Fluid Transmission Lines—Distributed Parameter Models Part 1: A Review of the State of the Art

This paper presents a hierarchical classification of linear, distributed parameter models which have been used in the study of rigid, uniform fluid transmission lines. The development of the models from the fundamental equations of fluid dynamics is discussed, and the assumptions necessary in obtaining each model are shown. The solutions to the models are presented in general Laplace forms, and the terms that appear in the solutions are discussed with reference to the initial and subsequent assumptions. The existence of seven distinct forms of models was identified and verified by comparison with a vast number of apparently different models quoted in over three hundred research papers covering various engineering, medical, and biological applications. Significant contributions by various researchers over the last eighty years to the development of distributed parameter models of fluid transmission lines are reviewed. The application of the various models based upon comparisons made in the literature is dealt with, and the effect of the initial assumptions on each model's accuracy is discussed. The aim of the paper is to assist in the identification of areas of research where future efforts should be directed and hopefully to prevent needless duplication of research effort.