This approach is simple however, the proof for arbitrarily shaped objects is more involved as stated above, and it works only for objects that are completely surrounded by fluid. In this approach, an object of simple geometry such as a rectangular or cylindrical block is considered and the net fluid force due to the difference of hydrostatic pressure at the top and the bottom of the block is calculated.
The second approach is based on the variation of hydrostatic pressure This argument applies to any object of any shape regardless of its position in the container. Therefore, the buoyant force is equal to the weight of the fluid displaced.
More specifically, the net fluid force on an arbitrarily shaped object would be the same as that on an equal volume of the fluid which was in equilibrium before it was displaced by the object. One is based on the plausible argument that if the principle were not true, the subvolume of a fluid displaced by an object would not be in equilibrium. This approach applies to objects of any shape however, it has the limitation that the object must be completely surrounded by the fluid and that it should not be in contact with the container.Īlternatively, there are two simpler derivations of the principle. In this method, the buoyant force is set equal to the negative of the gradient of the potential energy during an infinitesimal virtual displacement of the submerged object. It is therefore the objective of this article to derive the principle from a different point of view and answer some of the questions associated with the principle that have not been settled in the literature.Ī rigorous derivation of Archimedes’ principle involves the concept of virtual work. For instance, debates are still going on regarding the interpretation of the principle when an object rests on the bottom of a fluid-filled container, where it experiences a net downward force by the fluid. Thus, a boulder hanging from a spring or dial scale can be lowered into a large volume of water, such as a pond or a lake, and from the change of the reading of the scale, its volume can be determined.Įven though Archimedes’ principle is over 2200 years old and despite its importance in hydrostatics, there are still some questions about it that have not yet been fully answered in the literature. As the object is lowered into water, the reading of the scale decreases by an amount equal to the mass of the displaced water. Alternatively, the object can be hung above water from a scale. The reading of the scale will increase by the mass of the displaced water (assuming that the scale measures mass), from which the volume of the object can be determined. The object is then hung from a string above the water, and slowly lowered into it until it is completely submerged, but without touching the bottom of the container (if the object is less dense than water, it can be pushed under water). A container partially filled with water is placed on a scale and the reading of the scale is recorded. The problem, however, can be resolved by taking advantage of Archimedes’ principle. In addition, this method certainly cannot be used to measure the volume of a large object such as a boulder. This method, however, requires that the diameter of the cylinder be at least as large as the diameter of the object, which reduces the accuracy of the measurement. The increase in the level of water inside the cylinder is simply equal to the volume of the object. The object is then slowly lowered into the cylinder until it becomes completely submerged.
The simplest method is to use a graduated cylinder filled with water to a certain level. One of the applications of Archimedes’ principle is in measurement of density of an irregularly shaped object. The principle of isostasy, for example, which states that Earth’s crust is in floating equilibrium with the denser mantle below, is simply based on Archimedes’ principle. This principle, which is perhaps the most fundamental law in hydrostatics, explains many natural phenomena from both qualitative and quantitative points of view. Basically the principle states an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid that it displaces. Īrchimedes’ principle is one of the most essential laws of physics and fluid mechanics. More specifically, in the last two decade or so, more than a dozen papers have been published in different journals, ranging from pedagogical points of view to scrutinizing the original statements made by Archimedes. Although the law of buoyancy was discovered by Archimedes over 2200 years ago, even today from time to time new articles appear in the literature inspecting its various aspects.