Difference between revisions of "Reynolds number"
From Encyclopedia of Mathematics
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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: | 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]]). | |
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| − | The Reynolds number also determines the mode of flow of a liquid in terms of a critical Reynolds number, | ||
The Reynolds number is named after O. Reynolds. | The Reynolds number is named after O. Reynolds. | ||
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====References==== | ====References==== | ||
| − | <table><TR><TD valign="top">[a1]</TD> <TD valign="top"> G.K. Batchelor, | + | <table> |
| + | <TR><TD valign="top">[a1]</TD> <TD valign="top"> G.K. Batchelor, "An introduction to fluid dynamics" , Cambridge Univ. Press (1974) pp. Sect. 4.7</TD></TR> | ||
| + | <TR><TD valign="top">[a2]</TD> <TD valign="top"> M.I. Vishik, A.V. Fursikov, "Mathematical problems of statistical hydromechanics" , Kluwer (1988) pp. Chapts. 3; 4; 6 (Translated from Russian)</TD></TR> | ||
| + | <TR><TD valign="top">[a3]</TD> <TD valign="top"> L.D. Landau, E.M. Lifshitz, "Fluid mechanics" , Pergamon (1959) (Translated from Russian)</TD></TR> | ||
| + | </table> | ||
Latest revision as of 15:10, 10 April 2023
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.
References
| [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) |
How to Cite This Entry:
Reynolds number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reynolds_number&oldid=15768
Reynolds number. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Reynolds_number&oldid=15768
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