# Estimation Methodology of Pressure Losses in Non-circular Pipes

Document Type : Regular Article

Author

University of Warmia and Mazury in Olsztyn, Olsztyn, 10-900, Poland

10.47176/jafm.17.7.2518

Abstract

The article presents a methodology for determining the hydraulic resistance multiplier, used for a rapid estimation of linear losses in pipes with non-circular cross-sections. The numerical approach was applied using the Finite Volume Method and the ANSYS Fluent software. The research was conducted under turbulent flow conditions, covering two Reynolds number ranges: 10,000 to 100,000 (10 cases) and 100,000 to 1,000,000 (5 cases). The first section of the article presents calculations of losses for a circular pipe, accompanied by a mesh test and error estimation. The second section includes calculations conducted for a series of pipes with various selected cross-sectional shapes: half-circle, quarter-circle, square, rectangles with aspect ratios of 2:1 and 3:1, isosceles triangle, and equilateral triangle. The last section of the article discusses the calculation of linear losses and the hydraulic resistance multiplier for each tested shape. It was found that this coefficient ranged from 1.33 to 2.2, depending on the shape, with the influence of the Reynolds number being relatively insignificant.

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#### References

Abbas, A. S., & Mohammed, A. A. (2022). Augmentation of plate-fin heat exchanger performance with support of various types of fin configurations. Mathematical Modelling of Engineering Problems, 9(5), 1406-1414. https://doi.org/10.18280/mmep.090532
Abdi, H., Asaadi, S., Kivi, H. A., & Pesteei, S. M. (2019). A comprehensive numerical study on nanofluid flow and heat transfer of helical, spiral and straight tubes with different cross sections. International Journal of Heat and Technology, 37(4), 1031-1042. https://doi.org/10.18280/ijht.370412
ANSYS inc. (2022a) Ansys Fluent Theory Guide, Release 2022R1, January 2022.
ANSYS inc. (2022b) Ansys Fluent User’s Guide, Release 2022R1, January 2022.
Ayas, M., Skocilas, J., & Jirout, T. (2021). Friction factor of shear thinning fluids in non-circular ducts – a simplified approach for rapid engineering calculation, Chemical Engineering Communications, 208(8), 1209-1217. https://doi.org/10.1080/00986445.2020.1770232
Blasius, P. R. H. (1913). Das aehnlichkeitsgesetz bei reibungsvorgangen in flüssigkeiten (in German). Forschungsheft 131, 1-41.
BrkiÄ‡, D. (2011). Review of explicit approximations to the Colebrook relation for flow friction. Journal of Petroleum Science and Engineering, 77(1), 34-48. http://dx.doi.org/10.1016/j.petrol.2011.02.006
Brown, G. G. (2002, November 3-7). The history of the darcy-weisbach equation for pipe flow resistance. Environmental and Water Resources History Sessions at ASCE Civil Engineering Conference and Exposition, Washington, D. C., United States. http://dx.doi.org/10.1061/40650(2003)4
Cengel, Y. A., & Cimbala, J. M. (2018). Fluid Mechanics – Fundamentals and applications. 3rd ed. McGraw-Hill, New York.
Colebrook, C. F., & White, C. M. (1937). Experiments with Fluid Friction Factor in Roughened Pipes. Proceedings of the Royal Society of London. Series A: Mathematical and Physical Sciences, 161, 367-381. http://dx.doi.org/10.1098/rspa.1937.0150
Frate, L., Moretti, F., Galassi, G., & D’Auria, F. (2016). Limitations in the use of the equivalent diameter. World Journal of Nuclear Science and Technology, 6, 53-62. http://dx.doi.org/10.4236/wjnst.2016.61005
He, S., & Gotts, J. A. (2004). Calculation of friction coefficients for noncircular channels. Journal of Fluids Engineering, 126, 1033-1038. https://doi.org/10.1115/1.1845479
Khairunnisa, N., Arifin, Z., Kristiawan, B., Hijriawan, M., & Prasetyo, S. D. (2022). Investigation of spirals rectangular and rectangular tubes collector design in photovoltaic solar cell cooling systems. International Journal of Heat and Technology, 40(6), 1359-1365. https://doi.org/10.18280/ijht.400602
Miller, D. S. (1996). Internal flow systems, 2nd ed., BHR Group Limited, Bedfordshire, UK.
Moody, L. F. (1944). Friction factors for pipe flow. Transactions of the ASME, 66(8), 671-684.
Minhoni, R., Pereira, F., Silva, T., Castro, E., & Saad, J. )2020(. The performance of explicit formulas for determining the Darcy-Weisbach friction factor. Engenharia Agrícola, 40(2), 258-265. https://doi.org/10.1590/1809-4430-eng.agric.v40n2p258-265/2020
Muzychka, Y., & Yovanovich, M. (2009). Pressure drop in laminar developing flow in noncircular ducts: A scaling and modeling approach. Journal of Fluids Engineering, 131(11), 111105. https://doi.org/10.1115/1.4000377
Nikuradse, J. (1933). Strömungsgesetze in rauen rohren. Forschungsheft, Berlin.
Sobieski, W. (2011). The basic equations of fluid mechanics in form characteristic of the finite volume method. Technical Sciences, 14(2), 299-313.
Sobieski, W. (2013). The basic closures of fluid mechanics in form characteristic for the Finite Volume Method. Technical Sciences, 16(2), 93-107.
Štigler, J. (2014). Analytical velocity profile in tube for laminar and turbulent flow. Engineering Mechanics, 21(6), 371-379. https://doi.org/10.3390/fluids6100369
Weisbach, J. (1845). Lehrbuch der Ingenieur- und Maschinen-Mechanik, Theoretische Mechanik, Vieweg und Sohn, Braunschweig.