Knudsen number
Encyclopedia : K : KN : KNU : Knudsen number
The Knudsen number (Kn) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. This length scale could be, for example, the radius of a body in a fluid. The number is named after Danish physicist Martin Knudsen (1871–1949).
Definition
The Knudsen number is defined as:
- [\mathit = \frac = \frac \pi\sigma^2 P L} ]
- [\lambda] = mean free path (m)*
- L = representative physical length scale (m)
- kB = Boltzmann's constant (1.38×10-23 J/K)
- T = temperature (K)
- [\sigma] = diameter (m)
- P = total pressure (Pa)
Application
The Knudsen number is useful for determining whether statistical mechanics or the continuum mechanics formulation of fluid dynamics should be used: If the Knudsen number is near or greater than one, the mean free path of a molecule is comparable to a length scale of the problem, and the continuum assumption of fluid mechanics is no longer a good approximation. In this case statistical methods must be used.
Problems with high Knudsen numbers include the calculation of the motion of a dust particle through the lower atmosphere, or the motion of a satellite through the exosphere. The solution of the flow around an aircraft has a low Knudsen number. Using the Knudsen number an adjustment for Stokes' Law can be used in the Cunningham correction factor, this is a drag force correction due to slip in small particles (i.e. dp <5 µm).
See also
- Cunningham correction factor
- Fluid dynamics
- Mach number
- Reynolds number
External links
- [Gas Dynamics Toolbox] – Using the VHS model for calculating Knudsen numbers of gas mixtures
From Wikipedia, the Free Encyclopedia. Original article here. Support Wikipedia by contributing or donating.
All text is available under the terms of the GNU Free Documentation License See Wikipedia Copyrights for details.