Reynolds Number Calculator
Enter density, velocity, diameter and viscosity to compute Reynolds number Re=ρvD/μ and the flow regime. Water ρ=1000, v=1, D=0.05, μ=0.001 → Re=50000 (turbulent).
Input Data
Results
At a glance:The Reynolds number (Re) is the most important dimensionless number deciding whether pipe (internal) flow is laminar or turbulent: Re=ρvD/μ, with Re the Reynolds number (dimensionless), ρ fluid density (kg/m³), v the average velocity (m/s), D the pipe diameter (m) and μ the dynamic viscosity (Pa·s). It compares inertial forces (ρv²) to viscous forces (μv/D); when inertial force dominates, disturbances grow and the flow becomes turbulent, when viscous force dominates, the flow stays smooth and laminar. Regime: Re<2300 laminar (smooth layered flow, low resistance); 2300–4000 transition (unstable); Re>4000 turbulent (eddies, high mixing and resistance). The critical velocity is v_c=Re_crit·μ/(ρD)=2300μ/(ρD). Example: water ρ=1000, v=1 m/s, D=0.05 m, μ=0.001 → Re=1000×1×0.05/0.001=50000, turbulent. Example: blood in capillary D=0.000008 m, v=0.001, μ=0.0035 → Re=0.0023, laminar. History: Reynolds did pipe experiments in 1883, injecting dye to observe laminar/turbulent transition, giving the law his name. A related external-flow form uses length L: Re=ρvL/μ. Uses: (1) pipe design (pick diameter/flow to avoid turbulent energy loss); (2) drag and lift analysis; (3) heat-exchanger flow state; (4) blood-vessel flow; (5) aircraft wing boundary layer. Notes: (1) the regime thresholds are for circular pipe internal flow; external flow and non-circular sections differ; (2) Re is dimensionless — keep consistent units; (3) turbulent needs more pumping power; (4) at very low Re (creeping flow) inertia is negligible (Stokes law).
Formula
Reynolds: Re = ρ·v·D / μ
Regime: Re<2300 laminar; 2300–4000 transition; >4000 turbulent
Critical velocity: v_c = 2300·μ / (ρ·D)
Compare with Re_crit=2300
$$\mathrm{Re} = \frac{\rho\,v\,D}{\mu}$$How to Use
- Enter density ρ (water 1000).
- Enter velocity v, diameter D and dynamic viscosity μ (water 0.001).
- The tool gives Re, critical velocity v_c and Re/Re_crit to classify laminar/turbulent.
Case Studies
Water pipe and blood capillary
Water pipe: ρ=1000, v=1, D=0.05, μ=0.001 → Re=50000, turbulent (need more pumping).
Blood capillary: D=8e-6, v=0.001, μ=0.0035 → Re=0.0023, laminar (smooth).
Cooling water in a factory: raise D or lower v to drop Re below 4000 and cut energy loss.
Content review: Calculatorism Science Team. Results are for reference only; please refer to the relevant authorities for the official figures.