Why there's a whirl when you drain the bathtub?

Question

At first I thought it's because of Coriolis, but then someone told me that at the bathtub scale that's not the predominant force in this phenomenon.

Answer 1

The whirl is due to the net angular momentum the water has before it starts draining, which is pretty much random.

If the circulation were due to Coriolis forces, the water would always drain in the same direction, but I did the experiment with my sink just now and observed the water to spin different directions on different trials.

The Coriolis force is proportional to the velocity of the water and the angular velocity of Earth. Earth's angular velocity is $2\pi/24\ {\rm hours}$, or about $10^{-4}\ s^{-1}$. If water's velocity as it drains is $v$ the Coriolis acceleration is about $10^{-4} v\ s^{-1}$.

The water moves about a meter while draining, which takes a time $1\ m/v$, so the total velocity imparted by Coriolis forces could be at most $10^{-4} v\ s^{-1} * 1\ m/v = 10^{-4} \ m/s$.

So the Coriolis effect is quite a small effect. But this first-order Coriolis effect does not cause the water to rotate.

The direction of Coriolis force depends on your direction of motion. All the water in your tub is moving the same direction, so the Coriolis force pushes it all the same direction. The effect is that if the bathtub starts out perfectly flat and begins draining (and it points north), all the water will get pushed east. The two edges of the tub will have very slightly different depths of water, because the Coriolis force is pushing sideways.

The Coriolis force could create "spinning" on uniformly-moving water, but only as a second-order effect. As you move away from the equator, the Coriolis force changes. This change in the Coriolis force is because the angle between "north" and the angular velocity vector of Earth changes as you move around; as you go further north (in the Northern Hemisphere) the "north" direction gets closer and closer to making a right angle with the angular velocity vector, so the Coriolis force increases in strength. The size of this effect would be proportional to the ratio of the size of your tub to the radius of Earth. That ratio is $10^{-7}$, so this effect is completely negligible.

The Coriolis force could also create some "spinning" if different parts of the water are moving different speeds. If the tub is draining to the north in the northern hemisphere, and water near the drain is moving faster than water far away, then the water near the drain would be pushed east more than water far away is. If you subtracted out the average effect of the Coriolis force, what remained would be an easterly push near the drain and a westerly push far away. This gives a clockwise spin as viewed from above.

We've already estimated the typical velocities as $\omega L$, so the angular momentum per unit mass induced this way would be on the order of $\omega L^2$ (but maybe smaller by a factor of 10). That's only $10^{-4}\ m^2/s$. To get an equivalent effect, in a tub of $100\ L$, you could give just one liter of water on the edge of the pool a velocity of a few cm/s, something you surely do many time over when removing your body from the tub.

This effect is too small to affect your bathtub, but it's still observable under the right conditions. According to Wikipedia, Otto Tumlirz conducted several experiments in the early 20th century that demonstrated the effects of the Coriolis forces on a draining tub of water. The tub was allowed to settle for 24 hours in a controlled environment before the experiment began. This was enough to damp out the residual angular momentum left over from filling the tub up to the point where Coriolis effects were dominant.

Answer 2

The main effect is angular momentum (rotational inertia) in the water set up by various movements before you start observing, such as getting out of your bath.

This results in the water level being lower near the centre of rotation than further away, setting up centripital forces which maintain the rotation. When the difference in levels is significant relative to the average water level, you notice the typical whirl effect.

There are other things happening too, including the Coriolis force.

Answer 3

A discussion by 'The Straight Dope' website

http://www.straightdope.com/columns/read/149/do-bathtubs-drain-counterclockwise-in-the-northern-hemisphere

references experimental work carried out but Ascher Schapiro in 1962, which concluded something like it all depends on the shape of container and how its stirred before being left to empty.

Here is Schapiro's paper but I feel you will need academic access via a university or library to read the full PDF:

http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=368912

Answer 4

It's because of the Coriolis effect. In the Northern hemisphere, it goes around in one direction, in the Southern hemisphere around the opposite direction, and goes straight down bang on the equator.

Black natives demostrate the effect to white tourists in the video clip Water flow at the equator, Coriolis effect.

Answer 5

The whirl happens in the draining tube, whose optimal solution to drain the bathtub is a laminar flow allowing for some rotation in the tube. What you see in the surface is the match between the solution of flow in the tube and the solution of flow in the surface.

Angular momentum of the flow gets modified a lot as the tube twists and twists, sometimes even siphoning up and down.

Answer 6

Since you want to explain it to your daughter, take a plastic bottle, cut the bottom open, turn it upside town, hold the top closed and fill it with water. Give her that bottle and have her release the top (which is on the bottom now, sorry for the bad phrasing). The water will whirl in different orientations whenever you repeat this (if it whirls at all) and she can influence it by accelerating the bottle in a circular motion to understand that an initial disturbance is responsible for the whirl orientation.

Answer 7

You can think about it like this: It takes one day for the earth to perform a full rotation (about 86k seconds), on the other hand, it takes a few seconds for your sink to drain (lets say 10 seconds). So it takes 8600 times longer for the earth to do a full rotation than it takes the water to drain down the sink. It is not too hard to imagine that the earth's rotation can have no influence on the process of draining a sink.

However, if the sink was the size of lake Michigan and you were to drain it, Coriolis would play a role.