Flow Regimes
Laminar Flow (Re < 2300)Turbulent Flow (Re > 4000)Transition: 2300 < Re < 4000

Reynolds Number

The Reynolds number (Re) is a dimensionless quantity that predicts flow patterns in different fluid flow situations. It represents the ratio of inertial forces to viscous forces and determines whether flow is laminar, transitional, or turbulent.

Formula
Re = ρVD/μ = VD/ν
Units
Dimensionless

Flow Regime Classification

Fluid Dynamics
Flow RegimeReynolds NumberCharacteristicsExamples
LaminarRe < 2300Smooth, orderly, predictableHoney flow, capillary tubes
Transitional2300 < Re < 4000Unstable, intermittentWater in medium pipes
TurbulentRe > 4000Chaotic, mixing, efficientRiver flow, high-speed pipes
Laminar Characteristics
Laminar FlowSmooth & Orderlyv(r) = v_max(1 - r²/R²)

Laminar Flow

Laminar flow is characterized by smooth, parallel fluid layers with no disruption between them. Viscous forces dominate, and flow is highly predictable. Common in low velocities, small diameters, or high-viscosity fluids.

Formula
Re = ρVD/μ < 2300
Units
Dimensionless

Laminar Flow Applications

Re < 2300
ApplicationRe RangeRegimeSignificance
Blood FlowRe ~ 1000-2000LaminarReduces energy loss
Capillary TubesRe ~ 100-500LaminarPredictable behavior
Oil PipelinesRe ~ 500-1500LaminarHigh viscosity flow
Turbulent Characteristics
Turbulent Flowv(r) ≈ v_max(1 - r/R)^(1/n)

Turbulent Flow

Turbulent flow is characterized by chaotic, irregular fluid motion with mixing and eddy formation. Inertial forces dominate, and flow is highly efficient for heat and mass transfer. Common in high velocities, large diameters, or low-viscosity fluids.

Formula
Re = ρVD/μ > 4000
Units
Dimensionless

Turbulent Flow Applications

Re > 4000
ApplicationRe RangeRegimeSignificance
Water SupplyRe ~ 10,000-100,000TurbulentHigh flow rate
Aircraft WingsRe ~ 10⁶ - 10⁷TurbulentBoundary layer control
Heat ExchangersRe ~ 5,000-50,000TurbulentEnhanced heat transfer