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Annals of Nuclear Energy
journal homepage: www.elsevier.com/locate/anucene
Probability of pipe breakage regarding transient ﬂow in a small pipe network
Hyuk Jae Kwon a,⇑, Cheol-Eung Lee b
Department of Civil & Environmental Engineering, Cheongju University, Cheongju 360-764, Republic of KoreaDepartment of Civil Engineering, Kangwon National University, Chuncheon 200-701, Republic of Korea
a r t i c l e
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a b s t r a c t
A reliability model was developed for the calculations of the probability of pipe breakage associated with transient effect. The statistical distribution for the maximum pressure wave heights was determined from the results of 168 transient analyses. Itwas found that the statistical distribution for internal pressure among the random variables of reliability function is well matched with the Gumbel distribution. The probability of pipe breakage in a small pipe network was calculated according to pipe diameter, thickness, allowable stress, and internal pressure. From the results, it was found that transient effect signiﬁcantly increases theprobability of pipe breakage. Using the present reliability model, it could be possible to ﬁnd a pipe that contains the high probability of pipe breakage in a water distribution system. If the reliability model developed in the present study is applied for the design, a safe design will be accomplished. Furthermore, it can be effectively used for the management and maintenance of a water distributionsystem. Ó 2010 Elsevier Ltd. All rights reserved.
Article history: Received 19 May 2010 Received in revised form 2 September 2010 Accepted 10 September 2010 Available online xxxx Keywords: Pipe breakage Pipe network Reliability model Transient ﬂow
1. Introduction Nowadays, researches for water distribution system are facing so many engineering problems. For example, it is very difﬁcult toﬁgure out the corrosion and erosion of pipe which is laid under the ground. Furthermore, it is necessary to analyze the pressure oscillations of transient ﬂow. Mailhot et al. (2000) suggested a method to estimate the coefﬁcients of statistical model for water distribution system which has a short record of pipe breakage. And they showed how to apply the method to a real city water distribution system.Watson et al. (2004) suggested the Bayesian model to estimate the uncertain factors which should be determined by engineering experiences for the various decision making, maintenance, and management of water distribution system. Especially, they focused on the long-term management of water distribution system. They also showed the results of basic study for pipe breakage as a discrete event.However, these researches did not consider the effect of transient ﬂow. If a sudden change of water demand or sudden change of pressure is occurred in water distribution system, huge pressure wave can be produced. Certain rules and guide lines are applied for the design, management, and maintenance of water distribution system. If the speciﬁc rules and guide lines are overlooked, water distributionsystem can be damaged. Nowadays, many researches for pipe breakage are seriously discussed. Jönsson and Larson (1992) and Brunone (1999) developed time domain reﬂectometry that determines the
⇑ Corresponding author. Tel.: +82 43 229 8473; fax: +82 43 229 8466.
E-mail addresses: email@example.com (H.J. Kwon), firstname.lastname@example.org (C.-E. Lee). 0306-4549/$ - see front matter Ó 2010 Elsevier Ltd. Allrights reserved. doi:10.1016/j.anucene.2010.09.026
location and size of pipe breakage. Misiunas et al. (2005) developed a pipe breakage detection technique by monitoring transient pressure. In the present study, reliability model was developed for the calculation of probability of pipe breakage regarding transient ﬂow in water distribution system. Functional evaluation and risk analysis of...