Normalized Curves by Specific Speed

One slider, the whole pump universe: set the specific speed Ns and the simulator redraws the normalized characteristic curves — head h = H/Hn, power p = P/Pn and efficiency η against normalized flow q = Q/Qn — interpolated live from the seven classic table curves. A shape-and-stability verdict, a morphing impeller cross-section and a ψ/D2 estimate ride along. A pumpXSolver engineering tool.

h = H/Hn (head) p = P/Pn (power) η — right axis, % adjacent table curves BEP anchor (q = 1)

Results — your Ns, mapped onto the family

Shape & stability — head-curve verdict

Power behaviour — shut-off vs BEP

Specific speed Ns — master control

Slider steps in log-Ns space, so each pixel moves the curve family by an equal ratio; the buttons jump straight to the seven table speeds. Ns in US units (rpm·√gpm/ft0.75); metric nq = Ns/51.64.

Impeller cross-section — schematic, driven by Ns

Meridional section, schematic — proportions only, not to scale. Narrow radial passage → mixed-flow → axial propeller.

Head coefficient ψ & diameter D2 — estimate

ψ = gH/U2² at BEP
Relative D2 (same N & H)
80%100%120%140%160%
D2 ∝ 1/(N·√ψ) at fixed speed and per-stage head; 100 % = the Ωs = 1 reference (Ns ≈ 2733). Schematic, figure-read ±10 %.

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

$$q=\frac{Q}{Q_n},\qquad h=\frac{H}{H_n},\qquad p=\frac{P}{P_n},\qquad \eta=\frac{P_{\text{water}}}{P_{\text{shaft}}}$$

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.

CurveNs (US)nq (metric)ΩsSuctionh at shut-offp at shut-off
#1900170.33double1.100.30
#21500290.55double1.120.35
#32200430.80double1.200.50
#43000581.10double1.280.60
#54000771.46double1.480.95
#657001102.09single1.901.85
#792001783.37single≥ 2.002.35

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

CurvesHead-curve shapeStabilityWhat 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 possibleA 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 everywhereExactly 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 bandVerdictStart-up rule
< 100 % (curves #1–#5)🟢 Non-overloadingRadial 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 BEPMixed-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-headAxial 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

$$\frac{Q_2}{Q_1}=\frac{N_2}{N_1}\Big(\frac{D_2}{D_1}\Big)^{3},\qquad \frac{H_2}{H_1}=\Big(\frac{N_2}{N_1}\Big)^{2}\Big(\frac{D_2}{D_1}\Big)^{2},\qquad \frac{P_2}{P_1}=\Big(\frac{N_2}{N_1}\Big)^{3}\Big(\frac{D_2}{D_1}\Big)^{5}$$

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

$$\psi=\frac{g\,H_n}{U_2^{\,2}},\qquad U_2=\frac{\pi N D_2}{60} \;\;\Longrightarrow\;\; D_2=\frac{60}{\pi N}\sqrt{\frac{g\,H_n}{\psi}}\;\propto\;\frac{1}{N\sqrt{\psi\,}}$$

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:

CaseReadoutValueWhy exact
Ns = 2733, q = 1h, p, η1.000 / 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-off1.10Table-curve datum, no interpolation
Ns = 9200 (curve #7)p at shut-off2.35Table-curve datum, no interpolation