The three lines — what the animation shows
The chart plots static head above vapor pressure, \((p-p_v)/\rho g\), along the streamline that wraps the blade leading edge. Three lines tell the whole story: the blue inlet pressure line (its height above zero is exactly NPSHA), the red vapor line pv, and the dark local pressure curve — a valley carved by the acceleration around the inlet edge, deepest on the blade suction surface just downstream of the nose. Cavitation lives in exactly one sentence: wherever the dark curve dives below the red line, the liquid boils.
NPSHA — the installation's margin
| Symbol | Meaning | Units |
|---|---|---|
| \(p_{e,\text{abs}}\) | absolute pressure at the source liquid surface | psi (kPa) |
| \(p_v\) | vapor pressure of the liquid at the pumping temperature | psi (kPa) |
| \(Z_e-Z_s\) | source level above the pump datum — negative for suction lift | ft (m) |
| \(H_{vs}\) | suction-line friction and fitting losses | ft (m) |
| \(\Delta p(x)\) | local pressure depression from inlet to position x — maximal depression \(\Delta p_{max}\) sets the inception NPSH | psi (kPa) |
NPSHA belongs to the installation; the valley belongs to the pump. Lowering the slider pushes the blue line — and the whole valley riding on it — down toward pv. The valley bottom touches pv when \(NPSH_A=\Delta p_{max}/\rho g\): first bubbles, the inception value NPSHi.
Inception, the 3% criterion and the collapse
Between inception and the 3% point the pump "hides" its cavitation: a visible vapor pocket exists, the head barely moves. Catalog NPSHr is quoted at the 3% head-drop point — a performance criterion, not a damage criterion: at NPSH3% the pump has been cavitating hard for a long time. Below it the vapor pocket chokes the passage and the head falls off a cliff — in the simulator, watch the bar drop while the pocket blankets the valley.
Why erosion ∝ U⁶ — the violence of collapse
| Symbol | Meaning | Units |
|---|---|---|
| \(t_c\) | Rayleigh collapse time of a vapor cavity of initial radius \(R_0\) | s |
| \(p_\infty-p_v\) | driving pressure on the collapsing bubble | psi (kPa) |
| \(\dot{E}\) | erosion (material-loss) rate | mm/year |
| \(U_e\) | impeller eye tip speed | ft/s (m/s) |
A cavity does not fade — it implodes. The classical Rayleigh analysis of a collapsing empty sphere gives the millisecond time scale above; asymmetric collapse near a wall drives a micro-jet through the bubble at extreme velocity, producing impact pressures on the order of \(10^{4}\) atmospheres on a spot smaller than a grain of sand. The shock scales with the sixth power of tip speed: raise speed 25% on the same duty and the erosion rate multiplies by about \(1.25^{6}\approx 3.8\). A single bubble lives ≈ 0.003 s — but millions collapse on the blade every minute, which is why the red pitting marks accumulate so fast in the amber zone.
The R traffic light — margin ratio thresholds
| Margin ratio R | State | What it means | Verdict |
|---|---|---|---|
| R < 1 | Full cavitation | NPSHA below NPSH3%: vapor blankets the inlet, head collapsed below 97% and falling, gravel noise, strong vibration. Collapses are vapor-cushioned here, but the duty is unacceptable. | 🔴 |
| 1 ≤ R < 5 | Active erosion zone | Head looks fine, yet collapses attack the leading edge continuously. Erosion and pressure pulsation are most severe near R ≈ 2 — the worst place to sit. Continuous duty here slowly eats the impeller. | 🟡 |
| R ≥ 5 | Cavitation-free | NPSHA ≥ NPSHi: the valley bottom never reaches pv, no vapor forms. Recommended margin for continuous duty. | 🟢 |
| NPSHA < 0.6 m (2 ft) | Absolute floor | Installation floor for any liquid whatever the arithmetic says. | 🔴 |
The full margin ladder, bottom to top: NPSH3% (head −3%) → NPSH40 (≈ 40,000 h erosion-free impeller life) → NPSHi ≈ 5 × NPSH3% (first bubbles). The three simulator presets stand exactly on R = 1, R ≈ 2 (drag there) and R = 5.
Hot water and hydrocarbons — corrections to the picture
| Effect | What changes | Limit / value |
|---|---|---|
| Hot-water / hydrocarbon NPSHr reduction | Weak thermodynamic cushioning of bubble collapse allows the manufacturer's cold-water NPSHr to be reduced | reduction ≤ the smaller of 50% of the cold-water value and 3 m (10 ft) |
| Worst water temperature | water is most aggressive at 38–49 °C (100–120 °F); damage falls above that as vapor cushioning grows | peak at 38–49 °C |
| Vapor head eats NPSHA | water vapor head climbs from ≈ 0.24 m at 20 °C to ≈ 4.8 m at 80 °C — the red line rises toward the valley | ×20 from 20 → 80 °C |
| Hydrocarbon media | hydrocarbon vapors collapse so weakly that erosion is rarely observed — performance collapse still applies | erosion ≈ none |
| Dissolved gas | gas coming out of solution cushions collapses — erosion falls, but head can still sag | GVF > 0.07 → head decay 🔴 |
Worked example — the three presets
Reference duty NPSH3% = 14 ft (4.27 m). Every preset value below is reproduced exactly by the simulator buttons:
| Preset | NPSHA | R = NPSHA/NPSH₃ | Head retention | Erosion activity | Verdict |
|---|---|---|---|---|---|
| NPSHi (inception) | 70 ft (21.3 m) | 5.00 | 100% | ≈ 0% | 🟢 valley bottom touches pv, first bubbles |
| NPSH₃% (3% drop) | 14 ft (4.27 m) | 1.00 | 97.0% | ≈ 44% | 🟡 the 3% criterion point |
| Full cavitation | 7 ft (2.13 m) | 0.50 | ≈ 32% | ≈ 15% | 🔴 head collapsed, pocket blankets the inlet |
| — (drag here) | 28 ft (8.53 m) | 2.00 | 98.7% | 100% | 🟡 worst erosion + pulsation at R ≈ 2 |
Engineering criteria applied
- Inception — NPSHi ≈ 5 × NPSH3%; at R ≥ 5 the vapor volume is essentially zero (the preset "NPSHi" stands exactly there).
- 3% head-drop criterion — the industry definition of NPSHr: head = 97% of the non-cavitating value at R = 1; below it the collapse is modeled steeply (H ≈ 97%·R1.6).
- Erosion activity — bell-shaped in R, peaking at R ≈ 2 (worst erosion and pulsation), zero at inception, cushioned inside full cavitation; the pitting marks accumulate in proportion to it.
- Absolute floor — NPSHA ≥ 0.6 m for any installation, whatever the ratio says.
- Schematic geometry — the valley is a parametric parabola tuned to the criteria above; real blade pressure fields are measured or CFD-computed. The thresholds, not the curve, are the engineering.