Learning about the physics of the underwater world can help divers to have a more complete understanding of their sport. One essential concept is Archimedes' Principle, which states:
Any object wholly or partially immersed in a fluid will be buoyed up by a force equal to the weight of the fluid displaced. 
Archimedes' Principle in Plain English:
When an object is placed in water (or any other fluid), the water will exert an upward force on the object. The strength of the upward force is equal to the weight of the water displaced by the object.
To visualize this concept, imagine dropping a marble into a full glass of water. Some of the water will be displaced by the marble and will overflow the glass. If the displaced water is weighed, the weight of the water will be equal to the upward force.
Some objects, such as ping pong balls, will float partially above the water. In this case the upward force is equal to the weight of the water displaced by the submerged portion of the object.
How Does Archimedes' Principle Help to Determine an Object's Buoyancy?:
Archimedes' Principle describes the upward forces acting on an object immersed in water. However, an object's weight (a downward force) also affects its buoyancy. To understand an object's buoyancy, it is necessary to consider both the downward and upward forces present, and to determine if they are equal or whether one is greater than the other.
If the downward force on an object is stronger than the upward force, it will sink and is said to be negatively buoyant. If the upward force on an object is stronger than the downward force, the object will float and is said to be positively buoyant. Finally, if the two forces are equal, the object will remain suspended in the water and is said to be neutrally buoyant.
Essential Concepts for Scuba Diving:
In the case of the marble dropped into the water glass, the marble will sink because the weight of the marble (the downward force) is greater than the weight of the water it displaces (the upward force). A ping-pong ball, on the other hand, will float when placed in water.
Archimedes' Principle reveals why the ping pong ball and other air-filled objects tend to float. An air-filled object weighs little but displaces a relatively large amount of water. One example is a boat, which is basically an air-filled shell. Even a metal boat can float, provided that the water it displaces weighs more than it does.
What Does Archimedes' Principle Have to Do With Scuba Diving?:
Archimedes' Principle explains how various factors including a diver's size, weight, and dive gear affect his buoyancy. Here are a few examples of Archimedes' Principle in action:
• Buoyancy Compensators (BCs): In it's simplest form, a BC is an inflatable air cell that a diver carries with him underwater. He inflates and deflates the air cell during the dive to adjust his buoyancy. When the diver inflates his BC, the air cell expands, displacing a greater volume of water, and increasing the upward force on the diver. When the diver deflates his BC, the air cell loses volume, displaces less water, and weakens the upward force on the diver. Underwater, a diver uses his BC to maintain neutral buoyancy. On the surface, a diver inflates his BC almost completely to allow him to float on the surface.
• Weights: The use of lead weights in scuba diving is also justified by Archimedes' Principle. When fully geared up, most divers are positively buoyant on the surface. A scuba diver displaces quite a bit of water! To counteract the upward force, a diver wears lead weights, which are small and heavy; they increase the diver's weight but barely increase his water displacement.
• Wetsuits: A wetsuit increases a diver's water displacement without significantly increasing his weight, which makes the diver more buoyant. Even a thin wetsuit will increase a diver's buoyancy. The thicker his wetsuit, the greater a diver's water displacement, and the greater the upward force on his body will be. Drysuits are bulkier and much more positively buoyant than wetsuits.
• Tanks: Aluminum tanks also have an interesting affect on a diver's buoyancy. When full, a standard 80-cubic-foot aluminum tank (Al 80) is negatively buoyant. However, the shape and volume of an Al 80 is such that when the tank is empty, its water displacement is greater than its weight (aluminum is very lightweight). As compressed air is breathed from a full tank, the tank becomes lighter and lighter, until it eventually becomes positively buoyant. A diver must weight himself to counteract the buoyancy of the aluminum tank at the end of a dive, which means he will begin the dive slightly overweighted. He must inflate his BC to compensate for this negative buoyancy when he starts the dive, then gradually release air from the BC throughout the dive to maintain neutral buoyancy.
The Take-Home Message About Archimedes' Principle and Scuba Diving:
Archimedes' Principle states that the more water a diver displaces, the greater the upward force on his body will be. A diver's final buoyancy is determined by the combination of upward forces from water displacement and a downward forces from his weight. Dive gear, including weights and BCs can be used increase and decrease a these two forces, and to help a diver to control his buoyancy underwater.
 Ed. Joiner, James T, "NOAA Diving Manual for Science and Technology 4th Edition" pp 2-6 - 2-7. © 2001 US Department of Commerce, National Oceanic and Atmoshperic Association. Best Publishing Company.