UNIVERSITY OF EAST ANGLIA School of Mathematics Main Series UG Examination 2013-2014 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: Dr Lawrence Coates, MTH Copyright of the University of East Anglia Version: 2
0.8m 2 1. a) SECTION A Figure Q1 Given that the potential of iron (Fe) vs the standard hydrogen electrode (SHE) in aerated water was measured to be -0.4V, using the Pourbaix diagram provided as Figure Q1, predict what will happen to an iron component immersed in water. [4 marks] b) With reference to the Pourbaix diagram provided as Figure Q1, describe two methods of corrosion prevention that could be applied to iron in aerated water. Assume that the ph of the water environment is unchanged [8 marks] 2. Figure Q2 shows a pin-jointed structure comprised of light rods. a 2m b d 1m c 10kN Figure Q2 a) Calculate the horizontal and vertical reactions at the supports a and d. [3 marks] b) Calculate the tensile and compressive forces in each of the members and sketch a diagram showing these forces. [9 marks]
3 3. a) A horizontal transition pipe, carrying water under pressure, takes the diameter from 500 mm at point 1 to 300 mm at point 2, over a length of 15 m with a head loss of 50 mm. The velocity and pressure at point 1 are 0.2 m/s and 800 kpa respectively. Calculate the flowrate, velocity and pressure at point 2. [5 marks] b) Explain carefully using a neat annotated sketch the conditions that can cause cavitation in a pump. Explain also the impact that cavitation can have on a pump. [7 marks] 4. A vertical cylinder contains an ideal monoatomic gas. Inside is a piston which is leak-free and frictionless. The system is in equilibrium at 320K. The weight of the piston is 200N and its cross-sectional area 0.8 dm 2. During the initial state of equilibrium the bottom plane of the piston is at a height of 1m above the base plate of the cylinder. Consider the following two scenarios: a) An operator gently lowers a weight of 80N on top of the piston. Taken that the temperature remains constant, calculate the final height of the bottom plane of the piston above the base plate, the total work done on the gas, the work done by the operator and the heat transferred. [6 marks] b) We assume the same scenario of lowering the weight of 80N as in case a) but this time we insulate the cylinder and piston to prevent heat transfer in or out of the gas. Calculate the final height of the piston, the total work done on the gas and the heat transferred. [6 marks] TURN OVER
4 SECTION B 5. a) State the fast fracture condition and define all terms. [7 marks] b) A steel component with fracture toughness, K c of 54 MN m -3/2 is subjected to a tensile stress of 150 MNm -2. Calculate the critical crack length when fast fracture will occur in the material and state any assumptions made. [7 marks] c) Briefly describe what is meant by fatigue failure, using diagrams where appropriate [5 marks] d) Given that the fatigue crack growth rate for a material is described by: 5.1 Where A is a material constant and 5.2 Combine equations 5.1. and 5.2 to give a generalised expression for estimating the number of fatigue cycles, N, for which the initial crack length, a, doubles in length. [7 marks]
5 6. Figure Q6. shows a simply-supported beam of negligible weight supporting two vertical loads. a) Calculate the reactions at the supports a and d. [4 marks] b) Draw a clearly labelled shear force diagram for the beam. [5 marks] c) Calculate the bending moments at b and c. [5 marks] d) Draw the bending moment diagram for the beam. [6 marks] e) If the beam has a rectangular cross section of width 50mm and depth 300mm calculate the maximum bending stress in the beam. [6 marks] 100kN 50kN 1m 2m 1m a b c d Figure Q6 TURN OVER
6 7. a) A pipe of 200 mm diameter and 160 m long connecting two large, opentopped tanks is to be used to pump water from the lower to the upper tank. The difference in water levels of the tanks is 12.2m. Assuming that the pipe friction factor is 0.02 and allowing for abrupt entrance and exit losses show that the system characteristic is given by 2 12.2 904Q (m) where Q is in m 3.s -1. H sys [6 marks] Use gravitational acceleration as 9.807 m.s -2, and density of water as 1000 kg.m -3. b) A pump is to be positioned 20m along the pipeline from the lower tank at a position where the pipe is 3m above the lower tank water level. Sketch the situation and a typical energy and hydraulic grade line including entrance and exit losses. [5 marks] c) The data in table Q7 are from the centrifugal pump to be used. Plot the pump characteristic on the same graph as the system characteristic from part (a) and identify the duty point. Estimate the head, discharge, efficiency and input electrical power associated with the pump at this point. [10 marks] Table Q7. Centrifugal pump data for question 7. Q litres/s 0 20 40 60 80 100 H m 30.0 27.8 25.0 20.4 14.9 8.5 Efficiency % 0 45 65 71 65 45 d) Assuming that atmospheric pressure is 100kPa calculate the absolute pressure in the suction pipe just upstream of the pump. [5 marks] You are reminded that the head loss due to pipe friction may be expressed as, where the symbols have their usual meaning.
7 8. Consider a Carnot engine. a) Draw pv and TS diagrams of the Carnot cycle and describe each process within the diagram. [4 marks] b) Based on the work for each Carnot process, derive an expression for the Carnot efficiency. [8 marks] c) A Carnot engine operating on 1kg of air has the following state/process variables: Process 1-2 operates at T = 400K; Process 3-4 operates at T = 250K. State 3: V = 0.1m 3 ; State 4: p = 120kPa; Calculate the thermal efficiency and the work output for one cycle. [8 marks] (for air, the molecular mass is 28.97 g/mol and = 1.4) d) A Carnot engine produces 15 hp transferring energy between two reservoirs at 100⁰F and 250⁰F, respectively. Calculate the heat transfer rate in kj/s from the reservoir at the highest temperature. [6 marks] End of Paper
8 Thermodynamics information sheet INTEGRALS: CONSTANTS: Avogadro s number: 6.022 x 10 23 molececules/mol mono-atomic gas: = 5/3 1.67 air: = 1.4 CONVERSIONS: 1 atm = 101.325 kpa = 760 mmhg (torr) 1hp (horsepower) 745.7 W T(K) = (T(ºF) 32)/1.8 + 273.15