# Summary

Standard volumetric flow rates of a fluid are often used to describe the capacity of a vent or pressure relief device. To determine how this capacity compares for another fluid under different pressure and temperature conditions a conversion must be made on the basis of equivalent pressure loss. This article describes the method for calculating the volumetric flow rate of a gas which will give the equivalent pressure drop to another gas through a fixed restriction such as a vent.

# Definitions

: | Resistance Coefficient | |

: | Density of a specific fluid denoted by a subscript (kg/m^{3}) | |

: | Molecular Weight | |

: | Pressure (Pa) | |

: | Volumetric flow rate (m^{3}/s) | |

: | Temperature (K) | |

: | Velocity (m/s) | |

: | Compressibility Factor |

# Introduction

Standard volumetric flow rates denote volumetric flow rates of gas corrected to standardised properties of temperature, pressure and relative humidity. Its use is common across engineering and allows a direct comparison to be made between gaseous flows in a manner identical to comparing their mass flow rates. Standard volumetric flow is also commonly used by vendors when describing the capacity of vents or pressure relief devices, however for capacity checks at different conditions a comparison on a pressure loss basis is more appropriate.

To compare volumetric flow rates on a pressure loss basis the excess head method is used. This allows us to determine the flow rate under the actual process conditions that will give an equivalent pressure loss to the standard conditions under which the equipment was characterised.

The most common units to describe standard volumetric flows are standard cubic meters per hour (SCMH) in metric units and standard cubic feet per minute (SCFM) in imperial units.

However care must be taken when working with standard volumetric flows as the standard conditions may vary country to country or even region to region. The most common standards used are IUPAC (100kPa, 273.15K), ISO2533 (101.325kPa, 288.15K) and DIN1342 (101.325 kPa, 273.15K).

# Equivalent Flow Rate Calculation

There are several formulae that can be used to calculate the equivalent flow rate depending on the information available or simplifying assumptions. Here we will adopt the convention that subscript 'std' denotes properties of the standard fluid (usually air) at standard conditions and the subscript ‘actual’ denoted the process fluid at the actual process conditions. Following these conventions the equations to convert between standard volumetric flow and actual are presented below:

## Known Gas Density

The calculation of the equivalent flow rate can be completed with relative ease if the densities of the fluid at actual and standard conditions are known.

## Unknown Gas Density

If the density for the two fluids is not known for the required conditions the density may be approximated using the ideal gas equation yielding the following equations:

## Unknown Gas Density - Simplified

The above formula can be simplified if the same gas is considered and the pressure and temperature do not differ greatly between both sets of conditions. This simplification assumes that the molecular weight and compressibility do not change, which is generally safe for the same fluid at similar temperatures and pressures.

# Derivation

The conversion calculations above can be derived from the equation for pressure drop for fluid flow which is simply the multiple of the frictional pressure drop factor and the velocity head:

As the purpose of standard volumetric flow rates is to provide a standardised flow rate which gives an equivalent pressure drop across a particular fitting as the actual flow we may state that the pressure drops for both our standard and actual fluids are equal for a specific fitting:

As the fitting is the same for both the standard and actual fluid the K value will be identical and therefore we may simplify the previous equation as flows:

Given that velocity of a fluid is proportional to its volumetric flow rate we may express the ratio of standard and actual flow rates as follows:

This result may then be manipulated to give the conversion equations presented in the previous section.