# Newton Raphson Method for Solving the Friction Factor of Colebrook Equation in Water Pipeline

### Abstract

The internal flow of the piping system is important for constructing fluid mechanism. In order to calculate the elevation difference between two reservoirs, the Colebrook equation can be used. The Colebrook equation is used to find the Darcy friction factor of the pipe. However, the friction factor of the Colebrook equation cannot be extracted analytically. Hence, a numerical analysis is performed to find the Darcy friction factor from Colebrook equation. In this study, the Newton Raphson method is chosen as the suitable numerical method to solve Colebrook equation. The Darcy friction factor obtained from the numerical analysis is then compared to the value obtained from Moody chart. The results showed that the Newton Raphson method can give an accurate approximation with error of no more than 0.0001.

*Communications in Computational and Applied Mathematics*,

*1*(2). Retrieved from https://fazpublishing.com/ccam/index.php/ccam/article/view/9