The Earth's surface is mostly *water* and its atmosphere is an invisible mixture of gases (mostly nitrogen and oxygen) called *air*. *Water* and *air* belong to the group of substances called *fluids* (substances like liquids and gases that flow and take the shape of their containers).

An object placed in a fluid experiences an upward force of the fluid that act against the weight of the object plus the weight of the fluid above th object. This force is called the *buoyant force* and the phenomenon is called *buoyancy*. The great mathematician Archimedes of Samos (born about 287BC) discovered the method for determining the *buoyant force*. This method is known as the *Archimedes Principle*: *the buoyant force on an object is equal to the weight of the fluid displaced by the object*. An object placed in a fluid *floats when its weight is less than or equal to the buoyant force*. This condition for floating is also stated in terms of density: *an object floats in a fluid if the density of the object is less than the density of the fluid*. If the weight of a submerged object is exactly equal to the *buoyant force* (weight of the volume of fluid displaced by the object), the object will float at a constant depth. The *buoyant force* plays an important role in the motion of objects in fluids. For example, the volume of the gas-filled bladder of most fishes changes inorder to adjust to the *buoyant force* at various depths. Similarly, submerged submarines take on or discharge sea water to adjust to the *buoyant force* at various depths. The hot-air balloon pilot matches the buoyant force of air by adjusting the weight of the hot-air balloon.

The *fluid*, the *object* placed in the fluid, the weight of the volume of fluid displaced by the object and the *buoyant force* are all Pj Problems. Therefore, *buoyancy* is an expression of Pj Problems.

## For Knowledge Sake, One Code (S_{i}P_{j}A_{jk}) For All Knowledge
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