Flow of Gases through Pipes in a Vacuum

The flow conditions within a gas can be described through the Knudsen number. Flows through pipes are characterised through the Reynolds number. At relatively high pressures in a rough vacuum, a viscous flow is present which may either be laminar or turbulent. For a viscous flow, a mutual influence between the flowing particles is typical. In the turbulent range, the molecules behave chaotically. The Knudsen number is defined as follows  

A viscous gas flow is characterised through a Knudsen number of Kn 0.01. 

The pipe diameter d is here much bigger than the mean free path X of the molecules, and the gas flow is characterised by constant collisions amongst the particles. 

The boundary between a continuous flow and a turbulent flow can be characterised through the Reynolds number (Re) upd 1 

When the non-dimensional Reynolds number attains values of over 2200, then one speaks of a turbulent flow, in the case of values below 1200 one then speaks of a laminar flow. In the range in between, either turbulent or laminar flow conditions can be present. 

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