Fluid flow in pipes or equipment can be broadly classified into two regimes—laminar and turbulent—whose structures, energy consumption, and transport performances differ markedly.

1. Laminar (viscous) flow

   Occurs at low Reynolds numbers (Re < 2000). The fluid moves in smooth, parallel layers with no macroscopic mixing between them; transfer of momentum, heat, and mass in the radial direction proceeds solely by molecular diffusion. Viscous forces dominate, energy losses are small, but transport rates are slow.

2. Turbulent flow

   Develops when Re > 4000. Inertia dominates, the motion becomes unstable, and random, three-dimensional eddies appear. These fluctuations greatly enhance radial transport, yielding high heat- and mass-transfer coefficients; however, they also generate additional mechanical energy dissipation, manifested as larger pressure drops and noise.

3. Transitional regime

   For 2000 ≤ Re < 4000, the flow is highly sensitive to entrance conditions, wall roughness, and external disturbances. It may remain temporarily laminar or switch abruptly to turbulence; engineering practice therefore treats this region as turbulent to ensure safety.

4. Physical meaning of the Reynolds number

   Re = ρud/μ expresses the ratio of inertial to viscous forces:

   • ρu²/d represents the inertial term that drives the fluid forward and creates vortices;
   • μu/d² represents the viscous term that damps velocity gradients and stabilizes the flow.

   Consequently, higher Re implies a greater tendency for instabilities and turbulence.

5. Engineering implications
   • Pipes, heat exchangers, and other equipment are first sized by estimating Re to select the appropriate flow regime.
   • Turbulent flow allows more compact designs but demands higher pump or fan power.
   • Processes sensitive to laminar conditions (e.g., high-polymer melts, precision filtration) must keep Re below the critical value to avoid shear degradation or excessive pressure rise caused by turbulence.