Buoyancy is the tendency of an object to float in a fluid, such as air or water. The principle of buoyancy was first discovered by Greek mathematician Archimedes (c. 287–212 B.C. ) and is therefore often called Archimedes' Principle. Legend has it that Archimedes was working on a problem given to him by the king of ancient Syracuse, Hieron II. The king had paid a goldsmith to make him a new crown but suspected that some metal other than gold had been used in the crown. He asked Archimedes to find out if his suspicions were correct—but without destroying the crown.
One day, perhaps while pondering the problem, Archimedes stepped into his bath and noticed the overflow of water. He suddenly realized that the volume of water that had flowed out of the bath had to be equal to the volume of his own body that was immersed. His problem was solved. Later historians claim that Archimedes was so excited with his discovery that he ran naked through the streets of Syracuse shouting "Eureka!" ("I've found it!").
Archimedes began performing experiments with objects in liquids. He immersed the crown and measured the amount of water it displaced. Then he immersed an equal weight of gold in the
water. If the crown were pure gold, it would displace the same amount of water. But the crown displaced more water than the gold, indicating it was made of a mixture of gold and silver, which is a bulkier substance. The king had the deceitful goldsmith executed.
Suppose that you put a block of wood into a container of water. Two competing forces are at work. One force is the downward pressure of the wood on the water. That force is caused by the mass of the wood. The second force is the upward pressure of the water on the block. If the downward pressure of the wood is greater than the upward pressure of the water, the wood sinks. Otherwise, it floats.
The formal statement of Archimedes' Principle is this: the buoyant force acting on an object placed in a fluid is equal to the weight of the fluid displaced by the object. Suppose that the wood block in the example above has a volume of 1 cubic foot. A cubic foot of water weighs about 62.4 pounds. Therefore, water pushes upward on the wooden block with a force of 62.4 pounds.
But a cubic foot of most kinds of wood weighs about 40 to 50 pounds. So water pushes upward more strongly than the wood pushes downward, and the wood floats. If you substituted a block of lead for the wood, the result would be different. A cubic foot of lead weighs about 1,200 pounds. The block of lead pushes downward much more strongly than the water it displaces and it, therefore, will sink.
The principle of buoyancy is used in many forms of transportation. Some sailing ships are made out of materials that are less dense than water and that would, therefore, float under any circumstances. But how can a ship made out of steel float? Steel has a density of 487 pounds per cubic foot, so it would be expected to sink if placed into water.
The reason steel ships float is that they are not constructed of solid pieces of steel. Instead, they consist of hollow shells made of steel. Inside the shell is air, which is much less dense than water or steel. A hollow block of steel and air has an overall density that is less than that of water; therefore, it can float.
Airships such as balloons and dirigibles operate on the same principle. Some material (such as plastic or cloth) is filled with a gas that is less dense than air. The gases most commonly used are hydrogen and helium. The total package of balloon plus gas weighs less than the air it displaces and is, therefore, pushed upward by the air.