NORMAL DEPTH COMPUTATION IN A VAULTED RECTANGULAR CHANNEL USING THE ROUGH MODEL METHOD (RMM)

S. SEHTAL, B. ACHOUR

Abstract


Designing and maintaining open channels as well as studying nonuniform flow crucially depend on normal depth. In practical applications, the vaulted rectangular cross-section is widely applied. However, the form of the relationship determining the normal depth is implicit for this type of cross-section. Currently, trial and error procedures, the process of successively improving fitting, and regression-based fitting or the method of fitting curves are used to compute the normal depth for this type of channel. In this research, it is suggested to employ the rough model method (RMM) to estimate the normal depth in a vault-shaped rectangular cross-section. In this approach, knowing the Chezy or Manning coefficient will not be required in the process computation of normal depth in this conduit. However, it only needs measurable parameters, in particular, the impact of the absolute roughness. Based on well-known referential rough model properties, the RMM evaluates the normal depth using a dimensionless correction factor. The relationship that governs flow in the rough model allows for an explicit calculation of the normal depth in this kind of conduit. Calculation examples are given to illustrate how easy the calculation process is.


Keywords


Vaulted rectangular cross-section, Discharge, Normal depth, Manning's roughness coefficient, Rough model method, Uniform flow.

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References


ACHOUR, B. (2014a). Pressurized and free surface flow rectangular channel, Chapter II, Application courses and exercises. Editions Al Djazair, 65p. (In French)

ACHOUR B. (2014b). Computation of normal depth in horseshoe shaped tunnel using the rough model method, Advanced Materials Research, Vols. 1006–1007, pp. 826-832.

ACHOUR B. (2015). Computation of Normal Depth in a U-Shaped Open Channel Using the Rough Model Method, American Journal of Engineering, Technology and Society, Vol. 2, No 3, pp. 46–51.

ACHOUR B., BEDJAOUI A. (2006). Discussion to “Exact solution for normal depth problem, by SWAMME P.K. and RATHIE P.N.”, Journal of Hydraulic Research, Vol. 44, No 5, pp. 715-717.

ACHOUR B., BEDJAOUI A. (2012). Turbulent Pipe-flow Computation Using the Rough Model Method (RMM), Journal of Civil Engineering and Science, Vol. 1, No 1, pp. 36-41.

ACHOUR B., KHATTAOUI M. (2008). Computation of Normal Depth in Parabolic Cross Sections Using The Rough Model Method, Open Civil Engineering Journal, Vol. 2, pp. 9 -14.

ACHOUR B., SEHTAL S. (2014). The Rough Model Method (RMM) Application to The Computation of Normal Depth in Circular Conduit, Open Civil Engineering Journal, Vol. 8, No 1, pp. 57- 63.

CHOW V.T. (1959). Open Channel Hydraulics, McGraw-Hill, New York, USA, 680 p.

COLEBROOK C.F. (1939). Turbulent Flow in Pipes with Particular Reference to the Transition Region Between the Smooth and Rough Pipe Laws, Journal of the Institution of Civil Engineers, Vol. 11, pp. 133-156.

LAKEHAL M., ACHOUR B. (2017). New approach for the normal depth computation in a trapezoidal open channel using the rough model method, Larhyss Journal, No 32, pp. 269-284.

LIU J., WANG, Z. (2013). Equations for critical and normal depths of city-gate sections, Proceedings of the Institution of Civil Engineers: Water Management, Vol. 166, pp. 199-206.

LIU J., WANG Z., FANG X. (2010). Iterative Formulas and Estimation Formulas for Computing Normal Depth of Horseshoe Cross-Section Tunnel, Journal of Irrigation and Drainage Engineering, Vol. 136 , No 11, pp. 786-790.

RIABI M., ACHOUR B. (2019). Design of pressurized pipe-weir using the rough model method (RMM), Larhyss Journal, No 39, pp. 349-363.

SHANG H., XU S., ZHANG K. (2020). Improvements to solutions for normal depth in multiple sections of tunnels, Flow Measurement and Instrumentation, Vol.73, Paper 101723.

SWAMEE P.K. (1994). Normal Depth Equations for Irrigation Canals, Journal of Irrigation and Drainage Engineering, Vol. 120, No 5, pp. 942-948.

SWAMEE P.K., RATHIE P.N. (2004). Exact Solutions for Normal Depth Problem, Journal of Hydraulic Research, Vol. 42, No 5, pp. 543-550.

VATANKHAH A.R. (2012). Direct solutions for normal and critical depths in standard city-gate sections, Flow Measurement and Instrumentation, Vol. 28, pp. 16-21.

VATANKHAH A.R., EASA S.M. (2011). Explicit solutions for critical and normal depths in channels with different shapes, Flow Measurement and Instrumentation, Vol. 22, No 1, pp. 43-49.


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