1. Introduction and warning

2. Critical flow or subcritical flow ?

5. Other calculation codes

6. Selection of standard pressure
relief valve orifice

7. Excel calculation tool

The calculation below are derived
from API520 and adapted from various sources. **Those calculations
are valid for liquid only**. Other types of services will require
a different calculation code. API for example has other standards for
gas service or low pressure / vacuum valves. ASME or ISO have their
own guidelines.

For liquid, the following formula can be used (WARNING - This formula is not valid for gases, for gases under pressure, please refer to this page) :

With :

P_{1} = upstream relieving
pressure in kPa g (set pressure + allowable overpressure)

P_{2} = backpressure in
kPa g

A = required effective discharge
area of the safety valve in mm^{2}

Q = required flow through the valve in l/min

Q = required flow through the valve in l/min

G = specific gravity of the liquid
at the flowing temperature, referred to water in standard conditions

K_{d} = coefficient of
discharge, it can be read from manufacturer data for a given pressure
safety valve, however the following values can be used for a 1st
approximation :

K_{d} = 0.65 for a pressure relief valve,
with or without a rupture disc upstream

K_{d} = 0.62 for a rupture disc

K_{w} = capacity
correction factor due to back pressure

K_{w} = 1 for atm back pressure

K_{w} is not used for
conventional and pilot operated valves (don't require correction)

K

K_{w} to be estimated from tables and
charts for balance bellow valves (see figure 1)

Kc = correction factor if a
rupture disc is installed prior to the valve

Kc = 1 when no rupture disc is installed prior to
the valve

Kc = 0.9 if a rupture disc is used in combination
with the valve

Kv = correction factor due to
viscosity

T = temperature of the gas or
vapor upstream the valve at the moment it is released in K

Re = Reynolds number

Re = Reynolds number

μ = fluid viscosity in cP

The coefficient K_{w} to account for back pressure on
balanced bellow safety valves can be determined thanks to the
following abacus :

**Figure 1 : Capacity Correction
Factor, Kw, Due to Back Pressure on Balanced-Bellows**

The coefficient K_{v} can be calculated thanks to the
following formula :

**Equation 2 : coefficient K _{v} calculation**

The Reynolds number can be calculated thanks to the following equation :

**Equation 3 : Reynolds number calculation
**

Note that ISO 4126 also offers
correlations for safety valves sizing

The sizes of discharge areas is actually standardized and manufacturers will propose sizes accordingly. The Engineer, after having calculated the required size with the calculation sequence above, needs to select a standard size offering a discharge area higher than the calculated value.

Standard letter / designation | Orifice area in in^{2} |
Orifice area in cm^{2} |

D | 0.110 | 0.71 |

E | 0.196 | 1.26 |

F | 0.307 | 1.98 |

G | 0.503 | 3.24 |

H | 0.785 | 5.06 |

J | 1.28 | 8.30 |

K | 1.84 | 11.85 |

L | 2.85 | 18.40 |

M | 3.600 | 23.23 |

N | 4.340 | 28 |

P | 6.38 | 41.16 |

Q | 11.050 | 71.29 |

R | 16 | 103.22 |

T | 26 | 167.74 |

Note : the tool is supporting liquid flow in pressure, for gas
service please refer to this
page

WARNING

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held responsible for the use of the explanations, calculation and
calculation tools presented here, the use of the information is at the
user and its organization own risk and cost.

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