How does pressure vary with depth in liquids?

Pressure in liquids increases with depth due to the weight of the liquid above exerting a force downwards.

In more detail, pressure is defined as the force exerted per unit area. In the case of liquids, this force is due to the weight of the liquid above a certain point. As you go deeper into a liquid, there is more liquid above you, and therefore more weight. This increased weight exerts a greater force, leading to a higher pressure.

This concept can be understood by imagining a column of liquid. At the top of the column, the pressure is just the atmospheric pressure, as there is no liquid above to exert a force. As you move down the column, the pressure increases because there is more liquid above, and therefore more weight. The pressure at any point in the liquid is given by the equation P = ρgh, where P is the pressure, ρ is the density of the liquid, g is the acceleration due to gravity, and h is the height of the liquid column above the point.

This principle is fundamental to understanding many phenomena in physics and engineering, such as the operation of hydraulic systems and the behaviour of submarines. It's also why deep-sea divers must be careful to avoid 'the bends', a condition caused by the high pressure at depth causing dissolved gases in the blood to form bubbles when the pressure is reduced too quickly.

In summary, the pressure in a liquid increases with depth due to the weight of the liquid above. The increase in pressure is directly proportional to the depth, the density of the liquid, and the acceleration due to gravity.