Formula for Calculating Contracted Water Depth of Channel with Cubic Parabola Cross Section

The equation for calculating contracted water depth of a channel with cubic parabola cross section is a higher order implicit function equation which is not easy to solve.Due to the complex computation process and lower precision of calculation result,neither traditional graphic method nor trial calculation approach is convenient for practical application.In this paper,iterative formula with fast convergence for computing contracted water depth of a channel with cubic parabola cross section was obtained through proper transformation on basic equation.The iterative formula combined with rational initial iteration value was developed for calculating contracted water depth of a channel with cubic parabola cross section.Error analysis and calculation example indicate that,within the general engineering range,the maximum relative error of this formula is only 0.16%.The formula in this paper can provide a wide application with its simple form and relatively higher precision.