Deepa

Meet Deepa, a diver who feels the water hug a little harder with every metre down.

Pressure in a still fluid comes from the weight of the fluid above. Each layer of water must hold up all the layers above it, so pressure rises steadily with depth: p = p₀ + ρgh, where p₀ is the pressure at the surface. The shape of the container does not matter, only the depth.

For fresh water, ρ = 1000 kg/m³ and g = 9.80665 m/s². Ten metres down adds 1000 × 9.80665 × 10 ≈ 98,100 Pa, about 98 kPa, almost one extra atmosphere. In seawater, at about 1025 kg/m³, the same depth adds about 100 kPa.

Divers, submarine designers and dam engineers all use this rule. Dams are built thicker at the bottom because the water pushes hardest there.

The formula assumes the liquid's density stays constant. Water is only slightly compressible, so this is very good for most depths, but in the deepest ocean trenches the small increase in density and changes in temperature need correcting for.