# Summary

Power is consumed by a pump, fan or compressor in order to move and increase the pressure of a fluid. The power requirement of the pump depends on a number of factors including the pump and motor efficiency, the differential pressure and the fluid density, viscosity and flow rate. This article provides relationships to determine the required pump power.

# Definitions

\(P_{h}\) | : | Hydraulic power of the pump (kW). |

\(P_{s}\) | : | Shaft power of the pump (kW). |

\(P_{m}\) | : | Required power to the Motor (kW). |

\(Q\) | : | Volumetric flow of fluid through the pump (m^{3}/h). |

\(\rho\) | : | Density of the fluid being pumped (kg/m^{3}). |

\(g\) | : | Gravity (9.81 m/s^{2}). |

\(h\) | : | Head produced by the pump (m). |

\(dP\) | : | Differential pressure across the pump (kPa) |

\(\eta_{p}\) | : | Pump efficiency (%). |

\(\eta_{m}\) | : | Motor efficiency (%). |

# Hydraulic Power

The hydraulic power which is also known as absorbed power, represents the energy imparted on the fluid being pumped to increase its velocity and pressure. The hydraulic power may be calculated using one of the formulae below, depending on the available data.

Units | Formula |
---|---|

P - kW Q - m ^{3}/hρ - kg/m ^{3}g - m/s ^{2}h - m | \[ P_h = \frac{Q \rho g h}{3.6 \times 10^6} \] |

P - kW Q - m ^{3}/hrdP - kPa | \[ P_h = \frac{QdP}{3,600} \] |

P - kW Q - L/min dP - kPa | \[ P_h = \frac{QdP}{60,000} \] |

P - kW Q - L/s dP - kPa | \[ P_h = \frac{QdP}{1,000} \] |

# Shaft Power

The shaft power is the power supplied by the motor to the pump shaft. Shaft power is the sum of the hydraulic power (discussed above) and power loss due to inefficiencies in power transmission from the shaft to the fluid. Shaft power is typically calculated as the hydraulic power of the pump divided by the pump efficiency as follows:

\[ P_s = \frac{P_h}{\eta_p} \]# Motor Power

The motor power is the power consumed by the pump motor to turn the pump shaft. The motor power is the sum of the shaft power and power loss due to inefficiencies in converting electric energy into kinetic energy. Motor power may be calculated as the shaft power divided by the motor efficiency. \[ P_m = \frac{P_s}{\eta_m} \]

# Other Factors which Increase Required Power

There are several other pump and drive features which will increase the power requirement to achieve a particular fluid transfer, these include:

- Gearboxes
- Belt drives
- Variable speed drives (VSDs)

Each of these components will have their own efficiency ratings, which must be factored into the power delivered by the motor.

# Typical Pump and Drive Component Efficiency Ranges

The table below provides some typical efficiency values which may be used for power requirement estimation for a selection of pump types. These values are for correctly sized pumps, if a pump is oversized or poorly designed its efficiency may be much lower than the values quoted below, this is particularly common in small pumps.Pump Type/Component | Typcial Efficiency |

Centrifugal Pump | 60-85% |

Sliding Vane Pump | 60-90% |

Gearbox | 70-98% |

Belt Drive | 70-96% |

Variable Speed Drive at Full Speed | 80-98% |

Variable Speed Drive at 75% Full Speed | 70-96% |

Variable Speed Drive at 50% Full Speed | 44-91% |

Variable Speed Drive at 25% Full Speed | 9-61% |