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.