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 ( 03C1; )
divided by its absolute viscosity ( 03BC; ). 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.