Re: The 2005 hurricane season

Mark Atwood <me@xxxxxxxxxxxxxxxx> wrote:
David Dyer-Bennet <dd-b@xxxxxxxx> wrote:
Mark Atwood <me@xxxxxxxxxxxxxxxx> wrote:
ISTR that in such a situation, the pressure rises linearly with
depth, at least for water. I don't recall what the constant
of proportionality is, nor do I recall if it's different for
compressable vs uncompressable materials.

For an incompressible liquid, pressure rises linearly with depth. For
an ideal gas, pressure rises exponentially with depth. This assumes
that gravity, temperature, and composition are constant in both cases.

At reasonable pressures, water is fairly close to an incompressible
liquid, and air is fairly close to being an ideal gas. At the
pressures you'd get in a tunnel through the earth (just from the air
or water -- we're blocking the pressure from the surrounding rock)
water is no longer incompressible, and air is far from ideal.

Gravity would drop off linearly with depth (i.e. half a g when halfway
to the center) if the earth was a uniform sphere. It isn't. It's
believed that gravity is roughly constant all the way to the edge of
the core, and only then starts to seriously drop off. But nobody
knows for sure. Probably the only ways to find out are to either:

* Send a probe to the center of the earth.

* Build a gravitational wave telescope or a neutrino telescope in
space, about a light year away, and view some point source of
gravitational waves or neutrinos through the earth, using the
earth as a gravitational lens.

I wonder which would be more difficult?

Of course my proposed tunnel would be filled with vacuum, so what
would happen if it were open to the air is moot.

The atmospheric pressure around a gravitational mass falls off
according to the square of the distance, otherwise.

No, it falls off exponentially, and fairly rapidly. To a rough first
approximation, every additional five miles of altitude halves the
air pressure.
--
Keith F. Lynch - http://keithlynch.net/
Please see http://keithlynch.net/email.html before emailing me.
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