Mech280final_2022
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University of British Columbia *
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Course
280
Subject
Mechanical Engineering
Date
Dec 6, 2023
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Pages
20
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Mech 280, Final Exam: April 20
th
2022 Name: Student number: Exam duration 2.5 hours, closed book
Instructions: 1.
Check that you have 20 pages and 5 questions. Answer all questions. 2.
3 single sided letter-sized sheets of notes are permitted. 3.
You may use a calculator. 4.
No wireless communication devices are permitted. 5.
Write your answers on the same sheet as the question. 6.
Put your name and student number clearly on the top of each sheet. 7.
Write neatly and structure your answers in a clear way. State physical assumptions that you make. 8.
Underline or box your final calculated answer for ease 9.
Live long and prosper Useful data: •
1 ft = 0.3048 m; 1 inch = 0.0254 m •
P
atm
= 101.325 kPa •
g = 9.81 m/s
2
. Centroid and centroidal moments of inertia for some common shapes
Mech 280, Final Exam: April 20
th
2022 Name: Student number:
Mech 280, Final Exam: April 20
th
2022 Name: Student number: Question 1. (20 marks) The pressure rise, ∆
P = P
2
-P
1
, across the sudden expansion shown can be expressed as ∆
P = f(A
1, A
2
,V
1
,
ρ
) where A
1
and A
2 are the upstream and downstream cross-sectional areas, respectively, ρ
is the fluid density, and V
1
is the upstream velocity. a.
(7 marks)
Express the above relationship in dimensional terms, using the Buckingham Pi theorem
Mech 280, Final Exam: April 20
th
2022 Name: Student number: Question 1. continued b.
(13 marks) Water is circulated from a large tank, through a filter, and back to the tank as shown. The power added to the water by the pump is 300W. Determine the Reynolds number Re
in the pipe, and the flowrate Q
through the filter. Take ρ
=1000kg/m
3
and µ
=1.3x10
-3
Pa.s Use the Moody chart and iterate at most 3 times
100m of 5cm diameter pipe with ε
/D = 0.001
Mech 280, Final Exam: Winter 2022 Name: Student number:
Mech 280, Final Exam: Winter 2022 Name: Student number: Q
uestion 2. (20 marks) Water (density ρ
=1000 kg/m
3
) is to be pumped from a large reservoir, open to the atmosphere, into a pressurised tank that 10 m higher than the surface of the reservoir. The tank pressure is 98.1 kPa gage pressure
. The reservoir and tank are connected by 50 m of 10 cm diameter pipe, and 4 elbows each with loss coefficient K=1.25. A centrifugal pump with impeller of size 199 mm and rotational speed n = 2900 rpm, with pump chart shown below, is to be used. You may assume a friction factor is f=0.018 for this question. P
atm
= 101.325 kPa, P
vapor
= 2.3 kPa a.
(8 marks) Find the characteristic equation of the system (h vs Q) and plot it on the pump chart to find the operating point of the pump. b.
(4 marks) How much electrical power 𝑊𝑊
̇
, is required for the motor that drives the pump? c.
(3 marks) We would like to change the impeller diameter so that the pump works more efficiently. What is your suggestion? d.
(5 marks) The pump is placed a distance x
pump
= 10 m from the reservoir, after 2 elbows. Is there a risk of cavitation if the pump is located 1m below the surface of the reservoir? If so, what do you advise? Explain inn sufficient detail.
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