View source for Hydrostatic weighing

{{Short description|Technique for measuring the density of a living person's body}}

'''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 [[Albert R. Behnke|Behnke]], Feen and Welham as means to later quantify the relation between specific gravity and the fat content,<ref>{{cite journal | doi = 10.1002/j.1550-8528.1995.tb00152.x | journal = JAMA (reprinted in Obesity Research) | year = 1942 | author1 = Behnke AR | author2 = Feen BG | author3 = Welham WC | pages = 495-498 | volume = 118 | title = The Specific Gravity of Healthy Men}}</ref> 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&nbsp;°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&nbsp;°C).

In either of the examples above, the correct density can be calculated by the following equation:<ref>{{cite book |last1=McArdle |first1=William D |last2=Katch |first2=Frank I |last3=Katch |first3=Victor L |title=Exercise Physiology: Energy, Nutrition, and Human Performance (7th Edition)|publisher=Lippincott Williams & Wilkins |year=2010 |isbn=0-7817-4990-5 | page = 741}}</ref>

:<math>D_b = \frac{M_a}{\frac{M_a - M_w}{D_w} - RV} </math>

Where:  
*{{mvar|D{{sub|b}}}} = Density of the body;
*{{mvar|M{{sub|a}}}} = "Mass in air" (i.e. dry weight);
*{{mvar|M{{sub|w}}}} = "Mass in water" (i.e. underwater weight);
*{{mvar|D{{sub|w}}}} = Density of water (based on water temperature);
*{{mvar|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 [[Lung volumes|residual volume]] in the lungs can add error if not measured directly or estimated accurately. [[Lung volumes|Residual volume]] can be measured by gas dilution procedures or estimated from a person's age and height:<ref>{{cite journal | author = Quanjer P.H., Ed. | title = Standardized Lung Function Testing | publisher = European Community for Coal and Steel, Luxembourg | year = 1983 | journal = Bulletin Européen de Physiopathologie Respiratoire | volume = 19 (suppl. 5) | pages = 1-95}}</ref>
* 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.<ref>{{cite journal | journal = European Respiratory Journal | year = 1993 | title = Lung volumes and forced ventilatory flows | doi = 10.1183/09041950.005s1693 | volume = 6 (suppl. 16) | pages = 5-40 | author1 = Ph.H Quanjer | author2 = G.J. Tammeling | author3 = J.E. Cotes | author4= O.F. Pedersen | author5= R. Peslin | author6= J-C. Yernault}}</ref> [[Lung volumes|Residual volume]] may also be estimated as a proportion of [[vital capacity]] (0.24 for men and 0.28 for women).<ref>{{cite journal | author = Wilmore, J. H. | title = The use of actual predicted and constant residual volumes in the assessment of body composition by underwater weighing | journal = Med Sci Sports | year = 1969 | volume = 1 | issue = 2 | pages = 87–90 | doi=10.1249/00005768-196906000-00006| doi-access = free }}</ref>

==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<ref name="siri">{{citation | author = Siri, SE | chapter = Body composition from fluid spaces and density: analysis of methods |veditors= Brozek J, Henschel A | title = Techniques for measuring body composition | location = Washington, DC | publisher = [[United States National Academy of Sciences|National Academy of Sciences]], [[United States National Research Council|National Research Council]] | year = 1961 | pages = 223–34 }}</ref> and Brozek et al.:<ref name="brozek">{{citation | vauthors = Brozek J, Grande F, Anderson JT, Keys A | title = Densitometric Analysis of Body Composition: Revision of some Quantitative Assumptions | journal = Ann. N. Y. Acad. Sci. | volume = 110 | pages = 113–40 | date = September 1963 | pmid = 14062375 | doi = 10.1111/j.1749-6632.1963.tb17079.x | s2cid = 2191337 }}</ref>

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

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

== References ==
{{reflist}}

==See also==
*[[Body composition]]
*[[Composition of the human body]]
*[[Body fat percentage]]

{{DEFAULTSORT:Hydrostatic Weighing}}
[[Category:Anthropometry]]
[[Category:Classification of obesity]]