This came up in a different newsgroup, and upon trying to answer it I
blew it badly. I=92m not sure the original group really cares, but folks
here might, and it=92s kind of interesting to me, so=85
Let=92s say you have a person (named, let=92s say, =93Callie=94) standing
in=
the middle of a large airlock (10 [m] long by 3[m] by 3[m]). The bad
girl opens the large doors at the end, =93blowing the lock=94 (it starts
at 1 [Atm]). What happens to the helpless heroine? I understand
decompression, but I=92m trying to figure out how fast (if at all) they
=93exit=94 the airlock. For a first cut, I assumed the doors instantly
crack open 10 [cm] along their entire 3 [m] length, forming a =93breach=94
with an area of 0.3 [m^2] through which the air starts rushing at
roughly Mach 1 (I know it would be less, but ballpark). Back by
Callie, the cross-sectional area is about 9 [m^2], so conservation of
mass (assuming uniform density) says the airspeed by her is a gusty
11.1 [m/s]=85 which is pretty much trivial. I assumed she is accelerated
=93breachward=94 by the stagnation pressure of this flow against the front
of her body (frontal surface area 0.36 [m^2, mass of 45 [kg]), but the
result is a really trivial acceleration. Running it through Excel (to
keep track of the rapid density/pressure drop, which reduces the
stagnation pressure all the more), I get her hitting the breach after
a little over 8.5 [sec], and the leisurely pace of about 0.67 [m/s] (a
slow walk). She really only accelerates for the first couple seconds,
after that the lock is at such a low pressure that the remaining
=93wind=94 just doesn=92t have enough force to do anything.
OK, so what did I screw up? I realize approximating the exit velocity
as 333 [m/s] isn=92t good, and I=92m ignoring the question of adiabatic
vs. nonadiabatic effects, etc. I do take into account the increased
airspeed as she gets very close to the breach (closer than 2 [m] or
so). But anything major? Or does Callie really fully decompress in the
airlock, and gently drift out about 10 seconds later? One interesting
artifact of my calculation is that Callie takes a sharp jump up in
velocity during the brief time she =93wedges=94 in the breach, but I=92m
not=
as worried about that because in the real situation, the doors would
have been fully opened by then.
PS- I=92d love to take the rate of the doors opening (i.e., breach area
increasing) into account, but it makes things more difficult, and in
particular makes the assumption of sonicly-limited flow questionable
(if the =93breach=94 is one entire side of your airlock, I think I have to
worry about the force required to accelerate the mass of air in
addition to everything else, yes?).
--
Brian Davis
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