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UNIVERSITY OF SOUTHAMPTON FEEG1050W1
______________________________________________________
SEMESTER 2 SUMMATIVE ASSESSMENTS 2023-24
Engineering Problem Solving (Acoustical Engineering, Aeronautics
& Astronautics, Mechanical Engineering, Medical Engineering, Ship
Science)
DURATION: 8 Hours including up/download time
______________________________________________________
This paper contains 4 questions
Answer ALL questions.
Each question carries 25 marks out of a total of 100 marks for the exam paper.
You should be able to answer all these questions using the materials provided in your
modules. If you do use any other sources they should be referenced.
An outline marking scheme is shown in brackets to the right of each question.
Please put each solution in a separate PDF document and upload them all to the Part I
Blackboard site in accordance with the instructions given there.
Your documents can be computer-formatted, handwritten, or a combination of both. It is
your responsibility to ensure that the results are clear and legible.
Note that marks will only be awarded when appropriate working is given.
We recommend that you spend 120 minutes on this paper.
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Introduction
The Strenuis Ardua is a Tunnel Boring Machine (TBM) that is in the
final stages of detailed design. The project’s Chief Engineer, C. E.
Dunt, has identified several engineering problems that have arisen
in the design process, and has asked you to solve them.
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1. The TBM is propelled forwards by independently driven shafts.
Each cylindrical solid steel shaft (E = 205 GPa, ν = 0.3) has a
radius of 15 mm and is subject to torsion as shown in Figure.
Q1. A strain gauge attached to the outer surface of the shaft at
an angle of 35° with the longitudinal axis measures a strain of
460 μ-strain.
Figure Q1. Shaft subject to torsion.
i) Calculate the shear strain εxy at the surface of the shaft in the xy
reference frame and the corresponding shear stress σxy and
torque T.
[8 marks]
ii) Calculate the two-dimensional strain components εxx and εyy on
the surface if an additional tensile force F = 40 kN is applied to the
shaft in the longitudinal direction.
[3 marks]
iii) Draw Mohr’s circle for the two dimensional strain state at the
surface of the shaft for these combined loading conditions
including both torsion and uniaxial loading. Determine the
principal strains and the magnitude of the maximum shear strain
in any orientation. Clearly annotate your drawing with the values
of the relevant shear strains, position of the centre and principal
strains.
[7 Marks]
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iv)The yield stress of the material is 250 MPa and the safety factor
to be used in the design is 1.5. Maintaining the same torque as
before, use the Von Mises criterion to calculate the maximum
allowable tensile force.
[7 Marks]
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2. The rigid conveyor belt in Figure Q2.1 is used to move sample
bottles inside the TBM. As it accelerates along the line, the
bottle has two contact points with the belt at and .
Figure Q2.1 Sample Bottle on conveyor belt.
Table Q2.1 Parameters to be used in this question.
Description Parameter Value Units
Acceleration due to gravity 9.81 ms
2
Mass of a bottle 15 kg
Mass moment of inertia with
respect to G
0.328 kgm2
Distance between and 0.3 m
Position of 0.22 m
i) Draw the free body and kinetic diagram for the bottle in a condition
where there is no sliding, and the bottle does not tilt. You may
annotate the bottle diagram available in Figure Q2.3.
[5 marks]
ii) For the same condition as in (i), derive the equation of motion for
rotation with respect to point .
[4 marks]
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iii) Using the equation derived at (ii) calculate the value for the
acceleration of the belt that corresponds to the normal reaction
force at being equal to 10% of the bottle’s weight.
[4 Marks]
At the end of the line (position (1) in Figure Q2.2) the centre of
mass has a speed of 1 = 1.5 ms
1 and the bottle undergoes pure
rotation about point initially with angular speed 1 = 1/ . After
rotating 90 degrees about it reaches position (2) and then it
experiences free fall. Eventually it lands on a horizontal surface at
position (3).
Figure Q2.2: Bottle’s drop at the end of the line.
Table 2.2 Additional data for parts (iv) and (v)
Description Parameter Value Units
Distance between and 0.2 m
Speed of at (1) 1 1.5 ms
1
Angular speed at (1) 1 = / 7.5 rad/s
Drop distance m
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iv) Calculate the angular speed 2 of the bottle at the instant
corresponding to position (2).
[4 Marks]
v) Find an algebraic expression for and calculate the value of such
that the bottle rotates 180 degrees when in free fall between (2)
and (3) so that it lands on its side.
[8 Marks]
[Total 25 marks]
Figure Q2.3 For use in your free body and kinetic diagrams.
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3. At full scale when tunnelling through rock the Strenuis Ardua
ejects a rock/water slurry which has a density of 1220 kg.m-3 and
dynamic viscosity of 0.008 Pa.S. This fluid flows down a
trapezoidal channel at a velocity of 1 ms-1
, depth 200 mm. You
are asked to conduct small scale model testing where the depth
is 50mm.
i) Given that both Froude and Reynolds numbers must be
maintained between prototype and model determine the kinematic
viscosity of the fluid that must be used in the model.
[7 Marks]
The Strenuis Ardua will be powered by gas engine. The
temperature input to the turbine is 1120 degrees Kelvin and
pressure of 106 Pa. The turbine can be assumed to be adiabatic
and has a pressure ratio = 10. Assume air is used in the cycle
with properties R = 287 J.kg-1
.K-1
, CP = 1005 J.kg-1
.K-1 and
specific heat ratio γ = 1.4. The net work done by the engine is
15 MW.
ii) Determine the density and temperature of the air exiting the
turbine.
[8 Marks]
iii) Determine the specific work done by the turbine.
[2 Marks]
iv)If the work done by the compressor is 262 kJ.kg-1
, calculate the
required mass flow rate of air.
[2 Marks]
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Cutting oil of density ρ = 780 kg.m-3
is held in a reservoir within
the machine. The oil is delivered to the cutting head by
hydrostatic pressure, exiting the reservoir via a 1 m diameter
circular gate. The centre of pressure acts 50mm below the
centroid of the gate. Assume acceleration due to gravity g = 9.81
m.s
-2
.
v) Determine the depth of the oil above the upper edge of the gate.
[4 Marks]
vi) Calculate the force acting on the gate.
[2 Marks]
[Total 25 Marks]

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4.
Parts of a control circuit are shown below.
a) i) Calculate the current flowing through resistor R3 as shown
in Figure Q4.1.
[3 Marks]
Figure Q4.1
a) ii) Draw the Thevenin equivalent circuit of the network between
nodes A and B in figure Q4.2.
[3 Marks]
Figure Q4.2
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A logic circuit is shown in figure Q4.3 below:
Figure Q4.3. Logic circuit
a) iii) Write down an expression for the output, F, of this logic circuit.
[1 mark]
a) iv) Simplify your expression for F as much as possible using
Boolean algebra.
[2marks]
Consider a filter circuit depicted in Figure Q4.4, which consists of
a resistor and a capacitor. Applying AC circuit analysis
techniques, perform the following tasks:
b) i) Deduce the transfer function, denoted as ( ) =

, where
represents the angular frequency.
[3 Marks]
b) ii) Determine the circuit’s gain as ω approaches 0 and infinity
(∞). Based on these limits, conclude whether the circuit functions
as a low-pass or high-pass filter.
[2 Marks]
b) iii) Compute the circuit’s cutoff frequency, expressing your
answer in Hertz (Hz).
[2 Marks]
b) iv) Calculate the attenuation level introduced by the circuit to
a noise signal of 5Hz, presenting your answer in decibels (dB).
[2 marks]
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Figure Q4.4.
A Type K thermocouple (made of Chromel and Alumel) is
selected to condition monitor the head of the Tunnel Boring
Machine. The output voltage of the thermocouple is
approximated by V = aT + bT2
(in microvolts), where T is the
temperature difference between the junction and the reference,
maintained at 0oC (a = 39.45 μV.K-1 and b = 2.4×10-3 μV.K-2
).
c) i) Derive an equation for the sensitivity of this thermocouple as
a function of temperature.
[2 Marks]
c) ii) It is observed that under extreme conditions, the
temperature at the cutting head can reach up to 250oC. Calculate
the sensitivity of the thermocouple, when operating at this
temperature.
[2 Marks]
c) iii) Is sensitivity of this thermocouple linear or non-linear
Explain your reasoning.
[1 Mark]
c) iv) A non-inverting amplifier with gain 120 is used to amplify
the signal from the thermocouple. Draw a suitable circuit, with
appropriate resistor values. Do not consider reference junction
correction.
[2 Marks]
[Total 25 Marks]
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