Physics problem with a bottle?

Question

If there is some water in the vitreous bottle and we strike with a palm from the top to the bottleneck, we can knock out the bottom of the bottle. Why? How to evaluate the force which knocks out the bottom of the bottle?

Thanks in advance

Answer 1

It's hydraulics. Water has constant pressure.

Pressure on the top = Force applied / neck area
=
Pressure on the bottom = Force bottom/ bottom area

Force bottom = Force top * bottom area / neck area

So if the bottom is bigger than the neck, the force gets magnified. You get mechanical advantage--your force is increased, but it is applied over a smaller distance to conserve energy.

Answer 2

Hydrostatic experiment with an incompressible fluid.

The bottle better be full of water otherwise it will not work unless you compress the air to produce a shock wave sufficient to pop the bottom and that is practically impossible.

You are moving from a lower to a higher cross section in your case possibly with 6:1 ratio so a traditional application of force amplification will work only if the bottle is full of water and the smaler force moved a distance 6 times more than the force at a larger area. This is why we have to bleed our hydraulic brake system since even just a little air will prevent brakes from functioning properly.