How to use this calculator
Enter the average velocity and the pipe’s inside diameter, then pick a fluid or type its density and viscosity. For non-circular ducts, use the hydraulic diameter Dh = 4A/P.
Formulas
Reynolds numberRe = ρVDμ = VDν
Pipe flow regimesRe < 2,300 laminar · 2,300–4,000 transitional · > 4,000 turbulent
Entrance lengthLe ≈ 0.05 Re D (laminar) 4.4 Re1/6 D (turbulent)
Worked example
Water at 20 °C, 1.5 m/s in a 50 mm pipe (the default)
- ν = 1.002 × 10⁻³ / 998.2 = 1.004 × 10⁻⁶ m²/s.
- Re = 1.5 × 0.05 / 1.004 × 10⁻⁶ = 74,700: turbulent.
- Le ≈ 4.4 × 74,7001/6 × 0.05 = 1.43 m.
Frequently asked questions
What does the Reynolds number mean physically?
It is the ratio of inertial forces to viscous forces. Low Re means viscosity smooths out disturbances (laminar); high Re means they grow into turbulence.
Which viscosity do I use?
Dynamic viscosity μ (Pa·s or cP) with density, or kinematic viscosity ν = μ/ρ alone. Both give the same Re.
Is 2,300 an exact limit?
No. It is a typical value for ordinary pipes. Very smooth, quiet setups can stay laminar to much higher Re, which is why 2,300–4,000 is called transitional.