Error Review of Single Iteration Explicit Approximations of Colebrook's Equation
This paper reviews the common single iteration of explicit equations for estimating the friction factor in pipes. The friction factor values were computed using Microsoft Excel. Using absolute error, relative percentage error, mean absolute error (MAE), mean square error (MSE), and root mean square error (RMSE), the Colebrook’s equation comparison was expressed. The best equation to estimate the friction factor was Beluco-Schettini when looking at the average error, MSE, and RMSE. In contrast, of all the equations, the Haaland equation is the most consistent.
Beluco, A., & Beatriz Camano Schettini, E. (2016). An Improved Expression for a Classical Type of Explicit Approximation of the Colebrook White Equation with Only One Internal Iteration. International Journal of Hydraulic Engineering, 5(1), 19–23. https://doi.org/10.5923/j.ijhe.20160501.03
Churchill, S. W. (1973). Empirical expressions for the shear stress in turbulent flow in commercial pipe. AIChE Journal, 19(2), 375–376. https://doi.org/10.1002/aic.690190228
Colebrook, C. F. (1939). Turbulent Flow in Pipes, With Particular Reference To the Transition Region Between the Smooth and Rough Pipe Laws. Journal of the Institution of Civil Engineers, 11(4), 133–156. https://doi.org/10.1680/ijoti.1939.13150
Fang, X., Xu, Y., & Zhou, Z. (2011). New correlations of single-phase friction factor for turbulent pipe flow and evaluation of existing single-phase friction factor correlations. Nuclear Engineering and Design, 241(3), 897–902. https://doi.org/10.1016/j.nucengdes.2010.12.019
Ghanbari, A., Farshad, F., & Rieke, H. H. (2011). Newly developed friction factor correlation for pipe flow and flow assurance. Journal of Chemical Engineering and Materials Science, 2(6), 83–86.
Haaland, S. E. (1983). Simple and Explicit Formulas for the Friction Factor in Turbulent Pipe Flow. Journal of Fluids Engineering, 105(1), 89–90. https://doi.org/10.1115/1.3240948
Jaric, M., Genić, S., Arandjelović, I., Kolendić, P., Jarić, M., Budimir, N., & Genić, V. (2011). A Review of Explicit Approximations of Colebrook’s Equation. FME Transactions, 39(2), 39–67.
Levenspiel, O. (1998). Engineering Flow and Heat Exchange. In Antimicrobial Agents and Chemotherapy (Vol. 58, Issue 12). Springer US. https://doi.org/10.1007/978-1-4899-0104-0
Nekrasov, B. B. (1969). Hydraulics For Aeronautical Engineers. Peace Publisher.
Robaina, A. D. (1992). Análise De Equações Explicitas Para O Cálculo Do Coeficiente “F” Da Fórmula Universal De Perda De Carga. In Ciência Rural (Vol. 22, Issue 2, pp. 157–159). https://doi.org/10.1590/s0103-84781992000200006
Romeo, E., Royo, C., & Monzón, A. (2002). Improved explicit equations for estimation of the friction factor in rough and smooth pipes. Chemical Engineering Journal, 86(3), 369–374. https://doi.org/10.1016/S1385-8947(01)00254-6
Round, G. F. (1980). An Explicit Approximation for the Friction Factor Reynolds Number Relation for Rough And Smooth Pipes. The Canadian Journal of Chemical Engineering, 58(February), 122–123.
Swamee, P. K., & Jain, A. K. (1976). Explicit Equations For Pipe-Flow Problems. ASCE J Hydraul Div, 102(5), 657–664.
Winning, H. K., & Coole, T. (2013). Explicit friction factor accuracy and computational efficiency for turbulent flow in pipes. Flow, Turbulence and Combustion, 90(1), 1–27. https://doi.org/10.1007/s10494-012-9419-7
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