Fluid tracking with valve states

[StevenD]

Working on a project where I need to track the volume of 4 vessels plumbed into a flow path. Assume that I already know the flow rate coming into the top tube and can get a volume change from that. However there are many different flow paths and only a few of them would logically allow me to know where the fluid is going. 

For example, for vessel 1, V1 must be open and V5 OR V15 must be open as well. That would provide a path for fluid to flow through. However, if there is a path though the other vessels then there is no way to know which path the fluid will take and tracking is invalid.

If I wanted 5 possible states known: vessel 1, 2, 3, or 4 active, or tracking invalid, what would be the best way to determine that?

(ignore the squiggles, there is another plumbing path that is irrelevant) 

[santo_13]

Only robust way it to put a flow meter or level gauge into each of the vessels. You can only assume or approximate the fluid flow when multiple valves are open based on the pipes used but nor accurately measure.

What do you exactly mean by "want to know the vessel state?" ,do you mean the amount of fluid in that vessel at any time or flow rate through that vessel?