BEP · maximum impeller diameter · explicit unit convention

Rotodynamic Pump Specific-Speed Worksheet

Calculate metric and US customary specific-speed indices and the dimensionless type number without mixing their units, flow basis or operating point.

Metric n_sUS N_sDimensionless K

Index calculation only—not pump selection. The worksheet does not infer an impeller type, efficiency, acceptable operating region, cavitation margin, suction performance, fan/turbine equivalence or compliance. Use data from the same best-efficiency point (BEP), maximum-diameter curve/test condition.

Controlled BEP quantities

Rotational speed n at BEP rpm; positive

Total pump flow Q at BEP before any per-eye division; positive

Flow unit

Head H at BEP, per stage positive; not total multistage head

Head unit

Impeller flow entries / eyes

Pump / impeller identification

Curve, test or data-set identification

Curve/test revision and date

Maximum impeller diameter record

BEP determination and efficiency evidence

Speed source and uncertainty

Flow source, total/per-eye basis and uncertainty

Head source, per-stage basis and uncertainty

Stage and impeller-eye configuration record

Fluid, test condition and applicable corrections

Definition/source and edition used

Owner / reviewer

Review date

Notes and exclusions Optional: uncertainty, viscosity correction, trim, alternate flow-basis convention, comparison source

n, Q and H describe the same BEP condition at maximum impeller diameter; Q is total pump flow and H is head per stage.
The selected eye count is documented. Per-eye Q′ is Q for single-entry and Q/2 for double-entry; definitions using total flow and per-eye flow are not compared as though identical.
Metric n_s and US N_s are unit-convention indices. Only K below is dimensionless; the symbol, units and flow basis travel with every reported value.
No impeller, efficiency, fan, turbine, suction-specific-speed, NPSH, cavitation or compliance verdict will be inferred from these four numbers alone.

Documented arithmetic

Metric customary n_s,total

—

US customary N_s,total

—

Metric alternate n_s,eye

—

Dimensionless type number K_eye

—

Equations and exact basis

एन_s,total = n(rpm) · √Q_कुल(m³/s) / H_stage(एम)^3/4
एन_s,total = n(rpm) · √Q_कुल(US gpm) / H_stage(ft)^3/4
एन_s,eye = n(rpm) · √(Q_कुल/eyes) / H_stage^3/4
क_eye = 2π · (n/60) · √Q′ / (g_एनH′)^3/4

The first two are convention-dependent pump-performance indices, not dimensionless quantities. Hydraulic Institute’s public Data Tool uses total pump BEP flow for these equations and warns that an alternate per-eye definition exists. K is dimensionless and uses BEP flow per impeller eye, rotational speed in revolutions per second, first-stage head and g_एन = 9.80665 m/s².

Exact unit conversions used here are 1 international ft = 0.3048 m and 1 US gal = 0.003785411784 m³. Therefore the direct exact-unit calculations give N_s,total/एन_s,total ≈ 51.64523790; Hydraulic Institute publishes 51.6 as a rounded conversion factor. Also K = 0.01889679324·n_s,eye = n_s,eye/52.91903167 for the stated metric basis.

Model boundary and removed unsupported content

BEP and maximum diameter are mandatory. An arbitrary duty point or trimmed-impeller point does not satisfy the published definition used here.
Total versus per-eye flow is explicit. A double-entry per-eye result is √0.5 ≈ 0.70710678 times the total-flow index; the former page had no flow-basis control.
No invented impeller thresholds. The former JavaScript and FAQ used different radial/mixed/axial boundaries, and neither stated the unit convention, source figure, pump family or uncertainty.
No universal efficiency band. Specific speed is only one input to attainable-efficiency and hydraulic-design methods; “peak efficiency at 40–80” was unsourced and scope-free.
No fan shortcut. Replacing pump head by ΔP/ρ is dimensionally wrong because pressure head is ΔP/(ρg); fan/compressor definitions and compressibility require their own controlled source.
Not suction specific speed. NPSH3, per-eye flow and suction-characteristic definitions belong to a separate quantity and are not calculated here.

Source traceability

Claim	वर्गीकरण	Evidence
BEP/maximum-diameter definition; metric and US total-flow equations; units; 51.6 rounded conversion; alternate per-eye warning; dimensionless K equation.	Official Hydraulic Institute public technical resource	HI Data Tool, Pump Principles
ANSI/HI 14.1-14.2 current nomenclature/definitions edition is 2024 and supersedes 2019.	Official standard-owner status card; full clauses licensed	ANSI/HI 14.1-14.2 (2024)
ISO 17769-1:2012 covers pump terms, symbols and units; Edition 1 was confirmed in 2023 and remains current.	Official ISO status/scope card; exact clauses licensed	ISO 17769-1:2012
Metric n_s, per-eye double-entry convention and approximate K = n_s/52.9 relationship.	Official pump-manufacturer engineering reference; demonstrates convention variation	KSB Pump Lexicon: Specific speed
International-foot conversions and standard acceleration of free fall g_एन = 9.80665 m/s².	Official public metrology guidance	NIST SP 811 Appendix B.9

Accessed: 15 July 2026. Exact ANSI/HI and ISO clause text or normative conformance claims remain NEEDS_LICENSED_SOURCE; no clause or classification boundary is invented here.

Independent arithmetic reference

For n = 1450 rpm, total Q = 0.05 m³/s, H = 30 m per stage and one eye: n_s,total = 25.29368254; N_s,total = 1306.298252; n_s,eye = 25.29368254; K = 0.4779694892. These numbers do not select an impeller or predict efficiency.

प्रश्न

Why are there several “specific speed” numbers?

The exponent form is shared, but the numerical value changes with the prescribed units and with total-flow versus per-eye basis. Always report symbol, unit convention, operating point, stage basis and flow basis.

Can I enter the normal operating point?

Not for this definition. Enter the BEP flow and per-stage head at maximum impeller diameter from the same controlled curve or test.

Does a result prove radial, mixed or axial geometry?

No. Published figures may show approximate trends under a stated convention, but a standalone threshold is not a design or acceptance rule.