Approximate method for calculating normal water depth in common city-opening shaped cross-section

The city-opening shaped cross-section has been applied to hydroelectric engineering;it is a transcendental equation to solve the normal water depth with no analytical solution.An approximate calculation method is proposed with simple and direct,general,and high precision.For this approximate method for calculating normal water depth in city-opening shaped cross-section,the constant deformation is used on the basic equation,and then the dimensionless normal water depth and fitting optimization integrated parameters k and dimensionless depth x are introduced in according to optimization theory.The error analysis and case studies show that the maximum relative error of contraction water depth is less than 0.62% within the common project.The formula has a direct and simple form,high precision and wide application.