the forumla for why the water inside the cupwill not spill when you put a notecard on top of it and flipd it?

Answer 1

I know of no specific formula for this phenomenon.
It is simply the result of the atmospheric pressure against the note card is greater than the pressure above the water inside the cup - if this pressure is equalized (a small hole, for instance, in the bottom of the cup) gravity will surely take over.