Mahshid Alsadat Mousavian; Mohammad Mehdi Riyahi; Ali Haghighi
Abstract
To analyze transient flows, continuity and momentum equations must be solved. Due to the non-linear friction term in the momentum equation, numerical methods such as method of characteristics (MOC) are used to analyze the problem in thetime domain. Although numerical methods are easy to use, but they ...
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To analyze transient flows, continuity and momentum equations must be solved. Due to the non-linear friction term in the momentum equation, numerical methods such as method of characteristics (MOC) are used to analyze the problem in thetime domain. Although numerical methods are easy to use, but they are numerically expensive and time-consuming, especially for advanced applications of transient analysis, e.g., real-time evaluations and fault detection algorithms, including inverse problem solutions. To cope with mentioned problems, an approximate analytical solution should be investigated, which is not required high computational time. To this end, the nonlinear equations should be linearized. Thus, the focus of this paper is to investigate the linearization methods. Therefore, four different linearization methods are applied and the resultingequations of each method in different RPV systems are solved. The efficiency of each method is compared with the results obtained from the numerical analysis of nonlinear governing equations. The results show that linearized water hammerequations provide reasonable results in early pressure wave cycles. The obtained results show that the coefficient of determination (R2) of the linearized models changes from 0.92 to 0.99. Also, by comparing the results of linearization modelswith each other, the linearized momentum equation in the time domain by replacing the mean velocity instead of the instantaneous velocity is the most accurate model which R2 is 0.999452.
Majid Rahimpour; Mohamad Reza Madadi
Abstract
Friction factor is an important hydraulic parameter for design of pipeline systems. There are several formulations for calculating the friction factor, among which Colebrook–White equation is the most accurate and repute formula. Owing to the implicit nature of friction factor in Colebrook–White ...
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Friction factor is an important hydraulic parameter for design of pipeline systems. There are several formulations for calculating the friction factor, among which Colebrook–White equation is the most accurate and repute formula. Owing to the implicit nature of friction factor in Colebrook–White equation, iterative methods are required to calculate this factor. In this study, Regula Falsi iterative numerical scheme was used to solve the implicit nonlinear equation of friction factor in the Mathematica programming tool. Case examples including different series and parallel pipeline systems were presented and solved. The results indicated high capability of Regula Falsi method in solving both the parallel and series systems. It was found that the solution by Mathematica differ significantly from conventional methods and can be desirably used for solving different hydraulic problems. The use of Mathematica with its huge features permits the researchers to be more professional in formulations of engineering problems and interpretations of results.
