Law of Urination: all mammals empty their bladders over the same duration

Many urological studies rely upon animal models such as rats and pigs whose urination physics and correlation to humans are poorly understood. Here we elucidate the hydrodynamics of urination across five orders of magnitude in animal mass. Using high-speed videography and flow-rate measurement at Zoo Atlanta, we discover the “Law of Urination,” which states animals empty their bladders over nearly constant duration of 21 ± 13 seconds. This feat is made possible by larger animals having longer urethras, thus higher gravitational force and flow speed. Smaller mammals are challenged during urination due to high viscous and surface tension forces that limit their urine to single drops. Our findings reveal the urethra constitutes as a flow-enhancing device, enabling the urinary system to be scaled up without compromising its function. This study may help in the diagnosis of urinary problems in animals and in inspiring the design of scalable hydrodynamic systems based on those in nature. Significance Statement Animals eject liquid into environment for waste elimination, communication, and defense from predators. These diverse systems all rely on the fundamental principles of fluid mechanics, which have allowed us to make predictions about urination across a wide range of mammal sizes. In this study, we report a mathematical model that clarifies misconceptions in urology and unifies the results from over 50 independent urological and anatomical studies. The theoretical framework can be extended to study fluid ejection from animals, a topic which has received little attention.