Introduction

1 Introduction

Any system which uses fluids for transmission of power or information generally consists of a group of components connected by fluid-filled transmission lines. In the analysis of fluid control systems, it is often assumed that any dynamic characteristics of a system's behaviour are due entirely to the components and that the connecting lines behave as perfectly rigid, massless, lossless elements. Under steady flow conditions, and in many unsteady situations, the dynamic effects of the transmission lines are either unimportant or negligible compared to the component effects; however, fluid transmission lines have inertial, capacitive, and resistive properties distributed along their length. Depending on the particular system's configuration and end conditions, these effects may be essential to the understanding and prediction of the system's dynamic characteristics.

he dynamic nature of transmission lines is important in a number of fields covering a wide range of applications. These include highly dynamic conventional hydraulic and pneumatic control systems, novel hydraulic systems operating on alternating and pulsating flow concepts, hydroelectric power complexes and water distribution systems, which are subjected to unsteady flow conditions, chemical process control systems involving liquid transfer lines, fluidic systems, rocket and missile liquid propellant supply systems and even biological blood circulatory systems. Theoretical treatments of the transmission lines in these applications have many features in common with each other and with the analogous situations in related fields such as acoustics and electrical engineering.

A study of over three hundred research papers from these areas of applications showed that notwithstanding the commonality of the problem, the research efforts were often paralleled and there was a remarkable (although not surprising) lack of cross referencing between them. This led to the development of a vast number of 'apparently' different models and solutions and a paradoxical situation where some researchers claimed priority of their contribution whereas prior solutions existed-in other fields of applications. In addition construction of models and their solutions were often obtained without clear statement of underlying assumptions.

The objective is to show contributions by various researchers, over the last eighty years (till 1986), to the development of distributed parameter models of fluid transmission lines. This review is concerned with the historical development of individual models and it includes significant contributions, which either extended an existing model or dealt with the means of approximating or simplifying the use of a model.

Two other groups of transmission line models and their respective solutions exist in the literature, but are not discussed in this paper. The first group includes the numerical and analytical approximations of the full solutions. The second includes the various lumped parameter models and their solutions which are used to approximate the dynamic characteristics of the full distributed parameter models.