# C274 – ISO 5167 Sizing Calculation

## Description

This calculates the flow element size of various differential pressure based flow meters according to the ISO 5167 technical standard.

## References

ISO 5167: Measurement of fluid flows by means of pressure differential devices inserted in circular cross-section conduits running full

ISO TR9464: Guidelines for the use of ISO 5167

BS1042: Part 1. Pressure differential devices – Section 1.2 Specification for square-edged orifice plates and nozzles (with drain holes, in pipes below 50mm diameter, as inlet and outlet devices) and other orifice plates and Borda inlets (1984)

24509-54 – Flow Calculations for the V-Cone and Wafer-Cone Flow meters – McCrometer

24517-16 – V-Cone Flow Meter Technical Brief – McCrometer

Kelton calculation reference C274

Kelton calculation C270 – ISO 5167 Orifice Mass Flow Calculation

Kelton calculation C271 – ISO 5167 Venturi Mass Flow Calculation

Kelton calculation C272 – Cone Mass Flow Calculation

Kelton calculation C276 – ISO 5167-5:2016 Cone Mass Flow Calculation

## Options

### Meter Type

- Orifice
- Venturi
- V-Cone
- Wafer-Cone
- Cone (ISO 5167-5)

This option group allows selection of the meter type that the sizing calculation is to be performed on.

### Standard version

Allows user to select from different revisions of the standard being applied.

### Fluid

- Gas
- Liquid

This option allows selection of whether the fluid in question is a liquid or a gas.

### Expansibility factor

- User entered
- Calculated

This option give the choice of calculating expansibility or entering a known value when the fluid is a gas.

*For an orifice plate*

*For an orifice plate*

### Tapping Type

- Flange
- D/D2
- Corner

This option group allows the selection of the tapping type used for the pressure measurements on the orifice plate system.

### Drain Hole

- None
- BS 1042

This option allows for selection of a drain hole correction according to BS 1042.

*For venturi tubes and cones*

*For venturi tubes and cones*

### Discharge coefficient

- User entered
- Variable with Reynold’s number
- Classical venturi with ‘as cast’ convergent section
- Classical venturi with rough-welded convergent section
- Classical venturi with a machined convergent section
- Venturi nozzle
- Uncalibrated Cone

This option allows the user to choose how discharge coefficient will be determined for a venturi tube. If a cone meter is selected only the first two options will be available for selection.

### Exit cone angle

- 7°
- 15°

This option determines the equation used to calculate the permanent pressure loss associated with a venturi.

## Calculation

### Sizing Calculation

The orifice bore and venturi throat diameter are related to the diameter of the piping in the equation:

For cone meters the relationship is as follows:

Where | ||
---|---|---|

d | = | Flow element diameter |

D | = | Pipe diameter |

The following relationships are applied in an iterative loop to solve for the flow element diameter at operating temperature.

For an orifice plate:

For a venturi tube:

For V-cones and Wafer-cones:

In these equations X is calculated by:

Where | ||
---|---|---|

D | = | Pipe diameter |

Δp | = | Differential pressure |

ρ_{1} |
= | Upstream density |

C_{d} |
= | Discharge coefficient |

ε | = | Expansibility factor |

μ_{1} |
= | Dynamic viscosity |

Re | = | Reynold’s number |

q_{m} |
= | Mass flowrate |

A temperature correction is then made to calculate the size of the flow element diameter at calibration temperature:

Where | ||
---|---|---|

T_{1} |
= | Upstream temperature |

T_{dc} |
= | Calibration temperature of the flow element |

α_{d} |
= | Thermal expansion coefficient of flow element |

If a drain hole needs to be taken into account, orifice bore is calculated iteratively by employing a root finding algortihm around the equation:

Where | ||
---|---|---|

dr | = | Drain hole diameter |

d_{u} |
= | Orifice bore at calibrated temperature |

d | = | Orifice bore corrected for operating temperature |

C_{td} |
= | Temperature correction |