Design Charts and Design Equations for Trapezoidal Earthen Open Channels

Earthen trapezoidal open channels are widely used for various essential purposes. Easy and accurate design is necessary to obtain the dimensions that assure non-silting non-scouring water velocity to maintain these channels. In this paper, employing the Manning equation, design charts are established for each of the common equations of non-silting non-scouring water velocity. For each equation, relating water depth and bed width, three design charts are presented for different side slopes. Every design chart includes a direct relation between the discharge and the water depth for various longitudinal channel slopes. Knowing the discharge and the longitudinal slope, the water depth is obtained immediately from the design chart. Substituting in the velocity equation, the bed width is determined. From the established design charts, it is found that at each specific water depth, the relation between the discharge and the longitudinal slope is proportional for drains and is inversely proportional for canals. Regression analyses are employed to obtain design equations to find the water depth, which maintains non-silting non-scouring water velocity, for different types of soils and longitudinal channel slopes. For each longitudinal slope, a regression analysis is applied, and a design equation is obtained. All the obtained equations are integrated into only two general design equations for trapezoidal earthen open channels, which assure non-silting non-scouring water velocity and have coefficients of determination of almost 1.00. The developed design charts and equations are applied to a main canal in Egypt obtaining very accurate results.