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The Reynolds number (Re) is a dimensionless ratio of inertial to viscous forces in a fluid, predicting whether flow is laminar (smooth) or turbulent (chaotic).
Re = ρvD/µ = vD/ν. Laminar: Re < 2,300. Transitional: 2,300–4,000. Turbulent: > 4,000. Turbulent flow has 4–10× higher heat transfer and pressure drop than laminar.
The Reynolds number — determining whether flow is laminar or turbulent — was derived by Osborne Reynolds in 1883 using dye injected into glass pipes. His original experimental apparatus is still on display at the University of Manchester.
Using the same friction factor for all flow regimes. The Darcy friction factor in the Moody chart varies from f=64/Re (laminar) to f≈0.02 (fully turbulent, rough pipe). Using f=0.02 in laminar flow overestimates pressure drop by a factor of 10+ at Re=1,000.