Hydrostatic weighing, also referred to as underwater weighing, hydrostatic body composition analysis and hydrodensitometry, is a technique for measuring the

density Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' can also be used. Mathematical ...

of a living person's body. It is a direct application of

Archimedes' principle Archimedes' principle (also spelled Archimedes's 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. Archimede ...

, that an object displaces its own volume of water.

Method

The procedure is based on

, which states that: ''The buoyant force which water exerts on an immersed object is equal to the weight of water that the object displaces.'' Example 1: If a block of solid stone weighs 3 kilograms on dry land and 2 kilogram when immersed in a tub of water, then it has displaced 1 kilogram of water. Since 1 liter of water weighs 1 kilogram (at 4 °C), it follows that the volume of the block is 1 liter and the density (mass/volume) of the stone is 3 kilograms/liter. Example 2: Consider a larger block of the same stone material as in Example 1 but with a 1-liter cavity inside of the same amount of stone. The block would still weigh 3 kilograms on dry land (ignoring the weight of air in the cavity) but it would now displace 2 liters of water so its immersed weight would be only 1 kilogram (at 4 °C). In either of the examples above, the correct density can be calculated by the following equation: :

\mbox = \frac

Where: Db = Density of the body, Ma = "Mass in air" (i.e. dry weight), Mw = "Mass in water" (i.e. underwater weight), Dw = Density of water (based on water temperature), RV = Residual volume (the unfilled space enclosed by the body- e.g. volume of air in the lungs + respiratory passages after a maximum exhalation). The residual volume in the lungs can add error if not measured directly or estimated accurately. Residual volume can be measured by gas dilution procedures or estimated from a person's age and height: * Inches: RV-Est(Men) = 0.033 X Ht. (inches) + 0.022 X Age (yrs.) - 1.232 * Metric: RV-Est(Men) = 1.310 X Ht. (meters) + 0.022 X Age (yrs.) - 1.232 * Inches: RV-Est(Women) = 0.046 X Ht. (inches) + 0.016 X Age (yrs.) - 2.003 * Metric: RV-Est(Women) = 1.812 X Ht. (meters) + 0.016 X Age (yrs.) - 2.003 Residual volume may also be estimated as a proportion of

vital capacity Vital capacity (VC) is the maximum amount of air a person can inhale after a maximum exhalation. It is equal to the sum of inspiratory reserve volume, tidal volume, and expiratory reserve volume. It is approximately equal to Forced Vital Capacity ( ...

(0.24 for men and 0.28 for women).

Application

Once body density has been calculated from the data obtained by hydrostatic/underwater weighing,

body composition In physical fitness, body composition is used to describe the percentages of fat, bone, water, and muscle in human bodies. Because muscular tissue takes up less space in the body than fat tissue, body composition, as well as weight, determines ...

can be estimated. The most commonly used equations for estimating the percent of body fat from density are those of Siri and Brozek et al.: Siri (1956): Fat % = .950 /Density - 4.500�100 Brozek et al. (1963): Fat % = .570 /Density - 4.142�100

Method

Application

References

See also