An inverse glass of water

I have another neat Do-It-Yourself physics experiment for you to try.

Here’s what you need:

• Uniform drinking glass (in other words, not a funky shaped glass).
• Piece of sturdy, flat, smooth cardboard (that won’t curl up if wet). Big enough to completely cover the opening of the glass.
• Water.

The process is easy but it’s best to do it over a sink, just in case. Fill the glass with some water then place the piece of cardboard on top of the glass so that it covers it completely. Using your hand to keep the cardboard in place, quickly flip the glass and the cardboard upside down. Hopefully at this point you are not covered in water and no water is leaking out. Make sure the glass is completely upturned so that the cardboard is parallel to the ground. At this point, if all goes well, you should be able to remove your hand from the cardboard and the water should stay in!

Some of you have probably figured out that air pressure has something to do with this, and you are entirely correct. But there are a few subtle things I would like to point out. The rest of you who aren’t familiar with this kind of air pressure acrobatics are probably thinking…

…but why doesn’t the water fall out of the glass?

Well, first you need to realize that the water is not the only fluid substance in the glass, there is also air (which actually reminds me of a shirt I have). If the water were to fall out, then air would have to take its place, otherwise the same amount of air currently in the glass would occupy a larger volume than it did before, causing a huge pressure difference between the room and the glass.

Realistically, there must be a pressure difference between the room and the inside of the glass because something needs to cancel out the downward force of gravity of the water. A difference in pressure will create a net force upwards which cancels out the weight of the water. So the water is supported by the cardboard, and the cardboard is supported by thin air!

…but wait a second. Where did this pressure difference come from, you ask?

What’s going on here is that gravity is pulling the water down slightly, which increases the volume of the air inside the glass. If you increase the volume of a gas (without changing the temperature or number of molecules) you will decrease the pressure of the gas. So that means: lower pressure inside, higher pressure outside, giving a net force inwards which means a force upwards on the cardboard.

…but if gravity pulls the water down slightly then there must be a gap between the cardboard and the rim of the cup, so why doesn’t the water spill out from the gap?

Well, that’s an excellent question. The answer to this is: surface tension. Have you ever tried to float a paperclip on water? Despite the fact that the paperclip is denser than water, it is still possible. This is because the interface (boundary) between the water and the air can very loosely be thought of as an elastic band. It will resist distortion up to a certain point. This happens because nature likes to minimize energy, and in this case, that corresponds to minimizing the surface area of the interface between the air and the water. If you push it, that will put it into a  higher energy configuration, so the surface will push back. (For more, see wikipedia).

The gap between the glass and the cardboard is tiny (less than a millimeter). This is too small a gap for the air to break the surface tension. The air can’t bubble up through the gap into the glass while the water flows out so the water and the card just stay there, suspended. Not just suspended in mid air… but by mid air.

Edit: For another post about air pressure that really sucks, check out the “Everyday Physics: suction cups” post on Shores of the Dirac Sea. (…I just had to make that joke…)