Reynolds number [for Osborne Reynolds Reynolds, 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.
..... Click the link for more information. ], 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 friction, 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.
..... Click the link for more information. between these layers gives rise to viscosity viscosity, 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.
..... Click the link for more information. . 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 turbulence, 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
..... Click the link for more information. ), 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, 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.

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