Computationally Efficient and Accurate Solution for Colebrook Equation Based on Lagrange Theorem

Computationally efficient solutions (less computation time) for the Colebrook equation are essential for simulating pipeline networks. However, the friction law resistance formula has an implicit form for the friction factor. In this study, a computationally efficient and accurate solution for the friction head loss in pipeline networks is developed using the Lagrange inversion theorem. The results are in the form of fast converging power series. Truncated and regressed expressions are obtained using two and three terms of the expanded series that have maximum relative errors of 0.149% and 0.040%, respectively. The proposed solution is as accurate as existing analytic solutions but is computationally more efficient in estimating the friction head loss.