Page 78 - Fluid Power Engineering

56 Chapter Four

y
x
Boundary
Layer
Separation
Laminar Boundary Point Wake
Layer Turbulent Boundary
Layer

FIGURE 4-17 Formation of boundary layer on an airfoil.

of the tube; for an open rectangular channel, l is the ratio of cross-
sectional area of fluid and perimeter of the channel in contact with the
fluid; for a flat plate, l is the distance from the edge; for an airfoil, l is
the chord length.
Reynolds number is a dimensionless quantity that is used to de-
scribe when a flow transitions from laminar to turbulent. Consider
two examples below:
Flow in a pipe of diameter d,

Laminar flow when R < 2,300
Transient when 2,300 < R < 4,000 (4-28)
Turbulent when R > 4,000

Irrespective of the type of fluid, size of pipe, and free-stream speed v,
the flow will satisfy the conditions in Eq. (4-28).

Flow of Fluid over an Airfoil
On the surface of the airfoil, there is no slip, so the speed is zero. Away
from the surface, the speed increases and reaches the free-stream
speed. This region is the boundary layer. Skin-friction drag acts on
the airfoil because there is friction on the surface and shear force that
opposes the change in speed between layers.
In a laminar boundary layer, all the fluid flow is parallel to the
surface. In turbulent boundary layer:

The speed near the surface of the aerofoil is higher; that is,

there is a rapid change in speed from zero on the surface to
nonzero a short distance away from the surface.
The thickness of the boundary layer is larger.

Energy is exchanged from the faster moving particles in the

boundary layer to the slower moving particles near the sur-
face.