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Department of Biomedical Engineering

ENGR30002 – Fluid Mechanics

Semester 2, 2020 Final Exam

Online open-book strict-time-limit exam and submission via Canvas Quiz

This paper has 15 pages including this page, the exam and the supplementary material.

Timing



Authorised materials


Academic misconduct during exams
• Collusion is not allowed under any circumstances. Collusion includes, but is not
limited to, talking to, phoning, emailing, texting or using the internet to
communicate with other students. Similarly, you cannot communicate with any
other person via any means about the content of this exam during the examination
time. If another student contacts you during the examination period, please inform
the subject coordinator immediately.

• Exam start time: 3 pm Tuesday 17 November 2020
• Exam end time: 5.45 pm Tuesday 17 November 2020; you must submit all
responses by this time.
• Exam duration: 165 minutes in total composed of
o Reading time: 15 minutes
o Writing time: 120 minutes
o Submission time: 30 minutes from 5.15 pm to 5.45 pm Tuesday 17 November
2020

Alternative Exam Arrangements (AEAs) time settings may vary from the above.


This exam will be conducted in an online open-book format and the following materials
are permitted:
• Any material loaded onto Canvas as part of the subject content
• Notes (printed, hand-written, and digital/electronic)
• Textbooks
• Online books and materials
• Language dictionaries
• Calculators (any model), computers, electronic tablets, pens, rulers, etc.
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• Plagiarism/copying is not allowed under any circumstances. Your answers to the
exam must be in your own words and not directly copied from lecture notes, tutorial
materials, the internet or study notes you have prepared with your friends. You may
refer to sources, but answers should be written in your own words. This also applies
to programming (code) related answers. Code must be written on your own
displaying originality in the content.

• Any similarity detected between your answers, the answers from other students
and/or from the internet or other sources will be investigated and may result in
academic misconduct proceedings.

Instructions to students

• You will have only one attempt at completing this online exam.
• The recommended browser for this exam is Google Chrome.
• Total marks for this paper are [120].
• For this remotely conducted exam, you may write answers during reading time.
• Do not write answers during submission time. This time is for submitting your work.
• Attempt all 7 questions, which are of unequal value.

• Answer multiple-choice questions directly within the quiz.
• Answer short-answer and essay questions directly within the quiz.
• Answer file upload questions by uploading photos/scans of your responses.
• For file upload questions:
o Write legibly, preferably in blue or black pen.
o You may use an electronic tablet to write your answers, but all answers must
be written using a stylus pen or similar.
o Ensure your student number is written on each answer page that you upload.
o Start each question on a new page and write the question number in the top
right-hand corner.
o Number each page prior to submission to indicate the order of the pages
o Show all working for each question.
o Responses that span multiple images need be compiled into single PDF
documents.
o The Genius Scan phone app can be used to generate such PDFs.
o PDFs of responses written on electronic tablets are also acceptable.

Communication and issues during the exam
• Any updates to the exam will be made by the Subject Coordinator via a Canvas
Announcement during the exam.
• If you need to ask any exam content-related questions during the exam, please
contact your Subject Coordinator via the dedicated Exam Support Chat tool in your
Canvas subject immediately.
• If you run into any issues uploading your responses, please email your responses to
david.collins@unimelb.edu.au prior to the end of your submission time. In your
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email, attach your responses and clearly state the subject code, your name and
Student ID.
• For all technical and wellbeing enquiries, please contact Stop 1/13MELB via:
o Phone: 13 6352 (inside Australia) and +61 3 9035 5511 (outside Australia)
o Web chat: https://ask.unimelb.edu.au/app/ask?chat


Paper to be lodged with Baillieu Library























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Question 1 [22 marks]
Briefly answer the following questions.
A. Consider two pipes, one 0.5m in diameter and another that is 1m in diameter with a small but
non-zero surface roughness. The flow in both is turbulent, and has the same flow rate in both
cases.
a) Which of these will have a higher friction factor? The smaller diameter pipe or the larger
diameter pipe?
b) Over a given length of pipe, which one of these will have a greater proportion of energy that
is lost due to friction? The smaller diameter pipe or the larger diameter pipe?
[2 marks]

B. What are the SI units for each of these terms in the following equation?





[2 marks]

C. What are the SI units for each of these terms in the following equation?





[3 marks]

D. For each of these equations, write whether they are most appropriate for (1) Newtonian fluids,
(2) Shear-thinning fluids, (3) Shear-thickening fluids or (4) Bingham plastics.
a) || = + |


|

, || >
b) = −



c) || = |


|

, < 1
d) || = |


|

, > 1
[4 marks]



Question continued on next page
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E. Which of these parameters will remain constant along the length of a constant diameter pipe in
steady state compressible flow?
a) velocity
b) density
c) mass flow rate
d) pressure
[2 marks]
F. We have a pump moving fluid from a tank. Describe in a few sentences how to find this system’s
operating point.
[3 marks]
G. What is the equivalent hydraulic diameter (in m) of the trapezoid below?

[3 marks]
H. Examine the following figure and state whether each of the following statements (a to f) are true
or false. Path A and Path B start at the point where these paths branch off. The walls have a
finite roughness value (in mm) that is identical for both paths.

a) The frictional losses along path A are greater than along path B.
b) The flow rate along path A is less than the flow rate along path B.
c) If flow along path B is turbulent then flow along path A will always be laminar.
d) The pressure at the start of path A must be greater than the pressure at the start of path B.
e) The fluid velocities are identical in path A and path B
f) If both flows in A and B are turbulent, the fanning friction factor will be greater for path A
than path B
[3 marks]



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Question 2 [24 marks]
Water is pumped from a large open tank, through a filter, and back to the tank as shown in the
figure below. The power added to the water by the pump is 30 W. The piping has a length of 30 m
on the suction side of the pump and 30 m on the discharge side, a diameter of 3 cm, and contains
one valve and five elbows as shown below. The Fanning friction factor is 0.01.


Density of water
Atmospheric pressure
Vapour pressure of water

Equivalent length of one elbow
Resistance coefficient of the filter
Resistance coefficient of the valve
Resistance coefficient of pipe entry
Resistance coefficient of pipe exit
1000 kg/m3
101.3 kPa
2.3 kPa

25D
12
6
0.8
1.0

a) Determine the volumetric flowrate of water through the filter in liters per minute. You
should include the resistance of pipe entry and exit.
[9 Marks]

b) Calculate the available NPSH for the flow described above when the pump is located 3 m
below the surface of the water in the tank.
[6 Marks]

c) If the required NPSH is 2 m, is cavitation likely to occur? Explain your answer.
[3 marks]

d) Calculate the maximum vertical distance below the water surface that the pump can be
located without cavitation occurring.
[6 marks]





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Question 3 [18 marks]
Fluorine gas at 50 oC is flowing isothermally at a rate of 0.036 kg/s through 8 m of straight horizontal
pipe of internal diameter 13 mm and absolute roughness 0.04 mm. The pressure at the start of the
pipe is 342 kPa. Assume the gas behaves ideally.
Molecular weight of fluorine
Viscosity of fluorine at 50 °C
Gas constant
38 g/mol
0.31 x 10-4 Pa s
8.314 J/mol K
a) Calculate the pressure at the exit of the pipe. You may ignore the kinetic contribution to
simplify your calculation.
[8 marks]

b) Calculate the gas velocity at the exit of the pipe as a percentage of sonic velocity.
[5 marks]

c) Using the result from part b, is the flow choked? If not, what is the critical length so that the
flow will become choked?
[5 marks]



















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Question 4 [20 marks]
Couette flow describes the situation where flow is induced when a fluid is bounded by two flat walls.
In this case the bottom one is moving (left to right at velocity U) and the top one is stationary.

a) Use the equation of continuity and the equations of motion to derive an expression for the
x-component velocity profile as a function of the height between the two plates (H), the
velocity of the lower plate (U) and the distance above the bottom plate (y). Solve for the
velocity profile, v(y), as a function of these variables. This needs to be in the context of the
coordinate system shown in the diagram (the maximum velocity is at y = 0), and you
should show your work.
[14 marks]

b) If the height of the upper plate is 1 cm, the lower plate velocity is positive 0.1 m/s and the
fluid viscosity is 10 kg/ms, what is the magnitude of the shear stress acting on the top plate?
In which direction is it acting?
[6 marks]














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Question 5 [14 marks]
An open channel flow (moving left to right) encounters an obstacle with a height of 0.05 m, directly
above which the free surface drops so that its height above the bed is 0.5 meters. The flow above
this obstacle moving at 1 m/s. After the obstacle, the bed at ③ returns to the level as at ①. There
are no hydraulic jumps in this system.



a) What is the Froude number of the flow directly above the obstacle? Is this flow supercritical,
critical, or subcritical?
[4 marks]
b) Is the incoming flow supercritical, critical, or subcritical? What is the specific energy, in
metres, of the upstream flow?
[6 marks]
c) Solutions to the third-order polynomial to solve for the upstream height above the bed (h1)
are -0.13, 0.17 and 0.56. What is the height of the free surface above the bed downstream
of the obstacle (h3) in meters?
[4 marks]













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Question 6 [8 marks]
You’re working on a new microrobot with the same size and shape as a 3 µm long bacterium, which
typically travels at speeds of 10 µm/s in water (µ = 0.001 kg m s-1). Because microfabrication for
these microrobots is very expensive, you want to test cheaper larger scale models in your lab that
will allow you to optimize your design. If your models are each 1.5 cm long and your pump in your
test tank creates a flow of 0.1 cm/s, what is the viscosity of the fluid you should use with your model
that will allow you to best replicate the ratio of forces affecting the bacteria? You can assume that
you are adding a different fluid to water to modify the model fluid viscosity that does not noticeably
affect the density of the fluid, where the combined solution remains Newtonian.
























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Question 7 [14 marks]
A large container with pressurized gas is being held in place by a rod. The container is emitting air at
a velocity of 40 m/s through a small 0.5 cm diameter orifice on one side of the container. The density
of the gas emitted from the container is 1.9 kg/m3.
(a) Calculate the mass flux (in kg/m2s) at the outlet
[4 marks]
(b) Calculate the volumetric flow rate (in m3/s) at the outlet
[4 marks]
(c) Calculate the force exerted by the rod to keep the container in place. In which direction is
this force acting (give answer in terms of +, −, + and/or −)
[6 marks]


Supplementary materials only from this point














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Various constants

Parameter Value Units
Density of water 1000 kg/m3
Density of mercury 13600 kg/m3
Ideal gas constant 8.314 J/mol K
Atmospheric pressure on earth (sea level) 101.3 kPa
Molar mass of air 29 g/mol
Molar mass of carbon 12 g/mol
Molar mass of oxygen 16 g/mol
Molar mass of hydrogen 1 g/mol
gravity on earth 9.8 m/s2
gravity on mars 3.7 m/s2

Given equations

ℎ2
ℎ1
=
−1 + √8Fr2 + 1
2


ℎ =
(ℎ2 − ℎ1)
3
4ℎ1ℎ2






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END OF EXAM