The Reynolds number condenses a flow’s character into one dimensionless quantity: Re = ρ·v·D/μ, equivalently v·D/ν with the kinematic viscosity ν = μ/ρ. It weighs inertial forces against viscous ones, and for circular pipes the conventional thresholds put laminar flow below 2300, a transitional band from 2300 to 4000, and fully turbulent flow above 4000 — empirical boundaries, sensitive to disturbances, vibration, and inlet conditions rather than sharp physical walls.
Its practical job is selecting the friction-factor law. In laminar (Hagen-Poiseuille) flow the Darcy factor is exactly f = 64/Re, independent of roughness; once turbulent, f depends on both Re and the relative roughness e/D through the implicit Colebrook-White equation, solved by iteration or approximated explicitly by Swamee-Jain — the relationships the Moody diagram plots. Ordinary conditions are deep in the turbulent zone: water at 2 m/s in a 100 mm steel pipe runs Re = 200,000 with f ≈ 0.0186.
One convention caveat travels with the friction factor: the Darcy value used in hf = f·(L/D)·v²/(2g) is four times the Fanning factor, so a suspiciously small published f is usually the other convention.