Reynolds number

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One of the non-dimensional numbers which provide criteria of similarity for flows of viscous liquids and gases. It characterizes the relation between the inertial forces and the forces of viscosity: $$ \mathrm{Re} = \frac{\rho \, \nu \, l}{\mu} $$ where $\rho$ is the density, $\mu$ is the dynamical coefficient of viscosity of the liquid or gas, $\nu$ is the typical rate of flow, and $l$ is the typical linear dimension.

The Reynolds number also determines the mode of flow of a liquid in terms of a critical Reynolds number, $\mathrm{Re}_{\mathrm{cr}}$. When $\mathrm{Re} < \mathrm{Re}_{\mathrm{cr}}$, only laminar liquid flow is possible, whereas when $\mathrm{Re} > \mathrm{Re}_{\mathrm{cr}}$ the flow may become turbulent (cf. Turbulence, mathematical problems in).

The Reynolds number is named after O. Reynolds.


[a1] G.K. Batchelor, "An introduction to fluid dynamics" , Cambridge Univ. Press (1974) pp. Sect. 4.7
[a2] M.I. Vishik, A.V. Fursikov, "Mathematical problems of statistical hydromechanics" , Kluwer (1988) pp. Chapts. 3; 4; 6 (Translated from Russian)
[a3] L.D. Landau, E.M. Lifshitz, "Fluid mechanics" , Pergamon (1959) (Translated from Russian)
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This article was adapted from an original article by Material from the article "Reynolds number" in BSE-3 (originator), which appeared in Encyclopedia of Mathematics - ISBN 1402006098. See original article