Why does water run down a bathtub drain in a swirl?

Answer 1

Often in sinks, toilets, bathtubs, etc., the water is already moving, though

maybe very slowly. As the water drains, that slow rotation becomes more

visible. In the case of a sink or bathtub, where the width of the pool

decreases as it drains, the rotation increases speed as it drains. This is

because angular momentum is conserved (think of a figure skater speeding up

as she pulls her arms into her body -- it is the same effect). In a draining

tank, the water by the drain has the least momentum. As it leaves, the

remaining water with more momentum takes its place. If an object with

angular momentum moves closer to the center of its rotation, it speeds up.

So, the water gradually picks up speed, and you see rotation.

Even if there is *no* angular momentum to start with, fluid can start to

rotate. This is called a "secondary flow". To understand why secondary flows

develop, you have to understand the nature of viscosity. When molecules of a

liquid are attracted to each other, they resist being pulled apart. For

example, when you move your hand through water, you are dragging molecules

of water with your hand. Some of the resistance is simply the inertia of the

water, but much of it is viscosity. The molecules that you accelerate pull

on the ones next to them, and those next to them, etc. Moving water

molecules across each other, a 'sideways' force, is called 'shear'.

Resistance to shear is called viscosity.

Imagine a large cylindrical vessel full of water with a small drain at the

bottom. When you open the drain, water starts to flow down the hole. Of

course you have taken great care to ensure the water is completely

stationary first, and that opening the drain does not perturb it. As the

water flows downward, it drags the molecules around it due to viscosity. At

the point of the drain, some of the molecules go down the drain, but other

ones cannot fit. Yet, they have still gained some energy by being dragged by

the ones that did go down the drain. They have to go somewhere, and since

they cannot go down, and gravity makes it hard to go up, they go sideways.

Over time, they start a rotational flow, called 'secondary flow'. Over a

short period of time, viscosity, caused by the molecules' mutual attraction

to each other, ensures that they move together in the same direction. In

time, a vessel with a drain full of stationary water will develop a quite

noticeable rotation due to secondary flow.

Another place where secondary flows commonly occur is in tea. Here, the

opposite occurs: a rotational flow causes vertical motion. If you drink

green tea, watch the leaves as you stir it. Even though you are stirring the

tea in a rotational direction, you can see the leaves are pushed upward. The

upward motion, caused by viscosity in response to the rotation, is another

example of secondary flow. Of course, depending on how you stir, it could be

your spoon moving them up, not secondary flow. So be careful. :)

A lot of research has been performed to understand how and when secondary

flows occur. It turns out that any viscosity gradient can cause a secondary

flow. Sometimes secondary flows are hard to see (they can be very

small/slow), but they are there! This is the underlying reason for the

'swirl' you see.

If you travel from the northern hemisphere to the southern, you will notice that water 'swirls' counterclockwise. Simply enough, it is because of the rotation of the earth acting on the water in conjunction with gravity.