Formula for direct calculation of contracted depth of parabola-shaped canal

The analytical solution formula of contracted depth in parabola-shaped canal is very complex.In order to facilitate engineering,a direct calculation formula for approximate solution of contracted depth is proposed.After mathematical transformation of the basic equation for contracted depth,the amount of unknown and known are replaced by relative contraction water depth λ and integrated known quantity β,which are dimensionless parameters.Then the iterative formula is obtained by fixed-point iteration method.Firstly,selecting the initial preliminary by numerical method based on analysis of the monotonicity and convexity of function and equation root,along with the geometric function image.The direct calculation formula of contracted depth has obtained at last;after initial optimization as the target of the least number of iterations with the minimum relative error.After analyzing the relative error and application examples,the result shows that the direct formula is brief,widely suitable and exact;the maximum relative error is less than 0.43%.