buoyancy - Forces and equilibrium, Archimedes' principle, Density

The upward thrust on an object immersed in liquid or gas, equal to the weight of the displaced fluid. The human body is more buoyant in salt water than in fresh water, as the former is 3% denser.

In physics, buoyancy is the upward force on an object arising from the displacement of the fluid (i.e., a liquid or a gas) in which it is fully or partially immersed.

Forces and equilibrium

Buoyancy provides an upward force on the object. (Displacement is the term used for the weight of the displaced fluid and, thus, is an equivalent term to buoyancy.) The buoyancy of an object depends, therefore, only upon two factors: the object's volume, and the density of the surrounding fluid.

It should go without saying that if the buoyancy of an (unrestrained and unpowered) object exceeds its weight, it will tend to rise. And an object whose weight exceeds its buoyancy will tend to sink. The density of water is essentially constant: As a submarine expels water from its buoyancy tanks (by pumping them full of air) it rises because its buoyancy stays the same (because volume of water it displaces stays the same) while its weight is decreased.

As a floating object rises or falls the forces external to it change and, as all objects are compressible to some extent or another, so will the object's volume. Buoyancy depends on volume and so an object's buoyancy reduces if it is compressed and increases if it expands.

If an object's compressibility is less than that of the surrounding fluid, it is in stable equilibrium and will, indeed, remain at rest, but if its compressibility is greater, its equilibrium is unstable, and it will rise and expand on the slightest upward perturbation, or fall and compress on the slightest downward perturbation. Buoyancy depends upon the object's volume and the weight of the displaced fluid. Volume has decreased so the the weight displaced has decreased which means a decrease in buoyancy and the submarine tends to sink further. The balloon's buoyancy reduces because the weight of the displaced air is reduced.

Archimedes' principle

It was the ancient Greek, Archimedes of Syracuse, who first discovered the law of buoyancy, sometimes called Archimedes's principle:

The buoyant force is equal to the weight of the displaced fluid.

The weight of the displaced fluid is directly proportional to the volume of the displaced fluid (specifically if the surrounding fluid is of uniform density).

The density of the immersed object relative to the density of the fluid is easily calculated without measuring any volumes:

Density

If the weight of an object is less than the weight of the fluid the object would displace if it was fully submerged, then the object has an average density less than the fluid and has a buoyancy greater than its weight. If the fluid has a surface, such as water in a lake or the sea, the object will float at a level so it displaces the same weight of fluid as the weight of the object.

If the object has exactly the same density as the liquid, then it's buoyancy equals its weight.

An object with a higher average density than the fluid has less buoyancy than weight and it will sink.