How it works — the four faces of specific speed
Specific speed is a single number that fixes the shape of a centrifugal stage: all geometrically similar pumps operating at similar conditions share the same specific speed, regardless of size or rotational frequency. It exists in four equivalent notations — same physics, different unit systems.
1 · Definitions
All three are evaluated at BEP with head per stage. Note the metric nq uses flow in m³/s, not m³/h — a frequent source of factor-of-60 errors.
2 · Where the constant 2733.016 comes from
Converting the US form into the dimensionless one means converting flow (1 m³/s = 15,850.32 gpm), head (1 ft = 0.3048 m) and speed (rad/s → rpm):
$$\frac{N_s}{\Omega_s}=\underbrace{\frac{30}{\pi}}_{9.5493}\times \underbrace{\sqrt{\frac{Q_{\text{gpm}}}{Q_{\text{m}^3/\text{s}}}}}_{\sqrt{15850.32}=125.898}\times \underbrace{\frac{(g\,H_{\text{m}})^{3/4}}{H_{\text{ft}}^{3/4}}}_{(g\times 0.3048)^{3/4}=2.2733} \;=\;2733.016$$ $$\frac{n_q}{\Omega_s}=\frac{30}{\pi}\,g^{3/4}=52.93\qquad\Longrightarrow\qquad \frac{N_s}{n_q}=\frac{2733.016}{52.93}=51.64$$So the three scales are rigidly linked: Ns = 2733.016·Ωs, nq = 52.93·Ωs, and the handy Ns = 51.64·nq. This tool computes the dimensionless Ωs from strict SI inputs and derives the others — which is why switching US ↔ SI leaves every value unchanged.
3 · Impeller type bands
Because Ωs is a similarity parameter, it alone selects the passage geometry that can run efficiently at a given (flow, head, speed) duty — this is the theoretical basis for type classification. The classic US-gpm bands used here:
$$N_s<1500\;\text{radial},\qquad 1500\le N_s<4000\;\text{Francis},\qquad 4000\le N_s<8000\;\text{mixed flow},\qquad N_s\ge 8000\;\text{axial}$$| Band (Ns US) | Impeller type | Geometry & behaviour |
|---|---|---|
| < 1500 | Radial | Low specific speed — narrow radial vanes, large diameter-to-width ratio (D₂/b₂ large), essentially radial through-flow. High head, modest flow; disc friction and leakage penalise small stages, so efficiency rises as Ns approaches the Francis band. |
| 1500 – 4000 | Francis / vaned radial-mixed | The workhorse of single-stage process pumps: wider passage at exit, vanes continue radially to a vaned discharge — best-efficiency band of the curve family. Stable, continuously rising H–Q characteristics are easiest to achieve here. |
| 4000 – 8000 | Mixed flow | True mixed-flow impeller in a conical bowl; the passage turns from axial-induced inlet to diagonal discharge. High flow at moderate head; the H–Q curve can show a flat or unstable pocket, and power falls toward shut-off. |
| > 8000 | Axial propeller | Propeller impeller with through-flow along the machine axis; hub and blades tall and narrow. Steeply rising H–Q curve with a pronounced saddle and high shut-off power — start against an open valve. Diffusion must be produced in guide vanes, not the impeller. |
4 · Suction specific speed and cavitation
Same similarity logic applied to the suction side: Nss measures how aggressively an inlet design suppresses NPSHr (large eye area, extended inlet vanes — eventually an inducer). Screening bands for single-suction pumps on water:
| Nss (US) | Screening verdict | Meaning |
|---|---|---|
| ≤ 8,000 | Conventional | Standard end-suction impeller; trouble-free operation on cold water over the normal operating range. |
| 8,000 – 11,000 | Extended suction design | Two-phase (vapour) activity in the eye becomes significant; suction recirculation, noise and NPSH-margin discipline must be engineered deliberately. |
| > 11,000 | Beyond conventional limit | Above the usual industry design limit for conventional impellers. Dedicated high-suction designs of this class exist — with an inducer up to Nss ≈ 27,000. |
Ωss is the same statement in dimensionless dress (Ωss = Nss/2733.016): conventional ≈ 2.9, extended to ≈ 4.0, inducer designs to ≈ 9.9.
Worked example (handbook anchor)
Single stage at 1,780 rpm delivering 2,500 gpm at 104 ft of head. Enter N = 1780, Q = 2500, H = 104 (US view) — the calculator reproduces the published anchor values exactly:
| Input | Value | Output | Calculator | Anchor |
|---|---|---|---|---|
| N | 1,780 rpm | Ns (US) | 2,733 (2732.9) | 2,733 |
| Q (BEP) | 2,500 gpm = 567.8 m³/h | nq (metric) | 52.9 (52.92) | 52.9 |
| H (per stage) | 104 ft = 31.70 m | Ωs | 1.000 (0.9999) | 1.0 |
| — | — | Impeller type | Francis (1500 ≤ Ns < 4000) | |
Same machine, suction screening: catalogue NPSH3% = 14 ft gives Nss = 1780·√2500 / 140.75 = 12,296 ≈ 12,300 (anchor rounds to three figures), Ωss = 4.50 — the calculator flags it red, i.e. beyond the conventional limit and into dedicated-suction-design territory.
Engineering criteria applied
- Type bands — the four classical US-gpm segments (1500 / 4000 / 8000); the verdict turns amber within ≈ 4 % (log) of a boundary, since the classification is genuinely ambiguous there.
- Nss screening — 8,000 / 11,000 thresholds on water for single-suction impellers, inducer ceiling ≈ 27,000.
- Velocity triangles — Euler head He = U₂·Vw2/g; slip model of Stodola, ΔVw = π·U₂·sinβ₂/z; the φ-slider shows why higher flow (at fixed speed) collapses the tangential component and with it the head.