What is the maximum airspeed, in miles per hour, if a spacecraft suddenly decompresses in outer space?

HELP! I have asked this before, and people give vague or off-the-point replies, without providing numbers or answering the question. I would just like to know the MAXIMUM AIRSPEED during a sudden, explosive decompression in space, in MPH or KPH. Use the space shuttle, use the starship Enterprise, I do not care. Starting pressure 1 atmosphere. Aperture size about the size of a standard office door. Does the wind blow at 500 MPH? 20,000 MPH? Answers which also include formulae get extra points. Do math and physics exist in America, can anyone help me?

We are having a problem deciding what "air" is. I know that sounds stupid, but how many molecules per area need to be moved for it to be considered air? (as in airspeed) Even that leaves dilemmas.


For a fast estimate, you can assume that the air exiting through the hole will travel at the speed of sound.

Since the atmosphere drops in pressure as it moves through the hole, the effective rate at which the atmosphere leaves is at about 60% of the speed of sound, or about 200 meters/second for room-temperaure air (see derivation by Higgins):

P = Po exp[-(A/V)t*(200m/s)]

This gives you a quick rule of thumb, the one-one-ten-hundred rule:
A one square-centimeter hole in a one cubic-meter volume will cause the pressure to drop by a factor of ten in roughly a hundred seconds.
(for quick approximations; only roughly accurate). This time scales up proportionately to the volume, and scales down proportionately to the size of the hole. So, for example, a three-thousand cubic meter volume will decompress from 1 atmosphere to .01 atmosphere through a ten square centimeter hole on a time scale of a sixty thousand seconds, or seventeen hours. (it's actually 19 hours by a more accurate calculation).
The seminal paper on the subject is by Demetriades in 1954: "On the Decompression of a Punctured Pressurized Cabin in Vacuum Flight."

The decompression rate can be derived for laminar viscous flow (that is, near atmospheric pressure) using Prandtl's equation in the limit Po/P is zero, and assuming a simple aperture (a pipe of zero length). The gas flow conductance is Cvisc= 20 A liters/second (for A in square centimeters). As the pressure decreases the flow changes to molecular flow, and the depressurization rate decreases by about a factor of two. This is for air at 20 C; for the case of pure oxygen, the leak rate is about 10 percent slower.

Kalel - you need to phrase your question in a way that people can understand what you are asking.

The speed of the spacecraft has nothing to do with decompression.

There is no wind in outer space, it is virutally without atmosphere. The only thing that has an atmosphere is the space craft. If the air gets sucked out of the vessel in a time frame of 0.1 second or less it's called an explosive decompression. If a small hole causes the vessel to decompress it will go slower. Whether Enterprise or a Space shuttle there will sound some sort of warning for the crew to get in their space suits and repair the vessel or rescue themselves. Though Enterprise will likely deploy an emergency forcefield and bypass things that way.

So if you have to have a mileage per hour there are too many factors involved. You need to know the volume of the gases, the temperature of outer space (in case some of the gaseous properties will go liquid or solid), proximity to a large celestial object (gravity) or not, the minute gravity moment that the space craft itself has on the gases and the time frame of the decompression; whether explosive or rapid or gradual. After plasma though gases have the highest kinetic energy, so it will definitely be a spectacle in cases of explosive and rapid decompression. Whether it comes with sound as it does in popular science fiction is highly unlikely, because sound is an effect of vibrating air. And in space there is a virtual vacuum.

Hope this helps.

Kalel, I understand you perfectly. Rhythm has given a great answer and I cannot better it. What bothers me is that the other responders are misunderstanding your use of the word airspeed... one of them thinks you are mentioning craft speed when you never did, and another mentions windspeed and thinks you believe there is wind in space, and I think you know better. Your term was "airspeed," clearly denoting the event of the decompression itself.

I also believe the speed would be close to that of sound. I apologize for not having a formula to offer. Rhythm's reference looks excellent.