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Curve × Flow-Regime Simulator

One slider — q = Q/QBEP — walks a pump from shutoff to beyond runout. Left: the normalized H, η and P characteristic curves with the live duty point. Below: what the flow is actually doing inside the impeller — an inlet recirculation vortex at low flow, smooth shockless streamlines at the design flow, a jet-wake exit skew in overload — blending smoothly with the slider, with a synchronized 🟢🟡🔴 verdict card. A pumpXSolver engineering tool.

h = H/HBEP η/ηBEP p = P/PBEP Duty point (all three curves) q < 0.50 deep recirculation 0.50–0.70 onset · 1.10–1.20 overload 0.70–1.10 optimal

Duty point — synchronized with both canvases

Flow slider — the only knob

Reference duties — one click each

Each button sets q to the matching duty. Deep link: append ?q=0.35 to the URL.

How to read the chart

Blue / green / amber curves — head, efficiency and power, each divided by its own BEP value, so the three plot on one axis and meet at (1.00, 1.00).
Dark dashed line + dots — the current duty point on all three curves.
Tinted bands — the three operating zones; the traffic light below follows them.

Moving the duty point

Closing a throttle walks the duty up-left: h rises toward 1.18, p falls toward 0.50 — while η collapses and recirculation fills the passage. Opening it walks down-right: h falls, p climbs past 1.1, the wake lane thickens. A pump always sits where its curve crosses the system curve — q is the pump side of that meeting.

Fixed model — this simulator

Schematic radial stage, Ns ≈ 3,000 (Ωs ≈ 1.1)
Shutoff head 1.18 × HBEP — inside the stable 1.15–1.20 band
η = 0% at q = 0 · peak exactly at q = 1.00 · 88% at q = 1.30
Shutoff power p(0) = 0.50 × PBEP
Runout at q = 1.20 · MCSF ≈ 0.50 · curves are schematic — the thresholds are the engineering
Streamlines + flow particles Inlet recirculation vortex Wake lane (slow particles) Blades, z = 6 (schematic) Passage of the highlighted channel

What to watch — as the slider moves

Below q = 0.7 — the red spiral vortex at the eye grows and the particle lanes through the passage empty out: flow is spilling back through the inlet.
q = 0.7–1.1 — smooth, evenly spaced streamlines: the shockless design flow.
Above q = 1.1 — the exit jet hugs the pressure-side wall while the grey low-momentum wake lane thickens behind the suction-side blade: the jet-wake offset.

Three regimes in the passage

🔴 q < 0.50 · deep recirculation
Strong positive incidence separates the suction-surface boundary layer; a channel vortex rolls up and part of the flow spills back out of the eye. Pulsation, cavitation noise, heat. Continuous duty forbidden (below MCSF).

🟡 q = 0.50–0.70 · recirculation onset
The vortex sheds intermittently from the leading edges; vibration rises, efficiency bleeds away. Acceptable only briefly.

🟢 q = 0.70–1.10 · shockless smooth flow
Streamlines parallel and evenly loaded, thin wake — the design intent, and the only band for continuous duty.

🟡 q = 1.10–1.20 · overload, jet-wake growing
Negative incidence and rising blade loading pile low-momentum fluid behind the suction-side trailing edge; the exit jet hugs the pressure side. NPSHr climbs steeply.

🔴 q > 1.20 · beyond runout
Past the published curve end — performance undefined.

Blending — smooth, not stepped

Eye-vortex strength ramps linearly from q = 0.7 down to full at q = 0; the jet-wake skew ramps from q = 1.05 up to full at q = 1.30. Particle speed follows the through-flow; wake-lane particles slow and turn grey as the skew grows. The geometry is a schematic — not CFD.

Reading a pump curve by regime

A vendor curve is one line per quantity, but an operator lives in regions of it. Normalizing every axis by its own best-efficiency value collapses any pump onto one comparable picture, and the picture divides naturally into three regimes: a recirculation region at low flow, a best-efficiency region around the design flow, and an overload region toward runout. This simulator links the curve picture to what the fluid is doing between the blades at the same instant.

Normalized definitions

$$q=\frac{Q}{Q_{BEP}},\qquad h=\frac{H}{H_{BEP}},\qquad p=\frac{P}{P_{BEP}},\qquad \eta=\frac{\rho g Q_{BEP} H_{BEP}}{P_{BEP}}\cdot\frac{P}{\rho g Q H}$$

At the BEP itself: q = h = p = η/ηBEP = 1 exactly. Because the axes are fractions of BEP values, the picture is independent of units, size and speed — a 40 m³/h chemical pump and a 40,000 gpm water pump share it.

SymbolMeaningUnits
\(q\)flow fraction of BEP — the slider–
\(h\)head fraction of BEP head–
\(p\)shaft-power fraction of BEP power–
\(Q_{BEP},H_{BEP},P_{BEP}\)flow, head and shaft power at the best-efficiency pointany consistent set
\(MCSF\)minimum continuous stable flow — lowest flow at which continuous operation is allowed (thermal, vibration and recirculation limits)m³/h, gpm
runoutpublished end of the curve — the largest flow the vendor guaranteesm³/h, gpm

The schematic curve set used here

$$h(q)=1-0.298\,(q-1)-0.118\,(q-1)^{2}$$ $$\frac{\eta(q)}{\eta_{BEP}}=1-1.1142\,x^{2}-0.5884\,x^{3}-0.4742\,x^{4},\qquad x=q-1$$ $$p(q)=\frac{q\,h(q)}{\eta(q)/\eta_{BEP}}$$

The coefficients are tuned so the family satisfies the classic checks simultaneously and self-consistently:

AnchorValueWhy it matters
h(1), η(1), p(1)1.000 exactlythe BEP is the normalization point — all three curves meet there
h(0) — shutoff head1.18 × HBEPinside the 1.15–1.20 stable band, monotonic falling, no hump
η(0) — shutoff efficiency0 exactlyno flow, no useful work — all power becomes heat
η peak locationexactly q = 1η′(q) = −q·(positive polynomial): unique maximum at the BEP
p(0) — shutoff power0.50 × PBEPlimit p = h(0)/η′(0) = 1.18/2.36 — below BEP power, closed-valve start permissible
h(1.3) · η(1.3) · p(1.3)0.900 · 0.880 · 1.330overload: head slides down, efficiency falls, power climbs

Three-zone threshold table

q = Q/QBEPZoneWhat is happening inside the pumpDuty guidanceVerdict
< 0.50Deep recirculationsuction and discharge recirculation fully developed; inlet vortex fills the eye; low-frequency pulsation, cavitation, heat build-up — power churns a shrinking flowcontinuous operation forbidden (below MCSF ≈ 0.4–0.5 × QBEP for process pumps); seconds only🔴
0.50 – 0.70Recirculation onsetinlet vortices shed intermittently from the leading edges; vibration and noise rise; efficiency already 10–25 points downstart-up and brief transitions only🟡
0.70 – 1.10Best-efficiency zoneshockless entry, smooth parallel streamlines, thin wake; hydraulic excitation minimal the continuous-duty band; API-style preferred region 0.8–1.1🟢
1.10 – 1.20Overloadnegative incidence; jet-wake exit distortion grows; NPSHr climbs steeply; power reaches 1.08–1.18 × PBEPverify motor nameplate and NPSH margin before holding🟡
> 1.20Beyond runoutpast the published curve end: NPSHr and vibration escalate steeply, head slides toward 0.90 × HBEP while power keeps climbingperformance undefined — pull back below q = 1.2🔴

What the flow schematic shows

The right-hand canvas is a front view of a six-blade impeller with one passage highlighted. Bezier streamlines follow the blade passage from the eye to the OD, and particles ride them at a speed proportional to the through-flow. Three states blend smoothly as the slider moves:

The passage geometry is a schematic; particle motion is kinematic, not CFD. What is engineering are the thresholds: they decide how long a duty may be held, how the motor is sized, and where on the curve a pump should live.

Worked anchor set — reproduced exactly by the simulator

qh = H/HBEPη/ηBEPp = P/PBEPZoneVerdict
0.00118.0%0.0%50.0%deep recirculation🔴 shutoff — heat, no work
0.50112.0%76.5%73.1%recirculation onset🟡 MCSF reference
0.70107.9%91.2%82.8%best-efficiency zone🟢 continuous-duty band opens
1.00100.0%100.0%100.0%BEP🟢 the design duty
1.1096.9%98.8%107.9%best-efficiency zone edge🟢/🟡 preferred-region boundary
1.2093.6%95.0%118.2%overload🔴 runout line — curve ends
1.3090.0%88.0%133.0%beyond runout🔴 performance undefined

Engineering criteria applied

Try it interactively — background reading: Pump Characteristic Curve · Minimum Continuous Flow · System Curve Calculator