Friday, July 10, 2009

Buoyancy

In the 4th Edition of Intermediate Physics for Medicine and Biology, Russ Hobbie and I added a new section on Buoyancy (Sec. 1.12). After a fairly standard derivation of the buoyant force, we discuss the biological applications:
“The buoyant force on terrestrial animals is very small compared to their weight. Aquatic animals live in water, and their density is almost the same as the surrounding fluid. The buoyant force almost cancels the weight, so the animal is essentially ‘weightless.’ Gravity plays a major role in the life of terrestrial animals, but only a minor role for aquatic animals. Denny (1993) explores the differences between terrestrial and aquatic animals in more detail.”
The reference to Mark Denny is for his excellent book Air and Water. It is the best book I know of to gain insights into how physics impacts physiology, and it influenced many of the revisions to the 4th edition of Intermediate Physics for Medicine and Biology. Below is a sampler from Denny’s Chapter 4, Density: Weight, Pressure, and Fluid Dynamics
“What are the effective densities of plants and animals? Because the density of air is so small, it has little effect on the effective density of terrestrial organisms. For example, a typical density for an animal is 1080 kg m^-3 [this blog does not do math well, “^” means superscript] and in air its effective density is 1079 kg m^-3, a negligible difference. The effective weight in air of a 5000 N cow is 4995 N, for instance. For the same animal immersed in fresh water, however, its effective density is 80 kg m^-3, and its effective weight is 370 N, only 7% of its actual weight. Water obviously has a profound effect on effective density.

Furthermore, because the density of water is so close to the body density of animals, the effective density (and therefore the effective weight) of aqueous organisms is very sensitive to small changes in density of either the body or the surrounding fluid. For example, seawater is only about 2.5% more dense that fresh water, but the effective density of a typical animal (…1075 kg m^-3) is only 50 kg m^-3 in the ocean compared to 75 kg m^-3 in a lake. In this case, a 2.5% increase in water density results in a 33% decrease in effective weight. The same holds true if the density change is in the animal. For instance, if an animal reduces its density from 1075 to 1065 kg [m^-3], its effective weight in air changes by only about 1%. In seawater, the same change in body density incurs a 20% change in effective density (from 50 to 40 kg m^-3) and a concomitant change in effective weight.

Because the effective density of aquatic organisms is so sensitive to minor changes in body density, it is likely to have important biological consequences, and as a result, the density of aquatic organisms has received much attention. Some of the results are discussed below when we explore balloons and swim bladders…”

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