106年 - 106 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#146406

(a) Determine the volumetric dilation rate. Is this an incompressible flow field? Explain(5分)

(b) Determine the vorticity. Is this an irrotational flow field? Explain(5分)

(c) Determine the local acceleration and convective acceleration a fluid element at the point(x, y, z)=(1,1,1)(10分)

2. The pressure drop, \( \Delta p \), for incompressible turbulent flow in a horizontal round pipe of diameter \( D \) can be written in functional form as \[ \Delta p = F(V, D, l, \varepsilon, \mu, \rho) \] where \( V \) is the average velocity, \( l \) is the pipe length, \( \varepsilon \) is a measure of the roughness of the pipe wall, \( \rho \) and \( \mu \) are fluid density and viscosity, respectively. Find a non-dimensional relationship for \( \Delta p \). (use \( \rho \), \( V \), \( D \) as repeating variables) (20分)

3. Water flows through the pipe contraction shown in Fig.1. For the given 0.2m difference in the manometer level, determine the flowrate as a function of the diameter of the small pipe, D.(20分)

(a)若實體渠道的寬度是18公尺，則在模型裡渠道的寬度是多少？(5分)

(b)福勞德數是什麼力和什麼力的比值？(5分)

(c)若在試驗中量到某一點流速是0.5 m/s，則在實體渠道中所對應的那一點流速應該是多少？(10分)

(a)請計算雷諾數。(5分)

(b)請依據雷諾數判斷管中流況是層流還是紊流。(5分)

(c)請求出圓管中心軸之流速。(5分)

(d)管中每1公尺壓力差有多少。(5分)