Computing conjugate depths in trapezoidal channels

Abstract

Accurate calculation of conjugate depths in a hydraulic jump is important to hydraulic design in open channels. Iterative formulae for calculating conjugate depths in hydraulic jumps in trapezoidal open channels were developed using mathematical transformation of the momentum equation. Two formulae that are adjusted from the critical depth of trapezoidal channels were proposed to compute the initial values for iterative formulae. The iterative formulae described here can be used for computer program development to find accurate solutions of conjugate depths. Because the appropriate initial values were selected to accelerate the convergence rates of iteration procedures, the output from the first iteration can be treated as a reliable estimate of conjugate depths with the relative error less than 0·8% in most cases. The approximation formulae are well-suited for manual calculations.