Mass flow rate of gas fluid into volumetric flow

When converting the mass flow rate of a gas fluid into a volumetric flow rate, can easily calculate it if know the density at the corresponding pressure and temperature. If do not know the density, we can convert it using the ideal gas equation of state. If we translate the equation of state for an ideal gas into a volumetric flow rate, it is as follows.

Formula of EOS

Equation of state for an ideal gas

P * V = n * R * T
P * V = w / Mw * R * T
P * Q = m / Mw * R * T
Q = (m / Mw * R * T) / P

Here,

P     : pressure of gas
V     : volume of gas 
Q     : volumetric flow rate of gas
w     : wight of gas
Mw    : molecular weight
m     : mass flow rate of gas
R     : gas constant
T     : temperature of gas

Different gas constants must be used depending on the various units.

Universal gas constant R 

0.082 atm-l/mol-°K
8.314 kJ/kgmol-°K
8.314 kPa-m3/kgmol-°K
1.987 Btu/lbmol-°R
1,545 lbf-ft/lbmol-°R
10.73 psia-ft3/lbmol-°R (1 bar = 100 kPa)

Example of conversion

When using bar, m3, kg, kgmol, °C, and °K units, if the flow meter design temperature is 0 °C, converting the mass flow rate to volumetric flow rate is:

P * V = n * R * T

1 bar * 22.4 m3 = 1 kg-mol * 0.08314 bar-m3/kgmol-°K * 273°K
Q = (m / Mw * R * T) / P 
Q = (m / Mw * 0.08314 bar-m3/kgmol-°K * 273°K) / 1 bar
Q = m * 22.4 / Mw

For example, Nitrogen 1,000 kg/hr mass flow is
Q = m * 22.4 / Mw = 1000 * 22.4 / 28 = 800

Converted to 800 Nm3/hr volumetric flow.
When using psia, ft3, lb, lbmol, °F, and °R units, if the flow meter design temperature is 60 °F, converting the mass flow rate to volumetric flow rate is:

P * V = n * R * T
14.7 psia * 379.565 ft3 = 1 lbmol * 10.73 psia-ft3/lbmol-°R * 520 °R
Q = (m / Mw * R * T) / P 
Q = (m / Mw * 10.73 psia-ft3/lbmol-°R * 520 °R) / 14.7 psia
Q = m * 379.565 ft3 / Mw

For example, Nitrogen 1,000 lb/hr mass flow is
Q = m * 379.565 / Mw = 1000 * 379.565 / 28 = 13,556
Converted to 13,556 SCFH (standard ft3/hr) volumetric flow.

Here, 

0.08314 bar-m3/kgmol-°K (1 bar = 100 kPa)

1.987 Cal/mol-°K