6. 請推導理想氣體可逆絕熱過程其 P、V、T 之關係式(10％)

7. 請說明孔口流量計使用注意事項，應用原理，並推導出孔口流量計的 體積流率方程式(10％)

8. 請推導史托克方程式，並詳細說明實驗中如何應用史托克方程式測量 流體黏度(10％)

10. 請推導三台相同的批式反應器，第一台加入的速率定律式(Rate law) 為 R=k(常數)，第二台加入的速率定律式(Rate law)為 R=k[A]，第三 台加入的速率定律式(Rate law)為 R=k[A]2，請推導與說明濃度與時間 的線性式關係式、半生期。(依照詳細度不同進行扣分) (10％)

1. The venturi meter shown in Fig. I carries water at 60 ℃ (The specific weight γ = 9.65 kN/m3). The specific gravity of the gage fluid in the manometer is 1.25. Calculate the velocity of flow at scction A and the volume flow rate of water.

2. Water is added to the tank shown in Fig. 2 through a vertical pipe to maintain a constant (water) level. The tank is placed on a horizontal plane, which has a frictionless surface. Determine the horizontal force, F, required to hold the tank stationary. Neglcct all losses.

3. Consider steady, incompressible, parallel, taminar flow of a viscous fluid falling between two infinite vertical walls, as shown in Fig. 3. The distance between the walls is h, and the gravity acts in the negative z-direction. There is no applied pressure driving the flow； that is, the fluid falls by gravity alone. The pressure is constant everywhere in the flow field. Calculate the velocity field.

(a) Determine the constants a, band c. (6%)

(b) Show that , where δ is the boundary-layer thickness and , please find C=?

(c) Show that local skin friction coefficient . Please find D=? (10%) (4%)

5. As shown in Fig. 4, a tank with fixed volume,contains brine with initial density, ρi, greater than water. Pure water enters the tank steadily and mixes thoroughly with the brine in the tank. The liquid level in the tank remains constant. Derive expressions for (a) the rate of change of density of the liquid mixture in the tank, and (b) the time required for the density to reach the value  ρf, where, ρi ＞  ρf ＞ ρH2O Note: A first-order lincar differential equation:y'(x)+ p(x)y = q(x). Its solution is

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