The Buoyant Force

The principle of flotation, or buoyancy, was first developed by the Greek scientist Archimedes who lived from 287 to 212 B.C.  The buoyant force has been known to humankind for ages.  Fish have swim bladders that they can inflate or deflate, allowing them to sink or rise in the water.  Mammals also take advantage of the principle by filling their lungs with air to float and expelling air to sink.  However, Archimedes’ principle of buoyancy provides a way for scientists and engineers to harness the buoyant force and use it for practical purposes.

An object’s buoyancy is basically a comparison of its density to the density of the fluid in which it is immersed.  The density of an object can be determined by examining its effective mass.  When an object is immersed in a fluid, gravity pulls the object downward while the fluid exerts an upward force on it.  This is called the buoyant force of the fluid, and it reduces the weight of the immersed object.  This reduced weight is called the effective, or apparent, mass because a change in weight would equal a change in mass at the surface of the earth.  The apparent loss of mass in the object multiplied by the density of the fluid will give the volume that has been displaced, and this will also be equal to the volume of the object.  The true mass of the object divided by its volume will give the density of the object.  If the density of the fluid is not known, scientists can determine it using an instrument called a variable immersion hydrometer.  A variable immersion hydrometer is a hollow tube with a bulb at one end that can be filled with a substance of known density.  The levels to which the hydrometer sinks when empty and full are compared.  Using Archimedes’ principle of buoyancy, the density of the fluid can be determined.  One way scientists can use this technology is to measure the salinity of water to detect changes in ocean currents.

Another important aspect of the buoyancy principle is that the upward force exerted by the fluid on the submerged object is equal to the total weight of the fluid displaced.  If the effective mass of the object is equal to the weight of the displaced fluid, the object will float just beneath the surface of the fluid.  If the object weighs less than the water it displaces, the object will be pushed up over the surface until the effective mass of the object is equal to the weight of the displaced fluid.  This makes the principle of buoyancy useful in designing ships and submarines.  For example, a vessel that displaces 200 cubic meters of water will have a force of 200,000 kilograms per cubic meter exerted on it, because the density of water is 1000 kilograms per cubic meter.  If the object’s weight is equal to a mass of 100,000 kilograms, there will be a net upward force of 100,000 kilograms per cubic meter.  The vessel will rise to a point where its effective mass is equal to that of the displaced water.  Equilibrium will occur when the vessel is only displacing 100 cubic meters of water, which means that it will rise halfway out of the water.  Adding weight to the vessel, such as water or cargo, will increase its effective mass and cause it to sink.  Archimedes’ principle can be used to figure out how far it will sink, so engineers can determine the maximum load a ship can carry. 

In addition to the variable immersion hydrometer and aquatic vessels like ships and submarines, Archimedes’ principle of buoyancy has led to the development of a variety of technologies that rely on flotation.  One example is the hot air balloon, in which warm air is pumped into or released from a bladder to control altitude.  The Floating Instrument Platform (FLIP) research vessel relies on Archimedes’ principle of buoyancy to study waves.  The vessel is towed into position where it sits parallel to the ocean surface, and flips vertically when its ballast tanks are filled by waves.  The lock system in the Panama Canal also uses this principle.  Some parts of the canal are actually above sea level, requiring ships to travel vertically to cross them.  Engineers used the principle of buoyancy to create a lock system that pumps water in and out of channels, which allows ships to rise or sink to the level of the canal as they pass through it.

Archimedes’ principle of buoyancy has led to a variety of technological advances.  Like electricity, it has always existed, but without anyone to discover the principle many things that people depend on today would not have been possible.