Results of an experimental investigation of the laminar flow of air over a downstream-facing step are presented. The experiments include visual observations of smoke filaments (in the viscous layer), qualitative velocity fluctuation measurements, and mean velocity profiles. Results are reported over a range of 0.36 – 1.02 cm in step height, 0.61 – 2.44 m/sec in free stream velocity at the step, and 0.16 – 0.51 cm in boundary layer displacement thickness at the step. Laminar flow to reattachment of a free shear layer is observed for subsonic flow and two criteria for which transition to turbulence at reattachment exists are presented. The laminar reattachment length is not a constant number of step heights as for turbulent flow, but varies with Reynolds number and boundary layer thickness at the step. The shape of the velocity profile at reattachment is found to be similar to the shape of a laminar boundary layer profile at separation and the boundary layer profiles downstream of reattachment are similar to those in a laminar boundary layer developing toward separation except that they are traversed in the reverse sense.

Fully developed turbulent flow of air at Re = 28,000 to 82,000 entered a porous tube with circular cross section. Air was injected uniformly through the tube wall for 18 diameters at various ratios of mass velocity through the tube wall to the average mass velocity at the entrance cross section of the tube, ranging from 0.00246 to 0.0584. Tests were also made with zero entrance velocity at the upstream end of the porous tube so that the flow developed in the tube exclusively as a result of the uniform mass injection through the tube wall. Most of the change in the shape of the velocity profiles, in the internal and wall shear, in the momentum flux factor, and in the friction factor occurred within the first 10 to 12 diameters of the tube length. Some changes even persisted further downstream, caused by the fact that mass is continuously injected along the porous tube. The parameters mentioned above, however, become independent of axial position for normalized distances downstream from the entrance cross section larger than x/D = 10 to 12, when they are considered as function of the ratio of injection velocity to average main flow velocity at the specific axial location. Eddy diffusivity values agreed in this presentation reasonably with the results of measurements in turbulent tube flow without injection. Normalized friction factors agreed with values measured in external flow. Properly normalized velocity defect profiles with injection agreed with those for flow without injection.

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.It is well known that a fluid passing into a duct from a chamber of different cross-sectional area undergoes a development of its velocity profile in the course of its flow through the duct. At a sufficient distance from the duct entrance, a balance between the pressure and viscous forces is achieved and an essentially fully developed, unchanging velocity profile results. That length of duct required to attain essentially fully developed conditions is designated as the hydrodynamic entrance length. For practical purposes, it is usually sufficient to associate the entrance length with the distance from the duct entrance that is needed to approach to within some specified percentage of the fully developed pressure gradient. Entrance lengths in turbulent flow are generally shorter than those in laminar flow. For turbulent flow in circular tubes or parallel-plate channels, the entrance length is usually on the order of 20 (hydraulic) diameters (I ) . Additionally, the turbulent entrance length is only moderately affected by the magnitude of the Reynolds number.The only experiments relating to the hydrodynamic entrance region in annuli appear to be those of Rothfus and associates (2, 3 ) . The outer tube of their annulus had a square entrance, whereas their inner tube extended upstream into the supply reservoir. This geometry would probably be intermediate between the square and rounded entrances used in the present tests. Measurements are reported of the total shear force on the inner tube of various annuli (diameter ratios 2.97 and 1.78) with lengths of 4, 8, and 12 ft. The average skin friction on each 4-ft. section was assumed equal to the local values at the midpoint of the section. Results based on the ratio of the aforementioned local shear stress to the fully developed shear stress indicate an entrance reg...

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