tea, water way in toilet

Whatever it was, I couldn’t wait to go south of the equator. When I finally did—Windhoek, Namibia—I took a deep look into every flushing toilet I could find. Whatever image comes to your mind, I could not decide whether the vortices there were the opposite of vortices north of the equator.

Upshot: I was persuaded not to have the Coriolis effect, at least as it appears in flush.

Let’s try to understand what is happening here. Imagine that you are looking at a large disc that is rotating clockwise. You see that a small ball starts from the center and moves in a straight line on the spinning disc to its edge. Nothing dramatic there. But now imagine your friend Archana standing at the edge of the disc as it is spinning. What does she see the ball doing? Not making a straight line, that’s for sure. Instead, she’ll see it turning to her right, away from her. That’s the Coriolis effect.

Two things are worth noting. One, if the ball was at rest, it would rotate clockwise with the disc. But you will see that it moves in a straight line. Thus, there is clearly a force pushing it to the left of its direction of motion – or counterclockwise. This is what we call the Coriolis force. Two, Archana gets a distinct feel of what the ball is doing. That’s because he has a different frame of reference to you—moving along the edge of the disc and with it, as opposed to being stationary above it.

The mention of a frame of reference and, therefore, of something happening relative to such a frame, may bring to mind Albert Einstein and relativity. Certainly, Einstein appears in this story. Catch.

We associate the Coriolis effect with our planet because our planet rotates. If you were positioned directly above the North Pole, you would see the Earth rotating counterclockwise beneath you. Imagine a river flowing in a straight line from the pole. To make that straight line, the Coriolis force pushes the river flowing to the right. But now position yourself directly above the South Pole. Below you, you see the Earth rotating clockwise. A river flowing in a straight line from the South Pole will also be subject to the Coriolis force. This will push the flowing river to the left.

This difference between the two hemispheres is the Coriolis effect. Unfortunately, the force is negligible on the scale of a toilet flush and the force comes into play there. Any difference in how they drain north and south of the equator is really due to the size of the latrines and the force with which water enters them. No Coriolis effect.

And talking about rivers. In the 1850s, a French physicist named Jacques Babinet and a German scientist named Karl Ernst von Baeyer used the Coriolis force to propose the idea that, due to the Earth’s rotation, erosion caused by left banks of rivers. Will be higher, in the Northern Hemisphere. In the Southern Hemisphere, the opposite: the left bank will be more emaciated. This is known as Bayer’s law of stream deflection. He found various rivers which, he suggested, obeyed the law.

But his law has always been regarded with some scepticism. Just like in toilets, the Coriolis force is very weak compared to other forces – wind, or increased flow of meltwater from snow – that act on the soil along those rivers. As a result, Bayer’s law is more or less ignored today, being just a relic of history.

Cut to another incident you may have noticed – that happened just half an hour before I wrote these words. Take a cup of hot water and add some tea leaves to it. To aid in cooking, stir the water with a spoon. You would expect that the centrifugal force, due to the whirlpool of water, would push the leaves to the edge of the cup. After all, when you tie a stone to a long rope and swing it around your head, and then let go, the stone flies away from you due to centrifugal force. Surely the same as tea leaves?

But get ready for the tea leaf paradox. As you stir, the leaves move to the center of the cup, and settle to the bottom. (I noticed this happens with sugar I was adding to a solution of fresh lemon and water.) Why so?

The water definitely seeps into the cup. But it doesn’t do so uniformly: At the bottom, friction makes it rotate more slowly than at the top. Centrifugal force, then, is weaker near the bottom than near the top. This causes a distinct, invisible flow in the water: from top to bottom along the walls of the cup, to the bottom and back to the top.

“Tea leaves are swept into the center,” Albert Einstein wrote in a 1926 paper, “by circular motion … the same sort of thing happens with a swirling stream.” (Turning to the left, I should point.)

Einstein went on to say: “The particles in the fluid will move the fastest away from the walls. [or] In the upper part… [These] The side of the right hand wall will be driven by circulation, while the left hand wall receives water that comes from the area below and has a particularly low velocity. because [a river curving to the left] Erosion is necessarily stronger on the right than on the left.” (“The course of rivers and the reason for the formation of meanders in the so-called Bayer’s law”, Die Naturwissenschaften, 1926, https://www.ias.ac.in /article/fulltext/reso/005/03/0105-0108).

Einstein also considered the Coriolis effect. He wrote that the Earth’s rotation, and thus the Coriolis force, can cause this same circular motion, even where the river runs straight, but “on a smaller scale.” Again, minimal compared to other factors.

Overall, don’t pay attention to the fancy claims about the Coriolis effect. But watch your tea the next time you stir it.

Dilip D’Souza, once a computer scientist, now lives in Mumbai and writes for his dinner. His Twitter handle is @DeathEndsFun.

Updated: 15 June 2023, 10:30 PM IST