Online calculator to quickly determine Water Flow Rate through an Orifice. Includes 53 different calculations. Equations displayed for easy reference. The width of the slot opening determines the flow rate. To calculate the flow rate of a Slot Drain, you can use these formulas: 1/2 inch slot opening = 11 gallons per minute per foot of slot 1 inch slot opening = 18 gallons per minute per foot of slot.

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.

: | Diameter |

: | Area |

: | Discharge coefficient |

: | Gravitational acceleration |

: | Fluid head |

: | Change in fluid head |

: | Ratio of specific heats () |

: | Pressure |

: | Differential pressure () |

: | Expansion coefficient (for incompressible flow) |

: | Elevation |

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

: | Mass density |

*Subscripts*

: | Upstream of orifice or nozzle |

: | Downstream of orifice or nozzle |

: | Compressible fluid |

: | Incompressible fluid |

: | Orifice or nozzle |

: | Static pressure |

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 coefficientcharacterises 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.

The relationships for flow rate, pressure loss and head loss through orifices and nozzles are presented in the subsequent section. These relationships all utilise the parameter, the ratio of orifice to pipe diameter which is defined as:

Where the point downstream of the orifice is sufficiently far away that the fluid has returned to normal full pipe velocity profile.

## Horizontal Orifices and Nozzles

For orifices and nozzles installed in horizontal pipework where it can be assumed that there is no elevation change, head loss and flow rate may be calculated as follows:

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 vertical piping, with elevation change, the following head loss and flow rate equations may be used:

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

Flow rate (in terms of) | |

Flow rate (in terms of) | |

Pressure loss | |

Head Loss |

## Expansion Coefficient

The expansion coefficient takes account of the difference between the discharge coeffcicient for compressible and incompressible flows. It is defined as:

The expansion factoris typically determined empirically and can be calculated using one of the formulas below.

For incompressible fluids:

American Gas Association method as described in AGA 3.1:

International Standards Organistion method as described in ISO 5167-2:

Article Tags**Orifice Discharge into Free Air**

An orifice is an opening with a closed perimeter through which water flows. Orifices may have any shape, although they are usually round, square, or rectangular.

Discharge through a sharp-edged orifice may be calculated from:

Q = Ca?2gh

where

Q= discharge, ft^{3}/s (m^{3}/s)

### Water Flow Through A Small Block Chevy

C =coefficient of discharge

a =area of orifice, ft^{2} (m^{2})

g =acceleration due to gravity, ft/s^{2} (m/s^{2})

h =head on horizontal center line of orifice, ft (m)

The coefficient of discharge C is the product of the coef- ficient of velocity C_{v} and the coefficient of contraction C_{c}. The coefficient of velocity is the ratio obtained by dividing the actual velocity at the vena contracta (contraction of the jet discharged) by the theoretical velocity. The theoretical velocity may be calculated by writing Bernoulli’s equation for points 1 and 2.Thus

V_{2}= ?2gh

The coefficient of contraction C_{c} is the ratio of the smallest area of the jet, the vena contracta, to the area of the orifice.

### Water Flow Through A Slot Extruded

**Submerged Orifices**

Flow through a submerged orifice may be computed by applying Bernoulli’s equation to points 1 and 2 in figure below

Values of C for submerged orifices do not differ greatly from those for nonsubmerged orifices.