Attempt ALL QUESTIONS IN SECTION A and ANY TWO QUESTIONS IN SECTION B Linear graph paper will be provided.

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1 UNIVERSITY OF EAST ANGLIA School of Mathematics Main Series UG Examination ENGINEERING PRINCIPLES AND LAWS ENG-4002Y Time allowed: 3 Hours Attempt ALL QUESTIONS IN SECTION A and ANY TWO QUESTIONS IN SECTION B Linear graph paper will be provided. A thermodynamics 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 2 SECTION A. Answer ALL questions. 1. a) Explain the essential requirements of a corrosion cell. b) Two metals are bolted together in a structure that is located on the coast and exposed to aerated seawater. 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: A e A, E θ = 0.76V B e B, E θ = +0.34V O 2 + 4e + 4H + 2H 2 0, E θ = +0.40V Given that the Gibbs free energy change, G is related to the electrochemical cell emf, E cell, by G = nfe cell where the terms have their usual meanings. Calculate the corrosion cell potential, predict the anodic and cathodic reactions that will take place and calculate the Gibbs Free energy for the reaction. Comment on the limitations of your calculations and predictions. [8 marks] 2. Write short notes, supplemented by sketches and equations, to describe the threat that over-exploitation is having on our ability to support the development of modern technology. [12 marks]

3 3 3. Figure Q3 shows the vertical, tapered outlet pipe, called a draft tube, downstream of a Francis Turbine discharging into a large reservoir. The draft tube is tapered from a diameter of 3 m at the top to a diameter of 5 m where it enters the downstream reservoir at an abrupt exit. The flow, Q, is 35 m 3.s -1 and the inlet to the draft tube, labelled point 1, is 6 m above the downstream reservoir water level. Assume the head loss in the draft tube is 0.1 m. a) Copy the diagram, label it clearly and by indicating a streamline starting at point 1 write down the continuity and energy equations that apply to this specific case using clear subscripts. [3 marks] b) Calculate the velocities and velocity heads at the top and bottom of the draft tube, at points 1 and 3. c) Hence calculate the pressure at point 1 relative to atmosphere. Explain briefly why it is negative. [5 marks] 3m 6m 5m Figure Q3 4. a) A vertical cylinder contains an ideal monoatomic gas. Inside is a piston which is leak-free and frictionless. The weight of the piston is 200N. During the initial state of equilibrium the bottom plane of the piston is at a height of 0.5m above the base plate of the cylinder. An operator gently lowers a weight of 120N on top of the piston. Taken that the temperature remains constant, calculate: i. The final height of the bottom plane of the piston above the base plate; ii. The total work done on the gas; iii. The work done by the operator; iv. The heat transferred. [8 marks] b) 1.5kg of Neon is initially at 800K and cools down to 250K following the polytropic process: pv 3 = const. Calculate the change in entropy knowing that the molecular mass of Ne 20g/mol. TURN OVER

4 4 SECTION B. Answer any TWO questions. 5 a) Explain the difference between a ductile material and a brittle material in terms of mechanical behaviour and give at least one example of each. Your answer should include a stress-strain diagram to illustrate the typical behaviour of a brittle and a ductile material under loading and, where appropriate, you should indicate on your stress-strain diagram the onset of necking, the yield point, Young s modulus, 0.1% proof stress and the plastic strain at fracture. Your answer should also include a brief description of the typical fracture morphology. [10 marks] b) Explain how martensite is formed in steel and how it causes a hardening of the material. Include diagrams to support your answer where appropriate. [9 marks] c) Describe the Quench and Tempering process and how it can be used to modify the properties of a steel. [7 marks]

5 5 6. A 360m long pipe of 250mm diameter connects two large reservoirs. The lower reservoir level is 15m below the upper reservoir level. Two identical pumps have been installed, in parallel, at a point 10m along the pipe from the lower reservoir to pump water to the upper reservoir. a) Assuming that the friction factor for the pipe is constant at and neglecting local losses, establish an expression for the system curve for the pipe in the form, H = H s + K Q 2 stating the values of HS and K when Q is expressed in m 3.s -1. b) Table Q6 shows the pump data for a single pump. Copy the data and complete enough of a table to show both the system curve and the combined pump curve. Hence plot a graph to identify the duty point and state the pump head and flowrate at this duty point. [10 marks] Table Q6 Flowrate, Q m 3.s Head, H m Efficiency, % c) Add to your graph the efficiency curve. Identify carefully the efficiency that each pump will operate at for the duty point stated in (b). Hence determine the total electrical power required to deliver the flow. [6 marks] d) One of the pumps is taken out of service for maintenance. Find the new duty point head, flow and power, and indicate the percentage reduction in flow when compared to (b) above, for this maintenance case. [6 marks] You are reminded that the head loss due to pipe friction may be expressed as, h f = f l u 2 2 g d where the symbols have their usual meaning. = 8 f l Q2 π 2 g d 5 TURN OVER

6 6 7. a) i. Sketch p-v and T-s diagrams of the Otto cycle clearly labelling the four states. Name the state transitions according to their thermodynamic properties. ii. Considering the nature of each of the state transitions and their corresponding thermodynamic equations, show that the efficiency of the Otto cycle,, is given by: η = 1 ( 1 r ) γ 1 where r is the compression ratio. [6 marks] b) A Carnot engine operating on 2.2 kg of air has the following state/process variables: Process a-b operates at T1 = 500K; Process c-d operates at T2 = 280K. State c: V = 0.35m 3 ; State d: p = 240kPa; Calculate the thermal efficiency and the work output for one cycle. [8 marks] (for air, the molecular mass is g/mol and = 1.4) c) Consider a room at a temperature of 21ºC. Outside the temperature is -5ºC. The temperature of the outer surface of a window is 3ºC. The window glass has a thickness of 4mm, has a total area of 2.5m 2 and its conductivity is 1.5W/(m.K). Outside the wind is blowing with a convective heat transfer coefficient of 110 W/(m 2.K). Calculate the rate of heat transfer in the glass and the convective layer. Draw a figure showing the temperature gradients from outside the window to inside (room). d) A heat exchanger is used to cool hot oil flowing at 20 kg/s from 420K to 310K. Water is used as a coolant and enters at 290K through a bundle of 12 tubes. The average velocity of water in a 24 mm tube is 4 m/s. The average specific heats of oil and water are 2.12 and 4.18 kj/kg.k, respectively. Determine the exit temperature of the coolant. END OF PAPER

7 7 Information sheet INTEGRALS: ax n dx = axn+1 + C, n 1 n dx = ln x + C x CONSTANTS: R = J mol. K Avogadro s number: x molecules/mol Mono-atomic gas: = 5/ Air: = 1.4 Density of water: 1000 kg.m -3. Kinematic viscosity of water: 1 mm 2 /s CONVERSIONS: 1 atm = kPa = 760mmHg (torr) 1hp (horsepower) 745.7W T(K) = (T(ºF) 32)/

Attempt ALL QUESTIONS IN SECTION A and ANY TWO QUESTIONS IN SECTION B Graph paper will be provided.

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