Stargate Atlantis/ pressure and fluids

[chris_p_2005]

Hi,
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 realize 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

 

[mukundpa]

The Earth's atmosphere is open to space still the air is not geting sucked, Why?
Think...

 

[chris_p_2005]

uh...gravity?

What i was really getting at with the post though was asking about what the speed of a fluid would be through an opening that had a pressure difference across it.

 

[mukundpa]

go through Bernoulli’s equation if viscosity is negligible otherwise Poiseuille's equation

 

[CarlB]

If you want an approximation of the right answer, take into account the fact that the speed of sound is about 1000 feet per second. You won't find any air flow faster than that. Take the area of the stargate, multiply it by 1000 feet per second. The result is a volume per second. Divide the volume of the Earth's atmosphere by that figure. The result is a lot less than the time required to suck the air off the earth, but it will give you a nice order of magnitude.

I bet it will be a very long time.

Carl

 

[Tide]

Chris,

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.

That is essentially the principle Samantha Carter used to blow up a star! She sent a stargate into a star and the loss of mass caused the star to nova with the immediate benefit that it vaporized the Goa'uld fleet. I was impressed that it only took a few minutes - in the show! :)

 

[CarlB]

A stargate would reduce the mass of a star making it less likely to nova.

I worked out the time required to suck the Earth's atmosphere out through a stargate and I got 60 million years. Since a star is a lot hotter, the mass rate would be faster. But the Earth's atmosphere is tiny compared to the earth, and the Earth is tiny compared to a star, so putting a stargate on a star would have essentially no effect on the star. I'm going to guess that the time required to suck out half the star would be far, far in excess of the maximum lifetime of a star. Anyone want to work out the figures?

Carl

 

[Tide]

The "theory" was that by reducing the mass, gravity was no longer able to balance with the pressure.

 

[CarlB]

Interesting. But attaching a stargate would also reduce the pressure. I wonder which would dominate, in terms of causing a star to go nova.

Here's the figures for how fast you could reduce the mass of our sun using a stargate with a diameter of 4 meters:

Temperature = 14\times10^6 K
KE average = \frac{3}{2}kT = 29\times10^{-17}J
Mass Proton = 1.67 \times 10^{-27} kg
Typical velocity = Sqrt(2 KE/Mass) = 4.1 \times 10^5 m/sec
Specific Gravity = 1.4
Stargate Area = 4 \pi = 12.6 m^2
Mass flow rate = Vel. X Density X Area = 7.4 \times 10^5 kg/sec
Mass sun = 2 \times 10^{30} kg

Time to exhaust sun = Mass/Flow rate = 3.7 \times 10^{25} sec
= 1,200,000 trillion years

To make a substantial change in the sun's mass, for example to reduce it by 1%, would therefore require many thousands of trillions of years.

I suppose that in the Stargate future, mankind has solved the energy problem...

Carl

 

[Entropy]

Well if you remember from the Stargate: SG-1 episode "Watergate" where a gate is underwater. The gate has a built in function that stops ambient matter from traveling through the gate.

 

[FluxCapacitator]

I <3 this board. Physics and Stargates, what's next?

However, if you did have a non-sci-fi wormhole without any mystical ancient alien devices to make everything work nicely, and you had an exit in space and an entrance on Earth, you should be able to detect a noticeable flow of air, even if you wouldn't have to worry about losing the atmosphere.

 

[Tide]

Carl,

would therefore require many thousands of trillions of years.

Yes, but with budget and time constraints and the limited attention span of viewers you have to prune it down to a one hour episode! Besides, no one wants to see Amanda Tapping look quite that old! :)

 

[CarlB]

Physics and Stargates, what's next?

As it turns out, I got converted from being a math major to being a physics major because of a physics problem in Larry Niven's "Ringworld" series. It had to do with the fact that a ringworld is dynamically unstable. Niven ended up having to write a sequel taking into account the instability:


After I worked out the instability, I was hooked and decided to switch from mathematics to physics. I had a BS in math when I decided to switch majors. So while I was working on an MS in math, I took enough classes in physics to get myself admitted to physics grad school.

Carl