The AFU and Urban Legend Archive Science Coriolis Force coriolis quitt Select a topic - - - - - - - - Home Searches AFU FAQ - - - - - - - - AFU Animals Books Celebrities Classic Collegiate Death Disney Drugs Food GIF Language Legal Medical Misc Movies Politics Products Religion Science Sex Songs TV - - - - - - - - Other sites

Newsgroups: alt.folklore.urban
From: kdq@emoryi.jpl.nasa.gov (Kevin Quitt)
Subject: Re: coriolis effect debunked? (Re: Marilyn vos Savant Vectors Glass Flow)
Date: Sat, 9 Dec 1995 04:41:33 GMT

On Tue, 5 Dec 1995 22:52:51 GMT, hatunen@netcom.com (DaveHatunen) wrote: >May I humbly suggest that you provide an equation for the value of the
>coriolis effect v latitude for a container of, say 1m diameter? This
>would go a long way to end speculation on all sides, and constitute a
>serious contribution to the FAQ.

Consider the source of coriolis: It's the difference in the earth's rotational speed between the northern and southern latitudes of the body in question. The speed at any angle is the cosine of the angle times the speed at the equator. Note that at the equator (center of body over equator) the difference is zero - and if the edge is on the equator, you don't get much more. (So much for the guy walking back and forth across the equator.)

Now shall we calculate the delta vee on a one meter pool? Let's give it the benefit of the doubt and put it at 45 degrees. Using 40,000 KM as the circumference at the equator, the angular difference between the higher and lower latitude is:

1m 1 1Km 2PI rad
Da = -- * -------- * ------ * -------

1 40000 Km 1000 m 1

is 157 billionths of a radian or 4.5 millionths of a degree.

At the Earth's equator, assuming an exactly 24 hour day, the rotational velocity is:

40000 Km 1000 m 1 rot. 1 h Ve = -------- * ------ * ------ * ------

1 rot. 1Km 24 h 3600 s

is just under 463m/s.

The speed at 45 degrees is therefore

V1 = Cos[ Pi/4 ] * Ve

and the speed one meter further up is

V2 = Cos[ Pi/4 + Da ] * Ve

so our delta V in meters per second is

Dv = V1 - V2

which expands out to

                              5000001 Pi
                    12500 Cos[----------]
     6250 Sqrt[2]              20000000
Dv = ------------ - --------------------- = 0.0000514223 m/s = 0.0514223 mm/s
          27                 27

A circle of diameter 1 m has a circumference of 6283 mms, so our twentieth of a millimeter per second will cause the amazing speed of one rotation every 122,188 seconds, (1 day, 9 hours, 56 minutes and 28 seconds). Being perfectly reasonable about this, it's hard to see how you're going to see this in your sink (1/3m?) or bathtub. And at the equator, it's about 82 times slower. (This really sinks that guy with the sink). These numbers are so bloody small that my calculator couldn't handle them (*you* try the cosine of Pi * 5,000,001 / 2e7).

Now that we see how little motion is imparted by coriolis, factor in convection currents from temperature differentials in the water (which you *will* have unless the air's at 100% humidity and there's virtually no light and you don't go near it for fear of adding eat), other residual motions, friction, and the shape of the basin (perfectly symmetrical?), and that doesn't allow for much of an effect.

It's possible I made an error in the calculations - if I have, just point them out (no need to be vindictive), and I'll correct them. Someone else can have the joy of calculating what the maximum delta vee can be (one edge on the pole). Perhaps we can put both these results (once verified) into the FAQ and then we can all go home.