Specific speed

Pump

Specific Speed is an index that, in mechanical terms, represents the impeller speed of a pump necessary to generate 1 gallon per minute at 1 foot of head.

Ns = (n*sqrt(Q)) / (gH^(3/4))

Ns = specific speed (unitless) n = pump rotational speed in rpm Q = flowrate (GPM) H = total head per stage (feet) g = acceleration due to gravity

The specific speed is not a dimensionless quantity.

Standard impellers can have values from 500 to 10,000, with the highest efficiency at values between 2,000 and 3,000. It is effectively an index used to predict certain pump characteristics.

Turbine

The specific speed of a turbine can also be defined as the speed of an ideal, geometrically similar turbine, which yields one unit of power for one unit of head.

The specific speed of a turbine is given by the manufacturer (along with other ratings) and will always refer to the point of maximum efficiency. This allows accurate calculations to be made of the turbine's performance for a range of heads and flows.

$n_{s}=n{\sqrt {P}}/H^{5/4}$ (dimensioned parameter), $n$ = rpm

$N_{s}={\frac {\Omega {\sqrt {P/\rho }}}{gH^{5/4}}}$ (dimensionless parameter),

$\Omega$ = angular velocity (radians/second)

Example; Given a flow and head for a specific hydro site, and the rpm requirement of the generator, calculate the specific speed. The result is the main criteria for turbine selection.

The specific speed is also the starting point for analytical design of a new turbine. Once the desired specific speed is known, basic dimensions of the turbine parts can be easily calculated.

Application

For a given turbine application, if one knows the water head, desired wheel speed and output power, then the following formula can indicate the appropriate type of turbine.

Imperial Units

The "specific speed" is defined as n_s = n√(P)/h^5/4

• where 'n' is the wheel speed in RPM
• P is the power in HP
• h is the water head in feet

Metric Units

The "specific speed" is n_s = 0.2626 n√(P)/h^5/4

• where 'n' is the wheel speed in RPM
• P is the power in kW
• h is the water head in meters

Well-designed efficient machines typically use the following values: Impulse turbines have the lowest n_s values, typically ranging from 1 to 10, a Pelton wheel is typically around 4, Francis turbines fall in the range of 10 to 100, while Kaplan turbines are at least 100 or more.

See also

• Water turbine