THE PHYSICS OF FLOW

Smooth, then
swirling.

Watch the smoke above a candle.

For the first few centimetres it rises in a tidy thread. Then it wobbles and breaks into eddies. That switch, from laminar to turbulent flow, happens in air, water and pipes all around us.

RE ≈ 2,040 where pipe turbulence can first last

Check a flow

A thin ribbon of smoke rising from a snuffed candle against a dark background, smooth at first and then curling into swirls — AI-generated image, not a photograph of a real person or place.

Slow and sticky stays smooth
Fast and large turns swirly
Swirls break into smaller swirls
One number predicts the switch

THE SHORT ANSWER

Two ways
a fluid can move.

Laminar flow slides in neat layers.
Turbulent flow churns in eddies of many sizes.

SMOKE

A thread that breaks

Rising smoke is laminar for the first few centimetres, then turns turbulent as it speeds up and spreads. A candle plume shows the same switch.

Check a flow

PIPES

Reynolds' dye test

In 1883 Osborne Reynolds sent a thin jet of dye through water in a glass pipe. At low speed it stayed a distinct line; faster, it broke up and spread.

See the numbers

RIVERS

Eddies behind a pier

Slow river water flows smoothly round a bridge pier. When the flow is faster it separates from the pier and becomes turbulent downstream.

Spot it yourself

A QUICK FLOW CHECK

Smooth or swirling
in a pipe?

The Reynolds number compares a flow's push (speed and size) with its stickiness (viscosity). Pick a value for water in a straight pipe to see what research says happens.

Pipe check

Choose a Reynolds numberBelow about 2,000About 2,0402,040 to 4,000Above about 5,000Up to 13,000, with care

Below about 2,000Laminar

Viscous forces win and the flow stays smooth. Reynolds found that about 2,000 was the lowest value at which he saw the switch, even with a rough entrance.

About 2,040Turbulence can last

In pipe flow, turbulence can first be sustained above a critical value of about 2,040.

2,040 to 4,000Patchy

Turbulence generally comes in patches, interspersed with laminar flow, until a Reynolds number of about 4,000.

Above about 5,000Usually turbulent

Flows above about 5,000 are typically, but not necessarily, turbulent.

Up to 13,000, with careCan stay smooth

With a very smooth entry Reynolds kept the flow laminar up to about 13,000; with extreme care, the transition can be pushed as high as 40,000.

Sources: Wikipedia, Turbulence and Laminar–turbulent transition (summarising Reynolds 1883 and later pipe-flow studies); NASA Glenn Research Center, Reynolds number.

Pipe-flow values from Reynolds' 1883 experiment and later measurements, as summarised in reference works. Real pipes vary with entry and roughness.

TWO NUMBERS WORTH KNOWING

When smooth
stops being smooth.

One range from the original pipe experiment,
one from wind-tunnel work on golf balls.

2,000–13,000

Reynolds numbers where the switch happened

Reynolds found the transition from laminar to turbulent flow between about 2,000 and 13,000, depending on how smooth the entry conditions were.

PIPE FLOW · REYNOLDS, 1883

up to 50%

Drag cut by dimples on a sphere

Researchers at Seoul National University note that dimples can reduce drag on a sphere by as much as 50 percent compared with a smooth surface.

GOLF BALLS · PHYSICS OF FLUIDS, 2006

The dimple effect works because a little turbulence in the thin boundary layer helps the air cling to the ball for longer, which shrinks the turbulent wake behind it (University of Illinois Physics Van; Choi, Jeon and Choi, 2006).

FOUR PLACES TO SEE IT

Turbulence,
close to home.

You do not need a lab. These are everyday places where the switch from smooth to swirling is easy to watch.

Blow out a candle
Watch the smoke: a straight thread for the first few centimetres, then curls and eddies as the plume grows.
Stand on a bridge
Compare the water upstream of a pier with the swirls behind it. Faster water makes more of them.
Look at a golf ball
The dimples stir a thin layer of air so it hugs the ball longer and leaves a smaller wake.
Watch clouds and surf
Billowing storm clouds, breaking surf and chimney smoke are all everyday turbulence.

A river flowing past the stone pier of an old bridge, with swirling eddies and ripples forming downstream of the pier — AI-generated image, not a photograph of a real person or place.

A long glass tube of clear water on a laboratory bench with a thin thread of blue dye running straight along its centre — AI-generated image, not a photograph of a real person or place.

WHIRLS INSIDE WHIRLS

Big eddies
make little ones.

Richardson pictured turbulence as eddies of many sizes: large ones are unstable and break into smaller ones, handing their energy down until the eddies are so small that viscosity turns it into heat.

Leonardo da Vinci drew the same restless patterns around 1510 to 1512, sketching the rings, spirals and bubbles of water falling from a sluice into a pool. A full description of turbulence is still counted among the unsolved problems in physics.

Questions

Questions people ask

What is laminar flow?

Laminar flow is when a fluid moves in smooth, parallel layers with no disruption between them. It happens at low Reynolds numbers, where the fluid's stickiness (viscosity) dominates.

What is the Reynolds number?

A dimensionless number that compares inertial forces with viscous forces in a flow. NASA gives it as speed times a length scale divided by the kinematic viscosity. Low values mean viscosity matters; high values mean it matters much less.

Why do golf balls have dimples?

Dimples add a little turbulence close to the ball's surface. That helps the air stay attached for longer, so the turbulent wake behind the ball is smaller and drag falls, by as much as 50 percent in wind-tunnel work.

Who discovered the switch to turbulence?

Osborne Reynolds showed it in 1883 at what is now the University of Manchester, by sending a thin jet of dyed water through a glass pipe and changing the flow speed.

Is turbulence fully understood?

No. Physicists can predict when it is likely to start, but a complete description of turbulence remains an unsolved problem. Richard Feynman called it the most important unsolved problem in classical physics.

Smooth, then
swirling.