Under pressure

A recent issue of the London Review of Books had this:

The unit of measurement of this pressure is the atmosphere, named after the weight of the air bearing down on us at sea level. We don’t normally think of the air as having weight, but it does. Hold your hand out flat, and imagine an invisible column of air above each of your fingernails stretching up from where you are to the top of the Earth’s atmosphere. That column weighs 1.03 kg per square centimetre—in other words, about one kilogramme’s weight of air bears down on each fingernail. That amount of pressure is one atmosphere.

What is wrong with this is that it misses the point of pressure. The misconception is not unusual. A GCSE physics site says that atmospheric pressure is “about the same force as having over a dozen cars piled on top of you!”

So why are these statements wrong? The error is in the idea that pressure “bears down”. As engineers learn in their first course on fluid mechanics, pressure acts equally in all directions. When John Lanchester says that one kilogramme’s weight of air bears down on a fingernail, he would have been just as right, or wrong, if he had said that one kilogramme’s weight of air bears up on a fingertip. The force on the end of your finger, or anything else, is about one kilogramme of air pushing down, balanced by one kilogramme pushing up: in sum, almost nothing.

But, you object, things get squashed by atmospheric pressure, or by pressure in the deep ocean. The reason is not the pressure, but the pressure difference. When pressure inside a submarine, or an aeroplane, or a soft drinks can, is not the same as the pressure outside, the force is out of balance and the structure has to carry a load to maintain its shape. If you inflate a balloon, you can see how the material stretches as the internal pressure is increased until it is greater than the pressure on the outside. The rubber of the balloon stretches so that the total force due to the difference in pressure, and the tension in the rubber, is zero. Likewise, though you cannot see it, the shell of a drinks can expands slightly to balance the difference in pressure between inside and outside. An aeroplane fuselage behaves the same way; a submarine hull likewise, though with the high pressure on the outside, rather than the inside.

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