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Vacuum Mean Gas Velocity Equations and Calculator

Fluids Systems Design and Engineering

Vacuum Mean Gas Velocity Equations and Calculator

The residency time of various gases in a system (or the time taken to remove various gases) relates to their individual mean velocity. The following table shows mean velocities for some gases. It can be seen that very light gases travel significant faster than heavy gases. It should be noted that Hydrogen and Helium do not pump efficiently in turbo pumps or cryopumps but heavy gases generally do.

u = [ ( 8 · R · T ) / ( π · M ) ]^(1/2)

Where:

M = Molar mass (kg/mol)
R = General gas constant = 8.314510 kJ/(kmol K),
T = Thermodynamic temperature (K),
u = Mean Velocity (m/s)

For example: Mean velocity of Argon @ 20°C
u = SQRT (8 x 8.31451 x 293 / 0.039948 x 3.1416)
u = 394 m/s

Gas	Molar Mass kg/mol	Mean Velocity m/s	Mach Number
Air	0.028966	463	1.4
Ar	0.039948	394	1.2
Cl2	0.0709	296
CO	0.028011	471
CO2	0.04401	376	1.1
H2	0.002016	1762	5.3
He	0.00402	1246	3.7
Kr	0.0838	272
N2	0.02801	471	1.4
Ne	0.020179	555
O2	0.03199	441
Xe	0.1313	217
H2O	0.01802	587	1.8

Mean velocity of gases at 20°C
The Vacuum Technology Book – Pfeiffer Vacuum September 2008