Evaluación de ecuaciones para pérdidas de carga por fricción en tuberías de polietileno

Freddy Gavilánez-Luna; Jesús Chavarría

doi:10.24850/j-tyca-2026-06-05

Authors

Freddy Gavilánez-Luna Pontificia Universidad Católica del Ecuador-Sede Manabí, Manabí, Ecuador. Universidad Agraria del Ecuador, Guayaquil, Ecuador https://orcid.org/0000-0002-7861-514X
Jesús Chavarría Pontificia Universidad Católica del Ecuador-Sede Manabí, Manabí, Ecuador https://orcid.org/0000-0001-8868-394X

DOI:

https://doi.org/10.24850/j-tyca-2026-06-05

Keywords:

hydraulic equipment, hydrodynamics, plastics, equations, statistical analysis, measurement

Abstract

This study addressed the need to identify the most accurate formula for calculating friction head losses in pressurized systems with smooth pipes, evaluating the fit of expressions against experimental data. A test bench was implemented with polyethylene pipes of 25, 32, 40 and 50 mm diameter and 50 m length. Piezometric loads of 10, 15, 20, 25 and 30 m were applied, measured with a digital manometer. The observed load losses were corrected for the unevenness of the terrain by topographic leveling. Eleven equations selected from the literature were evaluated, including Darcy-Weisbach with Colebrook-White. An absolute roughness of 0.0015 mm and a roughness coefficient of 150 for Hazen–Williams were used, in addition to a kinematic viscosity of 1.049 x 10^-6 m²/s. The relative error (RE), the Willmott concordance index (WCI) and the root mean square error (RMSE) of each expression were calculated. Likewise, analysis of variance was applied using Fisher's LSD test to determine significant differences. Experimental head losses were reported between 1.747 and 5.896 m, with flow rates between 2.93 x 10^-4 and 3.525 x 10^-3 m³/s, with turbulent flow in all cases. All expressions reported an WCI > 0.97 and RMSE < 0.4 m; however, the Shaikh-Massan-Wagan formula obtained the lowest average RE (3.77 %), significantly (p < 0.05) different from the rest, standing out as the most accurate and precise for calculating pressure losses in smooth pipes such as those made of polyethylene.

References

Abdulameer, L. S., Dzhumagulova, N., Algretawee, H., Zhuravleva, L., & Alshammari, M.H. (2022). Comparison between Hazen-Williams and Darcy-Weisbach equations to calculate head loss through conveyancing treated wastewater in Kerbala City, Iraq. Eastern-European Journal of Enterprise Technologies, 1(115), 36-43. https://doi.org/10.15587/1729-4061.2022.251385

Achour, B., & Amara, L. (2020). Theoretical considerations on flow regime dependency of the Hazen-Williams coefficient. Larhyss Journal, (42), 53-62. https://www.larhyss.net/ojs/index.php/larhyss/article/view/727

Alambra, K. (2024, agosto 27). Calculadora de la viscosidad del agua. Omni Calculator. https://n9.cl/m9zwq

Alegret-Breña, E., & Martínez-Valdés, Y. (2019). Coeficiente de Hazen-Williams en función del número de Reynolds y la rugosidad relativa. Ingeniería Hidráulica y Ambiental, 40(3), 41-55. https://www.researchgate.net/publication/343573793_Hazen-Williams_coefficient_as_a_function_of_Reynolds_number_and_relative_roughness

Alfaro-Guerra, M., Guerra-Rojas, R. & Olivares-Gallardo, A. (2019). Evaluación experimental de la solución analítica exacta de la ecuación de Colebrook-White. Ingeniería Investigación y Tecnología, 20(2), 1-11. https://doi.org/10.22201/fi.25940732e.2019.20n2.021

Anaya-Durand, A., Cauich-Segovia, G., Funabazama-Bárcenas, O., & Gracia-Medrano-Bravo, V. (2014). Evaluación de ecuaciones de factor de fricción explícito para tuberías. Educación Química, 25(2), 128-134. https://doi.org/10.1016/S0187-893X(14)70535-X

Arumugam, A., Kibrom, H., Gebreamlak, M., Teame, M., & Mengstu, M. (2022). Comparative analysis and validation of selected explicit equation models for determination of Darcy friction factor to estimate major head loss for a pressurized flow system. Science & Technology Asia, 27(3), 216-235. https://ph02.tci-thaijo.org/index.php/SciTechAsia/article/view/241771

Barr, D., & White, C. (1981). Solutions of the Colebrook-White function for resistance to uniform turbulent flow. Proceedings of the Institution of Civil Engineers, 71(2), 529-535. https://doi.org/10.1680/iicep.1981.1895

Beltrán, L. (2021). Validación de las ecuaciones del factor de fricción en tuberías a presión [Tesis de grado, Universidad Católica de Colombia]. RIUCaC. https://hdl.handle.net/10983/26576

Brkić, D. (2011). Review of explicit approximations to the Colebrook relation for flow friction. Journal of Petroleum Science and Engineering, 77(1), 34-48. https://doi.org/10.1016/j.petrol.2011.02.006

Çengel, Y. A., & Cimbala, J. M. (2014). Fluid mechanics: Fundamentals and applications (3rd ed.). McGraw-Hill.

Colebrook, C. F., & White, C. M. (1937). Experiments with fluid friction in roughened pipes. Proceedings of the royal society A, 161(906), 367-381. https://doi.org/10.1098/rspa.1937.0150

Da Rocha, H. S., Marques, P. A., de Camargo, A. P., Frizzone, J. A., & Saretta, E. (2017). Internal surface roughness of plastic pipes for irrigation. Revista Brasileira de Engenharia Agrícola e Ambiental, 21(3), 143-149. https://doi.org/10.1590/1807-1929/agriambi.v21n3p143-149

Darweesh, M. S., Salah, W. A., Awwad, T. A., Ragad, E. M., & Ahmed, A. A. (2024). An improved form of Hazen-Williams equation for pressurized flow. Engineering, Technology & Applied Science Research, 14(3), 14640-14644. https://doi.org/10.48084/etasr.7511

Falkovich, G. (2011). Fluid Mechanics: A Short Course for Physicists. Cambridge University Press. https://doi.org/10.1017/CBO9780511794353

Gavilánez-Luna, F. (2019). Incidencia de la presión sobre el coeficiente de rugosidad C de Hazen-Williams. Tecnología y ciencias del agua, 10(5), 214-225. https://doi.org/10.24850/j-tyca-2019-05-08

Guerrero, J. (1995). Ecuación modificada de Colebrook-White. Ingeniería hidráulica en México, 10(1), 43-48.

Gutiérrez, H., & De-la-Vara, R. (2008). Análisis y diseño de experimentos (2ª ed.). McGraw-Hill Interamericana, S. A.

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

Jamil, R. (2020). Frictional head loss relation between Hazen-Williams and Darcy-Weisbach equations for various water supply pipe materials. International Journal of Water, 13(4), 333-347. https://doi.org/10.1504/IJW.2019.106047

Kaseng, F., Bayona, R., & Rodríguez, C. (2020). Alternate formula for calculating the Darcy coefficient in turbulent flow in pipes. 3C Tecnología. Glosas de Innovación Aplicadas a la Pyme, 9(3), 99-109. https://doi.org/10.17993/3ctecno/2020.v9n3e35.99-109

Liou, C. P. (1998). Limitations and proper use of the Hazen-Williams equation. Journal of Hydraulic Engineering, 124(9), 951-954. https://doi.org/10.1061/(ASCE)0733-9429(1998)124:9(951)

Monís, J. (2020). Historia, análisis y expresión gráfica de las fórmulas de pérdidas de carga utilizadas en la ingeniería hidráulica [tesis doctoral, Universidad de Córdoba]. Helvia: Repositorio Institucional de la Universidad de Córdoba. http://hdl.handle.net/10396/20203

Moody, L. F. (1944). Friction factors for pipe flow. Transactions of the American Society of Mechanical Engineers, 66(8), 671-678. https://doi.org/10.1115/1.4018140

Mott, R. (2006). Mecánica de fluidos (6ª ed.). Pearson Educación.

Munson, B. R., Okiishi, T. H., Huebsch, W. W., & Rothmayer, A. P. (2013). Fundamentals of fluid mechanics (7th ed.). John Wiley & Sons.

Narváez, P. (2000). Ecuaciones de flujo para líquidos: desarrollo histórico y características fundamentales. Revista Ingeniería e Investigación, (45), 33-38. https://doi.org/10.15446/ing.investig.n45.21313

Offor, U., & Alabi, S. (2016). An accurate and computationally efficient explicit friction factor model. Advances in Chemical Engineering and Science, 6(3), 237-245. https://doi.org/10.4236/aces.2016.63024

Ormsbee, L., & Walski, T. (2016). Darcy-Weisbach versus Hazen-Williams: No calm in West Palm. In: World Environmental and Water Resources Congress 2016 (pp. 455-464). https://doi.org/10.1061/9780784479865.048

Pérez-Pupo, J., Navarro-Ojeda, M., Pérez-Guerrero, J., & Batista-Zaldívar, M. (2020). On the explicit expressions for the determination of the friction factor in turbulent regime. Revista Mexicana de Ingeniería Química, 19(1), 313-334. https://doi.org/10.24275/rmiq/Fen497

Pimenta, B. D., Robaina, A. D., Peiter, M. X., Mezzomo, W., Kirchner, J. H., & Ben, L. H. (2018). Performance of explicit approximations of the coefficient of head loss for pressurized conduits. Revista Brasileira de Engenharia Agrícola e Ambiental, 22(5), 301-307. https://doi.org/10.1590/1807-1929/agriambi.v22n5p301-307

Revilla, J. (1991). Factores de pérdidas por cortante para flujo de agua en tuberías. Ingeniería hidráulica en México, 6(3), 9-17.

Round, G. F. (1980). An explicit approximation for the friction factor in turbulent pipe flow. The Canadian Journal of Chemical Engineering, 58(1), 122-123. https://doi.org/10.1002/cjce.5450580119

Saldarriaga, J. (2007). Hidráulica de tuberías. Alfaomega Bogotá.

Shaikh, M., Massan, S., & Wagan, A. (2015). A new explicit approximation to Colebrook’s friction factor in rough pipes under highly turbulent cases. International Journal of Heat and Mass Transfer, 88, 538-543. https://doi.org/10.1016/j.ijheatmasstransfer.2015.05.006

Sotelo, G. (1980). Hidráulica general. Editorial Limusa, S. A.

Streeter, V. L., Wylie, E. B., & Bedford, K. W. (1998). Fluid mechanics (9th ed.). McGraw-Hill.

Swamee, P. K., & Jain, A. K. (1976). Explicit equations for pipe-flow problems. Journal of the Hydraulics Division, 102(5), 657-664. https://doi.org/10.1061/JYCEAJ.0004542

Tarjuelo, J. (1999). El riego por aspersión y su tecnología (2ª ed.). Ediciones Mundi-Prensa.

Tolentino, S. L., & González, O. (2023). Correlación para el cálculo de la fricción turbulenta en tuberías. Ingenius, Revista de Ciencia y Tecnología, (30), 54-63. https://doi.org/10.17163/ings.n30.2023.05

White, F. M. (2011). Fluid mechanics (7th ed.). McGraw-Hill.

Willmott, C. J. (1981). On the validation of models. Physical Geography, 2(2), 184-194. https://doi.org/10.1080/02723646.1981.10642213

Zhao, Z., & Gao, J. (2020). Robustness of water hammer protection of different formulas of frictional head loss. Desalination and Water Treatment, 187, 172-177. https://doi.org/10.5004/dwt.2020.25314