Sampling the Darcy Friction Factor Using Halton, Hammersley, Sobol, and Korobov Sequences: Data Points from the Colebrook Relation

Dejan Brkić () and Marko Milošević
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Dejan Brkić: Faculty of Electronic Engineering, University of Niš, 18000 Niš, Serbia
Marko Milošević: Faculty of Electronic Engineering, University of Niš, 18000 Niš, Serbia

Data, 2025, vol. 10, issue 11, 1-13

Abstract: When the Colebrook equation is used in its original implicit form, the unknown pipe flow friction factor can only be obtained through time-consuming and computationally demanding iterative calculations. The empirical Colebrook equation relates the unknown Darcy friction factor to a known Reynolds number and a known relative roughness of a pipe’s inner surface. It is widely used in engineering. To simplify computations, a variety of explicit approximations have been developed, the accuracy of which must be carefully evaluated. For this purpose, this Data Descriptor gives a sufficient number of pipe flow friction factor values that are computed using a highly accurate iterative algorithm to solve the implicit Colebrook equation. These values serve as reference data, spanning the range relevant to engineering applications, and provide benchmarks for evaluating the accuracy of the approximations. The sampling points within the datasets are distributed in a way that minimizes gaps in the data. In this study, a Python Version v1 script was used to generate quasi-random samples, including Halton, Hammersley, Sobol, and deterministic lattice-based Korobov samples, which produce smaller gaps than purely random samples generated for comparison purposes. Using these sequences, a total of 2 20 = 1,048,576 data points were generated, and the corresponding datasets are provided in in the zenodo repositoryWhen a smaller subset of points is needed, the required number of initial points from these sequences can be used directly.

Keywords: Colebrook formula; explicit approximations; Darcy friction factor; pipe liquid flow; Halton distribution; Hammersley distribution; Sobol distribution; Korobov distribution; Colebrook–White experiment; Moody chart (search for similar items in EconPapers)
JEL-codes: C8 C80 C81 C82 C83 (search for similar items in EconPapers)
Date: 2025
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