🌊 Reynolds Number Calculator
Calculate the Reynolds number to determine whether fluid flow is laminar or turbulent.
🌊 Reynolds Number Calculator
Calculate the Reynolds number to determine whether fluid flow is laminar or turbulent.
✅ Calculation Result
Reynolds Number Scale (log)
Flow Pattern
Calculator Description
The Reynolds number (Re) is a dimensionless ratio of inertial to viscous forces in a fluid. From this single value we decide whether pipe flow is laminar, turbulent, or in between (transitional), and it is the starting point for friction-factor, heat-transfer and pressure-drop analysis.
What this calculator finds
It takes density (or specific gravity), velocity, pipe inner diameter and dynamic viscosity (or kinematic viscosity), computes Re, and reports the corresponding flow regime (laminar/transitional/turbulent).
Why it matters
- Selecting pipe friction factor and computing pressure drop (Darcy–Weisbach)
- Choosing convection correlations in heat-exchanger design
- Checking suitable velocity ranges for pumps, valves and meters
Formula
Reynolds Number Formula
For internal pipe flow it is the inertia force (ρVD) divided by the viscous force (μ). Using kinematic viscosity ν = μ/ρ it can also be written Re = VD/ν.
- Re — Reynolds number (dimensionless)
- ρ — Fluid density [kg/m³ or lb/ft³]
- V — Flow velocity (mean) [m/s or ft/s]
- D — Pipe inner diameter [m or ft]
- μ — Dynamic viscosity [Pa·s or lb/(ft·s)]
How the formula works
- Higher velocity V, larger diameter D or higher density raise Re, favouring turbulence.
- Higher viscosity μ (oils, cold liquids) lowers Re and keeps flow laminar.
- As a ratio of inertia to viscosity, small Re means viscosity dominates, large Re means inertia dominates.
Flow regimes
- Laminar Flow: Re < 2300 — smooth layered flow
- Transient Flow: 2300 ≤ Re ≤ 4000 — unstable region between laminar and turbulent
- Turbulent Flow: Re > 4000 — flow dominated by turbulent eddies
Worked example
For 20 °C water (ρ ≈ 998 kg/m³, μ ≈ 1.002×10⁻³ Pa·s) in a D = 0.05 m pipe at V = 1 m/s: Re = (998 × 1 × 0.05) / (1.002×10⁻³) ≈ 49,800 — turbulent. At V = 0.02 m/s the same setup gives Re ≈ 996 — laminar.
Useful Tips
Practical tips
- To cut pressure drop, lowering velocity in the turbulent region is effective (friction factor is high).
- Viscosity is very temperature-sensitive — use the operating-temperature properties, especially for oils.
- For non-circular ducts use the equivalent hydraulic diameter (d_e = 4A/P) in place of D.
Limitations & cautions
- The 2300/4000 thresholds are for smooth straight pipes; roughness, inlet and bends shift them.
- In the transitional range flow is unstable and correlations are inaccurate.
- This form is for internal pipe flow; external flow uses a different characteristic length.