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The Buckingham II theorem is applied to derive two sets of dimensionless parameters; one set for the quantities in the equations of Maxwell and Navier-Stokes, and the other containing the quantities involved in the Boltzmann equation. Ten independent dimensionless parameters are thus derived, which represent a complete set of scaling laws for phenomena describable by the these equations and which contain among them the ordinary fluid-dynamic scaling parameters: the Mach and Reynolds numbers.
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Beiser et al. (1961) studied this question.
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