91年 4月12日 11:00 ~ 12:30 化工系  誠實是我們珍視的美德， 我們喜愛「拒絕作弊，堅守正直」的你！ 
科目：輸送現象及單元操作 
Prob.1簡答題 (24%) ( 每小題6分)


(a)

當流體通過粒子填充床及流體化床時，床內粒子之重力(Fg)、浮力(Fb)及拖曳力(drag force, FD)等三者之相互關係各為何？於最小流體化(minimum fluidization)時，這三個力的相互關係又如何？ 


(b)

於圓管內平均對流熱傳係數(h)的實驗關係式中，除Reynolds number 及Prandtl number等無因次群外，為何尚需考慮D/L及m_{b}/m_{w}等兩因素？(其中D為管徑，L為管長，而m_{b}及m_{w}分別為流體於bulk flow平均溫度及管壁溫度時之黏度)。 




(c)

當設計直立平板以冷凝某一蒸氣時，若有兩種構造可被考慮，一為單一板其直立高度與水平寬度分別為L與W，另一為兩板，每板規格皆為L/2與W，則何種設計有較高之冷凝速率？請說明你答案的依據。 




(d)

於singlepass heat exchanger 計算與應用中，在何種情況下對數平均溫度差(LMTD)不能作為有效的平均溫度差？該heat exchanger 為何常以countercurrent flow 方式操作？於何需求下會考慮以cocurrent flow 方式操作？ 






Prob.2 (18 %)



Water is being pumped from an open vessel to a pressurized vessel of 3.0 atm through a pipe having an inside diameter of 0.1 m.The length of the pipe plus the equivalent length for fittings is 1000 m.If the pump has a power of 7.0 hp and an efficiency of70%, calculate the water flow rate in m^{3}/hr through the pipe. The water through the pipe is in turbulent flow and the Fanning friction factor you can calculate by f =0.046 , where NRe is the Reynolds number. The density and viscosity of the water are 1000 kg/m^{3} and 1.0 cp, respectively. 












Prob.3 (18%)



A long and thin rod(實心細桿) of radius R1 is being pulled at a constant velocity V through a Newtonian fluid in a horizontal pipe of inner radius R2. The rod is at the center of the pipe. Neglect the end effect and assume the fluid is in laminar flow withzero pressure gradient. The fluid density is r, and the viscosity is m. 




(a)Using the shell momentum balance to find the fully developed velocity distribution within the annular space.  
(b)Determine the drag force per unit length of the rod.  




Prob.4 (20%)



Apply the Buckingham Pi method to the case of mass transfer due to natural convection. (i.e. prove Sh= f ( Sc, Gr, l/d ) ) The variables are as follows: 


[Hint: Grashof Number, ; Sherwood Number, Sh; Schmidt Number, Sc]  




Prob. 5 (20%)



An absorber is employed to remove 90% of the ammonia in an air stream containging 3% ammonia by a countercurrent water stream. The inlet air stream rate based on per crosssectional area of the absorber is 100 lb mole/hr.ft^{2}. An ammoniafree waterstream is fed to the top of the absorber. Absorber temperature is to be kept at 68^{o}F and pressure at 2.0 atm. For dilute concentration of NH3 at ,68^{o}F the equilibrium relation is yi= xi, where yi and xi are the mole fractions of ammonia in the gas phase and liquid phase, respectively.  








(a)What is the minimum water rate in lb mole/hr. ft^{2} which might be used?  
(b)Using 2.0 times the minimum water rate and assuming the overall mass transfer coefficient, KGa, is 20 lb mole/hr.ft^{3}.atm, determine the required height of the absorber.  






Viscosity  Energy & Work  
1 cp=10^{3} kg/m.s  1 J= 1 W.s =1 N.m  
1 cal=4.184 J  

Pressure  1 hp=745.7 J/s 
1 atm =1.0133x10^{5} N/m^{2}  
Gravitational Acceleration  

Force  g=9.8 m/s^{2} 

1 N=1 kg.m/s^{2} 
 END