Geoscience Reference
In-Depth Information
Wind direction
C
Unmodified flow
velocity
B
Boundary
layer
Modified flow
velocity
Figure 21.1
Boundary layer
development above a flat plate in
horizontal wind flow. Laminar
flow occurs between A and B but
the flow is unmodified between
B and C.
A
Velocity
boundary-layer resistance
to momentum flow by skin friction per unit area of
plate,
τ
is given by:
(
U
R
−
)
tr
=
(21.2)
a
sf
M
Combining Equations (21.1) and (21.2), the effective value of the boundary-layer
resistance to momentum transfer for unit area of plate becomes:
0.5
l
1.5
⎛
⎞
R
sf
≈
1.5
≈
Re
0.5
(21.3)
⎜
⎟
M
U
ν
U
⎝
⎠
Equation (21.3) suggests that for a flat, horizontal plant leaf with characteristic
dimension 0.05 m in a canopy air stream of 1 m s
-1
,
R
M
sf
is about 100 s m
-1
per unit
area of leaf
. Were the leaf twice as large, the area to which momentum could be
transferred would be larger and the resistance for the leaf would be less. This is the
order of magnitude for the boundary-layer resistance for transfer of momentum
by skin friction and it is also the order of magnitude for the boundary-layer resist-
ance to exchange of other entities such as heat and water vapor that also diffuse
through a boundary layer to reach the surface.
However, if the body in the air stream presents a substantial cross-sectional area
perpendicular to air flow (e.g., a flat leaf at an angle to the flow), referred to as a
'
bluff body
' in aerospace engineering, momentum (but
not
other entities) can be
exchanged more efficiently via pressure forces. In this case the stress exerted via
pressure forces on the bluff body is called '
form drag
. The momentum exchanged
per unit cross-sectional area by form drag to a bluff body in air moving at speed,
U
, is given by:
r
t
=
f
c U
a
2
(21.4)
2
where
c
f
is an empirically determined '
drag coefficient
. Combining Equations
(21.1) and (21.4), if the bluff body is a flat leaf at an angle to the flow,
R
M
bb
, the
