Floatation and Archimedes' Principle

When a body presses on a surface, the perpendicular force it applies is called thrust. The same thrust spread over a small area presses far harder than over a large area, so we define pressure as thrust divided by area. This is why a sharp knife (tiny area) cuts easily while a wide camel foot (large area) does not sink in sand. In a fluid, pressure also increases with depth, because deeper layers carry the weight of everything above them.

Lift a stone in air, then lift it under water and it feels lighter. The fluid pushes up on any object placed in it; this upward force is the upthrust or buoyant force, and the property of fluids to provide it is called buoyancy. It arises because fluid pressure is greater at the bottom of the object than at the top, so the upward push on the base beats the downward push on the top, leaving a net force upward.

Archimedes found the exact size of the upthrust: when a body is immersed wholly or partly in a fluid, the upthrust on it equals the weight of the fluid it pushes aside (displaces). So apparent loss in weight of the body equals the weight of displaced fluid. Displace a litre of water and the water pushes up with the weight of one litre of water, no matter what the object is made of. This single rule explains floating ships, submarines and the lactometer.

Density is mass per unit volume. Relative density is how heavy a material is compared with water, so it has no unit; the relative density of a solid equals its weight in air divided by its loss of weight in water. Whether a body floats or sinks is decided by density: if the body is denser than the fluid it sinks; if less dense it floats, rising until the part still submerged displaces fluid weighing exactly as much as the whole body. That is the law of floatation, and it is why a steel ship, hollow and full of air, floats while a steel nail sinks.