HYDRODYNAMIC BOUNDARY LAYER
When a fluid flows around an object or when the object moves through
body of fluid, there exists a thin layer of fluid close to the solid surface
within which shear stresses significantly influence the velocity
distribution.
The fluid velocity varies from zero at the solid surface to the velocity of
free stream flow at a certain distance away from the solid surface.
This thin layer of changing velocity has been called the
hydrodynamic boundary layer.
1
HYDRODYNAMIC BOUNDARY LAYER
Flat Plate :
Consider a continuous flow of fluid along
the surface of a thin plate with its sharp
leading edge set parallel to flow direction.
The free stream undistributed flow has a
u∞ =V∞ in the x-direction.
Development of boundary layer on a flat plate
Particles of fluid adhere to the plate
surface as they approach it and fluid is
slowed down.
The fluid becomes stagnant at the plate
surface and this layer of changing
velocity has been called hydrodynamic
boundary layer.
¶u
The condition ¶ y ¹ 0
is true
for the zone within the
boundary layer whist the
conditions for flow beyond
the boundary layer and its
outer edge are ¶u = 0 and
¶y
u=V∞
Thickness of boundary layer
2
δ at u=0.99V∞
HYDRODYNAMIC BOUNDARY LAYER
The thickness of the boundary layer is variable along the flow
direction.
It is zero at leading edge of the plate and increase as the distance x
from the leading edge is increased due to force.
δ is governed by
- Magnitude of incoming velocity
- Kinematic viscosity of the flowing fluid
For some distance from the leading edge the boundary layer is laminar
and velocity profile is parabolic in nature.
Flow within the laminar boundary layer is smooth and the streamlines
are parallel to flow undergoes a change in its flow structure at a certain
point called transition point.
After going through transition zone of finite length, the boundary layer
3
entirely changes to turbulent boundary layer.
HYDRODYNAMIC BOUNDARY LAYER
The thickness of the boundary layer is variable along the flow
direction. It is zero at leading edge of the plate and increase as the
distance x from the leading edge is increased due to force.
δ is governed by
- Magnitude of incoming velocity
- Kinematic viscosity of the flowing fluid
For some distance from the leading edge the boundary layer is laminar
and velocity profile is parabolic in nature.
Flow within the laminar boundary layer is smooth and the streamlines
are parallel to flow undergoes a change in its flow structure at a certain
point called transition point.
After going through transition zone of finite length, the boundary layer
entirely changes to turbulent boundary layer.
The pattern of flow in boundary layer is judged by
Re =
v¥ x
g
4
HYDRODYNAMIC BOUNDARY LAYER
The thickness of the boundary layer is variable along the flow
direction. It is zero at leading edge of the plate and increase as the
distance x from the leading edge is increased due to force.
δ is governed by
- Magnitude of incoming velocity
- Kinematic viscosity of the flowing fluid
For some distance from the leading edge the boundary layer is laminar
and velocity profile is parabolic in nature.
Flow within the laminar boundary layer is smooth and the streamlines
are parallel to flow undergoes a change in its flow structure at a certain
point called transition point.
After going through transition zone of finite length, the boundary layer
entirely changes to turbulent boundary layer.
The pattern of flow in boundary layer is judged by
Re =
v¥ x
g
5