This document discusses boundary layer theory, which defines a thin layer of fluid near a solid boundary where viscosity is dominant. Ludwig Prandtl first proposed this theory in 1904 to model fluid flow. The boundary layer has different regions and is classified as laminar or turbulent. Key terms like displacement thickness, momentum thickness, and energy thickness are also defined. Boundary layer separation can occur in adverse pressure gradients and examples are given. Methods to prevent separation are outlined. The theory has applications in aerodynamics, heat transfer, and other fluid flow problems.
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
1. Introduction to Kinematics
2. Methods of Describing Fluid Motion
a). Lagrangian Method
b). Eulerian Method
3. Flow Patterns
- Stream Line
- Path Line
- Streak Line
- Streak Tube
4. Classification of Fluid Flow
a). Steady and Unsteady Flow
b). Uniform and Non-Uniform Flow
c). Laminar and Turbulent Flow
d). Rotational and Irrotational Flow
e). Compressible and Incompressible Flow
f). Ideal and Real Flow
g). One, Two and Three Dimensional Flow
5. Rate of Flow (Discharge) and Continuity Equation
6. Continuity Equation in Three Dimensions
7. Velocity and Acceleration
8. Stream and Velocity Potential Functions
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
1. Introduction to Kinematics
2. Methods of Describing Fluid Motion
a). Lagrangian Method
b). Eulerian Method
3. Flow Patterns
- Stream Line
- Path Line
- Streak Line
- Streak Tube
4. Classification of Fluid Flow
a). Steady and Unsteady Flow
b). Uniform and Non-Uniform Flow
c). Laminar and Turbulent Flow
d). Rotational and Irrotational Flow
e). Compressible and Incompressible Flow
f). Ideal and Real Flow
g). One, Two and Three Dimensional Flow
5. Rate of Flow (Discharge) and Continuity Equation
6. Continuity Equation in Three Dimensions
7. Velocity and Acceleration
8. Stream and Velocity Potential Functions
B.TECH. DEGREE COURSE
SCHEME AND SYLLABUS
(2002-03 admission onwards)
MAHATMA GANDHI UNIVERSITY,mg university, KTU
KOTTAYAM
KERALA
Module 1
Introduction - Proprties of fluids - pressure, force, density, specific weight, compressibility, capillarity, surface tension, dynamic and kinematic viscosity-Pascal’s law-Newtonian and non-Newtonian fluids-fluid statics-measurement of pressure-variation of pressure-manometry-hydrostatic pressure on plane and curved surfaces-centre of pressure-buoyancy-floation-stability of submerged and floating bodies-metacentric height-period of oscillation.
Module 2
Kinematics of fluid motion-Eulerian and Lagrangian approach-classification and representation of fluid flow- path line, stream line and streak line. Basic hydrodynamics-equation for acceleration-continuity equation-rotational and irrotational flow-velocity potential and stream function-circulation and vorticity-vortex flow-energy variation across stream lines-basic field flow such as uniform flow, spiral flow, source, sink, doublet, vortex pair, flow past a cylinder with a circulation, Magnus effect-Joukowski theorem-coefficient of lift.
Module 3
Euler’s momentum equation-Bernoulli’s equation and its limitations-momentum and energy correction factors-pressure variation across uniform conduit and uniform bend-pressure distribution in irrotational flow and in curved boundaries-flow through orifices and mouthpieces, notches and weirs-time of emptying a tank-application of Bernoulli’s theorem-orifice meter, ventury meter, pitot tube, rotameter.
Module 4
Navier-Stoke’s equation-body force-Hagen-Poiseullie equation-boundary layer flow theory-velocity variation- methods of controlling-applications-diffuser-boundary layer separation –wakes, drag force, coefficient of drag, skin friction, pressure, profile and total drag-stream lined body, bluff body-drag force on a rectangular plate-drag coefficient for flow around a cylinder-lift and drag force on an aerofoil-applications of aerofoil- characteristics-work done-aerofoil flow recorder-polar diagram-simple problems.
Module 5
Flow of a real fluid-effect of viscosity on fluid flow-laminar and turbulent flow-boundary layer thickness-displacement, momentum and energy thickness-flow through pipes-laminar and turbulent flow in pipes-critical Reynolds number-Darcy-Weisback equation-hydraulic radius-Moody;s chart-pipes in series and parallel-siphon losses in pipes-power transmission through pipes-water hammer-equivalent pipe-open channel flow-Chezy’s equation-most economical cross section-hydraulic jump.
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.
B.TECH. DEGREE COURSE
SCHEME AND SYLLABUS
(2002-03 admission onwards)
MAHATMA GANDHI UNIVERSITY,mg university, KTU
KOTTAYAM
KERALA
Module 1
Introduction - Proprties of fluids - pressure, force, density, specific weight, compressibility, capillarity, surface tension, dynamic and kinematic viscosity-Pascal’s law-Newtonian and non-Newtonian fluids-fluid statics-measurement of pressure-variation of pressure-manometry-hydrostatic pressure on plane and curved surfaces-centre of pressure-buoyancy-floation-stability of submerged and floating bodies-metacentric height-period of oscillation.
Module 2
Kinematics of fluid motion-Eulerian and Lagrangian approach-classification and representation of fluid flow- path line, stream line and streak line. Basic hydrodynamics-equation for acceleration-continuity equation-rotational and irrotational flow-velocity potential and stream function-circulation and vorticity-vortex flow-energy variation across stream lines-basic field flow such as uniform flow, spiral flow, source, sink, doublet, vortex pair, flow past a cylinder with a circulation, Magnus effect-Joukowski theorem-coefficient of lift.
Module 3
Euler’s momentum equation-Bernoulli’s equation and its limitations-momentum and energy correction factors-pressure variation across uniform conduit and uniform bend-pressure distribution in irrotational flow and in curved boundaries-flow through orifices and mouthpieces, notches and weirs-time of emptying a tank-application of Bernoulli’s theorem-orifice meter, ventury meter, pitot tube, rotameter.
Module 4
Navier-Stoke’s equation-body force-Hagen-Poiseullie equation-boundary layer flow theory-velocity variation- methods of controlling-applications-diffuser-boundary layer separation –wakes, drag force, coefficient of drag, skin friction, pressure, profile and total drag-stream lined body, bluff body-drag force on a rectangular plate-drag coefficient for flow around a cylinder-lift and drag force on an aerofoil-applications of aerofoil- characteristics-work done-aerofoil flow recorder-polar diagram-simple problems.
Module 5
Flow of a real fluid-effect of viscosity on fluid flow-laminar and turbulent flow-boundary layer thickness-displacement, momentum and energy thickness-flow through pipes-laminar and turbulent flow in pipes-critical Reynolds number-Darcy-Weisback equation-hydraulic radius-Moody;s chart-pipes in series and parallel-siphon losses in pipes-power transmission through pipes-water hammer-equivalent pipe-open channel flow-Chezy’s equation-most economical cross section-hydraulic jump.
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.
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a presentation about Reynolds Number prepared by a group for the course of soil mechanics and was presented to Dr. Mohamed El-Taher. PS we did not create slide no. 17 and don't know its main source
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We all have good and bad thoughts from time to time and situation to situation. We are bombarded daily with spiraling thoughts(both negative and positive) creating all-consuming feel , making us difficult to manage with associated suffering. Good thoughts are like our Mob Signal (Positive thought) amidst noise(negative thought) in the atmosphere. Negative thoughts like noise outweigh positive thoughts. These thoughts often create unwanted confusion, trouble, stress and frustration in our mind as well as chaos in our physical world. Negative thoughts are also known as “distorted thinking”.
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!
Unit 8 - Information and Communication Technology (Paper I).pdfThiyagu K
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3. CONTENT
• Boundary layer theory
1. Introduction
2. History of Boundary Layer Theory
3. Boundary Layer Theory
4. Boundary Layer Structure
5. Boundary Layer Terms
6. Boundary layer Types
7. Boundary layer theory Applications
• Boundary layer Separation
1. Introduction
2. Control of boundary layer separation
3. Examples of boundary layer separation
• References
SANMITA VARMA 3
4. INTRODUCTION
The Boundary Layer Theory defines the boundary as a layer of
fluid developing in flows with very high Reynolds Numbers Re,
that is with relatively low viscosity as compared with inertia
forces.
This theory was introduced in early 1900’s by L.Prandtl.
This theory is helpful in the application of science, technology,
sports and in our livelihood.
SANMITA VARMA 4
5. HISTORY OF THE BOUNDARY LAYER THEORY
• In August of 1904, Ludwig Prandtl Professor in University of
Gottingen presented a paper on ‘Boundary Layer’ in 3rd International
Mathematical Congress in Heidelberg.
• Prandtl was the first to realize that the relative magnitude of the
inertial and viscous forces changed from a layer very near the surface
to a region far from the surface.
• He first proposed the two layer solution which properly models many
flow problems.
SANMITA VARMA 5
6. BOUNDARY LAYER THEORY
It is the locus of a point which the velocity of a point at which the fluid
particles becomes equal to 0.99% of free stream velocity.
A thin layer of fluid acts in such a way ,as if it’s inner surface is fixed to
the boundary of the body.
Velocity of flow at boundary layer is zero.
The velocity of flow will go on increasing rapidly till at the extreme
layer.
The portion which is outside the boundary layer has a high value of
Reynold’s Number, because of the high velocity of flow.
SANMITA VARMA 6
8. BOUNDARY LAYER TERMS
I. Laminar Flow
II. Turbulent flow
III. Reynold’s Number
IV. Displacement Thickness
V. Momentum Thickness
VI. Energy Thickness
SANMITA VARMA 8
9. • It is the flow of a viscous fluid in which particles of
the fluid move in parallel layers, each of which
has a constant velocity but is in motion relative to
its neighboring layer.
• Each liquid particle has a definite path.
• The paths of individual particles do not cross
each other.
• All the molecules in the fluid move in the same
direction and speed.
• Laminar Flow is also called as Stream Line Flow.
I. LAMINAR FLOW
SANMITA VARMA 9
10. • It is the flow of a viscous fluid in which particles of fluid have no
uniform velocity and direction.
• Each liquid particle do not have a definite path.
• The path of individual particle cross each other.
II. TURBULENT FLOW
SANMITA VARMA 10
11. III. REYNOLD’S NUMBER
• It characterizes the flow of a liquid through a tube either as a laminar or
turbulent.
• It is a dimensionless variable.
Formula: Re =
Inertia forces
Viscous forces
=
ρ 𝑉𝐿
μ
Re Value
• Re < 2000 : Laminar flow
• 2000 < Re < 2800 : Transition flow
• Re > 4000 : Turbulent flow
SANMITA VARMA 11
Where,
ρ = density of the fluid
V = velocity of the fluid
L = length or diameter of the fluid
μ = viscosity of fluid.
12. IV. DISPLACEMENT THICKNESS
The distance the perpendicular to the
boundary, by which the free stream is
displaced due to the formation of boundary
layer is called Displacement thickness.
It is represented by (δ*).
By equating the flow rate for velocity to
flow rate for ideal fluid,
If the density if the fluid is constant, the
above equation further simplifies to
SANMITA VARMA 12
13. V. MOMENTUM THICKNESS
Momentum thickness is defined as the distance by which the
boundary should be displaced to compensate for the reduction in the
momentum of the flowing fluid on account of boundary layer formation.
It can also be defined as the distance that, when multiplied by the
square of free stream velocity, equals the integral of the momentum
defect.
It is denoted as θ
Formula :
SANMITA VARMA 13
14. VI. ENERGY THICKNESS
SANMITA VARMA 14
The distance measured perpendicular to the
boundary of the solid body, by which the
boundary should be displaced to compensate
for the reduction in kinetic energy of the
flowing fluid on account of boundary layer
formation.
It is denoted by δ** .
By equating the velocity transport rate for
velocity defect to that for ideal fluid, we get
If density is constant, this simplifies to
15. TYPES OF BOUNDARY LAYER
The viscous nature of airflow reduces the local velocities on a
surface and is responsible for skin friction. On the basis of that
boundary layers are further classified into two types
1. Laminar Boundary Layer.
2. Turbulent Boundary Layer.
SANMITA VARMA 15
16. APPLICATIONS OF BOUNDARY LAYER THEORY
Boundary layer flow is much applied in designing different objects which
have to overcome the flow of the fluids for smooth working. Some of them
are as follows.
I. Aerodynamics: Aircraft.
II. Heat Transfer Enhancement:
III. Particle Transportation: Dust blowing.
IV. To calculate the distance travelled by the golf ball.
V. Flow of liquid in flat plates
VI. Drag on sphere:
SANMITA VARMA 16
18. BOUNDARY LAYER SEPARATION
The detachment of a boundary layer from the surface of the body is
called body layer separation
This occurs when the rate of flow is slowed down and the pressure is
gradually increasing, when the layer passes through the thickest part of
a streamline.
It separates when it has advanced enough distance in an adverse
pressure gradient that the speed of the layer of boundary compared to
the surface has stopped.
Adverse pressure gradient occurs when the pressure increases with the
direction of the flow.
SANMITA VARMA 18
19. POINT OF SEPARATION
It is the point on the body at which the boundary layer is on the verge of
separation from the surface.
Robust thickening of the boundary layer takes place due to the backflow
near to the wall.
Further mass of the boundary layer is fetched up to the outer flow.
In a certain angle, the streamlines tend to leave the surface of the wall
at a point of separation.
SANMITA VARMA 19
21. METHODS TO PREVENT THE SEPARATION OF
THE BOUNDARY LAYER
By supplying additional energy.
By absorbing the slow moving fluid.
Streamlining reduces adverse pressure gradient beyond the
maximum thickness and delays separation.
Acceleration of the fluid in the boundary layer.
SANMITA VARMA 21
22. EXAMPLES OF BOUNDARY LAYER SEPARATION
Diffuser flow: Flow in widening channel(Diffuser)- Separation in both
diffusion walls
Separation at sharp corners: Corners, sharp turns and high angles
of attack all represent sharply decelerating flow situations where the
loss in energy in the boundary layer ends up leading to separation.
Flow over trucks: Flow over non-streamlined bodies such as trucks
leads to considerable drag due to recirculation and separation zones.
SANMITA VARMA 22
23. BOUNDARY LAYER SEPARATION EXAMPLES
SOURCE: WWW..PROJECTS.SKILL-LYNC.COM
FLOW OVER A TRUCK
DIFFUSER FLOW FLOW OVER SHARP EDGES
SANMITA VARMA 23
26. REFERENCE
SANMITA VARMA 26
Books
I. Frank M White, “Fluid Mechanics”,
II. R.K.Bansal, “Fluid Mechanics and hydraulic machines” , Laxmi Publications Pvt.Ltd.
Websites
https://en.wikipedia.org/wiki/Boundary_layer
https://www.grc.nasa.gov/WWW/K-12/airplane/boundlay.html
https://www.quora.com/
You Tube Channel
Julian Edgar: https://youtu.be/sorepmFw4SA
27. THANK YOU
SANMITA VARMA 27
Sanmita Varma Indukoori
Regd No: 318114508055
BTech Civil Engineering, II Semester, II Year,
Andhra University College of Engineering for Women.