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# Knudsen Number (relationship to Mach and Reynolds Numbers)

EmilyB.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**) This is the Mach Number_{a} - (
**R**) This is the Reynold's Number_{e} - (
**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)

**Knudsen Number (relationship to Mach and Reynolds Numbers)**, references 1 equation/constant.

**Equations and Constants **