关键词: 恒定渐变流基本微分方程, 相对水深, 数值拟合

Abstract: A new method to calculate the water surface curve along constant nonuniform flow in trapezoidal cross section of prismoidal open channel is presented. Through numerical analysis and the dimensionless basic differential equation of constant and gradually varied flow, a new equivalent basic differential equation which comprises the simple hyperbolic function is obtained. By variable separation and direct integral, the analytic functions between the flow path S and water depth h₁ and h₂ respectively in the beginning and final part are obtained, through which the water surface profile is computed. This method is simpler and more convenient than the trial-and-error procedure by partition and summation recommended in Spillway Design Standard. Especially for sections more sensitive to water depth, the error of the trial-and-error procedure is bigger owing to the accumulation of errors section by section. Computation example shows that results of this new method is generally consistent with that of the procedure in the Standard, and even more superior for long channels. This method meets the requirements of the project practices.

Key words: basic differential equation of constant and gradually varied flow, relative water depth, value fitting