Hole in Bernoulli's theorem when trying to blow ball into bottle According to Bernoulli's theorem while blowing a paper ball inside the bottle (as shown in this short video), the speed of the air at the mouth of bottle is higher and hence creates low pressure relative to the inside air, so the air blows from inside to outside bringing the paper out.
But when I made a hole in the bottle and repeated the same, this time the paper goes inside. Why ?
The pressure at the mouth is still lower than inside while blowing. Isn't it?
The pressure of the air at the hole and inside bottle should be same. Only at the mouth of the bottle is the pressure relatively lower because of higher speed (due to blowing). So, why doesn't the inside air come out through the mouth in this case ?
Also, when I replace the bottle with a tumbler with a wide mouth, the paper goes inside rather than coming out as in case of the bottle.
 A: Why it is almost impossible to blow the paper ball into the ball has little to do with Bernoulli's theorem. When you blow into the bottle there is initially some inward force on the paper ball, but the air mostly goes around the ball and into the bottle.  If there is no hole in the side of the bottle, the air pressure inside the bottle increases and pushes the paper out to start a return air flow.  This happens very quickly so the initial force pushing the paper into the bottle does not have time to move the ball before the return air flow pushes the ball out of the bottle.
When you make a hole in the side of the bottle, the air you are blowing into the bottle can escape through the hole. There is no need for air to come back out through the mouth, so the inward flowing air force on the ball blows it in.
You could try some experiments to find the minimum size hole needed in the side of the bottle that allows the ball to be blown into the bottle.
With the tumbler, the mouth is so wide that the return air flow has lots of room to move around the ball. If you blow directly on the ball, it will go into the bottle and the return air flow will be on the other side of the mouth. If you blow into the mouth on the side opposite to the ball, however, the air flow will push the ball out.
Similarly, if you blow though a drinking straw directly onto the ball in the bottle mouth, you should be able to blow it into the bottle. The inward force of the air is now concentrated on the ball and the return flow is around the periphery. If you move the straw and blow into the bottle beside the ball, the ball will come out.
It all has to do with air flow. Bernoulli may only come into it when getting the ball out by blowing sideways on the mouth, as shown at the end of the video.
