Formula to calculate air loss?

Is there a formula or rule-of-thumb for making a rough
estimate of the rate of air loss in a space craft for a
given size air leak?

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In article ,
JamesStep wrote:
Is there a formula or rule-of-thumb for making a rough
estimate of the rate of air loss in a space craft for a
given size air leak?

Hmm, a crude first approximation would be to assume that the air is moving
through the hole at the speed of sound ("choked flow"), with its density
and temperature unchanged. So if it's normal air at room temperature
(speed of sound about 350m/s), you lose about 35 liters per second through
a 1cm^2 hole.
--
MOST launched 1015 EDT 30 June, separated 1046, | Henry Spencer
first ground-station pass 1651, all nominal! |

(Henry Spencer) wrote in message ...
In article ,
JamesStep wrote:
Is there a formula or rule-of-thumb for making a rough
estimate of the rate of air loss in a space craft for a
given size air leak?

Hmm, a crude first approximation would be to assume that the air is moving
through the hole at the speed of sound ("choked flow"), with its density
and temperature unchanged. So if it's normal air at room temperature
(speed of sound about 350m/s), you lose about 35 liters per second through
a 1cm^2 hole.

Yep. The flow, Q (in liters/sec) ~ 9.1 * sqrt(Pressure (in psi)).
So if the space craft has an air pressure of 7 psi (about 1/2
atmosphere), you'd lose about 24 liters per second.

Erik Max Francis wrote in message ...
Bill Bogen wrote:

Yep. The flow, Q (in liters/sec) ~ 9.1 * sqrt(Pressure (in psi)).
So if the space craft has an air pressure of 7 psi (about 1/2
atmosphere), you'd lose about 24 liters per second.

How can that be right, since it doesn't take into account the area of
the hole? A bigger hole is going to spew more air than a smaller one.

I was assuming a 1 cm^2 hole, as Henry described. For larger/smaller
holes multiply accordingly.

In , Prof. Andrew
Higgins wrote a long discussion of formulae to calculate how long it
will take to decompress a volume to vacuum through a given leak.

I've been keeping a personal web page with information and links about
biology of vacuum exposure [ http://www.sff.net/people/geoffrey.landis/
vacuum.html ].
The information I had put on the page is this: How
Fast Will A Spaceship Decompress If It Gets Punctured?
The
decompression time will depend on how big the hole is. You should
consult a vacuum engineering handbook to get real engineering data; they
will have tables telling you how fast a given hole size will pump down a
given volume. For a quick (and only roughly accurate) rule of thumb, if
you put a one square centimeter hole in a one cubic meter volume, the
pressure will drop by a factor of ten every hundred seconds, and 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 (seventeen hours).
More accurately, 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) and hence the pressure drop is:
P
= Pinitial exp (-0.02 tA/V) where V is volume in cubic meters, t is
time in seconds, and A is area 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.
For
reference, when the pressure drops to about 50% of atmospheric, the
subject will be entering the region of "critical hypoxia"; when the
pressure drops to about 15% of atmospheric, the remaining time of useful
consciousness will have decreased to the 9-12 seconds characteristic of
vacuum.
You just posted a much longer and (I presume) more accurate
discussion here on sci.space.tech; could I have your permission to copy
your discussion onto my web site?



--
Geoffrey A. Landis
http://www.sff.net/people/geoffrey.landis