It is possible to obtain an estimate of body density without directly measuring weight underwater, and without directly measuring water displacement....
A person who neither floats nor sinks with empty lungs in water would have a density of approximately 1 kg/L (the density of water) and an estimated body fat percentage of 43% (Brozek) or 45% (Siri), which would be extremely obese. Persons with a lower body fat percentage would need to hold some kind of flotation device, such as an empty bottle, in order to keep from sinking.
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A light plastic bottle filled with air makes a convenient floater, since the amount of air in it can be adjusted and accurately measured. The plastic occupies only a small volume is about the same density as water so that there is very little error in not correcting for the plastic bottle. The measurement begins with the bottle completely empty. The subject is asked to expel as much as possible from the lungs and use the bottle as a completely submerged floater. Water is allowed to enter the submerged bottle until the person sinks beneath the surface without touching the bottom. The liters of air in the container is equal to the kg of water displaced. v is equal to this kg plus the estimated 1.2 kg of water displaced by the air remaining in the lungs after full exhalation.
Embedded in this description is an explanation of why someone could assist or participate in this procedure without understanding any of the science. In practice, the procedure uses shortcuts and lookup tables that eliminate the need for understanding the concept of displacement and relative density.
But here is the interesting phrase, following the formula:
where ρr is relative density, W is the weight of the body, and Wi is the apparent immersed weight of the body. Absolute density is determined from the relative density, and the density of the liquid. Because the density of water is very close to 1 , when density is computed relative to water, for many purposes it may be treated as absolute density.Note that it is unnecessary to actually weigh a body under water in order to determine its volume, density or, for that matter, its weight under water. Volume can be easily determined by measuring how much water is displaced by submerging that body.