What you Need
What to do
You are going to use the lemonade bottle as a kind of cannon to blow out the candles, but to do this you will have to hit them. So to start with you want to make some sights to help you aim.
If you look at the sides of your bottle, you should find a line running along the bottle where two parts of the mold used to make the bottle joined together. You could use this to aim along, but you will find it hard to see, so I attached a couple of pieces of tape to this line which were stuck to themselves to make an inverted T shape. These make quite acceptable sights.
Start off maybe 1m from your lighted candle, hold the bottle in the middle with one hand, aim carefully and slap the other side with your other hand.
What may happen
With a few tries you should be able to blow out the candle from even 2-3m away. Which is far further than you could blow the candle out from.
It is normally easier if the you are on the same level or below the candle rather than above it, as the column of rising air above the candle can deflect your shots.
Why does it happen?
When you hit the side of the bottle, this makes the bottle slightly smaller which causes a small puff of air to come out of the neck. When this rapidly moving air meets the stationary air outside, it will slow down at its sides. Because the air in the centre is still moving fast this tends to cause the moving air to bend towards the stationary air and start to spin. This is the same effect as you see when fast moving water meets slow water in a stream and small swirls of water called eddies (or vorticies) are formed.
Because the top of the bottle is circular, the vortex you create is a ring shape, spinning around the ring at its centre.
The air isn't just moving at the centre of the ring, it is still spinning a considerable distance from the ring itself. This means that the left hand part of the ring will create an upward wind on the right hand side and vice versa. So the ring blows iteself forward. In a very still room this ring vortex can travel a long way, and still have enough energy to blow out the candle.
Can you see these ring vorticies
If you blow them from an area full of smoke you can see them quite well. The video below is made by filling the bottle with dry ice smoke and squashing it. The video is slowed down by a factor of 10 so you can see what is happening.