Measurements of turbulent flow development in tubes and annuli with square or rounded entrances

Entrance‐region studies, based on static‐pressure measurements, were carried out with water flowing in annuli and a circular tube fitted with interchangeable square or rounded entrance sections. The tests covered the Reynolds number range from 16,000 to 70,000. For the annuli, the length of duct required to approach to within 5% of the fully developed pressure gradient was about 20 to 25 hydraulic diameters. This is in general accord with entrance length results for circular tubes and parallel‐plate channels but differs from prior results for the annulus which had indicated entrance lengths larger by a factor of ten. The results for the sharp entrance showed a definite effect of separation and were characterized by high loss coefficients. For the rounded entrance, the initial part of the flow development was laminar; the entrance‐region pressure drop did not substantially exceed (and in one case was less than) the corresponding fully developed pressure drop. Also for the rounded entrance, flow stability was improved and a monotonically decreasing pressure gradient obtained when a turbulent boundary layer was induced by means of a trip. Fully developed friction factors were calculated and compared with theory.