Limiting dimensions for trapezoidal channels and control notches (Design Aid)

Abstract

Determining the channel dimensions leading to critical flow conditions for given values of specific energy or specific force plays an important role in channel transition design. A closed-form analytical solution for the problem can only be derived for triangular, rectangular and parabolic channels. This is not possible, however, for other practical geometries, such as trapezoidal channels. The dimensions of the trapezoidal control notch are determined by simultaneously satisfying the critical state of flow and specific energy equation. At present, graphical solutions are used for design discharges less than 2.83 m3/s. In current study, direct solutions to compute the limiting dimensions of the trapezoidal channel and direct solutions to design of the trapezoidal control notch are derived. The proposed solutions are nearly exact and will be useful in the design and analysis of the trapezoidal channels and notches.