本文透過一維明渠理論並考慮水面斜率效應的水面動力條件，以求得適當水面邊界條件，採用流線座標法及搭配擴充型von Mises轉換，以"x=x(ξ)" 與"ψ=ψ(η)" 透過轉換後的Laplace方程式反求流線位置"y=y(ξ,η)" ，以進行內部流場分析，並進一步由一維明渠流概念，利用內部流線作為流管底部與自由液面形成流管，逐次往水面方向計算，以此方式獲得二維流場的水面位置及對應二維流量，並利用柏努力定理分析內部流場資訊。
　　本文為了獲得滿足包含水面斜率之水面動力條件以及發生臨界流條件的水面位置，利用三次式解析解分析臨界流條件之數學關係，並透過最佳化計算中目標函數及限制式條件的設定求解水面位置；但由於本問題難度為當上游亞臨界流跨越至下游超臨界流況時，其發生臨界條件時的臨界位置、臨界流量以及在臨界位置上的水面斜率皆為未知代解數，該臨界條件包含三種未知值，因此在限制式條件新增由臨界流條件及一階微分式推導出與底床及水面高度的一階與二階關係式，進一步計算並獲得水面位置。隨後，以此模式計算不同堰寬之寬頂堰底床，探討堰寬對流量造成的影響，以供讀者在研究此相關問題時參考。

The thesis analyzed the effects of top width on the two-dimensional (2D) open-channel transcritical flow over a broad-crested weir. Since the complete free-surface dynamic condition includes the square of unknown water-surface slope, the free-surface elevation the location of critical section and the critical flow discharge are better calculated by 1D optimization process. For the 2D transcritical flow simulation, the streamline method was applied. To do this, using the extensive von Mises transformation with prescribed" x=x(ξ)" and stream function"ψ=ψ(η)" , we obtained the elevation of internal streamlines "y=y(ξ,η)" by solving Laplace’s equation. The 2D free-surface elevation was analyzed based upon the 1D idea of several choked streamtubes bounded by the water surface and another streamline, starting from the bottom to the uppermost streamlines next to the free surface. As the converged elevations of the free surface and internal streamlines have been calculated, the velocity profile and pressure distribution in the entire flow field can be obtained by the Bernoulli's principle. In this study, the transcritical flows over a broad-crested weir of different top widths were calculated and flow discharge affected by top width is analyzed.

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