Re: toroidal perpetual motion machine

[John Denker <jsd@MONMOUTH.COM>]

At 06:33 PM 6/28/00 -0500, brian whatcott wrote in part:

> "You must be recalling that a narrow glass tube allows the interior
>  water level to rise above the outside meniscus."
>
> "Well, it stands to reason. If the inner capillary head did not
> balance the longer outside meniscus, the torus shape would rotate,
>  like a snake trying to shrug off its skin, wouldn't it?"

Nice try, but...

Consider a collection of inner tubes, all with the inner radius r, but with
differing outer radii R.  The amount of capillary rise will be the same for
all of them;  the water inside the hole can't know anything about the outer
radius.  The meniscus on the outside will be the same for all of them, to a
more-than-sufficient approximation.  BUT -- the imbalance in length of
meniscus will vary from tube to tube in proportion to R-r.

The suggested compensation mechanism doesn't scale properly.

========

The valiant attempt earns you another hint:

Hint #3:  The correct answer must predict the correct behavior for this
entire family of tubes.  It will pass dimensional-analysis
tests.  Conversely, dimensional analysis can help you more quickly escape
from the clutches of tempting but fruitless approaches.