Iterative algorithm of conjugate depth for parabolic channels

Channels with parabolic cross-section are widely used in water conservancy projects, so it is necessary to determine the accurate conjugate depth value in hydraulic design. In order to seek a simple method, the iterative formula of conjugate depth for parabolic channels is derived and the convergence of which is proved theoretically. Moreover, the direct calculation formula to determine the initial iterative value is derived in order to speed up the convergent rate. And finally an example proves that the method in this paper is simple, fast and clear in physical concepts.

Research highlights
► We derive a concise iterative formula of conjugate depth of hydraulic jump for parabolic channels and prove its convergence.
► We propose a formula of the initial iteration value by regression analysis, which accelerates iteration speed greatly.
► We prove the iterative formula is very practical and convenient in practical projects by a real example.