A WEIGHTING FUNCTION MODEL OF TRANSIENT TURBULENT PIPE FRICTION

A weighting function model of transient turbulent pipe friction at mod erate Reynolds Numbers is developed in a similar manner to Zielke's eq uivalent expression for laminar flow (1968). It is shown that a family of weighting function curves exists and that Zielke's curve is an upp er bound asymptote that is valid for low Reynolds numbers, not only fo r laminar flow. The new weighting function model is based on an approx imate representation of a turbulent pipe flow as a laminar annulus sur rounding a uniform core. The acceptability of this representation is d emonstrated by comparing wall shear-stress histories predicted using t his model with equivalent histories predicted using a five-region eddy viscosity model. It is shown that the new weighting function curves c an be represented with sufficient accuracy by exponential relationship s similar to those proposed by Trikha for transient laminar flows (197 5).