In fluid dynamics, the Knudsen equation is used to describe how

gas Gas is one of the four fundamental states of matter (the others being solid, liquid, and plasma). A pure gas may be made up of individual atoms (e.g. a noble gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or ...

flows through a tube in

free molecular flow Free molecular flow describes the fluid dynamics of gas where the mean free path of the molecules is larger than the size of the chamber or of the object under test. For tubes/objects of the size of several cm, this means pressures well below 10− ...

. When the

mean free path In physics, mean free path is the average distance over which a moving particle (such as an atom, a molecule, or a photon) travels before substantially changing its direction or energy (or, in a specific context, other properties), typically as a ...

of the

molecule A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...

s in the gas is larger than or equal to the diameter of the tube, the molecules will interact more often with the walls of the tube than with each other. For typical tube dimensions, this occurs only in high or ultrahigh vacuum. The equation was developed by

Martin Hans Christian Knudsen Martin Hans Christian Knudsen (February 15, 1871 in Hasmark on Funen – May 27, 1949 in Copenhagen) was a Danish physicist who taught and conducted research at the Technical University of Denmark. He is primarily known for his study of molec ...

(1871–1949), a Danish physicist who taught and conducted research at the

Technical University of Denmark The Technical University of Denmark ( da, Danmarks Tekniske Universitet), often simply referred to as DTU, is a polytechnic university and school of engineering. It was founded in 1829 at the initiative of Hans Christian Ørsted as Denmark's fir ...

Cylindrical tube

For a cylindrical tube, the Knudsen equation is: :

q = \frac16 \sqrt \Delta P \frac,

where: For nitrogen (or air) at room temperature, the conductivity

C

(in liters per second) of a tube can be calculated from this equation: :

\frac \approx 12 \, \frac

References

{{Reflist Fluid dynamics