Environmental Engineering Reference
In-Depth Information
Table 5.4
Example of the Decrease in Wind Speed
v
(
h
2
) at Height
h
2
= 10 m
as a Function of the Ground Class for
v
(
h
1
) = 10 m/s at
h
1
=50m
Ground
z
0
dv
(
h
2
) at
h
2
Ground
z
0
dv
(
h
2
) at
h
2
class
= 10 m
class
= 10 m
1
0.0002 m
0 m
8.71 m/s
5
0.25 m
0 m
6.96 m/s
2
0.005 m
0 m
8.25 m/s
6
0.5 m
3 m
5.81 m/s
3
0.03 m
0 m
7.83 m/s
7
1 m
5 m
4.23 m/s
4
0.1 m
0 m
7.41 m/s
8
2 m
6 m
2.24 m/s
With
and
Equation (5.6) becomes:
(5.7)
For
z
= 10 m and
z
0
= 0.01 m, the parameter
a
is about 1/7; this equation is
then called a 1/7 power law. However, this power law is only valid if the
displacement
d
of the boundary layer from the ground is equal to zero.
U
TILIZATION OF
W
IND
E
NERGY
Power content of wind
The
kinetic energy E
carried by a wind with speed
v
is given by the general
equation:
(5.8)
The
power P
that the wind contains is calculated by differentiating the energy
with respect to time. For a constant wind speed
v
the power is:
(5.9)
The density
ρ
and volume
V
determine the
mass
:
(5.10)
The derivative with respect to time results in the
air mass flow
:
(5.11)
This mass of air with density
ρ
flows through an area
A
with speed
v
. Hence
the power of the wind becomes:
