Knudsen Number Calculator

This calculator finds the Knudsen Number, which is the ratio of the molecular mean free path to the physical length scale. It is typically used to determine the regime of fluid flow. 
CalculationInputs﻿﻿Ma
:0.05​
﻿
﻿﻿Re
:1.00​
﻿
﻿﻿γ
:0.2​
﻿
Output﻿﻿Kn
:0.03​
﻿
﻿
Kn=MaReγπ2K_n=\dfrac{M_a}{R_e}\sqrt\dfrac{γπ}{2}Kn​=Re​Ma​​2γπ​​
Where:
﻿﻿Ma​
 is the Mach Number, which describes how fast an object is moving through a fluid, relative to the speed of sound in that fluid.
﻿﻿Re​
 is the Reynolds Number, which is the ratio of the inertia forces to the friction forces in flow. It is used to determine the transition from laminar flow to turbulent flow.
﻿﻿γ
 is the ratio of specific heat, which is a measure of how much more heat is needed to raise the temperature of a substance at constant pressure compared to constant volume.
﻿﻿Kn​
 is the Knudsen Number
ExplanationKnudsen Number is the ratio of the molecular mean free path to the physical length scale, and has a relationship to the Reynolds Number and Mach Number. It is typically used to determine the regime of fluid flow. Knudsen number was named after the Danish physicist Martin Knudsen. 
The rarefaction of flow can be determined from the Knudsen number. The following distinctions of flow can be made using the Knudsen Number:
﻿﻿Kn​<0.01
 is continuum flow, where conventional fluid dynamics equations are applicable, indicating that gas molecules interact with neighboring molecules
﻿﻿0.01≤Kn​<0.1
 is slip flow, where gas molecules experience slipping at the solid interface
﻿﻿0.1≤Kn​<10
 is transitional flow
﻿﻿Kn​≥10
 is free molecular flow, where gas molecules flow with minimal or no interaction with neighboring molecules
﻿
Different flow regimes corresponding to the Knudsen Number
Who was Martin Knudsen?
Martin Knudsen was a Danish physicist who taught and researched at the Technical University of Denmark. His work in the molecular gas flow led to the development of the Knudsen cell. He was well known for his work in kinetic molecular theory and low-pressure phenomena in gases.
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