aer205_exam_2006_questions - University of Toronto Faculty...

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Page 1 of 9 University of Toronto Faculty of Applied Science and Engineering FINAL EXAMINATION – December, 2006 SECOND YEAR -- ENGINEERING SCIENCE Program 5 AER205F FLUID MECHANICS and TRANSPORT PHENOMENA Examiners: Y-L Cheng and J. W. Davis _________________________________________________________ Instructions: (1) Closed book examination; except for a non-programable calculator, no aids are permitted (2) Write your name and student number in the space provided below. (3) Answer as many questions as you can. Parts of questions may be answered. (4) The questions are NOT assigned equal marks. (5) Boldface quantities represent vectors. (6) Use the overleaf side of pages for additional or preliminary work. (7) Do not separate or remove any pages from this exam booklet. (8) Use g = 10 m/s 2 , D water = 1000 kg/m 3 where appropriate. (9) Differential equations of change are included on pages 2-4 ____________________________________________________________________ Family Name:________________________________________________________ Given Name:________________________________________________________ Student #:________________________________________________________
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Page 2 of 9 1) a) [3 marks] A tank in the form of a right circular cylinder having its axis vertical and having cross-sectional area A 1 has a contoured orifice of exit area A 2 in its side near the bottom. As shown in the diagram, the tank is closed at the top, except that a large pipe having cross- sectional area A 3 extends vertically downward into the tank interior in such a way that it admits atmospheric air at a height H above the orifice axis. If the tank is filled with water to a height h above the pipe exit, assuming frictionless flow, calculate the volume flux out of the orifice. b) [3 marks] A clown is riding in an elevator, holding a large helium-filled balloon on the end of a string. The cable to the elevator snaps, allowing th elevator to fall freely. Due to her surprise, the clown lets go of the balloon string at exactly the instant the elevator cable breaks. According to the clown, what happens to the balloon? Explain. c) [5 marks] The pressure drop, ) p , for steady, incompressible viscous flow through a straight horizontal pipe depends on the pipe length, l , the average velocity, V , the fluid viscosity, : , the pipe diameter, D , the fluid density, D , and the average “roughness” height, e . Using , V and D as reference variables, determine a set of dimensionless groups that can be used to correlate data.
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Page 3 of 9 2) (a) [4 marks] A chemical species ”A” is soluble in X (a liquid), Y (a solid) and Z (a liquid). Experiments show that at equilibrium, the concentrations of ”A” in X, Y and Z are 10 mg/mL, 1 mg/mL and 5 mg/mL, respectively. In the two experiments shown below, a slab of Y is sandwiched between X and Z, both of which are being stirred. The concentrations of ”A” in the bulk of X and Z are maintained at the values shown for the duration of the experiments. Sketch the concentration profiles that will exist in the three phases at very long times for the two situations.
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This note was uploaded on 10/18/2010 for the course ENGINEERIN AER205 taught by Professor O.trass during the Fall '08 term at University of Toronto- Toronto.

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aer205_exam_2006_questions - University of Toronto Faculty...

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