# C186 – Pressure Calculation – Absolute and Gauge

## Description

This calculates pressure generated either using a pressure balance (dead weight tester) as the standard or a digital pressure indicator or gauge. Where appropriate the equation can be solved for either pressure or mass to generate pressure.

## References

Kelton calculation reference C186

KIMS calculation reference K200

FLOCALC calculation reference F018

This replaces calculation C130/K120

## Options

### Pressure Mode

- Absolute

This option enables the use of a reference pressure, for example, absolute pressure indicating instruments can be calibrated by generating gauge pressure using a dead weight pressure and adding a reference pressure which is equal to barometric pressure. If this is selected make sure that pressure input is set to use absolute pressure units.

- Gauge

If gauge mode is selected the reference pressure is taken to be 1 atmosphere.

### Reference standard

- Dead weight tester – ‘mass and effective area’ method

Use this option if you are generating pressure using a dead weight tester (pressure balance) which is calibrated to give values for mass and effective area.

- Dead weight tester – ‘Kn’ method

Use this option if you are generating pressure using a dead weight tester (pressure balance) which is calibrated to give the mass pressure ratio Kn.

- Dead weight tester – ‘pressure’ method

Use this option if you are generating pressure using a dead weight tester (pressure balance) using a nominal value with corrections.

- Digital pressure indicator or gauge.

Use this option if you are generating pressure using other methods, for example, a digital pressure indicator or gauge.

### Output Type

- Digital

For this option the output is in pressure units

- Analogue

Fot this option the output is converted to a voltage or current.

### Calibration Correction

- Apply

Select this option to apply a correction to account for values obtained through laboratory calibration, for example a

foot-printcalibration of a differential pressure transmitter.

### Correct For

- Head

If selected, the head correction is added to the calculated pressure output.

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

ρ | = | The density of the pressure transmitting fluid |

g | = | The local value for acceleration due to gravity |

h | = | The height of the tester above the instrument being calibrated |

- Temperature

If selected, allows the user to input values for Piston/Cylinder temperature, Calibration temperature and Temperature coefficient.

- Density of air

If not selected, the default value is 1.2kgm

^{-3}.

- Density of mass

If not selected, the default value is 8000 kgm

^{-3}.

- Surface Tension

If not selected, the default value is 0 N.

- Buoyancy

If not selected, the default value is 0 N.

- Gravity

If not selected, the local gravity is taken as 9.80665ms

^{-2}.

## Calculations

### Dead Weight Tester – ‘Mass and Effective Area’ Method

- Solving for Pressure

This equation calculates the pressure generated by loading a piston with mass.

- Solving for Mass

This equation calculates the applied mass required to generate pressure.

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

m | = | Mass |

P_{r} |
= | Residual Pressure; this will typically be barometric pressure or the bell jar pressure for an absolute DWT |

P | = | Pressure |

ρ_{a} |
= | Density of Air |

ρ_{m} |
= | Density of the Mass |

σ_{c} |
= | Force due to Surface Tension |

B | = | Force due to Piston Buoyancy |

g_{l} |
= | Local Gravity |

A_{o} |
= | Effective Area |

α | = | Pressure coefficient |

λ | = | Temperature coefficient (the combined temperature coefficient of the piston cylinder unit a_{p} + a_{c}) |

t_{c} |
= | Calibration temperature |

t | = | PC temperature |

### Dead Weight Tester – ‘Kn’ Method

- Solving for Pressure

This equation calculates the pressure generated by loading a piston with mass.

- Solving for Mass

This equation calculates the applied mass required to generate pressure.

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

m | = | Mass |

P_{r} |
= | Residual Pressure |

P | = | Pressure |

g_{l} |
= | Local Gravity |

g_{c} |
= | Calibration reference gravity |

K_{n} |
= | Pressure ratio |

α | = | Pressure Coefficient |

λ | = | Temperature Coefficient (the combined temperature coefficient of the piston cylinder unit a_{p} + a_{c}) |

t_{c} |
= | Calibration Temperature |

t | = | PC Temperature |

### Dead Weight Tester – ‘Pressure’ method

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

P_{r} |
= | Residual pressure |

g_{l} |
= | Local gravity |

g_{c} |
= | Calibration reference gravity |

λ | = | Temperature coefficient (the combined temperature coefficient of the piston cylinder unit a_{p} + a_{c}) |

t_{c} |
= | Calibration temperature |

t | = | PC temperature |

### Digital Pressure Indicator or Gauge

For this option the generated pressure is taken to be that which is indicated on the standard corrected for head where applicable.