What is pressure?

Stand on sand in flat shoes and you barely sink. Stand on one heel and you go straight in. Your weight didn't change: what changed was the area it was spread over. Pressure is force divided by area: P = F ÷ A.

Its SI unit is the pascal (Pa): one newton spread over one square metre. That is tiny, about the pressure of a banknote lying on a table, so we usually meet kilopascals (kPa). The air around you presses at about 101 kPa, which is called one atmosphere. Other units you will see: bar (tyres, 100 kPa), psi (pounds per square inch) and mmHg (blood pressure).

To measure it, you can divide a force by the area it pushes on, or use a pressure gauge: a spring or a bendy tube that moves further the harder it is pushed.

A brick weighs the same whichever way up it sits, but on its end it presses three times harder. And a person in a stiletto presses the floor far harder than an elephant: 588 N on 1 cm² beats 39,000 N on half a square metre. Pressure is also the idea behind Pascal's principle (PascalClear), Bernoulli (BernoulliClear) and the gas laws (GasLawClear).

Every cutting tool is a pressure machine. A sharp knife touches the tomato along an edge maybe a fiftieth of a millimetre wide, so a gentle 10 N push becomes a pressure of many megapascals, and the skin splits. A blunt knife spreads the same push over an edge 25 times wider: the pressure is 25 times smaller, and the tomato squashes instead.

A nail works the same way. The hammer hits the wide head (about 50 mm²) and the same force comes out of the point (about 0.5 mm²): a hundred times the pressure, enough to part the wood fibres.

Flip it round to spread a weight. Snowshoes put your weight on six times the area of your boots, so you stay on top of fresh snow. A bed of nails is safe for the same reason: a thousand points share your weight, so each presses gently. Just one would go straight through.

Tyres are the neat case: the patch touching the road grows until load ÷ area ≈ air pressure. A car tyre at 2.2 bar needs a patch about the size of your palm. A racing bike at 6 bar (CycleClear) touches with less than a postage stamp. A tractor runs its huge tyres at only about 1 bar, so it spreads its weight and doesn't pack down the soil.

Water is heavy. A column of water 10 m tall and 1 m² across weighs about 98,000 N, and all of it presses on the bottom. So the pressure under a liquid is P = ρ g h: the liquid's density ρ, times gravity g, times the depth h. Only the depth matters, not the shape or size of the container.

Every 10 m of water adds about 1 bar. A tank on a three-storey roof gives the ground-floor tap about 1 bar, and the top-floor tap hardly any. That's far too little for an RO membrane, which is why the purifier has a 5 bar booster pump (ROClear). A geyser is built to hold 6 to 8 bar (WaterHeaterClear), so a tank can't burst it.

Dams are thick at the bottom because the water pushes hardest there. At the foot of Bhakra Dam, 226 m of water press at over 2 MPa, 22 times the air.

Divers feel it in their ears. The air behind the eardrum stays at surface pressure unless you equalise (swallow or gently blow against a pinched nose), so the water pushes the eardrum in. Only a metre or two down it already hurts (EarClear).

Your blood is a liquid column too. Blood pressure, 120/80 mmHg (HeartClear), is measured at heart height: at your ankles it is almost 100 mmHg more, just from the blood above. The squeeze from the heart travels through the fluid in every direction, which is Pascal's principle (PascalClear).

The air above you is about 100 km deep, and it has weight. Above every square metre of ground sits about 10 tonnes of it, so at sea level air presses on everything at about 101 kPa: one atmosphere. You don't feel it because it pushes equally from every side, and the fluids inside you push back just as hard.

Take the air away from one side and you notice. In 1654 Otto von Guericke pumped the air out of two copper hemispheres. Teams of horses couldn't pull them apart. No glue: the outside air simply pushed them together with about 20 kN. Drinking through a straw and a suction cup work the same way: you lower the pressure on one side, and the air pushes from the other.

Climb and there is less air above you, so the pressure falls: about 89 kPa in Bengaluru, 65 in Leh, a third of sea level on Everest. A sealed chips packet puffs up on the way. Planes keep the cabin at about 0.75 atm, like a hill station at 2,400 m.

Pressure changes boiling. High on a mountain water boils below 90 °C and dal takes forever. A pressure cooker does the opposite: its whistle is a weight sitting on a tiny hole, and it holds the steam in until the pressure is about 1 bar above the air. Water then boils at about 120 °C and food cooks in a third of the time (ACClear shows the same trick in an AC).

A barometer weighs the air with a column of mercury, 760 mm tall on an average day. Falling pressure means rising air, clouds and rain. The gas laws (GasLawClear) explain how squeezing and heating air change its pressure.

Myth: “a flat tyre is empty.” A tyre gauge shows gauge pressure: how much more than the air around it. A flat tyre reads 0, but it is still full of air at 1 atm. Real, or absolute, pressure is gauge plus about 1 bar. A car tyre at 2.2 bar on the gauge holds 3.2 bar of air (CarClear).

Myth: “suction pulls.” A vacuum can't pull anything. When you press a suction cup to a tile, you squeeze the air out from under it, and the air outside pushes it on. So a suction cup is only as strong as the air around it: weaker in Leh, useless on Mars, and it drops straight off on the Moon. Straws, vacuum cleaners and your own breathing all work by letting the outside push.

Extremes. At the bottom of the Mariana Trench, almost 11 km down, the water presses at about 1,086 bar: a tonne on every square centimetre. In 1960 Jacques Piccard and Don Walsh went down in the Trieste, inside a steel ball with walls 12.7 cm thick. Polystyrene cups sent down come back shrunk to doll size.

Myth: “a bigger tank gives more pressure.” Fill vessels of any shape to the same depth and the pressure at the bottom is exactly the same, because P = ρ g h only cares about depth. This is the hydrostatic paradox, noticed by Simon Stevin in 1586. A huge tank on your roof gives the same tap pressure as a small one at the same height. It just lasts longer.