What physical principle explains why a full glass of water upside down in another container wont empty?

Answer 1

The force of the water pushing downward in the upside down glass is equal to the force of the water pushing upward from outside the glass (I presumed you immersed the glass upside down in a pool of water).

Force in the glass stems from the weight of the water distributed over the area of the mouth of the glass. Force from outside, pushing back against that column of water comes from the atmosphere shoving down on the basin of water the glass is in. When the force in the glass is equal to the force from outside the glass, the water in the glass will not flow.

Force from outside the glass is transmitted by something called Pascal's Law, which states that force is distributed equally in all directions in a liquid (the water in the basin). So when the water in the glass does not run out, we can say F = f; where F is the force from the basin and f is the force from the glass. F = pA and f = Pa; where p = atmospheric pressure and A = the area of the basin (minus the area of the glass in the basin).

P = the pressure of the water and a = the area of the glass mouth. P = W/a; where W is the weight of the water in the glass. Thus, when pA >= W; that is, when the atmospheric pressure times the area of the basin is greater or equal to the weight of the water in the glass, the water will not flow out.

Answer 2

It is the same principle that holds up the mercury in a barometer except the barometer is about 30 inches high and there is a vacuum above the mercury in the glass tube. The weight of the atmosphere pushes down on the mercury well and up the bottom of the glass tube preventing the mercury from pouring out, unless you let air into the tube. If you placed your full glass of water upside down in a dish of water and placed the item inside a bell jar while pulling a vacuum, the water would pour out as the vacuum increased. Of course the water must be near freezing to not boil too.

Answer 3

This truly looks like a miracle or some magic trick, but this trick shows the true force of air pressure. For the same reason it is impossible to create a perfect vacuum on Earth like in Space.