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Resonance in pressurized piping systems Chaudhry, Mohammad Hanif

Abstract

A new approach, based on the transfer matrix method used in the theory of vibrations, is presented to analyze the steady-oscillatory flows, and to determine the resonating characteristics of piping systems. By linearizing the friction loss term, considering the system as distributed and assuming the discharge and pressure head fluctuations as sinusoidal, field matrices for a simple pipeline and for a parallel system are derived. A numerical technique is presented to determine the field matrix for a pipe having variable characteristics along its length. Point matrices for orifices, and for oscillating valves are obtained by linearizing the gate equation. Point matrices for the junction of the main and a branch having various boundary conditions, e.g., dead end, reservoir, orifice, oscillating valve, are also derived. A numerical procedure is outlined for computing the resonant frequencies of piping systems. Expressions are developed to determine the frequency response of systems having periodic forcing functions, such as fluctuating pressure head; fluctuating discharge; and oscillating valve. A number of systems commonly used in waterpower development and water supply schemes are analyzed. The results obtained by the method presented herein are in close agreement with those obtained experimentally by earlier investigators; or determined by using the method of characteristics, impedance theory, or energy concepts.

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