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Nasal passages and nasal sounds

I'm just unlurking for a second to throw an a few questions and comments
on these two recent subjects.

Although I am guilty of not having read the Science article on the nasal
passages, I wonder about the following points:

Why is it clear that the width of nasal passages (I hope this is the
correct term) is strongly correlated with the metabolic rate?
Of course I am well aware of a connection of the form: The wider the
passage -- the more oxygen you can get in your system. (See below)

However, I always thought that birds (most of them, perhaps this is not
true for ratites) have a higher body temperature than mammals; therefore I
would expect them to need more oxygen. Why then do their data fall on the
same line as the data from the mammals?

The fact that all these data points fall on the same line also tells us,
that there is a factor limiting the size of nasal passages FROM ABOVE.
Otherwise, why shouldn't some critters have very wide passages. Is the
reason loss of water/heat? If so, what about animals living in hot and
humid areas? Do they have larger nasal passages?

Finally, it was stated that the correlation is clear because of the laws
of physics; especially the hagen-Poiseulle Law.
(It states that the flow through a long narrow pipe is proportional to the
fourth power of the radius).
Unfortunately, as a physicists I have to tell you that the laws of physics
seldomly are as straightforward as that - usually they apply only in
idealized situations. (And I'm somewhat surprised sometimes at the force
with which these laws are invoked on this list.)
It was already pointed out that the HP-law is only applicable for laminar
flow and has to be replaced by a similar law for turbulent ones. This,
however is not all of it. The laws only apply for long, straight tubes,
where long means that they must be at least five to ten times longer than
wide. In addition, it assumes that pressure differences are constant. In
other words, you could INCREASE the amount of air you want to get through
your pipe by increasing the pressure difference, which would mean
increasing the lung power you have. (You CAN breathe through a straw for
quite a while, it's strenuous, however.) So we could sneak around the laws
for instance by having more powerful lungs, or making the pasages quite
short, or other things I cannot think of at the moment.

I would be interested in the scaling of the nasal width with the body
size. This should give a clue whether there is a correlation between
nasal widths and metabolism.  To estimate the scaling theoretically,
one would have to know the following scaling laws (how do they vary
with the size)

Metabolic rate
Amount of oxygen needed
Lung power
Length and shape of nasal passage (to see whether the same laws apply)
and probaly some others.

Then we could find theoretically how the nasal width should vary with body
size and compare with the data. If they agree, fine; if not, nasal width
is governed by something completely different.

If you consider this idea as hopelessly naive (it comes from atheoretical
physicist, after all), just throw some oxygen-consuming phenomenon at me.

To comment briefly on the estimation of acoustic frequencies of
complicated air systems: The state-of-the-art method to find these out
would be to perform a finite-element analysis, which is able to solve all
the differential equations Dr. Rowe mentioned in his mail. However, to do
so you would need

Computerized data of the air system
A well-equipped computer with the appropriate software on it
Some experience with these kind of simulations.

I would guess that students in engeneering could do this within a few
weeks - for a school project it would probably be a bit ambitious.


                   Dr. Martin Baeker
                   Institut fuer Werkstoffe
                   Langer Kamp 8
                   38106 Braunschweig
                   Tel.: 00-49-531-391-3066
                   Fax   00-49-531-391-3058
                   e-mail <martin.baeker@tu-bs.de>