Notice also that in the above equation, the viscous terms vanish for Re → ∞. This is why mathematically all Newtonian, incompressible flows with the same Reynolds number are comparable.

The Reynolds number is defined as R e = u L ν = ρ u L μ Universal sedimentation equation - drag coefficient, a function of Reynolds number and shape factor, 2D diagram Universal sedimentation equation - drag coefficient, a function of Reynolds number and shape factor, 3D diagram turbulent flow occurs at high Reynolds numbers and is dominated by inertial forces, which tend to produce chaotic eddies, vortices and other flow instabilities.laminar flow occurs at low Reynolds numbers, where viscous forces are dominant, and is characterized by smooth, constant fluid motion.With respect to laminar and turbulent flow regimes: Such scaling is not linear and the application of Reynolds numbers to both situations allows scaling factors to be developed. This ability to predict the onset of turbulent flow is an important design tool for equipment such as piping systems or aircraft wings, but the Reynolds number is also used in scaling of fluid dynamics problems and is used to determine dynamic similitude between two different cases of fluid flow, such as between a model aircraft, and its full-size version. The Reynolds number quantifies the relative importance of these two types of forces for given flow conditions and is a guide to when turbulent flow will occur in a particular situation.

Counteracting this effect is the viscosity of the fluid, which tends to inhibit turbulence. This relative movement generates fluid friction, which is a factor in developing turbulent flow. A similar effect is created by the introduction of a stream of high-velocity fluid into a low-velocity fluid, such as the hot gases emitted from a flame in air. A region where these forces change behavior is known as a boundary layer, such as the bounding surface in the interior of a pipe. The Reynolds number is the ratio of inertial forces to viscous forces within a fluid that is subjected to relative internal movement due to different fluid velocities. The concept was introduced by George Stokes in 1851, but the Reynolds number was named by Arnold Sommerfeld in 1908 after Osborne Reynolds (1842–1912), who popularized its use in 1883. The predictions of the onset of turbulence and the ability to calculate scaling effects can be used to help predict fluid behavior on a larger scale, such as in local or global air or water movement, and thereby the associated meteorological and climatological effects. It is used to predict the transition from laminar to turbulent flow and is used in the scaling of similar but different-sized flow situations, such as between an aircraft model in a wind tunnel and the full-size version. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow ( eddy currents). At low Reynolds numbers, flows tend to be dominated by laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulent. In fluid dynamics, the Reynolds number ( Re) is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between inertial and viscous forces.

Osborne Reynolds popularised the concept. George Stokes introduced Reynolds numbers. This can occur around cylinders and spheres, for any fluid, cylinder size, and fluid speed provided that it has a Reynolds number between roughly. The transition from laminar (left) to turbulent (right) flow of water from a tap occurs as the Reynolds number increases.

Kinemtic viscosity units