# Summary

Pump Specific Speed, N_{S} is a method of characterising a pump duty by head, flow rate and rotational speed. Pump specific speed may be used to determine an appropriate pump design for a given application when choosing between axial, radial or multistage centrifugal designs or positive displacement pumps.

# Definitions

: | Diameter of impeller eye | |

: | Diameter of impeller | |

: | Acceleration due to gravity | |

: | Differential head across impeller at best efficiency point | |

: | Impeller revolutions per minute | |

: | Impeller revolutions per second, measured in radians | |

: | Dimensionless specific speed | |

: | Pump specific speed | |

: | Volumetric flow rate at best efficiency point |

# Introduction

Pump Specific Speed is a method of characterising pumping conditions and it may be used to determine the most appropriate pump design for a given application. Often pump characteristics such as NPSHr, suction lift and pump efficiency will be correlated against the pump specific speed.

Specific speed is the speed (in RPM) a geometrically similar impeller would need to operate in order to deliver 1 L/s of fluid at a head of 1 m (US units : 1 USgal/min at a head of 1 ft).

The common pump specific speed is not dimensionless, however its dimensions are only important for converting between different unit sets (eg converting and comparing pump specific speeds calculated on a Metric basis and US Customary basis). A truly dimensionless variation on the pump specific speed is available, but is less commonly used.

# Calculation of Pump Specific Speed

Pump specific speed is calculated using the relationship below.

Note that for multi-stage pumps the specific speed is calculated for the first stage only. For pumps with a double-suction inlet the flow rate , should be half the total flow rate for the pump.

## Dimensionless Form

The traditional pump specific speed is not a dimensionless number, thus it is critically important that the units used are reported along with the pump specific speed value. A dimensionless form can be created by multiplying the pump head by the gravitation constant and measuring the shaft rotation in radians.

The resulting will be dimensionless provided consistent units are used. Rotational speed should be measured in radians per second. The metric units m^{3}/s, m/s^{2} and m for , and respectively are consistent. The imperial units ft^{3}/s, ft/s^{2} and ft as the units of , and respectively also result in a dimensionless number.

# Centrifugal Impeller Design

Pump specific speed may be used to select the optimal impeller type for a specific application. Generally as the specific speed increases, the ratio of impeller diameter to impeller eye diameter decreases.

Pump impellers can be classified using the ratio of pump impeller diameter to pump eye diameter, and may be referred to as radial, axial, Francis vane or mixed flow impellers. Radial flow impellers generate all of their hydraulic head via centrifugal force while axial flow impellers generate head through primarily axial forces. Francis vane and other intermediate impeller designs use a combination of axial and centrifugal forces to generate hydraulic head.

The typical ranges of pump specific speed and the corresponding impeller diameter to eye diameter ratios for several impeller types are shown below.

Impeller Type | Metric units* |
US units** |
Dimensionless |
Characteristics | |
---|---|---|---|---|---|

Radial Flow | 500 - 1,700 | 800 - 2,800 | 0.3 - 1.0 | > 2 | Low flow, high head |

Francis Vane | 1,700 - 4,000 | 2,800 - 6,500 | 1.0 - 2.4 | 1.5 - 2 | |

Mixed Flow | 4,000 - 9,000 | 6,500 - 15,000 | 2.4 - 5.4 | < 1.5 | |

Axial Flow | > 9,000 | > 15,000 | > 5.4 | 1 | High flow, low head |

* Metric units - rpm, L/s, m

** US units - rpm, USgpm, ft

## Notes on Pump Selection

It should be noted that for metric specific speeds less than 1000 a multi-stage pump should be considered while for metric specific speeds less than 500, a positive displacement pump should be considered.

# Typical Impeller Performance

Below are typical head and power versus capacity curves for impellers with various pump specific speeds.