ChE 134 Long Exam 1.docx - Marin H Tam 2014-49289 ChE 134...

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Marin H. Tam 2014-49289 ChE 134 Long Exam 1 Submission INSTRUCTIONS Please read the instructions carefully. Use black or blue pen only. State all assumptions as needed. You are given three (3) hours to complete this sit-in exam. A candidate who is suspected of cheating in examinations is liable to disciplinary action. CONCEPTUAL In the 2002 World Cup qualifier against Greece, David Beckham stole the show with a 30-yard free kick at the 93 rd minute mark to send the Three Lions to South Korea and Japan. The ball started out to the right then dipped subtly into the top left hand corner to avoid the opposition’s goal keeper. The trajectory of the ball is largely dependent on its spin and the roughness of the object’s surface. For example, in baseball, a top spin results in a traditional curve ball, where the ball seemingly “drops”, while a screwball, or a sweeping curveball, occurs when the pitcher spins the ball perfectly sideways. Using your knowledge on flow separation, explain why the ball curves. PROBLEM SOLVING PROBLEM 1 MECHANICAL ENERGY BALANCE Using the virial equation truncated to the second term, prove that the mechanical energy balance for an isothermal compressible flow is given by: [ P 1 ( RT + B P 2 ) P 2 ( RT + B P 1 ) ] + ¿ MW Bg [ P 2 P 1 ln ( P 1 + RT B P 2 + RT B ) ] + f D G 2 L 2 Dg + ∑ K G 2 2 g = W s G 2 g ln ¿ Assumptions 1. Steady state 2. One dimensional 3. Negligible elevation/horizontal pipe
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4. Friction factor is constant Virial Equation Z = 1 + BP RT Units R [ ¿ ] Pa m 3 mol K P [ ¿ ] Pa B [ ¿ ] m 3 mol MW [ ¿ ] kg mol
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PROBLEM 2 LINE SIZING In an ethanol fuel plant, the final product—rectified alcohol (assumed to be pure ethanol)—is to be cooled from 78.1 to 40 in a shell and tube heat exchanger, using cooling water entering at 25 and exiting at 34.8 . The plant produces ethanol at a volumetric flow rate of 1075 cubic meters per day. Mr. James, one of the chemical engineers at the site, designed a system that delivers the cooling water from a source tank to the designated tank as shown below. The cooling water passes through two 90° elbows (shown in the diagram as bends), a check valve, and an orifice meter. The loss coefficient for a 90° elbow is given by: K = 30 f D where f D is the Darcy friction factor using the Colebrook correlation. Knowing of your expertise in line sizing, he requested your help to determine the nominal steel pipe sizes to be used and the pump horsepower required.
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Apply a 10% safety margin to the flow and a 20% margin to the calculated skin friction. 1. Determine the pump work required. 2. Suggest ways to reduce the work required by the pump. Properties of Fluids Fluid Density, kg m 3 Specific Heat, kJ kg K Ethanol 768.9 2.803 Water 1000 4.184 Recommended Velocities and Pressure Drops for Pipe Flows Fluid Maximum Velocity Maximum Pressure Drop Boiling liquids at pump suction 4 ft/s 0.25 psi/ 100 ft Subcooled liquids at pump suction 8 ft/s 1.0 psi/ 100 ft Boiling liquids at pump discharge 15 ft/s 4.0 psi/ 100 ft Subcooled liquids at pump discharge 15 ft/s 4.0 psi/ 100 ft Properties of Steel Pipe Nominal Pipe Size, in
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