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[smjjames]

ENCELADUS HAS AN HONEST-TO-GOD OCEAN.

Enceladus is Saturns Europa

[Parsely]

Help me with physics! For fun, I'm trying to find out how long it would take to drain all of Earth's atmosphere if you were to create a perfectly round portal that's 3m in diameter that led to some location in space.

P = Po exp[-(A/V)t*(200m/s)]                                        //po exp stands for... something :I, P = pressure in pascals, 1atm is 101.325kpa
pressure = Po exp[-(area/volume)time*(c*.6)                 //where c=speed of sound and gas escapes into a vacuum at approximately 60% of c, t = time in seconds
101,325 = Po exp[-(7.07/4.2billion km^3)t*(200m/s)]    //the equation so far; 3.15 is the area of the hole, 4.2bil is the effective volume of Earth's atmo

Solving for t of course.

[Darvi]

Why is c the speed of sound that's so confusing.

[Sergarr]

why pressure = 101,325

[Darvi]

The standard atmosphere (symbol: atm) is a unit of pressure equal to 101325 Pa[1] or 1013.25 hectopascals or millibars.

[Sergarr]

what is it doing on the left

this pressure should go instead of P0 not P

[Darvi]

Yeah that's a better point. I don't know my atmospheric formulae but I'm assuming that pressure = pressure of the out-going air? #darvicannotintowords

[Sergarr]

pressure = the pressure of atmosphere after (t) seconds pass.

And actually:

For fun, I'm trying to find out how long it would take to drain all of Earth's atmosphere if you were to create a perfectly round portal that's 3m in diameter that led to some location in space.

The answer is infinite time, because it's the time it would take to reach a complete equilibrium. You can, however, calculate how much time it would take to half the atmosphere - a half-life period. It would probably be pretty big. Around 1 million seconds.

[Frumple]

... a million seconds is something like 11-12 days. That's... not very big?

[Sergarr]

... a million seconds is something like 11-12 days. That's... not very big?

Yeah, it means I've messed up the units of area/volume.

Calculating... - (+1 - 9 - 3*3 (this is what I forgot about before) + 2) = +15

It's about 10^15 seconds. Quite a lot of time.

[Frumple]

... yeah, that's significantly longer. 31.7 mil years, give a bit because screw leap years?

[Sergarr]

And that's only to half the atmosphere. It would take the same amount of time again to make it 1/4th, again - for 1/8th, and so on.

[Parsely]

Haha! Your DOOM approaches!
...
I said, your DOOM approaches!
...
...
*pokes the doomsday with a stick*

Why is c the speed of sound that's so confusing.

It says on the list of common physics notation that c can mean the speed of sound or a few other things, normally I see it being used to mean the speed of light. But it doesn't matter, a variable can have any meaning that one assigns to it.

why pressure = 101,325

1 atmosphere of pressure = 101.325kpa OR 101,325pa

what is it doing on the left

this pressure should go instead of P0 not P

*shrug* I just looked up the formula and started doing algebra, i.e. plugging stuff in.

The answer is infinite time, because it's the time it would take to reach a complete equilibrium. You can, however, calculate how much time it would take to half the atmosphere - a half-life period. It would probably be pretty big. Around 1 million seconds.

I don't understand. So you're saying the time needed to reach equilibrium is just immeasurably high? Or complete equilibrium is impossible?

[Darvi]

Because the air pressure would be reduced over time, the air flow also slows down at the same rate. So even though there's less air left, you also lose air at a much slower rate. The atmospheric pressure would converge towards 0, but never actually reach that point.

[Sergarr]

I don't understand. So you're saying the time needed to reach equilibrium is just immeasurably high? Or complete equilibrium is impossible?

Complete equilibrium is always impossible. It's a mathematical abstraction that's as impossible to realize in reality as drawing an absolutely perfect circle. But you can get something which would be "almost" equilibrium. First though, you need to define the "almost" to something. And based on that, you can make further calculations on how much time it would take to reach an "almost" equilibrium.