Why is Reynolds number important?
The Reynolds number is a dimensionless ratio that compares inertial effects with viscous effects in a flow.
It is commonly used for a first-pass interpretation of whether internal pipe flow is approximately laminar, transitional or turbulent.
Formulas used
- Re = ρ × v × D / μ
- v = Re × μ / (ρ × D)
- D = Re × μ / (ρ × v)
Variables and SI units
- Re
- Dimensionless Reynolds number. No SI unit.
- ρ
- Fluid density. SI unit: kg/m³.
- v
- Average flow velocity. SI unit: m/s.
- D
- Characteristic pipe or channel diameter. SI unit: m.
- μ
- Dynamic viscosity. SI unit: Pa·s.
Flow-regime interpretation
- Re < 2300 is commonly treated as approximately laminar.
- Re between 2300 and 4000 is commonly treated as transitional.
- Re > 4000 is commonly treated as approximately turbulent.
- These limits are only approximate guides for internal pipe flow; geometry and inlet conditions can shift the effective regime boundaries.
- Water and air presets provide approximate room-condition properties; real operating data can change the outcome.
Technical reference
Reynolds-number flow-regime diagram
This diagram shows approximate Reynolds-regime boundaries used specifically for internal pipe flow.
Definition
The Reynolds number is a dimensionless quantity that compares inertial effects with viscous effects.
The thresholds shown here should be treated as instructional, approximate limits specifically for smooth internal flow in circular pipes.
Formula
- Re = ρ v D / μ
Variables
- Re
- Dimensionless Reynolds number
- ρ
- Density, kg/m³
- v
- Velocity, m/s
- D
- Characteristic diameter, m
- μ
- Dynamic viscosity, Pa·s
Short engineering example
For ρ = 998 kg/m³, v = 1.5 m/s, D = 0.025 m and μ = 0.001001 Pa·s, Re ≈ 37,400; on the diagram this falls in the turbulent region.
Validity conditions and assumptions
- The diagram should only be used in the context of internal pipe flow.
- Entrance effects, roughness, cross-section shape and flow disturbances can shift the effective boundaries.
- The same thresholds should not be applied directly to open-channel flow, external flow or special geometries.
| Regime | Re range | Interpretation |
|---|---|---|
| Laminar | Re < 2300 | Viscous effects dominate and mixing is limited. |
| Transition | 2300 ≤ Re ≤ 4000 | The regime is sensitive to inlet conditions and geometry. |
| Turbulent | Re > 4000 | Inertial effects dominate, with stronger mixing and friction. |
Use cases
- Turning a calculated Reynolds number into a quick regime interpretation.
- Presenting a flow-regime diagram in student reports.
- Supporting an initial internal-flow correlation choice.
Common mistake
- Treating these thresholds as universal for every flow problem.
Related calculator
Sources
- OpenStax University Physics Volume 1, 14.7 Viscosity and Turbulence
- NASA LLIS lesson on tubing and Reynolds transition
Water dynamic-viscosity reference
Technical reference
Dynamic viscosity of liquid water as a function of temperature
This technical sheet summarizes liquid-water viscosity data commonly used in Reynolds-number and internal-flow analysis.
Definition
Dynamic viscosity is a measure of resistance to shear deformation and directly affects internal-flow regime and friction loss.
Formula
- Re = ρ v D / μ
Variables
- μ
- Dynamic viscosity, Pa·s or mPa·s
- ρ
- Density, kg/m³
- v
- Velocity, m/s
- D
- Characteristic diameter, m
Short engineering example
Using μ ≈ 1.0014 mPa·s for water near 20 °C, a velocity of 1.5 m/s in a 25 mm pipe gives a Reynolds number of about 37,400, which falls in the turbulent range.
Validity conditions and assumptions
- The data are taken at a constant pressure of 0.101325 MPa on the liquid-water branch.
- The temperature range is approximately 0.01 °C to 99.97 °C.
- The chart uses mPa·s on the main axis, and the table lists both mPa·s and Pa·s.
| Temperature (°C) | Dynamic viscosity (mPa·s) | Dynamic viscosity (Pa·s) |
|---|---|---|
| 0.01 | 1.7911 | 0.001791132 |
| 10.01 | 1.3055 | 0.001305524 |
| 20.01 | 1.0014 | 0.001001351 |
| 30.01 | 0.7971 | 0.000797052 |
| 40.01 | 0.6526 | 0.000652606 |
| 50.01 | 0.5464 | 0.000546425 |
| 60.01 | 0.466 | 0.000465965 |
| 70.01 | 0.4035 | 0.000403493 |
| 80.01 | 0.354 | 0.000354006 |
| 90.01 | 0.3141 | 0.000314139 |
| 99.97 | 0.2817 | 0.000281658 |
Use cases
- Selecting realistic water viscosity for Reynolds-number calculations.
- Internal-flow pressure-drop and laminar-flow assessments.
- Temperature-dependent fluid-property analysis in lab work.
Common mistake
- Mixing dynamic viscosity with kinematic viscosity or converting cP and Pa·s incorrectly.
Related calculator
Sources
- NIST Chemistry WebBook - Thermophysical Properties of Fluid Systems (water query)
- IAPWS Formulation 2008 for the Viscosity of Ordinary Water Substance
Unit reference tables
Density units
| Unit name | Symbol | SI equivalent | Typical use |
|---|---|---|---|
| Kilogram per cubic meter | kg/m³ | 1 kg/m³ | Base SI density unit |
| Gram per cubic centimeter | g/cm³ | 1,000 kg/m³ | Practical density notation for liquids |
| Gram per liter | g/L | 1 kg/m³ | Gases and dilute mixtures |
| Pound per cubic foot | lb/ft³ | 16.018463374 kg/m³ | Imperial/US density tables |
| Pound per cubic inch | lb/in³ | 27,679.9047102 kg/m³ | Imperial/US notation for very dense materials |
Velocity units
| Unit name | Symbol | SI equivalent | Typical use |
|---|---|---|---|
| Millimeter per second | mm/s | 0.001 m/s | Very low flow velocities |
| Centimeter per second | cm/s | 0.01 m/s | Low velocities and laboratory setups |
| Meter per second | m/s | 1 m/s | Base SI velocity unit |
| Kilometer per hour | km/h | 0.277777777778 m/s | Practical flow and field velocities |
| Foot per second | ft/s | 0.3048 m/s | Imperial/US flow calculations |
| Mile per hour | mph | 0.44704 m/s | Imperial/US field velocities |
Characteristic-diameter units
| Unit name | Symbol | SI equivalent | Typical use |
|---|---|---|---|
| Micrometer | µm | 0.000001 m | Microchannels and very small characteristic lengths |
| Millimeter | mm | 0.001 m | Small pipe and channel diameters |
| Centimeter | cm | 0.01 m | Medium-scale pipe diameters |
| Meter | m | 1 m | Base SI characteristic-length unit |
| Inch | in | 0.0254 m | Imperial/US pipe sizes |
| Foot | ft | 0.3048 m | Imperial/US large duct sizes |
Dynamic-viscosity units
| Unit name | Symbol | SI equivalent | Typical use |
|---|---|---|---|
| Pascal-second | Pa·s | 1 Pa·s | Base SI dynamic-viscosity unit |
| Millipascal-second | mPa·s | 0.001 Pa·s | Practical engineering use for liquids |
| Poise | P | 0.1 Pa·s | CGS-based fluid-property data |
| Centipoise | cP | 0.001 Pa·s | Laboratory and fluid-property tables |
Worked examples
Re calculation for water
With ρ = 1000 kg/m³, v = 2 m/s, D = 50 mm and μ = 1 mPa·s, the Reynolds number is 100000, which falls in the turbulent range.
Required velocity for a target Re
For Re = 2000, ρ = 1000 kg/m³, D = 20 mm and μ = 1 mPa·s, the velocity is about 0.1 m/s.
Typical applications
- First-pass regime checks for internal pipe flow
- Estimating characteristic velocities in lab setups
- Preliminary channel and pipe diameter selection
- Comparing how fluid properties affect flow regime
Assumptions and limitations
- The calculation uses the base Reynolds-number definition and does not separately model entry effects, roughness or special geometries.
- The flow-regime interpretation uses approximate internal-pipe-flow limits; open channels, airfoils and complex ducts may require different criteria.
- Dynamic viscosity and density can vary strongly with temperature, so realistic property data should be selected whenever possible.