Environmental Engineering Reference
In-Depth Information
drivetrain and the generator, and aerodynamic losses through the action of
viscosity, is reasonable to assume that the power converted into electricity is about
40% of that given by (
1.3
).
It is important that the derivation of (
1.1
) be understood because the CV
analyses that will be undertaken in later chapters extend the ideas and manipu-
lations used to derive (
1.1
).
Example 1.1 Estimate the power extracted by a 5 m diameter wind turbine at a
wind speed of 10 m/s and determine the number of kWhs produced in a day.
Answer
From Eq.
1.3
and the discussion following the equation, assume
1
2
qAU
0
P
¼
0
:
4
¼
0
:
4
0
:
5
1
:
2
p
2
:
5
2
10
3
¼
4
:
71
10
3
Now check the units: density is in kg/m
3
; area in m
2
; and (velocity)
3
in m
3
/s
3
.
Their product gives kg m
2
/s
3
, which are the units of Watts. Thus the estimate for
the power output is 4,710 W or 4.71 kW. If the wind speed remained constant over
the day, then the number of kWhs produced is 24 9 4.71 = 113.04 kWhs per day.
Note that the ''units'' of kWhs per day or month or year are common ways of
expresses turbine output and are used despite the fact that they can all be reduced
to a multiple of Js.
Example 1.2 Sometimes wind resource surveys give the wind speed in terms of a
''power density'', PD, in W/m
2
which is equal to P/A from Eq.
1.1
. If the power
density is 100 W/m
2
what is the wind speed?
Answer
PD
¼
1
2
qU
0
so that
Þ
1
=
3
¼
5
:
5m
=
s
:
U
0
¼
2
100
=
1
:
2
ð
1.2 Examples of Wind Turbines
Wind turbines range in power output from a few Watts to tens of megawatts. The
IEC safety standard for small wind turbines, IEC 61400-2, defines a small turbine
as having a rotor swept area less than 200 m
2
, which corresponds roughly to
P \ 50 kW. The precise definition of the boundary between small and large is not
critical for this topic, so the IEC division is as good as any. The basic operating
principles are the same for turbines of all sizes. For example, the restriction on
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