Airplane Pilot's As Physicists

On 16 Oct, 16:17, Le Chaud Lapin wrote:
On Oct 16, 6:31 am, Thomas wrote:



On 9 Oct, 21:08, Le Chaud Lapin wrote:
You may want to check out my web pageshttp://www.physicsmyths.org.uk/bernoulli.htm
andhttp://www.physicsmyths.org.uk/drag.htmfor a closer examination
of the physics behind the aerodynamic lift and drag.

The main point I am making there is that it is physically nonsense to
claim that changing merely the tangential velocity of the air stream
relative to the surface would in any way produce a resultant force (at
least for a non-viscous gas).
What one needs for a pressure change
(and thus a force) on the surface is a change in the numbers and/or
the velocity of the molecules hitting it, i.e. it is only the vertical
component of the velocity that is relevant here. Only this can produce
the lift for an airfoil, either because of the increased number of
collisions on the lower side or the decreased number of collisions on
the upper side (both situations lead to a lift).

I agree, but there are some that seem to think the contrary, as you
know, with the Coanda effect.http://en.wikipedia.org/wiki/Coand%C4%83_effect

The Coanda effect is only due to the viscosity of the gas/fluid and
thus would not appear for a non-viscous gas, but the aerodynamic lift
does (so the Coanda effect can not possibly be an instrumental cause
for the latter).

Based on the simple kinematical model for the change of the molecular
collision rates with the wing surface, one can indeed get a good
estimate for the lift of Boeing 747 for instance:

consider first a plate of a size 1 m^2 moving head-on with a velocity
of 250 m/s in air; air has a number density of about 10^25 molecules/
m^3 (at 10,000 m), so in 1 sec the plate will be hit by 10^25*250 =
2.5*10^27 molecules. If you assume that each molecule has a weight of
4.5*10^-26 kg, this means that the force on the plate is 2.5*10^27
*4.5*10^-26 *250 = 5.6*10^4 N = 12,600 lb. Of course, the wing surface
is not directly facing into the airstream but only at a very shallow
angle. Let's assume that this angle (the average slope of the upper
wing surface) is about 5 deg; this means that the force calculated
above has to be multiplied by a factor sin(5)*cos(5) to obtain the
lift and by a factor sin^2(5) to obtain the drag force, which results
in about 1,100 lb and 95 lb respectively. Now this would be for a wing
surface of 1m^2; however the total wing area of the Boeing 747 is 541
m^2 (see http://www.airliners.net/info/stats.main?id=100 ), so the
forces become about 600,000 lb for the lift and 50,000 lb for the drag
(by the wings). Note that this figure for the lift force is pretty
close to the maximum weight of a 747 (considering the crude nature of
the derivation, in particular the assumption of a 5 deg angle for the
slope of the upper wing surface).


I just read both your web pages.

BTW, your explanation of d'Alembert's Paradox and the blow-over-paper-
attached-to-table experiment could both use diagrams. I am trying the
blow over the paper experiment now and I am not sure if I am doing it
as you described. Could you provide a more vivid description so I can
make sure?

Well, the point is that the commonly given example with blowing over
the sheet of paper only works because (due to the orientation of the
paper surface) you are blowing away from the paper. The (on avarage)
initially stationary air molecules will thus be pulled with the air
molecules coming out of your mouth, i.e. away from the paper, which
will thus create a corresponding reduction of the number of molecules
near the paper surface, i.e. a pressure reduction. However, this all
can only happen a) because of the viscosity of the air (the molecules
coming out of your mouth collide with the air molecules, and b)
because you are blowing to a certain degree away from the paper. Would
you blow exactly parallel to the surface of a flat sheet of paper,
nothing would happen at all (it is obvious that if the sheet would
lift up at the 'downstream' end, it would be pushed right back again
into a position where the surface is parallel to the airstream (as
this is the force free equilibrium position)).

So since this effect (llike the Coanda effect) relies on the
viscosity of the air, it has nothing to do with the aerodynamic lift
(which also would occur if the air was completely inviscid).

Thomas

On 16 Oct, 16:17, Le Chaud Lapin wrote:
On Oct 16, 6:31 am, Thomas wrote:



On 9 Oct, 21:08, Le Chaud Lapin wrote:
You may want to check out my web pageshttp://www.physicsmyths.org.uk/bernoulli.htm
andhttp://www.physicsmyths.org.uk/drag.htmfor a closer examination
of the physics behind the aerodynamic lift and drag.

The main point I am making there is that it is physically nonsense to
claim that changing merely the tangential velocity of the air stream
relative to the surface would in any way produce a resultant force (at
least for a non-viscous gas).
What one needs for a pressure change
(and thus a force) on the surface is a change in the numbers and/or
the velocity of the molecules hitting it, i.e. it is only the vertical
component of the velocity that is relevant here. Only this can produce
the lift for an airfoil, either because of the increased number of
collisions on the lower side or the decreased number of collisions on
the upper side (both situations lead to a lift).

I agree, but there are some that seem to think the contrary, as you
know, with the Coanda effect.http://en.wikipedia.org/wiki/Coand%C4%83_effect

What is troubling about many of these theories is that, at the precise
moment where the reader is most alert in anticipation of the meat of
the explanation, the hand-waving begins. In the link above, the clause
entitled Causes, it is written:

"The effect of a spoon apparently attracting a flow of water is caused
by this effect as well, since the flow of water entrains gases to flow
down along the stream, and these gases are then pulled, along with the
flow of water, in towards the spoon, as a result of the pressure
differential. "

Hmmm...."and these gases are then pulled"...

pulled? By what?


The Coanda effect is only due to the viscosity of the gas/fluid and
thus would not appear for a non-viscous gas, but the aerodynamic lift
does (so the Coanda effect can not possibly be an instrumental cause
for the latter).

Based on the simple kinematical model for the change of the molecular
collision rates with the wing surface, one can indeed get a good
estimate for the lift of Boeing 747 for instance:

consider first a plate of a size 1 m^2 moving head-on with a velocity
of 250 m/s in air; air has a number density of about 10^25 molecules/
m^3 (at 10,000 m), so in 1 sec the plate will be hit by 10^25*250 =
2.5*10^27 molecules. If you assume that each molecule has a weight of
4.5*10^-26 kg, this means that the force on the plate is 2*2.5*10^27
*4.5*10^-26 *250 = 5.6*10^4 N = 12,600 lb (the additional factor 2 is
due to the fact that in an elastic collision with the plate, the
momentum change is twice the momentum of the molecule). Of course, the
wing surface is not directly facing into the airstream but only at a
very shallow angle. Let's assume that this angle (the average slope of
the upper wing surface) is about 5 deg; this means that the force
calculated above has to be multiplied by a factor sin(5)*cos(5) to
obtain the lift and by a factor sin^2(5) to obtain the drag force,
which results in about 1,100 lb and 95 lb respectively. Now this would
be for a wing surface of 1m^2; however the total wing area of the
Boeing 747 is 541 m^2 (see http://www.airliners.net/info/stats.main?id=100
), so the forces become about 600,000 lb for the lift and 50,000 lb
for the drag (by the wings). Note that this figure for the lift force
is pretty close to the maximum weight of a 747 (considering the crude
nature of the derivation, in particular the assumption of a 5 deg
angle for the slope of the upper wing surface).

And it should be
obvious that for this to be the case, one must either have the lower
side of the wing facing to a certain degree into the airstream, and/or
the upper side facing to a certain degree opposite to the airstream.
This is why one either needs a certain 'angle of attack' or a
correspondingly shaped airfoil. And it should be obvious that in order
to have an asymmetric force (i.e. a higher upward than downward force)
one needs the surfaces of the airfoil to be orientated in some way
asymmetrical relatively to the airstream. So a perfectly symmetrical
airfoil (front to back) at a zero angle of attack (like I indicated in
Fig.1 on my pagehttp://www.physicsmyths.org.uk/bernoulli.htm) should
not produce any lift as the upward force (from the rear part) is
exactly equal to the downward force (from the front part). All that
would happen is that the wing experiences an anti-clockwise torque.
This is the reason why the rear part of the wing (behind the apex)
must always have a larger surface than the front part. At least I have
yet to see an airfoil where this is not the case and where it can be
used at a zero angle of attack.
(the Bernoulli principle is in direct contradiction to this as it
would also predict a lift for a perfectly symmetric airfoil in this
sense).

I just read both your web pages.

BTW, your explanation of d'Alembert's Paradox and the blow-over-paper-
attached-to-table experiment could both use diagrams. I am trying the
blow over the paper experiment now and I am not sure if I am doing it
as you described. Could you provide a more vivid description so I can
make sure?


Well, the point is that the commonly given example with blowing over
the sheet of paper only works because (due to the orientation of the
paper surface) you are blowing away from the paper. The (on avarage)
initially stationary air molecules will thus be pulled with the air
molecules coming out of your mouth, i.e. away from the paper, which
will thus create a corresponding reduction of the number of molecules
near the paper surface, i.e. a pressure reduction. However, this all
can only happen a) because of the viscosity of the air (the molecules
coming out of your mouth collide with the air molecules, and b)
because you are blowing to a certain degree away from the paper. Would
you blow exactly parallel to the surface of a flat sheet of paper,
nothing would happen at all (it is obvious that if the sheet would
lift up at the 'downstream' end, it would be pushed right back again
into a position where the surface is parallel to the airstream (as
this is the force free equilibrium position)).


So since this effect (llike the Coanda effect) relies on the
viscosity of the air, it has nothing to do with the aerodynamic lift
(which also would occur if the air was completely inviscid).

Thomas

On 16 Oct, 18:29, Thomas wrote:
If you assume that each molecule has a weight of
4.5*10^-26 kg, this means that the force on the plate is 2.5*10^27
*4.5*10^-26 *250 = 5.6*10^4 N = 12,600 lb. Of course, the wing

I forgot actually to write an additional factor 2 here which I added
because in an elastic collision with the plate, the momentum change is
twice the momentum of the molecule. So it should read:
"the force on the plate is 2*2.5*10^27 *4.5*10^-26 *250 = 5.6*10^4 N =
12,600 lb.

Thomas

Thomas wrote:
You may want to check out my web pages
http://www.physicsmyths.org.uk/bernoulli.htm and
http://www.physicsmyths.org.uk/drag.htm for a 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.

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.htm for a 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.
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.

Thomas

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.htmfor a 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.

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.

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.

-Le Chaud Lapin-

Le Chaud Lapin wrote in
ups.com:

On Oct 16, 10:20 am, "Androcles" wrote:
"Le Chaud Lapin" wrote in
oglegroups.com...
: On Oct 16, 3:47 am, "Androcles" wrote:
: "Le Chaud Lapin" wrote in
glegroups.com...
: : On Oct 15, 7:54 pm, "Androcles"
: : wrote:
: : "Le Chaud Lapin" wrote in
: messagenews:1192494448.158299.317200
@v23g2000prn.googlegroups.com.
: ..
: : : On Oct 15, 6:42 pm, "Gatt"
: : : wrote:
: : : "Le Chaud Lapin" wrote in
: : messagenews:1192488325.423647.30120
@i38g2000prf.googlegroups.c
: : om...
: : :
: : : I read last night in another piloting book, again, that
: : : the
common
: : belief
: : : about the dynamics of airfoils is wrong,
: : :
: : : Yeah? Which one?
: : :
: : : I'd have to go back to bookstore to find the name.
: :
: : AHAHAHAHAHAHA!
: : Or back to sleep to dream again...
: :
: : Barry Schiff, in "The Proficient Pilot", "An AOPA Book", writes
: : on page 2:
: :
: : "There is, for example, this amusing fable: "Air flowing above
: : the wing has a greater distance to travel (because of camber)
: : than air flowing beneath the wing. Therefore, air above the
: : wing must travel faster so as to arrive at the wing's trailing
: : edge at the same time as air flowing underneath. This is pure
: : nonsense."
:
: Since it is true Schiff must be a raving lunatic. Maybe you don't
: understand that travelling the greater path in the same time
: involves a greater speed.
:
: Perhaps you could explain in detail what you mean by this last
: statement. I am sure that there are plenty of people here would
: would like, for once, that a pilot explains what s/he means by
: this.

Really?
Ok, for plenty of cretins such as yourself...

Travelling 70 miles (distance) in one hour (duration of time)
is a speed of 70 mph by definition.
100 miles (the greater distance) in the same time (1 hour)
is 100 mph.
100 mph is faster than 70 mph.
People unaware of this simple fact are prone to getting
speeding tickets and losing their license.
Aircraft pilots are even more aware of it than motorists,
using their stop watches to compute distance.

In this video the air moves MUCH faster over the top of the wing
than it does over the bottom:
http://www.youtube.com/watch?v=KCcZyW-6-5o

I just looked at this video.

What you wrote and what this video demonstrates are two entirely
different things. There is no reason to say that the air moving above
the wing must meet beneath the wing.

I keep hearing people say,

"The air moves faster, therefore Bernoulli's Principle must be
invoked."

The thesis of what I have been saying all along can be seeing in an
inversion of this sentence.

"It is Bernoulli's principle that causes the air to flow faster."

In particular, it is the pressure gradient that causes the air in the
contstriction to flow faster. This same pressure gradient exists
above a wing in an air craft, and it has nothing to do with the
distance traveled. The camber of the wing is carefully designed my
airfcraft manufacturers to incudes, as much as possible, this pressure
gradient, at a particular speed, but *with* the conflicting
requirement that resulting drag must be reduced. This is why I said
earlier that pressure at the front of the wing is not necessarily bad.
It is desirable, but it also causes some laminar drag. Intuitively,
one can see what the edge must not be made sharp - doing that would
elimate the very pressure that is need to bring about the pressure
gradient.

Now you can go back to sleep and dream of Barry Schiff and
his "nonsense".

-Le Chaud Lapin-



Bad k00k! BAD!

Now shut up and go back in your box,


Bertie

Le Chaud Lapin wrote in news:1192554697.906337.44270
@v29g2000prd.googlegroups.com:

On Oct 16, 11:04 am, "Androcles" wrote:
"Le Chaud Lapin" wrote in
: In this video the air moves MUCH faster over the top of the wing
: than it does over the bottom:
: http://www.youtube.com/watch?v=KCcZyW-6-5o
:
: I just looked at this video.
:
: What you wrote and what this video demonstrates are two entirely
: different things. There is no reason to say that the air moving above
: the wing must meet beneath the wing.

What do you think it meets, water?

BTW, there is nothing in that video about airplane wings. It only
shows Bernoulli's principle using smoke stacks, hanging balls, piece
of paper, etc. At no point do I see any demonstration of air above
and below having disparity in speed, unless you count the book.


Give it up Anthony. Nobody's buying.

Bertie

Le Chaud Lapin wrote in
oups.com:

On Oct 16, 9:53 am, "Gatt" wrote:
Barry Schiff, in "The Proficient Pilot", "An AOPA Book", writes on
page 2:

"There is, for example, this amusing fable: "Air flowing above the
wing has a greater distance to travel (because of camber) than air
flowing beneath the wing. Therefore, air above the wing must travel
faster so as to arrive at the wing's trailing edge at the same time
as air flowing underneath. This is pure nonsense."

Like I said. Upper camber is a conspiracy by the aluminum
manufacturers to sell more metal... Bournoulli was a shill.

You wrote repeatedly that lack of attention to detail (mostly due to
my spelling errors) indicated lack of understangind, was not becoming
of a critical thinker, etc...yet you keep making spelling errors
youself.

I never disputed Bernoulli's Principle, not once. I said that there
was a lot of hand-waving going on when pilots uttered greater/lesser/
camber/Bernoulli in the same sentence.

Bernoulli's principle is correct.

That the camber influences lift is correct.

But how the camber influences lift has nothing to do with greater
distances traveled, IMO.



Guess what, Your opinion is worthless.

you don;t fly and you never will, so bernoulli wil never be your slave..




M
Bertie

Le Chaud Lapin wrote in
oups.com:

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.htmfor a 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.

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.

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.


Hey, i'm waving my hand!

Well, just one finger, to be precise..


Bertie