Efficient resolution of the Colebrook equation

TL;DR

This paper introduces a new algorithm for solving Colebrook-like equations that is faster, more accurate, and more robust than existing methods, including those based on the Lambert W-function, with implementations in MATLAB and FORTRAN.

Contribution

The paper presents a novel, efficient algorithm for solving Colebrook equations that outperforms existing methods in speed, accuracy, and robustness across all parameter ranges.

Findings

The new method achieves higher accuracy than simplified approximations.

It is faster and more robust than Lambert W-based solutions.

The algorithm is applicable across the entire parameter range of the Colebrook equation.

Abstract

A robust, fast and accurate method for solving the Colebrook-like equations is presented. The algorithm is efficient for the whole range of parameters involved in the Colebrook equation. The computations are not more demanding than simplified approximations, but they are much more accurate. The algorithm is also faster and more robust than the Colebrook solution expressed in term of the Lambert W-function. Matlab and FORTRAN codes are provided.