Knudsen equation
In fluid dynamics, the Knudsen equation is used to describe how gas flows through a tube in free molecular flow. When the mean free path of the molecules in the gas is less 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.
The equation was developed by Martin Hans Christian Knudsen (1871–1949), a Danish physicist who taught and conducted research at the Technical University of Denmark.
Cylindrical tube
For a cylindrical tube, the Knudsen equation is:[1]
\[q = \frac16 \sqrt{2 \pi} \Delta P \frac{d^3}{ l \sqrt{\rho_1}},\]
where:
| Quantity | Description |
|---|---|
| q | volumetric flow rate (volume/time) |
| ΔP | pressure drop from the beginning of the tube to the end |
| d | diameter of the tube |
| l | length of the tube |
| ρ1 | ratio of density and pressure |
References
- ↑ Loeb, Leonard B. (2004) [1927], The Kinetic Theory of Gases, Dover, p. 293, ISBN 978-0-486-49572-9
