# About an upside down cup of water against atmosphere pressure

There is an experiment we learned from high school that demonstrated how atmosphere pressure worked.

Fill a cup of water and put a cardboard on top of it, then turn it upside-down, the water will not fall out. The explanation said this was because the atmosphere pressure was greater than the water pressure, which holds the water up.

I believed this explanation once, until I found some points that confused me:

1. Is the water pressure in the cup really smaller than the atmosphere pressure?

This is what we have been taught through our life. However, consider an object in the water under sea level, it experiences the pressure from water plus atmosphere pressure. So the water under sea level must be greater than the atmosphere pressure. Even it is contained in a cup, the pressure wouldn't change. Is this True?

I read the webpage which gave the explanation excluding the reason of pressure. If the cup is fully filled, the compressibility of water is much greater than that of the air, also the surface tension of the water keeps the air out of the cup. So the water is held in the cup. This explains the problem. But I still want to ask if the water pressure smaller or greater than the atmosphere pressure in this situation.

2. When the cup is half filled with water, why it still holds?

I saw most of articles or opinions against this. They all agree that the water would not fall only if the cup is entirely filled. But I did the experiment myself, the water stayed still in the cup even it is not fully filled. Actually even with little amount of water, as long as it covers the open of the cup and the cardboard on it, the water stays in the cup.

Even the compressibility of water is much smaller, the air inside the cup provide enough compressibility, how come it still holds?

I assume you meant "cardboard", not "cupboard".

When the cup is full of water, it is empty of air, and water is relatively incompressible.

So when you turn it over, in order for the water to leak out, the cardboard would have to move a small amount away from the edge of the cup, which it cannot do without expanding the water slightly, which the incompressibility of the water does not allow. So if the seal around the edge of the cup is good, you cannot move the cardboard without reducing the pressure in the cup, and the air pressure outside is not being reduced, so the air pressure outside holds it in place.

If you did this in a vacuum (ignoring that the water would boil) it would not work. The cardboard would just fall off.

It is essentially no different that pressing the cardboard against a wet plate of glass. where it sticks unless somehow you can inject some air into the space, say by inserting a needle.

• Yes, cardboard :P. You are right the water is much less compressible. But how about the cup is half filled? the air in the cup will be compressible then, but the experiment still works... – AMing Aug 5 '13 at 3:38
• @AMing: It depends on the weight of water and amount of air. The weight of water is what the outside air pressure must hold up. The amount of air determines how much the cardboard is allowed to flex under the weight of the water, because air is springy. As you reduce the amount of water you'll get to a point where it doesn't work. Also, the whole thing depends on the area of the mouth of the container, because the pressure acts over that area. It should work better with a wide cup than a narrow glass. – Mike Dunlavey Aug 5 '13 at 11:57

In a simple words, I think everything takes up space, so if you prevent the water from falling out, you succeed in preventing the air from getting in. By this way, nothing will change, everything will stay the same.

Atmospheric pressure is caused by air gravity and air molecules movement, air pressure in the half filled upside-down cup is lower than the air pressure outside due to less gravity, so the air pressure can still hold the water in half filled cup.

• Why would there be less gravity inside the cup?! – Michiel Nov 16 '13 at 8:40
1. Is the water pressure in the cup really smaller than the atmosphere pressure?

The simple hydrostatic says,

The pressure along the depth of the water cup will increase.

So, net pressure in the bowl is more than the atmospheric pressure. !!!

Then, How the card board is held ?

The $\bf{Surface~tension}$ holds it.

1. When the cup is half filled with water, why it still holds?

Still, $\bf{Surface~tension}$ holds it.

The plate will be held as long as we are breaking the force, which is provided by the surafce energy of water (with contacting medium - air in the current case).

As Mike said, (in the answers) In vaccuum (assuming water not boilling !!!), there is No interface -> No surface energy -> Plate will not be held.

## protected by rob♦Nov 14 '17 at 17:53

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