What shape will cause Pascal's vases to have an uneven water level?

Question

http://www.oberlin.edu/physics/catalog/demonstrations/fluids/pascalvases.jpg

Answer 1

One in which the top of one or more is closed, and air pressure prevents the levels from equilibrating. Or possibly one where the diameter is small enough that capillary action becomes measurable.

But then, neither of those cases would actually be examples of Pascal Vases.

Other than that, there isn't really one. Which is the point of the device. It is specifically designed to demonstrate the principle that, as long as the liquid is free to flow between containers, and gravity is the only outside force, the levels in the containers will all always be equal. Shape is irrelevant - only depth matters.

Answer 2

None! Water will always have the same level despite the different shapes.

Answer 3

There is no such shape (unless you pinch off a connection). That's the point, the levels are the same irregardless of shape.