# Naked Science Forum

## Non Life Sciences => Physics, Astronomy & Cosmology => Topic started by: MichaelJPierce on 24/12/2009 17:10:54

Title: How does the length of a tunnel, at constant depth, vary with length?
Post by: MichaelJPierce on 24/12/2009 17:10:54
How does the length of a tunnel at a constant sea level directly relates to increasing atmospheric pressure in quantitative terms?

I understand that the atmospheric pressure increases with the length of the tunnel, but my google searches have failed to produce any data concerning any formula or model that could express in quantitative terms the effect of the length of a tunnel from a single entrance (such as a mine shaft or a tunnel digging operation in progress). Anyone know where I can find such data or can anyone have knowledge of a formula that I could use to gather data with?
Title: Re: How does the length of a tunnel, at constant depth, vary with length?
Post by: yor_on on 25/12/2009 00:45:04
As you do like Jules :)
Borrowing your way into earth, the gravity should be less right?
That should influence the atmospheric pressure, shouldn't it?
Title: Re: How does the length of a tunnel, at constant depth, vary with length?
Post by: Geezer on 25/12/2009 01:25:43
As you do like Jules :)
Borrowing your way into earth, the gravity should be less right?
That should influence the atmospheric pressure, shouldn't it?

It would if he burrowed into the earth. But I think he's at sea level all the time, so there will be no difference between the static pressure at the entrance and the end of the tunnel.
Title: Re: How does the length of a tunnel, at constant depth, vary with length?
Post by: yor_on on 25/12/2009 05:29:48
Then it makes no sense.

Any tunnel made will need in and outlets for air.

to keep it comparatively clean, assuming we're talking combustibles like cars you will need those to be so close each other that the air pressure will resemble the one above.
If you don't do so you will be poisoned?

Check it out on any longer tunnel made.

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Then, on the other hand? How do they fix the air flow between England/France?

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Let us assume that we build a tunnel one mile long fifty meter under the surface of a flat earth ::)) Without any in/out lets of air

And another ten mile long, should this mean that the ten mile long tunnel will have a higher atmospheric pressure?

Why?
Title: Re: How does the length of a tunnel, at constant depth, vary with length?
Post by: MichaelJPierce on 25/12/2009 16:33:46
Offhand, I don't see why the regular barometric equations wouldn't work.  You're talking about a tunnel into the earth and the pressure at various depths, right?

I don't know if it would apply. I'm assuming the tunnel is at a constant level.

Let's assume that this tunnel is in construction and only has one entrance and no traffic is yet going through it. if you needed to ventilate the area for workers while trying to remain efficient you would need to calculate how the pressure inside the tunnels are affected by its growing length. As mentioned breathable air at some point will not be able to reach the end of the tunnel at some point. So what factors must be taken into account and what are the existing formulas that would fit into this?

thanks guys, the dialog is inspirational so far.
Title: Re: How does the length of a tunnel, at constant depth, vary with length?
Post by: Geezer on 25/12/2009 20:35:40
Let's forget about ventilation etc. for a moment. If you bore a long horizontal tunnel, the air pressure at the entrance will be exactly the same at the entrance as it is at the end of the tunnel. The original post seems to suggest that is not the case.

Now, if you need to ventilate the tunnel for any reason, that may introduce a difference in pressure, but not necessarily.
Title: Re: How does the length of a tunnel, at constant depth, vary with length?
Post by: yor_on on 25/12/2009 20:44:51
The atmospheric pressure should be constricted by gravity right? Then what we have is a 'point' somewhere where gravity is at its most and on Earth that should be the surface. And any direction from that, upward or downward should then 'shrink' that atmospheric pressure it seems to me? As the gravity will shrink too. Am I wrong there?

If we then assume a tunnel which then is more like a hole, with only one entrance I would expect the air to fill it up, after all it's made out of molecules that obey gravity too, and after a while it should be 'everywhere' at an even mix as long as we don't 'disturb' it.

"Thomas Edison had contended it was impossible to ventilate a tunnel with the volume of traffic envisioned for the Holland Tunnel.[29] Previously, tunnels had been ventilated longitudinally. Engineer Ole Singstad pioneered a system of ventilating the tunnel transversely."
http://en.wikipedia.org/wiki/Holland_Tunnel#Ventilation_system

As for how those that build them count, maybe this can give you an idea.
http://www.desastres.org/pdf/tunnels.pdf
Title: Re: How does the length of a tunnel, at constant depth, vary with length?
Post by: yor_on on 25/12/2009 21:13:15
"And any direction from that, upward or downward should then 'shrink' that atmospheric pressure it seems to me? As the gravity will shrink too. Am I wrong there?"

If you look at as a 'pillar of air' then you might want to say that the higher the pillar the 'heavier' the pressure at it's bottom?

So if we made a hole straight down then the 'atmospheric pressure' would grow even though the gravity was less.

Any views on that?
Title: Re: How does the length of a tunnel, at constant depth, vary with length?
Post by: Geezer on 26/12/2009 00:38:24
It's really quite simple. It's just a question of the height of the air column. It makes no difference whether it's in a tunnel or anything else. Air is a fluid. The pressure it exerts at any height is simply determined by the amount of air above. Water does the same thing.
Title: Re: How does the length of a tunnel, at constant depth, vary with length?
Post by: yor_on on 26/12/2009 01:15:41
Yes, but then we have the decreasing gravity too, don't we?
Don't know how much difference it would make though.
Title: Re: How does the length of a tunnel, at constant depth, vary with length?
Post by: Geezer on 26/12/2009 02:20:46
Yes, but then we have the decreasing gravity too, don't we?
Don't know how much difference it would make though.

Yes we do, but it still will not make any difference whether the air is in a tunnel or not.
Title: How does the length of a tunnel, at constant depth, vary with length?
Post by: chris on 26/12/2009 10:53:53
If the tunnel is at a constant depth (i.e. relative to sea-level) then the air pressure recorded at any point along the tunnel will be the same and identical to the pressure in the open-air at the mouth of the tunnel.

Chris