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Title: Boundary Layer Theory
Description: Boundary layer theory and flow separation, flow around rigid bodies.
Description: Boundary layer theory and flow separation, flow around rigid bodies.
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CSE 352: HYDRAULICS II
FLOW AROUND IMMERSED BODIES
Introduction
When a solid body is held in the path of a moving fluid and is completely immersed in it, the
body will be subjected to some pressure or force
...
g
...
Pressure on a Body Immersed in a Moving Liquid
...
It has been experimentally found that if a plate is held immersed at some angle with the direction
of flow of the liquid, the streamlines of the liquid get deflected as shown below
...
Newton’s Law of Resistance
...
Mathematically the force,
=
K is a constant
...
The planes of the body are completely smooth
...
The space around the body is completely filled with the fluid
...
The fluid has large numbers of the particles having mass but no dimension
...
The fluid particles do not exert any influence on one another
...
The body experiences impacts from all the particles in its path
...
5 and less for skewed planes or
rounded bodies like spheres
...
K TARAGON 2015
Page 1
CSE 352: HYDRAULICS II
F=
As by Pascal’s law, the pressure exerted by the moving liquid will be at right angles to the plate
...
Drag
Whenever a plate is held immersed at some angle with its direction of flow of the liquid, it is
subjected to some pressure
...
The component of this pressure in the direction of the flow of the liquid is the drag
...
Lift
The component of the pressure in right angles to direction of flow is the lift
...
K TARAGON 2015
Page 2
CSE 352: HYDRAULICS II
Air Foil Theory
...
In practical aeronautics, we are interested in air foils, in which the resistant force is
nearly perpendicular to the direction of flow
...
Since the lift serves the purpose of supporting the aeroplanes thus more lift the better
...
It has been experimentally found that if a flat plate is inclined at 40, the ratio of force of lift to
force of drag (
is about 6 (six)
...
This ratio is further increased by nicely rounding off the front end of the plate
and providing a sharp edge to its tail
...
The above theory is popularly known as air foil theory
...
According to this theory, the liquid in the vicinity of the surface of the body
may be divided into two portions;
1
...
Since this
thin layer of the fluid acts in such a way as if its inner surface is fixed to the boundary of
the body, therefore velocity of the fluid at the boundary is zero
...
If we go away from the surface of the body, normal to the flow of the fluid till extreme
layer, the velocity of the flow is extremely/approximately equal to the velocity of fluid
outside the boundary layer (velocity approx
...
99 times velocity of flow of liquid)
2
...
Thickness of a Boundary Layer
The distance from the surface of the body, to a place where the velocity of flow is 0
...
For some
distance, from the leading edge, the flow is laminar which expands to transitional boundary then
turbulent boundary layer
...
J
...
ν is the kinematic viscosity
Then
Rx < 500,000 – fully lamina
500, 000 < Rx < 100,000 - transition
Rx > 100,000 – fully turbulent
The thickness of boundary layer is different in laminar flow and turbulent flow
...
Many scientists have conducted experiments to determine boundary layer thickness
...
Though there are many relations for finding out the thickness of the boundary layer in a turbulent
flow, yet Prandtl-Blassius relation is widely used, according to which the thickness of boundary
layer in a turbulent flow
Where ϰ is the distance between leading edge of the body and the section where thickness of the
boundary layer is required to be found
...
K TARAGON 2015
Page 4
CSE 352: HYDRAULICS II
Boundary Layer Separation
...
But if the immersed body is curved or angular one, the
boundary layer does not stick to the whole surface of the body
...
This phenomenon is known as boundary separation
...
Prandtl’s Experiment of Boundary Layer Separation
...
He held a cylinder in
flowing liquids and sprinkled a laminar particle, to aid in visibility of streamlines
...
He gradually increased the velocity of fluid and at a stage he found that the layer has separated
on both sides of D and vortices have formed as in Figure (b)
...
See Figure (c)
Magnus Effect in a Moving Liquid
Consider the streamline pattern as in Figure (a) below
...
The
phenomenon is called Magnus effect
...
J
...
The separation of the boundary layer in a turbulent flow may be prevented in order to have the
layer reduced drag
...
The
Figure (a) and (b) shows the effect of a slot on the streamline
...
b) The boundary layer separation may also be prevented by providing a rotating cylinder as
we have seen above
...
A flying object of surface area 0
...
25N, while moving with a
velocity of 16m/s in an air of specific weight of 11
...
What is the value of the
coefficient of lift?
2
...
If the
coefficient of lift and drag are 0
...
15 respectively, determine the resultant force
and power required to keep the plate in motion
...
A plate is held in a path of flowing water which has a uniform velocity of 3 m/s
...
Also
find the thickness of the boundary layer at this point
...
A plate 1
...
5 m wide is held in the path of flowing water at 200 C with a
velocity of 0
...
Find the type of flow near the trailing edge of the plate
...
J
Title: Boundary Layer Theory
Description: Boundary layer theory and flow separation, flow around rigid bodies.
Description: Boundary layer theory and flow separation, flow around rigid bodies.