A weighting function model of unsteady skin friction in smooth-walled, one-dimensional ducts is derived using an idealized form of the radial viscosity distribution. The model is an enhancement of earlier work by the authors in which additional simplifying assumptions were made. Important improvements include (1) replacing the assumption of uniform (solid) behaviour in an extensive core region by an assumption of uniform turbulent viscosity and (2) relating the wall shear stress to the mean flow velocity instead of to the maximum velocity. The resulting model can be used directly in numerical analyses of transient flows in pipes. It can also be used to deduce numerical values of an empirical coefficient in a popular alternative model of skin friction in which the unsteady contribution is assumed to be proportional to the instantaneous mean acceleration.