Fluid Mechanics- Boundary Layer Theory

1. FLUID MECHANICS

2. Sanmita Varma Indukoori
BOUNDARY LAYER THEORY

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
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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.
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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.
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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.
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7. BOUNDARY LAYER STRUCTURE
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8. BOUNDARY LAYER TERMS
I. Laminar Flow
II. Turbulent flow
III. Reynold’s Number
IV. Displacement Thickness
V. Momentum Thickness
VI. Energy Thickness
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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
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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
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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
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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
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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 :
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14. VI. ENERGY THICKNESS
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 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.
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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:
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17. BOUNDARY LAYER SEPARATION

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.
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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.
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20. BOUNDARY LAYER SEPARATION
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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.
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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.
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23. BOUNDARY LAYER SEPARATION EXAMPLES
SOURCE: WWW..PROJECTS.SKILL-LYNC.COM
FLOW OVER A TRUCK
DIFFUSER FLOW FLOW OVER SHARP EDGES
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24. LEADING EDGE SEPARATION EFFECT OF BODY SHAPE ON SEPARATION
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25. LAMINAR AND TURBULENT SEPARATION
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26. REFERENCE
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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
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Sanmita Varma Indukoori
Regd No: 318114508055
BTech Civil Engineering, II Semester, II Year,
Andhra University College of Engineering for Women.