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Hydrostatic weighing, also referred to as underwater weighing, hydrostatic body composition analysis and hydrodensitometry, is a technique for measuring the density of a living person's body. It is a direct application of Archimedes' principle, that an object displaces its own volume of water.
Archimedes' principle states that the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially, is equal to the weight of the fluid that the body displaces. [1] Archimedes' principle is a law of physics fundamental to fluid mechanics. It was formulated by Archimedes of Syracuse. [2]
The hydrometer makes use of Archimedes' principle: a solid suspended in a fluid is buoyed by a force equal to the weight of the fluid displaced by the submerged part of the suspended solid. The lower the density of the fluid, the deeper a hydrometer of a given weight sinks; the stem is calibrated to give a numerical reading.
The concept of Archimedes' principle is that an object immersed in a fluid is buoyed up by a force equal to the weight of the fluid displaced by the object. [2] The weight of the displaced fluid can be found mathematically. The mass of the displaced fluid can be expressed in terms of the density and its volume, m = ρV.
ρ a is the density of the air at the ambient pressure and ρ b is the density of the material of which the bottle is made (usually glass) so that the second term is the mass of air displaced by the glass of the bottle whose weight, by Archimedes Principle must be subtracted. The bottle is filled with air but as that air displaces an equal ...
The density is determined by weighing the sample in air and then in a liquid of known density. Application of Archimedes’ principle leads to the following expression for the measured density of the sample in terms of measured weight, where subscripts “a” and “L” refer to water and liquid, respectively: [5]
Archimedes' investigation of paraboloids was possibly an idealization of the shapes of ships' hulls. Some of the paraboloids float with the base under water and the summit above water, similar to the way that icebergs float. Of Archimedes' works that survive, the second book of On Floating Bodies is considered his most mature work. [6]
The fundamental principles of hydrostatics and dynamics were given by Archimedes in his work On Floating Bodies (Ancient Greek: Περὶ τῶν ὀχουμένων), around 250 BC. In it, Archimedes develops the law of buoyancy, also known as Archimedes' principle .