Failure of grey cast iron water pipe due to resonance phenomenon

Abstract

A condition of resonance in a hydraulic pipe supplied at the upstream end by a reservoir is analysed. The resonance appears in the pipe when the pressure-head at the reservoir vibrates at selected frequencies. The impedance theory is used in the analysis to determine the spectrum of these natural frequencies. For solution, the hydraulic system is programmed on digital computer using the method of characteristics. In these conditions, the pressure-head amplitudes increase gradually and build up to a steady-oscillatory flow. At the downstream dead end of the pipe the pressure can become very large. The effects of energy dissipation resulting from viscous friction are included and show to be of important consequence on the analysed systems. The maximum stresses in the pipes may be calculated via thin-walled hollow cylinder assumptions. In the case were the admissible stress can be reached, this may yield to the failure of the pipe if a corrosion crater exists. To investigate the defect geometry effects, semi-elliptical cracks are deemed to exist up to one-half thickness of the pipe wall. The outcomes have been introduced into the Failure Assessment Diagram (FAD) using the SINTAP code in order to obtain the safety factor value. It has been shown that the value of the safety factor depends on the length of the pipe.