The streamline flow of a fluid in which a fluid flows without fluctuations or turbulence. The velocities of fluid molecules are in the direction of flow with only minor (p. 214) movement across the streamlines caused by molecular diffusion. The existence was first demonstrated in 1883 by Osborne Reynolds, who injected a trace of coloured fluid into a flow of water in a glass pipe. At low flow rates the coloured fluid was observed to remain as discrete filaments along the tube axis, indicating flow in parallel streams. At increased flow rates, oscillations were observed in the filaments, which eventually broke up and dispersed across the tube. There appeared to be a critical point for a particular tube and fluid above which the oscillations occurred. By varying the various parameters Reynolds found that his results could be correlated into terms of a dimensionless number called the Reynolds number, Re, as:
where ρ is the density of the fluid, v is the velocity of the fluid, d is the diameter of the pipe, and μ is the viscosity of the fluid. The critical value of Re for the break-up of laminar flow in pipes of circular cross section is about 2,000.