本文主旨在提出天然渠道變量流之濃度擴散方程式線性解析解，主要方法是將聖凡納方程式中的連續方程式和動量方程式代入濃度擴散方程式中，合併成二階偏微分方程式。但由於水質模式是非線性微分方程式，無法求得解析解，多採用數值解法，可是數值解法只是近似解，有不穩定、發散及誤差的問題。所以本文提出線性解析解法，可用在求解及推導水流及濃度擴散方程式係數及其模式之解答。 在解析解求解過程中，經由基本假設，可以得到水流動量方程式，再忽略聖凡納動量方程式中不重要的慣性項。再考慮壓力項、重力項和摩擦項動量平衡，則可得擴散波動量方程式。利用連續方程式及擴散波方程式，兩方程式可以合併成一非線性的偏微分方程式，再代入運動波模式即考慮重力跟摩擦平衡來加以線性化，進而推求出流量解析解模式。所以本文所發展出的線性化解析解具有簡易、經濟、有效率、精確之工程實用價值。 In the study, an analytical solution is proposed for simulating unsteady open channel flow, and the linearized of the Saint Venant equation by small perturbation is used to obtain analytical solution. Because the De Saint Venant equations which contain the continuity and momentum equations, and the continuity equation of contraction are nonlinear partial differential equations, it is difficult to obtain the exact solution. In this study, a linearized analytical technique is provided, not only apply to the scheme of the nonlinear differential equations, and also apply to the coefficients of the diffusion terms of the water quality model. In the process, I neglected the inertia terms in the Saint-Venant moment equation. And obtained the linearized Saint-Venant equation by small perturbation method. Compare the analytical solutions with the numerical solutions, the linearized analytical solution can obtain a good approximation efficiently if we choose an appropriate reference discharge. This result shows that the analytical solution is good, economic, efficient approximation in practical cases.
