Reynolds number

(fluid mechanics) A dimensionless number which is significant in the design of a model of any system in which the effect of viscosity is important in controlling the velocities or the flow pattern of a fluid; equal to the density of a fluid, times its velocity, times a characteristic length, divided by the fluid viscosity. Symbolized N_Re. Also known as Damköhler number V (DaV).

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In fluid mechanics, the ratio &rgr:vd/μ, where &rgr: is fluid density, v is velocity, d is a characteristic length, and μ is fluid viscosity. The Reynolds number is significant in the design of a model of any system in which the effect of viscosity is important in controlling the velocities or the flow pattern. In the evaluation of drag on a body submerged in a fluid and moving with respect to the fluids, the Reynolds number is important.

The Reynolds number also serves as a criterion of type of fluid motion. In a pipe, for example, laminar flow normally exists at Reynolds numbers less than 2000, and turbulent flow at Reynolds numbers above about 3000. See also Dynamic similarity; Fluid mechanics; Laminar flow; Turbulent flow.

rheology. Symbol Re. Relating to momentum transport, the dimensionless ratio of the product of representative speed and length elements to kinematic viscosity (the ratio of the inertia forces to the viscous forces in a flowing fluid).International Standards Association
[ ISO 31-12:1992 Quantities and Units: Characteristic Numbers]
[Mills I., Cvitas T., Homan K., Kuchitsu K. Quantities, Units and Symbols in Physical Chemistry, 2nd edn (Oxford: Blackwell, 1993)] For flow through pipes, turbulence rather than laminar flow is indicated by a value greater than 2 000. See also Dean number; Taylor number.

The magnetic Reynolds number (Re_m, R_m), for fluids flowing in a magnetic field, is the ratio of mass transport diffusivity to magnetic diffusivity, identically the ratio of the product of fluid speed, permeability, and electrical conductivity to a representative length.

Four factors combine to determine whether the flow of water within a channel is turbulent or laminar: the density, velocity, and viscosity of the water, and the hydraulic radius of the channel. Since the density of water is 1, the Reynolds number expresses this combination as:

R_e =VRμ

A dimensionless quantity named after Osborne Reynolds (1842-1912), applied to a fluid flowing through a tube with a circular cross section. The Reynold's number is expressed by the equation Re = vpl/n, where v = velocity of flow, p = density of the liquid, l = diameter of the tube, and n = the coefficient of viscosity of the liquid. When the Reynolds number exceeds a critical value, the flow of the fluid changes from streamline or laminar flow of the fluid to turbulent.