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I understand that when you make a hole on a bottle filled with water and put the cap on tight the water will not flow out due to the atmospheric pressure acting on the hole.

My confusion is that, lets say there's some space remaining on top of the water, when you close the tap, there's still air inside it, so there is pressure from the atmosphere acting on the surface of water inside the bottle. And the hole is at a height $h$ below the surface of the water, so there's also pressure from the depth $h$ of water due to gravity.

So how does the atmospheric pressure on the hole equal the atmospheric pressure on top of the surface and the water pressure due to depth $h$?

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As you close the cap, you seal off the top of the bottle from the atmosphere. At first, some water will flow out, which will decrease the pressure of the air that is still in the bottle. Once the pressure difference between the air in the tip of the bottle and the outside atmosphere is large enough to counteract the force exerted by gravity on the water, it will stop flowing out and at that point is held in by the pressure difference from the air inside the bottle to the atmosphere outside.

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    $\begingroup$ Why does the pressure decrease? Is it due to there being more space for air and the molecules of air to spread out more thus reducing the overall pressure on the surface? As the volume increase pressure decreases? $\endgroup$
    – fardeen afsar
    Commented Sep 20, 2017 at 16:10
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    $\begingroup$ Yes. This is Avogadro's Law. $\endgroup$
    – noah
    Commented Sep 20, 2017 at 16:13
  • $\begingroup$ Does the pressure of the liquid at a depth h from above matter here? And when you initially make the hole almost no liquid comes out, then how does the pressure above decrease? $\endgroup$
    – fardeen afsar
    Commented Sep 20, 2017 at 16:29
  • $\begingroup$ Well yes, the higher the water rises above the hole, the greater the pressure difference must be. "Almost no" is not "no". So there you go. Small differences in pressure are enough to hold the water the height of a bottle. And the less air is in the bottle to begin with, the less water will come out initially. If you fill the bottle all the way, no water will come out (as long as it is shorter than about 10 m). $\endgroup$
    – noah
    Commented Sep 20, 2017 at 16:34

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