WONG Patrick (00548267)
1

WONG Patrick

CITY UNIVERSITY OF HONG KONG




Course code & title : MNE3122 Fluid Mechanics

Session : Semester B 2020-21

Paper : Paper B (Long Question)

Total time allowed : Two hours (120 minutes)



Instructions to candidates:

1. This paper consists of 4 questions.

2. Answer ALL questions and total mark is 70.

3. Give final answers with 3 significant figures and appropriate units.

4. Highlight all final answers.

5. Take g = 9.81 m/s2, water density = 1000 kg/m3 unless specified otherwise.


This is an open-book examination.
















IMPORTANT:
Submission MUST be via CANVAS. No other submission means, e.g., email, are accepted.
Academic Honesty Pledge

“I pledge that the answers in this exam are my own and that I will not seek or obtain an unfair
advantage in producing these answers;

I will not communicate or attempt to communicate with any other person during the exam; neither
will I give or attempt to give assistance to another student taking the exam; and

I understand that any act of academic dishonesty can lead to disciplinary action.”

Please reaffirm the honesty pledge by writing “I pledge to follow the Rules on Academic
Honesty and understand that violations may lead to severe penalties” onto the first
examination answer sheet.

WONG Patrick (00548267)
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Question (1): (20 marks)
(a) Water is to be heated from 20ºC to 87°C at a constant pressure of 100 kPa. The initial
density of water is 998 kg/m3 and the volume expansion coefficient of water is =
0.377 × 10ିଷ Kିଵ. Find the final density of the water.

(b) A container which is filled in three layers of different fluids is connected to a U-tube. For
the given specific gravities and fluid column heights, determine the gauge pressure at A.


(c) The two airflow networks [A] and [B] can also produce suction on the block mass.
(i) Describe the major difference between the design of [A] and [B].
(ii) Explain why network [B] is considered to be a better design than [A].
(iii) Which fluid mechanic theory is the design of network [B] based on?
(iv) Explain how the theory is applied in Design [B].

WONG Patrick (00548267)
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Question (2): (16 marks)
(a) A gas is accelerated from rest to a supersonic Mach number through a converging-diverging
duct. Consider it as an one-dimensional steady flow. Using the conservation of mass equation
( = constant) and the isentropic relations for the flow of a perfect gas with k = 1.4, show
that,

∗
=
(1 + 0.2 × ଶ)ଷ
1.728 ×

where A is the cross-sectional area of the duct and A* is the cross-section area at the throat.

(b) Dry air is to flow from a reservoir in which the temperature is 300 K through a convergent-
divergent nozzle at a mass flow rate of 0.8 kg/s. The entry velocity is negligible. At the
nozzle exit, the pressure is 20 kPa absolute and the Mach number 2.5. Assuming isentropic
flow, calculate:
(i) the reservoir pressure (଴),
(ii) the nozzle throat area (∗),
(iii) the nozzle exit area (ଶ), and
(iv) the air velocity at exit (ଶ).
Given: R = 0.287 kJ/kg K, and k of air = 1.4.



Question (3): (16 marks)
A fishing net consists of cylindrical threads 0.8 mm in diameter arranged on a square mesh of size
25×25 mm2. The size of the fishing net is 1 m2 square. If the net is towed at right angles to its plane
at 2.5 m/s through sea water (density 1026 kg/m3; absolute viscosity 1.20×10-3 Pa s),
(a) Determine the drag coefficient ஽ of smooth cylinder from Fig. 25 in lecture notes (Topic
10).
(b) Calculate the drag force.
(c) Find the power required to tow a net of total area 50 m2.


WONG Patrick (00548267)
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Question (4): (18 marks)
(a) A schematic of a number of streamlines with different stream functions is shown in the
following figure.

The fluid flow is two dimensional and incompressible. By the definition of streamline, the
velocity vector ሬ⃗ is always tangential to the stream line. Thus, there is no flow across a
stream line. It means that the flow rate between any of these lines are constant. and are
the velocity component of ሬ⃗ in x- and y-directions, respectively.
Prove the flow rate between any two streamlines to be the same by determining
i) the flow rate across AB, ୅୆,
ii) the flow rate across BC, ୆େ.
Hints:
=


+




(b) A two-dimensional duct is designed for a constant streamline flow field as,

2
+
3
2
+
7ଶ
40
= [mଶ s⁄ ]
The top and bottom walls of the duct are shaped following the streamlines. The stream
functions, , of the top and bottom walls are 5 and 0, respectively.
i) Using the result of part (a) to find the volume flow rate per unit width (into the page).
ii) State TWO assumptions that have been taken in the calculation of the volume flow
rate in (i).


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