The first demonstration of a bottle of water with a hole in it starts with no water coming out of the hole. This means that things are in equilibrium, balanced. The explanation of what is going on is a bit simplistic. It looks like the bottle is full of water so the pressure of the air outside of the bottle is enough to hold up the pressure of the column of water in the bottle above the level of the hole. But we know that the pressure of this water is much less than atmospheric pressure because the atmosphere can hold up a column of water around 10m high. So what is going on here? Why isn’t the air pushing into the bottle? (It would if the water could get out) The answer is because of the incompressibility of water. The air pushes on the water at the air-water interface and these water particles push on the particles behind them. Electrostatic forces then come in to play and push back just like you leaning on a wall, sitting on a chair or elbows on the desk. The water pushes on the walls of the bottle and lid and they push back, so everything is in balance.
Then the lid is unscrewed and pressure due to the atmosphere is added to the top of the water so the pressure at the hole is now atmospheric pressure on the outside and atmospheric pressure plus the pressure of water on the inside. Water therefore flows out of the hole and air flows in at the top to fill up the space. Once the lid is tightened again the water continues to flow out until the pressure is again equal at the hole i.e. water pressure plus pressure from the trapped air inside equals atmospheric pressure outside. So the pressure of the air inside is slightly less than the atmospheric pressure outside.
At any time you could squeeze the bottle and more water would come out because you have increased the inside pressure. Then when you release the squeeze on the bottle air bubbles into the bottle because the outside air pressure is greater than the inside pressure of water and air.
When you ask students to explain what is going on in their own words they will start to talk about a vacuum. Get them to look up the definition of a vacuum and ask them what would happen if there really was a vacuum in the bottle.
A colleague pointed out to me that in the glass half full demonstration there is a state of equilibrium so everything must be in balance i.e. air pressure on the underside of the card plus any resistance of the card to being “sucked up” into the glass must equal the pressure of the water pushing down on the card plus the pressure of the air inside the glass pushing down on the water. So in-fact the pressure provided by the air in the glass is significant and differs from atmospheric pressure only by the pressure of the water and the extra effect of the slight flexing of the card into the glass.
Where does this pressure of the trapped air come from? The number of particles in the volume of air and their kinetic energy, which is related to temperature. So this device could become a thermometer? The pressure would change with temperature? Which would change the volume if the seal on the glass was flexible enough? Do we even need to have water in the glass? Could a glass full of air with a flexible air tight cover be used to create a temperature scale? And one idea leads to another…
The plumbers plunger explanation is fine.