Density and Pressure Explained

Why ships float and ears pop — two simple ratios that govern solids, liquids and gases.

Why does a steel ship float while a steel nail sinks? Why do your ears pop in a plane or deep in a swimming pool? The answers lie in two closely related ideas — density and pressure — that govern the behaviour of solids, liquids and gases alike.

Density: how much matter is packed in

Density measures how much mass is contained in a given volume. It is defined as mass divided by volume:

ρ = mVdensity equals mass divided by volume

A block of lead and a block of foam might be the same size, but the lead contains far more mass in that volume, so it is much denser. Density is what determines whether an object floats: anything less dense than water floats on it, while anything denser sinks. A steel ship floats because its overall shape encloses a great deal of air, making its average density less than water's, even though steel itself is dense.

Try it in the calculatorCompute density with rho = m/V in the calculator.

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Pressure: force spread over area

Pressure is the force pressing on a surface divided by the area over which it acts:

P = FApressure equals force divided by area

The same force concentrated on a small area produces high pressure; spread over a large area it produces low pressure. This is why a sharp knife cuts easily — its thin edge concentrates your push into a tiny area — and why snowshoes stop you sinking, by spreading your weight over a large area. Pressure is measured in pascals, one pascal being one newton per square metre.

Pressure in fluids

In a liquid or gas, pressure increases with depth, because deeper layers must support the weight of everything above them. This is why your ears hurt at the bottom of a deep pool and why dam walls are built thicker at the base. The pressure in a fluid pushes equally in all directions at a given depth, a fact that underlies hydraulics — the technology that lets a small force on a small piston lift a heavy car through a larger one.

Atmospheric pressure: we live at the bottom of an ocean of air. The atmosphere presses on every surface at about 101,000 pascals at sea level — roughly the weight of a small car spread over every square metre — yet we don't feel it because it pushes equally from all sides and our bodies push back.

Buoyancy: the upward push

Because fluid pressure grows with depth, the bottom of a submerged object feels more upward pressure than its top feels downward. The difference is a net upward force called buoyancy, equal to the weight of the fluid the object displaces — a result known as Archimedes' principle. If that buoyant force exceeds the object's weight, it floats; if not, it sinks. This single idea explains ships, submarines, hot-air balloons and why you feel lighter in water.

A worked example

A block has a mass of 600 grams and a volume of 200 cubic centimetres. Its density is mass divided by volume: 600 divided by 200, which is 3 grams per cubic centimetre. Since water has a density of 1 gram per cubic centimetre, this block is three times denser than water — so it will sink. Had its density come out below 1, it would have floated.

Why these ideas matter

Density and pressure run through engineering, meteorology, medicine and daily life. They explain weather systems driven by pressure differences, blood pressure in the body, the design of ships and aircraft, and why mountaineers gasp for breath where the air is thin. Two simple ratios — mass over volume, and force over area — carry remarkable explanatory power.

Key takeaways

Density is mass per unit volume; objects less dense than a fluid float in it.
Pressure is force per unit area; small areas concentrate force into high pressure.
Fluid pressure rises with depth and pushes equally in all directions.
Buoyancy equals the weight of displaced fluid, explaining floating and sinking.