Reynolds Number Calculator
Calculate the Reynolds number for pipe flow and determine whether the flow is laminar, transitional, or turbulent. Essential for pressure drop calculations, heat transfer analysis, and process design.
🌊 Reynolds Number Calculator for Pipe Flow
The Reynolds number (Re) is a dimensionless quantity that predicts flow patterns in fluid dynamics. It represents the ratio of inertial forces to viscous forces and is used to characterize flow as laminar, transitional, or turbulent.
where:
Re = Reynolds number (dimensionless)
ρ = fluid density (kg/m³ or slug/ft³)
u = average flow velocity (m/s or ft/s)
D = pipe internal diameter (m or ft)
μ = dynamic viscosity (Pa·s or lb/(ft·s))
ν = kinematic viscosity (m²/s or ft²/s) = μ/ρ
Re < 2100
2100 < Re < 4000
Re > 4000
Input Method
📊 Result
Reynolds Number:
—
dimensionless
Understanding the Reynolds Number
Named after Osborne Reynolds (1883), the Reynolds number is the most important dimensionless parameter in fluid mechanics. It determines:
- Flow regime — laminar, transitional, or turbulent
- Friction factor — used in pressure drop calculations
- Heat and mass transfer coefficients — through Nusselt, Sherwood correlations
- Mixing effectiveness — turbulent flow enhances mixing
Critical Reynolds Numbers for Pipe Flow
| Regime | Re Range | Velocity Profile | Friction Factor |
|---|---|---|---|
| Laminar | Re < 2100 | Parabolic | f = 64/Re |
| Transitional | 2100 < Re < 4000 | Unstable, intermittent | Unpredictable |
| Turbulent | Re > 4000 | Flattened (1/7 power law) | Colebrook equation |
Typical Viscosity Values
| Fluid | Temperature | μ (Pa·s) | ν (m²/s) |
|---|---|---|---|
| Water | 20°C | 1.0 × 10⁻³ | 1.0 × 10⁻⁶ |
| Water | 80°C | 3.5 × 10⁻⁴ | 3.6 × 10⁻⁷ |
| Air | 20°C | 1.8 × 10⁻⁵ | 1.5 × 10⁻⁵ |
| Engine Oil (SAE 30) | 20°C | 0.29 | 3.2 × 10⁻⁴ |
| Glycerin | 20°C | 1.5 | 1.2 × 10⁻³ |
| Honey | 20°C | 2–10 | ~10⁻³ |
Frequently Asked Questions
Re represents the ratio of inertial forces (ρu²) to viscous forces (μu/D). Low Re means viscous forces dominate and the flow is smooth (laminar). High Re means inertial forces dominate and the flow becomes chaotic (turbulent).
These are empirical values from Osborne Reynolds' classic dye experiment (1883). Below Re ≈ 2100, dye travels in a straight line (laminar). Above Re ≈ 4000, dye disperses rapidly (turbulent). Between them, the flow is unpredictable.
Yes — use the hydraulic diameter Dₕ = 4A/P, where A is the cross-sectional area and P is the wetted perimeter. For rectangular ducts: Dₕ = 2ab/(a+b). Critical Re values are approximately the same.
In laminar flow, pressure drop is proportional to velocity (ΔP ∝ u). In turbulent flow, pressure drop is approximately proportional to velocity squared (ΔP ∝ u²). This is why turbulent flow requires significantly more pumping power.
The entrance length is the distance from the pipe inlet where the flow becomes fully developed. For laminar flow: Lₑ ≈ 0.06·Re·D. For turbulent flow: Lₑ ≈ 4.4·D¹ᐟ⁶·D (much shorter, typically 10–60 diameters).