Water Pressure at Depth

Finds the pressure of water as density × gravity × depth. Roughly one extra atmosphere piles on for every 10 m of descent. The total pressure including the atmosphere is also shown.

Underwater, the weight of the water overhead becomes pressure. The deeper you go, the more water sits above you and the harder it presses.

P=ρghP = \rho g h

where ρ\rho is the density of the liquid, gg is gravity and hh the depth.

Example

Find the pressure 10 m down, taking water at 1000 kg/m³.

P=1000×9.8×10=98000 Pa=98 kPaP = 1000 \times 9.8 \times 10 = 98000\ \text{Pa} = 98\ \text{kPa}

That is the water alone. The atmosphere still presses on the surface with 101.3 kPa, so the total is

98+101.3=199.3 kPa2 atmospheres98 + 101.3 = 199.3\ \text{kPa} \approx 2\ \text{atmospheres}

Ten metres down, the pressure on your body has doubled. Every further 10 m adds another atmosphere.

Why divers must never hold their breath

At 10 m the pressure is doubled, and by Boyle's law the air in your lungs is squeezed to half its volume.

Now reverse it. Fill your lungs at 10 m, hold your breath and swim up. The pressure halves, and the air tries to double in volume. The lungs tear. This is why every scuba course hammers home the rule: never hold your breath on the way up.

Depth is all that matters

Neither the shape of the container nor the amount of water changes anything.

The water in a thin straw and the water in a lake exert the same pressure at the same depth. Only the height of the column above you counts; how far the water spreads sideways is irrelevant. This is the road to Pascal's principle.

It is also why a dam thickens towards its base. The thickness is dictated by how deep the reservoir is, not by how wide.