fluid final exam

1. ENGR 2860U Exam Page 1 of 3
ENGR 2860U: Fluid Mechanics
Final Examination
December 10, 2013 8:00 – 11:00AM
UB2080
Professor: Dr. Jennifer McKellar
Instructions
1. Duration: 3 hours
2. Textbook allowed; this must be a published edition of Munson, Okiishi, Huebsch and Rothmayer.
Other resources, including class notes and aid sheets, are NOT allowed.
3. If you use text from the book, remember to make proper use of quotation marks and citations.
4. An electronic, non-programmable “hand” calculator is allowed. Other electronic devices, including
laptops and cellphones, are NOT allowed.
5. Answer each question in the exam booklets provided. CLEARLY INDICATE WHICH QUESTION YOU
ARE ANSWERING. Write your name and student number on each booklet that you submit.
6. All calculations must be shown. If you use a figure or table from the textbook, clearly indicate which.
7. Presentation is important. Marks will be deducted for poor presentation (e.g., illegible). Point form
is acceptable, but use complete sentences.
8. Some figures are from the textbook but have been modified.
Questions (38 marks total)
1. Answering the following questions.
a. Identify the absolute and gauge pressures at Points 1 and 2 from the figure below. (2 marks)
b. The stream function for an incompressible, two-dimensional flow field is given below. Is this an
irrotational flow? (3 marks)
Ψ = 5x2
+ 7y
c. For steady, laminar flow between fixed parallel plates, the velocity profile is parabolic in shape.
If the shear stress is given by τ = μ∂u/∂y, what is the shear stress at the midpoint between the
two plates? (1 mark)
i. maximum shear ii. negative shear
iii. zero shear iv. equal to the wall shear
Pressure(Pa)
120
100
80
60
Local atmospheric
pressure reference
Absolute zero reference
2
1

2. ENGR 2860U Exam Page 2 of 3
2. For the inclined-tube manometer shown below, the pressure in pipe A is 7.0 kPa, and that in pipe B
is 4.0 kPa. The gauge fluid in the manometer has a specific gravity of 3.0. What is the specific
gravity of the fluid that is in both pipes A and B? (3 marks)
3. You are designing the water system for a house next to a lake. Since the house is not connected to
the city water supply, water will be pumped directly from the lake to the house. The house is
situated 10 m (vertical) above the water level in the lake. You have a 15 cm diameter pipe running
from the lake to the house, and a pump located in the house’s basement that generates a pressure
of -20 kPa (suction) in the pipe. If you want to achieve a flowrate of at least 0.03 m3
/s, is your pump
strong enough? Neglect viscous effects for now. (3 marks)
4. The same house in Question 3 is thinking of using “pumped storage” as a means of reducing their
electricity bills. They will pump water from the lake up to a large reservoir overnight, and then
during times of peak power prices, release the water to run back down to the lake, through a
turbine. The turbine will generate power for the house. In this case, the large reservoir (a big pond)
is located 8 m (vertical) above the water level of the lake. The pipe exiting the turbine is 20 cm in
diameter; the turbine is at the same level as the lake. The homeowners plan to restrict the flowrate
to 0.2 m3
/s. What is the maximum possible power output of the hydroelectric turbine in this case?
(4 marks)
5. You work for a company that designs carnival games. You have been asked to design a game in
which a jet of air will be used to knock over a block (the first person to knock over all their blocks
wins). The air compressor at the carnival (portion shown below), will pressurise the air to 5 kPa.
The block is held in place by a force FH, acting through its centroid from behind. The air jet will hit
the block in its centre from the front. What is the maximum value FH can have in order for the game
to work? Assume the flow to be incompressible and frictionless. (4 marks)
SG = 3.0
35°
12 cm
10 cm
16 cm
p = 5 kPa
FH
Area = 0.04 m
2
Area = 0.01 m
2

3. ENGR 2860U Exam Page 3 of 3
6. Sluice gates are commonly used to regulate flow in open channels: sliding the gate vertically up or
down directly impacts the flowrate of fluid under the gate. The flowrate, Q, depends on the depth
of water behind the gate (i.e., upstream), the depth of the water downstream of the gate, the width
of the gate, and the acceleration due to gravity. You have been asked to do some experiments
related to sluice gate design. To simplify the process you first decide to identify a suitable set of
dimensionless variables for this problem. What are these variables? (6 marks)
7. You work for a solar energy company and have been tasked with helping to design the piping system
for a community-scale solar thermal water system. The system requires pumping a solution of
ethylene glycol (viscosity = 0.10 N∙s/m2
; density = 1100k g/m3
) through the system. You are focused
on one section of pipe: It is 5 m long, at an angle of 60° from the horizontal, and has a diameter of
20 cm. If you need to attain a flowrate of 0.04 m3
/s, what pressure drop will your pump need to
overcome? (4 marks)
8. As part of your work for the solar energy company, your boss has asked you to determine the head
loss for a solar hot water heating system for one house in particular. This consists of a loop of piping:
from the pump to the roof, through the solar collector, and down to the pump again. You are still
working with the ethylene glycol solution (viscosity = 0.10 N∙s/m2
; density = 1100 kg/m3
), but now
your entire system uses galvanized iron piping 11 cm in diameter and will have a flowrate of 0.09
m3
/s. You estimate you will have a total length of straight pipe of 25 m, four regular 90° flanged
elbows and one fully open globe valve. What is the head loss the pump will need to overcome? (6
marks)
9. You are assisting with the design of a new aircraft wing. You are at the very early stages of the
design and doing some preliminary calculations. For convenience, you decide to treat the wing as a
flat plate. To help with your experiments, you want to achieve a turbulent boundary layer at a
distance of 0.5 m from the leading edge of your prototype wing. What wind speed should you use in
the wind chamber to achieve this? (2 marks)
ENGR 2860U Exam FINAL 9Dec13.docx