Re: smoke-ring paradox

[William Beaty <billb@ESKIMO.COM>]

On Tue, 23 Jul 2002, Bob Sciamanda wrote:

> If rear flows = forward flows then there is no CM motion.  The equal
> rear/forward flows in the CM frame are superimposed upon the forward CM
> flow when viewed from the Lab frame, giving an unbalanced forward flow.

In the lab fram there can be no forward flow without equal rearward flow,
otherwise the fluid would build up in one place and be lacking in another
place.

Imagine a closed iron tank filled with water, with a vortex-ring launcher
inside.  If it shoots a series of vortex-rings, does water build up
anywhere?  Obviously not.  In other words, in the lab frame all
streamlines form closed loops.   How can momentum follow the vortex ring
along if for every parcil of fluid moving forwards, there MUST be a parcel
of fluid moving backwards?

> The launcher must exert a net forward force on the particle system ( and
> thus accelerate the CM forward), else it could only spin "in place".

I agree.  However, that doesn't answer MY question.  If ***NET*** fluid
cannot flow forwards within our water tank (if for every parcel which
moves forwards there must be a parcel moving backwards), how can a vortex
ring transport momentum?  If no fluid is created or destroyed, and if the
fluid density is constant, then in the frame of the water tank, the volume
of the forward-moving parcels MUST be exactly balanced by the volume of
the rearward-moving parcels.

Doesn't it follow that the momentum of the forward-moving fluid parcels is
exactly balanced by the rearward-moving parcels, hence the ring-vortex can
carry no momentum?

:)

(There's a hidden flaw in my reasoning.)

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