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# Buoyancy, principle of

The principle of buoyancy is also called Archimedes principle, as it was discovered by this Greek mathematician in the third century BC. The principle states that the buoyant force acting on an object immersed in or floating on a fluid is equal to the weight of the fluid displaced by the object. An object completely immersed in a fluid (liquid or gas) displaces a volume of fluid exactly equal to its own volume; a floating object displaces only part of its volume. The weight of that volume of displaced fluid is the buoyant force acting on the object. In the case of a floating object, it is exactly equal to the objects weight.

Fluids such as water or air exert pressure in all directions. The amount of pressure depends on the depth of the fluid. The pressure on the bottom of an object immersed in a fluid will be greater than the pressure on the top of the object. The imbalance of pressure acting on the object creates an upward force called the buoyant force. If the buoyant force is greater than the weight of the object, the object will float. If the buoyant force is less than the weight of the object, the object will sink in the fluid.

The density of a fluid is its mass per unit of volume. (If Earth-normal gravity is assumed, units of weight, such as pounds [lb], are often substituted for units of mass, such as kilograms; this is done in the following text, where density is treated as pounds per unit volume.) Liquids and gases exhibit widely different densities. The buoyant force, or the weight of the volume of displaced fluid, will depend on the density of the fluid as well as the displaced volume. Freshwater has a

density of 62.4 lb per cubic foot (pcf), saltwater density is, on average, 64 pcf. Air at sea level has a density of 0.08 pcf and at 10,000 ft (3,050 m), 0.06 pcf. Saltwater is denser than freshwater because of its salt content, and, as a result, a swimmer is more buoyant in the ocean than in a freshwater lake. The density of saltwater depends on its salinity and varies around the world. The molecular structure of water expands when it freezes, therefore, ice is less dense than liquid water. As a result, ice cubes float and lakes freeze from the top down rather than the bottom up.

Steel has a density of 487 pcf, about eight times that of water. Steel boats float, however, because they are hollow and shaped to displace a volume of water that weighs more than the boats weight. Ships are often rated by their displacement. Displacement is measured in units called tons, which are the weight of the water displaced by the ship. As a ship is loaded with cargo, it settles deeper into the water. This displaces an additional volume of water and produces the greater buoyant force required to support the added load. Plimsoll marks are painted onto the hull of cargo ships to indicate the depth to which the ship could be loaded. The different marks refer to fresh and saltwater and to the various seasons where temperature also effect water density.

Fish can alter their buoyancy by changing the volume of their internal swim bladder. Scuba divers can inflate their external buoyancy compensator vest to change its volume. Both of these changes alter the amount of displaced water and, thus, the buoyant force acting on the body. With this control, divers and fish can ascend or descend at will as they observe each other at play.

The principle of buoyancy applies to all fluids, including gases. A blimp is filled with very light helium gas with a density of 0.01 pcf. As a result, the weight of the blimp is less than the weight of the air that it displaces and the blimp will float in air. By dropping ballast or venting helium, the blimp can control its buoyancy and, thus, its altitude. A hot air balloon gets it buoyancy because hot air is less dense than cold air. The density of air at 200°F (93°C) at sea level is 0.06 pcf and serves the same function as the light helium gas in the blimp. Although highly flammable, hydrogen gas is much less dense than helium and was used for lift in dirigibles up until 1937, when the German airship Hindenberg burned and crashed. Recent years have seen a resurgence of interest in the use of buoyancy aircraft in the aerospace industry, due to the ability of airships to hover and lift very large loads with little power output.

Richard A. Jeryan