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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 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.
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.
A Cartesian diver or Cartesian devil is a classic science experiment which demonstrates the principle of buoyancy (Archimedes' principle) and the ideal gas law.The first written description of this device is provided by Raffaello Magiotti, in his book Renitenza certissima dell'acqua alla compressione (Very firm resistance of water to compression) published in 1648.
Ultrasonic density meters work on various principles to calculate the density. One of the methods is the transit-time principle (also known as the time of flight principle). With this technique, a sensor is typically installed in the pipe, which has an ultrasonic transmitter and an ultrasonic receiver in one construction.
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]
The ratio of the volume of a sphere to the volume of its circumscribed cylinder is 2:3, as was determined by Archimedes. The principal formulae derived in On the Sphere and Cylinder are those mentioned above: the surface area of the sphere, the volume of the contained ball, and surface area and volume of the cylinder.