Chapter 1 : Boundary Layer
INTRODUCTION
The condition of zero fluid velocity at the solid
surface is referred to as ‘no slip’ and the layer of
fluid between the surface and the free stream fluid is
termed BOUNDARY LAYER.
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Chapter 1 : Boundary Layer
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Chapter 1 : Boundary Layer
Shear stress,
τ
∂u
τ =µ
∂y
Reynolds number
The criterion which determines whether flow is
laminar or turbulent.
Reynolds number along a smooth flat plate:
ρU s x U s x
Re x =
=
µ
υ
Re < 5 x 105 : Laminar
Re ≈ 5 x 105 : Transition (Engineering critical
Reynolds number)
Re > 5 x 105 : Turbulent
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Chapter 1 : Boundary Layer
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Chapter 1 : Boundary Layer
Turbulent layer usually has a greater
velocity gradient at the surface, which cause greater
shear stress.
From a turbulent layer, there is a more ready
interchange of particles with the main flow, and this
explains the more rapid increase in thickness of a
turbulent layer.
The thickness of a laminar boundary layer
increases as x0.5 (when pressure is uniform), a
turbulent layer thickens approximately as x0.8.
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Chapter 1 : Boundary Layer
BOUNDARY LAYER IN PIPE
Laminar flow; Re < 2000
120 pipe diameters (=120D)
Turbulent flow; Re > 2000
60 pipe diameters (=60D)
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Chapter 1 : Boundary Layer
DEFINITION
z Boundary layer thickness, δ
z Displacement thickness, δ*
z Momentum thickness, θ
BOUNDARY LAYER THICKNESS, δ
Boundary layer thickness is defined as that distance
from the surface where the local velocity equals
99% of the free stream velocity.
δ = y(u =0.99U )
s
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Chapter 1 : Boundary Layer
DISPLACEMENT THICKNESS, δ*
The displacement thickness for the boundary layer is
defined as the distance the surface would have to
move in the y-direction to reduce the flow passing
by a volume equivalent to the real effect of the
boundary layer.
δ =∫
*
δ
0
u
(1 − )dy
Us
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Chapter 1 : Boundary Layer
MOMENTUM THICKNESS θ
Momentum thickness is the distance that, when
multiplied by the square of the free stream velocity,
equals the integral of the momentum defect.
Alternatively, the total loss of momentum flux is
equivalent to the removal of momentum through a
distance θ. It is a theoretical length scale to quantify
the effects of fluid viscosity near a physical
boundary.
δ
θ =∫
0
u ⎛
u ⎞
⎜⎜1 −
⎟⎟dy
Us ⎝ Us ⎠
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