الفهرس 
Introduction
Comparison between two and four equation modelsOnly 14 pages are availabe for public view
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Abstract
ABSTRACT Water hammer phenomena due to sudden closure of a valve, which may have destructive effects on water or oil pipelines, are studied both analytically and numerically. Usually, fluid compressibility and pipe elasticity are taken into consideration, which produces a two-equation model composed of continuity and fluid momentum equations. In relatively recent publications, interactions between pipe and fluid during water hammer were studied taking into consideration axial pipe motion as well as friction on outside pipe wall. This produces a four-equation model, where pipe wall momentum equation as well as stress-strain relation of pipe wall material are considered. Some numerical results were obtained in previous literature indicating the importance of this effect, although a systematic study of the effect of different parameters is still lacking. In this study, dynamic fluid pipe coupling is analyzed taking outside friction on pipe wall into consideration. The effects of different parameters are studied through a complete set of dimensionless parameters governing these phenomena. The problem is analytically solved using the method of characteristics. This approach helps clarifying different coupling mechanisms involved. A criterion that determines whether coupling needs to be considered or not is introduced based on the characteristic equations. Estimates of maximum pressure and stress are also obtained for a simple, but relevant, case. Novel numerical techniques are proposed (post-interpolation and wave-front-tracking) in the framework of the method of characteristics that considerably improve its precision. A code is constructed, and verified using analytical results obtained above. The code is used in a systematic exploration of the role of different parameters. It is shown that increasing outside friction damping coefficient ? reduces maximum pressure and stress as long as it is kept small (0.05 – 0.3) The trend is reversed for higher values of ?, Hence an optimum value of ? exists which is of importance for engineering pipe design. New data on the rate of pressure and stress signals damping are obtained as a function of either fluid shear or outside friction damping. This information is useful in pipe design taking fatigue into consideration.