Re: A Hole through Earth?


Ian Stirling wrote:
> Henry Lemington-Wholeflavors <cwocwocwo@xxxxxxxxxxx> wrote:
> >
> > Steven Gray wrote:
> <snip>
> >> I haven't done the calculation, but it may well be substantial.
> >> The pressure that we have at the surface results from a column of air
> >> only about 100 miles high, in a field that decreases as 1/r^2 as you
> >> go up.
> >
> > It would be a nice calculation do to. I might try it.
>
> Ballpark.
> Air pressure doubles (in the lower atmosphere) about every 6Km.
> Go down another 600Km, neglecting the diminuition in gravity, and
> you're at way beyond where air behaves like a gas, and it's
> more like a liquid.
> You can't breath this.
> Once you get down to -12Km or so, you're going to need breathing gear
> in order to survive long term, as you risk stuff like nitrogen narcosis,
> not to mention oxygen toxicity.
> You can go down a bit more than this, but well before -100Km (neglecting
> temperature) your body simply stops working in various ways that can't
> be bypassed due to things like protiens deforming under pressure.

It's worth checking whether this ballpark estimate survives the
correction due to the linear fall-off of gravity in the hole and other
effects. Basically, the analysis above assumes the behavior
P=(rho)*g*h, where rho is the density of the fluid (air). However:
1. g falls linearly to zero as you approach the center of the earth,
and this will *lower* the weight of the column of air above you
2. rho increases with pressure at constant temperature due to
Avogadro's law for a gas, and this will *increase* the weight of the
column of air above you
3. the pressure will increase due to rising temperatures, assuming
rough local thermal equilibrium with the walls of the hole

PD

.

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