Pressure in Liquids and Gases

What is pressure?

We often use the word "pressure" loosely, but in physics it has a precise meaning. Pressure is the amount of force pushing on a given area. The formula is simple:

Pressure = Force ÷ Area

We measure pressure in pascals (Pa), named after the scientist Blaise Pascal. One pascal is one newton of force spread over one square metre.

The key idea is that pressure depends not just on the force, but on the area that force is spread over. Spread a force over a large area and the pressure is low; concentrate the same force onto a tiny area and the pressure is high.

Think about it with everyday examples. A sharp knife cuts easily because all your pushing force is focused onto a razor-thin edge — a tiny area — creating enormous pressure. A blunt knife has a wider edge, so the same force gives less pressure and cuts poorly. Snowshoes work the opposite way: they spread your weight over a large area, lowering the pressure on the snow so you don't sink in. A drawing pin is sharp on one end (high pressure to pierce the wall) and flat on the other (low pressure so it doesn't hurt your thumb). Same force, different area, very different result.

This lesson is about pressure in fluids — a word that means both liquids and gases, because they both flow and behave in similar ways.

Pressure increases with depth

Imagine diving down into a swimming pool. Near the surface you feel fine, but as you go deeper your ears start to hurt. That is fluid pressure increasing with depth.

Why does this happen? A fluid has weight. When you are deep underwater, there is a tall column of water above you, and all of that water is being pulled down by gravity. Its weight presses down on you. The deeper you go, the taller and heavier the column of water above, so the greater the pressure.

The pressure in a liquid depends on three things, captured in the formula pressure = ρ × g × h:

• ρ (density) of the liquid — denser liquids press harder,
• g (gravity) — stronger gravity means more weight,
• h (depth) — the deeper you go, the higher the pressure.

This is why submarines must be built with incredibly strong hulls: deep in the ocean the water pressure is hundreds of times greater than at the surface and could crush a weak structure. It is also why dams are built thicker at the bottom than the top — the water pushes hardest near the base, so that is where the dam needs the most strength.

Pressure acts in all directions

Here is a fact that surprises many people. At any single point in a fluid, the pressure does not just push downwards — it pushes equally in all directions: up, down, and sideways.

You can see the evidence easily. Punch holes around the side of a plastic bottle full of water and the water squirts out sideways, not just downwards. The pressure is pushing outwards on the walls. And the holes nearer the bottom squirt water further, because the pressure is greater at greater depth.

This "all directions" rule is what allows fluids to push up on objects, which leads us to floating.

Buoyancy: the upward push

Because pressure increases with depth, the bottom of any submerged object feels more upward pressure than the downward pressure on its top. The result is a net upward force called the buoyant force, or upthrust.

Whether an object floats or sinks depends on whether this upthrust can balance the object's weight. An object floats if it is less dense than the fluid, and sinks if it is denser — the same density idea that explains why ships and corks float while stones sink. The upthrust is fluid pressure in action.

Atmospheric pressure: the ocean of air

We live at the bottom of a huge "ocean" of air — the atmosphere. Air has weight too, and the whole column of air above us, stretching tens of kilometres up into space, presses down and around on everything. At sea level this atmospheric pressure is about 100,000 pascals (roughly 101 kPa, or "1 atmosphere"). That is the equivalent of about 1 kilogram pressing on every square centimetre!

So why aren't we crushed? Because the pressure inside our bodies — our blood, fluids and air-filled spaces — is balanced with the pressure pushing in from outside. The forces are equal and cancel out, so we feel nothing.

Atmospheric pressure becomes obvious when there is an imbalance. When you drink through a straw, you suck some air out of the straw, lowering the pressure inside it. The greater atmospheric pressure on the surface of the drink then pushes the liquid up the straw into your mouth. You don't really "pull" the drink up — the air pressure pushes it up for you!

Atmospheric pressure also decreases with altitude. Higher up a mountain, or in a plane, there is less air above you, so the pressure is lower. That is why your ears "pop": the air trapped in your middle ear is now at a higher pressure than outside, so it pushes out until it escapes.

Pascal's principle and hydraulics

One of the most useful facts about fluids was discovered by Blaise Pascal. Pascal's principle states that pressure applied to an enclosed fluid is transmitted equally and undiminished throughout the whole fluid.

This has a remarkable consequence. Imagine two connected pistons sharing the same trapped liquid: a small one and a large one. Push down on the small piston with a small force and you create a certain pressure. That same pressure is transmitted through the liquid to the large piston. But because the large piston has a much bigger area, the same pressure produces a much bigger force (remember, force = pressure × area).

This is the principle of hydraulics. A small effort on the small piston becomes a huge force on the large piston. It is how hydraulic car lifts raise vehicles in a garage, how car brakes turn a gentle press of your foot into a powerful clamping force on the wheels, and how the mighty arms of diggers and bulldozers move tonnes of earth. Liquids are used rather than gases because liquids are almost impossible to squash, so they transmit the pressure instantly and efficiently.

Try it yourself: two pressure experiments

Experiment 1 — Pressure increases with depth. Take a tall plastic bottle and, with adult help, carefully make three small holes in a vertical line: one near the top, one in the middle, one near the bottom. Cover them with tape, fill the bottle with water, then peel off the tape over a sink. Watch the streams: the water from the bottom hole shoots out furthest, because the pressure is greatest there. The top stream is weakest. This proves pressure rises with depth.

Experiment 2 — Air pressure holds water in. Fill a glass to the brim with water, place a flat card over the top, hold it in place, and turn the glass upside down over a sink. Let go of the card. The card stays put and the water does not fall out! Atmospheric pressure pushing up on the card is greater than the weight of the water pushing down, so the air holds the water in.

Stay safe: make holes with adult supervision, work over a sink or outdoors, and clean up any spilled water immediately so no one slips.

Summary

Pressure is force divided by area, measured in pascals. In fluids — both liquids and gases — pressure increases with depth because of the weight of the fluid above, and at any point it pushes equally in all directions. This upward push gives rise to buoyancy. Our atmosphere presses on us with about 100,000 Pa at sea level, balanced by the pressure inside us. And Pascal's principle, by transmitting pressure equally through trapped liquids, lets hydraulic machines turn small forces into enormous ones. Pressure is one of the most powerful and practical ideas in all of physics.

To go further, see how the upward push of fluids leads to Floating and Sinking, and connect pressure to the broader idea of energy and forces in Forms of Energy.