This two-part paper investigates parameters that may significantly affect water-hammer wave attenuation, shape and timing. Possible sources that may affect the waveform predicted by classical water-hammer theory include unsteady friction, cavitation (including column separation and trapped air pockets), a number of fluid–structure interaction effects, viscoelastic behaviour of the pipe-wall material, leakages and blockages. Part 1 of this two-part paper presents the mathematical tools needed to model these sources. Part 2 of the paper presents a number of case studies showing how these modelled sources affect pressure traces in a simple reservoir-pipeline-valve system. Each case study compares the obtained results with the standard (classical) water-hammer model, from which conclusions are drawn concerning the transient behaviour of real systems.