Laminar velocity profile development in straight pipes of circular cross section

Velocity profile development has been studied experimentally in Newtonian and some non-Newtonian fluids. The entry length for the development of 99% of the terminal axial velocity from an initially flat profile has been found to be given byZ _e = 1.1–0.112N(Re) for laminar flow Reynolds numbers between 1 and 1500 with Newtonian fluids. There were substantial increases in this length for weakly visco-elastic aqueous solutions of polyethylene oxide and polyacrylamide in the Reynolds number range (between 1 and 10) where these have been studied.