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Is there a mammalian ‘law of urination’?

An elephant is able to empty its huge bladder in about the same time as smaller mammals.

Here’s some research that’s bound to be nominated for an Ig Nobel prize next year:

Researchers at the Georgia Institute of Technology report that a variety of different-sized mammals, such as dogs, goats, cows and elephants, seem to take about the same amount of time — an average of 21 seconds — to urinate.

That’s right. It didn’t matter whether an animal was expelling three ounces or 25 gallons of urine. It took each creature a remarkably similar number of seconds to get the job done.

The researchers have dubbed their discovery the “Law of Urination.”

Who says science (and math) isn’t fun?

The research also has a serious purpose, however. The authors of the research say their findings may help with the diagnosis of urinary problems in elephants and other large mammals.

Based on a mathematical model

As New Scientist reporter Jacob Aron reports, the researchers used video they took themselves at the Zoo Atlanta and other footage they gathered from YouTube to time how long it took each mammal to relieve itself. They then combined that information with data on the mass, urethra size and bladder pressure of each mammal species to create, says Aron, “a mathematical model of urinary systems to show why mammals take the same time to empty their bladder, despite the difference in bladder size.”

The model revealed that the size of an animal’s urethra was particularly important, as it gave urine time to pick up speed, increasing its flow rate. The result: An elephant is able to empty its huge bladder in about the same time as smaller mammals.

“Medium-sized animals like dogs and goats have shorter urethras, so get less of a gravitational boost: their flow is slower,” adds Aron. “In addition, they have smaller bladders. The result of both effects is that they empty their bladders in roughly the same time as elephants.”

The model also found that an animal’s overall mass has only a slight influence on urination time.

“[The researchers’] law of urination says that the time a mammal takes to empty a full bladder is proportional to the animal’s mass raised to the power of a sixth, meaning even very large changes in mass have little effect on the time,” Aron explains.

But, as he also points out, “there are limits to this scaling. Gravity only plays a small role in the urination of very small mammals like rats and bats, which urinate in under a second. Instead, viscosity and surface tension dominate, which explains why their urine is released as a stream of individual drops rather than the continuous jet seen in larger mammals.”

Caveats, caveats

Yes, yes, there are many limitations to this quirky study. Only a few animals were studied, and I’m not sure about the accuracy of time measurements taken off somebody else’s YouTube videos.

More important, the researchers report a standard deviation (how much the urination timing varied among the animals) of 13 seconds. That seems kind of large to me.

In addition, the study has yet to be published in a peer-reviewed journal. That’s usually a reason for me not to write about a study. But, hey, unlike with many other unpublished studies, there’s nothing in these findings that will encourage people to go out and change their behavior or try a new medical product. Nor do the findings promise a cure for anything.

If you know a teenager, though, this study might just perk up his or her interest in science.

You’ll find a preliminary abstract of the study published here. The research team has also put together an amusing video that accompanies the study.

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