Why does atmospheric pressure not keep liquids inside upside down cups?

[electronicsguy]

If I hold the top end of a straw filled with water, the water stays in the straw which is due to the atmospheric pressure. How come this effect is not seen in upside down cups? Should the atmospheric pressure keep the liquid inside it within the cup since the other end is closed? Also, the radius of the cup is greater which means greater upward force.

 

[Simon Bridge]

Welcome to PF;
You do see this effect in upside down cups - provided the mouth of the cup is below water level.
The key here is the width of the opening.

For the pressure difference to hold the water in the container, it needs to be exerted evenly over the whole surface.
A small variation, even for a moment, will make one side heavier, allowing a bubble of air to form and break the seal. You can see it if you use a glass jar - watch the opening as you lift it clear of the water.

Over a small surface, though, the variations do not usually build up so much.
You can break the symmetry by tilting the straw (if i's a wide one).
[If the straw is very narrow, then capillary effects can become important too.]

Your narrow straw is just restricting the number of things that can possibly go wrong ;)

The classic demonstration of the effect is in a vortex bottle -
http://www.instructables.com/id/How-to-Make-a-Vortex-in-a-Bottle/
... the connecting hole has to be small (how small? experiment!) to make it work.
If you just up-ended the bottles quickly, no vortex forms, and water does not flow from one bottle to the next.

 

[electronicsguy]

Ok so the uneven force of the atmospheric pressure due to a wide opening does not hold the liquid in tact. How does this have anything to do with the vortex bottle?

 

[Simon Bridge]

Try the bottle and see - experiment with different sized holes (without swirling the water).