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This isn't exactly a homework question, but it is about what I once did in class and about something I was thinking about while I was watching tv (hey I'm thinking about physics in my spare time!).

If you watch stargate atlantis, you'll know that they can create a gate in one place and go through it coming out somewhere else. I was thinking; what if they opened one up accidentally in space- then all the air would be sucked through from the planet into space. What I was trying to work out was how long it would take for say 10% of the air from the planet to be sucked through. I remember from class an equation for pressure and fluid speed (bernoullis?)- could I use this and the pressure difference between the two sides of the gate to work it out?

using: P=1/2[p]v^2 (with P=pressure, [p]=density and v=speed)

and V=Avt (V=volume of air)

so substituting for the speed and rearranging it would take time

t= V/A(2P/[p])^1/2

can anyone tell me if this seems right?

I'm not sure if I'm using the right equation to start with, because if I rearrange it to get v=(2P/[p])^1/2 and put in some values, I get v~ 450 m/s

-faster than the speed of sound- would the air really go that fast??

If I put in the other values (V=10% of atmosphere, for earth size planet~10^18m^3), A~20m^2, P~10^5 Pa, [p]~1 kg/m^3

I work out time t for about 10^14 seconds or about 3 million years!!!!!

Again, can anyone tell me if I worked this out correctly? I realise that the pressure wouldn't stay constant though, so would I use an integral for a more accurate answer?

thanks for reading all the way through! I enjoy using the physics I've learned to try and figure stuff out for myself- it'd be great to hear that I was on the right tracks with this one