Every flow is a tug-of-war: inertia wants to tumble, viscosity wants to smooth. One dimensionless ratio — the Reynolds number — predicts the winner. Osborne Reynolds settled it in 1883 with a thread of dye in a glass tube.
Inject a fine thread of dye into water gliding down a glass tube — exactly as Osborne Reynolds did in 1883. Open the valve and watch a single number, Re = ρVD/μ, decide whether the dye holds a razor-straight line or shatters into churning eddies. Change the speed, the pipe, the fluid — and feel where order gives way to chaos.
The dye filament is the real observable — exactly what Reynolds watched. Re below 2300 → one clean thread. Above 4000 → it bursts into eddies and the whole tube clouds with dye. The wavering grows downstream because the instability amplifies as it travels.
One number, three behaviours.
Reynolds discovered that flow doesn't care about speed, size, or stickiness separately — only about their combination Re = ρVD/μ. Push it up and ordered layers lose their grip.