Theoretical and experimental results for the dynamic response of pressure measuring systems

Abstract

For a series-connection of N thin tubes and N volumes a general recursion formula has been derived that relates the sinusoidal pressure disturbance in volume; to the pressure disturbances in the preceding volume j and the next volume j - 1. From this recursion formula the expressions for the complex ratio of the pressure fluctuation of each volume ; to the sinusoidal input pressure Po can be derived by successively putting j = N, N - 1,.. .2, 1. For a single pressure measuring system (N = 1) and a double pressure measuring system (N = 2) these dynamic response formulae are given explicitely. Theoretical results for single pressure measuring systems are presented that demonstrate the influence of the different parameters. As an illustrative example of the double pressure measuring system some calculations have been performed for a system with a discontinuity in tube radius. Comparison of theoretical and experimental results shows that the response characteristics of the pressure measuring systems considered can be predicted theoretically to a high degree of accuracy.