How to read a normalized curve family
Every catalogue curve can be redrawn without units: divide each coordinate by its own best-efficiency-point (BEP) value. What is left is pure shape — and shape is governed by a single number, the specific speed.
1 · Normalized variables
Subscript n marks the duty / BEP point, so by construction q = h = p = 1 and η = 100 % exactly at BEP — for every pump, at any size and any speed. The plot above spans q = 0 (shut-off) to q = 1.5 (runout).
2 · The seven reference curves
The family below spans the whole centrifugal range from low-Ns radial to axial propeller. Ns is the US notation (rpm, gpm, ft); the metric nq (m³/s, m) and the dimensionless Ωs are rigid conversions: Ns = 51.64·nq = 2733.016·Ωs.
| Curve | Ns (US) | nq (metric) | Ωs | Suction | h at shut-off | p at shut-off |
|---|---|---|---|---|---|---|
| #1 | 900 | 17 | 0.33 | double | 1.10 | 0.30 |
| #2 | 1500 | 29 | 0.55 | double | 1.12 | 0.35 |
| #3 | 2200 | 43 | 0.80 | double | 1.20 | 0.50 |
| #4 | 3000 | 58 | 1.10 | double | 1.28 | 0.60 |
| #5 | 4000 | 77 | 1.46 | double | 1.48 | 0.95 |
| #6 | 5700 | 110 | 2.09 | single | 1.90 | 1.85 |
| #7 | 9200 | 178 | 3.37 | single | ≥ 2.00 | 2.35 |
The simulator draws the curve for your Ns by log-Ns interpolation between the two neighbouring table curves, so any intermediate specific speed gets a physically consistent blend — not a jumped classification.
3 · Curve shape vs. stability
| Curves | Head-curve shape | Stability | What it means on the plant |
|---|---|---|---|
| #1–#2 (Ns ≤ 1500) | Rising: h climbs from shut-off to a part-flow peak (h ≈ 1.10–1.14) before falling | 🟡 Unstable region possible | A flat/rising start means the system curve can intersect the pump curve at two flows below the peak — hunt, surge and cavitation-like noise in parallel operation or at low load. Keep continuous operation right of the peak. |
| #3 (Ns ≈ 2200) | Flat: h ≈ 1.19–1.20 over q = 0–0.5 | 🟡 Borderline | Marginally stable alone; in parallel, load sharing between two flat curves is ill-conditioned — a small head-error shifts large flow. Throttling control loses sensitivity near shut-off. |
| #4–#7 (Ns ≥ 3000) | Steep and continuously falling: shut-off h from 1.28 up to ≈ 2.0 | 🟢 Stable everywhere | Exactly one operating point per system curve — single units parallel cleanly, control valves keep authority down to low flow (mind the minimum-flow line). |
4 · Power behaviour from radial to axial
Shut-off power ps/o rises monotonically with Ns across the family — this single number decides how the pump may be started:
$$p_{s/o}=\frac{P(q=0)}{P_n}:\quad \text{#1 0.30}\;\to\;\text{#4 0.60}\;\to\;\text{#5 0.95}\;\to\;\text{#6 1.85}\;\to\;\text{#7 2.35}$$| ps/o band | Verdict | Start-up rule |
|---|---|---|
| < 100 % (curves #1–#5) | 🟢 Non-overloading | Radial pumps draw the least power at shut-off (30–60 % of BEP power) and more as flow opens: start against a closed or throttled valve to cut motor inrush and system hammer; the motor is sized at runout, never at shut-off. |
| 100–150 % | 🟡 Shut-off above BEP | Mixed-flow machines already exceed BEP power closed-valve. Crack the valve open (~25–50 % flow) before start and reach full flow quickly; verify the motor thermal margin across the whole curve. |
| > 150 % (curves #6–#7) | 🔴 Overloading — never dead-head | Axial and high-specific-speed mixed-flow pumps peak at shut-off (185–235 % of BEP power): start strictly against an open valve, fit a minimum-flow bypass, and interlock the driver against dead-heading. |
5 · Why one family fits any pump — the similarity laws
Geometrically similar impellers obey these scaling laws exactly. Now divide every Q, H, P by its own BEP value: the factors (N2/N1) and (D2/D1) cancel, and what remains depends only on the ratio of the two flows — i.e. on where you sit on the q-axis. Equivalently, the normalized curves of all similar pumps collapse onto one curve per Ns: a 20 mm chip-pump impeller and a 2 m water-works impeller with the same Ns = 2733 share the very same h(q), p(q), η(q) page. That is why seven curves cover every centrifugal pump built.
6 · Head coefficient ψ and impeller diameter D2
The achievable head coefficient ψ falls as specific speed rises (ψ ≈ 0.64 at Ns 900 down to ψ ≈ 0.25 at Ns 9200 — a wide axial blade row cannot build pressure as efficiently as a narrow radial one). The side panel tracks ψ for the current Ns and the corresponding relative diameter at fixed N and H. Schematic, figure-read ±10 %.
Accuracy & anchors
The family is schematic by nature (the source figure is captioned "approximate performance curves"); the digitization used here is accurate to about ±0.05 on the normalized axes. Fixed anchor points the simulator reproduces exactly:
| Case | Readout | Value | Why exact |
|---|---|---|---|
| Ns = 2733, q = 1 | h, p, η | 1.000 / 1.000 / 100 % | BEP normalization holds for every curve, so any blend of them still passes exactly through (1, 1) |
| Ns = 900 (curve #1) | h at shut-off | 1.10 | Table-curve datum, no interpolation |
| Ns = 9200 (curve #7) | p at shut-off | 2.35 | Table-curve datum, no interpolation |
- Interpolation — linear in log-Ns between the two adjacent table curves, separately for h, p and η; shut-off extrapolates the lowest-q datum flat.
- Stability thresholds — rising/flat verdict up to Ns ≤ 2200 (🟡), steep-stable from Ns ≥ 3000 (🟢).
- Power verdict — ps/o < 100 % 🟢, 100–150 % 🟡, > 150 % 🔴.