Environmental Engineering Reference
In-Depth Information
The following example calculates approximately the used power of a cup
anemometer that is used for the measurement of the wind speed
v
. It consists
of two open hemispherical cups that rotate around a common axis. The wind
impacts the front of the first cup and the back of the second cup (Figure 5.6).
The resulting force
F
consists of a driving and a decelerating component
(Gasch and Twele, 2002):
(5.25)
The used power is:
(5.26)
The ratio of the circumferential speed
u
to the wind speed
v
is called the tip
speed ratio
λ
:
(5.27)
The tip speed ratio of drag devices is always smaller than one. Using the tip
speed ratio, the power is:
(5.28)
Hence, the
power coefficient of the cup anemometer
becomes:
(5.29)
The maximum value of the power coefficient of the cup anemometer is about
0.073. This is much below the ideal Betz power coefficient of 0.593. The cup
anemometer reaches its maximum power coefficient at a tip speed ratio of
about 0.16, when the wind speed
v
is about six times higher than the
circumferential speed
u
.
Figure 5.6
Model of Cup Anemometer for the Calculation of Power
