Reynolds Number Calculator

At a glance:The Reynolds number (symbol Re) is the most important dimensionless number in fluid mechanics, used to judge whether a flow is laminar (smooth, layered) or turbulent (chaotic, with eddies). It is the ratio of inertial to viscous forces: Re=ρ·v·L/μ, where Re is dimensionless, ρ is density (kg/m³), v is a characteristic velocity (m/s), L is a characteristic length (m; pipe diameter for internal flow, object size for external flow) and μ is dynamic viscosity (Pa·s). It can also be written Re=v·L/ν with kinematic viscosity ν=μ/ρ (m²/s). The numerator ρvL reflects inertial force — larger density, speed or scale make the fluid tend to keep moving and form disturbances; the denominator μ reflects viscous force — larger viscosity damps disturbances and keeps order. If Re is small, viscosity dominates and the flow is smooth (laminar); if Re is large, inertia dominates and the flow becomes turbulent. For circular pipe flow the empirical criteria are: Re<2300 laminar, 2300<Re<4000 transitional, Re>4000 turbulent. Example: water ρ=1000, v=1 m/s, diameter L=0.1 m, μ=0.001 → Re=1000×1×0.1/0.001=100,000, far above 4000, turbulent. At v=0.02 m/s, Re=2000<2300, laminar. Uses: (1) classify laminar/turbulent in pipes, open channels and external flow (which drag formula to use); (2) similarity criterion — model and prototype have the same Re, so the flow is similar (basis of wind-tunnel and hydraulic-model tests); (3) compute friction factor (laminar f=64/Re; turbulent via Colebrook or Swamee–Jain, both contain Re); (4) heat/mass-transfer correlations (Nu, Sh use Re). Notes: (1) the choice of L depends on the problem — pipe uses diameter (or hydraulic diameter), external flow uses the body's frontal size; (2) keep SI units; (3) the 2300/4000 thresholds are empirical for circular pipes, other geometries differ; (4) turbulence also depends on inlet disturbance and roughness.