Boundary-Layer Displacement Thickness on Flat Plates

The various types of flow in a boundary layer are reviewed with particular attention to the turbulent transition region on surfaces having an engineering roughness. The coefficient of total skin friction is compared with the friction factor for fully-developed flow in pipes and the criteria determining the limits of the smooth turbulent and rough turbulent regions of flow are compared and found to be similar. However, different criteria apply to surfaces with a sand roughness and the transition region is shown to be much shorter. Using the data on skin friction, the relative displacement thickness, δ_*/ x, has been calculated for laminar flow and for turbulent flow with engineering roughness. Curves in the laminar transition region between these two types of flow have also been determined. These curves can be used to calibrate a broad-crested weir using critical-flow theory modified to take into account the growth of the boundary layer on the crest.