Underwater Weighing
Underwater (hydrostatic) weighing is done based on Archimedes' Principle. Because body fat is less dense than water, it increases one's buoyancy while the fatfree mass, which has a density greater than water, makes one sink. This is once considered the gold standard, as it is more accurate than other methods such as skinfold measurement but the emergence of newer and more sophisticated methods are now more accurate than this method
Limitations
The largest source of error in underwater weighing is thought to be the determination of residual volume (RV; the amount of air remaining in the lungs following maximal expiration). When RV is estimated rather than measured, the precision of underwater weighing is little better than anthropometric (skinfold) determination.
 Weigh the subject to the nearest 0.1 kg.
 Measure or estimate the subject's RV. If possible, directly measure RV using the diluted helium or oxygen techniques. Otherwise, RV can be estimated by measuring vital capacity (VC) and multiplying it by 0.24 or 0.28 for males and females, respectively.
 VC is the amount of air that can be maximally exhaled. To measure VC, place a noseclip on the subject. Have the subject maximally inhale, place the mouthpiece from the spirometer in his/her mouth, and then maximally exhale. Perform 23 trials and use the highest volume. Also, correct the volume to BTPS by multiplying the volume by the correction factor (see an instructor for this value).
 Tare (zero) the scale in the underwater weighing tank. While seated in the tank, instruct the subject to blow out all the air that he/she can exhale, bend slowly forward until the top of his/her head is underwater, and to remain motionless until the scale has settled and the computer indicates that it has a reading. Have the subject perform 610 trials and average the heaviest 23 readings.
Determination of Body Density
Body Density = dry weight / [((dry weight  wet weight) / water density) RV  0.1]
Note: Units for all weights are in kg and RV is in L. The 0.1 represents an estimated volume (L) of gas in the GI tract.
Estimation of Percent Fat
The two most commonly used equations for estimating percent fat from body density are the Siri (1961) and Brozek (1963) formulae. A limitation to these formulae is that they assume the density of fatfree mass to remain a constant across the population when in fact is varies. Thus, the actual percent fat tend to be slightly higher than the measured percent fat in the lean, muscular individual and the opposite effect in obese individuals.
Siri

Percent Fat = [(495 / Body Density) 450] * 100

Brozek

Percent Fat = [(4.570 / Body Density)  4.142] * 100

http://wwwrohan.sdsu.edu/~ens304l/uww.htm
http://sportsmedicine.about.com/od/fitnessevalandassessment/g/UnderwaterWeigh.htm
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