Remarks on transition in a round tube

Abstract

This article has a twofold purpose: (1) to analyse the available theoretical and experimental knowledge concerning flow in the inlet region of a smooth round tube, and (2) to point out that the e⁹ amplification factor method apparently predicts natural transition correctly over a significant fraction of the entire inlet lenght of the tube. The successful prediction indicates, but does not prove, that flow in a smooth round tube becomes turbulent at higher Reynolds numbers because transition occurs in the inlet lenght—not in the fully developed Poiseuille régime. The close agreement between theory and a test result obtained by Pfenninger indicates that the e⁹ method is valid for a wide variety of flows having x Reynolds numbers of transition ranging from 570,000 to 40 million. The results are applicable to both plane and axially symmetric flows.