What is Bernoulli's principle?
Faster flow means lower pressure: the same rule lifts airliners, sprays perfume, fires the gas jet in your hob and lets a cyclist cheat the wind. Squeeze water through a 3D Venturi tube, fly a live wing, and bust the most famous myth in physics class.
▶ Play with it · Read the 60-second explainer · Watch the 40-second video
- Faster flow, lower pressure. Water squeezed through a narrow neck must speed up (A₁v₁ = A₂v₂), and the push that speeds it up comes from higher pressure behind it. So P + ½ρv² + ρgh stays constant along the flow: each litre keeps its energy, trading pressure for speed and height.
- Low pressure lifts liquids. Fast air over a tube is at lower pressure than still air on the liquid below, so the liquid is pushed up. A perfume atomiser needs about 20 m/s of air; a carburettor's venturi draws petrol into the engine in step with the air it breathes.
- Pressure turns into speed. Let a fluid out of a hole and v = √(2Δp/ρ). Half a bar makes a 10 m/s dishwasher jet, 29 mbar of LPG leaves a hob injector at about 50 m/s, and an RO purifier's tiny reject restrictor holds 5 bar on the membrane.
- Wings turn the air. A wing bends air downwards: fast, low-pressure air on top and higher pressure below lift it, and the downwash is Newton's half of the story. Riders drafting behind vehicles meet slower air, and a jet curving round a ball holds it in place.
- Where the rule breaks. Bernoulli assumes no friction, steady flow and a fluid that doesn't squash. Long pipes lose pressure to friction, air above Mach 0.3 compresses, and air over a wing doesn't wait to meet its partner: it arrives first.
| Term | Meaning |
|---|---|
| Continuity | Area × speed is the same at every section of a pipe, so flow speeds up where it narrows. |
| Static pressure | The push a fluid exerts on the walls around it, measured by a tube or gauge on the side. |
| Dynamic pressure | ½ρv², the energy of motion in each cubic metre of moving fluid. |
| Venturi | A tube that narrows and widens gently; the pressure drop in its neck measures or uses the flow. |
| Streamline | The path a bit of fluid follows in a steady flow. Bernoulli holds along it. |
| Lift | The force on a wing from lower pressure above than below, made by turning the air downwards. |
| Viscosity | A fluid's internal friction, which turns some flow energy into heat. |
| Mach number | Speed divided by the speed of sound; above about 0.3, air's squashing matters. |
From water spurting out of a tank to wings, carburettors and heart scans: three centuries of trading pressure for speed.
- 1738 · Hydrodynamica (Daniel Bernoulli, Written in St Petersburg; printed in Strasbourg)
- 1752 · Euler writes the equation (Leonhard Euler, Berlin)
- 1797 · The narrowing tube (Giovanni Battista Venturi, Modena (published in Paris))
- 1887 · The Venturi meter (Clemens Herschel, Holyoke Water Power Company, Massachusetts)
- 1893 · The spray-nozzle carburettor (Wilhelm Maybach, Cannstatt, near Stuttgart)
- 1901 · Two hundred wings in a box (Wilbur and Orville Wright, Dayton, Ohio)
- 1902 · Lift gets a theory (Martin Kutta and Nikolai Zhukovsky, Munich and Moscow)
- 2018 · 296 km/h on a bicycle (Denise Mueller-Korenek, Bonneville Salt Flats, Utah)
The full story, with 20 moments, charts, people and 26 sources: glassbox.how/e/bernoulliclear/history. The data lives in history.json.
Made with the Glassbox studio from this box's storyboard (window.glassbox.director). Free to reuse under CC BY 4.0.
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