Many urological studies rely on models of animals, such as rats and pigs, but their relation to the human urinary system is poorly understood. Here, we elucidate the hydrodynamics of urination across five orders of magnitude in body mass. Using high-speed videography and flow-rate measurement obtained at Zoo Atlanta, we discover that all mammals above 3 kg in weight empty their bladders over nearly constant duration of 21 ± 13 s. This feat is possible, because larger animals have longer urethras and thus, higher gravitational force and higher flow speed. Smaller mammals are challenged during urination by high viscous and capillary forces that limit their urine to single drops. Our findings reveal that the urethra is a flow-enhancing device, enabling the urinary system to be scaled up by a factor of 3,600 in volume without compromising its function. This study may help to diagnose urinary problems in animals as well as inspire the design of scalable hydrodynamic systems based on those in nature.urology | allometry | scaling | Bernoulli's principle M edical and veterinary urology often relies on simple, noninvasive methods to characterize the health of the urinary system (1, 2). One of the most easily measured characteristics of the urinary system is its flow rate (3), changes in which may be used to diagnose urinary problems. The expanding prostates of aging males may constrict the urethra, decreasing urine flow rate (4). Obesity may increase abdominal pressure, causing incontinence (5). Studies of these ailments and others often involve animal subjects of a range of sizes (6). A study of urination in zero gravity involved a rat suspended on two legs for long periods of time (7), whereas other studies involve mice (8), dogs (1), and pigs (9). Despite the wide range of animals used in urological studies, the consequences of body size on urination remain poorly understood.The bladder serves a number of functions, as reviewed by Bentley (10). In desert animals, the bladder stores water to be retrieved at a time of need. In mammals, the bladder acts as a waterproof reservoir to be emptied at a time of convenience. This control of urine enables animals to keep their homes sanitary and themselves inconspicuous to predators. Stored urine may even be used in defense, which one knows from handling rodents and pets.Several misconceptions in urology have important repercussions in the interpretation of healthy bladder function. For instance, several investigators state that urinary flow is driven entirely by bladder pressure. Consequently, their modeling of the bladder neglects gravitational forces (11-13). Others, such as Martin and Hillman (14), contend that urinary flow is driven by a combination of both gravity and bladder pressure. In this study, we elucidate the hydrodynamics of urination across animal size, showing the effects of gravity increase with increasing body size. ResultsIn Vivo Experiments. We filmed the urination of 16 animals and obtained 28 videos of urination from YouTube, listed in SI Appendix. Movies ...

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 StatementAnimals 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.