1. ## Drain the Atmosphere

I am reading a book where a character smashes open a door which contained a portal leading to interplanetary space. A gale force wind starts blowing out, and one character says it will drain all the air. The other replies that that will take millennia at least.
How long would it actually take?

2. How large is the door?

3. Would not the outgassing from the many active volcanoes around the planet replace the "air" as rapidly as a door sized gap would leak it out?

4. It's going to be an exponential decay. Very quick and dirty calculation:

t = -V/(Av).ln(P/P0)

where V is volume, A is cross-sectional area, v is mean velocity, and P/P0 is the atmospheric pressure as a proportion of the starting pressure.

Mass of the atmosphere is 5x1018 kg which is equivalent to 4x1018 m3 at one atmosphere.

So with a two-square metre door opening and a flow speed equivalent to the speed of sound, it will take 4x1015 seconds to drop the atmospheric pressure by 50% - on the order of a hundred million years.

Grant Hutchison

5. Originally Posted by Spacedude
Would not the outgassing from the many active volcanoes around the planet replace the "air" as rapidly as a door sized gap would leak it out?
Well, that depends on the door....

Flow from the atmosphere to interstellar space would be choked, so about 85,000 cubic ft per minute per square foot of opening from sea level, standard day conditions.

6. I think it also depends on where the door is. If it's at sea level it will drain more quickly than if it's say on the top of Mt. Everest.

7. And you should be able to seal it again pretty easily. Anything you put up against the door frame will be held in place by the pressure differential, so you just need something relatively strong.

8. Originally Posted by Jens
I think it also depends on where the door is. If it's at sea level it will drain more quickly than if it's say on the top of Mt. Everest.
Yes, my estimate applies at sea level. You'd need to recalculate the effective volume of the atmosphere for the pressure altitude of the door. But sea-level with speed-of-sound outflow is a worst case, and 100 million years to halve the pressure doesn't seem like a big worry.

Grant Hutchison

9. It seemed obvious at first glance, but now I have to ask, why the speed of sound?

10. Originally Posted by mkline55
It seemed obvious at first glance, but now I have to ask, why the speed of sound?
I was aiming for a worst-case OOM, and figure the flow is unlikely to be faster than that (and will likely be considerably slower).

Grant Hutchison

11. Originally Posted by mkline55
It seemed obvious at first glance, but now I have to ask, why the speed of sound?
It’s compressible flow, so the flow can not exceed the speed of sound unless the nozzle is expanding, but the mass flow rate is limited by the velocity of the throat, which cannot exceed the speed of sound.
Last edited by swampyankee; 2017-Sep-25 at 09:10 PM.

12. Originally Posted by Grey
And you should be able to seal it again pretty easily. Anything you put up against the door frame will be held in place by the pressure differential, so you just need something relatively strong.
Strong enough to hold back 45,500 pounds of pressure over an area 6 feet across. That's the weight of 15 cars resting on the door.

13. Originally Posted by DaveC426913
Strong enough to hold back 45,500 pounds of pressure over an area 6 feet across. That's the weight of 15 cars resting on the door.
I get that it sounds big. But let's imagine just using a bunch of 6" x 8" wooden beams stacked in parallel over the opening. The load there for each beam will be about 1,000 pounds per linear foot of beam (or 6,000 pounds total across the 6 foot weight bearing portion of the beam). From this document (page 64), it looks like that's easily within the allowable load for a beam that size, and since those numbers are for building houses, they're chosen with a certain amount of safety margin built in, I think.

14. Originally Posted by swampyankee
It’s compressible flow, so the flow can not exceed the speed of sound unless the nozzle is expanding, but the mass flow rate is limited by the velocity of the throat, which cannot exceed the speed of sound.
Thanks for the clue. I searched on the term "compressible flow", and sure enough, it's a thing. Here I was all ready to build an argument of sorts, but never mind. Thanks again.

15. Okay, then how big a hole do you need to halve the atmosphere in, let's say, five years?

And if said hole was in a remote place, how many days would you guess before some meteorologist said, "Hmmm, that's funny..."

16. Originally Posted by BigDon
Okay, then how big a hole do you need to halve the atmosphere in, let's say, five years?

And if said hole was in a remote place, how many days would you guess before some meteorologist said, "Hmmm, that's funny..."
Just using grant's equation above, the time is inversely proportional to the area. So if you want it to be 5 years instead of 100 million, that's a factor of about 20 million, so your opening needs to be 20 million times bigger. That's 40 million square meters, or 40 square kilometers. I'd expect something like that to affect the weather in pretty obvious manner.

17. Originally Posted by Grey
I'd expect something like that to affect the weather in pretty obvious manner.
Indeed. Niven's Fist-of-God-esque.

18. Originally Posted by Spacedude
Would not the outgassing from the many active volcanoes around the planet replace the "air" as rapidly as a door sized gap would leak it out?
This is a good point. At the moment the amount of carbon and oxygen that is subsumed into the crust is just about equal to the amount of carbon dioxide that is outgassed. So if this balance is maintained, the decline in atmospheric pressure through the open door would still be maintained. But over time this balance would change - I think that if atmospheric pressure drops too much, outgassing will actually increase, since there is a lot of gas trapped in the crust that would seek to find its way out.

19. Further along in the series...
The door leads to a parallel earth where Bad Guys imploded the planet into a marble sized Black Hole. The wind through the door spirals down into the BH's accretion disk nearly four thousand miles away. You can see the glow of the AD with the naked eye through the door.
Would this "nano-quasar" be visible to the naked eye from 4000 miles?

20. Originally Posted by Tom Mazanec
Further along in the series...
The door leads to a parallel earth where Bad Guys imploded the planet into a marble sized Black Hole. The wind through the door spirals down into the BH's accretion disk nearly four thousand miles away. You can see the glow of the AD with the naked eye through the door.
Would this "nano-quasar" be visible to the naked eye from 4000 miles?
The accretion disk should be a beacon of EMR, including X-rays, with all the matter getting squished. It should be very bright, yes.

21. The air should certainly get hot enough. I'm getting 4 x 1014 J/kg for the change in potential energy falling from a distance equivalent to Earth's radius to a metre from the black hole. (I was sufficiently surprised by this I had to double-check my recollection of the value for G and the mass of the Earth!)
So it depends on how much air is in the accretion disc at any given time.

Grant Hutchison

22. Established Member
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Originally Posted by DaveC426913
The accretion disk should be a beacon of EMR, including X-rays, with all the matter getting squished. It should be very bright, yes.
Would being 4000 mi away, unshielded, be survivable (ignoring the mach 1 winds pulling you closer)?

23. Originally Posted by VQkr
Would being 4000 mi away, unshielded, be survivable (ignoring the mach 1 winds pulling you closer)?
A 1 cm black holes masses as much as the Earth. So now you have two Earth masses separated by a mere 1 Earth radius.

Not only would it pull you and the Earth closer, but it would tear the Earth up, rock by rock. 4000 mi is within its Roche Limit of about 4,200mi.

Radiation is possibly the less imminent of the threats.

But we may have to revisit the scenario here. Since the door is a portal to somewhere else, it raises the question of whether Earth can orbit the BH (and the BH orbit the Earth). I guess, since the portal is techno-magically attached to the Earth, they can't orbit each other. Which means Earth and the BH are essentially free falling toward each other. Since the far side of the Earth is 7,800 mi more distant than the far side , tidal effects will apply. (3 times father away means the near side will experience about 9 times the gravitational attraction of the far side).
Last edited by DaveC426913; 2017-Oct-21 at 06:57 PM.

24. I think the idea is that our Earth is in one universe, and black hole Earth is in another universe. The doorway apparently lets matter and light pass in both directions, but I don't think the black hole and the Earth, in their separate universes, are supposed to be interacting gravitationally.
Even if they were, the parallel-universe black-hole Earth would presumably be sitting at a location equivalent to the centre of mass of our Earth, and so neither would fall towards the other.

Or so I read the scenario.

Grant Hutchison

25. If you want to look deeper into the scenario, it is from Charles Stross' The Merchant Princes series.

26. Originally Posted by Tom Mazanec
If you want to look deeper into the scenario, it is from Charles Stross' The Merchant Princes series.
I was actually going to ask what it was from, so that I could avoid it. Doesn't sound like my kind of plot.

Grant Hutchison

27. Actually I love this series myself. I preordered the next volume and look forward to the following one a year later.

28. Originally Posted by grant hutchison
Even if they were, the parallel-universe black-hole Earth would presumably be sitting at a location equivalent to the centre of mass of our Earth
But ... but ... he said it was 4000 miles on the other side of the portal...

Ohhh. I sortta missed the significance of the "parallel Earth" part - and now I understand why it's 4000 miles away. It's 4000 miles down to the centre of the parallel Earth.

Gotcha.
Last edited by DaveC426913; 2017-Oct-22 at 03:46 AM.

29. kzb
Established Member
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Then again, the atmosphere is right down in the Earth's gravitational potential well.

A portal to interplanetary space leads to a place outside this gravity well.

So this portal would actually have to supply a lot of energy to transport material from Earth surface to interplanetary space.

It would not be a passive operation, it would be actively pumping air out, and it could be simply turned off.

30. Originally Posted by kzb
Then again, the atmosphere is right down in the Earth's gravitational potential well.

A portal to interplanetary space leads to a place outside this gravity well.

So this portal would actually have to supply a lot of energy to transport material from Earth surface to interplanetary space.

It would not be a passive operation, it would be actively pumping air out, and it could be simply turned off.
It makes more sense when we have the Earth-mass black hole on the other side, occupying the same position as Earth on this side. That puts both sides of the door at the same potential energy. (If potential energy is even a transferable quantity between parallel universes.)

Grant Hutchison

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