Separate flow friction formulations for laminar and turbulent regimes of flow through pipes are in common use in engineering practice. However, variation of different parameters in a system of conduits during conveying of fluids can cause changes in flow pattern from laminar to fully turbulent and vice versa. Because of that, it is useful to unify formulations for laminar and turbulent hydraulic regimes in one single coherent equation. In addition to a physical interpretation of hydraulic friction, this communication gives a short overview of already available Darcy’s flow friction formulations for both laminar and turbulent flow and additionally includes two simple completely new approximations based on symbolic regression.

This paper indicates the importance and advantages of the application of hybrid models in the control of water supply systems. A range of possibilities provided by this scientific approach is presented in the practical examples related to the fault diagnostics and fault-tolerant control in the pumping station (PS) control systems. It is presented that continuous monitoring and recording of the data of the pumping stations operation processes (electrical parameters such as electrical power, pressure or flow in the pipelines, water levels in the tanks, changes in various discrete states, etc.) could represent a significant resource that can be used to develop various hybrid models using the appropriate “data-driven” techniques. During this process, data are transformed into information, and thereafter, information into knowledge. Based on this knowledge, the control of PS operation can be significantly improved and a significant increase in the user’s satisfaction can be achieved while the maintenance and operation costs can be reduced.

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 2²⁰ = 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.