Image credit: Dirtyboxface via Flickr (modified) [CC BY 2.0] (source)

The Myth of the Swirling Toilet Bowl Water

Prior to my first visit to Australia, I told a great number of people about my upcoming plans. A typical response was to mention toilet bowls — specifically, the direction that the water swirls when you flush the toilet. Sometimes the response involved a sink or a bathtub, but usually a toilet. Invariably I was told that the direction of the swirl will reverse the moment that I cross the equator. I was amazed at how often this point came up. The people who told me this story were all well-educated. And yet the story is nonsense — it simply isn’t true. Therefore I think of this odd belief as a “popular science myth for the well-educated”. What fascinates me is why this myth has so many believers among the well-educated. What cultural factors have led to this strange disconnect between reality and myth?

I would say that the source of this situation can be summarized by the following two points:

1) There is a genuine scientific principle underlying this belief, but in the popular imagination this principle has been completely misapplied and misconstrued.

2) People misapply and misconstrue the scientific principle because they don’t actually understand the principle. They have simply memorized a “fact” — a completely erroneous fact — without having formulated a reasonable model to explain why this fact could be true.

In other words, if I ask someone to give me a scientific explanation for this supposed phenomenon, then one of two things happens. 1) The person cannot provide an explanation at all, or 2) the person provides an explanation that quickly falls apart when I ask a few follow-up questions. Of course, people can get embarrassed when I do this — but I’m not trying to be cruel. I’m genuinely interested in understanding what causes people to think one way or another with regards to scientific principles. I really want to know what mental models people use to draw deductions regarding the world around them.

If I am not too worried about embarrassing the person I’m talking to, then my initial question is this: “What force acts on the water in the toilet bowl to cause the swirl, and why does the force change direction when you cross the equator?” Some people cannot even begin to offer an explanation — which suggests that they have not internalized any model to explain the supposed behavior. However, most people will provide some sort of explanation, ranging from quite vague to fairly specific, and this indicates that they have indeed formulated a mental model of some sort. These are the interesting cases, because then I want to understand the details of their mental model.

Some people actually know a valid name for the genuine scientific principle — the Coriolis Effect. However, almost no one that I talk to seems to understand the principle behind the Coriolis Effect. They remember the effect itself, but not what causes the effect. (Some people remember that the effect is somehow tied to the rotation of the Earth on its axis — but that’s about as far it gets.) As a result people misconstrue the principle and assume that it applies to toilet bowls. However, if we can teach people what actually causes the Coriolis Effect — in a manner that is easy to remember — then they will have a more solid understanding that is resistant to erroneous myths. And the good news is this — when presented in an appropriate manner, it’s not hard to understand the underlying principle behind the Coriolis Effect.

Before I provide an explanation, I’ll first provide a few intriguing hints.

1) We most often associate the Coriolis Effect with air masses and bodies of water. However, the Coriolis Effect applies to all objects, not just air and water.

2) When objects move away from the equator, their paths tend to curve towards the east. When objects move towards the equator, their paths tend to curve towards the west. (In a moment we’ll see why.) If you combine these two motions within a body of water, then you’ll get a clockwise circulation in the northern hemisphere, and a counterclockwise circulation in the southern hemisphere.

This effect is most easily noted in the major ocean currents. In the Northern Hemisphere, each ocean has a clockwise circulation — called a gyre — while in the Southern Hemisphere, each ocean has a counter-clockwise circulation. The Gulf Stream, for example, is part of the clockwise gyre in the North Atlantic Ocean.

The effect is more complicated when it comes to large air masses. If the Earth were not spinning, then air would travel in a straight line from the center of any high-pressure system to the center of a nearby low-pressure system. But the Coriolis Effect causes this path of travel to curve. In the Northern Hemisphere, the air is deflected to the right as it gets sucked towards the center of the low. Therefore the pathway soon points to the right of the center, instead of directly towards the center. As long as the air continues to get closer to the low, then this is fine. But the air is not allowed to move away from the low. The difference in air pressure is the main driving force here — a much stronger effect than the Coriolis Effect. Therefore the air is forced to curve back to the left, but always aiming a bit to the right of the center of the low. This results in a counter-clockwise spin to any low pressure system in the Northern Hemisphere — including hurricanes. This, of course, is the opposite spin from that of the ocean gyres, which can seem counter-intuitive.

But what causes the paths of objects to curve when they move in a northward or southward direction? The reason for the curvature in the paths is simply inertia — the tendency of a moving object to continue going in a straight line at a constant velocity unless acted upon by an outside force. But this explanation seems paradoxical. How does moving in a straight line result in a curved path? As it turns out, when dealing with objects that are traveling across the surface of a spinning sphere, held down by gravity, it is the “constant velocity” aspect rather than the “straight line” aspect that provides the best explanation.

Imagine an object sitting on the equator. Just for fun, imagine that the object is you, vacationing in a tropical paradise for a week. Meanwhile the earth continues to spin on its axis, one complete turn every day. The circumference of the earth is nearly 25,000 miles, so during each day of your vacation you and your paradise will make a 24,902 mile journey around the spinning earth — all in just 24 hours. In other words, you and your hotel and your sandy beach are all traveling around the earth at more than 1000 miles per hour. (The actual figure is approximately 1038 miles per hour.)

Now imagine your friend Martha who is not vacationing at this time, and therefore is spending the week in her hometown of Minneapolis, Minnesota. Her location is also spinning around the earth, but traveling in a much smaller circle than yours. That’s because a circle around the earth, along a specific latitude line, will be smaller towards the poles and larger towards the equator. However, it still takes exactly one day to do a complete rotation, regardless of the latitude. So instead of making a journey of 24,902 miles in 24 hours, she only travels 17,608 miles in 24 hours. Therefore, instead of traveling at 1038 miles per hour, Martha is traveling at only 734 miles per hour — a full 300 miles per hour slower than you. Now imagine an Arctic explorer vacationing at the North Pole. As he relaxes in his lawn chair on the ice field, he’s going 0 miles per hour, although he is very slowly rotating. In a 24-hour period, he will rotate through a complete 360 degree circle.

By the way, do you know what direction you and Martha are traveling — east or west? Here’s the easy way to remember. Everything in the sky — the sun, the moon, and the stars — rises in the east and sets in the west. Therefore the surface of the earth must be rotating towards the east, which would constantly expose new sky in the east. Consequently your vacation paradise is rotating towards the east at 1038 miles per hour, while Martha’s hometown is rotating to the east at 734 miles per hour.

Suppose that Martha is a bit jealous that you are vacationing in a tropical paradise on the equator, so she decides to have a little adventure of her own. On Saturday she goes for a ride in a hot air balloon — the first time that she’s ever done this. She’s having a wonderful time looking down on the green Minnesota countryside when a freak storm suddenly comes up from the south, blowing Martha and her balloon 200 miles to the north. But at this new latitude, the ground beneath her is rotating to the east at only 695 miles per hour, compared to 734 miles per hour in Minneapolis. Because of inertia, Martha and her balloon continue to travel eastward at 734 miles per hour. So even though the storm came directly out of the south, pushing Martha due north, she now finds herself drifting eastward at 39 miles per hour, relative to the ground.

Well, that was a fun example. Let’s do another.

The country of Ecuador sits directly on the equator — hence the name of the country. Now let’s imagine that Ecuador successfully builds a crude type of intercontinental ballistic missile. Ecuador has no nuclear bombs, so this is not a very dangerous missile. One day, just to make a point, Ecuador fires the missile due north at the United States. Ecuador expects the missile to fall to earth in the western suburbs of Washington, DC, because Washington is almost due north of Quito. (Surprised? Take a look at a world map!) However, as the missile rises upward from the mountains near Quito, traveling due north, its path begins to curve eastward. By the time the missile reaches the latitude of Washington, DC, the missile has tracked far to the east, and it falls harmlessly into the Atlantic Ocean.

So what happened? When the missile first took off from Quito, it had a hidden component to its direction of travel. Everything that sits on the equator is traveling eastward at more than 1000 miles per hour, but we don’t see this motion because our frame of reference is the surface of the earth. But Washington DC is spinning to the east at less than 800 miles per hour. So by the time the missile reached the latitude of Washington, its eastward rate of travel (relative to the surface of the earth) was more than 200 miles per hour, causing it to land far to the east of the intended target.

At this point in the discussion, we’ve seen that the Coriolis Effect is a genuine scientific principle, and that it applies to any object that travels north or south — not just to masses of air or bodies of water. So then why doesn’t it apply to toilet bowls, sinks, and bath tubs? The simple answer is that toilet bowls, sinks, and bath tubs are not big enough. The north rim of a toilet bowl is not traveling eastward at a different rate of speed than the south rim — or to be more precise, the difference in the eastward velocity between the north rim and the south rim is so miniscule as to be completely irrelevant. For the north rim to be traveling slower than the south rim, the north rim must be closer to Earth’s rotational axis than the south rim, resulting in a smaller circular path around the world. You need a basin of water that is hundreds of miles across — such as an ocean — before the difference in velocity between the two rims is great enough to have an effect. But the oceans are indeed big enough, and hence the Coriolis Effect does indeed have a major effect on the world’s ocean currents (and also on the world’s wind patterns).

An interesting component of the myth is that the story is always tied to draining a basin of water — that is, flushing the toilet or removing the stopper from the bottom of a sink or bathtub. But there is nothing about the real Coriolis Effect that requires the fluid to be going down a drain. After all, there is no drain at the bottom of the ocean. So if the Coriolis Effect actually did apply to a toilet bowl or a bathtub, then it should also apply to a full bathtub or toilet bowl that is not being drained. All that is required is that some disturbance has caused the water to slosh around a bit — such as tossing a rubber duck into the filled bathtub — and the Coriolis Effect should convert that disturbance into a rotational movement. Therefore the water in the toilet bowl should be rotating before we flush it, as a result of the disturbance that occurred when the bowl was refilled after the previous flush. But of course, that is not what actually happens — because a toilet bowl is too small to experience a Coriolis Effect.

So now we are starting to see how this myth got started. When we flush a toilet, we usually see the water swirling around the bowl. Likewise, when we drain a bathtub, we sometimes see a vortex develop directly above the drain hole. We see these two phenomena, and falsely associate them with what we have learned about ocean currents and wind patterns.

Now imagine for a moment that the Coriolis Effect were so powerful that it actually did apply to toilet bowls and bathtubs, accounting for the swirling water that we see. That would require an extremely strong force to have such a strong effect over so short a distance. After all, when we flush a typical toilet, the water immediately begins to race around the bowl at a rapid speed. But remember that the Coriolis Effect applies to all objects, not just water. So imagine a world — we’ll call it Hyper-Coriolis World — where the Coriolis Effect is so strong that it is indeed the reason that water races around toilet bowls when they are flushed. Any force so strong will have a dramatic effect on all moving objects.

In our imaginary Hyper-Coriolis World, it is very tricky to play baseball. If you throw a baseball in any direction other than due east or west, then the ball flies in a tight curve and ends up going either east or west. (In the northern hemisphere, the baseball curves to the right until it is traveling either due east or due west. In the southern hemisphere the baseball curves to the left until it is traveling either due east or due west.) In Hyper-Coriolis World, all highways go due east or west, because it is impossible to drive in any other direction without spinning off the roadway. Likewise, airplanes can only travel east or west. Even joggers feel a strong tug to the right or the left if they jog in any direction other than east or west.

Clearly we don’t live in this imaginary Hyper-Coriolis World. So in our real world, what causes the water to swirl in a toilet bowl or a bathtub? As it turns out, these are two very different situations.

When you flush a toilet, you open the drain hole at the bottom of the storage tank (not to be confused with the bottom of the toilet bowl). Water quickly drains from the storage tank into the bowl. But how does the water get from the tank into the bowl? In a typical toilet, there are several ducts within the rim of the ceramic bowl. These ducts usually do not point straight down the sides of the toilet bowl. Instead they are strongly angled. As the water, powered by gravity, races from the tank through the ducts into the bowl, the angle of the ducts sends the water swirling around the bowl. As a result, it doesn’t matter where in the world the toilet is located — the direction of the swirl is completely controlled by the angle of the ducts.

On the other hand, a bathtub is a completely different matter. When you first open the drain in a bathtub, you usually don’t see a vortex at all. But as the water drains lower and lower, sometimes a little vortex develops directly above the drain. In my own experience, it seems that the vortex doesn’t usually appear until the water is only a couple of inches deep. This is a complex phenomenon tied to the acceleration of the water as it approaches the drain, and the conservation of angular momentum. But the key point is that the direction of the vortex, if it appears at all, is essentially random. Unless there is some non-symmetrical detail in the shape of the tub or the drain opening, you’ve got a roughly 50% chance that the water will swirl clockwise, and a 50% chance that the water will swirl counter-clockwise. The direction of the swirl has nothing to do with the Coriolis Effect.

Earlier we stated that circles of latitude get shorter as you move from the equator to the poles. But regardless of our latitude, we do one complete circuit every 24 hours, and therefore the rate of travel of the earth’s surface is slowest nearest the poles and fastest at the equator. Another way of looking at the phenomenon is this: The farther you are from the Earth’s axis of spin, the faster your speed. The North Pole and South Pole sit directly on the earth’s axis, and therefore have a speed of zero. The equator is as far from the axis as you can get without leaving the surface of the earth, and therefore the equator has the highest rotational speed of any place on earth.

The upshot is that we see the Coriolis Effect in large masses of water or air (such as the North Atlantic Ocean) because the north and south edges of the mass are different distances from the earth’s axis.

Now let’s consider a fascinating consequence of this line of thinking. If you travel north or south from the equator, then at first you are traveling parallel to the earth’s axis. Therefore, as you first leave the equator, you really aren’t getting much closer to the earth’s axis. In contrast, if you travel south from the North Pole, or north from the South Pole, then at first you are traveling perpendicular to the earth’s axis. So as you leave either pole, you quickly increase your distance from the earth’s axis. Therefore if you have a mass of air or water that is 70 miles across (enough to span one degree of latitude), and the southern edge of the mass is sitting right on the equator, then you won’t get much of a Coriolis Effect. The difference in rotational speed between the northern edge and the southern edge is only 0.2 miles per hour. But if you have a mass of air or water of the same size (70 miles across), and the northern edge of the mass is sitting at the North Pole, then the difference in rotational speed between the northern edge and the southern edge is about 17 miles per hour. In other words, the Coriolis Effect would be nearly 100 times as strong.

So that’s the final nail in the coffin for the myth of the toilet bowl swirl. If the effect really were strong enough to see it in a toilet bowl, then the water wouldn’t change direction the moment you cross the equator. Instead, the effect would gradually weaken as you got closer and closer to the equator. After you crossed the equator, the effect — now reversed — would very gradually reappear as you made your way farther and farther from the equator. To put it another way, when you are near the equator, the surface of the toilet bowl water is parallel to earth’s axis, eliminating any chance of a Coriolis Effect. But when you are near the Earth’s pole, the surface of the water (assuming that it isn’t frozen) is perpendicular to the pole — and hence the opposite edges of the body of water truly are different distances from the rotational axis of the earth.

So now that you know why the Coriolis Effect happens, you can easily understand why it does not apply to toilets, bathtubs, and sinks — even though it does apply to large bodies of water and large masses of air. This should come as a great relief the next time you travel to Australia, because you won’t have to key an eye on the toilet.

[A slightly different version of this article first appeared on my blog on October 12, 2010.]

If you enjoyed this article, then please click the heart icon!