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To get the liquid to flow out of a medicine ampoule, you have to crack the class at both ends; one only one end is cracked open, the liquid remains inside even if the ampoule is held upside down.

Seems like a simple story of pressure difference: the air pressure is greater than the pressure on the other side of the opening, so the liquid doesn't flow out. Surface tension might also play a role, since the opening is very small.

Assuming there is very little air inside the ampoule, if the area of the opening is $A$ and the mass of the liquid is $m$, the liquid doesn't flow out as long as the pressure from the inside at the level of the opening is smaller than the air pressure: $P_{int}=mg/A<p_{atm}$.

But that can't be right, because experimentally if we increase the size of the opening (increase $A$) past a certain point, the liquid flows out?!??!

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The reason is that for a large area of the opening the liquid/air interface doesn't stay plane, it is not stable. For a small opening the surface tension stabilizes the interface. Also, there is a tendency to form bubbles which would rise due to the buoyancy. When a penetrating air pocket forms, it causes the same volume of liquid to flow out on the sides of it. Thus with a large area opening the liquid will finally flow out.

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