Flow Pattern and Frictional Losses in Pulsating Pipe Flow : Part 5, Wall Shear Stress and Flow Pattern in a Laminar Flow

By introducing four characteristic parameters defined for a pulsating turbulent pipe flow, the pattern diagrams for a pulsating laminar pipe flow are shown. The flow patterns are classified into three types, i. e., quasi-steady, intermediate, and inertia dominant ones with respect to the dimensionless frequency ω' and the limits between these three regions are determined. An alternative analytical representation for wall shear stress τw including acceleration term and its approximation are proposed. Various approximate representations for τw reported previously or proposed here are compared with the analytical one by means of the four characteristic parameters and their applicability is examined.