Program : Bachelor of Mechanical Engineering (Hons) Manufacturing (EM221)

Bachelor of Engineering (Hons) Mechanical (EM220)

Course : Thermalfluids Lab
Course Code : MEC554
Laboratory Name : Fluids Mechanic Lab
Lecturer Name : Puan Siti Norazlina Binti Abd Aziz
Title of Experiment : Compressible Flow (Flow Characteristic Through The Convergent-
Divergent Duct)
Group : EMD5M6A



No. Student Name Student ID Number Signature
1.

Nurul Anati Binti Zulkifli 2013642408
2.

Siti Suraiya Binti Mohamed Iqubal 2013293728
3.

Wan Nurul Afifah Binti Wan Tarmizi 2013652462
4.

Muhammad Syafiq Haikal Bin Mohd Riduan 2013844828
5.

Zulfarizan Bin Zakaria 2013603504


Date of Practical Session Staff Certification (Signature)

25/09/2014


Date of Report Submission Staff Certification (Signature)

02/10/2014




FACULTY OF MECHANICAL ENGINEERING,
UNIVERSITI TECHNOLOGI MARA (UITM)
LABORATORY REPORT

TABLE OF CONTENTS












Page No:

CONTENTS



1.0 Tittle




2.0 Objective(s)



3.0 Introduction (background and theory)



4. 0 Apparatus



5.0 Experimental Procedure



6.0 Results & Data Analysis



7.0 Discussion of Results



8.0 Conclusion



9.0 References



1.0 TITTLE : Compressible Flow (Flow Characteristic Through The Convergent-
Divergent Duct)


2.0 OBJECTIVES

- To study the pressure-mass flow rate characteristic for convergent-divergent duct.
- To demonstrate the phenomena of choking.


3.0 INTRODUCTION

Converging-diverging nozzles designed for the accurate measurement and control of all
gaseous flow rates. This situation can be found in many engineering application including
steam and gas turbine, aircraft and spacecraft propulsion system, and even industrial blasting
nozzle and torch nozzle. A flow is considered to be a compressible flow if the change in
density of the flow with respect to pressure is non-zero along a streamline.
In general, this is the case where the Mach number in part or all of the flow exceeds 0.3.
The Mach 0.3 value is rather arbitrary, but it is used because gas flows with a Mach number
below that value demonstrate changes in density with respect to the change in pressure of less
than 5%. Furthermore, that maximum 5% density change occurs at the stagnation point of an
object immersed in the gas flow and the density changes around the rest of the object will be
significantly lower.
The factor that distinguishes a flow from being compressible or incompressible is the
fact that in compressible flow the changes in the velocity of the flow can lead to changes that
the temperature which are not negligible. On the other hand in case of incompressible flow, the
changes in the internal energy such as temperature are negligible even if the entire kinetic
energy of the flow is converted to internal energy like the flow is brought to rest.
The Mach number of the flow is high enough so that the effects of compressibility can
no longer be neglected. For subsonic compressible flows, it is sometimes possible to model the
flow by applying a correction factor to the answers derived from incompressible calculations or
modeling. For many other flows, their nature is qualitatively different to subsonic flows. A
flow where the local Mach number reaches or exceeds 1 will usually contain shock waves.
The behaviour of a fluid changes radically as it starts to move above the speed of sound
in that fluid which is when the Mach number is greater than 1. For example, in subsonic flow, a
stream tube in an accelerating flow contracts. But in a supersonic flow, a stream tube in an
accelerating flow expands. Consider that steady flow in a tube that has a sudden expansion
where the tube's cross section suddenly widens, so the cross-sectional area increases. In
subsonic flow, the fluid speed drops after the expansion. In supersonic flow, the fluid speed
increases. The mass flux is conserved but because supersonic flow allows the density to
change, the volume flux is not constant.

3.1 THEORY

Figure 3.1 : Convergent-Divergent Duct
Referring to the figure above, the steady energy equation between 0 and 2 is given by:

) 1 (
2 2
2 2 2
2
2
2
0 0
0
0
0
2 2
+ + + + + = + + + + f w w U gz
V P
q U gz
V P



For gas with small elevations differences, 0 = Agz
For the isentropic flow where there is no work is transferred, q=w=0, 0 is showing the
stagnation conditions, so 0 0 = V
Therefore,
RT P But
CvT
V P
CvT
P
becomes Equation

=
+ + = + +

,
) 2 (
2
0
) 1 (
2
2
2
2
0
0
0


So, ) 3 ( =
R
P
T

) 4 (
1
1

=
+ = =
+ =

R
Cv
CV
R
Cv
Cp
R Cv Cp

Substitute (3) and (4) into (2),
( )
) 5 (
1
2
2 1 1
2 1
1
1
1
1
1
1 2 1
2
2
0
0
2
2
2
2
0
0
2
2
2
0
0
2
2
2
2
2
2
0
0
0
0
2
2

|
|
.
|

\
|

=
+

+
|
|
.
|

\
|

+ =
|
|
.
|

\
|

+ + =

+








P P
V
V P P
V P P
R
P R V P
R
P R P



For isentropic flow;
) 6 (
1
2
2
0
2
2
0
0

|
.
|

\
|
=
=

P
P
P P

Substitute (6) into (5)
( )
) 7 ( 1
1
2
1
2
1
2
1
0
0
2
0
2
0 0
2 0
0
0
2
0
2
0 0
2 0
0
0
2
1

|
|
.
|

\
|

=
|
|
|
|
.
|

\
|

=
|
|
|
|
.
|

\
|

|
|
.
|

\
|

r
P
V
P
P
P
P P P
V
P
P
P
P P P
V
i

Where
0
2
P
P
r =

2
2 2 0 2 2
1
0
2
0 2 2 2 r V A V A
P
P
V A m =
|
.
|

\
|
= =
= ) 8 (
1
2
1
2
0
0
2 0 |
.
|

\
|

r r
P
A



.
m
4.0 APPARATUS




Figure 4.1 : Compressible flow bench.




Figure 4.2 : U-tube manometer (s.g.f = 13.6) Figure 4.3 : Motor speed controller











Figure 4.3 : Convergent-divergent duct






Figure 4.4 : Inclined manometer (s.g.f = 0.784)
5.0 EXPERIMENTAL PROCEDURE



1. All the electrical supply were switched off.
2. The respective tube were all connected to the compressor inlet.
3. The objects that can cause blockage were removed around the duct so that it would not
interfere with the air flow into the duct.
4. The throat valve were closed to ensure that no unnecessary manometer fluid to be drawn
into the compressor.
5. The inclined manometer tube were connected to read the (P
0
P
1
) and u-tube manometer
connected to read (P
0
P
2
) and (P
0
P
3
).
6. The speeds of the motor were set to zero before the Run button were pushed. The speeds
of the motor were increased by pushing the arrow that pointing upwards button of the
motor speed controller.
7. The motor speed starts at 4mm reading of incline manometer and the speed to be keep
increasing every 4mm reading of incline manometer until all the 24 complete reading were
taken.
8. The readings of barometric pressure P
0
was taken.

6.0 RESULTS & DATA ANALYSIS

Table 6.1 : Data of Result

No

P
1
(kPa)

h
2
(mm)

h
3
(mm)

P
2
(kPa)

P
3
(kPa)

P
0
P
1
(kPa)

P
0
P
2
(kPa)

P
0
P
3
(kPa)


r


(kg/s)
1. 101.30 0.0 0.0 0.00 0.00 0.00 101.30 101.30 0.0000 0.0000
2. 101.28 0.0 0.0 0.00 0.00 0.02 101.30 101.30 0.0000 0.0000
3. 101.25 2.5 0.0 0.33 0.00 0.05 100.97 101.30 0.0033 0.0627
4. 101.23 5.0 2.0 0.67 0.27 0.07 100.63 101.03 0.0066 1.0012
5. 101.20 7.5 3.0 1.00 0.40 0.10 100.30 100.90 0.0099 1.3116
6. 101.18 10.0 4.0 1.33 0.53 0.12 99.97 100.77 0.0131 1.5774
7. 101.15 10.0 5.0 1.33 0.67 0.15 99.97 100.63 0.0131 1.5774
8. 101.13 14.0 5.0 1.87 0.67 0.17 99.43 100.63 0.0185 1.9752
9. 101.11 15.0 5.0 2.00 0.67 0.19 99.30 100.63 0.0197 2.0570
10. 101.08 18.0 6.0 2.40 0.80 0.22 98.90 100.50 0.0237 2.3164
11. 101.06 23.0 8.0 3.07 1.07 0.24 98.23 100.23 0.0303 2.7076
12. 101.03 25.0 10.0 3.33 1.33 0.27 97.97 99.97 0.0329 2.8515
13. 101.01 30.0 11.0 4.00 1.47 0.29 97.30 99.83 0.0395 3.1960
14. 100.99 34.0 13.0 4.53 1.73 0.31 96.77 99.57 0.0447 3.4494
15. 100.96 37.0 15.0 4.93 2.00 0.34 96.37 99.30 0.0487 3.6351
16. 100.94 42.0 16.0 5.60 2.13 0.36 95.70 99.17 0.0553 3.9264
17. 100.91 47.0 19.0 6.26 2.53 0.39 95.04 98.77 0.0618 4.1970
18. 100.89 52.0 21.0 6.93 2.80 0.41 94.37 98.50 0.0684 4.4574
19. 100.86 57.0 24.0 7.60 3.20 0.44 93.70 98.10 0.0750 4.7049
20. 100.84 74.0 34.0 9.86 4.53 0.46 91.44 96.77 0.0973 5.4626
21. 100.82 82.0 40.0 10.93 5.33 0.48 90.37 95.97 0.1079 5.7871



Figure 6.1 : Graph vs. (P
0
P
2
)






Figure 6.2 : Graph vs. P
2



-1
0
1
2
3
4
5
6
7
0 5 10 15 20 25 30
vs. (P0 P2)
-1
0
1
2
3
4
5
6
7
0 5 10 15 20 25 30
vs. P2


Figure 6.3 : Graph vs. (P
0
P
3
)








Figure 6.4 : Graph vs. P
3



-1
0
1
2
3
4
5
6
7
0 5 10 15 20 25 30
vs. (P0- P3)
-1
0
1
2
3
4
5
6
7
0 5 10 15 20 25 30
vs. P3






Figure 6.5 : Graph (P
0
P
2
) vs. (P
0
P
3
)


-20
0
20
40
60
80
100
120
0 5 10 15 20 25 30
(P0 - P2) vs.(P0 - P3)
7.0 DISCUSSION OF RESULTS

NURUL ANATI BINTI ZULKIFLI 2013642408

The flow passages whose cross sectional area decreases in the flow direction. However,
the highest velocity to which gases can be accelerate in a converging is limited to the sonic
velocity, which occurs at the exit plane. Acceleration a fluid to supersonic velocity can be
accomplished only by attaching a diverging flow section to the subsonic at the throat. The
resulting combined flow section is a converging-diverging nozzle, which is standard equipment
in supersonic aircraft and rocket impulsion.
When mach number is less than 1 (m<1), that is subsonic velocity, then when mach
number is equal to 1 (m=1), the flow is sonic velocity and happened at the throat. When mach
number greater 1 (m>1) , it is supersonic flow.as shown above:

Figure 1 : The effect of back pressure on the flow through a converging diverging.

Chock flow is fluid flow through a restricted area whose rate reaches a maximum when
the fluid velocity reaches the sonic velocity at some point along the flow path. The
Phenomenon of choking exists only in compressible flow and can occurs in several flow
situation. Choked flow can occur through a convergent flow area or nozzle attached to a huge
reservoir. Flow exits the reservoir through the nozzle if the back pressure is less than the
reservoir pressure. When the back pressure is decreased slightly below the reservoir pressure, a
signal from beyond the nozzle exit is transmitted at sonic speed to the reservoir. The reservoir
responds by sending fluid through the nozzle. Further, the maximum velocity of the fluid exists
at the nozzle throat where the area is smallest.
When the back pressure is further decreased, fluid exits the reservoir more rapidly.
However, the velocity at the throat reachesthe sonic velocity. Then the fluid velocity at the
throat is sonic, and the velocity of the signal is also sonic. Therefore, further decreases in back
pressure are not sensed by the reservoir, and correspondingly will not induce any greater
flow to exit the reservoir. The nozzle is thussaid to be choked, and the mass flow of fluid
is a maximum.
From the experiment, the data are calculated and the graphs are plotted. The data in the
table shown when the absolute pressure(P
1
) is 101.3 kPa until 101.25 kPa, the mass flow
rate() are from 0 kg/s until 0.0627 kg/s, it is in subsonic. For pressure 101.23 kPa until
101.20 kPa, the mass flow rate is in between 1.0012kg/s until 1.3116kg/s, it is in sonic velocity
that flow at throat. And for pressure 101.18 kPa until last reading of pressure, the mass flow
rate is start from 1.5774 kg/s and increases until the last reading.it is in supersonic condition.
The graph in result shown that versus (P
0
P
2
), P
2,
(P
0
P
3
) , P
3
and (P
0
P
2
) versus (P
0

P
3
). The graph are plotted based on the result of experiment.
For the first graph, versus (P
0
P
2
), when the value of mass flow rate () increase,
the value of (P
0
P
2
) are also increase. This graph show that the relationship between mass
flow rate() and (P
0
P
2
) are directly proportional.
For the second graph is versus P
2
, when the value of mass flow rate increase, P
2
also
increase. At the earlier, the mass flow rate are still no change, it is zero and after increase to the
several pressure, it were increase. P
2
is a pressure that measure from the manometer which is
converted from mercury to Pascal.
For the next graph is vs. (P
0
P
3
) . P
0
is the atmospheric pressure which is 101.3
kPa.. The relationship of mass flow rate with the change of pressure at tube 3 and atmospheric
are directly proportional.
The Graph of versus P
3
shown when mass flow rate are increase, the pressure at point
3 also increases. So the relationship between mass flow rate with P
3
is also directly
proportional.
For the last graph is (P
0
P
2
) versus (P
0
P
3
) is plotted using the data obtain from the
experiment. From the graph shown that (P
0
P
2
) will increases until achieved maximum point
and start to decreases.
The values obtained from the experiment are different from theoretical value, which is
caused by some possible errors. Some possible errors are human error, instrument error, and
parallax error. Human error occurred as the students did not properly set up the apparatus,
which might be the apparatus were not tighten fully, such as press the pressure button not
carefully. It can affect the reading of the data. Next is instrument error is error caused by the
instrument itself. As the equipment worn through many times of usage, the data recorded might
not have been accurate therefore leading to the false result obtained from the experiment.
Lastly is parallax error, it will happened during reading the height of mercury. This problem
can be solved by ensuring that the eye must be perpendicular to the scale to get a better result.

SITI SURAIYA BINTI MOHAMED IQUBAL 2013293728


Compressible flow test laboratory were conducted to collect all the data required to
calculate the value of P
0
P
1
, P
0
P
2
, P
0
P
3
, r and . This value is then used to plot the
graphs which enable to describe the characteristic of the compressible flow test machine used.
From graph versus (P
0
P
2
), as the value of mass flow rate () increase, the value of
(P
0
P
2
) are also increase. This shows clearly the relationship between mass flow rate and (P
0

P
2
) which they are directly proportional.
For graph versus P
2
, the flow of graph were similar to the graph versus (P
0
P
2
),
where, as the value of mass flow rate increase P
2
increase. P
2
is a pressure that measure from
the manometer which is converted from mercury to Pascal.
Graph vs. (P
0
P
3
) is also plotted. P
0
is the atmospheric pressure which is 101.3 kPa.
As can be seen from the graph of mass flow rate versus (P
0
P
3
) is not much different from the
graph before. The relationship of mass flow rate with the change of pressure at tube 3 and
atmospheric was still directly proportional.
Relationship of mass flow rate with P
3
is also identified by constructing the Graph vs.
P
3
graph. As the value of mass flow rate increase slightly, while P
3
is also increase accordingly.
This proves their relationship to be directly proportional.
Lastly, graph (P
0
P
2
) versus (P
0
P
3
) is plotted using the data gain in the experiment.
As a result, there is a point which is the maximum value of (P
0
P
2
). Where before reaching
that maximum point of (P
0
P
2
), (P
0
P
3
) increases as (P
0
P
2
) increase. After that critical or
maximum point (P
0
P
2
), the value of (P
0
P
2
) started to decrease while (P
0
P
3
) increase
continuously.



Figure 1 : Converging Diverging Duct

The experiment is conducted by consequently increase the length by 5 mm. This length
effect the result. Especially the value of P
2
, where it increase fast compare to P
3
. This reflects
the value (P
0
P
2
) and (P
0
P
3
). It is increasing with a small different. Mass flow rate of this
Converging Diverging Duct is small. Where we can see theoretically, normally the value of
mass flow rate is not big.

WAN NURUL AFIFAH BINTI WAN TARMIZI 2013652462

Choked flow is a compressible flow effect which being influenced by fluid velocity.
Choked flow is a fluid dynamic condition associated with the Ventures effect. When a flowing
fluid at a given pressure and temperature passes through a restriction such as the throat of a
convergent-divergent nozzle into a lower pressure environment, the fluid velocity increases.
The choked flow circulation computes the mass flow rate through a pipe based on tank pressure
and temperature, pipe length and diameter, minor losses, discharge pressure, and gas
properties. This phenomenon usually occurs at the throat area or also known as the exit plane
of converging nozzle. This is because at the throat area only can produce the maximum Mach
number equals to 1.
The experiment used inclined manometer and U-tube manometer to measure pressure.
By looking at the graphs plotted, mass flow rate has linearly relationship with P
0
P
2
, P
2
, P
0

P
3
and P
3
. As the pressure values increases, the mass flow rate will also increase. Therefore, we
can conclude that as the different in pressure at convergent duct increase, the pressure of air
flow also increase. This is due to the increasing of velocity after passing through throat
although the flow area increase rapidly in the region. When the fluid density decrease, the
velocity passing the throat also increase.


Graph P2/P0 against

The values obtained are different from theoretical value, which is caused by some
possible errors. Those possible errors are human error and instrument error. Human error
occurred as the students did not properly set up the apparatus, which might be the apparatus
0
0.02
0.04
0.06
0.08
0.1
0.12
0 1 2 3 4 5 6 7
P
2
/
P
0


P2/P0 against
were not tighten fully. Apart from that it can also be due to the readings that we measured,
parallax error. This problem can be prevented by ensuring that the eye must be in line or
perpendicular to the scale to get an accurate reading. Instrument error is error caused by the
instrument itself. As the equipment worn through many times of usage, the data recorded might
not have been accurate therefore leading to the false result obtained from the experiment.



Figure above shows that the converging-diverging duct was cracked. This condition would
affect the results. Thus, for better result, maintenance should be done on the machines or
equipment.

MUHAMMAD SYAFIQ HAIKAL BIN MOHD RIDUAN 2013844828


1) Comparison of experimental results with the theoretical results.

The first part of this lab was to investigate the mass flow rates that were obtained from
different pressure ratios by using the Converging-Diverging nozzle. From calculations, using
some equations we resulted with a theoretical value of = 0.1186 kg/s.

On continuation of the experiment, and completion of result table using related
equations, the maximum mass flow rate achieved is 5.7871 kg/s. This is a very undesirable
result as it completely differs by 100 % of the maximum theoretical value. The possible error
for this outrange result is miscalculation. Next, the minimum pressure ratio (P
2
/P
0
) for
experimental value is 0. That means, it same with the theoretical minimum pressure ratio which
is also 0. However, the maximum theoretical value for pressure ratio (P
2
/P
0
) had been
calculated is 0.528 by using below equations:





While, for our maximum experimental value of pressure ratio (P
2
/P
0
) is 0.1079. The
percentage of error is about 20.44%, so it considered a quite accurate result. Based on the
experimental data, the graphs of versus (P
0
-P
2
), P
2
, (P
0
-P
3
), and P
3
were plotted. All of the
graphs showed that the relationship between and (P
0
-P
2
), P
2
, (P
0
-P
3
), and P
3
are directly
proportional. That means the higher either the values of (P
0
-P
2
), P
2
, (P
0
-P
3
), and P
3
, the higher
the value of mass flow rate, . However, on plotting out (P
0
P
2
) vs (P
0
P
3
), we found that
the corresponding relationship between both parameters is unstable. At first, the graph show a
steeply increased and then decreased gradually.


2) The discrepancies that bring about these differing results will be further discussed.

The second objective of this lab was to demonstrate the phenomena of choking. In the
experiment, the isentropic expansion of the fluid to supersonic flow is
dependent on the pressure ratios applied to the system. By measuring the linear variation of
pressure at different lengths through the nozzle it can be determined from existing literature
about what type of flow is occurring. These flow patterns can be seen over in Figure 1. During
the laboratory, these values were recorded in results table and plotted in graphs.

3) Analysis of experimental error.

It was felt after the conclusion of the lab, that number of factors could have caused P/P
0
discrepancies between the experimental and the theoretical results.


The biggest contributor to these, it was felt, was the positive displacement compressor. The
reason for this is the fluctuations that occur because of its method of operating in load and
unload cycles. Even with the pressure regulator and plenum being incorporated to the system to
smooth out the fluctuations there is still level of inherit error present. A very high level of
maintenance and calibration would be necessary to reduce these to a certain extent.

Next the fact that there was possible leaks in the back of the rig which can cause deviations
in the actual results obtained for which we could not correct. There possibly may have been
errors that went unnoticed in the lab with pressure gauges which could not count for a small
level of error.

It has to be mentioned that there could have been possible meniscus errors made by us
when reading the inclined manometer, although these are unnecessary mistakes they still need
to be mentioned.


Figure 1 : Different flow patterns for different pressure ratios.


ZULFARIZAN BIN ZAKARIA 2013603504


The term of Compressible Flow can be interpreted as the flow of fluid in which
variation in fluid properties such as density is significant due to pressure deviations. The
mechanics of compressible flow had been extensively employed in wide range of engineering
applications and technological processes such as the converging-diverging nozzles employed in
rocket engine, the steam and gas turbines In order to examine the characteristics of pressure
flow of air through a convergent-divergent duct and to visualize on how the properties of air
being affected by Mach number, the rightful comprehending on the fundamental theories
behind the physics of compressible flow are significant. The aim of this practical was to
investigate compressible flow in a convergent-divergent nozzle.
Theoretical value were done to find the maximum mass flow rate through the duct
which is ( = 0.1186 kg/s) as shown in equation below, and this was compared against actual
maximum recorded values that managed to get ( = 5.7871kg/s.) . Some of the factors that cause
different flow patterns are due to the defects or environmental factors that may be occur
during the experiment. For the minimum value for P
2
/P
o
of theoretical is ( = 0.528 kg/s) which
is differ to the experimental one that are managed to get around (=0.0627 kg/s).


Figure 2:Theoritical equation of
From the figure 1 that was stated in result analysis of graph (kg/s) vs (P
o
-P
2
) (kPa), it
can be concluded that the value of is directly proportional towards (P
o
-P
2
). As the value of
is increase, the value of (P
o
-P
2
) also increase. Figure 2 of graph vs P
2,
figure 3 of graph vs
(P
o
-P
3
), figure 4 of graph vs. P
3
are also in the same pattern which is directly proportional
between each other. However, on figure 5 for graph of (P
0
P
2
) vs. (P
0
P
3
), as the value of
(P
0
P
3
) increase, the value of (P
0
P
2
) are slightly in flat manner after reach of maximum
value for about 101.30 kPa.
The error that occur also may be influenced by the random error especially during the
experiment was conducted. For example the parallax error made by the observer during the
measurement of the inclined manometer. The eye of the observer does not point directly to the
right view. To overcome this problem, placing the eye vertically above the marking on the
scale or in specific word known as meniscus to be read. There are also systematic error occur
which that affected the calibration of the manometer that does not pointed on the right scale.
There are also possibly may have been errors that went unnoticed in the lab with pressure
gauges which could account for a small level of error.


.



8.0 CONCLUSION

In conclusion, the main objectives of this experiment were successfully achieved.
Following this laboratory it is evident that the analysis of a simple device like the Converging
Diverging nozzle is more involved than was originally anticipated. Main objective of this
experiment which to study the mass flow rate characteristic for convergent divergent duct was
obtained. Other than that, the phenomenon of choking was totally observed as another
objective.
For the results obtained for the maximum mass flow rates, the theoretical value is 0.1186
kg/s, while the experimental value is 5.7871 kg/s. It is assumed that the experimental value differed
very far to the theoretical value. There were some major errors that contributed to these results.
The first one is human errors which occurred caused by the students which did not properly set
up the apparatus, which might be the apparatus were not tighten fully. Besides that, the data
measured could be some sort of error. The second is instrument errors, which failure came
from instrument itself. The converging-diverging duct was cracked before starting the
experiment yet.
As the error prevention methods, data measured problem can be prevented by ensuring
that the eye must be in line or perpendicular to the scale to get an accurate reading. Moreover,
the apparatus should undergo maintenance time by time to provide the best result. The
challenges involved with designing such nozzles, for the hugely stressful environments that
occur in such applications varying from aerospace to civil engineering uses is made very
apparent.


9.0 REFERENCES

1. Fluid Mechanics Fundamentals And Applications Second Edition In SI Unit; by Yunus A. engel And
John M. Cimbala, Published By McGraw Hill International Edition 2010. In Singapore.

2. Fundamentals Of Fluid Mechanics 5
th
Edition, by Bruce R. Munson, Donald F. Young, Theodore H.
Okiishi, Publisher John Wiley & Sons, Asia, 2001.

3. Introduction To Fluid Mechanics Second Edition, by Robert W. Fox, Alan Mcdonald, Publisher John
Wiley & Sons.

4. Compressible flow (October 16, 2013). Retrieved November 10, 2013, from
http://en.wikipedia.org/wiki/Compressible_flow

5. Converging diverging nozzle (Mac 1, 2001). Retrieved November 10, 2013, from
http://www.engapplets.vt.edu/fluids/CDnozzle/cdinfo.html