The dynamic characteristics of liquid line systems have been a subject of interest to many researchers for a long time. The most popular mathematical model seems to be the one given in matrix form in A. F. D'Souza and R. Oldenburger's paper. This model is based on unsteady laminar flow of a viscous and compressible liquid.
It is well known that the numerical calculations obtained using the above-mentioned model are in good agreement with experimental results. But the model contains hyperbolic functions and Bessel functions and is so complicated that one usually needs a digital computer to obtain numerical results.
Therefore, many papers have been published on approximation methods of these numerical calculations from an engineering view point. But all approximation methods are still considerably complicated and it is almost impossible to estimate immediately the characteristics of liquid line systems for arbitrary load conditions.
Referring to a method which is often used in the field of an electrical wave transmission line with distributed parameters, the author proposes a graphical calculation method of the frequency characteristics of liquid line systems with arbitrary boundary conditions.
In the proposed method, reflection coefficients and mapping play very important roles. The frequency characteristics of liquid line systems can be easily calculated with only arithmetical operations and a chart without the need of a computer. Furthermore, the trends of frequency characteristics that have been almost impossible to obtain up to now, can be grasped both qualitatively and quantitatively.
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