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1. BOUNDARY LAYER
THEORY
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Name :- Gaurang Atul Thakare ( SYMEB261 )
Roll No.:- SYMEB261
Div.:- B ( Mechanical )

2. Introduction
 The concept of boundary layer was first introduced by a German engineer, Prandtl in 1904.
According to Prandtl theory, when a real fluid flows past a stationary solid boundary, the
flow will be divided into two regions. i) A thin layer adjoining the solid boundary where the
viscous force and rotation cannot be neglected. ii) An outer region where the viscous
force is very small and can be neglected. The flow behaviour is similar to the upstream
flow.
 When a real fluid flow past a solid boundary, a layer of fluid which comes in contacts with
the boundary surface adheres to it on account of viscosity. Since this layer of fluid can not
slip away from the boundary surface it attains the same velocity as that of the boundary.
 This is also called as no slip condition.
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3. Contd..,
 When a real fluid flow past a solid body or a solid wall, the fluid particles adhere to
the boundary and condition of no slip occurs. This means that the velocity of fluid
close to the boundary will be same as that of the boundary.
 If the boundary is stationary, the velocity of fluid at the boundary will be zero. Farther
away from the boundary, the velocity will be higher and as a result of this variation of
velocity, the velocity gradient du/dy will exit. The velocity of fluid increases from zero
velocity on the stationary boundary to free stream velocity (U) of the fluid in the
direction normal to the boundary.
 Because of this velocity gradient the fluid exerts a shear stress on the wall in the
direction of motion. The value of shear stress is given by
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4. Laminar & turbulent zones in boundary layer
 Laminar zone: Near the leading edge of
the surface of plate, where the thickness is
small, the flow in the boundary layer is
laminar. This is shown by AB.
 Transition zone:
The short length over which the boundary
layer flow changes from laminar to
turbulent is called transition zone. This is
shown by BC.
 Turbulent zone:
For down stream to the transition zone ,
the boundary layer is turbulent and
continuous to grow in thickness. This layer
is called turbulent. This is shown by CD.
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5. Boundary layer thickness
 It is defined as the distance from the boundary of the solid body measure in the y-
direction to the point, where the velocity of the fluid is approximately equal to 0.99 times
the free stream velocity of the fluid.
 This variation of velocity from zero to 99%free stream velocity in the direction normal to
the boundary takes place in a narrow region in the vicinity of solid boundary. This narrow
region of the fluid is called boundary layer. The theory dealing with boundary layer flows
is called boundary layer theory.
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6. Displacement Thickness ,
Momentum Thickness &
Energy Thickness
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7. A boundary layer is the layer of fluid in the immediate vicinity of a bounding surface
where the effects of viscosity are significant.
Boundary
Layers
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8. 8
There are Four main definitions of boundary layers
:
1.Boundary layer thickness
2.Displacement thickness
3.Momentum thickness
4.Energy thickness

9. 9
Assumptions
The boundary layer equations require several assumptions about the flow in the boundary layer.
1. All of the viscous effects of the flow field are confined to the boundary layer, adjacent to
the wall . Outside of the boundary layer, viscous effects are not important, so that flow can
be determined by in viscid solutions such as potential flow or Euler equations.
2. The viscous layer is thin compared to the wall.
3. The boundary conditions of the boundary layer region are the no-slip condition at the wall.

10. It is defined as the distance by which the boundary should be displaced to compensate for the
reduction in flow rate of mass of the flowing fluid on account of boundary layer formation.
δ(x) is the boundary layer thickness when u(y) =0.99V
 V is the free-stream velocity
 The purpose of the boundary layer is to allow the fluid to change its velocity from the upstream
value of V to zero on the surface
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Boundary Layer
Thickness

11.  There is a reduction in the flow
rate due to the presence of the
boundary layer
 This is equivalent to having a
theoretical boundary layer with
zero flow
Displacement Thickness 11

12. Mathematically
:
Because of the velocity deficit, within the boundary layer, the flow rate across section b–b is
less than that across section a–a. However, if we displace the plate at section a–a by an
appropriate amount the boundary layer displacement thickness, the flow rates across each
section will be identical.
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Where b is plate width

13. Momentum Thickness 13
 Momentum thickness is a measure of the boundary layer thickness.
 It is defined as the distance by which the boundary should be displaced to compensate
for the reduction in momentum of the flowing fluid on account of boundary layer
formation
 The momentum thickness, symbolized by Ө is the distance that, when multiplied by the
square of the free-stream velocity, equals the integral of the momentum defect, across
the boundary layer.

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It is often used when determining the drag on an object. Again because of the velocity deficit U-u, in
the boundary layer, the momentum flux across section b–b in Fig. 9.8 is less than that across
section a–a. This deficit in momentum flux for the actual boundary layer flow on a plate of width b is
given by

15. Mathematically
:
which by definition is the momentum flux in a layer of uniform speed U and thickness Ө.That is,
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16. 16
It is often used when determining the drag on an object. Again because of the velocity deficit U-u, in
the boundary layer, the kinetic energy across section b–b in Fig. 9.8 is less than that across section
a–a. This deficit in kinetic energy for the actual boundary layer flow on a plate of width b is given by

17. Energy Thickness
 Energy thickness is a measure of the boundary layer thickness.
 It is defined as the distance 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
 The energy thickness, symbolized by Ө** is the distance that, when multiplied by the cube
of the free-stream velocity, equals the integral of the energy defect, across the boundary
layer.
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19. Separation of boundary layer
 As the flow proceed over a soil surface , the boundary layer thickness increases .
 The velocity profile change from parabolic to logarithmic .
 The fluid layer adjacent to the solid surface has to do work against surface friction by
consuming some kinetic energy. This loss of kinetic energy recovered from adjacent fluid layer
through momentum exchange process.

20.  Thus the velocity of the layer goes on decreasing.
 Along the length of solid body, at a certain point a stage may come when the boundary layer
may not be able to keep sticking to the solid body .
 In other words , the boundary layer will be separated from the surface . This phenomenon is
called the boundary layer separation.
 The point on the body at which the boundary layer is on the verge of separation from the surface
is called point of separation.

21. Disadvantage of boundary layer separation
 Separation of boundary layer greatly affect the flow as a whole.
 In particular the formation of a weak zone of disturbed fluid on the downstream, in which the
pressure is approximately constant and much less than that on the upstream, gives rise to
boundary forces.
 Thus, the separation of boundary layer gives to additional resistance to flow.
 Separation of boundary layer from the surface of a body is a accompained by reversed flow in
the vicinity of the body.
 Reversal of flow and consequent eddy formation are generally undesirable because
considerable amount of energy is lost in the process of eddying.
 It is therefore necessary to control the separation of boundary layer as far as possible.

22. Method of controlling separation of boundary layer
1. Acceleration of the fluid in the boundary layer:
 This method consist of supplying additional energy to the particle of fluid which are being
retarded in the boundary layer.
 This may be achieved by injecting fluid into the region of boundary layer from the interior of
the body with the help of some suitable device shown in fig.

23. 2. Suction of the fluid from the boundary layer :
 In this method the slow moving fluid in the boundary layer is removed by suctions through
slots, so that on the downstream of the point of suction a new boundary layer starts
developing which is able to withstand an adverse pressure gradient and hence separation
is prevented.
3.Motion of solid boundary :
 The formation of the boundary layer is due to the difference between the velocity of the
flowing fluid and that of the solid boundary.
 As such it is possible to eliminate the formation of boundary layer by causing the solid
boundary to move with the flowing fluid.
4. When the flow take place round a bend, a pressure gradient is generated and there is a
tendency of separation at the inner radius of the bend.

24. Control of separation.

25. Streamlined body
 It is defined as the type of body whose surface coincides with the stream – lines, when the body is
placed in a flow. In this case the flow separation does not occur up to rear most of the body.
 Thus behind a stream lined body, wake formation zone will be very small. The total drag on the
streamlined body drag will be very small.
 A streamlined body is a shape that lowers the friction drag between a fluid, like air and water, and
an object moving through that fluid.
 Drag is a force that slows down motion; friction drag is a special kind of drag.
 It occurs when the fluid closest to the object sticks to its surface, exerting a force that opposes the
object’s motion.
 Many animals, such as birds and dolphins, and many machines such as airplanes and submarines,
have streamlined bodies to reduce friction drag as they move through either air or water.
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26. Bluff body
 It is defined ass that type of body whose surface does not coincide with the streamlines,
when placed in a flow.
 Bodies subjected to fluid flow are classified as being streamlined or blunt/bluff, depending
on their overall shape.
 A bluff body can be defined as a body that, as a result of its shape, has separated flow over
a substantial part of its surface. Any body which when kept in fluid flow, the fluid does not
touch the whole boundary of the object. An important feature of a bluff body flow is that
there is a very strong interaction between the viscous and inviscid regions.
 Cylinders and spheres are considered bluff bodies because at large Reynolds numbers the
drag is dominated by the pressure losses in the wake.
 Therefore, when the drag is dominated by a frictional component, the body is called
a streamlined body; whereas in the case of dominant pressure drag, the body is called
a bluff body.
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28. Thank You
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