Simplified Accurate Solution for Design of Erodible Trapezoidal Channels

The sides and bottoms of earthen irrigation channels are erodible. The main design criterion for the earthen channel is to minimize or eliminate channel erosion under design flow conditions. The Manning formula and the tractive force equation were used as governing equations to design erodible and riprap channels. The traditional design approach involves a tedious trial procedure to find the bottom width of trapezoidal channels. Some hydraulic engineering problems require the solution of the bottom width from the Manning formula for nonerodible channels. An approximate equation is available for determining channel bottom width, but it is not applicable for channels with side slopes $z<1$ (1 vertical and $z$ horizontal), which are encountered in practice for nonerodible channels. This technical note presents a direct and accurate equation for determining the channel bottom width (with errors less than 0.1%) using the tractive force concept and a dimensionless form of the Manning formula. The proposed direct solution facilitates the design of erodible and riprap-lined channels. Moreover, the proposed equation can be used to accurately determine the bottom width of rigid (nonerodible) channels for any side slope.