The Archimedes Principle

Archimedes Principle explains the displacement of fluid by an object by reference to the concept of buoyancy. More precisely the fluid weight displaced by an object equals the buoyant force on that object. The linked article Physics Tutorial: Archimedes Principle and Battery Indicators provides details. Here's one:

FB=Wfluid

The force of buoyancy equals the weight of the displaced fluid.

Why Archimedes? Because the ancient Greek genius is credited with the discovery. Archimedes is one of the giant intellects of history whose accomplishments were prolific.

This next link titled Buoyancy: Archimedes Principle makes the following important point (quote in blue):

Using the aluminum as our example, it has a specific gravity of 2.8. Water has a specific gravity of 1.0. This means that a cubic centimeter of water would have a mass of 1.0 grams, while aluminum of the same size would have a mass of 2.8 grams. Since the aluminum cube displaces 1 cubic centimeter of water, it has a buoyancy of 1.0 grams. Since buoyancy is a force and not a mass, it must be converted to the proper units, which when multiplied by the acceleration of gravity (980 cm/s2) gives the units of dynes. That is,

(1.0 grams) (980 cm/s2) = 980 grams cm /s2 or dynes

So our aluminum cube immersed in water would not 'weigh' (2.8 x 980) dynes or 2744 dynes. It would weigh less due to the fact it has a buoyant force of (1 x 980) dynes from the water. So it would weigh (2744-980) dynes or 1764 dynes while immersed in the water.

Indeed there is a need for a proper conversion as buoyancy is a force and units are expressed in dynes.

This next site is my favorite of the group. This linked article has visual aids combined with ample explanations addressing various aspects of buoyancy. Volume is discussed. An example of three objects of equal volume but different weights is cited to illustrate and explain their different behavoir, in response to equal buoyant force, upon release in water. There are equal buoyant forces on objects having the same volume.

An equation can be set up to determine the volume of an object in water. The density of water is known- 1 gram/cm3.

At the same website view this page to study equations related to viscosity and sinking objects.

Archimedes's Principle explains that apparent weight of block x when x is immersed in water is the difference if the weight of the displaced water.

Incidentally, do not presume that whether or not an object floats is dependent on its density being less than water. Surface tension enables a steel needle to float and a steel chip can likewise float. In the case of the chip it floats because it displaces a volume of water that equals its weight.1

The mathematical equation relevant to finding the weight of displaced fluid is:

W = mg and mass can be found by:

m = pV where p is the density of the liquid. Finally,

W = pVg (credit (2) follows below)



References:

1. Physics by Jonathan S. Wolf; Published by Barron's Educational Series, Inc.; copywrite 1996.

2. Ibid.