Performance Evaluation of Selected Explicit Friction Models In Pipe Network Analysis

This Accurate estimation of friction factor is essential for determining head loss and flow distribution in pipe networks. Although the Colebrook equation remains the benchmark, its implicit nature makes it computationally intensive. As a result, many explicit friction factor models have been developed as alternatives. This study evaluated the performance of 38 selected explicit models in solving pipe network problems using a non-linear gradient-based method in MATLAB. Four networks of increasing complexity (10, 24, 34, and 74 pipes) were used to assess each model's computational efficiency, accuracy, numerical stability, and complexity. The Colebrook equation, solved using the Clamond method, served as the benchmark. Across all networks, the number of iterations remained nearly constant for most models, but convergence times and computational efficiencies varied widely. Computational efficiencies ranged from 1.042 to 2.791 for network 1, 1.122 to 8.227 for network 2, 1.023 to 2.050 for network 3 and 1.001 to 1.794 for network 4. Although some explicit models, such as Swamee-Jain, Cojbasic Brkic A, Niazkar A, and Serghides A, showed good performance, the Colebrook equation remained the fastest and most stable across all networks. Error analysis using mean square error (MSE) across four pipe networks showed that Niazkar A, Cojbasic Brkic A, and Serghides A consistently produced the lowest errors and they closely matched Colebrook's results in both nodal heads and flow rates. For these models, nodal head MSE values ranged from 6.26×10⁻¹² to 6.75×10⁻¹² and flow rate MSE values from 6.61×10⁻11 to 6.17×10⁻10 in Network 1; 1.415×10⁻¹⁷ to 1.3529×10⁻16 for nodal head and 3.980×10⁻19 to 9.579×10⁻18 for flow rate in Network 2; 1.14×10⁻10 to 1.88×10⁻5 for nodal head and 2.179×10⁻14 to 1.0795×10⁻12 for flow rate in Network 3; and 2.46×10⁻18 to 5.43×10⁻18 for nodal head and 2.851×10⁻18 to 4.449×10⁻18 for flow rate in Network 4. In contrast, models such as Avci Karagoz, Buzzelli, and Fang exhibited convergence failures in the most complex network, indicating numerical instability in highly interconnected systems. In conclusion, while a few explicit models are suitable alternatives in specific scenarios, the Colebrook equation remains the most reliable choice for pipe network analysis.