Fitting Hazen-Williams Roughness Coefficient to the Head Loss Obtained by Darcy-Weisbach Equation in PVC Pipes

Document Type : Original Article

Authors

1 Professor, College of Civil Engineering, Estácio University of Juiz de Fora, MG, Brazil

2 Undergraduate Researcher, College of Civil Engineering, Estácio University of Juiz de Fora, MG, Brazil

3 Professor, Engineering Faculty, Federal University of Juiz de Fora, MG, Brazil

10.30469/arce.2022.150292

Abstract

There are still today discussions about what formula shall be used to calculate head loss in water pipelines. Especially in academic circles, the Darcy-Weisbach (DW) equation is highly recommended, with a series of articles and scientific evidence on the subject. In the context of water supply companies, the Hazen-Williams (HW) equation gains a lot of strength, possibly even because, within the speed ranges that the systems operate, it can provide acceptable results. Thus, the present research provides a series of curves to adjust the HW roughness coefficients C, in order to make the obtained head loss results to be very similar to those derived from the DW equation. For the diameters of 50, 75, 100, 150, and 200 mm, spreadsheets were prepared, which indicated which value of C was generated for each flow rate, whose variation ranged from 0.05 to 287.00 L/s. It was verified in the spreadsheets, for each same value ​​of C, which were the combinations of flow and diameter ​​that produced it, and the same procedure was repeated for all C. Thus, each curve of C could be plotted. In order to assess the accuracy of the fit curves, points generated by the combination of flow and diameter outside the Hazen-Williams region of application were taken. Such points were plotted in the curves to obtain the adjusted C. This procedure made the results of HW much closer to those of DW, which when such a comparison was made using the values ​​of C from the literature.

Keywords


[1]- Azevedo Netto, J. M., Fernandez, M. F., Araujo, R., Ito, A. E., 1998, Hydraulics manual, Blucher, 669, (in Portuguese).
[2]- Brown, G. O., 2002, The history of the Darcy-Weisbach equation for pipe flow resistance. In Proceedings of the Environmental and Water Resources History Sessions at ASCE Civil Engineering Conference and Exposition, Washington. https://doi.org/10.1061/40650(2003)4.
[3]- Heurich, G., Pizzo, H. S., Fernandes, V. M. C., and Deboni, R., 2005, Analysis of the errors obtained by comparing the universal and Hazen-Williams formulas in the calculation of head loss. In Proceedings of Brazilian Symposium on Water Resources, João Pessoa, (in Portuguese).
[4]- Lamont, P. A., 1981, Common pipe flow formulas compared with the theory of roughness. Journal of American Water Works Association: Research and Technology, 73(5), 274–280. https://doi.org/10.1002/j.1551-8833.1981.tb04704.x.
[5]- Assy, T. M., 1977, The use of the universal head loss formula and the limitations of empirical formulas, CETESB, (in Portuguese).
[6]- Sharp, W. W., and Walski, T. M., 1988, Predicting internal roughness in water mains, Journal of American Water Works Association: Management and Operation, 80(11), 34–40. https://doi.org/10.1002/j.1551-8833.1988.tb03132.x.
[7]- Diskin, M. H., 1960, The limits of applicability of the Hazen-Williams formula, La Houille Blanche, 46(6), 720–726. https://doi.org/10.1051/lhb/1960059.
[8]- Rocha, H. S., Marques, P. A. A., Camargo, A. P., Frizzone, J. A., and Saretta, E., 2017, Internal surface roughness of plastic pipes for irrigation, Revista Brasileira de Engenharia Agrícola e Ambiental, 21(3), 143–149. http://dx.doi.org/10.1590/1807-1929/agriambi.v21n3p143-149.
[9]- 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).
[10]- Swamee, P. K., 2000, Limitations and proper use of the Hazen-Williams equation – Discussion, Journal of Hydraulic Engineering, 126(2), 169–170. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:2(167).
[11]- Christensen, B. A., 2000, Limitations and proper use of the Hazen-Williams equation – Discussion, Journal of Hydraulic Engineering, 126(2), 167–168. https://doi.org/10.1061/(ASCE)0733-9429(2000)126:2(167).
[12]- Mohan, D. M., 1986, Modified Hazen-Williams formula, Ph.D. thesis, Indian Institute of Technology, Mumbai.
[13]- Pallepati, R. R., 2014, On estimation of friction loss in pipes using Hazen-Williams and Modified Hazen-Williams formulae, Journal of Indian Water Works Association, July–Sept., 107–108.
[14]- Associação Brasileira de Normas Técnicas, 2017, NBR 12215-1: Project guidelines for water mains, 21, (in Portuguese).
[15]- Associação Brasileira de Normas Técnicas, 2017, NBR 12218: Project of water distribution network for public supply – Procedure, 29, (in Portuguese).
[16]- Bombardelli, F. A., and García, M. H., 2003, Hydraulic design of large-diameter pipes, Journal of Hydraulic Engineering, 129(11), 839–846. https://doi.org/10.1061/(ASCE)0733-9429(2003)129:11(839)
[17]- Allen, R. G., 1996, Relating the Hazen-Williams and Darcy-Weisbach friction loss equations for pressurized irrigation, Applied Engineering in Agriculture, 12(6), 685–693, https://doi.org/10.13031/2013.25699.
[18]- Alazba, A. A., Mattar M. A.; ElNesr M. N; and Amin M. T., 2012, Field assessment of friction head loss and friction correction factor equations, Journal of Irrigation and Drainage Engineering, 138(2), 166–176. https://doi.org/10.1061/(ASCE)IR.1943-4774.0000387.
[19]- Achour, B., and Amara, L., 2020, Theoretical considerations on flow regime dependency of the Hazen-Williams coefficient, Larhyss Journal, 42, 53–62.
[20]- Taş, E., Ağıralioğlu, N., Danandeh Mehr, A., and Tür, R., 2019, A brief review of experimental friction loss studies for polyetylene pipes. In Proceedings of International Scientific Conference on Production Engineering: Development and modernization of production, 12, 256–261, Sarajevo.
[21]-  Seifollahi-Aghmiuni, S., Haddad, O. B., Omid, M. H, and Mariño, M. A., 2013, Effects of pipe roughness uncertainty on water distribution network performance during its operational period, Water Resources Management, 27, 1581–1599. https://doi.org/10.1007/s11269-013-0259-6.
[22]- Sampaio, S. C., Cilene, K., Vilas Boas, M. A., Queiroz, M. M. F., Gomes, B. M., and Fazolo, A., 2007, Hazen-Williams equation corrected for swine wastewater, Revista Brasileira de Engenharia Agrícola e Ambiental, 11(1), 5–10, (in Portuguese). 
[23]- Alazba, A. A., and ElNesr, M. B., 2011, Simple iterative model for adjusting Hazen-Williams friction coefficient for drip irrigation laterals, Australian Journal of Basic and Applied Sciences, 5(12), 1079–1088.
[24]- Jamil, R., and Mujeebu, M. A., 2019, Empirical relation between Hazen-Williams and Darcy-Weisbach equations for cold and hot water flow in plastic pipes, Water, 10, 104–114. http://dx.doi.org/10.14294/WATER.2019.1.
[25]- Niazkar, M., Talebbeydokhti, N., and Afzali, S. H., 2017, Relationship between Hazen-William coefficient and Colebrook-White friction factor: Application in water network analysis, European Water, 58, 513–520.
[26]- Valiantzas, J. D, Explicit power formula for the Darcy–Weisbach pipe flow equation: Application in optimal pipeline design, Journal of Irrigation and Drainage Engineering, 134(4), 454–461. https://doi.org/10.1061/(ASCE)0733-9437(2008)134:4(454).
[27]- Travis, Q. B., and Mays, L. W., 2007, Relationship between Hazen–William and Colebrook–White roughness values, Journal of Hydraulic Engineering, 133(11), 1270–1273, https://doi.org/10.1061/(ASCE)0733-9429(2007)133:11(1270)
[28]- Uribe, J., Saldarriaga, J., and Páez, D., 2015, Effects of the use of Hazen-Williams equation on large WDS’s planning models. In Proceedings of World Environmental and Water Resources Congress, 881–889, Austin. https://doi.org/10.1061/9780784479162.083.
[29]- Genić, S., and Jaćimović, B., 2019, Reconsideration of the friction factor data and equations for smooth, rough and transition pipe flow. In Proceedings of ITM Web of Conferences (ICCMAE 2018), 29, 1–20. https://doi.org/10.1051/itmconf/20192902001.
[30]- Taş, E., Ağıralioğlu, N., Danandeh Mehr, A., and Tür, R., 2020, Energy loss investigation in submarine pipelines: Case study of Cyprus water supply project, Advance Researches in Civil Engineering, 2(2), 31–44. https://dx.doi.org/10.30469/arce.2020.108582.
[31]- E. Tourasse, E., 1986, Explicit equation for coefficient of friction and duct calculation, Engenharia Sanitária, 25(2), pp. 177–178, (in Portuguese).