Why does a ball come out on blowing into the bottle?

Question

I take a ball smaller than the mouth of the bottle and blow into the bottle (The bottle is horizontal).

When I blow I create a low pressure, outside the bottle at the mouth and there is high pressure inside the bottle so it pushes the ball out. But you said that the increased air speed results in low pressure. That is the reason. This is justified of you think of wind blowing above the door as it carries wind particles with it. But what about this case? If the wind took away the air particles where did it took them away. Above the mouth or where? Shouldn't it be straight in the bottle and if you say it is because There is more air pressure in the bottle the wind went above the mouth but this $\implies$ The higher air pressure in the bottle would cause it to burst.

So why in the world the high wind speed created low pressure at the mouth of the bottle?

This is the main question.

Answer 1

Bernoulli's principle states that $p + 1/2$$\rho$$v^2$ + $\rho$$gh = const.$

This equation is strictly for incompressible (const. density) fluids, but it simplifies the problem . So the air you blow into the bottle has to come back out through the smaller opening, which means its velocity increases compared to the velocity inside. By the above equation, h is unchanged so the increase in velocity is balanced by the reduced pressure.

Answer 2

I think this is better understood by imagining the velocity field of the flow than through pressure. Yes, at some level pressure is what causes it to move, but it is simpler just to say that the ball is swept along with the motion of the air.

When you blow into the mouth of the bottle, you tend to form a jet that is most intense near the axis of the neck. The injected air wants to escape, and it does so mostly along the walls of the neck (the middle being taken up by the jet going the opposite direction). As the ball rests at the bottom, it falls within this outward-flowing region. In an experiment where the ball was somehow constrained to remain on the centerline, I think it would go into the bottle.