Viscous flows generically fall into two categories, laminar and turbulent, but the boundary between them is imperfectly defined
Reynolds’s experiment to distinguish between laminar and turbulent flows
At low flow rates, the dye stream was observed to follow a well-defined straight path, indicating that the fluid moved in parallel layers (laminae) with no unsteady macroscopic mixing or overturning motion of the layers. Such smooth orderly flow is called laminar
However, if the flow rate was increased beyond a certain critical value, the dye streak broke up into irregular filaments and spread throughout the cross-section of the tube, indicating the presence of unsteady, apparently chaotic three-dimensional macroscopic mixing motions. Such irregular disorderly flow is called turbulent
Reynolds demonstrated that the transition from laminar to turbulent flow always occurred at or near a fixed value of the ratio that bears his name, the Reynolds number, Re = \(Ud/ν\) ∼ 2000 to 3000 where \(U\) is the velocity averaged over the tube’s cross-section, \(d\) is the tube diameter, and \(ν = μ/ρ\) is the kinematic viscosity