Laboratory Manual for Basic Mechanical Engineering by Dr. Anil Singh Yadav & Prof. Sachin Kumar Nikam

Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

Q8. What type valve is a feed check valve of a boiler?
a) One-way valve
b) Globe valve
c) Reversible valve
d) Disc check valve

Q9. What is the function of safety valves in the boiler?
a) To prevent excessive steam pressure
b) To prevent excessive air pressure
c) To prevent water pressure
d) To prevent from rising temperatures

Questions for Viva-Voce Q10. What happens due to high temperature of feeds water in the
economizer?
a) Fuel consumption increases
b) Fuel mechanical efficiency increases
c) Fuel consumption decreases
d) Fuel mechanical efficiency decreases

Mechanical Engineering Department | Lab Manual | Basic Mechanical Engineering [BT-203] 170

In fluid dynamics, Bernoulli's
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micrometer screw gauge, is a device
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amesneecwrhgaeynll.icTaalsheenmgpoirnsitenecmriipnelgcehaiansndincmaamlacethrdiandaienfstg,er
aDloanngiel Bweritnhoulliotwhehro pumbelitsrohleodgiictalin
ihnisstrubmoeonkts Hsuycdhroadsydniaaml, ivcearniienr, 1a7n3d8.
dAigltihtaolucgahlipeBrse.rnoulli deduced that
pressure decreases when the flow
speed increases, it was Leonhard
Euler who derived Bernoulli's
equation in its usual form in 1752.

Bernoulli's Principle

Experiment# 15

Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

15 EXPERIMENT NO. 15

Bernoulli's Theorem

Bernoulli's Theorem AIM
To verify the Bernoulli’s theorem.

APPARATUS
Experimental test rig, stop watch and scale

THEORY
The principle of conservation of energy gives rise to Bernoulli’s which
states that if an incompressible ideal fluid (i.e. no losses and specific mass
constant throughout) flows through a closed passage, the total head, i.e.
the sum of datum head Z, pressure head P/w and velocity head V2/2g will
be constant at all points. i.e.

P/w +Z +V2/2g = constant at all points

But the validity of above theorem is subject to
(i) the flow being steady,
(ii) fluid being frictionless, that is, inviscid
(iii) an ideal fluid.

A real fluid encounters a continuous loss of energy (or head loss) due to
friction and minor losses. Taking into account a loss of head hL between
section 1 and 2

P1/w+Z1+V12/2g = P2/w+Z2+V22/2g+hL

In this equation the sum of P1/w+Z1 is known as piezometric head
measured above an arbitrary datum. The sum of piezometers head and
kinetic head (i.e. P/w+V2/2g+Z) is called total energy.

EXPERIMENTAL SET UP

Fig. 15.1 shows the schematic diagram of apparatus for verification of
Bernoulli's theorem. This Bernoulli's theorem Apparatus does not require
any foundation, trench work, etc., so that we can conduct experiment with
keeping the unit anywhere. The apparatus consists of a converging
diverging duct issuing out of a water container and discharging into
another. Piezometric connections are made at equal intervals to show
pressure heads at different sections. The discharge is measured by
collecting a known volume of water in time t. The water flow to the
apparatus can be regulated by inlet valve. Another valve is fitted at the
end of duct to get sufficiently low pressure at the central tube. A scale
may be used for measurement of water level in piezometric tubes.

Mechanical Engineering Department | Lab Manual | Basic Mechanical Engineering [BT-203] 171

Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

Bernoulli's Theorem Figure 15.1 Apparatus for Verification of Bernoulli's Equation

Part names:

1-7: Piezometers (a transparent tube with scale) are connected at

various cross sections of the duct (cm2).

S. No. 1 2 345 6 7

Cross sections 20.25 14.44 9.61 5.76 9.61 14.44 20.25
area

8: Stainless Steel duct (for low friction).
9: Single Phase motor with pump (pump capacity is 0.5 HP, single

phase 20 volts, 2800 RPM and pump of size 25 mm to discharge
about 15 LPM at 30 Meter total head).
10: Flow control valve.
11: Supply tank.
12: Delivery Tank.
13: Supply tank drain control valve.
14: Out flow Control valve.
15: Drain valve from discharge tank.
16: Discharge measuring tank (25cm x 25cm Area).
17: Water storage tank.

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Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

OBSERVATION
Area of collecting tank, A = 25cm x 25cm= 625 cm2

OBSERVATION/CALCULATION TABLE

Area Discharge

of Rise of
Square H= P/w
S. Passage Water Time Q= V V/2g h= +Z
No. level (t) RxA/t =Q/A (cm) P/w + Z
(A= (sec) (cm3/s) (cm/s) + V2/2g
BxW) R (cm) (cm)
(cm2) =r2 –r1
(cm) h1= H1=
h2= H2=
A1=20.25 V1= h3= H3=
h4= H4=
Bernoulli's Theorem A2=14.44 V2= h5= H5=
h6= H6=
A3=9.61 V3= h7= H7=
Q1= V4=
1. h1= H1=
A4=5.76 h2= H2=
h3= H3=
A5=9.61 V5= h4= H4=
h5= H5=
A6=14.44 V6= h6= H6=
A7=20.25 V7= h7= H7=
A1=20.25 V1= h1= H1=
A2=14.44 V2= h2= H2=
h3= H3=
A3=9.61 V3= h4= H4=
h5= H5=
2. A4=5.76 Q2= V4= h6= H6=
h7= H7=
A5=9.61 V5=

A6=14.44 V6=
V7=
A7=20.25 V1=
A1=20.25 V2=

A2=14.44

A3=9.61 V3=

3. A4=5.76 Q3= V4=

A5=9.61 V5=

A6=14.44 V6=
A7=20.25 V7=

PROCEDURE

1. Clean the apparatus and make all tanks free from dust.
2. Ensure that On/Off Switch given on the panel is at Off position.
3. Close the all drain valves provided.

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Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

Bernoulli's Theorem 4. Now switch On the main power supply (220 Volts AC, 50 Hz).
5. Switch On the Pump.
6. Fill sump tank atleast ¾ with clean water and ensure that no

foreign particles are there.
7. Operate the flow control valve to regulate the flow of water.
8. Close the flow control valve given at the end of test section
9. Open By-Pass Valve given on the water supply line.
10. Measure pressure head by Piezometer tubes.
11. Measure the height of water level in tubes after the steady state

condition achieve.
12. Measure the flow rate using the water collected in the measuring

tank during the particular time interval.
13. Repeat steps the same procedure for different flow rates of water

operating control valve and By-Pass valve.
14. When experiment is over, Switch Off Pump.
15. Switch Off Power Supply to Panel.
16. Drain water from all tanks with the help of given drain valves.

FORMULAS USED

Compute the area of cross section ‘A’ at a given section (if not given)

A=B x D

Discharge Q=A x (r2 – r1)/t

Velocity of flow V=Q/A
V2 /2g (Take g=981 cm/sec2)
Velocity head

Datum head should be taken as zero (Z=0)

Piezometric head h=P/w+Z
H=P/w +Z +V2/2g
Total head

CALCULATIONS =
Case-1:
Q1=A x (r2 – r1)/t = V12 /2g=
V22 /2g=
V1= Q/A1= = V32 /2g= =
V2= Q/A2= = V42 /2g= =
V3= Q/A3= = V52 /2g= =
V4= Q/A4= = V62 /2g= =
V5= Q/A5= = V72 /2g= =
V6= Q/A6= = =
V7= Q/A7= = =

Mechanical Engineering Department | Lab Manual | Basic Mechanical Engineering [BT-203] 174

Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

Bernoulli's Theorem H1= P/w+ Z+ V12/2g= =
H2= P/w+ Z+ V22/2g= =
H3= P/w+ Z+ V32/2g= =
H4= P/w+ Z+ V42/2g= =
H5= P/w+ Z+ V52/2g= =
H6= P/w+ Z+ V62/2g= =
H7= P/w+ Z+ V72/2g= =

Case-2: =
Q2=A x (r2 – r1)/t =
V12 /2g=
V1= Q/A1= = V22 /2g= =
V2= Q/A2= = V32 /2g= =
V3= Q/A3= = V42 /2g= =
V4= Q/A4= = V52 /2g= =
V5= Q/A5= = V62 /2g= =
V6= Q/A6= = V72 /2g= =
V7= Q/A7= = =

H1= P/w+ Z+ V12/2g= =
H2= P/w+ Z+ V22/2g= =
H3= P/w+ Z+ V32/2g= =
H4= P/w+ Z+ V42/2g= =
H5= P/w+ Z+ V52/2g= =
H6= P/w+ Z+ V62/2g= =
H7= P/w+ Z+ V72/2g= =

Mechanical Engineering Department | Lab Manual | Basic Mechanical Engineering [BT-203] 175

Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

Case-3:

Q3=A x (r2 – r1)/t = =

Bernoulli's Theorem V1= Q/A1= = V12 /2g= =
V2= Q/A2= = V22 /2g= =
V3= Q/A3= = V32 /2g= =
V4= Q/A4= = V42 /2g= =
V5= Q/A5= = V52 /2g= =
V6= Q/A6= = V62 /2g= =
V7= Q/A7= = V72 /2g= =

H1= P/w+ Z+ V12/2g= =
H2= P/w+ Z+ V22/2g= =
H3= P/w+ Z+ V32/2g= =
H4= P/w+ Z+ V42/2g= =
H5= P/w+ Z+ V52/2g= =
H6= P/w+ Z+ V62/2g= =
H7= P/w+ Z+ V72/2g= =

RESULT

For different flow rates of water, it is observed that
Total head H=P/w +Z +V2/2g ≈ constant at all seven points

Hence, Bernoulli’s theorem is verified.

PRECAUTIONS

1. Never switch on power supply before ensuring that all the on/off
switches given on the panel are in off position.

2. Never run the pump at low voltage.
3. Never fully close the Delivery & By-pass line valves

simultaneously.
4. Always keep the apparatus free from dust.
5. Frequently grease/Oil the rotating parts, once in three months.
6. Always use clean water.
7. If the apparatus will not be in use for more than one month, drain

the apparatus completely.

Mechanical Engineering Department | Lab Manual | Basic Mechanical Engineering [BT-203] 176

Questions for Viva-Voce Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

REVIEW QUESTIONS
Q1. What is Bernoulli equation?
Q2. What are the assumptions used in Bernoulli Equation?
Q3. What is an ‘ideal fluid’?
Q4. What will be the value of Reynolds number for an ideal fluid?
Q5. Write some practical applications of Bernoulli's equation.

WRITE YOUR ANSWERS HERE
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Mechanical Engineering Department | Lab Manual | Basic Mechanical Engineering [BT-203] 177

Questions for Viva-Voce Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

MULTIPLE CHOICE QUESTIONS (✔)

Q1. Chimney works best on principle of
a) equation of continuity
b) Bernoulli's equation
c) light equation
d) speed equation

Q2. Fundamental equation that relates pressure to fluid's speed and
height is known as
a) equation of continuity
b) Bernoulli's equation
c) light equation
d) speed equation

Q3. Which of the following device uses Bernoulli's equation as its
working principle?
a) Venturimeter
b) Orifice-meter
c) Pitot tube
d) All of the above

Q4. Which of the following sentences are true for Bernoulli's
equation?
1. Bernoulli's principle is applicable to ideal incompressible fluid
2. The gravity force and pressure forces are only considered in
Bernoulli's principle
3. The flow of fluid is rotational for Bernoulli's principle
4. The heat transfer into or out of fluid should be zero to apply
Bernoulli's principle
a) (1), (2) and (3)
b) (1), (3) and (4)
c) (1), (2) and (4)
d) (1), (2), (3) and (4)

Q5. In a steady, ideal flow of an incompressible fluid, total energy at
any point of the fluid is always constant. This theorem is known
as
a) Euler's theorem
b) Navier-stockes theorem
c) Reynold's theorem
d) Bernoulli's theorem

Q6. Bernoulli’s equation cannot be applied when the flow is
a) rotational
b) turbulent
c) unsteady
d) all of the above

Mechanical Engineering Department | Lab Manual | Basic Mechanical Engineering [BT-203] 178

Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

Q7. Bernoulli's theorem is applicable to
a) surface tension
b) viscosity
c) flow of liquids
d) static fluid pressure

Q8. Bernoulli’s equation can be directly applied to viscous flow.
a) True
b) False

Questions for Viva-Voce Q9. Bernoulli’s principle is derived from which of the following?
a) Conservation of mass
b) Conservation of energy
c) Newton’s law of motion
d) Conservation of momentum

Q10. According to statement of Bernoulli’s theorem if Kinetic or
Potential Energy is changing then overall energy changes and
hence energy is not constant at all the places.
a) True
b) False

Mechanical Engineering Department | Lab Manual | Basic Mechanical Engineering [BT-203] 179

Blank Page Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

Mechanical Engineering Department | Lab Manual | Basic Mechanical Engineering [BT-203] 180

Experiment #

1A bibliography is a list of the books

and other sources that are referred
to in a scholarly work-such as an
essay, term paper, dissertation,
manual or a book.
.

BIBLIOGRAPHY

BIBLIOGRAPHY

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4. Bejan, A., Advanced engineering thermodynamics. 2016: John Wiley & Sons.
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1991: MacMillan, New York.
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McGraw-Hill.
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McGraw-Hill.
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336. 1951: North-Holland Amsterdam.
11. Dorfman, J.R. and J. Kestin, A Course in Statistical Thermodynamics. 1971: Academic

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181

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Education.
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Learning Pvt. Ltd.
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Publications.
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183

184

Experiment #

1An author is the creator or

originator of any written work such
as a book, manual or play, and is
also considered a writer. More
broadly defined, an author is "the
person who originated or gave
existence to anything" and whose
authorship determines responsibility
.for what was created.

ABOUT THE AUTHORS

Dr. Anil Singh Yadav

Dr. Anil Singh Yadav is a Professor in the Department of Mechanical
Engineering at Lakshmi Narain College of Technology (LNCT), Bhopal
(MP). He received his Bachelor’s Degree in Mechanical Engineering from
Madhav Institute of Technology & Science, Gwalior (MP). He received his
Master’s Degree in Thermal Engineering and PHD from Maulana Azad
National Institute of Technology, Bhopal (MP). He has more than 17 years of
vast teaching experience in various subjects of Mechanical Engineering
disciplines.
His area of research includes CFD Modelling & Simulation, Heat Transfer,
and Renewable Energy. He has published/presented more than 80 research
papers to his credit in reputed National and International
Journals/Conferences. He has also published 12 research papers in SCI journals as a ‘First Author’.
He has filed a Patent as a Sole inventor of ‘Camless & Valveless Internal Combustion Engine’. He
has filed a Patent as a co-inventor of ‘An Apparatus for Measuring Water Absorption Capacity of
Building Material’. Recently he has also filed two design Patent on ‘Laptop Case’ and ‘Laptop Stand’.
His research papers have more than 600 Citations along with his 12 h-index & 13 i10-index. He is the
author of three books. From last few years his prime focus is on the research issues in internal
combustion engine and CFD modelling & simulation of thermal systems. He is editor of four
international journals. He is also reviewer of more than 100 International Journals of Elsevier, Taylor
& Francis, ASME, Springer, Hindawi, SAGE, Wiley etc.
He has expertise in ANSYS Fluent, SOLIDWORKS, AutoCAD, SigmaPlot, MATLAB, CorelDRAW
and EndNote. He has participated in more than 75 Faculty Development Programme/Short Term
Training Programme/Workshop/Conferences/Seminars etc. He is life member of various professional
bodies like IE, ISTE, SESI, CRSI, AMM etc. More than 20 times print media (newspapers) covered
his academic/research excellence.
Dr. Anil Singh Yadav may be reached at: anilsinghyadav@gmail

Sachin Kumar Nikam

Mr. Sachin Kumar Nikam is an Assistant Professor in Mechanical Engineering
Department in Lakshmi Narain College of Technology, Bhopal. He received his
Bachelor’s Degree in Mechanical Engineering from RGPV, Bhopal. He obtained
his Master’s Degree in Heat Power and Thermal Engineering with 1st division
(Hons.) from Lakshmi Narain college of Technology, Bhopal.
His main research interest includes Heat and Mass Transfer, Refrigeration and
Air Conditioning and Renewable Energy Sources. He has published/presented
various research papers in reputed National/International Journal/Conferences.
He is expert in ProE, AutoCAD and Ansys. He has participated in various
Faculty Development Programme/Short Term Training Programme/Workshop/Conferences/Seminars
etc.
Mr. Sachin Kuamr Nikam may be reached at: [email protected]

185

186





Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

Bernoulli's Theorem H1= P/w+ Z+ V12/2g= =
H2= P/w+ Z+ V22/2g= =
H3= P/w+ Z+ V32/2g= =
H4= P/w+ Z+ V42/2g= =
H5= P/w+ Z+ V52/2g= =
H6= P/w+ Z+ V62/2g= =
H7= P/w+ Z+ V72/2g= =

Case-2: =
Q2=A x (r2 – r1)/t =
V12 /2g=
V1= Q/A1= = V22 /2g= =
V2= Q/A2= = V32 /2g= =
V3= Q/A3= = V42 /2g= =
V4= Q/A4= = V52 /2g= =
V5= Q/A5= = V62 /2g= =
V6= Q/A6= = V72 /2g= =
V7= Q/A7= = =

H1= P/w+ Z+ V12/2g= =
H2= P/w+ Z+ V22/2g= =
H3= P/w+ Z+ V32/2g= =
H4= P/w+ Z+ V42/2g= =
H5= P/w+ Z+ V52/2g= =
H6= P/w+ Z+ V62/2g= =
H7= P/w+ Z+ V72/2g= =

Mechanical Engineering Department | Lab Manual | Basic Mechanical Engineering [BT-203] 175

Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

Case-3:

Q3=A x (r2 – r1)/t = =

Bernoulli's Theorem V1= Q/A1= = V12 /2g= =
V2= Q/A2= = V22 /2g= =
V3= Q/A3= = V32 /2g= =
V4= Q/A4= = V42 /2g= =
V5= Q/A5= = V52 /2g= =
V6= Q/A6= = V62 /2g= =
V7= Q/A7= = V72 /2g= =

H1= P/w+ Z+ V12/2g= =
H2= P/w+ Z+ V22/2g= =
H3= P/w+ Z+ V32/2g= =
H4= P/w+ Z+ V42/2g= =
H5= P/w+ Z+ V52/2g= =
H6= P/w+ Z+ V62/2g= =
H7= P/w+ Z+ V72/2g= =

RESULT

For different flow rates of water, it is observed that
Total head H=P/w +Z +V2/2g ≈ constant at all seven points

Hence, Bernoulli’s theorem is verified.

PRECAUTIONS

1. Never switch on power supply before ensuring that all the on/off
switches given on the panel are in off position.

2. Never run the pump at low voltage.
3. Never fully close the Delivery & By-pass line valves

simultaneously.
4. Always keep the apparatus free from dust.
5. Frequently grease/Oil the rotating parts, once in three months.
6. Always use clean water.
7. If the apparatus will not be in use for more than one month, drain

the apparatus completely.

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Questions for Viva-Voce Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

REVIEW QUESTIONS
Q1. What is Bernoulli equation?
Q2. What are the assumptions used in Bernoulli Equation?
Q3. What is an ‘ideal fluid’?
Q4. What will be the value of Reynolds number for an ideal fluid?
Q5. Write some practical applications of Bernoulli's equation.

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Questions for Viva-Voce Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

MULTIPLE CHOICE QUESTIONS (✔)

Q1. Chimney works best on principle of
a) equation of continuity
b) Bernoulli's equation
c) light equation
d) speed equation

Q2. Fundamental equation that relates pressure to fluid's speed and
height is known as
a) equation of continuity
b) Bernoulli's equation
c) light equation
d) speed equation

Q3. Which of the following device uses Bernoulli's equation as its
working principle?
a) Venturimeter
b) Orifice-meter
c) Pitot tube
d) All of the above

Q4. Which of the following sentences are true for Bernoulli's
equation?
1. Bernoulli's principle is applicable to ideal incompressible fluid
2. The gravity force and pressure forces are only considered in
Bernoulli's principle
3. The flow of fluid is rotational for Bernoulli's principle
4. The heat transfer into or out of fluid should be zero to apply
Bernoulli's principle
a) (1), (2) and (3)
b) (1), (3) and (4)
c) (1), (2) and (4)
d) (1), (2), (3) and (4)

Q5. In a steady, ideal flow of an incompressible fluid, total energy at
any point of the fluid is always constant. This theorem is known
as
a) Euler's theorem
b) Navier-stockes theorem
c) Reynold's theorem
d) Bernoulli's theorem

Q6. Bernoulli’s equation cannot be applied when the flow is
a) rotational
b) turbulent
c) unsteady
d) all of the above

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Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

Q7. Bernoulli's theorem is applicable to
a) surface tension
b) viscosity
c) flow of liquids
d) static fluid pressure

Q8. Bernoulli’s equation can be directly applied to viscous flow.
a) True
b) False

Questions for Viva-Voce Q9. Bernoulli’s principle is derived from which of the following?
a) Conservation of mass
b) Conservation of energy
c) Newton’s law of motion
d) Conservation of momentum

Q10. According to statement of Bernoulli’s theorem if Kinetic or
Potential Energy is changing then overall energy changes and
hence energy is not constant at all the places.
a) True
b) False

Mechanical Engineering Department | Lab Manual | Basic Mechanical Engineering [BT-203] 179

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Experiment #

1A bibliography is a list of the books

and other sources that are referred
to in a scholarly work-such as an
essay, term paper, dissertation,
manual or a book.
.

BIBLIOGRAPHY

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Lakshmi Narain College of Technology (LNCT) Bhopal (MP)

BIBLIOGRAPHY

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1991: MacMillan, New York.
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21. Leach, J.A., Engineering Thermodynamics. 2007: Juta and Company Ltd.
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45. Singal, R.K. and M. Singal, Engineering thermodynamics. 2010: IK International Pvt
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