An investigation of turbulent developing flow at the entrance to a smooth pipe

An attempt is made to explain the flow regimes at the entry region of a pipe. Developing turbulent flow was examined and three theoretical models were evolved to explain the three most important regimes: the region of flat plate flow, the region of transition from flat plate to pipe flow, and the region of boundary layer interaction. The model for the flat plate flow was based on the velocity power law but experimental data showed that the exponent was not constant as generally assumed. There was good agreement between the theoretical models and the experimental data for the boundary layer development.

A simple empirical formula was obtained from which it is possible to predict the length of the entry region. The onset of the increase in turbulence intensity at the core, which marks the start of transition from flat plate flow to pipe flow, seems to occur at a particular Reynolds number, based on distance into pipe, of about 3.15×10⁶. This figure may vary with inlet flow condition.