A simplified formula to calculate the initial value of iteration for contracted depth in quadratic parabola shaped channels

摘要

At present, the complexity of calculation process and expression form of the initial value of iteration for contracted depth in quadratic parabola shaped channels，Seek a new iterative initial value formula for contracted depth in quadratic parabola shaped channels. Through an identical deformation on the basic equation for contracted depth in quadratic parabola shaped channels. Deduce the iterative formula for computing the quadratic parabola section contraction water depth. Introduction the dimensionless contraction water depth concept, plot the dimensionless contraction water depth and the dimensionless parameter relationship curves. Determine the iterative formula of initial value form for quadratic parabolic shaped channels, and based on the theory of optimum fitting, by the minimum residual standard differential and simple form of formula as the goal, the initial iteration value formula for calculation contracted depth in quadratic parabola shaped channels was obtained. It is greatly accelerating the convergence rate iterative calculations. The calculation of a practical case and error analysis of the depth calculations show that in the utility range of α ∈ [0, 0.5], its maximum relative error is less than 0.26% after performing one iteration. This formula has definite physics concept, easy calculation, high precision and wide range compared with the existing formulas. It will bring great convenience for designers.