Atmospheric Pressure

Right now, without noticing it, you are sitting at the bottom of an ocean of air. The atmosphere is not weightless — a single cubic metre of air near the ground weighs about the same as a bag of sugar. It doesn't seem like much, until you remember how tall the atmosphere is: the air stacks up above your head for tens of kilometres, layer upon layer, all the way to space.

Gravity pulls that whole towering column of air down. So the air above any surface — the top of your head, your desk, a puddle, the sea — presses down on it with the weight of everything stacked above. That press, shared out over the area it acts on, is atmospheric pressure. Like every pressure, it is a force divided by an area:

p = \dfrac{F}{A} \qquad\text{(pressure} = \text{force} \div \text{area).}

At sea level the number comes out surprisingly large: about 100\,000\ \text{Pa}, which we usually write as 100\ \text{kPa} (a pascal, Pa, is one newton pressing on one square metre). That is roughly the weight of a small car pressing on every single square metre of the world around you.

So why aren't we crushed?

If the air presses that hard, why don't we feel it? Why isn't a sheet of paper squashed flat, or your chest caved in? The answer is that atmospheric pressure does not push only downward — it pushes equally in every direction: down, up, sideways, at a slant, everywhere at once. The air under your hand pushes up just as hard as the air on top pushes down, so the pushes cancel.

And there is a second reason. Your body is full of fluids and gas at the same pressure as the air outside, so your insides push out exactly as hard as the atmosphere pushes in. The two are perfectly balanced, and balanced pushes are pushes you never notice. It is only when we deliberately make the pressure unequal — take the air away from one side — that the atmosphere reveals just how strong it really is. That is the trick behind everything that follows.

Just how big is that force?

Because pressure is force over area, we can rearrange it to F = p \times A and work out the actual push the atmosphere puts on things.

Example 1 — a school desk. A desk-top has an area of about 0.5\ \text{m}^2. The atmosphere presses down on it with

F = p \times A = 100\,000 \times 0.5 = 50\,000\ \text{N},

the weight of about five small cars — yet the desk doesn't collapse, because the same 50\,000\ \text{N} of air presses up underneath it too.

Example 2 — the back of your hand. Your hand covers roughly 0.008\ \text{m}^2. The air pushes on it with

F = 100\,000 \times 0.008 = 800\ \text{N},

about the weight of a grand piano — and yet you lift your hand without a thought, because that 800 N is met by an equal 800 N of air pushing on the palm from the other side. The atmosphere is enormous; we survive it only because it is balanced.

Higher up, the air runs out

Here is the key idea: the pressure at any height is set by how much air is stacked above you. Stand at sea level and the whole atmosphere presses down — full pressure. Climb a mountain, and some of the air is now below you, so there is less left above to press down — the pressure drops. Fly in an airliner and most of the atmosphere is beneath you; the air outside is thin and its pressure is only a fraction of sea-level pressure.

Drag the slider to raise yourself from sea level up towards space. Watch the dashed "you" line climb through the air column: fewer and fewer air particles are left above you, the downward "air above" arrow shrinks, and the pressure gauge on the right falls.

This is why your ears pop as a plane climbs or a lift shoots up a tall building: the air pressure outside your eardrum falls, but the air trapped inside your ear is briefly still at the higher pressure, so it bulges the eardrum outward until it "pops" back to balance. It is also why aircraft cabins are pressurised — at cruising height the outside air is far too thin for a person to breathe, so the cabin is pumped up close to sea-level pressure. And it is why a mountaineer on Everest carries oxygen: up there the air is so thin that each breath contains far fewer oxygen molecules than a breath at the bottom.

The atmosphere at work: cans, straws and suction cups

Once you know the air is always pushing — hard, and from every side — a whole set of everyday tricks suddenly makes sense. Each one works by lowering the pressure on one side so that the ordinary atmosphere on the other side can push.

A crushed can. Pump the air out of a sealed can (or let steam inside it cool and collapse) and there is nothing left pushing outward. The atmosphere outside — still at full strength — simply crushes it inward. No one touched it; the air did it.
Drinking through a straw. When you "suck", you lower the air pressure in your mouth and in the top of the straw. The full atmospheric pressure still pressing on the surface of your drink then pushes the liquid up the straw into the low-pressure region. You don't pull the drink up — the air pushes it up for you.
A suction cup. Press one onto a smooth surface and you squeeze the air out from underneath. With almost no air left inside to push back, the atmosphere pressing on the outside holds it firmly against the wall.
A barometer. This is an instrument built to measure atmospheric pressure directly — the atmosphere pushing on a pool of liquid holds a column of it up a tube, and how high it stands tells you the pressure. When the reading falls, stormy weather often follows.

You don't "suck" a drink up a straw — the atmosphere pushes it up. Sucking only lowers the pressure inside your mouth; it is the air pressing down on the drink from outside that does the actual lifting. (This is also why there is a limit: no matter how hard you suck, ordinary air pressure can push water up a straw only about 10 metres — beyond that even a perfect vacuum isn't enough.)
Atmospheric pressure acts in all directions, not just downward. The weight of the air column is what creates it, but once created the pressure presses equally up, down and sideways — which is exactly why a suction cup can grip a vertical wall or even a ceiling.
Pressure falls with height because there is less air above you — not because gravity gets weaker. Gravity is almost exactly as strong on a mountain top as at sea level; what has changed is the amount of air left overhead to press down.

In 1654, in the German town of Magdeburg, the mayor Otto von Guericke staged one of the great science demonstrations of all time. He made two hollow copper hemispheres that fitted together into a sphere about half a metre across, put them together, and used his newly invented pump to suck all the air out from inside. Then he harnessed a team of horses to each half — eventually eight horses on each side, sixteen in all — and had them heave in opposite directions.

The hemispheres would not come apart. There was no glue, no latch, nothing holding them but the atmosphere itself: with the air removed from inside, there was nothing pushing the halves outward, so the ordinary air pressure on the outside squeezed them together with a force of thousands of newtons. When von Guericke finally let a little air back in, the two cups fell apart in his hands. It was the first time anyone had shown, unmistakably, that the invisible air around us presses with real and mighty force.