An Experimental Investigation of the Circumstances Which Determine Whether the Motion of Water Shall Be Direct or Sinuous, and of the Law of Resistance in Parallel Channels
Whether a flow stays smooth or turns turbulent is decided by one dimensionless number.
Turn a tap slowly and the water comes out as a clear glassy rod; open it more and it suddenly froths and roars. Reynolds found the number that decides which one you get.
The big idea
Flowing fluids come in two characters. Smooth, orderly flow — where every bit of fluid glides along in neat layers — is called laminar. Churning, swirling, mixing flow is called turbulent. The same water can do either, and Reynolds set out to find what tips it from one to the other.
His answer was beautifully economical. It isn't speed by itself, or thickness, or pipe size — it's a particular combination of all of them, now called the Reynolds number. When that number is small, the fluid's internal stickiness keeps things smooth; when it grows past a critical value (around two thousand), the flow's own momentum takes over and it breaks into eddies. One number, and you can predict the change.
How it came about
Osborne Reynolds was an engineering professor in Manchester in the 1880s, fascinated by why water in pipes sometimes flowed cleanly and sometimes resisted far more than expected. His experiment was disarmingly simple: a long glass tube, water from a still tank, and a fine jet of coloured dye injected right down the middle so he could see the motion.
Crank the flow up slowly and the dye drew a perfect straight line. Then, at a certain speed, the line would 'all at once' shatter and smear into a cloud of swirls. By repeating this with different tubes and fluids, Reynolds realised the tipping point always came at the same value of his combined number — not at the same speed. He had found a law hiding inside a thread of dye.
Why it mattered
Because the same number governs every fluid at every scale, it became the single most useful quantity in fluid engineering. It tells you whether a pipeline will run smooth or rough, how much an aeroplane will drag, how a heart valve flows — and, crucially, it lets engineers test a small model and trust the result for the full-size machine, as long as the Reynolds numbers match.
A way to picture it
Think of a crowd leaving a stadium. Walking slowly, people file out in tidy lanes — that's laminar. Speed everyone up and the lanes dissolve into a jostling, swirling crush — that's turbulent. Whether you get lanes or chaos doesn't depend on speed alone; it depends on speed, how packed the crowd is, and how wide the exit is, all together. The Reynolds number bundles exactly that kind of combination for a fluid.
Where it sits
Reynolds' transition is the doorway to one of physics' great unsolved problems: turbulence. Smooth flows can be calculated exactly, but turbulent ones still defy a complete theory — they are a prime example of deterministic chaos, the same family of behaviour that Edward Lorenz stumbled on in weather models in 1963. Reynolds' little number is where the order ends and the chaos begins.
When the velocities were sufficiently low, the streak of colour extended in a beautiful straight line through the tube.
As the velocity was increased by small stages, at some point in the tube, always at a considerable distance from the trumpet or intake, the colour band would all at once mix up with the surrounding water, and fill the rest of the tube with a mass of coloured water.