116 lines
3.9 KiB
Plaintext
116 lines
3.9 KiB
Plaintext
From fork-admin@xent.com Tue Sep 17 23:29:46 2002
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To: fork@example.com
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Subject: Re: The Big Jump
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In-Reply-To: Message from fork-request@xent.com of
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"Mon, 09 Sep 2002 19:25:02 PDT."
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<20020910022502.8777.4915.Mailman@lair.xent.com>
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From: Dave Long <dl@silcom.com>
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Date: Tue, 17 Sep 2002 12:40:05 -0700
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> All else being equal, the terminal velocity is inversely proportional to the
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> square root of air density. Air density drops off pretty quickly, and I
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> really should be doing something other than digging up the math for that. I
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> think it involves calculus to integrate the amount of mass as the column of
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> the atmosphere trails off.
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Chemistry types have a method for
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dealing with this question without
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dragging in the calculus:
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Suppose an atmosphere to be mainly
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affected by gravity, resulting in
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the potential energy for a mass M
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to be linear in height h: Mgh.
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What relative concentrations will
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we have when two different packets
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of air are in equilibrium?
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If they are at the same height, we
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will have half the mass in one, and
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half the mass in the other, and the
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amount flowing from one to the other
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balances the amount flowing in the
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opposite direction.[0]
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If they are at differing heights,
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then a greater percentage of the
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higher air tends to descend than
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that percentage of the lower air
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which ascends. In order for the
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two flows to balance, the higher
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packet must contain less air than
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the lower, and the mass balance
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of the flows corresponds thusly:
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high percentage of thin air
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---------------------------
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low percentage of dense air
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Now, rates are exponential in
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energy differences[1], so that
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theoretically we should expect
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an exponential decay in height,
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to compensate. How does it go
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in practice?
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-Dave
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[0] How well does it balance?
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Chemical equilibria seem
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stable, as they deal with
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very large numbers over a
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very long time. Economic
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equilibria are viewed from
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the mayfly standpoint of
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individual people, and so,
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at best, the shot noise is
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very visible.
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[1] That is to say, rates will
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be exponential in the free
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energy differences between
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endpoints and a transition
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state. We can ignore that
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complication in this model.
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