Abstract: In order to get the direct calculation formula of water depth in semi-cubic, square, and cubic parabola-shaped channels with contracted section, we identically transformed the basic equation of contraction water depth and obtained higher degree equation of non-dimensional contraction depth. But it could not be solved theoretically, so we obtained the iterative calculation formula of non-dimensional contraction depth by further transformation. Furthermore we employed 1stOpt software to optimize and fit the established nonlinear model parameters based on genetic algorithm and built the direct calculation formula of contraction depth for the semi-cubic, square, and cubic parabola-shaped sections. Error analysis and calculation example show that the maximum relative error is respectively 0.064%, -0.091%, and 0.136% within common engineering range λ∈[0.01,0.6]. The direct calculation formula is convenient, and has high precision and wide range of application.

Key words: semi-cubic parabola-shaped section, square parabola-shaped section, cubic parabola-shaped section, 1stOpt software, genetic algorithm, contraction water depth