Hydrostatic weighing


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.

Method

The procedure is based on Archimedes' principle, 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, it follows that the volume of the block is 1 liter and the density 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 but it would now displace 2 liters of water so its immersed weight would be only 1 kilogram.
In either of the examples above, the correct density can be calculated by the following equation:
Where: Db = Density of the body, Ma = "Mass in air", Mw = "Mass in water", Dw = Density of water, RV = Residual volume.
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 = 0.033 X Ht. + 0.022 X Age - 1.232
Metric: RV-Est = 1.310 X Ht. + 0.022 X Age - 1.232
Inches: RV-Est = 0.046 X Ht. + 0.016 X Age - 2.003
Metric: RV-Est = 1.812 X Ht. + 0.016 X Age - 2.003

Residual volume may also be estimated as a proportion of vital capacity.

Application

Once body density has been calculated from the data obtained by hydrostatic/underwater weighing, body composition 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 : Fat % = ×100
Brozek et al. : Fat % = ×100