The Knudsen number can be used to guide the choice between statistical mechanics and the continuous formulation of aerodynamics.
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Airflow around an aircraft has a low Knudsen number, making it firmly in the realm of continuum mechanics.
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His name is associated with the Knudsen flow, Knudsen diffusion, Knudsen number, Knudsen layer and Knudsen gases.
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The Knudsen number helps determine whether statistical mechanics or the continuum mechanics formulation of fluid dynamics should be used to model a situation.
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This requires the Knudsen number to be small, as is also a pre-requisite for the continuum hypothesis to be a valid one.
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Additionally, rarefied hypersonic flows ( usually defined as those with a Knudsen number above 0.1 ) do not follow the Navier Stokes equations.
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Problems with high Knudsen numbers include the calculation of the motion of a dust particle through the lower atmosphere, or the motion of a satellite through the exosphere.
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Statistical mechanics can also describe work in non-linear dynamics, chaos theory, thermal physics, fluid dynamics ( particularly at high Knudsen numbers ), or plasma physics.
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Physical systems with Knudsen numbers at or above unity require the use of statistical mechanics, which itself provides the underlying physics of fluids which is an input to fluid mechanics.
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Problems with Knudsen numbers below 0.1 can be evaluated using continuum hypothesis, but molecular approach ( statistical mechanics ) can be applied for all ranges of Knudsen numbers.
