Part -1:

Question 1:

(a) Choose an engineering solution that you consider to be ‘innovation by context' i.e. an invention, and explain why you consider your example fits this category of solution.

(b) Determine the increase in circumference of a copper hoop that is 1500 mm in diameter, when it is uniformly heated from 20 °C to + 350 °C. Take the temperature linear coefficient of expansion for copper as 17 × 10^-6 K^-1.

Question 2: Describe the principle of static equilibrium and explain how it is used in order to determine the distribution of internal forces within a truss.

Question 3:

A 500 g hammer, moving at 8 m s-1, strikes a nail and exerts a constant force on the nail of 4 × 10⁵ N. If the hammer bounces off at almost the same speed, determine the time the hammer is in contact with the nail.

Question 4: A small un-geared d.c. electric motor is powered using the manufacturer's recommended voltage for which it has a stall torque of 0.05 Nm and no-load speed of 7500 rpm.

When the motor is used to generate a steady torque of 0.032 Nm determine:

(a) The rate at which the motor spindle rotates.
(b) The mechanical power generated.

Question 5: A turbine disc in a modern jet engine has a mass of 150 kg, and spins at 10 000 rpm. Modelling the shape of the disc as a hollow shaft on axis where the inner and outer diameters are 250 mm and 1000 mm respectively calculate its kinetic energy when spinning at full speed.

Question 6:

(a) Calculate the thermodynamic efficiency of a steam turbine whose input and output temperatures are 560°C and 145°C respectively.

(b) Power generation companies spend millions of pounds researching high temperature materials for use in power stations. Explain how the calculation you have just done justifies this expense.

Question 7: Explain briefly how a correctly installed and operated ball bearing assembly, using a clean and appropriate lubricant, may still fail by metal fatigue when in use.

Question 8:

Explain why dislocations can strengthen metals but are unable to do so in ceramics.

A component made from steel, with a fracture toughness of 82 MPa√m, contains a crack that is known to be growing due to fatigue. At what stress can the component safely operate when the crack is 15 mm long? Take the value of Y for this geometry to be 1.12.

Question 9: (a) Sketch a cylindrical pressure vessel subjected to an internal pressure P, showing the three primary stress orientations indicating in which direction a crack-like defect would be most likely to cause failure when the internal pressure reaches a critical value.

(b) Determine the maximum stress in the wall of a cylindrical pressure vessel that is pressurized to 25 MN m-2. The vessel has a mean diameter of 1.6 m and a wall thickness of 0.05 m.

Question 10: (a) In terms of engineering solutions, briefly explain how ‘Innovation by development' differs from ‘Innovation by context'.

Briefly suggest how the development of the cantilevered diving board would fit into these two engineering solutions.

(b) A built-in cantilever carrying a uniformly distributed load, where w is 500 Nm-1, is illustrated in figure 1:
(i) Determine the maximum shear force on the cantilever.
(ii) Determine the maximum bending moment on the cantilever.
(iii) If the deflection of a cantilever is given by wL4/8EI, and the second moment of area, I, of the cantilever, is ab3/12, show that the cantilever deflects by about 40 mm.

Take L = 4.5 m, E = 25 GPa, a = 90 mm, b = 150 mm.

(c) Given that you are able to optimize both the cantilever's properties and dimensions, use the formulae given in b (iii) to explain how a cantilever can have a reduced deflection.

Figure 1 Figure for question 10, a built-in cantilever supporting a uniformly distributed load wL.

Question 11: (a) Full film lubrication implies complete separation of two components, one of which is moving relative to the other, yet there is still an energy loss. Explain briefly why this is and define the characteristic property of the lubricant that gives rise to this energy loss.

(b) Briefly outline the differences between full film and hydrodynamic lubrication, giving a practical example of each type.

(c) A simple sliding bearing with steel surfaces supports a steel block of mass 550 kg. Estimate,

(i) The horizontal force that would be required to initiate sliding under the following frictional conditions, no lubrication, mineral oil and molybdenum disulphide where = 1, 0.4 and 0.15 respectively.

(ii) The work done in displacing the mass a distance of 12 m when no lubrication is used.

(iii) Assuming you have a mass of 85 kg state with reasons, whether or not, you would be able to provide such a force on your own under any of these frictional conditions.

(d) Energy losses due to a lubricant can be considerable.

(i) Derive the formula for the power absorbed by the lubricant in one of the main bearings of a high-performance engine in terms of Petrov's equation; indicate what variable each term represents. Hence calculate the total power absorbed by a 6 bearing engine which has a radial speed of 6,750 rpm and in which each bearing produces a torque of 4.4 N m.

(ii) Calculate the energy lost by the bearings in 3 hours of continuous running.

Question 12 (a) Table 1 shows the galvanic series for metals in sea-water and beer.

(i) Explain when it would be appropriate to use each of the series to determine the possibility of corrosion.

(ii) Explain why, in industries handling various chemical solutions, neither of these galvanic series might be appropriate.

(iii) An aluminium pipe carrying beer is connected to a stainless steel tank. Determine the potential difference between the two and state which metal would corrode.

Table 1: Measured potentials, relative to mild steel, for metals in sea-water and in beer.

Metal                             Potential in 3% brine/V          Potential in beer/V

Aluminium                               -0.59                                -0.13

Brass                                      0.12                                 0.47

Copper                                    0.20                                 0.59

Graphite                                  0.42                                 0.75

Lead                                       -0.22                               0.21

Magnesium                               -1.40                               -1.25

Mild steel                                    0                                     0

Stainless steel                          0.11                                0.67

Titanium                                  0.30                                0.74

Zinc                                       -0.66                               -0.38

(b) During a fracture toughness test on a specimen made from aluminium with a yield strength of 410 MN m^-2, the failure stress was measured as 158 MN m^-2. Prior to testing, the length of the edge crack was measured and was found to be 7.5 mm long.

(i) Calculate the value of fracture toughness, KIC, for this particular aluminium. (Assume Y for this specimen geometry = 1.2).

(ii) This aluminium is used to manufacture the pipe for carrying beer. What is the maximum depth of an edge crack that can be tolerated, if the component is guaranteed not to fail by brittle fracture at a maximum service load equivalent to 50% of its yield strength? (Take Y for this geometry as 1.4).

(c) The aluminium pipe is expected to experience cyclic loading. Explain how failure may occur as a result of this form of loading.

(d) Periodically the pipe will be sterilized by maintaining it at an elevated temperature which may be sufficient to cause the pipe to creep. Briefly explain the mechanism of creep and how it can be avoided.

(e) Explain why, when an aluminium alloy is strengthened with a second phase, its optimum strength is dependent on time and temperature.

Part -2:

Question 1:

(a) Choose an engineering solution that you consider to be ‘innovation by development', and explain why you consider your example fits this category of solution.

(b) Determine the percentage increase in circumference of an aluminium hoop that is 0.75 m in diameter, when it is uniformly heated from -15 °C to + 250 °C. Take the temperature linear coefficient of expansion for aluminium as 24 × 10^-6 K^-1.

Question 2: Describe what is meant by a ‘composite material', and explain how reinforced concrete can be regarded as a composite material.

Question 3: Determine the angular velocity (in radians per second) a cylindrical space station must have in order to create a centripetal acceleration equal the acceleration due to gravity on Earth. The space station has a diameter of 750m.

Take the acceleration due to gravity as 9.81 ms^-2.

Question 4: Below is a specification table of a small d.c. electric motor:

(a) Calculate the motor efficiency if it is used at the ‘rated' torque and speed recommended by the manufacturer for continuous operation.

(b) Comment on what is likely to happen if the rated values are exceeded.

Question 5:  The maximum take-off mass of an Airbus A380 passenger jet is about 600,000 kg. The lift is provided by the wings which have a total area of 845 m².

Determine:

(i) the approximate take-off velocity of the jet when the lift-coefficient of its wings reaches 2.1.

Take the air density as 1.225, kgm^-3 and the acceleration due to gravity as 9.81 ms^-2.

(ii) the minimum thrust required from its engines to accelerate the jet to the take off velocity calculated in (i) if the runway length is 2.9 km.

Question 6:  (a) In considering heat engines what is meant by thermodynamic efficiency?

(b) A power station burns 155 kg of coal every second. Each kilogram of coal contains 23 MJ of chemical energy. The inlet stream temperature to the turbine is 395°C and the temperature at the outlet of the turbine is 205°C.

Determine the following:

(i) The total input power

(ii) How much power the station produces if the operational efficiency of the station is 27%

(iii) The theoretical thermodynamic efficiency, expressed as a percentage.

Question 7: Briefly describe what friction is and describe the mechanisms that gives rise to friction. Explain how lubrication reduces the effect of friction.

Question 8: Briefly explain the difference between yield strength and fracture toughness.

A component made from aluminium, with a fracture toughness of 35 MPa√m, contains a crack that is known to be growing due to fatigue.

At what stress can the component safely operate when the crack is 15 mm long? Take the value of Y for this geometry to be 1.12.

Question 9: To what temperature, in centigrade, does ice need to be cooled to prevent it from undergoing creep?

Question 10: (a) Discuss how the development of a supporting member such as I-beams and girders would fit into the three engineering solutions; ‘routine solutions', ‘innovation by development' and ‘innovation by context'.

(b) Figure 1 below shows a freely supported I-beam 4.0 m long which carries a point load and a uniformly distributed load. The point load, W, is 2500 N and acts 1.5 m from VA, while the uniformly distributed load w has a magnitude of 800 N m^-1.

(i) Establish the equation that satisfies vertical equilibrium for all of the forces acting on the I-beam shown in figure 1.

(ii) Using your equation from (i) and taking moments determine the vertical forces VA and VB, as shown in figure 1, required to support the I-beam.

Figure 1 Figure for question 10, a freely supported I-beam combining a uniformly distributed load, wL, with a point load W.

(c) Using the Engineer's Bending Equation:

(i) Show that the stress in an I-beam is zero at the neutral axis and a maximum on the surfaces farthest from the neutral axis.

(ii) For the same bending moment, explain how the radius of curvature of an I-beam can be maximized.

Question 11: (a) Explain briefly how a roller bearing can eventually fail even when clean and correctly lubricated.

(b) There is an energy loss associated with full film lubrication. Explain briefly why this is and define the characteristic property of the lubricant that gives rise to this energy loss.

(c) A turbine disc in a modern jet engine has a mass of 150 kg, and spins at 10000 rpm. Modelling the shape of the disc as a hollow shaft on axis where the inner and outer diameters are 250 mm and 1000 mm respectively calculate:

(i) The kinetic energy of the disc when spinning at full speed.

(ii) The linear velocity that a mass of 0.75 tonnes would achieve if all the energy calculated in (i) was available.

(d) Energy losses due to a lubricant can be considerable.

(i) Calculate the total power absorbed by one of the bearings in the jet engine which has a journal diameter of 55 mm, length 50 mm, radial clearance 0.025 mm and the oil has a dynamic viscosity = 32.5 x 10^-3 Pa s.

(ii) Calculate the energy lost by the bearing in 5 hours of continuous running.

Question 12 (a) Explain the mechanisms of deformation in metals, (such as stainless steel), ceramics and polymers outlining how their atomic structure is related to their behaviour during deformation.

(b) During a fracture toughness test on a specimen made from stainless steel with a yield strength of 525 MN m-2, the failure stress was measured as 335 MN m-2. Prior to testing, the length of the edge crack was measured and was found to be 8.0 mm long.

(i) Calculate the value of fracture toughness, KIC, for this stainless steel.

(Assume Y for this specimen geometry = 1.13)

(ii) This stainless steel is used to manufacture a pressure vessel which will operate at an internal pressure of 15 MPa. If the vessel has a diameter of 2.5 m and a wall thickness of 45 mm, determine the maximum stress in the wall of the vessel

(iii) Determine the maximum length of crack that the pressure vessel can contain if the vessel requires a safety factor of 2. (Assume Y for this specimen geometry = 1.2)

(c) The pressure vessel will be operated at an elevated temperature that may be sufficient to cause the vessel to creep. Briefly explain the mechanisms of creep and how its effect it can be avoided or reduced.

Part -3:

Question 1:  

(a) In cold climates, the temperature on the outward facing side of a window pane is often many degrees cooler than that on the side facing inwards. Describe the nature of thermal stress arising in such a glass pane that is tightly constrained around its edges and explain why they occur.

(b) Determine the percentage increase in circumference of an aluminium hoop that is 0.72 m in diameter, when it is uniformly heated from -20 °C to + 200 °C. Take the temperature linear coefficient of expansion for aluminium as 24 × 10-6 K-1.

Question 2: Sketch a typical stress-strain plot for steel that has a total elongation of 20% and a failure strength of 400 MPa. On your sketch, label the axes of your plot and the following points: elastic limit, tensile strength and 0.2% proof strength.

Question 3: A small un-geared d.c. electric motor is powered using the manufacturer's recommended voltage for which it has a stall torque of 0.05 Nm and no-load speed of 7000 rpm.

When the motor is used to generate a steady torque of 0.03 Nm determine:

(a) The rate at which the motor spindle rotates.

(b) The mechanical power generated.

Question 4:  The static coefficient of friction between the block shown in Figure 1 and the surface of the hinged ramp is θ and the mass of the block is m.

(a) show the forces acting on the block when it is on the point of sliding down the ramp.

(b) determine the minimum angle of the ramp at which the block will suddenly start to slide and accelerate down the ramp.

(c) calculate the angel in (b) if the coefficient of friction between the block and the surface of the ramp is 0.2.

Figure 1 Figure for Question, a block on a hinged ramp. (Recall that tan θ = )

Question 5: After take-off a large jet airliner climbs to altitude at an angle of 18° to the horizontal.

(a) Sketch and label the forces due to lift and the weight of the airliner acting on the airframe.

(b) If the airliner weighs 300 tonnes, calculate the lift force when climbing at this angle. Explain how the remainder of the lift force is generated.

Question 6:  Describe the difference between boundary lubrication and full film lubrication, giving an example of each.

Question 7:

(a) A 400 kg communications satellite orbits the Earth in geostationary orbit (i.e. it remains in a fixed position in the sky from the point of view of an observer on Earth) at an altitude of approximately 36200 km. Given that the radius of the Earth is about 6400 km, calculate the following:

(i) The satellite's tangential velocity.

(ii) The satellite's kinetic energy.

(b) Explain why much more energy than that calculated in (ii) had to be supplied to launch the satellite into this orbit.

Question 8:

(a) Two potential failure mechanisms for metals are creep and fatigue. Briefly explain the difference between creep and fatigue of metals.

(b) An alloy steel has a melting temperature of 1327 °C, determine whether this steel will creep when operating at a temperature of 600 °C.

Question 9:  A gas cylinder has a diameter of 300 mm and is required to store compressed gas at a pressure of 50 MPa. What is the minimum thickness that the cylinder needs to have if the maximum permissible stress in the cylinder wall is 250 MPa?

Question 10: (a) List the three categories of engineering solutions to problems.

Using the three categories referred to in part (a), consider the historical development of boats. Discuss how the progressive development of boats would fit in to each of these categories.

(b) A cantilever beam carrying a uniformly distributed load is shown in Figure 2:

(i) Sketch the free-body diagram of the beam.

(ii) If the length of the beam is 2m and the uniformly distributed load, w, has a magnitude of 800 Nm-1 calculate the reaction forces and the moment at the built-in support end of the beam.

(iii) Derive expressions for bending moment and force equilibriums and explain how the shear force and bending moment vary along the length of the beam.

(iv) Sketch a bending moment diagram for the beam.

(c) Using the Engineer's Bending Equation explain with the aid of a sketch how the bending stress is distributed through the thickness of the beam.

Figure 2 Figure for question 10, a cantilever beam carrying a uniformly distributed load, wL.

Question 11: (a) Corrosive wear is one of the four mechanisms of wear between two surfaces in contact. Briefly explain the process of corrosive wear.

(b) Give one example where the wear of materials in sliding contact is undesirable and one situation where friction between materials in sliding contact is desirable.

(c) A turbine disc in a modern jet engine has a mass of 125 kg, and spins at 8000 rpm. Modelling the shape of the disc as a hollow shaft on axis where the inner and outer diameters are 300 mm and 1000 mm respectively calculate:

(i) The kinetic energy of the disc when spinning at full speed.

(ii) The linear velocity in kmh-1 that a 2 tonne mass would achieve if all the energy calculated in (i) was available.

(d) (i) A high performance engine has 5 main crankshaft bearings and runs at 18,500 rev min^-1. Other data for the bearing are given below. Calculate the maximum torque and therefore the power absorbed in the main bearings when the engine is running at the oil reference temperature of 40° C.

Bearing Parameters:

Journal diameter = 52 mm

Bearing axial length = 26.4 mm

Radial clearance = 0.025 mm

Oil viscosity = 35.2 x 10^-3 m² s^-1

Oil density = 890 kg m^-3

(ii) Calculate the total energy loss of bearings in 3 hours of continuous running.

Question 12: (a) A steel pressure vessel is operating at a power station. Answer the following questions relating to potential corrosion issues:

(i) Stress-corrosion cracking is the accelerated corrosion of a material. List three important factors that lead to stress-corrosion cracking.

(ii) Figure 3 shows the design for a joint of the pressure vessel connecting two pipes that carry flowing water. You should assume that the pipes are full of flowing water. Identify two possible corrosion mechanisms that might arise in service from the use of this design, and suggest how they could be alleviated.

Figure 3 Figure for question 12(a)(ii), connection between two pipes.

(b) The power station burns 140 kg of coal every second. Each kilogram of coal contains 30 MJ of chemical energy. The electrical power output of the station is 980 MW. The inlet steam temperature to the turbine is 380 °C and the temperature at the outlet of the turbine is 160 °C.

Calculate:

(i) The total input power.
(ii) The operational efficiency of the station, expressed as percentage.
(iii) The theoretical thermodynamic efficiency, expressed as percentage.

(c) For operational safety the design of the pressure vessel requires that the stress intensity at the tip of any crack-like defect should not exceed 40% of the fracture toughness of the steel used, and any defect should not exceed a length of 8 mm.

Under these conditions determine the maximum permissible stress that the steel, which has a toughness of 160 MPa √m, can experience. Take Y = 1.12 for this geometry.

(d) Grain size strengthening is one of the methods to increase the strength of the steel used to manufacture the pressure vessel. By aid of a mathematical model explain how change in grain size is used to strengthen the steel.