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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

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