Knudsen Number (relationship to Mach and Reynolds Numbers)

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Equation / Last modified by KurtHeckman on 2018/08/15 14:49
`"Kn" = `
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EmilyB.Knudsen Number (relationship to Mach and Reynolds Numbers)
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The Knudsen Number calculator computes the Knudsen Nmber based on the Mach Number, Reynolds Number and the ratio of specific heats.

INSTRUCTIONS: Enter the following:

Knudsen Number (Kn): The calculator returns the Knudsen Number.

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The Math / Science

The Knudsen Number (relationship to Mach and Reynold's Number) 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 Knudsen Number helps to 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 the problem, and the continuum assumption of fluid mechanics is no longer a good approximation.
The Knudsen Number formula shows the relationship between the Knudsen number and the Mach and Reynolds Numbers: 

`"Kn"=M_a/R_esqrt((gamma*pi)/2)`

where:

References


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