Question

A water bottle has a hole somehwre along the side. However, the water only comes out if the bottle cap has been removed, but does not come out if the bottle cap is on tight. Explain using physics principles.

preferably the physics principles of Bernoulli's principle and pascal's law

Answer 1

When the cap is closed, 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 (i.e. from bernoulli equation: sum pressure head at top and elevation is equal to atmosphere pressure when exit velocity is zero), 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. Thus, higher atmosphere pressure at bottom of hole holds the weight of water when pressure inside is decreased.