NEW THEORETICAL CONSIDERATIONS ON THE ROUGH TURBULENT FLOW PARAMETERS

Abstract

The field of rough turbulent flow occupies an important place in the practical applications of hydraulic engineer. It is for this reason that the present study is interested in the most important parameters of this flow namely the characteristic length, the average velocity, the Reynolds number, and the hydraulic diameter. To express these parameters, new theoretical considerations are developed based on the combination of Darcy-Weisbach and Nikuradse rational relationships. The implicit form of the equation which governs the characteristic length has been transformed into an explicit power law by a correlation procedure with a very high coefficient of determination. An exact analytical solution in terms of Lambert function was also developed. Thus, the characteristic length can be evaluated explicitly provided the flow rate, the absolute roughness, the channel bed slope and the aspect ratio of the wetted area are given, which is generally the case in practice. The explicit characteristic length equation has been judiciously used to derive the mean flow velocity relationship. This is in the form of that of Manning-Strickler but with slightly different coefficients. The interest of the new velocity model lies in the fact that the resistance coefficient has been determined analytically contrary to the empirical nature of the Manning and Strickler coefficients. The resistance coefficient is explicitly related to absolute roughness and gravity through a physically justified relationship. The last two parameters studied namely the Reynolds number and the hydraulic diameter were deduced from mathematical manipulations and expressed by simple and practical relationships which do not contain the characteristic length.