The other "Golden Rule" - David L. Hu

A cat’s bladder can only store a golf ball’s worth of urine.

For humans, it’s a coffee mug and for elephants, a kitchen trash can.

An elephant’s bladder is 400 times the size of a cat’s,

but it doesn’t take an elephant 400 times longer to pee.

So, how does this work?

The answer lies in what scientists call the “Other Golden Rule.”

It applies to mammals, which pee out some of their wastes in a yellowy liquid.

Other classes of animals use different systems and methods to excrete waste.

The Rule describes how urinary organs and forces change with body size,

enabling a range of mammals to achieve similarly rapid relief.

There are two main factors contributing to urination speed:

bladder pressure and gravity.

Bladder pressure is created when mammals contract their muscles

to squeeze urine out.

This pressure is equal to the applied muscular force per unit area but,

since these factors scale proportionally,

bladder pressure doesn’t actually change much depending on body size.

Meanwhile, the effects of gravity do vary across species.

Mammals have a pipe-like organ called the urethra

that transports urine from a higher elevation to a lower one—

specifically, from the bladder down to where urine exits the body.

In doing so, the urethra harnesses the power of Torricelli’s Law,

which states that flow rate increases with container height.

Take these two containers holding the same volume of liquid.

When identically punctured at the bottom,

the vertical container drains nearly twice as fast.

This is because the water’s falling from a greater elevation difference.

By transporting urine from high to low, the urethra has a similar effect.

The urethra is probably not perfectly vertical,

so its length doesn’t tell us exactly how far the urine falls.

However, it’s a good approximation.

The urethra’s diameter also affects flow rate.

When that vertical container’s exit hole has a larger diameter,

the water drains out even faster.

The length and diameter of an animal’s urethra varies

depending on its species and whether it has a penis or vagina.

For example, a female elephant has a meter-long urethra

with a thirty-five millimeter diameter.

A person with a vagina has a urethra that is more than 20 times shorter

and 5 times thinner.

The elephant’s longer, wider urethra is what allows it to urinate

for a comparable amount of time as a human.

Indeed, if an elephant had the urethra of a housecat,

it might take it about 2 hours to drain its bladder.

It’s hypothesized that the Other Golden Rule

is conserved because quicker pees may both reduce vulnerability to predators

and flush out disease-causing pathogens.

But the Rule has limitations.

It’s only been shown to apply to non-aquatic mammals.

And the Rule doesn’t apply to mammals under three kilograms.

They actually pee in droplets, not continuous streams,

because surface tension breaks up their tiny jets of urine.

Even within non-aquatic mammals above three kilograms,

different behaviors disrupt the Other Golden Rule.

Male dogs don’t always fully empty their bladders

and will instead tinkle in short spurts to mark their territory.

Male pandas sometimes pee in handstands, marking bark higher up on trees

in order to broadcast their scent to potential mates.

Handstand pees take longer because urine must work against gravity.

Underwater pees are also lengthier

because the external water pressure counteracts the internal forces

resulting from elevation difference.

Whether it’s with the intensity of a fire hydrant or a squirt gun,

this system swiftly delivers our urine to the outside world.