本文利用鏈微律(chain differentiation rule)將卡氏座標系統轉換為更具實用性的一般座標系統之連續方程式，使用擴充型Von Mises流線座標系統 與流函數 反求流線位置 。穩態自由液面自有一條流線滿足動力條件，若由一維明渠流的概念考慮水面斜率使每條線均與水面形成一條流管，每條流管均產生臨界流，用此方法計算二維堵塞流的流量與內部流場資訊。
然而即使是僅考慮邊界底床( )之一維越臨界流況，亦未能有在現有的明渠水利學理論中獲得明確可遵循的分析方法，這類的問題難度最主要是當流況在下游發生臨界流時，如何得知流量及控制流量大小的斷面位置，必須進行合理簡化假設以求解問題。
本文透過將水面斜率項為已知，簡化水面動力條件中的未知數，並依照數學三次函數的重根概念將臨界流條件加入，透過數值迭代方法嘗試將精確的控制流量及其位置搜尋出來，得到合理的流量後，即可迅速使用函數解析解計算水面高程之位置。
若欲將一維概念延伸至二維流場中，由實驗觀察可以得知，水流在底床有明顯的高程變化時壓力分佈都為非靜水壓分布，速度也非均勻分布，因此使用一維平均流速的方式處裡二維流場是有問題的。故本文提出分析二維堵塞流場的計算程序，提供讀者在接觸此相關研究時可提供參考。

This study applied the streamline method to analyze the steady free-surface elevation of two-dimensional (2D) chocked transcritical flow. With the extensive von Mises transformation by given x=x(ξ) and streamfunction ψ=ψ(η) along a streamline η= constant, the method is applied to calculate the position of streamline y=y(ξ,η) in the 2D flow. In any curvilinear flow, since the velocity distribution is non-uniform and the pressure distribution is not hydrostatic either, the traditional one-dimensional (1D) theory of open channel flow must be justified accordingly. Moreover, it is not clear to judge where a critical section is, for example, over a flat top submerged weir. The steady free surface can be described as one streamline and it satisfies the dynamic condition which in general involves the effects of the slope of the free surface. Thus, not only the bottom height but also the free-surface slope is coupled to determine the choking discharge and the location of its critical section. The study also extends the concept of 1D choked flow using a streamtube, enclosed by one interior streamline and the free-surface one, for its transcritical flow condition. In this conceptual way one might obtain the critical flow rates in many streamtubes and then accumulate information for a 2D chocked transcritical flow. By such an algorithm, the present study applies the iterative scheme to obtain the convergent result of free surface and other flow variables.

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