# Resolving water sink problem

There is a common myth that water flowing out from a sink should rotate in direction governed by on which hemisphere we are; this is shown false in many household experiments, but how to show it theoretically?

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I would go about this by computing the magnitude of the Coriolis effect in a typical sink drain and comparing it to other effects that might change the direction of the drain, e.g. some tilt in the sink or faucet. –  j.c. Nov 2 '10 at 20:32
Exactly what @J.C. said. Other factors, namely the angle of the sink's axis relative to gravity and how the water enters the sink or bowl. –  Mark C Nov 22 '10 at 18:07
@Mark For breaking 1k? Thanks. Now its time to make some edits [-; –  mbq Nov 22 '10 at 20:35
Yes, I like to be the one to give the "deciding" vote. –  Mark C Nov 22 '10 at 23:06

The calculation of the Coriolis force is dependent on latitude:
$F = m a$ where $a = 2 \Omega sin(lat)$, with $\Omega$ being the Earth's angular velocity
$m$ is the mass of the object in question

The Earth's angular velocity is (about) $7.29 \times 10^{-5}$ rad/sec

So, for a sink with a couple gallons of water in it at 45 degrees north... the Coriolis force is about $7.57 \times 2 \times 7.29 \times 10^{-5} = 1.10 \times 10^{-3}$ N.

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The Coriolis force is dependent on velocity. You can't get it just from the latitude. –  Mark Eichenlaub Mar 29 '11 at 12:45
One way of seeing that this answer is wrong is by noting that the units don't make sense. –  Ben Crowell Jul 25 at 17:39
The Coriolis acceleration goes like $-2\omega \times v$, which for the sake of an order of magnitude estimate we can take to be $a\sim \omega v$. But in order to get an observable effect, we don't just need an acceleration, we need a difference in acceleration between the two ends of the tub, which are separated by some distance $L\sim 1$ m. The accelerations differ because $v=\omega r$, and $r$ differs by $\Delta r\sim L$. The result is that the difference in acceleration is $\omega^2 L$, which is on the order of $10^{-8}$ m/s2. This is much too small to have any observable effect in an ordinary household experiment.
Detecting the Coriolis effect in a draining tub requires very carefully controlled experiments (Trefethen 1965; also see this web page by Baez). Lautrup 2005 gives numerical estimates showing that in order to see the Coriolis effect, the the water must be very still ($v\lesssim 0.1$ mm/s), the water must also be allowed to settle for several days, and precautions have to be taken in order to prevent convection.