Transient, turbulent, smooth pipe friction

Two of the most promising analytical models of unsteady friction in turbulent pipe flows are based on sharply contrasting hypotheses. One uses the history of the flow; the other uses instantaneous conditions. The purposes of this paper are to present an analysis using the former approach and to indicate how to determine which of the two methods is appropriate. A weighting function model of transient friction is developed for flows in smooth pipes by assuming the turbulent viscosity to vary linearly within a thick shear layer surrounding a core of uniform velocity and is thus applicable to flows at high Reynolds number. In the case of low Reynolds number turbulent flows and short time intervals, the predicted skin friction is identical to an earlier model developed by Vardy et al (1993). In the case of laminar flows, it gives results equivalent to those of Zielke (1966, 1968). The predictions are compared with analytical results for the special case of flows with uniform acceleration. It is this case that enables clarifying comparisons to be drawn with "instantaneous" methods of representing transient skin friction.