Improvement of Clamonds solution of the Colebrook-White equation: highest accuracy for engineering purposes with one iteration
For engineers needing fast and accurate friction factor calculations, this provides a more efficient solution with minimal computational cost.
The paper improves Clamond's iterative solution for the Colebrook-White equation, achieving a maximal error of 2.79E-7 with only one iteration, which is sufficient for engineering purposes. The solution is the most accurate among the fastest methods requiring only two logarithm calls.
The Colebrook-White equation is the widely used basis for the calculation of the friction factor lambda for flows in pipes and ducts. Because this equation is implicit in lambda, many solutions have been developed to ease the calculation in order to reduce the effort and to reach a sufficient accuracy. Clamond has proposed in 2008 an iterative solution that requires maximally two iterations to obtain the machine double precision. Here an improvement of this solution is presented, that achieves already with one iteration a maximal error of 2.79E-7, what is more than sufficient for most engineering purposes. This solution is compared in a chart of CPU time versus accuracy with 28 solutions from the literature and in the group of the fastest solutions, that require only two calls of the logarithm function, it proved to be by far the most accurate one.