Limit Slope in Uniform Flow Computations: Direct Solution for Rectangular Channels

The slope classification concept has many applications in open-channel flow problems. Many analyses have been made to find the depth of flow necessary for generating a uniform flow of a given Froude number and roughness in a rectangular channel of known bed slope. No analytical solutions are available in technical literature for this problem until date. The existing methods for solution of the analyzed problem are trial-and-error procedure, also generalized flow curves. In the current study, the analyzed problem in a rectangular channel is expressed by a nondimensional fourth degree equation. In the next step, this equation is solved numerically by applying Ferrari’s and Cardan’s techniques to find an analytical solution for depths in a rectangular channel with a given Froude number, bed slope, and roughness. The derived solution was applied to find the transitional depth in a GVF in a rectangular channel.