Pressure and Buoyancy
The Push of a Crowd Too Small to See
A Push From Every Side
Lie on a bed of nails and nothing happens. Stand on one nail and it goes through your foot. Your weight is the same both times. What changes is the area it is spread over, and pressure is exactly that: a push divided by the area it pushes on. A knife puts a modest push on a very thin edge. A snowshoe spreads a person over so much snow that they barely sink.
In air and in water, pressure has a cause too small to see. Air is a crowd of molecules flying every which way, at about 470 meters per second at room temperature. Each one that meets a wall bounces off and gives it a tiny tap. At sea level, a few times 10²³ of them strike every square centimeter of everything, every second.
No single tap can be felt. Together they make a push so steady that it seems smooth. Because the molecules move every which way, flying free in air and jostling shoulder to shoulder in water, the push is the same in every direction, and it always meets a surface square on. A body under water is not just pressed down. It is squeezed from every side, and nearly everything that follows comes from what happens when that squeeze is not quite even.
Deeper Means Harder
Water has weight, and every layer of it holds up the layers above. So the pressure grows with depth: one more atmosphere, the pressure of all the air above us, for about every ten meters down. At the bottom of the Challenger Deep in the western Pacific, 10,935 meters down, it is more than a thousand atmospheres.
What the pressure does not depend on is the surprise. The shape of the vessel does not matter, and neither does how much water it holds. Join vessels of any shape at the bottom and the water stands at one level in all of them, unless a tube is so thin that the water creeps up its glass. At any depth, the pressure is the same in each, whether a wide funnel or a thin tube rises above it.
It looks wrong, because the funnel holds far more water than the tube. But the funnel’s sloping walls carry part of that weight, and the bottom carries only the column straight above it.
The even push of a liquid makes something else possible. Press a small piston into a sealed vessel of water and the pressure rises everywhere in it. A second piston with a hundred times the area is then pushed a hundred times harder. One person pushing the small piston has the strength of a hundred, though the small piston must travel a hundred times as far as the big one. Car brakes and hydraulic lifts work this way.
Depth also sets the shape of a dam. Hoover Dam is 221 meters high. It is 14 meters thick at the top and 201 meters at its base, where a full lake presses on every square meter with the weight of about 220 tonnes. And your ears feel three meters of a swimming pool as they would feel three meters of the open sea.
Why Anything Floats
Because pressure grows with depth, the water pushes harder on the bottom of a sunken body than on its top. The difference is an upward push called buoyancy, and its size is easy to find. Imagine the body gone and its place filled with water. That water would hang there at rest, held up by the very same pushes. So the push equals the weight of the water the body takes the place of, whatever the body is made of.
This is Archimedes’ principle. A solid less dense than water sinks only until it pushes aside its own weight of water. A solid denser than water goes to the bottom, and weighed there it comes out lighter by the weight of the water it pushes aside.
So floating is not about being light. Steel is nearly eight times as dense as water. Yet a steel hull encloses so much air that it pushes aside its own weight of water long before the sea reaches the deck. What counts is the average density of everything inside the hull’s outline. A loaded ship rides lower. A submarine dives by letting water into tanks and rises by blowing it out with compressed air. Ice is about a tenth less dense than seawater, so about nine tenths of an iceberg is under the sea.
Buoyancy can even show what a thing is made of. Is a gold crown pure, or has silver been mixed in? Comparing how much water spills for the crown and for the same weight of pure gold is a crude test. A balance does better: weigh the crown against the gold under water, where Archimedes’ principle makes any difference plain.
The Ten-Meter Ceiling
Well diggers knew a puzzle. A suction pump, however well it was made, would not lift water more than about ten meters. The natural guess was that a taller column of water broke under its own weight, like a rope that is too long.
The limit shows without a pump too. Fix a pipe about 11 meters tall upright, fill it with water and open its foot in a tub. The water falls until it stands about ten meters high, and above it is a space that seems to hold nothing.
Now try mercury, nearly fourteen times as dense as water. Fill long glass tubes with it and turn them upside down into a dish of it. The mercury falls and stands about 76 centimeters high, even in a tube that ends in a large glass ball.
What holds the column up is the weight of the air pressing on the mercury in the dish. We live at the bottom of a sea of air. The mercury weighs as much as a column of air of the same width, all the way to the top of the sky. Above the mercury is nearly empty space: a vacuum.
So suction is the wrong word. A vacuum cannot pull, because there is nothing in it to pull with. When you drink through a straw, you lower the pressure in your mouth, and the air pressing on the drink pushes it up. A pump works the same way, and the air can push water only so high. In a sealed tube at room temperature the column stands at about 10.1 meters. The water at its top boils, cold, and fills the space above with its vapor.
An Ocean of Air
The air above every square meter of ground weighs about ten tonnes, and the air above every square centimeter about a kilogram. Over the whole skin of an adult, pressing from every side, that comes to some twenty tonnes.
We do not feel it because the push is not one-sided. The air presses from every side, and the fluids in our bodies press back out just as hard. What we notice is only a change. A few hundred meters up or down, in an elevator or a plane, is enough to make the ears pop.
Carry the tube up a mountain and the mercury sinks. On one mountain, about a kilometer above the town at its foot, it stood some 8.5 centimeters lower. Higher up, less air lies overhead to press down. The pressure roughly halves with every 5.5 kilometers of height, and on the top of Everest it is about a third of what it is at sea level.
One of the first air pumps was used to empty the space between two copper hemispheres nearly half a meter across, laid rim to rim. Teams of horses pulling on the two sides could not part them. Let back in, the air left them to fall apart on their own.
Nothing pulled the hemispheres together. The air outside pushed them together, with no air inside to push back. Even a classroom pair 10 centimeters across, with all the air gone, takes a pull equal to the weight of about 80 kilograms to part.
Pulling Water Up a Tree
Yet the tallest trees lift water far above ten meters. A coast redwood in California called Hyperion stands about 116 meters tall. The air cannot push sap that high, so something must pull it.
The pull starts in the leaves. Water evaporates from them, and the water left behind is drawn up to take its place. It rises along unbroken threads of water in the wood, all the way from the roots. Water molecules cling to each other so strongly that a thin, clean thread can hang under tension, like a rope, without breaking.
In clean glass tubes water has held under tensions of hundreds of atmospheres, and in tiny pockets sealed inside quartz under more than a thousand. A tree needs far less. Gravity alone asks for a tenth of an atmosphere more pull for every meter of height, so the top of a hundred-meter redwood must pull its sap at least ten atmospheres harder than its foot.
The danger is a bubble. If air gets into one thread, the thread snaps and that channel goes dry. Drought kills trees mostly this way, snapping thread after thread until too few are left. A taller tree needs a harder pull, so its highest leaves get less water and grow smaller. Scientists have climbed the tallest redwoods to measure this, and put the limit for the species at 122 to 130 meters.
When the Taps Stop Averaging Out
A steady pressure is the average of countless taps. On anything small enough, the taps no longer average out. Watch tiny particles released from pollen grains in water, and they jiggle without end. Each speck is knocked about by the uneven taps of the molecules around it. Measuring the jiggling gave a count of the molecules, and that count settled that atoms are real.
That is the quiet power of pressure. Nobody follows the molecules. Their taps, and in stretched water their hold on one another, are replaced by a single number, and the number keeps simple rules of its own. Those rules hold up ships, size dams, weigh the sky and lift water to the top of a redwood.
