Turbine Specific Speed Calculator

Turbine specific speed Ns is a single number, calculated from rotational speed, power, and head, that characterizes the shape of a turbine runner independent of its physical size. Turbines with similar Ns values are geometrically similar and behave the same way hydraulically, which is why Ns is the standard first step in choosing between Pelton, Francis, and Kaplan turbine types for a given site.

Ns = N x sqrt(P) / H^(5/4), where N is rotational speed in rpm, P is shaft power output in kW, and H is net head in metres, using the metric convention. This formula comes from combining the turbine's power, head, and flow relationships into one dimensionless-looking group that stays the same for geometrically similar runners at any scale.

No, not in the strict sense used for the Reynolds or Froude number. Turbine specific speed carries units that depend on the unit system chosen for N, P, and H, so a value calculated with N in rpm, P in kW, and H in metres is not directly comparable to one calculated with P in horsepower and H in feet. It is sometimes called quasi-dimensionless because the same formula shape recurs across unit systems, but the numeric value itself is not universal.

Specific speed reflects the ratio of flow-handling capacity to head-handling capacity a runner needs. Low specific speed values correspond to impulse turbines like the Pelton wheel, which are suited to high head and comparatively low flow, mid-range values correspond to Francis turbines, and high values correspond to Kaplan or propeller turbines, which are suited to low head and high flow. The exact numeric boundaries between these bands differ depending on which unit convention is used, so this calculator reports Ns itself rather than assigning a fixed cutoff.

This calculator uses the metric convention throughout: rotational speed N in revolutions per minute (rpm), shaft power P in kilowatts (kW), and net head H in metres (m). If your source data is in horsepower or feet, convert to kW and metres first, since mixing unit systems produces an incorrect Ns value.

Specific speed is directly proportional to rotational speed N, so doubling N while holding power and head constant exactly doubles Ns. This is why the same hydraulic site can be matched to different turbine types depending on the generator speed chosen, a slower-spinning runner produces a lower specific speed and a faster-spinning runner produces a higher one for identical power and head.

Specific speed is inversely proportional to head raised to the power 5/4, so Ns falls sharply as net head H increases. This is the mathematical reason high-head sites (several hundred metres) pair naturally with low specific speed Pelton wheels, while low-head sites (a few metres to a few tens of metres) pair with high specific speed Kaplan turbines.

Specific speed increases with the square root of shaft power P, so a turbine rated for four times the power at the same speed and head has exactly double the specific speed. Because the relationship is a square root rather than direct proportionality, power has a weaker effect on Ns than either rotational speed or head.

Net head H is the head actually available to the turbine runner after subtracting losses in the penstock, intake, and draft tube from the gross head between the reservoir surface and the tailwater. Using gross head instead of net head in the specific speed formula overstates Ns and can lead to selecting the wrong turbine type.

Yes, that is its main purpose. Two turbines with the same specific speed, regardless of physical size or the actual head and power of the site they serve, have geometrically similar runners and equivalent hydraulic behaviour. Manufacturers use measured specific speed to select an existing runner design or scale a proven design to a new site rather than developing new blade geometry from scratch.