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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