Knudsen equation

 ( Fluid Dynamics ) 

In fluid dynamics, the Knudsen equation is used to describe how gas flows through a tube in free molecular flow. When the mean free path of the in the gas is larger than or equal to the diameter of the tube, the molecules will interact more often with the walls of the tube than with each other. For typical tube dimensions, this occurs only in high or ultrahigh vacuum.

The equation was developed by Martin Hans Christian Knudsen (1871–1949), a Danish physicist who taught and conducted research at the Technical University of Denmark.

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Cylindrical tube For a cylindrical tube, the Knudsen equation is:

$q\; =\; \backslash frac16\; \backslash sqrt\{2\; \backslash pi\}\; \backslash Delta\; P\; \backslash frac\{d^3\}\{\; l\; \backslash sqrt\{\backslash rho\_1\}\},$

where:

volume flow rate at unit pressure (volume×pressure/time)

pressure drop from the beginning of the tube to the end

diameter of the tube

length of the tube

ratio of density and pressure

For nitrogen (or air) at room temperature, the conductivity $C$ (in liters per second) of a tube can be calculated from this equation:

$\backslash frac\{C\}\{\backslash mathrm\{L\}/\backslash mathrm\{s\}\}\; \backslash approx\; 12\; \backslash ,\; \backslash frac\{d^3/\backslash mathrm\{cm\}^3\}\}$

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