The document summarizes key concepts regarding boundary layer theory. Some key points include:
- Boundary layer theory describes fluid flow very close to a solid surface, where viscosity is important.
- In the boundary layer, velocity increases from zero at the surface to the free stream value over a thin region called the boundary layer thickness.
- Boundary layers can be laminar or turbulent, with turbulent layers having greater thickness. Transition from laminar to turbulent occurs due to instabilities.
- Important parameters like displacement thickness, momentum thickness, and drag coefficients are defined. Blasius solutions provide relationships between boundary layer properties for simple cases.
Reynolds number and geometry concept, Momentum integral equations, Boundary layer equations, Flow over a flat plate, Flow over cylinder, Pipe flow, fully developed laminar pipe flow, turbulent pipe flow, Losses in pipe flow
It includes details about boundary layer and boundary layer separations like history,causes,results,applications,types,equations, etc.It also includes some real life example of boundary layer.
Reynolds number and geometry concept, Momentum integral equations, Boundary layer equations, Flow over a flat plate, Flow over cylinder, Pipe flow, fully developed laminar pipe flow, turbulent pipe flow, Losses in pipe flow
It includes details about boundary layer and boundary layer separations like history,causes,results,applications,types,equations, etc.It also includes some real life example of boundary layer.
Nucleation and avalanches in film with labyrintine magnetic domainsAndrea Benassi
Experimental investigations of the scaling behavior of Barkhausen avalanches in out-of plane ferromagnetic films yield widely different results for the values of the critical exponents despite similar labyrinthine domain structures, suggesting that universality may not hold for this class of materials. Analyzing a phase-field model for magnetic reversal, we show that avalanche scaling is bounded by characteristic length scales arising from the competition between dipolar forces and exchange interactions. We compare our results with the experiments and find a good qualitative and quantitative agreement, reconciling apparent contradictions. Finally, we make some prediction, amenable to experimental verification, on the dependence of the avalanche's behavior from the film thickness and disorder.
Máy đo góc tiếp xúc Phoenix 300 - Cách đơn giản để kiểm tra bề mặt vật liệuMinh Thư Nguyễn
Tính chất của bề mặt vật liệu là yếu tố vô cùng quan trọng cần kiểm tra trong các ngành, bán dẫn, linh kiện điện tử, sơn phủ, polymer, chất hoạt động bề mặt,... Vì vậy việc kiểm tra xem tính chất bề mặt của vật liệu sau sản xuất như thế nào để từ đó biết cách xử lý cho phù hợp với từng ứng dụng riêng biệt sẽ giúp tiết kiệm thời gian và quản lý chất lượng sản phẩm hiệu quả hơn rất nhiều. Sản phẩm máy đo góc tiếp xúc nhằm đánh giá tính chất bề mặt của vật liệu là cách đơn giản nhất để kiểm tra bề mặt vật liệu
Nucleation and avalanches in film with labyrintine magnetic domainsAndrea Benassi
Experimental investigations of the scaling behavior of Barkhausen avalanches in out-of plane ferromagnetic films yield widely different results for the values of the critical exponents despite similar labyrinthine domain structures, suggesting that universality may not hold for this class of materials. Analyzing a phase-field model for magnetic reversal, we show that avalanche scaling is bounded by characteristic length scales arising from the competition between dipolar forces and exchange interactions. We compare our results with the experiments and find a good qualitative and quantitative agreement, reconciling apparent contradictions. Finally, we make some prediction, amenable to experimental verification, on the dependence of the avalanche's behavior from the film thickness and disorder.
Máy đo góc tiếp xúc Phoenix 300 - Cách đơn giản để kiểm tra bề mặt vật liệuMinh Thư Nguyễn
Tính chất của bề mặt vật liệu là yếu tố vô cùng quan trọng cần kiểm tra trong các ngành, bán dẫn, linh kiện điện tử, sơn phủ, polymer, chất hoạt động bề mặt,... Vì vậy việc kiểm tra xem tính chất bề mặt của vật liệu sau sản xuất như thế nào để từ đó biết cách xử lý cho phù hợp với từng ứng dụng riêng biệt sẽ giúp tiết kiệm thời gian và quản lý chất lượng sản phẩm hiệu quả hơn rất nhiều. Sản phẩm máy đo góc tiếp xúc nhằm đánh giá tính chất bề mặt của vật liệu là cách đơn giản nhất để kiểm tra bề mặt vật liệu
Final project report on grocery store management system..pdfKamal Acharya
In today’s fast-changing business environment, it’s extremely important to be able to respond to client needs in the most effective and timely manner. If your customers wish to see your business online and have instant access to your products or services.
Online Grocery Store is an e-commerce website, which retails various grocery products. This project allows viewing various products available enables registered users to purchase desired products instantly using Paytm, UPI payment processor (Instant Pay) and also can place order by using Cash on Delivery (Pay Later) option. This project provides an easy access to Administrators and Managers to view orders placed using Pay Later and Instant Pay options.
In order to develop an e-commerce website, a number of Technologies must be studied and understood. These include multi-tiered architecture, server and client-side scripting techniques, implementation technologies, programming language (such as PHP, HTML, CSS, JavaScript) and MySQL relational databases. This is a project with the objective to develop a basic website where a consumer is provided with a shopping cart website and also to know about the technologies used to develop such a website.
This document will discuss each of the underlying technologies to create and implement an e- commerce website.
Explore the innovative world of trenchless pipe repair with our comprehensive guide, "The Benefits and Techniques of Trenchless Pipe Repair." This document delves into the modern methods of repairing underground pipes without the need for extensive excavation, highlighting the numerous advantages and the latest techniques used in the industry.
Learn about the cost savings, reduced environmental impact, and minimal disruption associated with trenchless technology. Discover detailed explanations of popular techniques such as pipe bursting, cured-in-place pipe (CIPP) lining, and directional drilling. Understand how these methods can be applied to various types of infrastructure, from residential plumbing to large-scale municipal systems.
Ideal for homeowners, contractors, engineers, and anyone interested in modern plumbing solutions, this guide provides valuable insights into why trenchless pipe repair is becoming the preferred choice for pipe rehabilitation. Stay informed about the latest advancements and best practices in the field.
About
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Technical Specifications
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
Key Features
Indigenized remote control interface card suitable for MAFI system CCR equipment. Compatible for IDM8000 CCR. Backplane mounted serial and TCP/Ethernet communication module for CCR remote access. IDM 8000 CCR remote control on serial and TCP protocol.
• Remote control: Parallel or serial interface
• Compatible with MAFI CCR system
• Copatiable with IDM8000 CCR
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
Application
• Remote control: Parallel or serial interface.
• Compatible with MAFI CCR system.
• Compatible with IDM8000 CCR.
• Compatible with Backplane mount serial communication.
• Compatible with commercial and Defence aviation CCR system.
• Remote control system for accessing CCR and allied system over serial or TCP.
• Indigenized local Support/presence in India.
• Easy in configuration using DIP switches.
Welcome to WIPAC Monthly the magazine brought to you by the LinkedIn Group Water Industry Process Automation & Control.
In this month's edition, along with this month's industry news to celebrate the 13 years since the group was created we have articles including
A case study of the used of Advanced Process Control at the Wastewater Treatment works at Lleida in Spain
A look back on an article on smart wastewater networks in order to see how the industry has measured up in the interim around the adoption of Digital Transformation in the Water Industry.
Automobile Management System Project Report.pdfKamal Acharya
The proposed project is developed to manage the automobile in the automobile dealer company. The main module in this project is login, automobile management, customer management, sales, complaints and reports. The first module is the login. The automobile showroom owner should login to the project for usage. The username and password are verified and if it is correct, next form opens. If the username and password are not correct, it shows the error message.
When a customer search for a automobile, if the automobile is available, they will be taken to a page that shows the details of the automobile including automobile name, automobile ID, quantity, price etc. “Automobile Management System” is useful for maintaining automobiles, customers effectively and hence helps for establishing good relation between customer and automobile organization. It contains various customized modules for effectively maintaining automobiles and stock information accurately and safely.
When the automobile is sold to the customer, stock will be reduced automatically. When a new purchase is made, stock will be increased automatically. While selecting automobiles for sale, the proposed software will automatically check for total number of available stock of that particular item, if the total stock of that particular item is less than 5, software will notify the user to purchase the particular item.
Also when the user tries to sale items which are not in stock, the system will prompt the user that the stock is not enough. Customers of this system can search for a automobile; can purchase a automobile easily by selecting fast. On the other hand the stock of automobiles can be maintained perfectly by the automobile shop manager overcoming the drawbacks of existing system.
CFD Simulation of By-pass Flow in a HRSG module by R&R Consult.pptxR&R Consult
CFD analysis is incredibly effective at solving mysteries and improving the performance of complex systems!
Here's a great example: At a large natural gas-fired power plant, where they use waste heat to generate steam and energy, they were puzzled that their boiler wasn't producing as much steam as expected.
R&R and Tetra Engineering Group Inc. were asked to solve the issue with reduced steam production.
An inspection had shown that a significant amount of hot flue gas was bypassing the boiler tubes, where the heat was supposed to be transferred.
R&R Consult conducted a CFD analysis, which revealed that 6.3% of the flue gas was bypassing the boiler tubes without transferring heat. The analysis also showed that the flue gas was instead being directed along the sides of the boiler and between the modules that were supposed to capture the heat. This was the cause of the reduced performance.
Based on our results, Tetra Engineering installed covering plates to reduce the bypass flow. This improved the boiler's performance and increased electricity production.
It is always satisfying when we can help solve complex challenges like this. Do your systems also need a check-up or optimization? Give us a call!
Work done in cooperation with James Malloy and David Moelling from Tetra Engineering.
More examples of our work https://www.r-r-consult.dk/en/cases-en/
Student information management system project report ii.pdfKamal Acharya
Our project explains about the student management. This project mainly explains the various actions related to student details. This project shows some ease in adding, editing and deleting the student details. It also provides a less time consuming process for viewing, adding, editing and deleting the marks of the students.
Forklift Classes Overview by Intella PartsIntella Parts
Discover the different forklift classes and their specific applications. Learn how to choose the right forklift for your needs to ensure safety, efficiency, and compliance in your operations.
For more technical information, visit our website https://intellaparts.com
Immunizing Image Classifiers Against Localized Adversary Attacksgerogepatton
This paper addresses the vulnerability of deep learning models, particularly convolutional neural networks
(CNN)s, to adversarial attacks and presents a proactive training technique designed to counter them. We
introduce a novel volumization algorithm, which transforms 2D images into 3D volumetric representations.
When combined with 3D convolution and deep curriculum learning optimization (CLO), itsignificantly improves
the immunity of models against localized universal attacks by up to 40%. We evaluate our proposed approach
using contemporary CNN architectures and the modified Canadian Institute for Advanced Research (CIFAR-10
and CIFAR-100) and ImageNet Large Scale Visual Recognition Challenge (ILSVRC12) datasets, showcasing
accuracy improvements over previous techniques. The results indicate that the combination of the volumetric
input and curriculum learning holds significant promise for mitigating adversarial attacks without necessitating
adversary training.
COLLEGE BUS MANAGEMENT SYSTEM PROJECT REPORT.pdfKamal Acharya
The College Bus Management system is completely developed by Visual Basic .NET Version. The application is connect with most secured database language MS SQL Server. The application is develop by using best combination of front-end and back-end languages. The application is totally design like flat user interface. This flat user interface is more attractive user interface in 2017. The application is gives more important to the system functionality. The application is to manage the student’s details, driver’s details, bus details, bus route details, bus fees details and more. The application has only one unit for admin. The admin can manage the entire application. The admin can login into the application by using username and password of the admin. The application is develop for big and small colleges. It is more user friendly for non-computer person. Even they can easily learn how to manage the application within hours. The application is more secure by the admin. The system will give an effective output for the VB.Net and SQL Server given as input to the system. The compiled java program given as input to the system, after scanning the program will generate different reports. The application generates the report for users. The admin can view and download the report of the data. The application deliver the excel format reports. Because, excel formatted reports is very easy to understand the income and expense of the college bus. This application is mainly develop for windows operating system users. In 2017, 73% of people enterprises are using windows operating system. So the application will easily install for all the windows operating system users. The application-developed size is very low. The application consumes very low space in disk. Therefore, the user can allocate very minimum local disk space for this application.
3. CHAPTER- 11 BOUNDARY LAYER
THEORY
• Boundary layer theory was given by “Prandtl” and it is valid for real fluid
flowing over infinitely large medium.
• When a real fluid flows past a solid surface, fluid particles adheres to the
boundary due to no –slip condition i.e. if boundary is stationary, fluid on it will be
stationary and if boundary is moving, fluid attached to it also moves.
• As distance from boundary increases, velocity gradually increases upto certain
distance (𝛿) and then becomes constant.
• This region “𝛿” is termed as “Boundary Layer Region”.
• There exist velocity gradient inside the boundary region and it varies from
maximum at boundary of solid surface to zero at “𝛿” from boundary of solid
surface.
• Hence, shear stress is also maximum at boundary of solid surface (τ = μ
du
dy
).
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4. Essential boundary conditions are as follows:
a) x = 0, 𝛿 = 0, v = 0
b) y = 0, u = 0
c) y = 𝛿, u = Vo
d) y = δ,
du
dy
= 0,
d2u
dy2 = 0
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5. NOTE: When fluid flows pass a flat plate, the velocity at leading edge is zero and
retardation of fluid increases as the plate is exposed to flow. Hence, boundary layer
thickness increases as the distance from leading edge increases. This statement is
valid for both laminar and turbulent flow.
• Upto a certain distance from leading edge, flow in boundary layer is laminar
irrespective of approaching flow nature.
• As depth of laminar boundary layer increases, it cannot dissipate the effect of
instability in flow, hence transition of flow to turbulent takes place.
• Thereby, thickness of turbulent boundary layer is more.
• For calculation purpose, the presence of transition region is neglected.
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7. The change of boundary layer from laminar to turbulent is affected by:
a) Roughness of plate: Greater roughness leads to early transition.
b) Intensity and scale of turbulence: Greater turbulence leads to early transition.
c) Pressure gradient: Positive pressure gradient (pressure increases in direction of
flow) leads to early transition and negative pressure gradient leads to delayed
transition.
d) Plate curvature:
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8. • Transition of boundary layer from laminar to turbulent is assumed to occur at
“Rex = 5×105” (for flat plate)
𝐑𝐞𝐱 =
𝐯𝐨𝐱
𝛎
Where, vo = free stream velocity
x = distance from leading edge
ν = kinematic viscosity
Hence, if Rex < 5×105 : Boundary layer is laminar
If Rex > 5×105 : Boundary layer is turbulent
• Thickness of boundary layer depends on following:
A. Velocity of flow: As velocity increases, boundary layer thickness at a given ‘x’
distance decreases, as flow is constant.
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9. Vo2 > vo1
Ao2 < Ao1
δ2x1 < δ1x1
𝛅𝟐 < 𝛅𝟏
B. Viscosity: As viscosity increases, boundary layer thickness increases as Rex =
vox
ν
∝
1
δ
.
For a particular value of x, if Rex increases, boundary layer thickness decreases.
C. Pressure Gradient: More negative pressure gradient reduces boundary layer
thickness (Q = constant).
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10. • If the plate is smooth, then even in the region of turbulent layer, there is very thin
layer adjacent to the boundary, where flow is laminar, termed as “Laminar Sub-
Layer”.
• Thickness of laminar sub- layer (𝛿′) decreases with increase in Reynolds number
(𝛅′ ∝
𝟏
𝐑𝐞
).
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11. NOTE:
1. Velocity profile in Laminar boundary layer is “parabolic.”
𝐮
𝐯𝐨
=
𝐲
𝛅
𝟐
2. Velocity profile in Turbulent boundary layer is “exponential.”
𝐮
𝐯𝐨
=
𝐲
𝛅
ൗ
𝟏
𝟕
3. Velocity profile in laminar sub- layer is actually parabolic but as thickness is very
less, it may be taken as “linear.”
𝐮
𝐯𝐨
=
𝐲
𝛅′
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12. Q. Assertion (A): Boundary layer theory is applicable only in the vicinity of the
leading edge of the plate.
Reason (R): Boundary layer theory is based on the assumption that its thickness is
small when compared to other linear dimensions.
a) Assertion (A) and Reason (R) are individually true and Reason (R) is correct
explanation of Assertion (A)
b) Assertion (A) and Reason (R) are individually true but Reason (R) is not the
correct explanation of Assertion (A)
c) Assertion (A) is correct but Reason (R) is incorrect
d) Assertion (A) is incorrect but Reason (R) is correct.
[IES: 2006]
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13. IMPORTANT TERMINOLOGY
1. NOMINAL BOUNDARY LAYER THICKNESS (𝜹)
It is the distance from the boundary surface in which velocity reaches 99% of free
stream velocity.
2. DISPLACEMENT THICKNESS (𝜹*)
It is defined as distance by which the boundary should be displaced/ shifted in order
to compensate for the reduction in mass flow rate on account of boundary layer
formation.
ሶ
m= mass flow rate (mass of fluid flowing in unit time)
ሶ
mC = ሶ
mD
ρQC = ρQD
ρAvo = ρ න dQ
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14. δ∗
× 1 vo = න dA(vo − u)
δ∗vo = න(dy × 1)(vo − u)
𝛅∗ = න
𝟎
𝛅
𝟏 −
𝐮
𝐯𝐨
𝐝𝐲
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15. 3. MOMENTUM THICKNESS (𝛉)
It is defined as the distance by which the boundary should be shifted in order to
compensate for the reduction in momentum on the account of boundary layer
formation.
( ሶ
mv)C= ( ሶ
mv)D
𝛉 = න
𝟎
𝛅
𝐮
𝐯𝐨
𝟏 −
𝐮
𝐯𝐨
𝐝𝐲
4. ENERGY THICKNESS (𝛅𝐄)
It is defined as the distance by which boundary layer must be shifted to compensate
the loss of energy.
𝛅𝐄 = න
𝟎
𝛅
𝐮
𝐯𝐨
𝟏 −
𝐮𝟐
𝐯𝐨
𝟐
𝐝𝐲
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16. Q. What is the momentum thickness for the boundary layer with velocity
distribution
u
U
=
y
δ
?
a) δ/6.
b) δ/2
c) 3 δ/2
d) 2 δ
[IES: 2008]
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17. Q. The displacement thickness of a boundary layer is
a) The distance to the point where (v/V) = 0.99
b) The distance where the velocity ‘v’ is equal to the shear velocity V*, that is,
where v = V*
c) The distance by which the main flow is to be shifted from the boundary to
maintain the continuity equation.
d) One- half the actual thickness of the boundary layer
[IES: 1997]
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18. NOTE: 1. Here,
𝛅∗
𝛉
is termed as “Shape factor” for boundary layer.
2. 𝛅∗ > 𝛅𝐄 > 𝛉
3. For laminar boundary layer on flat plate,
𝛅∗
= 𝟎. 𝟑𝟓𝟔, 𝛉 = 𝟎. 𝟏𝟑𝟓𝟔
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19. BOUNDARY LAYER EQUATION
a)
𝜕u
𝜕x
+
𝜕u
𝜕y
= 0 (Continuity equation in 2-D flow)
b) −
1
ρ
𝜕P
𝜕y
= 0 (Pressure gradient across the boundary layer is constant at a particular
section)
P1 = P1’ = P1’’ and P2 = P2’ = P2’’
c) u
𝜕u
𝜕x
+ v
𝜕u
𝜕y
= −
1
ρ
𝜕P
𝜕x
+
1
ρ
𝜕τ
𝜕y
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20. VON KARMAN MOMENTUM INTEGRAL EQUATION
𝛕𝐨
𝛒𝐯𝐨
𝟐
=
𝐝𝛉
𝐝𝐱
Where, τo = Boundary shear stress
ρ = density; vo = free mean velocity; θ = momentum thickness
x = distance from leading edge
This equation is valid for:
a) Laminar boundary layer (however approximately true for turbulent boundary
layer also)
b) Steady flow
c) 2-D flow
d) Incompressible flow
e) Pressure gradient in direction of flow is also zero, i.e.
dP
dx
= 0
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21. DRAG CO- EFFICIENTS
A. LOCAL DRAG CO- EFFICIENT (Cfx)
It is the ratio of wall shear stress at any distance ‘x’ from leading edge to the
dynamic pressure.
𝐂𝐟𝐱 =
𝛕𝐨
𝛒
𝐯𝐨
𝟐
𝟐
B. AVERAGE DRAG CO- EFFICIENT (Cf, avg)
It is the ratio of average wall shear stress to dynamic pressure.
Cf,avg =
τo,avg
ρ
vo
2
2
=
FD
ρ
vo
2
2
. A
𝐂𝐟,𝐚𝐯𝐠 =
𝛕𝐨𝐝𝐀
𝛒
𝐯𝐨
𝟐
𝟐
. 𝐀
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22. BLASIUS EXPRESSION
• In absence of velocity profile, “Blasius Expressions” are used:
A. For laminar boundary on smooth plate:
𝛅
𝐱
=
𝟓
𝐑𝐞𝐱
; 𝐂𝐟𝐱 =
𝟎. 𝟔𝟔𝟒
𝐑𝐞𝐱
; 𝐂𝐟,𝐚𝐯𝐠 =
𝟏. 𝟑𝟐𝟖
𝐑𝐞𝐋
NOTE: These are applicable when boundary layer is laminar throughout, i.e. ReL <
5× 105. Also, δ ∝ x, τo ∝
1
x
.
B. For turbulent boundary layer on smooth plate:
𝛅
𝐱
=
𝟎. 𝟑𝟕𝟔
𝐑𝐞𝐱
ൗ
𝟏
𝟓
; 𝟓 × 𝟏𝟎𝟓
< 𝐑𝐞 < 𝟏𝟎𝟕
𝛅
𝐱
=
𝟎. 𝟐𝟐
𝐑𝐞𝐱
ൗ
𝟏
𝟔
; 𝟏𝟎𝟕 < 𝐑𝐞 < 𝟏𝟎𝟗
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23. NOTE: δ ∝ x Τ
4
5, hence boundary layer thickness increases more rapidly in
turbulent boundary layer than in laminar boundary layer.
Also,
𝐂𝐟𝐱 =
𝛕𝐨
𝛒𝐯𝐨
𝟐
𝟐
=
𝟎. 𝟎𝟓𝟗
𝐑𝐞𝐱
ൗ
𝟏
𝟓
; 𝟓 × 𝟏𝟎𝟓 < 𝐑𝐞 < 𝟏𝟎𝟕
𝐂𝐟𝐱 =
𝛕𝐨
𝛒𝐯𝐨
𝟐
𝟐
=
𝟎. 𝟑𝟕
[𝐥𝐨𝐠𝟏𝟎 𝐑𝐞𝐱 ]𝟐.𝟓𝟖
; 𝟏𝟎𝟕 < 𝐑𝐞 < 𝟏𝟎𝟗
NOTE: τo ∝
1
x ൗ
1
5
, hence boundary shear stress decreases less rapidly in turbulent
boundary layer than in laminar boundary layer.
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24. Also,
𝐂𝐟,𝐚𝐯𝐠 =
𝟎. 𝟎𝟕𝟗
𝐑𝐞𝐋
ൗ
𝟏
𝟓
; 𝟓 × 𝟏𝟎𝟓
< 𝐑𝐞 < 𝟏𝟎𝟕
𝐂𝐟,𝐚𝐯𝐠 =
𝟎. 𝟒𝟓𝟓
[𝐥𝐨𝐠𝟏𝟎 𝐑𝐞𝐋 ]𝟐.𝟓𝟖
; 𝟏𝟎𝟕 < 𝐑𝐞 < 𝟏𝟎𝟗
NOTE: All the above expressions are applicable only if turbulent boundary layer is
present throughout.
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25. Q. The ratio of the co- efficient of friction drag in laminar boundary layer compared
to that in turbulent boundary layer is proportional to
a) RL
1/2
b) RL
1/5
c) RL
3/10
d) RL
-3/10.
[IES: 1996]
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26. Q. If δ1 and δ2 are the laminar boundary layer thickness at a point M distant x from
the leading edge when the Reynolds number of the flow are 100 and 484,
respectively, then the ratio of
δ1
δ2
will be
a) 2.2.
b) 4.84
c) 23.43
d) 45.45
[IES: 2018]
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27. BOUNDARY LAYER SEPARATION
• The boundary layer is formed when fluid flows over the solid surface.
• The velocity in this thin layer of fluid varies from zero to free stream velocity in a
direction normal to the surface.
• The fluid layer adjacent to solid body has to overcome surface friction at the
expense of kinetic energy.
• This loss of kinetic energy can be recovered by momentum exchange (not possible
in laminar boundary layer, but takes place in turbulent boundary layer).
• Thus, velocity of fluid layer goes on decreasing.
• At a certain point on solid body, a stage may come when the boundary layer may
not be able to keep adhering (sticking) to solid body (as at this point, kinetic
energy is not sufficient to overcome resistance offered by the body).
• This results in separation of boundary layer from the body surface. This process is
termed as “Boundary Layer Separation” and point ‘D’ is termed as “Point of
Separation”.
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29. If we consider flow over curved surface ABCDE,
a) In region ABC, area of flow reduces, hence velocity of flow increases due to
which pressure decreases in the direction of flow (
𝐝𝐏
𝐝𝐱
< 𝟎).
b) Along region CDE, area of flow increases, hence velocity of flow decreases due
to which pressure increases in the direction of flow (
𝐝𝐏
𝐝𝐱
> 𝟎).
c) As velocity of flow decreases in this region, at a point, it reduces to such a value
that it is not capable of overcoming the resistance offered by surface.
d) At such point ‘D’, boundary layer separation takes place.
e) Downstream of point ‘D’, the flow takes place in the reverse direction and
velocity gradient becomes negative (
𝐝𝐮
𝐝𝐲
< 𝟎).
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30. • Boundary layer separation is observed in pumps, fans, diffusers, turbine blades,
aero-foils, open channel transitions, etc.
• Boundary layer separation leads to increase in pressure drag, magnitude of which
is more than frictional drag.
• Boundary layer separation can be controlled by:
a) By accelerating the fluid in boundary layer by injecting another/ same fluid.
b) By creating suction of fluid from boundary layer.
c) By streamlining the body.
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31. Q. Flow separation is likely to occur when the pressure gradient is
a) Positive.
b) Zero
c) Negative
d) Negative and only when equal to -0.332
[GATE: 1992]
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32. Q. Which of the following is responsible for the separation of boundary layer?
a) Positive pressure gradient.
b) High viscosity of fluid
c) Low viscosity of fluid
d) None of these
[SSC: 2017]
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33. Q. Separation of flow occurs when pressure gradient
a) Tends to approach zero.
b) Becomes negative
c) Changes abruptly
d) Reduces to a value when vapor formation starts
[SSC: 2016]
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34. Q. Assertion: At the point of boundary layer separation, the shear stress is zero.
Reason (R): The point of separation demarcates between zones of forward and
reverse flow close to the wall.
a) Assertion (A) and Reason (R) are individually true and Reason (R) is correct
explanation of Assertion (A).
b) Assertion (A) and Reason (R) are individually true but Reason (R) is not the
correct explanation of Assertion (A)
c) Assertion (A) is correct but Reason (R) is incorrect
d) Assertion (A) is incorrect but Reason (R) is correct
[IES: 2011]
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35. Q. Consider the following statements:
The critical value of Reynolds number at which the boundary layer changes from
laminar to turbulent depends upon
1. Turbulence in ambient flow
2. Surface roughness
Which of the above statements is/ are correct?
a) Neither 1 nor 2
b) 1 only
c) 2 only
d) Both 1 and 2.
[IES: 2008]
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36. Q. Which one of the following assumptions in deriving the boundary layer equation
of flow past a flat plate at zero incidence is not correct?
a) Uniform flow = 0
b) Outside boundary layer velocity is vo throughout
c) The boundary layer thickness 𝛿 is very small compared to distance x
d) Pressure remains constant throughout the flow both within and outside the
boundary layer.
[IES: 2006]
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37. Q. Match List-I with List- II and select the correct answer:
Codes: A B C D
a) 1 2 3 4
b) 2 1 3 4
c) 1 2 4 3
d) 2 1 4 3.
[IES: 2002]
List- I List- II
A.
𝜕u
𝜕y y=0
is zero 1. The flow is attached flow
B.
𝜕u
𝜕y y=0
is positive 2. The flow is on the verge of separation
C. Displacement thickness 3. 0
δ u
U
1 −
u
U
dy
D. Momentum thickness 4. 0
δ
1 −
u
U
dy
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38. Q. A flat plate is kept in an infinite fluid medium. The fluid has a uniform free
stream velocity parallel to the plate. For the laminar boundary layer formed on the
plate, pick the correct option matching List- I and List- II.
Codes: A B C
a) 1 2 3
b) 2 2 2
c) 1 1 2
d) 2 1 3.
[GATE: 2003]
List- I List- II
A. Boundary layer thickness 1. Decreases in the flow direction
B. Shear stress at the plate 2. Increases in the flow direction
C. Pressure gradient along the plate 3. Remains unchanged
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