Knudsen Number (relationship to Mach and Reynolds Numbers)

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:

• (M_a) This is the Mach Number
• (R_e) This is the Reynold's Number
• (γ) This is the ratio of specific heats

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

Related Calculators

• Grashof Number (pipes)
• Grashof Number (bluff bodies)
• Grashof Number (flat vertical plate)
• Richardson Number 
• Reynold's Number
• Knudsen Number

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:

• Kn = Knudsen Number formula
• `M_a` = Mach Number
• `R_e` = Reynold's Number
• `gamma` = ratio of specific heats

References

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