This paper aims to investigate a laminar incompressible internal flow, which takes place in a random-shaped conduit. Evidently, the randomness of its boundary does not permit its consideration as a duct or a tube. To overcome the difficulty of identifying such a flow, we propose a mathematical criterion for its characterization as fully developed. Here, we should emphasize that this criterion though its qualitative character, may serve as a useful strict test for those desiring to identify beforehand the velocity profile ranges in a duct or a nozzle from the engineering viewpoint, or for examining the behavior of a closed-form representation of velocity profile.

internal flow, random-shaped conduit, fully developed flow, frictionless core.