## Wednesday, May 18, 2011

### Coriolis Effect and sink drainage

This old saw came up in conversation the other day (don't ask why) about water in a sink or toilet draining counter (anti) clockwise in the Northern Hemisphere and clockwise in the Southern Hemisphere.

The trouble is that it's true. For a given value of true. That is given a large enough volume of water and no other factors water will drain in this fashion. When I say no other factors I mean absolutely still water with a uniform surface over which it drains. But why not in normal sinks and toilets?

Well the physics is quite simple - if you set something spinning that has two markings on it one on the edge and one near the centre the one on the edge is travelling a greater distance than the one nearer the centre but is doing so in the same time. As speed equals distance/time the outer edge is travelling faster than the inner edge.

The Earth is like that- take the Northern hemisphere and view it from the North Pole and it looks just like a record spinning. The outer edge is the Equator and that mark towards the centre is London. It completes a spin every 24 hours so again as speed equals distance/time the Equator is moving faster than London.

So what's that got to do with sinks draining? Well imagine driving a tank with each of the treads moving at a different speed. Face East and set the right-hand (equatorial) tread at max speed and your left-hand tread (London) at half-speed. You end up driving around in circles in an anti-clockwise manner. If you have water receiving an extra push of speed as it nears the Equator it will influence the direction it travels.

So that's the physics, but the real question is - what's the speed difference between our two 'treads'? To work that out we need to know the different distances each tread is travelling over our 24 hour period to determine the speed. To keep things simple I'll treat the Earth as a perfect sphere that rotates in exactly 24 hours (it's not, but it's close enough in this instance).

I'm going to put this tank down with a width of 10m (0.01km) so that one edge is on the equator and the opposite edge at the farthest point North so both treads are parallel to the equator. Thinking of this as my record I need to work out the circumference at the edge and the circumference at the other end of my tank.

At the Equator the Earth has a radius of 6,378.14km using Circumference=Diameter/Pi that gives me a distance of 40,075km. Treating that 10m tank as an arc I know that the angle formed between the two edges of my tank is 0.01/63718.14 in radians. Using similar triangles I can determine my second radius rcos(angle) and from that a new circumference. The difference between them is 0.007cm.

Both completing one revolution in 24 hours means the Equator is travelling at 1670km/hour the other side of our tank is travelling at 1670km/hour. Well not quite the difference is 0.000000002052730km/hour or 0.000000570202246mm/second.

So let's rev our tank forward by the amount of time it takes to drain a sink say 30 seconds. Our Equatorial tread will have travelled an extra 0.000017106mm (1.71x10-5mm)

Try it with an actual sink of say 1m diameter draining in 30 seconds and the water at the Equatorial point will travel an extra 0.000000174mm. (1.74x10-7mm)

In comparison a human hair ranges in width from 0.017mm to 0.181mm

Over time and a large enough area and with no other factors this speed difference will influence the direction of flow. In a normal sink or bathtub with the speed of draining... well what do you think?

For those still arguing the point both my sink and shower drain clockwise the direction of water flow easily overpowering any Coriolis effect.