# 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, pioneered by Behnke, Feen and Welham as means to later quantify the relation between specific gravity and the fat content,[1] 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 (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:[2]

${\displaystyle D_{b}={\frac {M_{a}}{{\frac {M_{a}-M_{w}}{D_{w}}}-RV}}}$

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:[3]

• RV-Est(liters, Men) = 1.310 × Ht. (meters) + 0.022 × Age (yrs., take as 25 for 18-25) − 1.232
• RV-Est(liters, Women) = 1.812 × Ht. (meters) + 0.016 × Age (yrs., take as 25 for 18-25) − 2.003

It is worth noting that these estimates are for adults aged 18-70, have standard deviation of about 0.4 litres and have dependence on ethnicity, environmental factors, etc.[4] Residual volume may also be estimated as a proportion of vital capacity (0.24 for men and 0.28 for women).[5]

## 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[6] and Brozek et al.:[7]

Siri (1956): Fat % = [4.950 /Density - 4.500]×100

Brozek et al. (1963): Fat % = [4.570 /Density - 4.142]×100

## References

1. ^ Behnke AR; Feen BG; Welham WC (1942). "The Specific Gravity of Healthy Men". JAMA (Reprinted in Obesity Research). 118 (3): 495–498. doi:10.1002/j.1550-8528.1995.tb00152.x. PMID 7627779.
2. ^ McArdle, William D; Katch, Frank I; Katch, Victor L (2010). Exercise Physiology: Energy, Nutrition, and Human Performance (7th ed.). Lippincott Williams & Wilkins. p. 741. ISBN 978-0-7817-4990-9.
3. ^ Quanjer P.H., Ed. (1983). "Standardized Lung Function Testing". Bulletin Européen de Physiopathologie Respiratoire. 19 (suppl. 5). European Community for Coal and Steel, Luxembourg: 1–95.
4. ^ Ph.H Quanjer; G.J. Tammeling; J.E. Cotes; O.F. Pedersen; R. Peslin; J-C. Yernault (1993). "Lung volumes and forced ventilatory flows". European Respiratory Journal. 6 (suppl. 16): 5–40. doi:10.1183/09041950.005s1693.
5. ^ Wilmore, J. H. (1969). "The use of actual predicted and constant residual volumes in the assessment of body composition by underwater weighing". Med Sci Sports. 1 (2): 87–90. doi:10.1249/00005768-196906000-00006.
6. ^ Siri, SE (1961), "Body composition from fluid spaces and density: analysis of methods", in Brozek J, Henschel A (eds.), Techniques for measuring body composition, Washington, DC: National Academy of Sciences, National Research Council, pp. 223–34
7. ^ Brozek J, Grande F, Anderson JT, Keys A (September 1963), "Densitometric Analysis of Body Composition: Revision of some Quantitative Assumptions", Ann. N. Y. Acad. Sci., 110 (1): 113–40, Bibcode:1963NYASA.110..113B, doi:10.1111/j.1749-6632.1963.tb17079.x, PMID 14062375, S2CID 2191337