Reynolds Number Calculator – Pipe Flow Reynolds Number
Calculate the Reynolds number for pipe flow to determine if flow is laminar, transitional, or turbulent.
Enter flow velocity
Input the fluid velocity in meters per second flowing through the pipe.
Enter pipe diameter
Input the internal diameter of the pipe in meters.
Enter fluid properties and calculate
Input density (kg/m³) and dynamic viscosity (Pa·s). Click Calculate to get Reynolds number and flow regime.
| Fluid | Density (kg/m³) | Viscosity (Pa·s) | Temperature |
|---|---|---|---|
| Water | 998 | 0.001 | 20°C |
| Water | 958 | 0.00028 | 100°C |
| Air | 1.2 | 0.000018 | 20°C |
| Engine Oil (SAE 30) | 891 | 0.29 | 20°C |
| Glycerin | 1260 | 1.5 | 20°C |
| Mercury | 13546 | 0.00155 | 20°C |
What Is Reynolds Number?
Reynolds number (Re) is a dimensionless quantity that predicts flow patterns in fluids. It represents the ratio of inertial forces to viscous forces. Low Re means viscous forces dominate (smooth, laminar flow). High Re means inertial forces dominate (chaotic, turbulent flow).
The Reynolds Number Formula
Re = ρvD / μ, where ρ is fluid density, v is velocity, D is pipe diameter, and μ is dynamic viscosity. Alternatively, Re = vD / ν, where ν is kinematic viscosity (ν = μ/ρ). Higher velocity, larger pipes, and lower viscosity all increase Re.
Flow Regime Classifications
Laminar flow (Re < 2000) is smooth and orderly with parallel streamlines. Transitional flow (2000-4000) is unstable and may switch between laminar and turbulent. Turbulent flow (Re > 4000) is chaotic with eddies and mixing. These thresholds apply to pipe flow; other geometries have different critical values.
Laminar Flow (Re < 2000)
Smooth, predictable flow with parabolic velocity profile. Low energy loss. Dye injected stays in a straight line. Common in small pipes, viscous fluids, or slow flow.
Transitional Flow (2000-4000)
Unstable flow that may fluctuate between laminar and turbulent. Unpredictable behavior. Avoid designing systems to operate in this range.
Turbulent Flow (Re > 4000)
Chaotic flow with eddies and mixing. Flat velocity profile. Higher energy loss but better mixing. Most common in industrial piping systems.
Why is Reynolds number important?
Reynolds number determines flow regime, which affects pressure drop, heat transfer, and mixing. Laminar and turbulent flows require different calculation methods. Engineers use Re to select appropriate formulas and predict system behavior.
What is the critical Reynolds number?
For pipe flow, the critical Reynolds number is approximately 2300. Below this, flow is typically laminar. Above 4000, flow is typically turbulent. The exact transition point depends on pipe roughness and inlet conditions.
How does temperature affect Reynolds number?
Temperature changes fluid viscosity. For liquids, higher temperature means lower viscosity, which increases Re. For gases, higher temperature increases viscosity, which decreases Re. Density also changes with temperature.
Can Reynolds number be used for non-circular pipes?
Yes, use hydraulic diameter instead of actual diameter. Hydraulic diameter = 4 × cross-sectional area / wetted perimeter. For a square duct, hydraulic diameter equals the side length.
What's the difference between dynamic and kinematic viscosity?
Dynamic viscosity (μ) measures internal resistance to flow. Kinematic viscosity (ν) equals dynamic viscosity divided by density (ν = μ/ρ). Reynolds number can use either: Re = ρvD/μ or Re = vD/ν.
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