Reynolds Number: Laminar to Turbulent

Osborne Reynolds' 1883 experiment: a thread of dye is released into a fluid flowing along a glass pipe. At low Reynolds number the thread stays a straight filament (laminar flow); above about 2,300 it begins to waver, and above 4,000 it breaks into eddies that mix across the whole pipe (turbulent flow). The dimensionless ratio Re = ρ v D / μ, inertial forces over viscous forces, decides which. Change the fluid, the mean velocity and the pipe diameter and watch the dye, the velocity profile and the friction factor respond.

Reynolds number  Re = ρ v D / μ
24,905
inertial forces ÷ viscous forces, dimensionless
Flow regime
Turbulent
Darcy friction factor  f
0.02515
Blasius, smooth pipe
Kinematic viscosity 1.004e-6 m²/s
Entrance length 0.594 m
Pressure drop per metre 502.2 Pa/m
Velocity profile 1.22 centreline ÷ mean velocity
Fluid
water · ρ 998.2 kg/m³ · μ 1.002 mPa·s
Mean velocity v1.00 m/s
Pipe diameter D25.0 mm
Re above 4,000: eddies mix the whole cross-section
ν = μ / ρ, 1 cSt = 1e-6 m²/s · Δp / L = f ρ v² / (2 D), Darcy–Weisbach, smooth pipe · Le = 0.06 Re D laminar, 4.4 Re1/6 D turbulent
Fluids at 20 °C (oil at 40 °C): water ρ 998.2 kg/m³, μ 1.002 mPa·s · air 1.204 kg/m³, 0.01825 mPa·s · glycerine 1261 kg/m³, 1412 mPa·s · SAE 30 oil 876 kg/m³, 83.2 mPa·s · laminar below Re 2,300, turbulent above 4,000
Tip: at 1.0 m/s water in a 25 mm pipe is well into turbulence (Re 24,905). Slow it to 0.05 m/s and the same pipe is laminar (Re 1,245); switch to glycerine and almost nothing you do will make it turbulent.