Knudsen Number (Boltzmann gas)

Last modified by

on

Jul 24, 2020, 6:28:07 PM

Created by

on

Aug 15, 2016, 12:46:38 PM

Kn = \frac{k_{B} \cdot T}{\sqrt{2} \cdot π \cdot d^{2} \cdot p \cdot L}

$"Kn" = (k_B* T )/(sqrt(2)*pi* d ^2* p * L )$

(T) thermodynamic temperature

$(T)"thermodynamic temperature"$

(d) particle hard-shell diameter

$(d)"particle hard-shell diameter"$

(p) total pressure

$(p)"total pressure"$

(L) representaive physical length scale

$(L)"representaive physical length scale"$

Tags

UUID

4efd0767-62e6-11e6-9770-bc764e2038f2

The Knudsen Number (Boltzmann gas) is a dimensionless number defined as the ratio of the molecular mean free path length to a representative physical length scale. This length could be, for example, the radius of a body in a fluid.
The Knudsen Number helps determine whether statistical mechanics or the continuum mechanics formulation of fluid dynamics should be used to model a situation. If the Knudsen number is near or greater than one, the mean free path of a molecule is comparable to a length scale of a problem, and the continuum assumption of fluid mechanics is no longer a good approximation.
The following formula is used for a Boltzmann gas: $Kn = \frac{k_{B} T}{\sqrt{2} π d^{2} p L}$ $"Kn"=(k_BT)/(sqrt(2)pid^2pL)$ , where:

$k_{B}$ $k_B$ = Boltzmann constant
$T$ $T$ = thermodynamic temperature
$d$ $d$ = particle hard-shell diameter
$p$ $p$ = total pressure
$L$ $L$ = representative physical length scale

References

Wikipedia (https://en.wikipedia.org/wiki/Knudsen_number)

This equation, Knudsen Number (Boltzmann gas), references 2 pages

Equations and Data Items

• Boltzmann constant (J/K) with Units by MichaelBartmess

•

π

$pi$ by MichaelBartmess

Comments
Attachments
Stats

No comments

No attachments

Last 12 Months

This site uses cookies to give you the best, most relevant experience. By continuing to browse the site you are agreeing to our use of cookies.

Knudsen Number (Boltzmann gas)

References

Datasets

Equations and Data Items

Calculators

Equations and Data Items

Collections