A weighting function model of transient turbulent pipe friction

Abstract

Abstract A weighting function model of transient turbulent pipe friction at moderate Reynolds Numbers is developed in a similar manner to Zielke's equivalent expression for laminar flow (1968). It is shown that a family of weighting function curves exists and that Zielke's curve is an upper bound asymptote that is valid for low Reynolds numbers, not only for laminar flow. The new weighting function model is based on an approximate representation of a turbulent pipe flow as a laminar annulus surrounding a uniform core. The acceptability of this representation is demonstrated by comparing wall shear-stress histories predicted using this model with equivalent histories predicted using a five-region eddy viscosity model. It is shown that the new weighting function curves can be represented with sufficient accuracy by exponential relationships similar to those proposed by Trikha for transient laminar flows (1975).