On the dynamic behavior of the current in the condenser of a boost converter ...TELKOMNIKA JOURNAL
In this paper, an analytical and numerical study is conducted on the dynamics of the current in the condenser of a boost converter controlled with ZAD, using a pulse PWM to the symmetric center. A stability analysis of periodic 1T-orbits was made by the analytical calculation of the eigenvalues of the Jacobian matrix of the dynamic system, where the presence of flip and Neimar–Sacker-type bifurcations was determined. The presence of chaos, which is controlled by ZAD and FPIC techniques, is shown from the analysis of Lyapunov exponents.
On the dynamic behavior of the current in the condenser of a boost converter ...TELKOMNIKA JOURNAL
In this paper, an analytical and numerical study is conducted on the dynamics of the current in the condenser of a boost converter controlled with ZAD, using a pulse PWM to the symmetric center. A stability analysis of periodic 1T-orbits was made by the analytical calculation of the eigenvalues of the Jacobian matrix of the dynamic system, where the presence of flip and Neimar–Sacker-type bifurcations was determined. The presence of chaos, which is controlled by ZAD and FPIC techniques, is shown from the analysis of Lyapunov exponents.
Introduction to AI for Nonprofits with Tapp NetworkTechSoup
Dive into the world of AI! Experts Jon Hill and Tareq Monaur will guide you through AI's role in enhancing nonprofit websites and basic marketing strategies, making it easy to understand and apply.
How to Make a Field invisible in Odoo 17Celine George
It is possible to hide or invisible some fields in odoo. Commonly using “invisible” attribute in the field definition to invisible the fields. This slide will show how to make a field invisible in odoo 17.
Operation “Blue Star” is the only event in the history of Independent India where the state went into war with its own people. Even after about 40 years it is not clear if it was culmination of states anger over people of the region, a political game of power or start of dictatorial chapter in the democratic setup.
The people of Punjab felt alienated from main stream due to denial of their just demands during a long democratic struggle since independence. As it happen all over the word, it led to militant struggle with great loss of lives of military, police and civilian personnel. Killing of Indira Gandhi and massacre of innocent Sikhs in Delhi and other India cities was also associated with this movement.
Macroeconomics- Movie Location
This will be used as part of your Personal Professional Portfolio once graded.
Objective:
Prepare a presentation or a paper using research, basic comparative analysis, data organization and application of economic information. You will make an informed assessment of an economic climate outside of the United States to accomplish an entertainment industry objective.
2024.06.01 Introducing a competency framework for languag learning materials ...Sandy Millin
http://sandymillin.wordpress.com/iateflwebinar2024
Published classroom materials form the basis of syllabuses, drive teacher professional development, and have a potentially huge influence on learners, teachers and education systems. All teachers also create their own materials, whether a few sentences on a blackboard, a highly-structured fully-realised online course, or anything in between. Despite this, the knowledge and skills needed to create effective language learning materials are rarely part of teacher training, and are mostly learnt by trial and error.
Knowledge and skills frameworks, generally called competency frameworks, for ELT teachers, trainers and managers have existed for a few years now. However, until I created one for my MA dissertation, there wasn’t one drawing together what we need to know and do to be able to effectively produce language learning materials.
This webinar will introduce you to my framework, highlighting the key competencies I identified from my research. It will also show how anybody involved in language teaching (any language, not just English!), teacher training, managing schools or developing language learning materials can benefit from using the framework.
Read| The latest issue of The Challenger is here! We are thrilled to announce that our school paper has qualified for the NATIONAL SCHOOLS PRESS CONFERENCE (NSPC) 2024. Thank you for your unwavering support and trust. Dive into the stories that made us stand out!
Synthetic Fiber Construction in lab .pptxPavel ( NSTU)
Synthetic fiber production is a fascinating and complex field that blends chemistry, engineering, and environmental science. By understanding these aspects, students can gain a comprehensive view of synthetic fiber production, its impact on society and the environment, and the potential for future innovations. Synthetic fibers play a crucial role in modern society, impacting various aspects of daily life, industry, and the environment. ynthetic fibers are integral to modern life, offering a range of benefits from cost-effectiveness and versatility to innovative applications and performance characteristics. While they pose environmental challenges, ongoing research and development aim to create more sustainable and eco-friendly alternatives. Understanding the importance of synthetic fibers helps in appreciating their role in the economy, industry, and daily life, while also emphasizing the need for sustainable practices and innovation.
Biological screening of herbal drugs: Introduction and Need for
Phyto-Pharmacological Screening, New Strategies for evaluating
Natural Products, In vitro evaluation techniques for Antioxidants, Antimicrobial and Anticancer drugs. In vivo evaluation techniques
for Anti-inflammatory, Antiulcer, Anticancer, Wound healing, Antidiabetic, Hepatoprotective, Cardio protective, Diuretics and
Antifertility, Toxicity studies as per OECD guidelines
Honest Reviews of Tim Han LMA Course Program.pptxtimhan337
Personal development courses are widely available today, with each one promising life-changing outcomes. Tim Han’s Life Mastery Achievers (LMA) Course has drawn a lot of interest. In addition to offering my frank assessment of Success Insider’s LMA Course, this piece examines the course’s effects via a variety of Tim Han LMA course reviews and Success Insider comments.
Acetabularia Information For Class 9 .docxvaibhavrinwa19
Acetabularia acetabulum is a single-celled green alga that in its vegetative state is morphologically differentiated into a basal rhizoid and an axially elongated stalk, which bears whorls of branching hairs. The single diploid nucleus resides in the rhizoid.
Safalta Digital marketing institute in Noida, provide complete applications that encompass a huge range of virtual advertising and marketing additives, which includes search engine optimization, virtual communication advertising, pay-per-click on marketing, content material advertising, internet analytics, and greater. These university courses are designed for students who possess a comprehensive understanding of virtual marketing strategies and attributes.Safalta Digital Marketing Institute in Noida is a first choice for young individuals or students who are looking to start their careers in the field of digital advertising. The institute gives specialized courses designed and certification.
for beginners, providing thorough training in areas such as SEO, digital communication marketing, and PPC training in Noida. After finishing the program, students receive the certifications recognised by top different universitie, setting a strong foundation for a successful career in digital marketing.
3. CHAPTER- 7 FLUID DYNAMICS
• It is the study of flow of fluid along with the forces responsible for it.
• Hence, Newton’s second law of motion ( Ԧ
𝐅 = 𝐦𝐚) is used to analyze dynamic
behavior of fluid flow.
• In the fluid flow, various forces acting on it are as follows:
❑ Gravity force
❑ Pressure force
❑ Viscous force
❑ Turbulent force
❑ Force due to compressibility
❑ Force due to surface tension
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
4. NOTE: 1. When all forces are taken into account, the equation of motion is termed
as “Newtonian equation of motion”.
2. When compressibility and surface tension is neglected, it is termed as “Reynold’s
equation of motion”.
3. When compressibility, surface tension and force due to turbulence is neglected
(i.e. only gravity, pressure and viscous force is considered), the equation is termed
as “Navier Stokes equation”.
4. When only gravity and pressure forces are considered, it is termed as “Euler’s
equation of motion”.
(It will be used in dynamics for analysis of fluid flow).
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
5. BERNOULLI’S EQUATION
• It is based on “conservation of energy”.
• It is obtained by integration of Euler’s equation of motion, along a streamline
under steady incompressible flow.
As per Newton’s second law of motion, σ 𝐅𝐬 = 𝐦𝐚𝐬
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
6. Euler’s equation of motion: P dA − P + dP dA − W sinθ = mas
−dP dA − γwdV sinθ = ρwdV
dvs
dt
−dP dA − γwdA ds sinθ = ρwdA ds ×
𝜕v
𝜕s
ds
dt
+
𝜕v
𝜕t
dt
dt
For steady flow,
𝜕v
𝜕t
= 0
−dP − γwds sinθ = ρwds vs
𝜕v
𝜕s
𝐯𝐬𝐝𝐯 + 𝐠 𝐝𝐲 +
𝐝𝐏
𝛒𝐰
= 𝟎
After integrating,
𝐯𝟐
𝟐
+ 𝐠𝐲 + න
𝐝𝐏
𝛒𝐰
= 𝟎
For incompressible fluid, ρw = constant
𝐏
𝛒𝐰
+ 𝐠𝐲 +
𝐯𝟐
𝟐
= 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
7. NOTE: 1. The value of constant in above equation is same along a stream line.
However, if flow is irrotational, the value of constant is same along all the
streamlines.
(i) If flow is rotational, C1 = C2 ≠ C3
P1
ρw
+ gy1 +
v1
2
2
=
P2
ρw
+ gy2 +
v2
2
2
≠
P3
ρw
+ gy3 +
v3
2
2
(i) If flow is irrotational, C1 = C2 = C3
P1
ρw
+ gy1 +
v1
2
2
=
P2
ρw
+ gy2 +
v2
2
2
=
P3
ρw
+ gy3 +
v3
2
2
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
8. 2. While analyzing Bernoulli’s equation, only gravity and pressure forces are
considered, hence if any other force except these two is present in the system, then
this equation will not be applicable.
For example:
(i) It is not applicable for long narrow flow passage as viscosity would also be
there.
(ii) It is not applicable beyond Mach number ≥ 0.3, as compressibility would also
be there.
(iii) It is not applicable in diverging flow section as flow separation and energy
losses takes place.
(iv) It is not applicable in flow section that involves fan and turbine or any other
mechanical unit as it involves energy loss and gain or work transfer.
(v) It is not applicable in flow section that involves temperature change as
compressibility comes in picture.
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
9. Q. Bernoulli’s equation is applicable for
a) Viscous and compressible fluid flow
b) Inviscid and compressible fluid flow
c) Inviscid and incompressible fluid flow.
d) Viscous and incompressible fluid flow
[GATE: 2018]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
10. Q. Bernoulli’s equation is an equation of:
a) Conservation of mass
b) Conservation of linear momentum
c) Conservation of energy.
d) Conservation of angular momentum
[GATE: 1992]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
11. DIFFERENT FORMS OF BERNOULLI’S EQUATION
Different energy terms in the Bernoulli’s equation can be reported in the following
forms:
a) Per unit mass:
𝐏
𝛒
+
𝐯𝟐
𝟐
+ 𝐠𝐲 = 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭 (𝐂)
Pressure energy
mass
Kinetic energy
mass
Potential energy
mass
b) Per unit weight:
𝐏
𝛄
+
𝐯𝟐
𝟐𝐠
+ 𝐲 = 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭 (𝐂)
Pressure energy
mass
Kinetic energy
mass
Potential energy
mass
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
12. c) Pressure:
𝐏 +
𝛒𝐯𝟐
𝟐
+ 𝛄𝐲 = 𝐜𝐨𝐧𝐬𝐭𝐚𝐧𝐭 𝐂
Where, P = static pressure (actual pressure in fluid)
ρv2
2
= dynamic pressure (pressure developed when fluid in motion is brought to rest)
γy = hydrostatic pressure (pressure due to weight of fluid)
NOTE: 1. Here, sum of static pressure (P) and dynamic pressure (
ρv2
2
) is termed as
“stagnation pressure”.
𝐏𝐬𝐭𝐚𝐠𝐧𝐚𝐭𝐢𝐨𝐧 = 𝐏 +
𝛒𝐯𝟐
𝟐
Measurement of stagnation pressure helps in finding the velocity in any system
(pipe flow).
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
13. v = 2
[Pstagnation − P]
ρ
2. Here, sum of static pressure and hydrostatic pressure is termed as “piezometric
pressure”.
𝐏𝐩𝐢𝐞𝐳𝐨𝐦𝐞𝐭𝐫𝐢𝐜 = 𝐏 + 𝛄𝐲
Piezometric head h =
Piezometric pressure
γw
=
P + γy
γ
=
P
γ
+ y
3. Absolute level of water in piezometer indicates pressure head (static), but if level
of water in piezometer is measure from datum, it is termed as “piezometric head”.
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
14. 4. Piezometric head is constant at all the depth at a particular section, if stream lines
(pipe) are straight, but if stream lines (pipe) are curved, the piezometric head will
vary across the depth at a particular section.
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
15. NOTE: In real situation, where energy transfer (i.e. energy gain and loss) and head
loss takes place, the Bernoulli’s equation can be modified as follows:
𝐏𝟏
𝛄
+
𝐯𝟏
𝟐
𝟐𝐠
+ 𝐲𝟏 + 𝐄𝐠𝐚𝐢𝐧 =
𝐏𝟐
𝛄
+
𝐯𝟐
𝟐
𝟐𝐠
+ 𝐲𝟐 + 𝐄𝐥𝐨𝐬𝐬 + 𝐡𝐟
Where,
Egain = gain of energy
Eloss = loss of energy
hf = head loss due to friction
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
16. Q. In a Bernoulli’s equation used in pipe flow, each term represents
a) Energy per unit weight.
b) Energy per unit mass
c) Energy per unit volume
d) Energy per unit flow length
[GATE: 2001]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
17. Q. Water flows steadily down in a vertical pipe of constant cross- section.
Neglecting friction, according to Bernoulli’s equation,
a) Pressure is constant along the length of the pipe
b) Velocity decreases with height
c) Pressure decreases with height.
d) Pressure increases with height
[GATE: 1996]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
18. CORRECTION FACTORS
• While analyzing Bernoulli’s equation, fluid is considered to be ideal, hence,
velocity is taken to be constant across the section, but in real, velocity varies
across the section.
• Hence, if we want to calculate actual kinetic energy in terms of average velocity, a
factor ‘α’ termed as “kinetic energy correction factor” is to be used along it.
α
1
2
mvavg
2 =
1
2
mvactual
2
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
19. α =
Actual Kinetic Energy
Average Kinetic Energy
K.E. of elemental area = dKE =
1
2
dmv2 =
1
2
ρdAv v2 =
1
2
ρdAv3
Total K.E. = dKE =
1
2
ρdAv3
=
1
2
ρ v3
dA … … … … . . (i)
Total K.E. using average velocity =
1
2
ρAvavg
2 α … … … … . . (ii)
From (i) and (ii),
1
2
ρAvavg
2 α =
1
2
ρ v3dA
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
20. 𝛂 =
𝐯𝟑
𝐝𝐀
𝐀𝐯𝐚𝐯𝐠
𝟐
To find vavg, use continuity equation
Q = A vavg = v dA
vavg =
v dA
A
Hence, Bernoulli’s equation using K.E. correction factor is:
P
γ
+ α
v2
2g
+ y = constant
A similar parameter, termed as “momentum correction factor (β)” is defined in
momentum equation.
β mvavg = න dm v
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
21. β ρAvavg vavg = න ρdAvactual v
𝛃 =
𝐯𝟐
𝐝𝐀
𝐀𝐯𝐚𝐯𝐠
𝟐
Here also, vavg =
v dA
A
NOTE: 1. For laminar flow condition:
(i) In circular pipe, α =2
(ii) In parallel plates, α = 1.543
2. For turbulent flow condition, in circular pipe, α = 1.03 – 1.06
3. For ideal flow condition, for all pipes, α = 1
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
22. Q. If the velocity distribution is rectangular, the kinetic energy correction factor is
a) Greater than zero, but less than unity
b) Less than zero
c) Equal to zero
d) Equal to unity.
[GATE: 1990]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
23. Q. Statement (I): Bernoulli’s equation is applicable to any point in the flow field
provided the flow is steady and irrotational.
Statement (II): The integration of Euler’s equation of motion to derive Bernoulli’s
equation involves the assumptions that velocity potential exists and that the flow
conditions do not change with time at any point.
a) Both statement (I) and statement (II) are individually true, and statement (II) is
the correct explanation of statement (I).
b) Both statement (I) and statement (II) are individually true, but statement (II) is
NOT the correct explanation of statement (I)
c) Statement (I) is true; but statement (II) is false
d) Statement (I) is false; but statement (II) is true
[IES: 2018]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
24. APPLICATION OF BERNOULLI’S
EQUATION
A. VENTURIMETER
• It is a device used to find out discharge through a pipeline.
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
26. • Working principle of venturimeter includes reduction in area at throat, that
results in increase in velocity in steady flow, which further causes decrease in
pressure, the value of which gives the discharge in pipe.
Applying Bernoulli’s equation at section 1 and 2,
P1
γ
+ y1 +
v1
2
2g
=
P2
γ
+ y2 +
v2
2
2g
P1
γ
+ y1 −
P2
γ
+ y2 =
v2
2
− v1
2
2g
= h
Where, h = piezometric head difference =
v2
2−v1
2
2g
h =
Q
a2
2
−
Q
a1
2
2g
𝐐 =
𝐚𝟏𝐚𝟐 𝟐𝐠𝐡
𝐚𝟏
𝟐
− 𝐚𝟐
𝟐
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
27. • In above expression, theoretical discharge losses are not being considered, hence,
actual discharge is given by:
Qactual = Cd Qtheoretical
Where, Cd = co- efficient of discharge which accounts for losses in pipe section
𝐐𝐚 =
𝐂𝐝𝐚𝟏𝐚𝟐 𝟐𝐠𝐡
𝐚𝟏
𝟐
− 𝐚𝟐
𝟐
… … … … … … . (𝐀)
Here,
𝐚𝟏𝐚𝟐 𝟐𝐠
𝐚𝟏
𝟐−𝐚𝟐
𝟐
= 𝐊 = Venturi constant
𝐐𝐚 = 𝐂𝐝𝐊 𝐡
To compute Cd, losses can be considered in energy equation:
P1
γ
+ y1 +
v1
2
2g
=
P2
γ
+ y2 +
v2
2
2g
+ hL
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
28. P1
γ
+ y1 −
P2
γ
+ y2 − hL =
v2
2
− v1
2
2g
Since
P1
γ
+ y1 −
P2
γ
+ y2 = h
𝐐𝐚𝐜𝐭𝐮𝐚𝐥 =
𝐚𝟏𝐚𝟐 𝟐𝐠(𝐡 − 𝐡𝐋)
𝐚𝟏
𝟐
− 𝐚𝟐
𝟐
… … … … (𝐁)
Qactual =
Cda1a2 2gh
a1
2
− a2
2
=
a1a2 2g(h − hL)
a1
2
− a2
2
𝐂𝐝 =
𝐡 − 𝐡𝐋
𝐡
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
29. • In Venturimeter, gradual contraction and expansion is ensured to avoid flow
separation, hence:
a) a2 can be taken as complete area of throat
NOTE: Here, reduction in area of flow is expressed in terms of co- efficient of
contraction (Cc).
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
30. b) Losses due to eddy formation does not takes place (hence, value of Cd is
comparatively more (around 0.98)).
• Since tendency of flow separation is more during expansion than contraction,
angle of divergence (5.6o) is kept less than angle of convergence (22o), and this
portion is not used for discharge measurement.
• Cross- sectional area of throat cannot be reduced beyond a certain limit, as
pressure may fall below vapor pressure leading to cavitation, hence,
𝐝𝟐 =
𝟏
𝟑
−
𝟑
𝟒
𝐝𝟏
Where, d2 = diameter of throat, d1 = diameter of pipe
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
31. Q. Venturimeter is advantageous because:
a) It has much smaller head loss
b) Its co- efficient of discharge is more than for an orifice meter
c) Its accuracy is quite good
d) All of the above.
[SSC: 2009]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
32. INCLINED VENTURIMETER WITH
DIFFERENTIAL MANOMETER
Case (i): GM (G2) > GL (G1)
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
33. Using Pascal’s law, PC = PD
PA + G1γwx1 = PB + G1γwx2 + G2γwx
PA
γw
−
PB
γw
= G1x2 + G2x − G1x1
PA
G1γw
+ ya −
PB
G1γw
+ yb = x2 +
G2
G1
x − x1 + ya − yb
Where, h =
G2
G1
x − x
𝐡 =
𝐆𝟐
𝐆𝟏
− 𝟏 𝐱 = 𝐏𝐢𝐞𝐳𝐨𝐦𝐞𝐭𝐫𝐢𝐜 𝐡𝐞𝐚𝐝 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐞
𝐐 =
𝐂𝐝𝐚𝟏𝐚𝟐 𝟐𝐠
𝐆𝟐
𝐆𝟏
− 𝟏 𝐱
𝐚𝟏
𝟐
− 𝐚𝟐
𝟐
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
34. Case (ii): GM (G2) < GL (G1)
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
35. Using Pascal’s law, PC = PD
PA − G1γwx1 = PB − G1γwx2 − G2γwx
PA
γw
−
PB
γw
= G1x1 − G2x − G1x2
PA
G1γw
+ ya −
PB
G1γw
+ yb = x1 −
G2
G1
x − x2 + ya − yb
Where, h = 𝑥 −
G2
G1
x
𝐡 = 𝐱 𝟏 −
𝐆𝟐
𝐆𝟏
= 𝐏𝐢𝐞𝐳𝐨𝐦𝐞𝐭𝐫𝐢𝐜 𝐡𝐞𝐚𝐝 𝐝𝐢𝐟𝐟𝐞𝐫𝐞𝐧𝐜𝐞
𝐐 =
𝐂𝐝𝐚𝟏𝐚𝟐 𝟐𝐠 𝟏 −
𝐆𝟐
𝐆𝟏
𝐱
𝐚𝟏
𝟐
− 𝐚𝟐
𝟐
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
36. Q. Statement (I): When flow through a pipeline is measured through fixing a
venturimeter, the computed flow will not be sensitive to the alignment of the centre
line of the set- up (horizontal or sloping, up or down), along the flow direction.
Statement (II): The difference in the readings of the manometer limbs is by itself
always adjusted for the ratio of the densities of the two liquids- the manometer
liquid and the liquid whose flow rate is being measured- in the development of the
formula for computing the discharge
a) Both statement (I) and statement (II) are individually true, and statement (II) is
the correct explanation of statement (I).
b) Both statement (I) and statement (II) are individually true, but statement (II) is
NOT the correct explanation of statement (I)
c) Statement (I) is true; but statement (II) is false
d) Statement (I) is false; but statement (II) is true
[IES: 2017]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
37. Q. The co- efficient of discharge for venturimeter (Cd) ranges from
a) 0.50 – 0.55
b) 0.61 – 0.69
c) 0.95 – 0.99.
d) 0.61 – 0.65
[SSC: 2018]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
38. Q. A venturimeter has a differential mercury water manometer connected to its inlet
and throat for a given discharge in the pipe
a) Is independent of the orientation of venturimeter.
b) Depends on the orientation of venturimeter
c) Varies with the slope of the venturimeter with respect to horizontal
d) None of these
[SSC: 2007]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
40. • It is used to measure discharge through pipe.
• In this case, a circular plate, with concentric sharp- edged hole is installed in a
pipe such that the plate is perpendicular to the axis of pipe.
• It is comparatively cheaper than venturimeter, as its size is comparatively smaller,
hence it finds its application if there is space restriction.
• As flow separation takes place in this case, head losses are more, which also
results in lower value of Cd = 0.6.
NOTE: 1. The region where flow area is minimum is termed as “Vena Contracta”
(VC).
2. As it is difficult to find the area (a2) at vena contracta, it is expressed in terms of a
parameter, called co- efficient of contraction (Cc).
𝐂𝐜 =
𝐚𝟐
𝐚𝐨
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
41. Applying Bernoulli’s equation at section 1 and 2:
P1
γ
+ y1 +
v1
2
2g
=
P2
γ
+ y2 +
v2
2
2g
= h
Q
a2
2
−
Q
a1
2
= 2gh
Q =
a1a2 2gh
a1
2
− a2
2
Q =
Cca1ao 2gh
a1
2
− [ ao
2
Cc]2
Qactual = Cd Qtheoretical
𝐐𝐚𝐜𝐭𝐮𝐚𝐥 =
𝐂𝐝𝐚𝟏𝐚𝐨 𝟐𝐠𝐡
𝐚𝟏
𝟐
− 𝐚𝐨
𝟐
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
42. NOTE:
Co- efficient of discharge = co- efficient of contraction × co- efficient of velocity
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
43. 𝐐𝐚 =
𝐂𝐝𝐚𝟏𝐚𝐨 𝟐𝐠𝐡
𝐚𝟏
𝟐
− 𝐚𝐨
𝟐
• If area of flow is not reduced after passing through orifice, i.e. ao = a2, i.e. Cc = 1
and Cd = Cv.
• At Vena Contracta, streamlines are straight, hence piezometric head is constant
throughout the section.
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
44. Q. The discharge co- efficient (Cd) of an orifice meter is:
a) Greater than Cd of a venturimeter
b) Smaller than the Cd of a venturimeter.
c) Equal to the Cd of a venturimeter
d) Greater than one
[GATE: 1998]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
45. C. NOZZLEMETER
• The nozzle meter is a truncated form of venturimeter, without diverging portion.
• It is simply a contraction, with well- rounded entrance placed in the pipe line.
• It is simpler than venturimeter.
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
46. D. ELBOWMETER
• It is also used to measure discharge in pipe.
• It is based on the principle that when liquid moves along pipe bend, it follows
“free vortex” condition.
i.e. vR = constant (C)
𝐯 =
𝐂
𝐑
Since R1>R2, v1 < v2
From energy conservation,
P1 > P2
Qact = CdA 2gh (A= area of pipe)
h = x
G2
G1
− 1
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
47. Q. Which of the following parameter is measured with the help of elbow meter?
a) Acceleration
b) Velocity
c) Viscosity
d) Discharge.
[SSC: 2017]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
48. E. PITOT TUBE
• It is used to measure velocity of fluid, when section of pipe is straight.
• Difference in reading of pitot tube and piezometer (h) is noted, which indicates the
velocity head.
h =
vB
2
2g
vB = 2gh
vactual = Cv vB = Cv 𝟐𝐠𝐡
Cv = 0.98 (for pitot tube)
NOTE: Anemometer is used to measure air/ gas velocity.
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
49. F. PITOT- STATIC TUBE/ PRANDTL TUBE
• This is also used to measure velocity at a point in fluid flow (specially when
stream lines are curved).
• As, if stream lines are curved, the piezometric head is not constant throughout the
section, hence, in such case, it is necessary to find out the piezometric head at
same point at which velocity is to be measured.
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
50. • Hence, Prandtl tube/ pitot static tube is used in this case, as it satisfies the above
purpose.
• The front portion of this tube is rounded to avoid separation of flow and on it,
shaft holes are provided at certain distance, where stream lines become parallel.
v2
2g
= h
𝐯 = 𝟐𝐠𝐡
Vact = Cv v = Cv 𝟐𝐠𝐡
Where, Cv = 0.99
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
52. Q. Pitot tube is used to measure
a) Static pressure of a flowing fluid
b) Dynamic pressure of a flowing fluid
c) Total pressure of a flowing fluid.
d) Surface tension of a flowing fluid
[GATE: 1992]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
53. Q. The pitot- static tube measures
a) Static pressure
b) Dynamic pressure
c) Difference in static and dynamic pressure
d) Difference in total and static pressure.
[GATE: 1989]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
54. MOMENTUM EQUATION AND ITS
APPLICATION
• Momentum is a vector quantity and its direction is given by the direction of
velocity.
• To apply the momentum equation for a flowing fluid, we have to consider the
volume of fluid, termed as “control volume”.
• Control volume is selected in such a way that force needed to calculate becomes
the external force to the control volume.
• According to momentum equation,
Net force on C.V. in given direction (σ 𝐅) = Change in momentum flux in same direction (
∆𝐦𝐯
𝐭
)
σ F= [momentum flux going out of C.V. in given direction]-[momentum flux
coming into the C.V. in given direction]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
55. 𝐅 = 𝛃𝟐𝛒𝐐𝐯𝟐 − 𝛃𝟏𝛒𝐐𝐯𝟏
• The above equation is valid for steady flow only.
• If flow is unsteady, add one more term
d(mv)
dt
on R.H.S.
Where, m = mass of fluid in C.V.
v = velocity of C.V. in given direction
mv = momentum of C.V. in given direction
v2 and v1 are velocity component for outgoing fluid and incoming fluid in given
direction
NOTE: 1. v2 and v1 can be absolute velocity or relative velocity.
2. Velocity w.r.t. ground is “absolute velocity” and velocity w.r.t. some other
reference is termed as “relative velocity”.
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
56. APPLICATION OF MOMENTUM EQUATION
• According to this, net torque on fluid in any direction equals to change of angular
momentum flux in same direction.
• It find its application in sprinkler problems:
a) Discharging arm in same direction
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
57. u1 and u2 are relative velocity of jet at points 1 and 2 (i.e. velocity of jet w.r.t.
sprinkler)
v1 and v2 are absolute velocity of jet at points 1 and 2
ωr1 and ωr2 are absolute velocity of sprinkler at points 1 and 2
Torque on jet in ACW direction = ρQ1v1r1 − ρQ2v2r2 − [0]
T = ρ A1u1 v1r1 − ρ(A2u2)v2r2
v1 = u1 + ωr1; v2 = u2 − ωr2
𝐓 = 𝛒 𝐀𝟏𝐮𝟏 (𝐮𝟏 + 𝛚𝐫𝟏)𝐫𝟏 − 𝛒(𝐀𝟐𝐮𝟐)(𝐮𝟐 − 𝛚𝐫𝟐) 𝐫𝟐
Also, torque applied by jet on sprinkler is same in magnitude but opposite in
direction.
NOTE: If sprinkler is frictionless, torque, T = 0
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
58. b) Discharging arm in opposite direction
Torque on jet in ACW direction = Torque going out - torque coming in
= ρQ1v1r1 − ρQ2v2r2 − [0]
T = ρ A1u1 v1r1 − ρ(A2u2)v2r2
v1 = u1 + ωr1; v2 = −(u2 + ωr2)
𝐓 = 𝛒 𝐀𝟏𝐮𝟏 𝐮𝟏 + 𝛚𝐫𝟏 𝐫𝟏 + 𝛒(𝐀𝟐𝐮𝟐)(𝐮𝟐 + 𝛚𝐫𝟐) 𝐫𝟐
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
59. Q. Which of the following pairs are correctly matched?
a) 1, 2 and 3 only
b) 1, 3 and 4 only.
c) 2, 3 and 4 only
d) 1, 2, 3 and 4
[IES: 2012]
1. Piezometric head Sum of datum head and pressure head
2. Dynamic head Sum of datum head and velocity head
3. Stagnation head Sum of piezometric head and velocity head
4. Total head Sum of piezometric head and dynamic head
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
60. Q. A fire hose has a nozzle attached to it, and the nozzle discharges a jet of water
into the atmosphere at a velocity of 20m/s. This causes the joint of the nozzle with
the hose to be in:
a) Tension.
b) A state of zero stress
c) Compression
d) Bending stress
[IES: 2011]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
61. Q. Match List- I with List- II and select the correct answer using the code given
below the lists:
Codes: A B C D
a) 4 1 2 3
b) 2 3 4 1.
c) 4 3 2 1
d) 2 1 4 3
[IES: 2005]
List -I List - II
A. Equation of motion along a streamline 1. Principle of moment of momentum
B. Euler’s equation 2. Bernoulli’s equation
C. Pressure exerted by a free jet 3. equation for conservation of momentum
D. Rotating lawn sprinkler 4. Momentum equation
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
62. Q. Assertion (A): Pressure intensity in a liquid flow is a form of energy
Reason (R): The pressure gradient is a measure of the rate of energy dissipation in
steady uniform flow
a) Both Assertion (A) and Reason (R) are individually true, and (R) is the correct
explanation of (A).
b) Both Assertion (A) and Reason (R) are individually true, but (R) is NOT the
correct explanation of (A)
c) (A) is true; but (R) is false
d) (A) is false; but (R) is true
[IES: 1997]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
63. Q. Match List- I (Device) with List- II (Use) and select the correct answer using the
codes given below:
Codes A B C D
a) 1 2 4 3
b) 2 1 3 4
c) 2 1 4 3.
d) 4 1 3 2
[GATE: 2010]
List - II List- II
A. Pitot tube 1. Measuring pressure in a pipe
B. Manometer 2. Measuring velocity of flow in a pipe
C. Venturimeter 3. Measuring air and gas velocities
D. Anemometer 4. Measuring discharge in a pipe
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
64. Q. Speed of a submarine can be measured by-
a) Pitot tube.
b) Hot wire anemometer
c) Pirani gauge
d) Inclined manometer
[SSC: 2016]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.
65. Q. Energy loss in flow through nozzle as compared to venturimeter is
a) Same
b) More.
c) Less
d) Unpredictable
[SSC: 2016]
J
a
s
p
a
l
S
i
r
Use code "JASPALLIVE" for instant maximum discount on Unacademy Plus subscriptions.