Vacuum Technology Know How - Triumf

Formula 1-9
Knudsen number
Formula 1-10
Reynolds number
www.pfeiffer-vacuum.net
The dimensionless Knudsen number Kn is defined as the ratio between mean free path and
component diameter
In this case, Kn is < 0.01. In addition, the term viscous flow is used if the product of pressure p
and diameter d of the components through which gas is flowing is p . d ≥ 6 . 10 -1 mbar . cm
for air.
In the case of viscous flow, a distinction is made between laminar and turbulent flow. Laminar
flow prevails at low flow speeds. At higher flow speeds, this changes to a turbulent flow [2].
The occurrence of turbulent flow is contingent upon the Reynolds number
Where is:
� = density [kg / m³]
� = viscosity [Pas]
v = flow velocity [m / s]
d = tube diameter [m]
Kn =
l –
d
�
Re = . v . d
�
Up to values of Re < 2,300 the flow will be laminar, and where Re > 4,000 the flow will be
turbulent. In vacuum systems, the lines are dimensioned in such a manner that turbulent flow
occurs only briefly at relatively high pressures, as the high flow resistance that occurs in this
process necessitates that the pumps produce higher volume flow rates.
Knudsen flow in medium vacuum, p = 100 – 10-3 mbar, mit l – ≤ d
If the Knudsen number is between 0.01 and 0.5, this is termed Knudsen flow. Because
many process pressures are in the medium vacuum range, this type of flow occurs with corresponding
frequency. Since this is a transitional flow, this range is transited relatively quickly
when pumping down vacuum chambers. This means that the influence of this conductivity
on pump-down times is correspondingly low. It is a complicated endeavor to perform a
precise calculation of conductivity where the flow range is still laminar and yet already molecular,
and this will not be discussed here. A simple approximation for the Knudsen range can
be obtained by adding the laminar and molecular conductivities. Figure 1.7 shows the
conductivities of round, one meter long tubes of differing diameters in all three flow ranges.
Molecular flow in high vacuum, (p = 10-3 – 10 -7 mbar), where l – > d and in ultra high
vacuum (p < 10 -7 mbar), mit l – >> d
At Knudsen numbers of Kn > 0.5 molecular interaction virtually no longer occurs. What
prevails is molecular flow. In this case, the product of pressure p and component diameter d
is p . d ≤ 1.3 . 10 - 2 mbar . cm.
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