Pressure under the sea

Pressure is force per area. At the surface you already live under one atmosphere (1 atm = 101,325 Pa), the weight of the air column above you. Under water you also carry the weight of the water above you, and water is heavy. The absolute pressure at depth z is

P = P₀ + ρ·g·z

where P₀ is the pressure at the surface (1 atm), ρ is the density (about 1,025 kg/m³ for sea water) and g is 9.81 m/s². Put the numbers in: ρ·g is about 10,055 Pa for every metre, so each extra ≈10 m of sea water adds about 1 atm (101,325 ÷ 10,055 = 10.08 m).

That gives easy rules of thumb for absolute pressure:

• 0 m (surface): 1 atm
• 10 m: about 2 atm
• 30 m: about 4 atm
• 1,000 m: about 100 atm
• 10,900 m: about 1,100 atm (about 110 MPa)

These use a constant density. Real sea water is squeezed a little at depth, so the true values are a few percent higher in the deep.

Gas is squeezed more than water. Water is almost incompressible, but a gas can be compressed. Boyle's law says that at constant temperature, pressure times volume stays constant, so V = V₀ × P₀ / P. A balloon at 10 m is under 2 atm, so it shrinks to half its surface volume. At 20 m the pressure is 3 atm and the volume is one third. At 30 m it is one quarter.

A foam cup taken deep shrinks for the same reason. The cup is full of tiny trapped air bubbles, and the pressure squeezes them, so the whole cup contracts to a small hard toy. It is the air, not the foam, that is being squashed.

Two common ideas about pressure are wrong. First, pressure does not only push from above: in a fluid it acts equally in every direction, so a diver is squeezed from all sides. Second, deep-sea fish are not crushed. Their bodies are mostly water, and the pressure inside their cells matches the pressure outside. Trouble starts only for gas spaces, which is why many deep animals have no gas-filled organs (Lesson 8).