In one dimensional unsteady open channel flow, the de St . Venant hypotheses are utilized to describe the unsteady behavior for the discharge and water depths in the flow domain. One of the de St. Venant hypotheses is that the friction force in the iongitudinal momentum equation (dynamic equation) is described by uniform flow empirical relation, which involves the local unknow variables (discharge and water depth). Therefore, the numerical model based on Pressimann scheme needs further cares to make the solutions convergent . In this study, a new method by treating the friction slope, Sf' as the third dependent variable with a third equation in solving for the problem is proposed. To utilize the empirical friction force relation as the third equation with time dependence makes the system of equations complete and enables the time dependent local friction slope, Sf' to be calculated directly . The direct computation of St at various time steps eliminates the necessity of iterations while two-equation method (continuity and dynamic equations) with two dependent variables is used in solving for the problem.。 應用聖凡南特假設(de St . Venant Hypotheses) 數學模式求解一維明渠變量流係目前水力 計算學之主要部份。一般之水理計算以求解: (1) 水之傳輸量，即是斷面流量(Discharge) 或斷面平均流速(Cross Sectional Mean Velocity) 及(2)水道之大小，即水位(Water Stage)或水深(Water Depth) 或斷面積(CrossSectional Area) 。本文提出同時考慮並求解水之阻力，即是能量坡降(EnergyS1 ope) ，而且係假設能量坡降為顯性型時間及主軸之函數。於動力方程式中，其摩擦項之能量坡降一般以流量除以輸送係數之平方代替。應用有限差分法線性化時，由於輸送係數(conveyance factor) 對水深之變化值極大而引起不收斂性。本文乃提出增設一因變數(能量坡降)及一坡降方程式。坡降方程式係導源於水力指數(Hydraulic Exponent) 之定義。因此可直接求取渠道各斷面之流量，水深，及能量坡降
關聯:
第四屆水利工程研討會論文集=Proceedings of 4th Conference on Hydraulic Engineering，頁167-177
