# Summary

This article provides calculation methods for correlating design, flow rate and pressure loss as a fluid passes through a nozzle or orifice. Nozzles and orifices are often used to deliberately reduce pressure, restrict flow or to measure flow rate.

# Definitions

: | Diameter | |

: | Area | |

: | Discharge coefficient | |

: | Gravitational acceleration | |

: | Fluid head | |

: | Change in fluid head | |

: | Pressure | |

: | Differential pressure () | |

: | Elevation | |

: | Ratio of pipe diameter to orifice diameter () |

*Subscripts*

: | Upstream of orifice or nozzle | |

: | Downstream of orifice or nozzle | |

: | Orifice or nozzle |

# Introduction

In the case of a simple concentric restriction orifice the fluid is accelerated as it passes through the orifice, reaching the maximum velocity a short distance downstream of the orifice itself (the Vena Contracta). The increase in velocity comes at the expense of fluid pressure resulting in low pressures in the Vena Contracta. In extreme cases this may lead to cavitation when the local pressure is less than the vapour pressure of a liquid. Downstream of the Vena Contracta in the recovery zone, the fluid decelerates converting excess kinetic energy into pressure as it slows. When the fluid has decelerated and returned to the normal bulk flow pattern the final downstream pressure has been reached. The discharge coefficient characterises the relationship between flow rate and pressure loss based on the geometry of a nozzle or orifice. You can find typical values in our article on discharge coefficients for nozzles and orifices.

# Calculations

Here we present relationships for flow rate, pressure loss and head loss through orifices and nozzles. We will use the relationship for below:

## Horizontal Orifices and Nozzles

For orifices and nozzles installed horizontally, with no elevation change.

Property | Equation |
---|---|

Flow rate (in terms of ) | |

Flow rate (in terms of ) | |

Pressure loss | |

Head Loss | |

## Vertical Orifices and Nozzles

For orifices and nozzles installed in horizontal piping, with elevation change .

Property | Equation |
---|---|

Flow rate (in terms of ) | |

Flow rate (in terms of ) | |

Pressure loss | |

Head Loss | |