# Reynolds number

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## Reynolds number

[for Osborne ReynoldsReynolds, Osborne,
1842–1912, British mechanical engineer. He was educated at Cambridge and became (1868) the first professor of engineering at the Univ. of Manchester, where his courses attracted a number of outstanding students.
], 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 frictionfriction,
resistance offered to the movement of one body past another body with which it is in contact. In certain situations friction is desired. Without friction the wheels of a locomotive could not "grip" the rails nor could power be transmitted by belts.
between these layers gives rise to viscosityviscosity,
resistance of a fluid to flow. This resistance acts against the motion of any solid object through the fluid and also against motion of the fluid itself past stationary obstacles.
. 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 turbulenceturbulence,
state of violent or agitated behavior in a fluid. Turbulent behavior is characteristic of systems of large numbers of particles, and its unpredictability and randomness has long thwarted attempts to fully understand it, even with such powerful tools as statistical
), 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.

## 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.
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 = vav, where vav 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 Recr, also depends on the Reynolds number. When Re < Recv only a laminar flow of the fluid is possible, and when Re > Recr, the flow may become turbulent. The value of Recr depends on the type of flow. For example, for the flow of a viscous fluid in a circular cylindrical pipe, Recr = 2,300.

S. L. VISHNEVETSKII

## 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 NRe . 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.
References in periodicals archive ?
Both the definitions of the Reynolds number are the accepted methods of nondimensionalizing the flow turbulence characteristics in modern bearing treatments .
Figures 21(a) and 21(b) present the variations of Nu/[Nu.sub.0] with the Reynolds number at various flow attack angles for V-Downstream and V-Upstream wavy surfaces in the heat exchanger tube, respectively.
As can be observed in Figure 2, a typical characteristic at low Reynolds number flow is represented by a practically flat region in the pressure coefficient distribution followed by an abrupt break, which corresponds to the existence of the separation bubble.
The Effect of the Reynolds Number. In this section, we study the effect of the Reynolds number on the particle migration in the serpentine channel shown in Figure 1.
This gives some confidence to move to more challenging cases with higher Reynolds number and the results are to be presented in the following sections.
Reynolds number = 800, the diameter = 2 mm, the sheet position = 3 mm, and the distance between the cylinder and the slot was 5.9 cm.
The variation of the f/[f.sub.0] with the flow attack angle for the square channel heat exchanger inserted with wavy plate at various Reynolds numbers is depicted as Figures 11(a) and 11(b), respectively, for V-Downstream and V-Upstream.
Before discussing the results, here's a quick refresher on the Reynolds number (Re) calculation and what it means:
From the critical evaluation of the mentioned literature in this field, it is obvious that although there are some available results for mixed convection heat transfer analysis around a confined cylinder by opposing buoyancy, there is no reported work on effect of opposing buoyancy of the fluid flow and heat transfer around a circular cylinder confined within a horizontal channel at low Reynolds number. For that purpose, our objective is to investigate correctly the role of opposing thermal buoyancy on the momentum and heat transfer characteristics of circular cylinder situated between parallel walls.
As high Prandtl number flows (implying very thin conductive sublayers) typically involve low Reynolds numbers, it is strongly recommended to avoid wall functions if flow conditions allow affordable meshes that are sufficiently fine for the integration to the wall.
It is a kind of Reynolds number. Since it is calculated during the flutter speed, it can be called flutter Reynolds number.
The horizontal flow demonstrated an increasing linear trend as the main flow rate was also increasing (see Figure 2) whereas the ratio of the horizontal flow rate appeared to maintain the linear trend and did not significantly change when the Reynolds number was increasing (see Figure 4).

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