The transition from laminar to turbulent flow depends on the geometry, surface
roughness, flow velocity, surface temperature, and type of fluid, among
other things. After exhaustive experiments in the 1880s, Osborne Reynolds
discovered that the flow regime depends mainly on the ratio of inertial
forces to viscous forces in the fluid. This ratio is called the Reynolds number
and is expressed for internal flow in a circular pipe as (Fig. 8–5)