Reynolds Number (redirected from Reynold's number)

Reynolds number [for Osborne Reynolds], dimensionless quantity associated with the smoothness of flow of a fluid. It is an important quantity used in aerodynamics and hydraulics. At low velocities fluid flow is smooth, or laminar, and the fluid can be pictured as a series of parallel layers, or lamina, moving at different velocities. The fluid friction between these layers gives rise to viscosity. As the fluid flows more rapidly, it reaches a velocity, known as the critical velocity, at which the motion changes from laminar to turbulent (see turbulence), with the formation of eddy currents and vortices that disturb the flow. The Reynolds number for the flow of a fluid of density &rgr; and viscosity η through a pipe of inside diameter d is given by R=&rgr;dv/η, where v is the velocity. The Reynolds number for laminar flow in cylindrical pipes is about 1,000.

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Reynolds number

In fluid mechanics, a number that indicates whether the flow of a fluid (liquid or gas) is absolutely steady (in streamlined, or laminar flow) or on the average steady with small, unsteady changes (in turbulent flow; see turbulence). The Reynolds number, abbreviated N_Re or Re, has no dimensions (see dimensional analysis) and is defined as the size of the flow—as, for example, the diameter of a tube (D) times the average speed of flow (v) times the mass density of the fluid (ρ)—divided by its absolute viscosity (μ). Osborne Reynolds demonstrated in 1883 that the change from laminar to turbulent flow in a pipe occurs when the value of the Reynolds number exceeds 2,100.

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Reynolds number [′ren·əlz ‚nəm·bər]

(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. SymbolizedN_Re. Also known as Damköhler number V (DaV).

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Reynolds number

In fluid mechanics, the ratio ρvd/μ, where ρ 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 Dynamic similarity, Fluid mechanics, Laminar flow, Turbulent flow

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Reynolds Number 

one of the similarity criteria for flows of viscous fluids and gases, characterizing the relationship between inertial and viscous forces: Re = ρvl/μ, where ρ is the density, μ the dynamic viscosity coefficient of the fluid or gas, v the characteristic flow velocity, and l the characteristic length. Thus, for the flow in a circular cylindrical pipe, l = d, where d is the diameter of the pipe, and v = v_av, where v_av is the average flow velocity. For the flow of fluids or gases around bodies, l is the length or transverse dimension of the body, and v = v∞, where v∞ is the velocity of the undisturbed flow striking the body. The number was named after O. Reynolds.

The flow pattern of a fluid, characterized by the critical Reynolds number Re_cr, also depends on the Reynolds number. When Re < Re_cv only a laminar flow of the fluid is possible, and when Re > Re_cr, the flow may become turbulent. The value of Re_cr depends on the type of flow. For example, for the flow of a viscous fluid in a circular cylindrical pipe, Re_cr = 2,300.

S. L. VISHNEVETSKII