CAJ | 학술논문

针对目前差分试算法、迭代法及图解法求解水面线存在着计算过程繁复、误差较大的问题，该文通过对抛物线断面渠道恒定渐变流水面线微分方程进行恒等变形，并对引入的特征水深与特征湿周的关系进行分析及计算，重点考察工程实际中常用的特征水深范围为0.6～1.5 m的抛物线形断面渠道，依据最小二乘法进行回归分析将方程中的特征湿周由不可积函数替代为可积分的幂函数，实现了由有限差分逐一断面推算到数值积分法的直接求解。与现有方法相比，该抛物线形断面渠道恒定渐变流水面线简化计算公式具有工作效率明显提高、精度好的特点。实例计算及误差分析表明：在工程实用范围内（特征水深范围0.6～1.5 m）该公式最大相对误差仅为0.17%，对生产实践具有实用推广意义。
침대목전차분시산법、질대법급도해법구해수면선존재착계산과정번복、오차교대적문제，해문통과대포물선단면거도항정점변류수면선미분방정진행항등변형，병대인입적특정수심여특정습주적관계진행분석급계산，중점고찰공정실제중상용적특정수심범위위0.6～1.5 m적포물선형단면거도，의거최소이승법진행회귀분석장방정중적특정습주유불가적함수체대위가적분적멱함수，실현료유유한차분축일단면추산도수치적분법적직접구해。여현유방법상비，해포물선형단면거도항정점변류수면선간화계산공식구유공작효솔명현제고、정도호적특점。실례계산급오차분석표명：재공정실용범위내（특정수심범위0.6～1.5 m）해공식최대상대오차부위0.17%，대생산실천구유실용추엄의의。
The parabola shaped channel has an excellent hydraulic performance and strong ability of anti-frost heave, and is used widely in the field of spillway and irrigation channels. The water surface profile of gradually varied steady flow is an important hydraulic element for the channel design and the operational management, but the differential equation of water surface profile is the transcendental equation with no analytic solution. The current differential test algorithm, iterative method and graphical method for solving the water surface profile has complex calculation process, large errors and low efficiency, so on. To obtain the simplified calculation formula of water surface profile of parabolic cross-section, we introduced the concepts of the parabolic cross-sectional characteristic water depth (that is the product of the water depth and the parabolic shaped perimeter) and characteristic wetted perimeter (2 times of the product of parabolic shaped perimeter and wetted perimeter), and did the identical deformation for the basic differential equations of the gradually varied steady water surface profile of the parabolic cross-sectional channel. The optimal hydraulic cross-sectional parabolic cross-sectional characteristic water depth is 0.947 m. In practical engineering, the design of the parabolic cross-sectional channel is required to be close to the optimal hydraulic cross-section as far as possible under permissive conditions so that it would obtain good hydraulic conditions, save the substantial cultivated land, reduce project expense and achieve better economic benefits. The study here focused on the common parabolic cross-sectional channel in the engineering practice with the range of characteristics water depth of 0.6-1.5 m. Since the characteristic wetted perimeter of the original differential equations is a complex non-integrable function within the most commonly used scope in practical engineering, we analyzed the interrelation between characteristic water depth and characteristic wetted perimeter, plotted a curve with characteristics water depth as ordinate against characteristic wetted perimeter. The results showed that the relationship between characteristics water depth and characteristic wetted perimeter followed the power function. The equation coefficients were fitted by the least squares method, and then a simple integral expression of characteristics wetted perimeter was obtained. The error analysis showed that the absolute value of the relative error of the proposed formula was smaller than 1.08%, indicating that this method is effective to solve the unintegrable equation of characteristic wetted perimeter. As a result, the direct numerical integration method had been deduced by the beginning and final section water depth for determination of the flow distance of the water surface profiles in parabola shaped channel. To test the feasibility of the proposed integration method in calculating the flow distance of water surface profile, it was used to compare with the difference method for 2 cases. Results showed that the maximum relative error was less than 0.2%between both methods, indicating the high efficiency and high precision of the proposed method. In addition, the proposed formula also has simple form, clear physical concept, easiness to use and wide applications. The direct integration formula proposed here is useful in the channel design and management.