Warning: No, this post will not contain an analytic general solution to Navier-Stokes - sorry to disappoint the hopeful ones.
Suggestion: IF the player select a vessel containing a fluid, then (left)clicks another, empty container of the same kind, THEN the fluid in the first container will be split equally (or near equally) between the two.
Rationale for this extra interface-clutter:
1. It does not interfer with any other operation the player could possibly currently want to do with the two containers (at least I cannot see any situations where the player e.g would want to contain the fluid in a different quality container).
2. Specific situation where this would come in handy:
Player is making rennet small-scale, say he wants to make 4 units, and wants to use of his limited stock of high q water. However, using a whole bucket would be a waste, as half of it would boil away unused. With this mechanic in place, he can quite easily subdivide the water into any amount of empty buckets in his rennet-cupboard.