The history
From water spurting out of a tank to wings, carburettors and heart scans: three centuries of trading pressure for speed.
People knew for centuries that water squirts faster from a deeper hole, but nobody linked pressure and speed until Daniel Bernoulli poked a tube through a pipe wall in the 1730s. Euler turned the idea into an equation, Venturi and Herschel put it to work, and engineers learned where friction and turbulence spoil it. Then flight made it famous, along with a myth about wings that took a century to shake off.
1643
Speed from a hole's depth, v = √(2gh)
Evangelista Torricelli, Italy
1732
A tube to measure flow speed
Henri Pitot, France
1738
Pressure falls where flow is fast
Daniel Bernoulli, Switzerland
1752
The equation P + ½ρv² + ρgh = constant
Leonhard Euler, Switzerland
1797
Pressure drop in a narrowing pipe measured
Giovanni Battista Venturi, Italy
1887
Venturi flow meter
Clemens Herschel, USA
1893
Spray-nozzle carburettor
Wilhelm Maybach, Germany
1901
Wind-tunnel data for wing design
Wilbur and Orville Wright, USA
1640 – 1745
Torricelli, Pitot and the Bernoullis discover that pressure and speed trade off in flowing water.
1643
Torricelli proposed that water spurting from a hole in a tank leaves as fast as a drop falling from the water's surface down to the hole. Today we write it v = √(2gh).
Why it mattered. It was the first speed-from-pressure rule, and turned out to be a special case of Bernoulli's principle.
1732
Working on rivers and aqueducts, Pitot pointed a bent glass tube into the flow of the Seine. The faster the water, the higher it rose in the tube. He published the idea in 1732, and Henry Darcy gave it its modern form in 1858.
Why it mattered. Pitot tubes still tell every airliner how fast it is flying through the air.
1738
Bernoulli's book on the forces and motions of fluids showed that where water flows faster, its pressure is lower. He measured pressure by poking an open tube through a pipe's wall and watching how high the water rose. The same book sketched the first kinetic theory of gases.
Why it mattered. It gave the principle its name and began the science it called hydrodynamics.
1743
1743 (dated 1732)
Daniel's father Johann published his own Hydraulica, which borrowed key ideas from his son's work, and dated it 1732 so that it seemed to come first. Father and son had already fallen out after sharing a Paris Academy prize.
Why it mattered. One of the most bitter priority fights in the history of science.
1750 – 1895
Euler writes the law down. Venturi, Darcy, Reynolds and Herschel test its limits and put it to work in meters and carburettors.
1752
1752 (published 1757)
Bernoulli's friend Euler turned the idea into mathematics: equations for any moving fluid without friction. He presented them to the Berlin Academy in 1752 and published them in 1757. The formula we call Bernoulli's equation, P + ½ρv² + ρgh = constant, comes out of Euler's work.
Why it mattered. Bernoulli had the insight; Euler wrote down the law in the form used today.
1797
Venturi measured water flowing through pipes that narrowed and widened again, and showed that the pressure drops in the narrow part. He also studied how a fast jet drags still water along beside it.
Why it mattered. His name went on every tube with a neck, from carburettors to gas burners.
1845
1845 and 1857
Real water loses pressure along a pipe because it rubs on the walls. Weisbach wrote the friction loss as f × (L/D) × ½ρv² in 1845, and Darcy's careful pipe experiments of the 1850s pinned down how the factor f depends on the pipe.
Why it mattered. It fixed Bernoulli's biggest blind spot for engineers who build water mains.
1883
Reynolds let a thin thread of dye into water flowing through a glass pipe. At low speed it stayed a neat line; faster, it suddenly broke into swirls. The switch depends on speed × width ÷ viscosity, a ratio later named the Reynolds number.
Why it mattered. It explained when friction in pipes changes its behaviour.
1887
1886–1888
Herschel built a pipe with a gentle neck and read the flow from the pressure drop across it. He tested it from 1886, filed a patent in December 1887 and named it after Venturi. The patent was granted in April 1888.
Why it mattered. Water companies used it to measure huge flows with no moving parts.
1893
Maybach's carburettor put a fuel jet in the narrow throat where the engine's incoming air is fastest. The low pressure there sprays petrol into the air in step with how hard the engine breathes. In Hungary, Donát Bánki and János Csonka patented a carburettor the same year.
Why it mattered. Most petrol engines used this idea for about a century, until fuel injection took over.
1900 – 1910
Wind tunnels, lift theory and the boundary layer explain how wings really work.
1901
The Wright brothers found that published lift data were wrong, so they built a small wind tunnel and tested about 200 model wing shapes. Two years later, on 17 December 1903, their Flyer made the first controlled powered flight.
Why it mattered. Measured lift, not guesswork, made the first aeroplane possible.
1902
1902 and 1906
Kutta and Zhukovsky (Joukowski) showed independently that a wing's lift equals air density × speed × the circulation of air around it. The flow must leave a wing's sharp back edge smoothly, and that fixes how much lift it makes.
Why it mattered. It is why the wing in chapter 4 can be calculated at all.
1904
8 August 1904
At a mathematics congress Prandtl explained that friction matters only in a thin layer next to a surface. Outside it, Euler's and Bernoulli's frictionless rules work well; inside it, the flow can peel off, which causes stalls and drag.
Why it mattered. It showed when Bernoulli can be trusted and why it sometimes can't.
1930 – today
Jets, supersonic flight, heart scans, shower curtains and bicycle records: the law in its many modern forms.
1934
Coandă patented a way to bend a jet of fluid by running it along a curved surface. He had noticed the effect years earlier, when flames from his experimental plane seemed to cling to its sides.
Why it mattered. The Coandă effect holds a ball in a hair-dryer jet and helps explain many 'Bernoulli' tricks.
1947
14 October 1947
The rocket-powered Bell X-1 flew level faster than the speed of sound. Near that speed air squashes and shock waves form, so the simple, incompressible Bernoulli equation no longer holds.
Why it mattered. High-speed flight needed the compressible version of the law.
1978
February 1978
Doctors used Doppler ultrasound to measure how fast blood squirts through a narrowed heart valve, then worked out the pressure drop with a simplified Bernoulli equation: Δp ≈ 4v². It matched pressures measured with catheters.
Why it mattered. Cardiologists still use this every day to judge valve disease without surgery.
2001
Schmidt simulated a shower on his home computer and found that falling spray sets up a sideways vortex whose low-pressure centre pulls the curtain in. It won him an Ig Nobel prize.
Why it mattered. A reminder that everyday 'Bernoulli' puzzles often have more than one cause.
2003
Babinsky filmed smoke pulses flowing past a wing in a wind tunnel. The smoke over the top reached the back edge well before the smoke underneath, and never met up again, disproving the popular 'equal transit time' explanation of lift.
Why it mattered. It is the experiment chapter 5's myth-buster recreates.
2009
1 June 2009
Ice crystals briefly blocked the Pitot tubes of an Airbus A330 flying from Rio de Janeiro to Paris. With confusing airspeed readings the crew lost control and all 228 people on board died. Investigators found the icing was a contributing factor.
Why it mattered. Airspeed from ½ρv² is so vital that airliners carry several Pitot tubes and heat them.
2018
16 September 2018
Pedalling in the still air behind a dragster's fairing, Mueller-Korenek averaged 296 km/h over a measured mile, beating Fred Rompelberg's 268.8 km/h from 1995.
Why it mattered. Drafting at its most extreme: the fairing takes the air's ½ρv² so the rider doesn't have to.
By the numbers
Drafting records: each rider pedalled in the slow air behind a train, a car or a dragster's fairing.
Did you know?
One kilopascal of pressure is exactly one joule of energy per litre, so Bernoulli's equation is really an energy budget for each litre of fluid.
Air over the top of a lifting wing reaches the back edge well before the air underneath. It does not wait to meet up.
A table-tennis ball floating in a hair-dryer jet is held by the jet curving round it, not by low pressure: the jet is at room pressure.
Daniel Bernoulli's father banned him from the family house after they shared a prize, then published a backdated book to claim his ideas.
Riding 2.6 m behind a motorbike roughly halves a cyclist's air drag.
An airliner's wing holds up about 636 kg on every square metre at take-off.
The people
1700 – 1782 · Mathematician and physician · Switzerland (born in Groningen)
Wrote Hydrodynamica, the book that named hydrodynamics, while working in St Petersburg.
1707 – 1783 · Mathematician · Switzerland
Bernoulli's friend, who wrote the equations of frictionless flow in 1752–57.
1695 – 1771 · Hydraulic engineer · France
Invented the tube that still measures airspeed.
1746 – 1822 · Physicist and priest · Italy
Measured the pressure drop in a narrowing pipe; the Venturi tube bears his name.
1842 – 1912 · Engineer · United Kingdom (born in Belfast)
Showed when smooth pipe flow turns turbulent.
1842 – 1930 · Hydraulic engineer · United States
Built the Venturi meter at Holyoke and named it after Venturi.
1875 – 1953 · Engineer and physicist · Germany
Found the thin boundary layer where friction lives, and founded modern aerodynamics at Göttingen.
1886 – 1972 · Inventor and aircraft designer · Romania
Studied and patented jets that follow curved surfaces.
Where it happened
Sources
Dates marked “c.” are approximate, and historians sometimes disagree about who was first. If you spot a mistake, tell us.
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