The Reynolds number (Re) = ρvD/μ, where ρ = fluid density, v = velocity, D = characteristic length, μ = dynamic viscosity.
Flow Regimes
- Re < 2,300: Laminar flow (smooth, predictable)
- 2,300 < Re < 4,000: Transitional
- Re > 4,000: Turbulent flow (chaotic, high mixing)
Applications
Pipe design, aerodynamics, blood flow analysis, heat exchanger sizing. Higher Re means more energy loss due to friction.
Why Small Objects "Feel" Thicker Fluid
Reynolds number scales with size, so a bacterium swimming through water experiences an environment dominated by viscosity (very low Re) — more like a human swimming through honey than through water. This is why microscopic organisms evolved completely different swimming strategies (corkscrewing flagella) than fish or humans.
Practical Design Impact
Golf ball dimples deliberately trigger turbulent flow at a lower speed than a smooth ball would, which counterintuitively reduces drag and lets the ball travel farther — a direct, everyday application of Reynolds number effects in aerodynamic design.