General Solution of Conjugate Depth Ratio (Power-Law Channels)

Abstract

Conjugate flow depth is of high practical importance and should be accurately determined in hydraulic design projects. Quantifying the hydraulic jump phenomenon is an application of specific force relation. This relation has a simple analytical solution only for the horizontal rectangular channels. The power-law section is very versatile and allows suitable modeling for both artificial and natural channels. These channels are used in irrigation and drainage projects. No explicit solution is available in the technical literature for the conjugate depth in general power-law channels for the exponent parameter 1≤n≤2. For this channel, the conjugate depth is currently obtained by trial and error procedures. Numerical solutions of the conjugate depth problems can always be established, though such numerical solutions are devoid of any physical interpretation. In contrast, an explicit solution involves all the input variables in functional form; and thus the dependence of the conjugate flow depth on each input variable can be interpreted. This study presents accurate explicit solutions that can be used to calculate the conjugate depths of open channels with power-law sections. If the initial depth of the hydraulic jump is known, the sequent depth can be determined using the proposed solution with a maximum error less than 0.35%. Inversely, if sequent depth is known, the initial depth can be determined with a maximum error less than 0.55%. The generic results presented in this research for power-law channels can be applied to its special forms such as rectangular, triangular, and parabolic channels. The proposed direct solutions are general, simple, accurate, and useful for studying the power-law channels.