EXACT SOLUTION FOR NORMAL DEPTH COMPUTATION IN SOME OPTIMAL CHANNEL CROSS-SECTIONS

I. RAMDANI, F. SEKIOU, M. LAKEHAL, B. ACHOUR

Abstract


The normal depth is an important hydraulic element in the design, operation and maintenance of canals. The calculation of this normal depth is based on Manning's formula, which has long been considered applicable only in the rough turbulent domain, and Manning's coefficient is considered in several works as a constant of the problem. The objective of this study is to express the normal depth in different semipolygonal canals as the optimal cross-section (semicircular, rectangular, triangular and trapezoidal), taking into account the variation in Manning's coefficient as a function of all the parameters governing the uniform flow, including the viscosity of the liquid. The study led, through the application of the rough model method (RMM), to a dimensionless expression of Manning's coefficient, written as a function of the characteristics of the rough model, allowing the construction, for each chosen cross-section, of a diagram similar to Moody's. The diagrams give Manning's coefficient in the whole turbulent domain (smooth, transition and rough), which is considered a generalization of Manning's formula in the whole turbulent domain instead of only the rough domain. The exact solution of normal depth by using the equation of Manning’s coefficient has therefore been proposed.


Keywords


Normal depth, Manning’s resistance coefficient, Optimal cross section, Rough model method (RMM), Semipolygonal channels

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References


ABDULRAHMAN A. (2007). The best hydraulic section of a composite channel, Journal of Hydraulic Engineering, Vol. 133, Issue 6, pp. 695–697.

ACHOUR B. (2007). Calculation of pipes and channels by RMM: pipes and channels in charge, Larhyss Capital Edition, Biskra, Algeria, 610 p. (In French).

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

ACHOUR B., BEDJAOUI A. (2006). Discussion of “Exact solutions for normal depth problem” by SWAMEE P.K., RATHIE P.N, Journal of Hydraulic Research, Vol. 44, Issue 5, pp. 715-717.

AKGIRAY Ö. (2005). Explicit solution of the Manning’s equation for partially filled circular pipes, Canadian Journal of Civil Engineering, Vol. 32, Issue 3, pp. 490–499.

AZAMATHULLA H.M., AHMED Z., AB GHANI A. (2013). An expert system for predicting Manning’s roughness coefficient in open channels by using gene expression programming, Neural Computing & Applications, Vol. 23, Issue 5, pp. 1343–1349.

BABAEYAN-KOOPAEL K. (2001). Dimensionless curves for normal-depth calculations in canal sections, Journal of Irrigation and Drainage Engineering, Vol. 127, Issue 6, pp. 386–389.

BARR D.I.H., DAS M.M. (1986). Direct solutions for normal depth using the Manning equation, Water Engineering Group, Vol. 81, Issue 3, pp. 315–333.

CHOW V.T. (1959). Open channel hydraulics, Mc Graw-Hill, New York, USA

DAI S., YANG J., MA Y., JIN S. (2020). Explicit formulas of normal, alternate and conjugate depths for three kinds of parabola-shaped channels, Flow Measurement and Instrumentation, Vol. 74, Issue 4, Paper 101753.

ELHAKEEM M. (2017). Explicit solution for flow depth in open channels of trapezoidal cross-sectional area: classic problem of interest, Journal of Irrigation and Drainage Engineering. Vol. 143, Issue 7, pp. 1-11.

FROEHLICH D.C. (2008). Most hydraulically efficient standard lined canal sections, Journal of Irrigation and Drainage Engineering, Vol. 134, Issue 4, pp. 462–470.

GARCÍA-DÍAZ R. (2005). Analysis of Manning coefficient for small-depth flows on vegetated beds, Hydrological Processes, Vol. 19, Issue 16, pp. 3221–3233.

HAGER W.H. (1989). Discussion of ''Non circular sewer design'' by SWAMEE P.K., BHARGAVA W.H.R., SHARMA A.K, Journal of Environmental Engineering, Vol. 115, Issue 1, pp. 274–276.

HAN Y.C., EASA S.M. (2016). Superior cubic channel section and analytical solution of best hydraulic properties, Flow Measurement and Instrumentation, Vol.50, Issue 4, pp. 169- 177.

LAKEHAL M., ACHOUR B. (2014). Computation of normal depth in an egg-shaped conduit using the rough model method, Larhyss Journal, No 19, pp. 101–113. (In French)

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., 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, Issue 11, pp. 786–790.

LI Y., GAO Z. (2014). Explicit solution for normal depth of parabolic section of open channels, Flow Measurement and Instrumentation, Vol. 38, Issue 4, pp. 36–39.

LOUKAM I., ACHOUR B., DJEDDOU M. (2019). Manning’s resistance coefficient in an egg-shaped conduit, The First International Conference on Water and Climate, University of Annaba, Algeria.

RAIKAR R.V., SHIVA-REDDYM M.S., VISHWANADH G.K. (2010). Normal and critical depth computatios for egg-shaped conduit section, Flow Measurement and Instrumentation, Vol. 21, Issue 3, pp. 367–372.

SWAMEE P.K. (1994). Normal-depth equation for irrigation canals, Journal of Irrigation and Drainage Engineering, Vol. 120, Issue 5, pp. 942–948.

SWAMEE P.K., CHAHAR B.R. (2015). Design of channels, Springer, India.

VATANKHAH A.R. (2014). Semiregular polygon as the best hydraulic section in practice (generalized solutions), Flow Measurement and Instrumentation, Vol. 38, Issue 4, pp. 67–71.

YEN B.C. (1992). Dimensionally Homogeneus Manning’s formula, Journal of Hydraulic Engineering, Vol. 118, Issue 9, pp. 1326–1332.

ZEGAIT R., ACHOUR B. (2016). Flow study with variable coefficient of resistance, new evaluation method for Manning's coefficient in horseshoe pipes, Journal of Advanced Research in Science and Technology, Vol. 3, Issue 2, pp. 369–383.

ZHANG X.Y., WU L. (2014). Direct solutions for normal depths in curved irrigation canals, Flow Measurement and Instrumentation, Vol.36, Issue 2, pp. 9–13.


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