# Principle of Buoyancy

The principle of buoyancy is called Archimedes' Principle, since it was discovered by this Greek mathematician in the third century B.C. The principle states that the buoyant force acting on an object placed in 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 the volume of the object. The weight of that volume of displaced fluid is the buoyant force acting on the object.

Fluids such as water or air exert pressure in all directions and 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 weight per unit of 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. Fresh water has a density of The molecular structure of water begins to expand once it cools beyond 39.4°F (4°C) and continues to expand until it becomes ice. For this reason, ice is less dense than water, floats on the surface, and retards further cooling of deeper water, which accounts for the survival of freshwater plant and animal life through the winter. Illustration by Hans & Cassidy. Courtesy of Gale Group. 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 boat's 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.

Richard A. Jeryan