Mammals need a way to excrete extra fluids and the waste products of metabolism. But they also have to do it over a massive range in body sizes, from a 3 kg cat to a 5000 kg elephant. How do they use physics to make sure they can all pee in a reasonable amount of time?

The law of urination is an example of allometry, the study of the relationship of body size to any number of variables, including body shape, anatomy, physiology, or behavior. In this study, we examined how quickly animals can release urine, despite being a factor of 1000 in size. The wide range of animal body sizes is one reason animals look and move so differently, from sperm to sperm whales.

Understanding urination required us to use laws from fluid mechanics, the study of the motion and forces of gases and liquids, like air and water. Fluid mechanics makes sports exciting, like softball, soccer, and surfing. Phenomena like turbulence, the inherent unpredictability of fast fluid flows, can influence weather and airplane travel. Ideas from fluid mechanics can even be used to model the motion of ants or cars in traffic.

If you want to go into the equations that dictate Toricelli’s law, Hu has written another lesson for MIT Blossoms. Here is an hour of activities interspersed with lecture. A similar style lesson goes over how mosquitoes fly in the rain.

If the physics of animal motion interest you, this is just the beginning. Learn how snakes can fly, ants can link their bodies to build waterproof rafts, and how robots can be designed after jellyfish, water striders, and cockroaches. This field is called comparative biomechanics, and David Hu has a book on the subject with Princeton University Press.

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