A Boundary-Layer Theory for Transient Viscous Losses in Turbulent Flow

A laminar boundary-layer model is proposed to account for viscous losses during the transient turbulent flow of a liquid in a tube. In this model, inviscid slug flow is assumed for the core and all viscous effects are assumed to occur in the boundary layer. The transient boundary-layer velocity distribution is determined as a function of a prescribed variation in core velocity and the associated pressure gradient. Both analytical and numerical solutions are presented. This transient flow information is used to calculate local and integrated energy dissipation rates which are then combined, with one-dimensional energy analyses. The result is a prediction of the decrease in pressure-wave magnitude due to viscous dissipation, and a comparison is made with experimental data for rapid flow extinction. Good agreement between the observed and predicted results is obtained.