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Volume 3 | Issue 2 | Year 2024 | Article Id: DST-V3I2P101 DOI: https://doi.org/10.59232/DST-V3I2P101
Graphical Application of The Colebrook-White Equation to the Songloulou and Lagdo Dam Penstocks
Tchawe Tchawe Moukam, Tientcheu Nsiewe Maxwell, Djiako Thomas, Nkontchou Ngongang François Legrand, Tcheukam-Toko Dénis, Kenmeugne Bienvenu
| Received | Revised | Accepted | Published |
|---|---|---|---|
| 07 Apr 2024 | 02 May 2024 | 30 May 2024 | 13 Jun 2024 |
Citation
Tchawe Tchawe Moukam, Tientcheu Nsiewe Maxwell, Djiako Thomas, Nkontchou Ngongang François Legrand, Tcheukam-Toko Dénis, Kenmeugne Bienvenu. “Graphical Application of The Colebrook-White Equation to the Songloulou and Lagdo Dam Penstocks.” DS Journal of Digital Science and Technology, vol. 3, no. 2, pp. 1-8, 2024.
Abstract
This work is an implementation of research carried out over the last few years. It is about obtaining the coefficient of head loss (also known as the coefficient of friction) in a straight pipe using a graphical approach. The aim is to estimate it using an approach deemed to be direct and capable of producing more convincing results. Our approach consists of modeling two structures on which we have been working for some time in order to deduce the friction on the walls of their penstocks. It results from this work that, once the input data have been mastered, the graphical approach can be very useful for determining the friction on the walls of a pipe, whatever the fluid in transit.
Keywords
Modeling, Colebrook-White equation, Pressure drop coefficient, Penstock, CFD
References
[1] Jean Leonard Poiseuille, Recherches Expérimentales Sur Le Mouvement Des Liquides Dans Les Tubes De Très Petits Diamètres, Mémoire lu (3e partie, suite), Imprimerie Royale, 1844.
[Google Scholar] [Publisher Link]
[2] H. Blasius, “Das Aehnlichkeitsgesetz bei Reibungsvorgangen in Flüssigkeiten,” Forschungsheft, vol. 131, pp. 1-41, 1913.
[CrossRef] [Google Scholar] [Publisher Link]
[3] T. Blench, Regime Behaviour of Canals and Rivers, Butterworths, London, 1957.
[Google Scholar] [Publisher Link]
[4] Hug, Michel, Mécanique des Fluides Appliquée Aux Problèmes D’aménagement et D’énergétique, Eyrolles, 1975.
[Google Scholar] [Publisher Link]
[5] Julius Weisbach, Lehrbuch der Ingenieur- und Maschinen-Mechanik, F. Vieweg und Sohn, 1850.
[Google Scholar] [Publisher Link]
[6] Darcy, Henry, “Recherches Experimentales Relatives au Mouvement de L'Eau dans les Tuyaux,” Mallet-Bachelier, Paris, vol. 2, pp. 268, 1857.
[Google Scholar] [Publisher Link]
[7] Manning, Robert, “On the Flow of Water in Open Channels and Pipes,” Transactions of the Institution of Civil Engineers of Ireland, vol. 20, pp. 161-207, 1891.
[8] Frederick Charles Scobey, “The Flow of Water in Riveted and Analogous Pipes,” USDA, Washington, vol. 150, 1930.
[Google Scholar] [Publisher Link]
[9] C.F. Colebrook, and C.M. White, “Experiments with Fluid Friction in Roughened Pipes,” Proceedings of the Royal Society A, vol. 161, no. 906, pp. 367-381, 1937.
[CrossRef] [Google Scholar] [Publisher Link]
[10] Prabhata K. Swamee, and Akalank K. Jain, “Explicit Equations for Pipe-Flow Problems,” Journal of the Hydraulics Division, vol. 102, no. 5, pp. 657-664, 1976.
[CrossRef] [Google Scholar] [Publisher Link]
[11] Dejan Brkić, “New Explicit Correlations For Turbulent Flow Friction Factor,” Nuclear Engineering and Design, vol. 241, no. 9, pp. 4055-4059, 2011.
[CrossRef] [Google Scholar] [Publisher Link]
[12] Maiquel López-Silva et al., “Explicit Pipe Friction Factor Equations: Evaluation, Classification, and Proposal,” Faculty of Engineering Magazine, 2024.
[CrossRef] [Google Scholar] [Publisher Link]
[13] S. Lukman, and I. A. Oke, “Accurate Solutions of Colebrook-White’s Friction Factor Formulae,” Nigerian Journal of Technology, vol. 36, no. 4, pp. 1039-1048, 2017.
[CrossRef] [Google Scholar] [Publisher Link]
[14] G. Manadilli, “Replace Implicit Equations with Signomial Functions,” Chemical Engineering Journal, vol. 104, no. 8, pp. 129-130, 1997.
[15] Marco Alfaro-Guerra, Rodrigo Guerra-Rojas, and Alan Olivares-Gallardo, “Experimental Evaluation of Exact Analytical Solution of the Colebrook-White Equation,” Engineering, Research and Technology, vol. 20, pp. 1-11, 2019.
[CrossRef] [Google Scholar] [Publisher Link]
[16] Jim McGovern, “Friction Factor Diagrams for Pipe Flow,” Technical Note, Technological University Dublin, 2011.
[Google Scholar] [Publisher Link]
[17] B.J. McKeon et al., “Friction Factors for Smooth Pipe Flow,” Journal of Fluid Mechanics, vol. 511, pp. 41-44, 2004.
[18] B.J. McKeon, C.J. Swanson, and A.J. Smits, “A New Friction Factor Relationship for Fully Developed Pipe Flow,” Journal of Fluid Mechanics, vol. 538, pp. 429-443, 2005.
[CrossRef] [Google Scholar] [Publisher Link]
[19] Yozo Mikata, and Walter S. Walczak, “Exact Analytical Solutions of the Colebrook-White Equation,” Journal of Hydraulic Engineering, vol. 143, no. 2, 2015.
[CrossRef] [Google Scholar] [Publisher Link]
[20] Viktor Mileikovskyi, and Tetiana Tkachenko, “Precise Explicit Approximations of the Colebrook-White Equation for Engineering Systems,” Lecture Notes in Civil Engineering, vol. 100, pp. 303-310, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[21] Marko Miloševic et al., “Hydraulic Losses in Systems of Conduits with Flow from Laminar to Fully Turbulent: A New Symbolic Regression Formulation,” Axiomes, vol. 11, no. 5, pp. 1-11, 2022.
[CrossRef] [Google Scholar] [Publisher Link]
[22] Renata T. de A. Minhoni et al., “The Performance of Explicit Formulas for Determining the Darcy-Weisbach Friction Factor,” Engenharia Agrícola, vol. 40, no. 2, pp. 258-265, 2020.
[CrossRef] [Google Scholar] [Publisher Link]
[23] Saeed Kazemi Mohsenabadi, Mohammad Reza Biglari, and Mahdi Moharrampour, “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.
[24] Lewis F. Moody, “Friction Factors for Pipe Flow,” Transactions of the ASME, vol. 66, no. 8, pp. 671-684, 1944.
[CrossRef] [Google Scholar] [Publisher Link]
[25] Energy of Cameroon (ENEO) S.A. [Online]. Available: https://eneocameroon.cm/index.php/en/l-entreprise-a-propos-d-eneo-l-entreprise-en/l-entreprise-a-propos-d-eneo-en#:~:text=In%20generation%2C%20Eneo%20has%20an,Eneo%20generation%20is%20from%20hydro
[26] Tchawe Tchawe Moukam et al., “Numerical Study of the Flow Upstream of a Water Intake Hydroelectric Dam in Stationary Regime,” American Journal of Energy Research, vol. 6, no. 2, pp. 35-41, 2018.
[CrossRef] [Google Scholar] [Publisher Link]
[27] L. Levin, “Etude Hydraulique de Huit Revêtements Intérieurs de Conduites Forcées,” La Houille Blanche, vol. 58, no. 4, pp. 263-278, 1972.
[CrossRef] [Google Scholar] [Publisher Link]
[28] L. Levin, “Difficultés du Calcul des pertes de Charge Linéaires dans les Conduites Forcées,” La Houille Blanche, no. 1, pp. 41-54, 1966.
[CrossRef] [Google Scholar] [Publisher Link]
[29] Fluent 6.3, User Guide, 2006. [Online]. Available: https://romeo.univ-reims.fr/documents/fluent/fluentUserGuide.pdf