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ECE 333 Homework 4 Solutions :: Spring 2010
1
A horizontalaxis wind turbine with rotor 20 meters in diameter is 30percent efficient in 10 m/s winds at 1
atmosphere of pressure and 15
o
C temperature.
a. How much power would it produce in those winds?
P
!"#
P
wind
!"#
1
2
$
A v
3
!
0.3
"
1
2
1.225
#
4
20
2
10
3
!
P
$
57.73
kW
b. Estimate the air density on a 2500meter mountaintop at 10
o
C.
From Table 6.1 the density at 10
o
C is 1.247 kg/m
3
, yielding a K
T
ratio of 1.247/1.225 = 1.018.
Using (6.13), the density ratio, K
A
, can be found:
P
!
P
0
exp
!"
1.185x10
"
4
#
2500
$%
0.9109
K
A
!
0.9109
1.225
!
0.743
The air density at 2500meters can now be found using (6.14):
"!
1.225
K
T
K
A
!
1.225
"
1.018
"
0.743
#$!
0.927
kg
%
m
3
Note that (6.7) could also be used to find the same solution.
c. Estimate the power the turbine would produce on that mountain with the same windspeed assuming its
efficiency is not affected by air density.
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 Spring '09
 Overby

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