An Improved Form of Hazen-Williams Equation for Pressurized Flow
Received: 16 April 2024 | Revised: 26 April 2024 | Accepted: 29 April 2024 | Online: 29 May 2024
Corresponding author: Wael A. Salah
Abstract
This study performed a sensitivity analysis to correlate the frictional head loss calculated by the Darcy-Weisbach (D-W) and the Hazen-Williams (H-W) formulas. For a broad variety of fluid temperatures, velocities, and pipeline diameters, this study considered an extensive discussion and analysis to determine friction loss within pressurized pipelines using Microsoft Excel. Regression analysis and statistical tools were applied to improve the relationship between the two equations. A more accurate expression was developed to calculate the friction loss in terms of the H-W equation. The estimated values were compared with previous experimental and numerical studies, and a good agreement was observed. The proposed model was evaluated using WaterGEMS software in an application example of a water supply system against the D-W and H-W equations. Good agreements were recorded between predicted values and previous studies, with an error of less than 1%. These findings can be used to improve the hydraulic design of engineering applications.
Keywords:
friction, Darcy-Weisbach, Hazen-Williams, computation, WaterGEMS, application exampleDownloads
References
F. Belloum, L. Houichi, and M. Kherouf, "The Performance of Spectral Clustering Algorithms on Water Distribution Networks: Further Evidence," Engineering, Technology & Applied Science Research, vol. 12, no. 4, pp. 9056–9062, Aug. 2022.
A. A. Kapse, V. C. Shewale, S. D. Barahate, A. B. Kakade, and S. J. Surywanshi, "Experimental Investigation of Heat Transfer and Pressure Drop Performance of a Circular Tube with Coiled Wire Inserts," Engineering, Technology & Applied Science Research, vol. 14, no. 1, pp. 12512–12517, Feb. 2024.
D. J. Wood, "An explicit friction factor relationship," Civil Engineering, vol. 36, no. 12, pp. 60–61, 1966.
C. F. Colebrook, C. M. White, and G. I. Taylor, "Experiments with fluid friction in roughened pipes," Proceedings of the Royal Society of London. Series A - Mathematical and Physical Sciences, vol. 161, no. 906, pp. 367–381, Jan. 1997.
S. W. Churchil, "Friction Factor Equations Spans All Fluid-Flow Regimes," Chemical Engineering Journal, vol. 84, pp. 91–92, 1977.
A. Gupta, N. Bokde, D. Marathe, and K. Kulat, "Leakage Reduction in Water Distribution Systems with Efficient Placement and Control of Pressure Reducing Valves Using Soft Computing Techniques," Engineering, Technology & Applied Science Research, vol. 7, no. 2, pp. 1528–1534, Apr. 2017.
P. K. Swamee and A. K. Jain, "Explicit Equations for Pipe-Flow Problems," Journal of the Hydraulics Division, vol. 102, no. 5, pp. 657–664, May 1976.
B. C. Yen, "Open Channel Flow Resistance," Journal of Hydraulic Engineering, vol. 128, no. 1, pp. 20–39, Jan. 2002.
F. Z. Kamand, "Hydraulic Friction Factors for Pipe Flow," Journal of Irrigation and Drainage Engineering, vol. 114, no. 2, pp. 311–323, May 1988.
R. G. Allen, "Relating the Hazen-Williams and Darcy-Weisbach Friction Loss Equations for Pressurized Irrigation," Applied Engineering in Agriculture, vol. 12, no. 6, pp. 685–693, 1996.
L. F. Moody, "Friction Factors for Pipe Flow," Transactions of the American Society of Mechanical Engineers, vol. 66, no. 8, pp. 671–678, Dec. 2022.
F. A. Bombardelli and M. H. Garcia, "Hydraulic Design of Large-Diameter Pipes," Journal of Hydraulic Engineering, vol. 129, no. 11, pp. 839–846, Nov. 2003.
J. H. Kim, S. H. Kwon, K. S. Yoon, D. H. Lee, and G. Chung, "Hydraulic Experiment for Friction Loss Coefficient in Non-circular Pipe," Procedia Engineering, vol. 154, pp. 773–778, Jan. 2016.
R. Jamil, "Frictional head loss relation between Hazen-Williams and Darcy-Weisbach equations for various water supply pipe materials," International Journal of Water, vol. 13, no. 4, pp. 333–347, Jan. 2019.
L. S. Abdulameer, N. Dzhumagulova, H. Algretawee, L. Zhuravleva, and M. H. Alshammari, "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, vol. 1, no. 1, pp. 36–43, 2022.
K. K. Kuok, P. C. Chiu, and D. C. M. Ting, "Evaluation of ‘C’ Values to Head Loss and Water Pressure Due to Pipe Aging: Case Study of Uni-Central Sarawak," Journal of Water Resource and Protection, vol. 12, no. 12, Dec. 2020, Art. no. 1077.
S. K. Mohsenabadi, "Comparison of Explicit Relations of Darcy Friction Measurement with Colebrook-White Equation," Applied Mathematics in Engineering, Management and Technology, vol. 2, no. 4, pp. 570–578, 2014.
J. D. Valiantzas, "Modified Hazen–Williams and Darcy–Weisbach Equations for Friction and Local Head Losses along Irrigation Laterals," Journal of Irrigation and Drainage Engineering, vol. 131, no. 4, pp. 342–350, Aug. 2005.
A. A. Alazba, M. A. Mattar, M. N. ElNesr, and M. T. Amin, "Field Assessment of Friction Head Loss and Friction Correction Factor Equations," Journal of Irrigation and Drainage Engineering, vol. 138, no. 2, pp. 166–176, Feb. 2012.
T. Ishida, K. Maekawa, and T. Kishi, "Enhanced modeling of moisture equilibrium and transport in cementitious materials under arbitrary temperature and relative humidity history," Cement and Concrete Research, vol. 37, no. 4, pp. 565–578, Apr. 2007.
V. Bagarello, V. Ferro, G. Provenzano, and D. Pumo, "Experimental Study on Flow-Resistance Law for Small-Diameter Plastic Pipes," Journal of Irrigation and Drainage Engineering, vol. 121, no. 5, pp. 313–316, Sep. 1995.
O. Rettore Neto, T. A. Botrel, J. A. Frizzone, and A. P. Camargo, "Method for determining friction head loss along elastic pipes," Irrigation Science, vol. 32, no. 5, pp. 329–339, Sep. 2014.
Y. Lahiouel and R. Lahiouel, "Evaluation of energy losses in pipes," presented at the CFM 2015 - 22ème Congrès Français de Mécanique, Lyon, France, Aug. 2015.
"Hammer Connect Edition Help." Bentley, 2018, [Online]. Available: https://docs.bentley.com/LiveContent/web/Bentley%20HAMMER%20SS6-v1/en/.
"WaterGEMS Connect." Bentley, 2018, [Online]. Available: https://docs.bentley.com/LiveContent/web/Bentley%20WaterGEMS%20SS6-v1/en/81230.html.
F. White and H. Xue, Fluid Mechanics, 9th ed. New York, NY, USA: Mc Graw-Hill, 2020.
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Copyright (c) 2024 Moustafa S. Darweesh, Wael A. Salah, Tarek M. Awwad, Ehab M. Ragab, Anwar A. Ahmed
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