Velocity profiles at the exit of circular tubes

An investigation has been carried out on velocity profiles of Newtonian liquids at the exit of circular tubes for Reynolds numbers from about 50 to 1000. A simple expression which asymptotically approaches a Poiseuille parabolic distribution for higher Reynolds numbers is obtained. Experimental measurements of extrudate swell ratios were used as criteria for convergence to the solution. Comparison with jet shapes from previous experimental and theoretical studies supports the obtained results. The work also illustrates a straightforward method for simplifying and solving the governing equations for laminar flows of thin liquid layers.