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Unformatted text preview: ChBE421 Final Exam Dec. 10, 2009 1. (45 pts) Please answer 9 (5pts/ea) out of the 14 questions. Answer each briefly a. A metal pipe wrapped with a layer of insulation is carrying condensing steam at temperature To in a room at temperature T∞. If the thickness of the insulation is increased causing q to decrease, how does the temperature change (i) at the outside metal surface of the pipe, (ii) at the outside surface of the insulation? You may assume hi and ho are constant b. What is the physical significance of the Material derivative, D/Dt? c. An object of a specific shape requires a time ‘t’ to cool to a given temperature (Bi = 0.07). If the size of the object (length) is tripled while the thermal conductivity of the solid is halved how does (i) the cooling time ‘t,’ and (ii) the Prantl number describing the system change? d. A heat exchanger converts saturated water into saturated steam at atmospheric pressure using hot combustion gases (hot fluid). Discuss the relative advantages of concurrent and countercurrent designs e. What are the three conditions required to be met for simplification of the integral mass, energy and momentum balances to their respective special cases? f. Sketch the velocity profile for a shear thickening fluid flowing down a wall under gravity. g. The Bernoulli equation was derived under the assumption of inviscid, irrotational flow; yet we use the Bernoulli equation to predict the pressure in a viscous, rotational boundary layer. Explain h. In a drip coffee maker, water requires a certain time T to flow through the ground coffee. How does this time change if the coffee is ground finer, so the grounds are half as large? Assume low Reynolds number flow where fP ≈ 150/ReP i. What fraction of radiative energy is transmitted in: (i) a black body, (ii) an opaque body, (iii) a gray surface? j. Considering turbine efficiency (ηt): (i) what are the limits of the size of ηt; (ii) is the lw term in the mechanical energy balance equation now negligible; if not, what is it’s physical meaning? k. Give an expression for the drag force on a rectangular prism (length = a; width, depth = b) in an irrotational, inviscid, incompressible flow. Please express your answer in the simplest form. l. The heat transfer coefficients on opposite sides of a wall are 4 and 25 cal/sec cm2 °C. To which side of the wall should fins be added for the greatest effect? m. What type of body emits the greatest amount of radiative energy in response to a constant radiation source? n. What is the physical significance of the Reynolds and Biot numbers? Provide key values for each. 1 2. (30 pts) A large bronze figure acts as the nozzle for the center jet of a public fountain. Unfortunately, the engineer for the department of public monuments forgot to bolt the figure down. For low flow rates all is well, but if the height of the jet is 80 ft, the force of the water is sufficient to blow the statue off its pedestal. • What is the weight of the statue? Nozzle dimensions: entrance diameter 4 in., exit diameter 2 in. Neglect all frictional losses. Neglect changes in potential energy over the length of the nozzle. Hints: * You may need two separate control volumes to solve this problem. * At the top of the jet, the velocity is approximately zero and you may model it as an outlet with very large radius. ρH20 = 62.4 lbm/ft3 1 lbf = 32 lbm ft/sec2 3. (30pts) Hydroelectric dams are a major source of energy in the US. When excessive rainfall occurs, the water level in the reservoir behind the dam may build up too high and emergency bypass pipes are installed to allow the water to flow directly downstream. Consider a rectangular concrete (e = 0.12 in) bypass pipe with crosssection 2ft × 3ft and length 300 ft. Water enters the pipe from an intake below the surface of the reservoir and discharges to the atmosphere at a point 200 ft below the surface of the reservoir. • Find the flow rate in the bypass pipe. Do not neglect changes in kinetic energy. Assume a constant ub for calculating lw 4. (35 pts) A pump with a cons...
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