Reynolds Number

laminar vs turbulent · dimensionless flow · Osborne Reynolds 1883

20
30
10
Physics: Reynolds number Re = ρUL/μ = UL/ν (ratio of inertial to viscous forces). Laminar flow: Re < 2300 (parallel streamlines, parabolic profile); turbulent: Re > 4000 (chaotic mixing); transition: 2300–4000. Osborne Reynolds (1883) injected dye into pipe flow and photographed the transition. Turbulence adds effective viscosity ν_t ≫ ν; drag coefficient: laminar C_d = 24/Re (Stokes drag), turbulent C_d ≈ 0.44 (Newton). The no-slip condition at walls drives viscous forces.