UNIVERSITY OF EAST ANGLIA School of Mathematics Main Series UG Examination 2017-2018 ENGINEERING PRINCIPLES AND LAWS ENG-4002Y Time allowed: 3 Hours Attempt ALL QUESTIONS IN SECTION A and ANY TWO QUESTIONS IN SECTION B Graph paper will be provided. An information sheet is attached to the examination paper. Notes are NOT permitted in this examination. Do not turn over until you are told to do so by the Invigilator. ENG-4002Y Module Contact: Prof Lawrence Coates, MTH Copyright of the University of East Anglia Version: 1
2 SECTION A. 1. a) Define all the following terms and indicate units where appropriate, Yield strength, Limit of proportionality Ultimate Tensile Strength, Young s modulus, E Plastic strain after fracture,. [5 marks] b) Draw a stress-strain curve for a typical ductile metal and indicate on your diagram each of the terms described in (a) above. [3 marks] c) Explain, with the use of a force-distance curve for an atomic bond, each of the following: i. The breaking force of a bond, the equilibrium bond separation and the disassociation radius [2 marks] ii. How the magnitude of the binding energy typically relates to the Young s modulus of the bulk material [2 marks] 2. a) Describe the key indicators of criticality associated with the depletion of a material resource. Your answer should include at least one example of a material that is becoming scarce. [8 marks] b) Briefly describe how material-efficient design can be used to improve material sustainability. You should include at least one specific example in your answer.
3 3. Figure Q3 shows a constriction in a horizontal pipe with a flow of water passing from point 1 to point 3. The main pipe is 300mm diameter and the constriction is 150mm diameter. The velocity at point 1 is 2m/s. The pressure at point 2 is 80kPa and at point 3 is 100kPa. a) What is the head loss between points 2 and 3? Explain with the aid of a diagram how this head loss may have occurred. [8 marks] b) Justify any assumptions you make and then calculate the pressure at point 1. 300mm 150mm Figure Q3 4. a) Water is to be boiled at 100 C at sea level (1 atm pressure) in a 28cm diameter stainless steel pan placed on top of a 2.8kW electric burner. If 65% of the heat generated by the burner is transferred to the water during boiling, determine the rate of evaporation of water in kg/h. You may assume that the property of water: hfg = 2256.4kJ/kg at 100 C and 1 atm pressure. b) Argon in the amount of 2kg fills a 0.05m 3 piston-cylinder device at 600kPa. The piston is now moved by changing the weights until the volume is twice its original size. During this process the temperature of the argon is maintained constant. Determine the final pressure in the device. Take the gas constant of argon as R = 0.2081kJ/kg.K c) The inner and outer surfaces of a 5m x 6m brick wall of thickness 35cm and thermal conductivity 0.69W/m.K are maintained at temperatures of 25 C and 7 C, respectively. Determine the rate of heat transfer through the wall in W. TURN OVER
4 SECTION B. 5 a) Describe the essential requirements of a corrosion cell. Use a diagram of a corrosion cell to support your answer. [7 marks] b) In an off-shore structure that is exposed to aerated seawater, two dissimilar metals are bolted together. The standard electrode potentials, measured against the standard hydrogen electrode (SHE), of the two metals A and B and of the cathodic oxygen reduction reaction are given below: +2, = 1.06 +2, =+0.34! +4 +4" 2" 0, =+0.40 Given that the Gibbs free energy change, $ is related to the electrochemical cell emf, %&'', by $ = () %&'' where the terms have their usual meanings, i. Calculate the corrosion cell potential [2 marks] ii. Predict the anodic and cathodic reactions that will take place, state the overall reaction occurring and calculate the Gibbs Free energy for the reaction [6 marks] iii. Comment on the limitations of your calculations and predictions c) Considering the example given in (b), briefly describe methods that could be used to limit the corrosion rate or to prevent corrosion from occuring. [7 marks]
5 6. a) For flow in a pipe, the Darcy-Weisbach equation and the local loss equation are given respectively by, h = ' +,-. / and h '%0' =1 +,-. Express these equations in terms of the flowrate, Q, in the form, h = 2 3 and h '%0' = 4 3 stating clearly the expressions for K and C. b) Figure Q6 shows two reservoirs connected by two pipes in series. Pipe AB is 300mm diameter and 30m long. Pipe BC is 200mm diameter and 100m long. The difference in water level between the two reservoirs is 20m. Assume that the friction factor for both pipes is 0.018. i. Calculate the K values for the friction loss in the two pipes. ii. The head losses in addition to pipe friction include the entrance loss, the exit loss and a loss at the junction with a local loss k-factor of 1.2 based on the velocity head in the smaller pipe. Calculate the C values. iii. Determine the flowrate, Q, between the two reservoirs. k = 0.5 k = 1.2 20m A B k = 1 C Figure Q6 [Not to scale] c) To increase the flow a pump which delivers a head of 28.5m is used at the junction, B, and replaces the local loss at that point. By identifying a streamline from point 1 through to point 2, and allowing for head losses and head gains, or otherwise, determine the new flow. [5 marks] d) If the pump is 22m below the starting reservoir level calculate the pressure just upstream of the pump. Why is it important to check this pressure and is it likely to be a problem in this case? [5 marks] TURN OVER
6 7. a) A Carnot engine absorbs 280J of heat from a reservoir at 110 o C and rejects heat to a reservoir at 22 o C. Find, i. the heat rejected. [2 marks] ii. the work done by the engine,. [3 marks] iii. the thermal efficiency. [2 marks] b) A scientist claims to have developed a heat pump that produces a 250kW heating effect for a 22 o C heated zone while only using 80kW of power and a heat source at 5 o C. Justify the validity of this claim by calculation. [7 marks] c) A standing man can be modelled as a 32cm diameter, 177cm long vertical cylinder with both the top and bottom surfaces insulated and with the side surface at an average temperature of 35 o C. For a windy day, with a convection heat transfer coefficient of 12W/m 2 o C and the emissivity of the surface of his clothes is 0.9, determine the rate of total heat loss from this man in an environment at 18 o C. Given: Stefan Boltzmann constant: 5.670 10 8 W/m 2.K 4. [6 marks] d) Cold water at 12 o C (cp: 4180 J/kg.K) flowing at a rate of 1.5kg/s is to be heated to 45 o C by hot water (cp: 4190 J/kg.K) that enters at 95 o C at a rate of 3kg/s in a double pipe counter-flow heat exchanger. The overall heat transfer coefficient is 900W/m 2.K. Determine, i. the rate of heat transfer, [3 marks] ii. the heat transfer surface area of the heat exchanger [3 marks]
7 Information sheet INTEGRALS: 567 8 d7 = 678: +4, ( 1 (+1 5 1 d7 =ln7+4 7 CONSTANTS: R =8.31441 J mol.k Avogadro s number: 6.022 x 10 23 molecules/mol Stefan Boltzmann constant: 5.670 10 8 W/m 2.K 4 Mono-atomic gas: γ = 5/3 1.67 Air: γ = 1.4 Density of water: 1000 kg.m -3. Kinematic viscosity of water: 1 mm 2.s -1 CONVERSIONS: 1 atm = 101.325kPa = 760mmHg (torr) 1hp (horsepower) 745.7W T(K) = (T(ºF) 32)/1.8 + 273.15 END OF PAPER