# Flushing water-Is it related to Coriolis force? [duplicate]

There are videos and articles on the internet which demonstrate that water flows down a flush clockwise in Northern Hemisphere and anti-clockwise in Southern Hemisphere.

There are others which call this a total myth, and one of them is a very popular website. Link : http://science.howstuffworks.com/science-vs-myth/everyday-myths/rotation-earth-toilet-baseball2.htm

Interestingly, I got introduced to this by a Children's Fact Book. I am not quite convinced that it is a myth.

Can you suggest a way to proceed towards an analytical treatment?

Well, first we know that the Coriolis force acting on the scale of a toilet is going to be a pretty small force. So the question can generally be tackled in the following way:

1. Estimate the magnitude of the Coriolis force on the toilet water. Use this to estimate the magnitude of effect of the Coriolis force on the toilet water spin.
2. Enumerate the possible other sources of spin for the toilet water. The two major ones off the top of my head would be any angling of the water jets, and the shape of the toilet bowl. Estimate the magnitude of the effect of these sources of spin.
3. Compare the two effects. You'll probably find an answer which is something of the form:

"If the angling of the toilet jets is less than $\theta$ for a jet velocity of $v$, then the Coriolis force should dominate"

Essentially what I'm doing is asking "How idealized would this toilet have to be for the Coriolis force to be the dominant source of spin in the toilet water?"

• I'll try that.. – Cheeku Feb 26 '13 at 17:30

The Coriolis effect cannot possibly account for this. Other factors (e.g the shape of the basin and initial conditions for the water flow) should have a comparatively huger effect. This is intuitively obvious---if you are not convinced you should perform an experiment. Could be fun!

You could also estimate characteristic scales (via dimensional analysis) for the problem and compare with the estimated effect of the Coriolis force. This should yield that the Coriolis effect is smaller by a few orders of magnitude.

• Dimensional Analysis is something I could do! I didn't really think about it. – Cheeku Feb 26 '13 at 17:29

Here's how you might proceed analytically.

On the surface of the Earth, the Earth's rotation causes the introduction of fictitious forces. The total effective apparent force is $$\mathbf F_{\mathrm{eff}} = \mathbf F_{\mathrm{ext}} + m\mathbf g_{\mathrm{ eff}} - 2m\vec\omega\times\mathbf v$$ The last term is the Coriolis term where $\vec\omega$ is the angular velocity of the Earth due to its spin, and $\mathbf v$ is the velocity of whatever object you are considering as measured in the Earth's frame. In the Northern Hemisphere, at a latitude $\lambda$, one has $$\omega_x = -\omega\cos\lambda, \qquad \omega_y = 0, \qquad \omega_z = \omega\sin\lambda$$ Where the $x$ and $y$ axes have been oriented parallel to the surface of the Earth ($y$-axis pointing West-East).

Using these facts, you can estimate the strength of the coriolis force and compare it to the other forces that are being exerted on the water as it flushes. I'll let you try this! My guess is that you should find the magnitude of the Coriolis force to be negligible, and this is the origin of the claim that it is a myth that it is responsible for toilets flushing in certain directions.