The Twisted Garden Hose and the Myth of the Toilet Flush

If you have wrapped your head around why and how the U-shaped tube in the flow meter (described in my previous post) is twisted by the Coriolis force – here is a video of a simple experiment brought to my attention by the author of the quoted article on gyroscope physics:

You could also test it yourself using a garden hose!

Accidentally you can observe this phenomenon so clearly because the typical angular frequencies of manual rotation result in a rather strong Coriolis force – in contrast to other every day phenomena that are falsely attributed to the Coriolis force associated with the rotation of the earth.

It is often stated – and I even found this in lecture notes and text books – that the Coriolis force is accountable for the unambiguously different sense of rotation of vortices in water flowing down the sink of your bathtub or toilet: In the Northern hemisphere water should spin anti-clockwise, in the Southern hemisphere clockwise. Numerous articles debunk this as an urban legend – I pick a random one.

On principle the statement on the sense of rotation is correct as the rotation of hurricanes is impacted by the Coriolis force. But for toilet flushes and the like the effect is negligible compared to other random factors impacting the flow of water. As pointed out in this article the momentum of leaves thrown into a bowl of water at a location near the equator of the earth (often used in demonstrations of entertain tourists) do have more impact than the Coriolis force.

Near the equator the Coriolis force is nearly zero, or more precisely: Since it is both perpendicular to the velocity and the axis of rotation the Coriolis force would be directed perpendicular to the surface of the earth – but there is no component of the Coriolis force that would allow water to flow North-South or East-West. Thus very near the equator the force is infinitesimally small – much smaller than the forces acting on, say, middle European or Austrian bathtubs. And even with those the Coriolis force does not determine the spin of rotation unambiguously.

How to estimate this impact – and why can we observe the twist in the garden hose experiment?

The size of the acceleration due to the Coriolis force is

2 times (angular frequency [rad/s]) times (component of the velocity [m/s] perpendicular to the axis of rotation)

The angular frequency in radians per second is 2 Pi times the number of rotations per second. Thus the angular frequency of the rotation of the earth is about 0,0000727 radians per second. The frequency of the motion of the garden hose was rather several turns per second, thus about 1 radians per second.

Imagine a slice or volume element of water flowing in a sink or a garden hose: Assuming a similar speed with an order of magnitude of 1 meter per second. The Coriolis force differs by several orders of magnitude

  • Bathtub vortex: 0,00015 m/s2
  • Garden hose: 2 m/s2

On the other hand, the acceleration due to gravity is equal to 9,81 m/s2.

The garden hose in the video moves under the influence of gravity – like a swing or pendulum – and the Coriolis force (The additional force due to motion of the hands of the experimenter is required to overcome friction). Since the Coriolis force is of the same order of magnitude as gravity you would expect some significant impact as the resulting force on every slice or volume element of water is the vector sum of the two.

It is also important to keep track of the origins of the components of the velocity:

The radial flow velocity (assumed to be about 1 m/s) in the hose is constant and simply dictated the by the pressure in the water line. There is no tangential flow velocity unless caused by the Coriolis force.

In case of the bath tub the assumed 1 m/s do not refer to the velocity of the tangential motion in the vortex, but to the radial velocity of the water flowing “down” the sink. The tangential velocity is what would be caused by the Coriolis force – ideally.

Any initial velocity is is subject to the initial conditions applied to the experiment.

Any random tangential component of the flow velocity in the vortex increases when the water flows down:

If there is a small initial rotation – a small velocity directed perpendicular to the symmetry axis of the flush – pronounced vortices will develop due to the conservation of angular momentum: As the radius of rotation decreases – dictated by the shape of the bathtub or toilet – angular frequency needs to increase to keep the angular momentum constant. Thus in your typical flush you see how a random and small disturbance is “amplified”.

However, if you would conduct such experiment very carefully and wait long enough for any disturbance to die out, you would actually see the vortices due to Coriolis force only.[*] I have now learned from Wikipedia that it was an Austrian physicist who published the first paper on this in 1908 – Ottokar Tumlirz. Here is the full-text of his German paper: Ein neuer physikalischer Beweis für die Achsendrehung der Erde.  (Link edited in 2017. In 2013 I haven’t found the full text but only the abstract).

Tumlirz calculated the vortices’ velocity of rotation and used the following setup to confirm his findings:

My sketch of the experimental setup Ottokar Tumlirz used in 1908 as it is described in the abstract of his German paper “New physical evidence on the axis of rotation of the earth”. The space between the two plates is filled with water, and the glass tube is open at the bottom. Water (red) flows radially to the tube. The red lines are bent very slightly due to the Coriolis force.

Holes in a cylindrical tube – which is open at the bottom – allow water to enter the tube radially. This is not your standard flush, but a setup built for preventing the amplification of tangential components in the flow. Due to the Coriolis force the flow lines are not straight lines, but slightly bent.

Tumlirz noted that the water must not flow with a speed not higher than about 1 mm per minute.

Edit, Oct 2, 2013: See Ernst Mach’s original account of Tumlirz’ experiment (who was Mach’s student)

Edit, June 3, 2015: Actually somebody did that careful experiment now – and observed the tiny effect just due to the Coriolis force, as Tumlirz. Follow-up post here.

Edit, Augist 2016: Stumbled upon another reference to an experiment done in 1962 and published in Nature (and filmed) – link added to the post from 2015.

5 Comments Add yours

  1. M. Hatzel says:

    Admittedly, it took work to begin understanding these last two articles, but in the end I feel quite smug about getting a sense of it. I could never wrap my head around people (including teachers) telling me that the movement of water in the toilet bowl related to the earth’s spin. When I was a kid, I couldn’t see how the force of the water flow would be overcome by the spinning earth when water coming out of the kitchen tap didn’t do a loop around the room before coming back to the sink…. (When I couldn’t understand this contradiction I assumed I wasn’t smart enough to get it, and eventually stopped thinking about it.) Nice to see that the business about the toilet was a load of crap, and to be engaged again. I have no trouble seeing the Coriolis forice at work with weather systems. I’m still working on the other examples… I thought I had it but then I was a bit thrown off by the Wikipedia article. I’ll have to let it settle in my head, and come back again in another day or two. Thanks for this!

    1. elkement says:

      Thanks for reading and commenting – I know two articles of that kind have been probably a bit too much!
      Classical mechanics and, in particular, fluid mechanics are not at all that easy and intuitive to understand. To me, this is as fascinating as quantum theory that is hyped a bit too much in my opinion because of its “spookyness”. The calculation of the motion of the water in the sink is daunting task – the related equations are among the most complicated in physics.
      What I attempted in these articles was to show how you could use some rather simple calculations to verify or falsify claims, such as the sudden turn of the sense of rotation at the equator. While it is true on principle that the Coriolis forces acts on the water in the sink in the same way as on a hurricane, the effect is too small compared with lots of other factors. If you do the experiment far away from the equator and in the way the Austrian physicist did it in 1908, you would observe a tiny bent in the expected direction.

      1. M. Hatzel says:

        “What I attempted in these articles was to show how you could use some rather simple calculations to verify or falsify claims” … I was thinking of this today, and also musing over the way we humans get trapped into simple acceptance of things, despite our deeper urges to question and to explore. Even if we’re completely wrong, the process of learning that is really important.

  2. I’ll have to read through this again … but the first time through has clearly blown out-of-the-water the tourist demonstrations of Coriolis force depicted in travel films such as those presented by Ewan McGregor and Michael Palin. Both videos (especially the first) are really nice … as was the really nice insert of the oscillating tube from the last past. Nice, instructive, non-trivial, challenging, neat, interesting, educational, enlightening, cool … what else can I say? D

    1. elkement says:

      Thanks a lot – you are too kind :-) I was not sure if two successive posts about similar physics stuff had probably been too much ;-)
      Yes, the tourist demonstrations definitely do not work the way they are explained. If different bowls are used above and below the equator, then I guess these might be shaped in different ways – supporting either sense of rotation. If leaves or other particles are thrown into the bowl, it could depend on the details of the throw.
      I found tons of videos of people’s sinks – the funny thing is that some of them “give proof” of the wrong sense of rotation, so the experimenters were not aware of the one to the expected (as per the Coriolis effect). There was also one video demonstrating that the sense of rotation is quite random – and can change for each attempt.

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