B Water doesn’t fall in inverted half cup

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The discussion centers on the phenomenon of water not falling from an inverted half-filled cup, as demonstrated by Brian Cox. The explanation involves the development of negative pressure inside the cup due to paper deformation, which balances the atmospheric pressure outside. The gauge pressure created by the water is approximately 0.005 atm, requiring a slight expansion of air to maintain suction. Additionally, the hydrophilic properties of the paper and glass enhance surface tension, helping to keep the paper in place. The conversation concludes with a suggestion to devise experiments to further test this explanation.
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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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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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