dynamic loading.
Flashing	Downstream pressure remains at or below vapor pressure.	Two phase mixture persists downstream.	High velocity erosion, vibration, and large volume expansion; collapse may occur farther away if pressure later rises.

4.2.4 Piping Locations and Control Measures

Cavitation can also occur at orifices, reducers, partially open isolation valves, strainers, pump bypasses, sudden contractions, elbows with separation, nozzles, and high velocity branch connections. The vulnerable surface may be downstream rather than inside the restriction because cavity collapse follows the recovering jet. A change that moves the minimum pressure without examining the collapse region can simply transfer damage [5], [7–9].

Stage the pressure drop. Multiple restrictions or multistage trim can keep each local pressure reduction below a damaging level and distribute dissipation.

Use tortuous path or multi orifice trim. Many small jets reduce individual jet energy and can move collapse into a protected region, but passages must remain compatible with solids and fouling.

Increase downstream pressure. A backpressure valve or process change can raise the entire pressure profile, provided the added pressure does not create another cavitating restriction.

Increase valve size or change valve style. Lower velocity and lower recovery geometry can reduce the minimum pressure, but oversized control valves may have poor controllability and operate at unstable low travel.

Protect the downstream pipe. Increase pipe size, use a diffuser, provide straight length, avoid close elbows, and select resistant material where residual cavitation cannot be eliminated.

Distinguish flashing. Anti cavitation trim cannot condense vapor if downstream thermodynamic conditions require a two phase state. Flashing service requires erosion resistant geometry and appropriate downstream sizing.

4.3 Marine Propellers, Waterjets, and Hydrofoils

4.3.1 Local Cavitation Number and Unsteady Loading

A marine propeller blade experiences a combination of axial inflow, rotational velocity, induced velocity, and a strongly nonuniform hull wake. The local pressure margin changes with radius and blade angle. A representative local cavitation number is $\sigma (r)$ where $p_a$ is atmospheric or chamber pressure, h is local immersion, and $V_R(r)$ is a stated local resultant velocity. Propeller calculations use additional nondimensional coefficients for thrust, torque, advance, and loading. Low immersion, high shaft speed, heavy loading, wake peaks, maneuvering, roughness, and appendage interaction all promote cavitation [10–12].

$$\sigma (r)=\frac{p_a+\rho gh-p_v}{\frac{1}{2}\rho V_R^2(r)}$$

(4.8)

Figure 4.5. Cavitating propeller in a water tunnel at the David Taylor Model Basin. U.S. Navy photograph, public domain [13].

4.3.2 Cavitation Forms on Propulsors

Marine cavitation is classified by the geometry and persistence of the vapor structure and by its location on the propulsor or appendage. These categories are descriptive rather than exclusive: an attached sheet may shed a cloud, and a tip vortex may interact with a rudder or hull surface during the same operating condition.

Figure 4.6. Idealized locations and forms of marine propeller cavitation.

Table 4.3. Marine propeller cavitation forms.

Form	Typical location and cause	Principal consequence
Back sheet cavitation	Suction side near the leading edge under high positive loading.	Thrust and torque change, cloud shedding, erosion, and pressure pulses.
Face cavitation	Pressure side under negative incidence, crash astern, or local wake reversal.	Severe off design loading and localized erosion.
Tip vortex cavitation	Low pressure core of the rolled up tip vortex.	Radiated noise, long range interaction, and possible rudder or hull erosion.
Hub vortex cavitation	Vortex downstream of the hub or boss cap.	Noise, hub and rudder interaction, and efficiency loss.
Root cavitation	Blade root or fillet under concentrated loading and three dimensional flow.	Local erosion and crack sensitive surface damage.
Cloud cavitation	Periodic breakup of an attached cavity.	Strong unsteady loads, broadband noise, and high erosion potential.
Bubble cavitation	Isolated nuclei grow over a blade pressure minimum.	Inception signature and scattered pitting.

4.3.3 Erosion, Noise, and Structural Loading

Propeller cavitation can be acceptable, limiting, or destructive depending on its extent and collapse location. A stable tip vortex may be dominated by radiated noise, while a highly unsteady cloud collapse near the blade can produce severe erosion. Pressure pulses can excite the hull, stern structure, shaft line, rudder, or appendages. For naval and research vessels, cavitation also increases acoustic detectability. For commercial vessels, comfort, fatigue, efficiency, and maintenance are often the controlling concerns [10–12,14,15].

Figure 4.7. Cavitation erosion concentrated near the outer edge of a marine propeller. Photograph by Erik Axdahl, [16].

4.3.4 Waterjets, Pumpjets, Hydrofoils, and Rudders

Waterjet and pump jet systems can cavitate at inlet lips, rotor leading edges, stator vanes, tip clearances, and nozzle regions. Inlet distortion, air ingestion, shallow operation, fouling, and maneuvering can produce rapid changes. Hydrofoils and rudders cavitate at leading edges, tips, gaps, hinges, and separation zones. Tip or propeller vortices may strike an appendage and collapse on a surface that is not itself the formation site. The same analytical principle applies throughout: identify the minimum pressure region and then track cavity transport to the collapse region [17], [10–12,14,15].

4.3.5 Hydraulic Turbines and Thoma Coefficient

Reaction turbines can cavitate on runner blades, at the runner outlet, in tip or seal vortices, and in the draft tube. The Thoma cavitation coefficient ${\sigma }_T$ is commonly written as where $H_a$ is atmospheric pressure head, Hv is vapor pressure head, $H_s$ is suction head or setting referenced according to the convention, and H is turbine head. Installation elevation, tailwater level, temperature, and operating point determine the available coefficient. Plant specific model tests and manufacturer limits remain necessary because turbine geometry and scale effects are decisive [5], [18], [5]:

$${\sigma }_T=\frac{H_a-H_v-H_s}{H}$$

(4.9)

4.3.6 Model Tests and Scaling

Cavitation tunnels and model basins reproduce a target cavitation number while controlling water quality, nuclei, pressure, velocity, and observation. Complete similitude is difficult because Reynolds number, nuclei distribution, surface roughness, gas content, structural stiffness, and acoustic propagation cannot all be scaled independently. ITTC procedures therefore specify model preparation, observation, erosion assessment, and noise measurement practices to improve repeatability [14], [15]. Model results should be interpreted with stated nuclei and roughness conditions, not only with a nominal cavitation number.

4.4 Negative Effects and Failure Mechanisms

4.4.1 Performance Degradation

Vapor occupies volume that would otherwise carry liquid and changes momentum transfer. In pumps it can reduce head, capacity, efficiency, and stability. In valves it can limit flow, change gain, and increase required actuator effort. On propellers and hydrofoils, it can alter lift, thrust, torque, and control force. Large cavities can block passages, create rotating asymmetry, and cause abrupt load changes [5,18], [1], [7], [10].

4.4.2 Noise, Vibration, and Pressure Pulsation

Individual bubble collapse produces high frequency content, while cloud shedding and blade interactions create lower frequency modulation. The fluid forcing is transmitted through casings, pipes, shafts, foundations, and hull structures. A small cavity can be acoustically conspicuous without causing measurable erosion; conversely, a remote collapse can damage a surface while the formation site appears benign. Frequency content must therefore be interpreted with machinery orders, blade passing frequency, structural resonances, and structural transmission paths [5,17,18].

4.4.3 Erosion, Corrosion, and Fatigue

Cavitation erosion is an accumulation of microscopic plastic deformation, work hardening, cracking, grain removal, and pit coalescence caused by repeated liquid impact and shock loading. Material loss often includes an incubation period followed by acceleration and a later rate change as surface geometry and residual stress evolve. Corrosion can remove protective films and weaken the surface between impacts, while cavitation removes corrosion products and exposes fresh metal. The combined loss can exceed the sum of separate mechanical and electrochemical effects [5], [5], [10,19–21].

A commonly reported mean depth of erosion rate MDER is where ΔV is volume loss, Δm is mass loss, ${\rho }_s$ is solid density, A is exposed area, and Δt is the reporting interval. Test methods such as vibratory apparatus and cavitating liquid jets provide comparative material data, but direct ranking can change with amplitude, liquid, temperature, specimen geometry, and exposure regime [20], [21]:

$$MDER=\frac{\mathrm{\Delta }V}{A\mathrm{\Delta }t}=\frac{\mathrm{\Delta }m}{{\rho }_{s}A\mathrm{\Delta }t}$$

(4.10)

Table 4.4. Negative effects and representative failure pathways.

Effect	Immediate mechanism	Potential consequence	Engineering evidence
Head, thrust, or control loss	Vapor blockage and altered pressure distribution.	Reduced capacity, unstable control, overspeed risk in coupled systems.	Performance curve shift, flow limitation, transient logs.
Noise	Bubble collapse, cloud shedding, vortex oscillation.	Nuisance, detectability, regulatory or comfort issue.	Operating condition correlation and characteristic spectral pattern.
Vibration and pulsation	Unsteady fluid force and asymmetric vapor.	Bearing load, piping fatigue, fastener loosening, structural resonance.	Pressure and vibration trends correlated with operating state.
Erosion	Microjets, shock waves, and repeated localized strain.	Loss of blade or trim profile, leakage, perforation, debris.	Pit morphology, mass or volume loss, replica or 3D scan.
Corrosion acceleration	Film removal and enhanced mass transfer.	Rapid loss in aggressive liquid.	Chemistry, potential, deposits, pit chemistry, material comparison.
Thermal and process effects	Two phase volume, local heating or cooling, gas release.	Temperature excursions, degassing, altered reaction or product quality.	Temperature, dissolved gas, composition, residence time.
Secondary mechanical failure	Imbalance, hydraulic instability, cyclic load.	Seal, bearing, shaft, weld, or support failure.	Alignment, orbit, shaft current, crack examination, fatigue assessment.

4.4.4 Why Visible Cavitation Does Not Equal Damage

Erosion requires collapse energy to be delivered close enough to a susceptible surface with sufficient repetition. A large, attached cavity may collapse far downstream and cause little local damage. A smaller cloud that collapses repeatedly at a blade trailing edge of a blade can be highly erosive. Gas content may increase cavity volume while cushioning collapse. Material hardness alone is not a reliable universal predictor because strain rate response, toughness, phase stability, residual stress, corrosion resistance, and coating adhesion also matter [5], [10], [19].

4.5 Prevention, Mitigation, and Operational Control

4.5.1 Control Hierarchy

The most effective control removes the hydraulic cause before relying on surface resistance. A practical hierarchy is: increase the minimum pressure or reduce local velocity; reduce the time or volume of cavity growth; prevent coherent cloud shedding; move collapse into the liquid or a replaceable protected region; reduce rebound intensity by controlled gas where appropriate; and improve material or coating resistance. Operational limits and maintenance complete the design. Because one measure can shift the pressure field, every change should be checked for a new formation or collapse location [5,18], [1,3,4,7–12,14,15].

Table 4.5. Prevention and mitigation measures.

Control level	Representative measures	Best suited to	Important caution
System pressure and static head	Raise suction level or vessel pressure; lower equipment; increase downstream pressure; reduce lift.	Pumps, valves, turbines, and process loops.	Added backpressure or elevation change can move the problem elsewhere.
System loss and velocity	Larger pipe, smoother inlet, open valves, clean strainers, lower speed, lower flow, parallel equipment.	Suction systems, bypasses, and high velocity restrictions.	A lower flow can worsen recirculation cavitation in pumps.
Geometry	Larger leading edge radius, lower loading, staged trim, diffuser, improved inlet bell, reduced clearance, vortex control.	Impellers, valves, propellers, hydrofoils, and nozzles.	Geometry changes affect efficiency, control range, solids passage, and structural stress.
Operating envelope	Preferred operating region, minimum flow, speed schedule, immersion limit, valve travel limit, transient ramp.	Installed machinery with variable duty.	Limits must cover start, stop, emergency, and degraded conditions.
Collapse management	Move collapse away from walls, use sacrificial liner, enlarge downstream pipe, controlled air or gas injection.	Residual cavitation that cannot be eliminated.	Gas can reduce performance, alter process chemistry, or increase cavity volume.
Material and surface	Tough alloy, hardfacing, resilient coating, polished finish, repairable insert.	Known unavoidable exposure zones.	Material changes do not correct blockage, vibration, or system instability.
Inspection and maintenance	Operating condition review, inspection interval, nuclei or gas control, and fouling control.	Critical equipment and variable liquids.	Criteria without operating context can be misleading.

4.5.2 Pumps and Suction Systems

For pumps, the first priority is reliable $NPS{H}_A$ at every credible operating condition. The calculation should include the lowest tank level, highest liquid temperature, lowest barometric or vessel pressure, maximum suction loss, strainer fouling, simultaneous flow in common headers, and transient acceleration. The pump should then be selected and operated within an appropriate region with application specific NPSH margin [1,3,4].

• Use a flooded suction where practical and avoid high points that trap gas. Provide adequate submergence and anti-vortex arrangements at intakes.

• Select a larger or slower pump, a double suction impeller, an inducer, or a booster pump when inlet energy density is too high.

• Maintain clearances and leading edges. Wear can increase leakage vortices and roughness; an overaggressive repair can distort the inlet profile.

• Use variable speed rather than suction throttling for routine control where the system and process permit.

• Provide minimum flow protection and avoid prolonged shutoff or very low flow operation. Recirculation heating can also raise vapor pressure locally.

• Verify the actual installed datum, pressure reference location, and velocity head convention when comparing field data with pump curves.

4.5.3 Valves and Piping

Valve control focuses on limiting the pressure reduction per stage and managing recovery. Multistage and multipath trims divide the pressure drop. Low recovery valve styles, diffusers, larger downstream piping, and straight outlet runs reduce collapse intensity at vulnerable surfaces. A valve that spends most of its life near the seat may require a different trim or smaller parallel valve rather than a larger body. For dirty service, the minimum passage size and plugging risk may dominate an otherwise attractive anti cavitation design [7–9].

4.5.4 Marine Propulsors and Hydrofoils

Marine mitigation includes increased blade area, reduced loading, appropriate skew, refined leading edge and tip geometry, wake improvement, adequate immersion, surface finish control, and operating limits for speed or maneuvering. Boss cap fins, ducts, pre swirl stators, and wake equalizing devices can alter vortices and inflow, but their net benefit must include resistance, structural load, fouling, and off design behavior. Air injection can reduce erosive collapse or radiated noise in specialized cases, but it may reduce efficiency and change signatures [10–12,14,15].

4.5.5 Materials, Coatings, and Surface Strategy

Table 4.6. Materials and surface strategies for cavitation exposure.

Strategy	Potential benefit	Limitations and selection factors
Tough stainless or duplex alloy	Good combination of corrosion resistance, strength, and strain hardening.	Weld procedure, phase balance, chloride cracking, cost, and galvanic compatibility.
Nickel aluminum bronze or other marine alloy	Established propeller and seawater service with repair experience.	Casting quality, selective corrosion, weld repair, and actual cavitation regime.
Hardfacing or thermal spray	High hardness and local repairability.	Brittleness, porosity, residual stress, bond strength, and edge failure.
Elastomeric or compliant coating	Absorbs impact and can delay pitting.	Adhesion, swelling, temperature, abrasion, edge lifting, and process compatibility.
Polishing and profile restoration	Reduces roughness nuclei and local separation.	Cannot correct an adverse bulk pressure field; excessive grinding changes geometry.
Sacrificial or replaceable insert	Moves maintenance to a controlled component.	Interface sealing, fastener fatigue, debris, and replacement access.
Cathodic or corrosion control	Reduces electrochemical contribution in conductive liquids.	Does not prevent mechanical impact; excessive hydrogen may affect some alloys or coatings.

Comparative cavitation tests are useful for screening, but field performance also depends on geometry, impact spectrum, corrosion, residual stress, welds, and repair quality. A hard material can fail by brittle spallation, while a tougher material can absorb repeated strain. Surface finish should be documented because roughness changes both nuclei activation and local stress concentration [5], [10,19–21].

4.5.6 Operational Control and Verification

Operational control can be implemented as a speed schedule, minimum pressure override, minimum flow recirculation, valve travel restriction, backpressure control, temperature limit, or marine speed and immersion envelope. The control variable should be tied to the actual mechanism. For example, reducing pump flow may improve $NPS{H}_A$ but worsen inlet recirculation; increasing valve backpressure may suppress cavitation but reduce process throughput. Verification should repeat the original performance check and include a review for displaced damage.

Nomenclature

The following key defines the symbols and abbreviations used in this chapter. Unless otherwise stated, quantities are expressed in SI units.

Symbol	Definition	SI unit or status
A	Exposed area used in erosion measurements	m²
$C_p$	Pressure coefficient	dimensionless
$f_0$	Small amplitude bubble resonance frequency	Hz
$F_L$	Liquid pressure recovery factor for a control valve	dimensionless
H	Pump or turbine head	m
$h_{f,s}$	Suction line friction and minor loss	m
M	Absolute NPSH margin	m
$M_R$	NPSH margin ratio	dimensionless
MDER	Mean depth of erosion rate	m s⁻¹ or µm h⁻¹
n	Rotational speed	s⁻¹ or r min⁻¹
$NPS{H}_A$	Net positive suction head available	m
$NPS{H}_R$	Net positive suction head required	m
$NPS{H}_3$	NPSH at a 3 percent pump head drop	m
$N_{ss}$	Suction specific speed under a stated unit convention	convention dependent
p	Absolute static pressure	Pa
$p_B$	Pressure at the bubble wall	Pa
$p_v$	Saturation vapor pressure	Pa
$p_{vc}$	Pressure at the vena contracta	Pa
$P_h$	Hydraulic power	W
$P_{shaft}$	Pump shaft power	W
Q	Volumetric flow rate	m³ s⁻¹
R	Bubble radius	m
$t_c$	Ideal collapse time	s
V	Mean liquid velocity	m s⁻¹
$V_{R(r)}$	Local resultant propeller velocity at radius r	m s⁻¹

Greek Letters

Symbol	Letter name	Meaning in this chapter
γ	Gamma	Surface tension
κ	Kappa	Polytropic exponent
μ	Mu	Dynamic viscosity
ρ	Rho	Liquid or solid density
σ	Sigma	Cavitation number
${\sigma }_v$	Sigma	Valve cavitation index
${\sigma }_T$	Sigma	Thoma cavitation coefficient
η	Eta	Efficiency
Δ	Delta	Finite difference or measured change

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