課程名稱︰單元操作 課程性質︰必修 課程教師︰蔡偉博 開課學院：工學院 開課系所︰化工系 考試日期（年月日）︰96年6月26日 考試時限（分鐘）：120分 是否需發放獎勵金：是 （如未明確表示，則不予發放） 試題 : Close Book (30 points) 1. (5 points) What is the sphericity of a half-spherical particle with a diameter D? 2. (5 points) Why does the drag coefficient of a spherical particle drop when the corresponding Reynolds number reaches 200,000. 3. (10 points) Please draw a plot of pressure drop and bed height versus super -ficial velocity for a bed of solids. Also draw the lines for the reduced flow rate in the fluidized bed. Specify the point where the particles start to move, and the minimum fluidization velocity. 4. (10 points) Please answer the following questions based on Figure 1. a. On the line of aba’, where does the maximum velocity occurs ? (2 points) b. At which point the velocity becomes sonic? (2 points) c. What dose the line gg’ mean? (2 points) d. Draw a plot for mass flow rate vs. pressure ratio. (4 points) Figure 1. Variation of pressure ratio with distance from nozzle inlet. (請見"UNIT OPERATIONS OF CHEMICAL ENGINEERING" McCabe 第140頁 圖6.2) Open Book (80 points) 5. (25 points) For a laminar boundary layer, assuming the velocity profile is Ux/Uy = 2y/δ-(y/δ)^2 , (i) Derive an expression for δ as a function of x and Us. (12 points) (ii) Calculate the displacement thickness of laminar boundary layer. (6 points) (iii) Derive an expression for τ/ρUs^2 as a function of Rex (7 points) 6. (15 points) Calculate the source pressure required to deliver 20 x 10^6 standard cubic feet per day (SCFD) of CO to a customer 50 mi. away. By contract the pressure at the customer's site must be at least 350 lbf/in.^2 gauge. The pipe is 12 in. in diameter. Long pipelines may be considered isothermal at the ground temperature of 80oF. Standard conditions are T = 70oF, P = 1 atm. 7. (20 points) The diameter of a baseball is 2.9 in, and its mass is 0.32 lbm. If the drag coefficient is CD = 0.5, obtain an expression in terms of u^2 for the drag force of the air (ρ= 0.075 lbm/ft^3) on the baseball. If a baseball leaves the pitcher on the mound at 110 mph, estimate its velocity by the time it crosses the plate, 60 ft away. Hint: Eventually use the relation u = dx/dt to change the standard momentum balance into a differential equation in which the variables are u and x before integrating. 8. (20 points) A horizontal water purification unit consists of a hollow cylinder that is packed with ion-exchange resin particles. Tests with water flowing through the unit gave the following results: Flow rate Q (liters/hr): 40.0 80.0 Pressure drop, -Δp (atm): 0.27 0.68 If the available pump limits the pressure drop over the unit to a maximum of 3.67 atm, what is the maximum flow rate of water that can be pumped through it? _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ Bonus question (15 points) This question is only for those students who may fail in this course. It is not applicable to those who definitely pass this course. Calculate the thickness of the laminar sub-layer when water flows through a pipe of 50 mm diameter at 0.003 m3/s at 25?C. What is the velocity of the water at the edge of the laminar sub-layer? Assume fully developed flow exists within the pipe. --

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