The present Note reports a detailed analysis of some of the specific flow properties which are associated with the development region of circular pipes and ducts of square or rectangular cross-sections in turbulent conditions. Indeed, there are no data presently available to determine a priori the acceleration effect which results from the progressive thickening of the boundary layers on the pipe walls. In addition, published results concerning the longitudinal extension of this development region are rather confusing. Through our study, on the one hand, the litigious points are clarified, and, on the other hand, the pertinent grouping of variables (which include the hydraulic diameter   and the boundary layer displacement thickness  ) providing the parameter relevant for obtaining similarity between all the situations is displayed. To cite this article: F. Anselmet et al., C. R. Mecanique 337 (2009).