Reynolds number

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

McGraw-Hill Concise Encyclopedia of Physics. © 2002 by The McGraw-Hill Companies, Inc.

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. Symbolized N_Re . Also known as Damköhler number V (DaV).

McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.

Reynolds number

Effect of Reynolds number on boundary layer flow. In case 1, it is low Reynolds number, i.e., low velocity, while in case 2, it is high Reynolds number, i.e., high-velocity.

A dimensionless number that establishes the proportionality between the fluid inertia and the sheer stress as a result of viscosity. The work of Osborne Reynolds has shown that the flow profile of fluid in a closed circuit depends upon the conduit diameter, the density and the viscosity of the flowing fluid, and the flow velocity. In the simplest form, it can be described as R = ρVl/μ, where ρ is the density in kilograms per cubic meters (1.2250 for air at sea level), V is the velocity of the fluid in meters per second, l is the linear dimension of the body (chord length, in airfoils), and μ is the coefficient of the viscosity of the fluid.

An Illustrated Dictionary of Aviation Copyright © 2005 by The McGraw-Hill Companies, Inc. All rights reserved

The following article is from The Great Soviet Encyclopedia (1979). It might be outdated or ideologically biased.

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

The Great Soviet Encyclopedia, 3rd Edition (1970-1979). © 2010 The Gale Group, Inc. All rights reserved.