Darcy-Weisbach resistance coefficient determination using Newton-Raphson approach for android 4.0

Abstract

Context: The article presents the friction coefficient calculation for pressure pipes, from Newton-Raphson numerical method, under JavaScript source code for Android 4.0 or higher. Methodology: The code development is based on Colebrook-White model for turbulent flows. The app also establishes the friction coefficient for laminar flows from the Poiseuille equation and determines the range for the enter flow in a transition zone (unstable flow). An algorithm of successive approximations was implemented for non-linear equation solution based on the relative roughness and Reynolds number. Results: In the Newton-Raphson method, if the initial value moves away from zero or presents different inflection points, the probability of divergence of the method increases significantly. To overcome this anomaly, a friction coefficient equal to 0.015 was proposed as initial (seed) value; thereby we guarantee the convergence for turbulent flows with an approximation of 0.0000001. The values ​​calculated by the app were calibrated with the Excel analysis tool (Goal Seek). Conclusion: The app is available for free in Google Play Store, and is a tool to support educational processes and the professional field.

Keywords

• Android
• coefficient of friction
• Colebrook-White
• Darcy-Weisbach
• head losses in pipes
• Newton-Raphson
• numerical methods
• JavaScript code