Explaining the Obvious

Question: If you fill a drinking glass with water and then turn the glass upside down, what happens? What a dumb question that is! The water falls out of the glass, what else would you expect? Yet this is not as obvious as it seems. Here is an experiment that puts the obvious into question.

As before fill the glass of water, but now make sure you fill it to the brim, absolutely full. Now take a thin piece of cardboard and place it over the top of the glass. Holding the cardboard in place, turn the glass upside down. Now remove your hand from the cardboard. What do you think will happen?

If your too timid to try this you'll just have to take my word for the result, which is that the cardboard stays in place, and the water does not fall out of the glass. Note that the cardboard is not holding the water back as it isn't glued or fixed to the glass rim! So why does the water and the cardboard both stay put?

The answer is air pressure, which exerts enough force to hold the cardboard and the water in place. Lots of kids know this trick, after turning the glass + cardboard upside down they place it on a table and slide the cardboard out. When mom or dad pick up the glass they get a surprise.

But why does air pressure suffice to hold the water in this case but not the first? The answer to this is quite subtle and involves the notion of stability. You can in principle balance a pencil on its point, but if the center of gravity of the pencil deviates in the slightest from being directly above the pivot point, the pencil will fall. The same is true of the water surface. If the surface is flat it has minimum area, however if it even slightly deviates from the flat position the surface area increases. As the water is denser then the air, this sets the forces acting on the water to further increase the area, and the whole surface falls apart. The cardboard serves to keep the area in a stable or flat form. Another way to look at this, if you remember some basic physics, is that the total potential energy of the water-air interface is at a maximum when the surface is flat. Just think of a little bit of water getting lower while a equal volume of air gets higher. Again, as the air is less dense, the total potential energy will decrease. It's just like a ball rolling off the top of a hill.

I'll end this with a question? Why does the cardboard fall off if you place it on the top of an empty glass and turn the glass upside down?

If all this gives you a headache try the experiment with whiskey, then when you are finished you can at least have a good drink.

Cheers,
Marty