I was dumping some old 1L bottles of soda down the sink by putting the bottle upside down into the drain. The soda was glug-glugging down the drain since air was coming up through the spout while soda was going down. It would drain faster if I punched a hole in the bottom of the bottle since air didn’t have to enter at the spout anymore.
This got me thinking: What was the smallest hole I could make so that the soda still flowed out as fast as possible? So between these ranges:
Max hole: Cut the entire bottom of the soda bottle off. Soda flows out at rate A
Min hole: Use a pin to make a tiny hole in the bottom. Soda flows out at rate B
What is the smallest hole I can make so that the fluid still flows at rate A? And will the answer always be a percentage of the size of the drain hole?
If the shape of a real soda bottle complicates things, just assume it’s a perfect cylinder with a flat top and bottom.