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Analytical Investigation of Stage-Discharge Relationships of Compound-Composite Channels

Many formulas have been proposed over the last century for the evaluation of Manningʹs n in composite material both for single and compound channels. However, when stage is plotted as a function of discharge, many of them show discontinuity at the junction of the main channel and flood plain. These discontinuities have not been observed in other hydraulic parameters such as specific energies, and mean velocities. The discontinuity arises from two major sources, firstly Manningʹs n and secondly AR2/3. Investigations of 26 formulas for equivalent Manningʹs ne in composite channels show that many of them cannot be applied for a two-stage channel because of the discontinuity. It is observed that only three of those formulas can be used to meet this requirement. In order to solve the problem of the lack of continuity for the second term a new technique is proposed. Using this technique a number of geometrical parameters of a trapezoidal channel such as the ratio of the flood plain to main channel as well as the side slope of the main channel and flood plain are altered to graphically investigate their behaviour on the stage-discharge diagrams. The results show that as the ratio of flood plain to the main channel area is increased, the differences between the hydraulic variables will be increased. Also the increment of the side slope of the main channel and flood plain do not show a significant change in the dimensionless discharge especially when the water level is above the flood plain stage.