View source for Reynolds number

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:

<table class="eq" style="width:100%;"> <tr><td valign="top" style="width:94%;text-align:center;"><img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081710/r0817101.png" /></td> </tr></table>

where <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081710/r0817102.png" /> is the density, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081710/r0817103.png" /> is the dynamical coefficient of viscosity of the liquid or gas, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081710/r0817104.png" /> is the typical rate of flow, and <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081710/r0817105.png" /> is the typical linear dimension.

The Reynolds number also determines the mode of flow of a liquid in terms of a critical Reynolds number, <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081710/r0817106.png" />. When <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081710/r0817107.png" />, only laminar liquid flow is possible, whereas when <img align="absmiddle" border="0" src="https://www.encyclopediaofmath.org/legacyimages/r/r081/r081710/r0817108.png" /> the flow may become turbulent.

The Reynolds number is named after O. Reynolds.



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====References====
<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>