Energy analysis for the illustration of inaccuracies in the linear modelling of pipe fluid transients

Transmission line models, in the form of either transfer matrices or impedance functions, are linear approximations to the governing one-dimensional equations for pipe flow. Despite their growing popularity, the accuracy of these models is not well studied and their ability for reproducing responses from the nonlinear and robust method of characteristics model is largely untested. This paper proposes the use of the energy phase diagram to compare the accuracy of the transmission line model with that of the method of characteristics model. The energy phase diagram is a powerful method for summarizing the head and flow responses for all points in the system and for all times into a single plot and is ideal for the comparison of responses from different numerical models. This study identifies errors from the transmission line model that were undetected previously when the head responses at a single point were used to gauge model accuracy.