2021_Final_Exam
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Queensland University of Technology *
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Course
CIVL3150
Subject
Geography
Date
Dec 6, 2023
Type
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8
Uploaded by DrAlbatrossPerson87
Semester Two Final Examinations, 2021
ENVE3150 Environmental Systems Dynamics
and Modelling
Page 1 of 8
This exam paper must not be removed from the venue
School of Civil Engineering
EXAMINATION
Semester Two Final Examinations, 2021
ENVE3150 Environmental Systems Dynamics and Modelling
This paper is for St Lucia Campus students.
Venue
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Seat Number
________
Student Number
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First Name
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Semester Two Final Examinations, 2021
ENVE3150 Environmental Systems Dynamics
and Modelling
Page 2 of 8
Examination Duration:
120 minutes
Reading Time:
10 minutes
Exam Conditions:
This is an Open Book examination
Casio FX82 series or a calculator on the UQ approved list
During planning time - students are encouraged to review and plan responses to
the exam questions
This examination paper will be released to the Library
Materials Permitted In The Exam Venue:
(No electronic aids are permitted e.g. laptops, phones)
None
Materials To Be Supplied To Students:
1 x 6-Page Answer Booklet
1 x Multiple Choice Answer Sheet
Instructions To Students:
Additional exam materials (eg. answer booklets, rough paper) will be
provided upon request.
Answer part A on MCQ answer sheet.
Answer part B in answer booklet
For Examiner Use Only
Question
Mark
Total
________
Semester Two Final Examinations, 2021
ENVE3150 Environmental Systems Dynamics
and Modelling
Page 3 of 8
Part A.
True/False. Each question worth 0.5 mark.
1. Sensitivity analysis is the systematic variation of model inputs to examine the
resulting change in model output.
T
2.
A parameter is a value, which is constant in the case concerned but may vary from
case to case where a case can represent a different model run.
T
3.
Black-box
models are used when the equations describing the system are
inaccessible.
T
4.
Unlike static models, a dynamic model omits reaction processes that generate or
consume the stocks.
F
5.
A system can stop being at steady state and become dynamic again through the
incorporation of new inflows or modifications in their parameter values.
T
6. In systems with overshoot and collapse, the system contains at least two
interdependent stocks.
T
7.
In a model that calculates the volume of water in a reservoir, if the variation of the
surface area is given by a table displaying the values as a function of the depth,
the surface area is still considered an algebraic variable.
T
8.
A model is validated by fitting it to data that cannot be used to calibrate the model.
T
9.
An analytical solution can be applied to determine how sensitive the model output
is to each of the input parameters.
F
10. Algebraic variables are functions of stocks and therefore the value of an algebraic
variable must be updated at each timestep.
T
MCQ questions
11. (2 marks) Consider a lagoon at constant volume with the outflow equal to
the inflow q (L ·h
-1
). The water contains dissolved organic matter at a
concentration of S
o
[mg.L
-1
], which is reduced due to biological degradation
(k[h
-1
]) to concentration S. Which of the following expressions is the correct
stock flow equation for the dissolved organic matter?
a.
V(dS/dt)=q(So-S)-kSV
(Correct solution)
b. S=qSo/q+kV
c. V(dS/dt)=qSo-qSi-kV
d. S=Si
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Semester Two Final Examinations, 2021
ENVE3150 Environmental Systems Dynamics
and Modelling
Page 4 of 8
e.
None of the above
12. (2 marks) Analyse the following SFD diagram, which of the flows contribute to
a linear decay?
a.
The Pumped outflow
(Correct solution, but this will have relied
on some assumptions for this particular system covered in
ENVE3150 in 2021)
b. The Produced outflow
c. The Consumed outflow
d. Pumped and Consumed outflows
13. (3 marks) Select the code that can solve for X the following microbial growth
equation with µ
max
, K
s
, b and S constant parameters for a time length of 40 days.
a. i=1:40; X=i.*Y*X-b*X; % Y=(µ
max
*S/Ks+S) is a constant value
b.
for
i=1:40
X(1)=x0;
X(i+1)=X(i)+((X*U*S))/(K+S)- b*X) *1; %All constants have been assigned.
end
c. [t,X]=ode45(@microbialgrowth,[0 10], X0) %%All constants have been
assigned
gen = (X*V*Y*q*S))/(K+S);
death = b*X*V;
function X= microbialgrowth(t,X)
X=gen-death;
end
(Answer c. was assigned as the correct solution, although there is an error in this
solution.
Time span in [t,X]=ode45( . . . ) should be [0 40], not [0 10]).
Semester Two Final Examinations, 2021
ENVE3150 Environmental Systems Dynamics
and Modelling
Page 5 of 8
Part B. Open answers
14. Draw the causal loop diagram of the following systems and indicate any
reinforcing feedback loop or dampening feedback loop.
a. (2 mark) As global temperatures rise, the polar ice caps may begin to
melt. This will increase the surface area of water on the earth and
decrease the surface area of the ice caps. Because water is less
reflective than ice, the earth's albedo will decrease, and more sunlight
will be absorbed by the earth's surface. Temperatures will climb as this
happens.
b. (2 mark) Sunlight increases vegetation, vegetation decreases soil
erosion, soil erosion decreases mass of soil, mass of soil increases
vegetation growth.
Global
temperature
Polar ice
Surface area
of water
Albedo
Sunlight energy
absorbed by earth
-
-
-
-
+
(+)
Sunlight
Vegetation
Soil erosion
Mass of soil
+
-
-
+
(+)
Semester Two Final Examinations, 2021
ENVE3150 Environmental Systems Dynamics
and Modelling
Page 6 of 8
15. In project 1 you developed a model describing the combustion of a liquid fuel
assuming that the temperature of the flame was constant (Tf). The maximum
rate that Tf can increase can be approximated by considering the heat of
combustion (H
c
), which is the total amount of heat released when a unit
quantity of a fuel (at 25°C and at atmospheric pressure) is oxidized
completely and assuming there is no heat transfer to the surrounding air or
the liquid. The energy balance for the flame will therefore be:
where χ is an efficiency factor (<1.0) that accounts for incomplete
combustion, ṁ is the rate that liquid fuel is vaporised and Cp is the heat
capacity of air.
a.
(2 marks) Draw the Stock and flow diagram that represents the energy
of the flame.
b. (2 marks) Indicate any algebraic variable in the system.
Question 15 related to last year’s 1
st
project on the combustion of a pool of
petroleum.
The analysis involved a number of assumptions, knowledge of
which is required to solve this problem.
This is out of scope of the material
covered in ENVE3150 this year.
16. (2 marks) Explain the difference between sampling time and time step in
models and provide an example where these two differ.
Solution
Projects 1 and 2 in 2022 presented examples of this difference.
In Project 1, the
mass of the ice cylinder was measured on 6 occasions in 3 replicate experiment,
while you simulation of the melting process may have involved hundreds of time
steps (e.g.,
t = 1 sec).
Similarly, the algae concentration in 2019 was measured
on 12 occasions, but your simulation may have involved
t values of 1 day or
smaller.
17.
A river section as shown in the figure below receives contaminated water
from an upstream tributary (A). The contaminated water mixes with the clean
water from another tributary (B) at the junction and flows downstream
through the river section (a fully mixed condition is assumed at the junction).
The discharges from tributary A and B are 5 and 15 m
3
/s, respectively. The
cross-sectional area of the river is constant and equals 200 m
2
. The
concentration of the concerned chemical in the water from tributary A is 15
g/l. The flow in the river is assumed to be uniform and at the steady-state.
The initial concentration of the chemical in the river is assumed to be zero.
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Semester Two Final Examinations, 2021
ENVE3150 Environmental Systems Dynamics
and Modelling
Page 7 of 8
a. (2 marks) Develop a model to quantify the mass of contaminant in the 200 m
river section, which can be considered as a single stock. Include all the
stock-flow balance equations, flow rate equations and other needed
equations involved in the model.
Solution
Consider the mass of contaminant as a stock:
𝑉
𝑑𝐶
𝑑𝑡
= 𝑄
𝐶
− (𝑄
+ 𝑄
)𝐶
where
C = concentration of contaminant in the river section [g.m
-3
]
b. (2 marks) Develop a numerical solution to the mathematical model (using the
Euler method) and write down the pseudo code (algorithm) for
implementing this solution.
Solution
C(1) = 0;
t
= 5;
For i = 1:nt
𝐶(𝑖 + 1) = 𝐶(𝑖) + (𝑄
∗ 𝐶
− (𝑄
+ 𝑄
) ∗ 𝐶(𝑖))
∆௧
;
end
c. (2 marks) Show how the size of time step affects the numerical solution. For
each time step size, carry out the calculations by hand (following the
algorithm from b) for three different time steps.
Solution
I will not ask a lengthy calculation question like this in the 2022 exam. To
illustrate the calculation, the first 3 steps for
t = 5 sec would be:
C(5)
= 0 + [5*15x10
3
-
(5 + 15)*0 ]*5/(200
2
)
=
9.375 g.m
-3
C(10) = 9.375 + [5*15x10
3
-
(5 + 15)*9.375 ]*5/(200
2
)
Semester Two Final Examinations, 2021
ENVE3150 Environmental Systems Dynamics
and Modelling
Page 8 of 8
= 18.727 g.m
-3
C(10) = 18.727 + [5*15x10
3
-
(5 + 15)*18.727 ]*5/(200
2
)
= 18.73 g.m
-3
END OF EXAMINATION