Uniform flow depth in trapezoidal open channels

Abstract

Uniform or normal flow depth is a key parameter for designing the open channels. The majority of irrigation channels are trapezoidal. Developing an explicit single-step solution based on Manning's formula to calculate the normal depth in trapezoidal open channels is not a simple task. This is due to special mathematical behavior of the governing uniform flow equation for some values of z < 1 (z = side slope of the channel). This work has focused on analytical-based solution. In this study, for the first time, explicit solutions for trapezoidal channels have been developed using asymptote matching technique (power mean concept). This technique enables to develop a solution for the entire flow depth range. The maximum error of proposed solution for z ≥ 1 is less than 0.7%. The efficiency of the asymptote matching technique can be improved by adding a power-law relation. According to this feature, a direct solution with a wider applicable range of z is developed. The maximum error of this solution for z ≥ 0.25 is less than 0.72%. A full range solution is also developed for rectangular channels with a maximum error less than 0.1%. The proposed explicit solutions have physical concept and high accuracy and are well-suited for practical applications.