On the Relationship between Manning’s Roughness Coefficient and Relative Roughness

ORAL

Abstract


Manning’s roughness coefficient n is widely used in hydraulic engineering to estimate flow resistance, yet it lacks direct linkage to measurable physical parameters of flow and roughness geometry. In contrast, the Darcy–Weisbach friction factor f offers a physically grounded description of resistance through its direct link to surface roughness. This study provides a quantitative relationship between n and relative roughness ε/D by reconciling the Manning and Darcy–Weisbach formulations under fully rough, turbulent conditions. Using synthetic flow scenarios generated via numerical modeling, we examine how n systematically varies with ε/D in shallow open-channel flows. Results show that n increases monotonically with relative roughness, following trends consistent with the Moody diagram. This connection enables a more mechanistic interpretation of empirical resistance and provides a practical framework for estimating n from known roughness scales, bridging empirical and theoretical models in wall-bounded turbulent flow.

*¹ Department of Civil and Environmental Engineering, Colorado State University, Fort Collins, CO, USA ² Missouri University of Science and Technology, Rolla, MO, USA3 King Abdulaziz University,Jeddah, Saudi Arabia

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Publication: References
1. Nikuradse, J. (1933). Laws of Flow in Rough Pipes. NACA Technical Memorandum 1292.
2. Darcy, H. (1857). Les fontaines publiques de la ville de Dijon. Dalmont, Paris.
3. Bazin, H. (1865). Expériences nouvelles sur l'écoulement de l'eau. Imprimerie Nationale.
4. Manning, R. (1891). On the flow of water in open channels and pipes. Transactions of the Institution of Civil Engineers of Ireland.
5. Jimenez, J. (2004). Turbulent Flows Over Rough Walls. Annu. Rev. Fluid Mech., 36, 173–196.
6. Moody, L.F. (1944). Friction Factors for Pipe Flow. Transactions of the ASME, 66(8), 671–684.
7. Colebrook, C.F. (1939). Turbulent flow in pipes, with particular reference to the transition region between smooth and rough pipe laws. Journal of the Institution of Civil Engineers, 11(4), 133–156.
8. Townsend, A.A. (1976). The Structure of Turbulent Shear Flow. 2nd Edition. Cambridge University Press.
9. Clauser, F.H. (1954). Turbulent boundary layers in adverse pressure gradients. Journal of the Aeronautical Sciences, 21(2), 91–108.
10. Schultz, M.P. & Flack, K.A. (2007). The rough-wall turbulent boundary layer from the hydraulically smooth to the fully rough regime. Journal of Fluid Mechanics, 580, 381–405.
11. Chan, L., MacDonald, M., Chung, D., Hutchins, N., & Ooi, A. (2015). Direct numerical simulation of a rough-wall turbulent channel flow. Journal of Fluid Mechanics, 771, 743–777.
12. Zhao, J., & Hu, H. (2021). A review on turbulent flow over rough surfaces: Fundamentals and theories. Journal of Hydrodynamics, 33(1), 1–17. https://doi.org/10.1007/s42241-021-0006-5

Presenters

  • Faisal A Alsultan

    • Colorado State University

Authors

  • Faisal A Alsultan

    • Colorado State University

  • Subhas Karan Venayagamoorthy

    • Colorado State University , Missouri University of Science and Technology
    • Colorado State University, Missouri University of Science and Technology