Calculation method for conjugate depths in quadratic parabolic channels

Quadratic parabolic channels are widely used in irrigation and drainage engineering projects. Up until today there are no an effective method for computing the conjugate depths of quadratic parabolic channels. In this paper, calculation method for calculating the conjugate depths of quadratic parabolic channels was studied. Dimensionless depths were selected to simplify momentum equation for determining conjugate depths. Iterative equation for downstream depth was developed by suitable mathematical transformation on the momentum equation. If one knows dimensionless upstream depth, one can obtain dimensionless downstream depth by using iterative equation. Based on a large number of data of dimensionless conjugate depths, explicit equations with simple form for conjugate depths of quadratic parabolic channels were obtained by running a MATLAB program. Relative error analysis indicates that the proposed explicit equations which are employed to calculate conjugate depths (downstream depth and upstream depth) have high accuracy and wide application range. In the practical range of downstream depth to upstream depth ratio [1, 77.33], the maximum relative error is less than 0.30%.