Authors: Patricia J. Yang, Jonathan C. Pham, Jerome Choo, and David L. Hu
Schools of Mechanical Engineering, Biomedical Engineering, Biology and Physics, Georgie Institute of Technology (USA)
The urinary system evolved to eject fluids from the body quickly and efficiently. Despite a long history of successful urology treatments in humans and animals, the physics of urination has received comparatively little attention. In this combined experimental and theoretical investigation, we elucidate the hydrodynamics of urination across five orders of magnitude in animal mass, from mice to elephants. Using high-speed fluid dynamics videos and flow-rate measurement at Zoo Atlanta, we discover the "Law of Urination", which states animals empty their bladders over nearly constant duration of average 21 seconds (standard deviation 13 seconds), despite a difference in bladder volume from 100 mL to 100 L. This feat is made possible by the increasing urethra length of large animals which amplifies gravitational force and flow rate. We also demonstrate the challenges faced by the urinary system for rodents and other small mammals for which urine flow is limited to single drops. Our findings reveal the urethra evolved 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.