Water doesn’t fall in inverted half cup

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SUMMARY

The phenomenon of water not falling from an inverted half-filled cup is explained by the principles of air pressure and surface tension. When the cup is flipped, the paper creates a seal that allows negative pressure to develop inside the glass, counteracting the weight of the water. The gauge pressure produced by the 5 cm of water is approximately 0.005 atm, which requires the air volume to expand by 0.5% to maintain suction. The hydrophilic properties of both the paper and glass enhance this effect by increasing surface tension at the boundary.

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Kashmir
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I just happen to see a show about air pressure host by Brian Cox. As the link:https://i.stack.imgur.com/vfZlI.jpg shows, he flipped a half-filled water cup upside down then the paper on cup doesn't drop:
It puzzled me, because the cup is half-filled, the pressure shouldn't balance since inside water pressure+atmosphere pressure should be bigger than outside atmosphere pressure only.

What’s the explanation?
 
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What does the film say?
The paper deformation will allow a negative pressure to develop inside the glass. The 5 cm of water in the glass will produce a gauge pressure of ~.005atm (10 m is one atm) so the air volume will need to expand by .5% to create that suction. In addition both paper and glass are hydrophyllic and the surface tension at the boundary will tend to retain the paper in place. Apparently the combination is enough.
Can you devise an experiment to test this explanation? I can think of two different ones.
 
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