 
Buoyancy is the tendency of an object to float or to rise in a fluid when submerged. This fluid can be either a liquid or a gas.Gravity is a downward force that acts on all objects. When objects are placed in a fluid, the fluid must supply a force equal in magnitude but opposite in direction to the gravitational force for the objects to float. This force is referred to as the buoyant force. Archimedes' principle, the physical law of buoyancy, was discovered by the ancient Greek mathematician and inventor Archimedes, stating that: "Any body completely or partially submerged in a fluid (gas or liquid) at rest, is acted upon by an upward, or buoyant force, the magnitude of which is equal to the weight of the fluid displaced by the body". The weight (a force) of the displaced portion of the fluid is equivalent to the magnitude of the buoyant force. If the weight of an object is less than that of the displaced fluid, the object rises, as in the case of a block of wood that is released beneath the surface of water, or a helium-filled balloon that is let loose in air. An object heavier than the amount of the fluid it displaces, though it sinks when released, has an apparent weight loss equal to the weight of the fluid displaced. The buoyant force always opposes gravity. Fluid pressure increases with depth because of the (gravitational) weight of the fluid above. This increasing pressure applies a force on a submerged object that increases with depth. The result is buoyancy. Extremely heavy objects such as ships can float in water, as long as the objects contain enough pockets of air to make the object's average density less than that of water. Buoyancy is closely tied to density, which is defined as the ratio of the mass of an object to its volume. The density of an object in comparison to the density of water is called its specific gravity. Objects that float when placed in a fluid have a lower specific gravity than the fluid, while objects that sink in a fluid have a higher specific gravity than the fluid. Most buoyant objects are objects that have a relatively large volume and a relatively low density.  Steel sinks in water because it's denser; it displaces less water than its own weight. Steel boats are designed so that they displace a greater amount of water than their weight, which creates buoyancy and lets them float, due to the presence of air-filled compartments that help decrease the ship's average density.
A ship must float level at no greater depth than the design waterline, typically indicated by a Plimsoll line. The Plimsoll line indicates the maximum depth to which the ship can be safely loaded.  Fish are able to sink and rise in water by using a swim bladder. The bladder has flexible walls, and is lined with guanine crystals, which makes it impermeable to gases. By adjusting the gas (air) pressure in the bladder, the fish is able to increase (less gas) or decrease (more gas) its overall density, allowing it to sink or rise.  In similar fashion, submarines have ballast tanks that can be opened to allow sea water to flow in. As water is added, the submarine's mass increases, but since its volume stays the same, the sub's average density increases, causing it to descend.Conversely, by filling those same tanks with compressed air that forces out the water, the sub's mass (and density) decreases, allowing it to rise. Here's the formula for calculating the buoyant force: 
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