Alicat VC Series Volumetric Flow Controller - Manual (Page 29)

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Once the corrected mass flow rate at standard conditions has been determined and the density at
standard conditions is known (see the density table at the back of this manual), a true mass flow can
be calculated as detailed in the following example:
Mass Flow Meter Reading = 250 SCCM (Standard Cubic Centimeters/Minute)
Gas: Helium
Gas Density at 25C and 14.696 PSIA = .16353 grams/Liter
True Mass Flow = (Mass Flow Meter Reading) X (Gas Density)
True Mass Flow = (250 CC/min) X (1 Liter / 1000 CC) X (.16353 grams/Liter)
True Mass Flow = 0.0409 grams/min of Helium
Volumetric and Mass Flow Conversion: In order to convert volume to mass, the density of the gas
must be known. The relationship between volume and mass is as follows:
Mass = Volume x Density
The density of the gas changes with temperature and pressure and therefore the conversion of
volumetric flow rate to mass flow rate requires knowledge of density change. Using ideal gas laws, the
effect of temperature on density is:
ρ
a
/ ρ
s
= T
s
/ T
a
Where: ρ
a
= density @ flow condition
T
a
= absolute temp @ flow condition in °Kelvin
ρ
s
= density @ standard (reference ) condition
T
s
= absolute temp @ standard (reference) condition in °Kelvin
ºK = ºC + 273.15 Note: ºK=ºKelvin
The change in density with pressure can also be described as:
ρ
a
/ ρ
s
= P
a
/ P
s
Where: ρ
a
= density @ flow condition
P
a
= flow absolute pressure
ρ
s
= density @ standard (reference ) condition
P
s
= Absolute pressure @ standard (reference) condition
Therefore, in order to determine mass flow rate, two correction factors must be applied to volumetric
rate: temperature effect on density and pressure effect on density.
Compressibility: Heretofore, we have discussed the gases as if they were “Ideal” in their characteristics.
The ideal gas law is formulated as:
PV=nRT
where: P = Absolute Pressure
V = Volume (or Volumetric Flow Rate)
n = number moles (or Molar Flow Rate)
R = Gas Constant (related to molecular weight)
T = Absolute Temperature
Most gases behave in a nearly ideal manner when measured within the temperature and pressure
limitations of Alicat products. However, some gases (such as propane and butane) can behave in a less
than ideal manner within these constraints. The non-ideal gas law is formulated as:
PV=ZnRT
Where: “Z” is the compressibility factor. This can be seen in an increasingly blatant manner as gases
approach conditions where they condense to liquid. As the compressibility factor goes down (Z=1 is
the ideal gas condition), the gas takes up less volume than what one would expect from the ideal gas
calculation.