The ratio of the mean free path to a macroscopic length compares collision and transport scales. Small Knudsen number motivates the hydrodynamic limit of the Boltzmann equation; large values favor a direct kinetic description. The scaling of time, velocity and space must also be stated when using it as a coefficient in a kinetic equation.
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The Knudsen number (Kn) is a dimensionless quantity used in fluid dynamics and kinetic theory to characterize the flow of gas. It is defined as the ratio of the mean free path of gas molecules to a characteristic length scale, such as the diameter of a pipe or the dimensions of an object through which the gas is flowing.