Pressure in fluids

Stand at the bottom of a column of water and every layer above you is resting on the layer below. Each one adds its weight, so the pressure builds steadily with depth: P = P₀ + ρgh, where P₀ is whatever presses on the surface — usually the atmosphere. Ten metres of water adds roughly one extra atmosphere, which is why divers' ears complain so quickly.

Look at what is in that formula and, more tellingly, what is not. Depth, density and gravity appear. The width of the vessel, its shape and the total volume of liquid it holds do not. A thin tube and a wide tank filled to the same level have exactly the same pressure at the bottom, which strikes most people as wrong the first time they meet it — the "hydrostatic paradox". The resolution is that pressure is force per unit area: the wide tank holds more water but spreads it over proportionally more base.

The second thing worth unlearning is direction. Pressure originates in weight, so it is tempting to think of it as a downward push. In a fluid at rest it acts equally in every direction at any given point — up, down and sideways alike. That is why a submarine hull is squeezed from all sides, why a dam must be built thicker at the base than at the top, and why liquid pushes outwards hard enough to burst a container that has no lid at all.