Analytical Model of Hydraulic Geometry Functions in Meander River

Regime and hydraulic geometry are two of the most important proposed models over the past century in the related disciplines of river engineering and fluvial geomorphology. Therefore, the hydraulic geometry is of prime importance in planning, design, and management of river engineering and training works (Huang, 1996). The first systematic analysis was conducted on canal systems in India by Kennedy (1895) who exhibited a relation between velocity and depth. Downstream hydraulic geometry relationships describe the shape of bank-full alluvial channels in terms of bank-full width, average flow depth, average flow velocity and channel bed slope. Although some concepts of hydraulic geometry were proposed toward the end of the nineteenth century, the real impetus toward formulating a theory of hydraulic geometry was provided by the work of Leopold and Maddock (1953). Leopold and Maddock (1953) adapted the ideas from regime relations for canals to the description of natural stream channels. Generally, there are two experimental and analytical methods to obtain the hydraulic geometry relations in order to determine the stable geometric dimensions of the rivers. Different researchers have studied hydraulic geometry relations for straight rivers without considering the effect of the secondary flow. The main focus of this study is to analytically derive the hydraulic geometry equations considering the concept of secondary flow in meandering channels.