Free Engineering Tool
Reynolds Number Calculator
Calculate Reynolds number from velocity or flow rate. Visual laminar/transition/turbulent indicator. Entry length calculation and common fluid presets.
Results
Reynolds Number
The Reynolds number is the ratio of inertial forces to viscous forces in a flowing fluid:
- v — flow velocity (m/s)
- D — pipe inner diameter (m)
- ν — kinematic viscosity (m²/s); 1 cSt = 10⁻⁶ m²/s
- ρ — fluid density (kg/m³)
- μ — dynamic viscosity (Pa·s)
Flow Regime Thresholds
| Reynolds Range | Regime | Characteristics |
|---|---|---|
| Re < 2,300 | Laminar | Smooth, orderly layers; friction factor f = 64/Re; predictable |
| 2,300 – 4,000 | Transition | Unstable; intermittent turbulence; avoid designing here |
| Re > 4,000 | Turbulent | Chaotic; higher friction; use Colebrook-White for f |
Hydrodynamic Entry Length
The distance from the pipe inlet until the velocity profile becomes fully developed:
Common Fluid Viscosities
| Fluid | Temperature | ν (cSt) | ρ (kg/m³) |
|---|---|---|---|
| Water | 20°C | 1.004 | 998 |
| Water | 40°C | 0.658 | 992 |
| Water | 80°C | 0.365 | 972 |
| Hydraulic Oil ISO VG 32 | 40°C | 32 | 870 |
| Hydraulic Oil ISO VG 46 | 40°C | 46 | 870 |
| Hydraulic Oil ISO VG 68 | 40°C | 68 | 880 |
| Air | 20°C, 1 atm | 15.6 | 1.204 |
| Engine Oil SAE 30 | 40°C | 100 | 880 |
Practical Example
Given: v = 2 m/s, D = 25 mm, Oil ISO VG 32 at 40°C (ν = 32 cSt)
Re = 2 × 0.025 / (32 × 10⁻⁶) = 1,563
Regime: Laminar (Re < 2300)
Entry length: Le = 0.06 × 1563 × 0.025 = 2.34 m
Critical velocity for Re = 2300: v_crit = 2300 × 32 × 10⁻⁶ / 0.025 = 2.94 m/s
💡 Tip: In hydraulic systems with oil (ν = 30–100 cSt), flow is almost always laminar due to high viscosity. Water systems typically have turbulent flow because ν ≈ 1 cSt.
The Reynolds number Re = vD/ν is a dimensionless number that compares inertial forces to viscous forces in a flowing fluid. It predicts whether flow will be laminar (smooth) or turbulent (chaotic).
Named after Osborne Reynolds who demonstrated the transition in his famous 1883 experiment using dye in a glass tube.
For pipe flow, the critical thresholds are:
- Re < 2,300: Laminar — fluid moves in smooth parallel layers
- 2,300 – 4,000: Transition — flow is unstable, may switch between laminar and turbulent
- Re > 4,000: Turbulent — chaotic mixing, eddies, higher energy loss
These thresholds are for circular pipes. For open channels and other geometries, different critical values apply.
Kinematic viscosity ν = μ/ρ, where μ is dynamic viscosity and ρ is density.
Units: m²/s or cSt (centistokes). 1 cSt = 10⁻⁶ m²/s.
Common values: water at 20°C ≈ 1 cSt; hydraulic oil VG 32 at 40°C ≈ 32 cSt; air at 20°C ≈ 15.6 cSt (much higher than water due to low density despite low dynamic viscosity).
When fluid enters a pipe, the velocity profile is initially flat (uniform). As viscous effects propagate from the wall, the profile gradually develops into the fully-developed shape (parabolic for laminar).
The entry length is the distance needed:
- Laminar: Le ≈ 0.06 × Re × D (can be very long at high Re)
- Turbulent: Le ≈ 4.4 × Re1/6 × D (relatively short, 10–60 diameters)
Temperature strongly affects viscosity, especially for oils. Hydraulic oil viscosity drops approximately 50% for every 20°C increase.
Example: ISO VG 46 oil is ~46 cSt at 40°C but ~200 cSt at 0°C and ~15 cSt at 80°C. This dramatically changes the Reynolds number — cold-start conditions may have very different flow regimes than operating temperature.
Water viscosity changes less dramatically: ~1.8 cSt at 0°C, ~1 cSt at 20°C, ~0.3 cSt at 80°C.
The procedures described on this page were developed and field-tested by the Vibromera team using the Balanset-1A, a portable dual-channel balancer and vibration analyzer for on-site rotor balancing.
Professional field balancing instruments and software. Used in 50+ countries.
Nikolai Shelkovenko
Nikolai Shelkovenko is a vibration analysis engineer and the founder and CEO of Vibromera. For more than 15 years he has balanced rotating equipment in the field rather than on a test bench: mulchers, industrial fans, crushers, centrifuges, shafts and spindles. That work is what the Balanset instruments grew out of — they were designed as a tool a specialist can carry to the machine and use alone, on site, not as laboratory equipment. Vibromera was founded in 2017 and has been based in Porto, Portugal, since 2023. Development, assembly and support of the Balanset line all happen here. The flagship instrument is the Balanset-1A, a portable analyser for single- and two-plane balancing and for vibration diagnostics. Nikolai is personally involved in customer support, in working through difficult balancing cases and in the development of the software. He works with customers worldwide, in any language.
