LECTURE NO 1 BL

1. RSR RUNGTA COLLEGE OF ENGINEERING AND
TECHNOLOGY, BHILAI (C. G.)
Department of Mechanical Engineering
BE - 5th Semester
Name of Subject: Fluid Machinery
Subject Code: 337554 (37)
Lecture No.: Unit 1 : L 1
Topic: INTRODUCTION OF SUBJECT ACCORDING TO SYLLAYBUS AND
BOUNDARY LAYER ANALYSIS
Name of Faculty: ANKIT KUMAR DUBEY

2. Introduction
• External flows past objects encompass an extremely wide variety of fluid
mechanics phenomena. Clearly the character of the flow field is a function of the
shape of the body.
• For a given shaped object, the characteristics of the flow depend very strongly on
various parameters such as size, orientation, speed, and fluid properties.
• According to dimensional analysis arguments, the character of the flow should
depend on the various dimensionless parameters involved.
• For typical external flows the most important of these parameters are the Reynolds
number, Re =UL/ν, where L–is characteristic dimension of the body.

3. Introduction
• For many high-Reynolds-number flows the flow field may be divided into two region
i. viscous boundary layer adjacent to the surface
ii. The essentially in viscid flow outside the boundary layer
• We know that fluids adhere the solid walls and they take the solid wall velocity. When
the wall does not move also the velocity of fluid on the wall is zero.
• In region near the wall the velocity of fluid particles increases from a value of zero at the
wall to the value that corresponds to the external ”frictionless” flow outside the
boundary layer

4. : Visualization of the flow around the car. It is visible the thin layer along the body cause by viscosity of the
fluid. The flow outside the narrow region near the solid boundary can be considered as ideal (inviscid).

5. 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 at
large values of the Reynolds number, the flow will be divided into two regions.
i.A thin layer adjoining the solid boundary, called the boundary layer, where the viscous
effects and rotation cannot be neglected.
ii.An outer region away from the surface of the object where the viscous effects are very
small and can be neglected. The flow behavior is similar to the upstream flow. In this
case a potential flow can be assumed.

6. Introduction
• Since the fluid at the boundaries has zero velocity, there is a steep velocity gradient from the
boundary into the flow. This velocity gradient in a real fluid sets up shear forces near the boundary
that reduce the flow speed to that of the boundary.
• That fluid layer which has had its velocity affected by the boundary shear is called the boundary
layer.
• For smooth upstream boundaries the boundary layer starts out as a laminar boundary layer inwhich
the fluid particles move in smooth layers.
• As the laminar boundary layer increases in thickness, it becomes unstable and finally transforms into
a turbulent boundary layer in which the fluid particles move in haphazard paths.
• When the boundary layer has become turbulent, there is still a very thon layer next to the boundary
layer that has laminar motion. It is called the laminar sublayer.

7.  Therefore, there will be presence of velocity gradient
(du/dy) due to variation of velocity of fluid particles.
 The variation in the velocity of the fluid particles,
from zero at the surface of stationary boundary to the
free stream velocity (U) of the fluid, will take place
in a narrow region in the vicinity of solid boundary
and this narrow region of the fluid will be termed as
boundary layer.
 Science and theory dealing with the problems of boundary layer flows will be
termed as boundary layer theory.
According to the boundary layer theory, fluid flow around the solid
boundary might be divided in two regions as mentioned and displayed here
in following figure.

9. First region
A very thin layer of fluid, called the boundary layer, in the immediate region
of the solid boundary, where the variation in the velocity of the fluid particles, from zero at the
surface of stationary boundary to the free stream velocity (U) of the fluid, will take place.
There will be presence of velocity gradient (du/dy) due to variation of velocity of fluid
particles in this region and therefore fluid will provide one shear stress over the wall in the
direction of motion.
Shear stress applied by the fluid over the wall will be determined with the help of following
Equation.n𝜏 = μ x (du/dy)
Second region
Second region will be the region outside of the boundary layer. Velocity of the fluid
particles will be constant outside the boundary layer and will be similar with the free stream
velocity of the fluid.
In this region, there will be no velocity gradient as velocity of the fluid particles will be
constant outside the boundary layer and therefore there will be no shear stress exerted by
the fluid over the wall beyond the boundary layer.

10. BASIC DEFINITIONS
• 1. Laminar boundary
layer
Length of the plate from the
leading edge up to which
laminar boundary layer
exists will be termed as
laminar zone. AB indicates
the laminar zone in above
figure. Length of the plate
from the leading edge up
to which laminar
boundary layer exists i.e.
laminar zone will be
determined with the help
of following formula as
mentioned here.

11. 2.Turbulent boundary layer fundamentals
If the length of plate is greater than the value of x which is determined
from above equation, thickness of boundary layer will keep increasing in the downstream
direction.
Laminar boundary layer will become unstable and movement of fluid particles within it will
be disturbed and irregular. It will lead to a transition from laminar to turbulent boundary
layer.
This small length over which the boundary layer flow changes from laminar to turbulent will
be termed as transition zone. BC, in above figure, indicates the transition zone.
Further downstream the transition zone, boundary layer will be turbulent and the layer of
boundary will be termed as turbulent boundary layer.
FG, in above figure, indicates the turbulent boundary layer and CD represent the turbulent
zone.

12. BOUNDARY LAYER THICKNESS
• Boundary layer thickness
• Boundary layer thickness is basically defined as the distance from the surface of the
solid body, measured in the y-direction, up to a point where the velocity of flow is
0.99 times of the free stream velocity of the fluid.
• Boundary layer thickness will be displayed by the symbol δ.
• We can also define the boundary layer thickness as the distance from the surface of
the body up to a point where the local velocity reaches to 99% of the free stream
velocity of fluid.

13. Displacement thickness
• Displacement thickness is basically defined as the distance,
measured perpendicular to the boundary of the solid body, by which
the boundary should be displaced to compensate for the reduction in
flow rate on account of boundary layer formation.
• Displacement thickness will be displayed by the symbol δ*.
• We can also define the displacement thicknessas the distance,
measured perpendicular to the boundary of the solid body, by which
the free stream will be displaced due to the formation of boundary
layer

14. Momentum thickness
Momentum thickness is basically defined as the distance, measured perpendicular to
the boundary of the solid body, by which the boundary should be displaced to
compensate for the reduction in momentum of the flowing fluid on account of
boundary layer formation.
Momentum thickness will be displayed by the symbol θ.
Energy thickness
Energy thickness is basically defined as 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. Energy thickness will be displayed by the symbol δ**.

15. Applications of Boundary Layer