Duration of urination does not change with body size

Edited by David A. Weitz, Harvard University, Cambridge, MA, and approved May 14, 2014 (received for review February 6, 2014)
June 26, 2014
111 (33) 11932-11937

Significance

Animals eject fluids for waste elimination, communication, and defense from predators. These diverse systems all rely on the fundamental principles of fluid mechanics, which we use to predict urination duration across a wide range of mammals. In this study, we report a mathematical model that clarifies misconceptions in urology and unifies the results from 41 independent urological and anatomical studies. The theoretical framework presented may be extended to study fluid ejection from animals, a universal phenomenon that has received little attention.

Abstract

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.

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Acknowledgments

We acknowledge photographer C. Hobbs and our hosts at Zoo Atlanta (R. Snyder), the University of Georgia (L. Elly), the Atlanta Humane Society (A. Lopez), and the animal facilities at Georgia Tech (L. O’Farrell). We thank YouTube contributors, including Alex Cobb, Cole Onyx, demondragon115, drakar2835, ElMachoPrieto83, Ilze Darguže, Joe BERGMANN, Joey Ponticello, krazyboy35, laupuihang, MegaTobi89, Mixetc, mpwhat, MrTitanReign, relacsed, RGarrido121, ronshausen63, Sandro Puelles, Silvia Lugli, and Tom Holloway. Our funding sources were National Science Foundation Faculty Early Career Development Program (Division of Physics) Grant 1255127 for the modeling and Georgia Tech President's Undergraduate Research Awards for the experiments.

Supporting Information

Appendix (PDF)
Supporting Information
Supporting Information (PDF)
Supporting Information
pnas.1402289111.sm01.mov
pnas.1402289111.sm02.mov
pnas.1402289111.sm03.mov
pnas.1402289111.sm04.mov

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Information & Authors

Information

Published in

Go to Proceedings of the National Academy of Sciences
Go to Proceedings of the National Academy of Sciences
Proceedings of the National Academy of Sciences
Vol. 111 | No. 33
August 19, 2014
PubMed: 24969420

Classifications

Submission history

Published online: June 26, 2014
Published in issue: August 19, 2014

Keywords

  1. urology
  2. allometry
  3. scaling
  4. Bernoulli's principle

Acknowledgments

We acknowledge photographer C. Hobbs and our hosts at Zoo Atlanta (R. Snyder), the University of Georgia (L. Elly), the Atlanta Humane Society (A. Lopez), and the animal facilities at Georgia Tech (L. O’Farrell). We thank YouTube contributors, including Alex Cobb, Cole Onyx, demondragon115, drakar2835, ElMachoPrieto83, Ilze Darguže, Joe BERGMANN, Joey Ponticello, krazyboy35, laupuihang, MegaTobi89, Mixetc, mpwhat, MrTitanReign, relacsed, RGarrido121, ronshausen63, Sandro Puelles, Silvia Lugli, and Tom Holloway. Our funding sources were National Science Foundation Faculty Early Career Development Program (Division of Physics) Grant 1255127 for the modeling and Georgia Tech President's Undergraduate Research Awards for the experiments.

Notes

This article is a PNAS Direct Submission.

Authors

Affiliations

Patricia J. Yang
Schools of aMechanical Engineering and
Jonathan Pham
Schools of aMechanical Engineering and
Jerome Choo
Schools of aMechanical Engineering and
Schools of aMechanical Engineering and
Biology, Georgia Institute of Technology, Atlanta, GA 30332

Notes

1
To whom correspondence should be addressed. Email: [email protected].
Author contributions: P.J.Y. and D.L.H. designed research; J.P. and J.C. performed research; P.J.Y. and D.L.H. analyzed data; and P.J.Y. and D.L.H. wrote the paper.

Competing Interests

The authors declare no conflict of interest.

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    Duration of urination does not change with body size
    Proceedings of the National Academy of Sciences
    • Vol. 111
    • No. 33
    • pp. 11907-12270

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