TECHNICAL NOTE: ANALYTICAL RELATIONSHIP BETWEEN THE STRICKLER ROUGHNESS COEFFICIENT AND THE ABSOLUTE ROUGHNESS IN ROUGH TURBULENT FLOW REGIME

B. ACHOUR, L. AMARA

Abstract


Manning-type relations do not contain the term viscosity, which limits their use to the field of rough turbulent flow. Strickler roughness coefficient k or n of Manning are estimated with great difficulty, requiring a proven practical experience. In order to simplify the problem and allow a rapid calculation of k, the main objective of the present study is to establish an explicit analytical relation which links k and the absolute roughness e. To do this, it was useful to combine the rational Darcy-Weisbach relationship and the empirical Manning-Strickler formula. After some development, the function , where  is the relative roughness, was clearly defined. It was possible to calculate the mean value of the function z in the practical range of such that F is equal to a constant. This constant is different from that proposed by the literature.


Keywords


Darcy-Weisbach, Friction factor, Manning-Strickler, Relative roughness, Rough turbulent flow, Roughness coefficient.

Full Text:

PDF

References


ACHOUR B. (2014). Uniform flow in a rectangular channel, Chapter II, Ed. Al Djazair, 62p., In French. Available at:

https://www.researchgate.net/publication/265413350_Canal_rectangulaire_en_charge_et_a_surface_libre_Chapitre_II

ACHOUR B., AMARA L. (2020a). Manning’s roughness coefficient in a trapezoidal shaped channel, Larhyss Journal, No 44, pp. 89-96.

ACHOUR B., AMARA L. (2020b). Proper relationship of Manning’s coefficient in a partially filled circular pipe, Larhyss Journal, No 42, pp. 107-119.

ACKERS P. (1958). Resistance to Fluids Flowing in Channels and Pipes, Hydraulic Research Paper No 1, H.M.S.O., London.

ACKERS P. (1959). Discussion of "Relationships Between Pipe Resistance Formulas", by Moore, W.L., American Society of Civil Engineers, Journal of Hydraulic Division, Vol. 85, HY7, pp. 155-159.

CHRISTENSEN B.A. (1984). Discussion of “Flow Velocities in Pipelines” by Richard D. Pomeroy, Journal of Hydraulic Engineering, ASCE, Vol. 110, Issue 10, pp. 1510-1512.

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, Vol. 11, pp. 133-156.

COMMITTEE ON CHANNEL STABILIZATION (1985). Arizona Canal Diversion Channel, Selection of Roughness Coefficients for Designing the Concrete-Lined Channel, Corps of Engineers, US Army, Technical Report No 14.

FALVEY H.T. (1987). Friction Resistance in Open and Closed Conduits, Technical Update Lecture, Hydraulic Investigations and Laboratory Services, Official File Copy, U.S. Bureau of Reclamation, Paper 1156.

FREDERIKSEN H.D., De VRIES J.J. (1965). Selection of Methods Used for Computing the Head Loss in the Open Canals of the California Aqueduct, State of California, Department of Water Resources, Technical Memorandum No 18, Oct.

GEORGE J., ARCEMENT J.R., SCHNEIDER V.R. (1989). “Guide for Selecting Manning's Roughness Coefficients for Natural Channels and Flood Plains”, Prepared in cooperation with the U.S. Department of Transportation, Federal Highway Administration, Water-supply paper / United States Geological Survey, Paper 2339.

HAGER W.H. (1985). Abflusseigenschaften in offenen Kanalen, Discharge Characteristics in Open Channels, Schweizer Ingenieur und Architekt, Vol. 13, pp. 52-64, In Germen.

HAGER W.H. (1987) Computation of Turbulent Conduit Flows (In german), 3R international, 26th year, No 2, pp. 116-121.

HAGER W.H. (1989). Discussion of “Noncircular Sewer Design”, by Prabhata K. Swamee, Renu Bargava, and Ashok K. Sharma, Journal of Environmental Engineering, ASCE, Vol. 115, Issue 1, pp. 274-276.

MANNING R. (1891). On the flow of water in open channels and pipes. Transaction of the Institution of Civil Engineers of Ireland, Vol. 20, pp. 161–207.

PROGRESS REPORT OF THE TASK FORCE on Friction Factors in Open Channels of the Committee on Hydromechanics of the Hydraulics Division. (1963). Friction Factors in Open Channels, Journal of Hydraulic Division, American Society of Civil Engineers, ASCE, Vol. 89, HY2, pp. 97-143.

SINNIGER R.O., HAGER W.H. (1989). Constructions hydrauliques, Hydraulic Constructions, Ed. Presses Polytechniques Romandes, Switzerland, In French.


Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.