Re: A Hole through Earth?

PD <TheDraperFamily@xxxxxxxxx> wrote:
>
> 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.
<snip>
> 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

Pretty much irrelevant - I only considered the first 600Km, at which gravity
is only down to 9m/s^2 or so.

> 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

That's why the scale height thing happens.

> 3. the pressure will increase due to rising temperatures, assuming
> rough local thermal equilibrium with the walls of the hole

I was assuming magically insulated holes, as otherwise you can't breath
in it anyway.
.

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