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Turbine Specific Speed Calculator

Pick the right hydraulic turbine: compute Ns from head, flow, efficiency and speed (direct rpm or synchronous N = 120·f/poles), in both the power method (N·√P/H1.25) and the Q method (N·√Q/H¾) notations, then read the Pelton / Francis / Kaplan / bulb selection bands with typical head ranges and a schematic runner profile. A pumpXSolver engineering tool.

Pelton < 20 Pelton multi / low-Ns Francis 20–60 Francis 60–220 Kaplan 220–450 Bulb 450+

Results

Synchronous-speed ladder — Ns per pole count

Runner schematic — switches with type

① Site duty — head, flow, efficiency

② Runner speed — direct or synchronous

Generator poles (2–24)6 poles · N = 1000 rpm

How it works

A turbine's specific speed fixes the runner shape just as it does for pumps — but the definition swaps flow for power, because a turbine's job is power extraction. The tool computes every common notation, places the machine on the type-selection bands, and checks which synchronous generator speeds are realistic.

1 · The notations

$$N_s \;=\; \frac{N\,\sqrt{P}}{H^{1.25}}\quad\text{(power method: rpm, hp, ft — the classic US turbine notation)}$$ $$n_s \;=\; \frac{N\,\sqrt{P_{kW}}}{H_m^{1.25}}\quad\text{(power method, metric)} \qquad\qquad n_q \;=\; \frac{N\,\sqrt{Q}}{H_m^{3/4}}\quad\text{(Q method: rpm, m³/s, m — same form as pump } n_q\text{)}$$
SymbolMeaningUnit
\(N\)runner speed (synchronous: \(N = 120\,f/p\))rpm
\(P\)shaft power at the turbine (η × water power)hp / kW
\(Q\)turbine flowcfs / m³/s
\(H\)net headft / m
\(f,\,p\)line frequency, pole countHz, —

P-method vs Q-method: they are not proportional — the power form folds efficiency and head into the numerator, so two machines with identical nq can carry different Ns if their efficiencies differ. Always compare turbines in one notation; this tool prints all three.

2 · Type selection bands (power-method Ns)

Ns (rpm·hp^½/ft^1.25)MachineTypical head
< 20Pelton, single jet🟢 100 – 2 000 m (multi-nozzle Peltons push Ns toward ~60)
20 – 60Pelton (multi-nozzle) or low-Ns Francis
60 – 130Francis (radial)🟢 20 – 700 m
130 – 220Francis, high-Ns / mixed-flow exit
220 – 450Kaplan / propeller (adjustable blades)🟢 2 – 80 m
≥ 450Bulb / tubulartypically < 20 m

Schematic band positions — treat the boundaries as design guidance with soft edges, not gates: real machines overlap by tens of Ns at the seams.

3 · Synchronous speed and the ladder

$$N \;=\; \frac{120\,f}{p}$$

Grid-connected runners can only spin at synchronous speeds. The tool builds the full ladder (2–24 poles, 50 or 60 Hz), computes each option's Ns for your head and power, and colors it by the machine type it would imply — the fastest way to see which pole counts are realistic.

4 · Specific speed and efficiency

Runner geometry is a compromise: high Ns means a wide, axial runner that handles big flow at low head but suffers at high head (cavitation, mechanical stress); low Ns means compact radial buckets and runners for the mountain heads. Each family's best efficiency peaks inside its band — Pelton ≈ 90% at its optimum jet-to-bucket speed ratio, Francis ≈ 92–94% mid-band, Kaplan ≈ 92% with the blades on-cam — and falls away toward the band edges. Operating a machine far from its design Ns means leaving efficiency on the table.

Worked anchor — the page opens on it

Net head 200 m, turbine flow 5.665 m³/s (200 cfs), η = 90% → shaft power ≈ 10.0 MW (13,410 hp). Synchronous 50 Hz, 6 poles → N = 1 000 rpm: power-method Ns = 34.9 — the Pelton-multi / low-Ns Francis seam; nq (Q method) = 44.8; ns (kW·m) = 133.0. The ladder shows the trade: 2 poles (3 000 rpm) lands at Ns ≈ 105 (proper Francis), 12 poles (500 rpm) drops to Ns ≈ 17 (single-jet Pelton). All positions are schematic — real machines overlap across the seams.