Question

when the water bottle cap is open why the water comes out if we press the water bottle and why the water donot comes out if the cap is close and if we press the water bottle

Answer 1

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 the there's some space remaining on the 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.