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Apparent staining inside the window

On a recent flight, I noticed a pattern of staining or dust particles inside the window, on the plastic reveal within the cavity.

It looked as though a long-term and consistent pressure differential between the cabin and the cavity had drawn a stream of air into the cavity, resulting in what looked like a sooty stain.

And even more oddly, as you can see in the picture, right opposite the vent, the mark is very concentrated, as though formed by a high-pressure stream - which I presume isn't actually the case.

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    $\begingroup$ Related: aviation.stackexchange.com/questions/2454/… $\endgroup$
    – Peter Kämpf
    Commented Aug 26, 2017 at 19:31
  • $\begingroup$ @mins The mark in the photo is not on the external glass but on the plastic surround or reveal inside. I find it hard to credit that cabin pressure could increase so rapidly as to produce such a tightly-focused stream of air onto the surround. Look at the diameter of the black centre of the stain. $\endgroup$
    – Daniele Procida
    Commented Aug 26, 2017 at 20:22
  • $\begingroup$ It was just an ordinary 737 or E170, no fancy electronic windows. $\endgroup$
    – Daniele Procida
    Commented Aug 27, 2017 at 11:15

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I believe the stain is caused by air going through the hole relatively fast due to compression of the cabin. Assuming the window is 40x40 cm large, and there is 10 cm between the panels, the volume of air in it is 16.000.000 mm3. About 30% of this air comes out due to the lower pressure at altitude, that is 4.800.000 mm3. Assuming it takes 600 seconds (10 min) to pressurize the space again, the flow will be 800 mm3/s. Assuming the hole has a diameter of 2 mm, it has an area of 3.14 mm2. The average flow velocity is then 254 mm/s. It looks like the spot is only 20 mm away from the hole, so it would take a dirt particle less than 0,1 second to get to the spot from the hole. I think that is not much time to deflect, hence the concentration in the middle.

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    $\begingroup$ @mins: Thanks! I suppose I should have been a bit more clear there. I mean that 30% of the air between the two window planes comes out of that space, and goes in to the cabin. This is because the cabin pressure is kept at approximately 70% of the pressure at sea level, and the space between the windows will have the same pressure. Then according to the ideal gas law, assuming constant temperature, if the pressure is reduced by 30%, the volume of the gas increases by 30%. Since the space does not get any bigger, 30% of the gas will move to the cabin. $\endgroup$
    – Orbit
    Commented Oct 29, 2017 at 22:14
  • $\begingroup$ Ah indeed, btw an interesting answer. $\endgroup$
    – mins
    Commented Oct 29, 2017 at 22:28
  • $\begingroup$ This is a brilliant answer, and an excellent example of how calculation can arrive at a truth that confounds intuition. Two questions however: A) Is the plastic pane sealed? They often feel quite rattly; if air can enter the void from around the edges of the pane, then the sums would be quite different. And B) there's considerably less than 10cm between the panels, it's more like 4 or 5cm. Do the sums still work? $\endgroup$
    – Daniele Procida
    Commented Oct 30, 2017 at 18:40
  • $\begingroup$ @DanieleProcida: Thanks for the complement, I found it a very interesting question. About the questions; A) If it is not sealed, none of it will hold. Even a 0,2 mm gap, which is not even visible from this angle, would make an opening about 100 times bigger than the hole. 99% of the air would come in through the sides and the speed would be 100 times lower. That won't leave much of a stain. I believe it is sealed though. Left of the hole you can see the seal alignment tab, also shown in the first figure Peter Kampf referred to. Without seal it would rattle like crazy due to engine vibration. $\endgroup$
    – Orbit
    Commented Oct 30, 2017 at 20:51
  • $\begingroup$ Continued: B) It looks like at least 10 cm to me, I was even thinking about going for 15 cm. But with 5 cm the speed would be half as high, 127 mm/s, which is still a lot. Imagine scaling the whole thing to human size, a 2 meter hole. The speed would then be equivalent to 127 m/s, or 457 km/h. If a car were to pass close by at that speed it would be gone already before you even realize what just happened. $\endgroup$
    – Orbit
    Commented Oct 30, 2017 at 20:58

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