Some Elementary Aspects of Boundary Layer Theory
R. Shankar Subramanian
The failure of potential flow theory to predict drag on objects when a fluid
flows past them provided the impetus for Prandtl to put forward a theory of
the boundary layer adjacent to a rigid surface.
Prandtl’s principal
assumptions are listed below.
Assumptions
1. When a fluid flows past an object at large values of the Reynolds number,
the flow region can be divided into two parts.
(i) Away from the surface of the object, viscous effects can be considered
negligible, and potential flow can be assumed.
(ii) In a thin region near the surface of the object, called the boundary layer,
viscous effects cannot be neglected, and are as important as inertia.
2. The pressure variation can be calculated from the potential flow solution
along the surface of the object, neglecting viscous effects altogether, and
assumed to be impressed upon the boundary layer.
U
x
laminar
y
turbulent
Transition from laminar to turbulent flow in the boundary layer on a flat
plate occurs at
, where
5
Re
5
10
x
≈×
Re
x
xU
ν
=
.
Here,
is the
kinematic viscosity of the fluid.
1
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View Full DocumentThe following approximate estimates can be written for the thickness of
laminar and turbulent boundary layers.
Laminar Boundary Layer
5
Re
x
x
δ
∼
Turbulent Boundary Layer
()
1/7
0.16
Re
x
x
∼
Some aspects of the drag on a body when a fluid flows past it at
high Reynolds number
From the four videos by Professor A. Shapiro, we learned some important
ideas about the drag experienced by a body when a fluid flows past it.
Professor Shapiro showed experimental observations that initially appeared
to be paradoxical, and later explained them using physical aspects of
boundary layer theory.
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 Spring '10
 handsome
 Fluid Dynamics, Professor A. Shapiro

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