series and parallel pipelines system solutions using regula falsi method scripted in mathematica

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.