107年 - 107 國立嘉義大學_碩士班(乙組)招生考試試題_土木與水資源工程學系：流體力學#146093

1. Given a three-dimensional flow field as\( V = 3ti + xj + ty^2k \)Find the local acceleration, convective acceleration, and total acceleration of a particle when it passes the location \( (x, y, z) = (1, 1, 1) \) in meters, at time \( t = 1 \) sec. (20%)

2. Water flows in a rectangular channel that is 3.0m wide as shown in Fig. 1. The upstream depth is 70mm, and the water surface rises 40mm as it passes over a portion where the channel bottom rises 10mm. If viscous effects are negligible, what is the flowrate?(20%)

3. The concrete dam of Fig. 2 weighs 23.6KN/m³ and rests on a solid foundation. Determine the minimum coefficient of friction between the dam and the foundation required to keep the dam from sliding at the water depth shown. Assume no fluid uplift pressure along the base. Base your analysis on a unit length of the dam.(20%)
Fig. 2

(1) 基於哪四個條件之流況，才可以用伯努利方程式來分析？ (8%)

(2) 推導伯努利方程式時，沿著流線方向之受力只有壓力和重力需要被考慮，這是基於哪一個條件？(3%)

(3)推導伯努利方程式時，有用到加速度 \( a = v \frac{\partial V}{\partial s} \) 之公式，這是基於哪兩個條件？ (6%)

(4) 推導白努利方程式時，最後把 \( \frac{1}{2}d(V^2) + gdz + \frac{dP}{\rho} = 0 \) 沿著流線方向積分 \( \frac{V^2}{2} + gz + \frac{P}{\rho} = c \)，是基於哪一個條件？ (3%)

(1) 圖中的A點和B點，均距容器底部20cm，這兩點之相對壓力(絕對壓力減大氣壓力)分別為多少kgf/m²？(10%)

(2) 卡榫至少要能承受多大的力，小門才不會被翻開？(10%)