Engineering
Reynolds Number (Re) formula: Laminar vs Turbulent pipe flow regime
Calculate dimensionless Reynolds Number Re = (ρ · v · D) / μ in SI units and classify Laminar (< 2,300), Transitional, and Turbulent (> 4,000) flow.
Inertial forces over viscous forces: keep ρ, v, D, and μ in consistent SI units!
Pipe friction factor (Darcy-Weisbach), heat-exchanger Nusselt numbers, and flow-meter accuracy all depend on the dimensionless Reynolds Number: Re = (Density_kg_m3 × Velocity_m_s × PipeID_m) / DynamicViscosity_Pa_s! Because Re is dimensionless, mixing mm with meters or centipoise (cP) with Pa·s (1 cP = 0.001 Pa·s!) introduces a 1,000× error!
For 20 °C water (ρ = 998 kg/m³, μ = 0.001 Pa·s = 1.0 cP) flowing at v = 1.50 m/s inside a D = 0.05 m (50 mm) pipe: Re = (998 × 1.50 × 0.05) / 0.001 = 74,850 -> fully Turbulent! Standard circular-pipe regime thresholds: Re < 2,300 = Laminar; 2,300 <= Re <= 4,000 = Transitional; Re > 4,000 = Turbulent.
The thresholds are a conventional guide for internal flow in a circular pipe with a Newtonian fluid, not universal boundaries for all geometries or fluids. Use mean speed, internal diameter and dynamic viscosity at the operating conditions. Entry conditions and disturbances affect transition; the example fluid properties are rounded illustrative inputs.
| Fluid Scenario (50 mm Pipe) | Inputs (ρ, v, D, μ) | Reynolds Number Re | Flow Regime |
|---|---|---|---|
| Water @ 1.50 m/s | 998 kg/m³, 1.5 m/s, 0.05 m, 0.001 Pa·s | 74,850 | Turbulent (Re > 4,000) |
| Heavy Oil @ 0.50 m/s | 900 kg/m³, 0.5 m/s, 0.05 m, 0.050 Pa·s | 450 | Laminar (Re < 2,300) |
| Glycol Mix @ 0.30 m/s | 1,050 kg/m³, 0.3 m/s, 0.05 m, 0.005 Pa·s | 3,150 | Transitional (2,300–4,000) |
Dimensionless Reynolds Number and flow-regime classifier formulas
If viscosity is quoted in centipoise (cP), divide cP by 1,000 first since 1 cP = 0.001 Pa·s.
=IF(OR(COUNT(A2:D2)<>4,A2<=0,B2<0,C2<=0,D2<=0),"Invalid inputs",ROUND(A2*B2*C2/D2,1))Classify Laminar (< 2,300), Transitional (2,300–4,000), or Turbulent (> 4,000)
Uses IFS to route Re into the three standard hydraulic pipe-flow regimes.
=IF(OR(COUNT(A2:D2)<>4,A2<=0,B2<0,C2<=0,D2<=0),"Invalid inputs",LET(re,A2*B2*C2/D2,IFS(re<2300,"Laminar",re<=4000,"Transitional",TRUE,"Turbulent")))Try the example
Use the original values or change them to test your understanding.