The myth of the toilet drain

Can you tell if I've flipped this picture?

Have you ever heard that toilets in the northern hemisphere drain in one direction while those in the southern hemisphere drain in opposite direction? It's not true. Who knows why people think it is. It's sort of a harmless myth, a little science factoid that people enjoy perpetuating. I guess it just isn't terribly important to most people whether these science factoids are true or not. Though it's as harmless as they come, debunking this myth is fun, because I get to talk about some real science in the process.

The Coriolis Force

Supposedly, the reason that the water drains one way rather than the other is because of the Coriolis force. The Coriolis force is a "fictitious" force that appears when you consider a rotating reference frame, such as a point on Earth's rotating surface. By "fictitious", we don't mean it's not real. That just means that it appears in one reference frame, but not another. In more advanced theories, gravity is considered a fictitious force too, since it disappears when you consider a free-falling reference frame such as a space-station in orbit.

So what causes this Coriolis force? Usually, an object will move in a straight line unless there are some external forces changing its direction. But in a rotating reference frame, we would expect the direction to rotate along with the frame. Thus, when an object is moving, the Coriolis force causes it to slowly change its direction.* In the northern hemisphere, a moving object will slowly turn right. In the southern hemisphere, a moving object will slowly turn left. The further away from the equator, the more quickly it turns. This has to do with the orientation of earth's surface relative to the axis of rotation.

The reason the Coriolis force does not affect a toilet is because it's far too weak. Think about how slowly the Earth turns. That's right, it takes a whole day to make a complete rotation! Unless the toilet takes a whole day to drain, the Coriolis force can have hardly any effect at all. It will be extremely small in comparison to other effects like the shape of the toilet bowl, or the direction of the water as it comes in. On the other hand, the Coriolis force has a huge effect on ocean and air currents, as well as the direction of hurricanes, since all these phenomena last much longer than a day.

That said, it is possible for the Coriolis force to determine the direction that a sink drains. You just need to have a highly symmetrical basin, and make sure that the water is not moving initially or anything. And then you need to let it drain for maybe several hours. It's not an easy experiment.

*This is just the short, lying-to-children explanation. To get the full picture, you have to include another fictitious force that can also affect the direction, called the centrifugal force. Only together do these forces change the magnitude and direction of the velocity in the correct manner.

The Vortex Direction

Time for a quiz. If the Coriolis force did have a large effect on toilets, which way would they drain in the northern hemisphere?

Initially, I thought it would drain clockwise, because the Coriolis force makes the path turn right, creating clockwise circles. But I was wrong! As the water begins draining towards the center, its path is deflected to the right. Then the water goes counter-clockwise around the drain, because the Coriolis force is balanced by the force of water pressure. This really needs an illustration:

Image from Bad Science's Bad Coriolis FAQ. Cf (red) indicates the direction of the Coriolis force, while pgf (purple) indicates the direction of water pressure.

The direction actually depends on whether the center of the vortex is low pressure (such as a drain or a hurricane) or high pressure. In the absence of a vortex, I think the body of water or air will rotate clockwise according to my previous analysis.

As for the picture at the beginning, it's true, I flipped it. No, you can't tell which hemisphere it's from.