# 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

## 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).

## 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.
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