Sunday, January 18, 2009

B71 #82: Coriolis effect

During our re-union gathering on December 28, 2008, the subject of Coriolis effect was raised and discussed. It leads to the following finding:

a) that the Earth's Coriolis effect (an effect of differential surface velocity) is theoretically true (see Part 1).

b) that the Earth's Coriolis effect is hard to demonstrate as it requires a large bath/pool 2 yards across, to drain through a pin-hole for 12-15 minutes before the effect can be seen (see Part 2).

c) that we can emulate the Coriolis effect by rotating a half globe on a platform (see Part 3).

I would await some interested parties to assemble an experimental unit.

///// Part 1: Explanation of Coriolis effect /////

Blog version:

Website version:

///// Part 2; The lack of good demonstration kit /////

Website discussing the difficulty of setting up an Ideal Sink experiment:

Can You Detect The Coriolis Effect in your Sink?
Dr Karl Kruszelnicki, University of Sydney, Australia

Chris - What we've been doing this evening is asking people all around the East of England to fill sinks and baths with water, pull out the plug and see which way the water swirls down the plug hole. We've got a mixture of results this evening, but is this experiment actually possible? Can we detect the spinning of the Earth using this approach?

Karl - You can get it to work. However, you're looking at a thing called the Coriolis force, which is actually angular momentum under a different name. The Coriolis force on the small bodies of water you're working on is roughly 10 million times smaller than the gravity force, so you really need to do the experiments delicately. Let's just back up a bit here. The thing about angular momentum is the same as when ice skaters go faster when they pull their hands into their body. They speed up because they bring more of their mass to the spin axis of the body. If you think about the Earth spinning, at the equator it's a long way from the spin axis, and at the poles it's right on the spin axis. If you get a storm brewing just above the equator, they spin and move away from the equator towards the poles. As they do so, they head towards the spin axis of the Earth. There's a bit of angular momentum that needs to be accounted for. If you do the equations, this leads to clockwise rotation of a hurricane in the southern hemisphere and anticlockwise rotation in the northern hemisphere. But here you're looking at something tens or hundreds of kilometres across. How can you hope to see that same effect in a tiny tub? The answer is that if you do the experiment very carefully, you should be able to see it. This has been done once or twice.

Chris - So it is possible?

Karl - Yes. In a fine journal called Nature in 1962, there was a paper by Shapiro who did the experiment at MIT. A few years later at the University of Sydney, also published in Nature, a paper by Trefethen in 1964 about the bath tub vortex in the Southern hemisphere. What you do is get a special bath tub, which is two yards across, six inches deep and has a tiny tiny central hole. You put a cork there so you can see which way the water's going. You let the water settle for a day or two so you lose all the residual spin from putting it in there and then you open the drain plug. The water begins to flow out very slowly and nothing very significant happens for about twelve to fifteen minutes. At around that stage, you can begin to see the cork take on a clockwise or anticlockwise rotation depending on your hemisphere. It happens slowly at first and then increases to one rotation every four seconds by the end. Shapiro wrote that when all the precautions prescribed were taken, the vortex was invariably in the anti clockwise direction. Soif you're a fair way away from the equator and you it carefully, you can see it. However if you just rush off the plane at Singapore which is one degree from the equator, and the surface of the Earth is about parallel to the spin axis, put some water in an oval bowl and pull the plug straight out, you're only going to see local effects.

Chris - So in other words, Michael Palin was fooled into thinking this was true at the equator.

Karl - Mate, there's an old Polish saying. If you've got a dog, don't bark. It's fairly obscure, but what it means is stick to your speciality. The number of areas of ignorance we have are huge. In this particular case in the TV series Pole to Pole, Michael Plain meets a man called Michael McCleary, who says that this line here on the ground is the equator. He has a little square tub which he's holding in his hands with floating matchsticks. He then walks off in one direction and spins as he turns around to face the tourists. That gives a spin to the water. He takes his finger off the bottom and you can see the matchsticks going round clockwise or anti clockwise as he's being told. Poor Mr Palin is being conned!

Chris - It just goes to show that even the great Michael Palin can be conned sometimes. Thanks very much for joining us Dr Karl and helping us to avoid throwing out the baby with the bath water and debunking the myth of the Coriolis effect and how it effects spin when water goes down the plug hole.

December 2005

///// Part 3 Suggested demonstration kit /////

I would suggest to use a rotating platform to rotate a double-layer half globe on a cylindrical upright pillar, with the following set-up.

Set-up 1: Pin-ball experiment

1a) While the platform is rotating from west to east, shoot a pin-ball from the equator to the north pole along the zero meridian. We predict that it would deflect to the right. If there are three holes at the 45 degree latitude, namely one at the zeroth meridian, one on the right and one on the left, the pin ball would "fall" into the right hole.

1b) If a pin-ball is shot from the north pole along the zero meridian to the equator, it will "fall" into the left hole.

1c) If similar arrangement is mounted on the cylindrical part, both balls will "fall" into the zeroth meridian hole.

1d) If we reverse the rotation of the platform from east to west, in the half globe, the ball shot from the equator will fall into the left hole and the ball shot from the north pole will fall into the right hole (different from (a) and (b)). In the cylindrical column, all balls will fall into the zeroth meridian hole (same as in (c)).

Set up 2: Air suction

2a) In the inner globe of the double layer, punch four holes:
(i) a hole at the north pole,
(ii) a hole in the equator at the zeroth meridian,
(iii) a hole in the 45 degrees north latitude and the 45 degrees east longitude,
(iv) a hole in the 45 degrees north latitude and the 45 degrees west longitude.
2b) If we punch punch a hole in the outer globe of the double-layer at the position of zeroth meridian and 45 degrees north latitude, air will be centrifuged out of the globe while the globe rotates. We can put sensors around the hole for detecting air current.

2c) Instead of punching a hole in the outer globe, we shall punch a hole in the inner globe at the same position (zeroth meridian and 45 degrees north latitude), and use a pump to pump air out of the double-layer there. The sensors in (b) will detect the current flow, which according to Coriolis effect should be in counter-clockwise direction.

2d) If we install similar things on the cylindrical column as a control experiment, the air flow direction may not form a pattern.

2e) If we reverse the direction of the rotation, we would expect the air flow in (c) will be in clockwise direction. Again, the control experiment installed in the cylindrical column will not display a clear pattern.

Set up 3: Water flow

3a) Mount two water reservoirs at the equator (called them the left and right side of heart), linked with pipe to enable water flow in-between.

3b) Mount two water reservoir at the north pole (called them the left and right side of the cerebrum), again linked with pipe to enable water to flow in-between

3c) Use a rubber tube (right tube) to connect the water outlet at the right heart to the water inlet at the right celebrum.

3d) Use a rubber tube (left tube) to connect the water outlet at the left celebrum to the water inlet at the left hear.

3e) Use a pump to pump water from the right heart upwards. Water would flow upward along the right tube to the right celebrum, then to the left cerebrum, fall down along the left tube to the left heart and return to the right heart to complete the circulation.

3f) As the globe rotates from west to east, the right tube will bulge to the right, and the left tube will bulge to the left, leaving a hollow for the anti-clocwise cyclone to form, as predicted by the Coriolis effect.

3g) Suggest to clamp the rubber tubes in place, activate the pump to circulate the water, then rotate the globe. When condition stabilizes, release the clamp and observe how the rubber tubes will bend. For better effect, install sensors to detect the bending of the rubber tubes. One form of sensor is to use florescent water and transparent rubber tubes, so that we can observe the bending of the rubber tubes without having to stop the globe from rotating.

3h) If we change the direction of the rotation, we would expect that rubber tubes to bend towards each other instead of bulging out.

3i) The control experiment installed at the side of the cylinder would not display the bending effect.

3j) To demonstrate the effect side by side, we may install similar water inlet and outlets at the 180 degrees meridian with water pumped up along the left rubber tube and water returning downward along the right rubber tube. It is predicted that the opposite effect of (3f) and (3h) would be observed.

Set up 4: Further improvement

4a) It may be desirable to divide the the globe and the cylinder into 4 compartments, two for the water pipes, one for the pin-ball and one for air flow.

4b) It may also be desirable to change the half globe design to a pyramid design (with a square base) to house the 4 compartments.

4c) It may also be desirable to build two units, one rotating from west to east (to emulate the northern hemisphere), and the other rotating from east to west (to emulate the southern hemisphere). If successful, this will explain everything in one go.

No comments: