Forces Exerted on an Immersed Object

An object is immersed in a fluid, which can be a liquid or a gas. Buoyancy is a net upward force that acts on the object.

The force of pressure on the bottom of the object is greater than that on the top. The top and bottom pressures both increase with the depth in the fluid; their difference is the buoyancy.

Formally, the buoyant force can be defined as the product of the weight of the fluid displaced by the object (Subscript[w, f]), the acceleration due to gravity g, and the object's volume V. In symbols, F=(Subscript[w, f]) g V.

If the buoyancy is less than the weight of the object, the object will sink; otherwise it will rise to the top of the fluid and float. In symbols, the object sinks if (Subscript[w, f])g V<(Subscript[w, o]), where (Subscript[w, o]) is the weight of the object, and rises if (Subscript[w, f])g V>(Subscript[w, o]).

Notice that the object's volume in this example is constant (and therefore so is the volume of the displaced fluid), but you can vary the weight.

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Contributed by: Enrique Zeleny

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