The card and water glass trick is fun--I hope you use it to make and win lots of

Question

The card and water glass trick is fun--I hope you use it to make and win lots of bets with your non-engineer friends. There is of course a limit as to how much water the atmospheric pressure can support over a particular area. Some volume of water will have enough mass to overcome the air pressure, making the card fall when the glass is inverted. If I use a cylindrical glass with a diameter of about 5 cm, what is the maximum height of water the card will support assuming typical atmospheric pressure of 101 kPa and water density of 1000 kg m-3. Also assume the card is the same diameter as the glass, and the glass is super thin (no need to worry about inner vs. outer diameter—just use 5cm). Also assume the glass is completely full when inverted.

Explanation / Answer

Note: The height required will not depend on the radius of the glass or the paper, because the surface tension force will be very low as compared to water and air.

Force would be equal on both sides.

Fatm + Fsurface tension = F water

Fatm = F water

Patm * A = Pwater * A (A cancels out)

101 * 103 = 9.8 * 1000 * h (in SI units)

h=10.1 m.

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