To clarify the question: do you mean that the flow is such that you can clearly see motion, or that the stream of pitch flowing down does not break up into droplets? (The latter depends also on surface tension, the former does not.)

I was thinking such that there is sufficient flow to see motion (say 1 mL/min). I think the boundary between droplets vs continuous flow is a more difficult problem.

Interesting question. It depends of course on the combination of how restrictive the nozzle is (as compared to the width of the column above), and the height of the pitch above the nozzle. If you take the geometry of the pitch drop experiment as fixed, varying only the radius (of both nozzle and column), keeping the pitch height constant, I believe that problem can be solved. Will think about it.