On 17 Oct, 00:48, Le Chaud Lapin wrote:
On Oct 16, 3:31 pm, Thomas wrote:



On 16 Oct, 19:41, Jim Logajan wrote:

Thomas wrote:
You may want to check out my web pages
http://www.physicsmyths.org.uk/bernoulli.htmand
http://www.physicsmyths.org.uk/drag.htmfora closer examination of
the physics behind the aerodynamic lift and drag.

You might want to actually _include_ Bernoulli's theorem somewhere in your
pages. You talk about Bernoulli's equation, Bernoulli's principle, and
Bernoulli's law. And yet none of them are actually presented. Are you
saying they all the same or all different? Why not use the terminology used
by the professionals and stick with "Bernoulli's theorem"? How about
including references to relevant texts on your pages? It's not like serious
texts and lab experiments haven't been done on the subject for a zillion
years. It helps to show you know what you're talking about by showing
you've first read the professional literature on the subject and done your
own relevant research.

You might also want to redraw your figures so they include vertical labeled
arrows. Then present the assumptions and math needed to show your work and
why you think the vertical magnitudes sum to zero. Just saying they do, or
they only yield a torque, isn't good enough. It is more useful to _show_ -
not pontificate and hand-wave.

P.S. Chapter section 40-3 in volume 2 of Feynman's Lectures on Physics is
as good a place as any to start.

Bernoulli's theorem is not a fundamental physical law and thus not
required to understand the principle behind the aerodynamic lift. And
its misinterpretation and misapplication quite evidently leads to
incorrect physical conclusions, like the claim that a moving gas would
inherently have a lower static pressure than a stationary one. The net
flow velocity of a gas has per se nothing to do with the static
pressure.

I so agree. The amout of hand-waving that goes on when (presumably
technically-inclined) individuals invoke Bernoulli is perplexing.
Oddly, my college physics book is almost as guilty - after chapters
and chapters of Newtonian mechanics that are quite clear, they seem to
imply just that.

It is not so much a case of 'hand waving' arguments, but of
insufficient and contradictory physical definitions (especially with
regard to the notion of an 'inviscid' gas). Applying some physical
equation to a situation where it can not be applied is bound to lead
to paradoxes and wrong results.




As a thought experiment, consider a large tank containing gas with a
pipe attached to it which leads into a vacuum space. Assume first this
pipe is closed at the end; then the flow velocity in the pipe is zero
because the molecules heading outwards will be reflected at the end
and reverse their velocity (assume for simplicity that the molecules
do not collide with each other but only with the walls of the pipe and
the tank). If one now opens the pipe, the only thing that changes is
that the molecules heading outwards will not be reflected anymore at
the end but simply carry on heading into the vacuum space (with the
corresponding loss of molecules being replaced from the large tank).
So we now have a net flow velocity within the pipe without that either
the density nor the speed of the molecules has changed in any way.
This means that the pressure exerted on the inside wall of the pipe is
unchanged despite the fact that we now have a net flow velocity within
it. So Bernoulli's theorem would quite evidently give a wrong result
here.

Hmmm...technically, someone could argue that, in the vicinity of the
exit hole of the tank, there would be resulting decrease in pressure,
which would be true.

As should be evident from what I said above already, for an inviscid
gas (i.e. assuming the molecules do not collide with each other but
only with the walls), it should not make any difference whatsoever if
the pipe is open or closed at the end. The rate with which the
molecules hit the inside wall (and thus the pressure on it) is exactly
the same anywhere within the pipe (assuming the lost molecules for the
open pipe situation are readily replaced from the tank).


The misapplication, I think, results from too much hand-waving and not
being very specific about what pressure decreases over what. A venturi
apparutus, for example, very clearly demonstrates a drop in pressure,
and that drop is real, but the points chosen to measure the pressure
in the apparutus is very specific.

The Venturi effect (like the paper sheet example, the Coanda effect
and the Magnus effect) is merely a result of the viscosity of the
medium. It does not occur for an ideally inviscid medium (i.e. if the
collisions of molecules amongst each other can be neglected), whereas
the aerodynamic lift does.

Thomas