Reynolds number
Dimensionless. For internal pipe flow: laminar below 2,300, transitional to 4,000, then turbulent as an indicative guide.
Fluid mechanics · Flow rate and pipe flow
Reynolds number: laminar or turbulent flow
Calculate Re = ρvDₕ/μ or Re = vDₕ/ν. For a duct, Dₕ is hydraulic diameter; the dimensionless result compares inertial and viscous effects.
Created v1.0
By Thibaut Grzelak, Mechanical Analysis Engineer
02
Results
Relation and numerical substitution
Re = ρ · v · Dₕ / μ = v · Dₕ / ν—
Properties evaluated for the same fluid at the same temperature. Newtonian fluid for direct use of μ or ν. For a full circular pipe, Dₕ is the inside diameter. Thresholds 2,300 and 4,000 are indicative for internal flow; inlet conditions, roughness and disturbances can shift transition.
01Formulas and symbols
Formulas used
Re
ρ·v·Dₕ/μUsing dynamic viscosityRe
v·Dₕ/νUsing kinematic viscosityν
μ/ρRelationship between both viscositiesDₕ
4A/PmGeneral hydraulic diameter02Assumptions and limits
Scope of validity
- Properties evaluated for the same fluid at the same temperature.
- Newtonian fluid for direct use of μ or ν.
- For a full circular pipe, Dₕ is the inside diameter.
- Thresholds 2,300 and 4,000 are indicative for internal flow; inlet conditions, roughness and disturbances can shift transition.
03Validation example
Reference numerical case
- v = 1.5 m/s, Dₕ = 50 mm, ρ = 1,000 kg/m³ and μ = 1 mPa·s.
- Re = 1,000 × 1.5 × 0.05 / 0.001 = 75,000.
- With ν = 1 mm²/s, Re = 1.5 × 0.05 / 10⁻⁶ = 75,000: both modes agree.
04References
Technical references
- NASA Glenn Research Center, Reynolds Number: Re = ρVL/μ and Re = VL/ν.
- NASA Glenn Research Center, Viscosity: ν = μ/ρ.
- Engineering ToolBox, Reynolds Number for Flow in Pipe or Duct: hydraulic diameter and indicative 2,300/4,000 thresholds.