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I've notied that when I get down to the last part of a box of wine, the flow slows to a trickle. If I open the nozzle, tilt the box back (letting air gurgle into the bladder) and then tilt it back forward the flow is greatly increased.

Why does letting air into the bladder help increase the flow?

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+1 for boxed wine –  Ryan Thorngren Sep 11 '12 at 5:01
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Without air in the bag, the wine is all forced (by atmospheric pressure) to the bottom of the bag, which is below the tap. The bag itself is scrunched around the wine at the bottom of the box. That makes it more difficult for the wine to reach the tap, when the level is low, even if you tilt the bag. As long as the level of the wine is above the tap, there is no problem.

If you let air in, then the wine can slosh around in the bag, so that it can reach the tap more easily. This only helps when the wine level is getting very low, when access to the tap is obstructed. As long as most of the bag (and wine) is still above the tap this has no effect.

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I guess when you pour wine the volume of air in the box increases, so air pressure in the box decreases, so a pressure differential is created between atmospheric pressure and air pressure in the box. This pressure differential limits the flow. When you let some air in the box, this pressure differential decreases.

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This is correct, but it seems to me the questioner has no idea of how a vacuum can be created using the balance of air pressure and weight of fluid, as in the Toricelli barometer. en.wikipedia.org/wiki/Evangelista_Torricelli. –  anna v Sep 10 '12 at 12:00
    
You get the same effect with portable water coolers:if air is not allowed to enter the water stops flowing after a while, the air pressure balances the weight of water+low-pressure-air left in the cooler. –  anna v Sep 10 '12 at 12:03
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In those boxes the wine is in a plastic bladder inside the box, so atmospheric pressure should keep forcing the wine out, regardless of the amount of wine left. –  hdhondt Sep 11 '12 at 3:50
    
@hdhondt: Atmospheric pressure (outside of the box) is higher than air pressure in the box. How can it force the wine out? –  akhmeteli Sep 11 '12 at 4:47
    
@hdhondt, is correct. The box is not air tight so the air pressure is the same. There is a plastic bladder in the box that actually contains the wine, but air can easily go in and out of the box. –  Abe Miessler Sep 15 '12 at 1:20
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