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The leak reportedly led the ISS to lose 0.8 millibars of air pressure per hour, which is both big considering what was at stake and low for a 2-mm hole when the outside is near to complete vacuum. Am I missing something? How could the German astronaut even block it with his finger without any damage if complete vacuum was on the other side?

Per this comment, the value of 0.8 mbar/hr seems to come from:

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    $\begingroup$ Small holes and vacuum in general aren't as lethal as sci-fi would make you think. In fact, humans can produce quite a bit of suction by themselves. If you hold a drinking straw to your skin and suck in using your mouth, you can achieve down to around %10 air pressure and you won't be injured or probably even uncomfortable. See here someone measures human suction power: youtu.be/ANVI04QmthE $\endgroup$
    – Dragongeek
    Commented Sep 6, 2018 at 21:51
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    $\begingroup$ I was blocking a 10-bar hose of about 5mm diameter with my finger just fine. Blocking a hole against 1 bar suction is really nothing. $\endgroup$
    – SF.
    Commented Sep 6, 2018 at 22:42
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    $\begingroup$ There is a video on youtube by CodysLab who showed exactly that: blocking a tiny hole in vacuum against the pressure. $\endgroup$
    – PlasmaHH
    Commented Sep 7, 2018 at 11:08
  • $\begingroup$ I'm curious, where did the "0.8 millibars of air pressure per hour" figure come from exactly? Do you have a source? $\endgroup$
    – uhoh
    Commented Sep 7, 2018 at 18:16
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    $\begingroup$ @uhoh the only source is Stephen Clark from spaceflightnow.com/2018/08/30/…. There is no any mentions of the leak rate on other sources, including NASA site. But usually spaceflightnow.com is rather reliable source. $\endgroup$
    – Heopps
    Commented Sep 8, 2018 at 6:28

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The ISS is at 1 bar, i.e. 1 kgf/cm2, or 10 gramsf/mm2. So the pressure on that 2 mm hole is 31.4 gramsf, well within the range a human finger can handle.

Also, the ISS is really big compared to the hole. It takes a long time for hundreds of m3 to evacuate through a 2 mm hole.

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    $\begingroup$ thank you, intuitively I thought the pressure would be much higher on the finger and as you say 2 mm is not much compared to the volume of the ISS, so it makes sense! I guess I must have been influenced by SF movies where everything explodes as soon as there's a leak ^^ I should have made the calculation instead of relying on my physical intuition. $\endgroup$
    – tsnobip
    Commented Sep 6, 2018 at 14:15
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    $\begingroup$ @tsnobip check this video Use Your Finger to Stop a Leak on the Space Station? . You can see how easy it's to stop the leak with your finger without any issue (maybe just a small hickey on your finger :) ) $\endgroup$
    – bitcell
    Commented Sep 7, 2018 at 6:17
  • $\begingroup$ well nice finding @bitcell, that's exactly the kind of thing I was looking for! But still, I think I would have probably hesitated a bit before putting my finger on a leak of the ISS in real life! ^^ $\endgroup$
    – tsnobip
    Commented Sep 7, 2018 at 9:05
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This is the image of the hole (news source, although the image is from NASA)

Soyuz hole

The hole is 2mm in diameter. Even with a total vacuum on the other side, you're not talking a lot of volume getting through that hole. I used this calculator with a pressure gradient of 101kPa (ISS standard) and 0.1 kPa through a 2mm hole and got a water flow rate of ~0.1 cubic meters of water per hour (or 26.6 gallons per hour). For contrast, the US has a hard rule limit of 10 gallons per minute on gasoline pumps. As such, the pressure exerted through that 2mm hole is not going to be enough to pull much more than air or a nearby viscous liquid out.

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    $\begingroup$ You don't need a flow rate calculator. Simply use $\dot p/p=\dot m/m = \dot V/V$ and convert that 0.8 mb/hr pressure loss to a mass loss of about 0.9 kg/hr or a volumetric flow rate of 0.8 m$^3$/hr. (I'm keeping all the numbers to one place of accuracy, since that's what was given originally.) $\endgroup$
    – David Hammen
    Commented Sep 6, 2018 at 14:32
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    $\begingroup$ Also, the hole wasn't all the way through from the interior of the hull to the exterior. It was a hole in the internal layer of the hull, with a bunch of kevlar, aluminum, and other materials in-between that would further insulate his skin and may have potentially lowered the leak rates even more. $\endgroup$
    – Magic Octopus Urn
    Commented Sep 6, 2018 at 19:08
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    $\begingroup$ Using water or gasoline flow rates for comparison is, at least without further discussion, pretty useless. One might also compute that only, like, two grams of honey would drip the hole per second or something, but this wouldn't tell us anything about how much air goes through it. $\endgroup$
    – leftaroundabout
    Commented Sep 7, 2018 at 12:23
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    $\begingroup$ @leftaroundabout My point (which I guess got lost here) is that if not much liquid can escape that hole, air (which is mostly empty space itself) would produce even less pressure. Hobbes' answer was better by calculating pressure itself. $\endgroup$
    – Machavity
    Commented Sep 7, 2018 at 13:40
  • $\begingroup$ You should have used the right one calculator for an air flow. The water flow rate calculator is the wrong one. $\endgroup$
    – Uwe
    Commented Dec 26, 2019 at 21:00
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It's not really that the leak was slow, more that it took some time to manifest:

Another source told the news agency the worker did not report the error and instead applied a sealant of some sort. After two months in orbit, the sealant apparently dried out, the source said, and was expelled by the cabin air pressure, opening up a leak.

(The article is slightly incorrect; MS-09 docked with the ISS on June 06 and the leak was detected on the 29/30 August, so it actually took almost three months to become apparent).

After the sealant failed, the leak was detected very quickly, and its small size meant that relatively little atmosphere escaped before the astronauts were able to patch it. Their temporary repair will not be a long-term issue for the ISS - the module with the leak is the orbital module of Soyuz, which is jettisoned to burn up into the atmosphere after the astronauts depart the ISS.

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    $\begingroup$ According to the article I referenced, the worker used glue to fix the hole. Had they reported it, they could have fixed it by welding it.. $\endgroup$
    – Machavity
    Commented Sep 7, 2018 at 13:37
  • $\begingroup$ @tsnobip have you seen this answer yet? I think this addresses the timing nicely, but it may have been posted after you accepted the other answer. $\endgroup$
    – uhoh
    Commented Sep 7, 2018 at 18:18
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tl;dr:

How could the 2018-08-30 Soyuz MS-09 / ISS leak be so slow?

Answer:

By being about 2 millimeters in diameter!

@DavidHammen's comment converts 0.8 mbar/hr to about 0.8 m^/hr air loss rate presumably at standard conditions. Let's see how that's done, how it checks against "a 2mm hole" and what it means if there were no response of any kind (human or make-up air).

He uses the first order relationships

$$ \frac{\dot{p}}{p}=\frac{\dot{m}}{m}=\frac{\dot{V}}{V} = 0.8 \times 10^{-3}/hr$$

where I'm guessing $p$ is the pressure of the remaining air (assuming no make-up air and no change in temperature, which is reasonable considering the air is in intimate contact with so much solid surface area), $m$ is the mass of the remaining air, and $V$ is the equivalent volume of the remaining air if it were at standard conditions.

An ISS pressurized volume above about 938 m^3 (matches values on the internet) times $$0.8 \times 10^{-3}/hr$$ does indeed give about 0.8 m^3/hr!

Now let's see what a 2 mm hole in a thin plate is expected to do. I found two online calculators, although they may have somewhat different assumptions, and the hole has some depth (the wall thickness of the Soyuz at this location) and side roughness, but still we can try.

  1. http://www.efunda.com/formulae/fluids/calc_orifice_flowmeter.cfm#calc
  2. https://www.tlv.com/global/TI/calculator/air-flow-rate-through-orifice.html

Number 1. gives 2.74E-04 m^3/sec or 1.0 m^3/hr, almost identical to the quoted 0.8 m^3/hr value, and number 2 gives something at least close; about 3 m^3/hr.

So baring any make-up air, that's about a 1% drop in pressure every ten hours. That's enough to be alarming, and of course would probably trigger an alarm in less than ten hours since strikes by meteorites and debris so likely over time that one would expect the ISS to be hyper-vigilant about leaks.

So to answer the question

How could the 2018-08-30 Soyuz MS-09 / ISS leak be so slow?

The answer is

By being about 2 millimeters in diameter!

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    $\begingroup$ An upper limit would be the speed of sound within the hole. That is 3.7 m^3/hr at a pressure of 1 bar. But pressure should be lower at the point where the speed of sound is reached. $\endgroup$
    – Uwe
    Commented Sep 17, 2018 at 11:08
  • $\begingroup$ @Uwe I never thought about that, it's a handy insight thanks! $\endgroup$
    – uhoh
    Commented Sep 17, 2018 at 11:10
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    $\begingroup$ It was somewhat over simplified. A pressure drop of at least 2:1 is needed to accelerate the gas to the speed of sound. When the pressure drops 0.5 bar, the volume expands to double. The volume flow is therefore not 3.7 m^3/hr but about 1.85 m^3/hr. But that is still only an upper limit. $\endgroup$
    – Uwe
    Commented Sep 17, 2018 at 19:52
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    $\begingroup$ The flow would be choked (pressure ratio > critical pressure ratio of ~ 2, exact value unimportant since the downstream pressure is zero). That simplifies calculation somewhat. $\endgroup$
    – Organic Marble
    Commented Oct 14, 2018 at 16:45

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