LARHYSS Journal
Volume 20, Numéro 3, Pages 135-150
2023-12-25
Exact Solution For Normal Depth Computation In Some Optimal Channel Cross-sections
Authors : Ramdani Imene . Sekiou Fateh . Lakehal Moussa . Achour Bachir .
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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