The density of air at sea level and 20 °C is pair 1.2 kg/m3 1 Joule 1kg-m2/s2. v
ID: 1867911 • Letter: T
Question
The density of air at sea level and 20 °C is pair 1.2 kg/m3 1 Joule 1kg-m2/s2. v in m/s A in m2 The equation given in Lecture 8 for the power delivered to a given area by wind moving at v (m/s) is Power Delivered (J/s, or w)-(1/21paí. A Power Delivered (MW)-10*x(1/2) pair V A Now, power extracted-efficiency (8) x power delivered so so Power Extracted (MW) ? x 10-6 x (1/2) Par-A so As noted above, "The rated speed is usually in the range of 25 to 35 mph." https://www.wind- watch.org/faq-technology.php a. Taking 30 mph as the rating speed, convert to m/s (of course) for v, and estimate ? for each of the wind turbine sizes b. Are the bigger/newer turbine more efficient?Explanation / Answer
A) Given equation
P = E*10-6 * (1/2)?* v3 A
For v = 30 mph = (30 *1609) / (60 * 60) = 13.41 m/s and ? = 1.2 kg/m3
P = E*10-6 * (1/2)*1.2* 13.413 *A
P = 1.447 ?*10-3 * A
Or E = 691.13 (P / A)
We use the above equation to find the efficiencies
Turbine
Area
Power (MW)
Efficiency
% Efficiency
Suzlon 950
3217
0.95
0.20
20.41
Suzlon S64
3217
1.25
0.27
26.85
GE 1.5s
3904
1.5
0.27
26.55
Siemens
4536
2.3
0.35
35.04
GE 1.5sle
4657
1.5
0.22
22.26
Vestas V82
5281
1.65
0.22
21.59
Siemens
5333
2.5
0.32
32.40
Gamesa G87
5945
2
0.23
23.25
Suzlon S88
6082
2.1
0.24
23.86
Clipper Liberty
6221
2.5
0.28
27.77
Vestas V90
6362
1.8
0.20
19.55
Vestas V90
6362
3
0.33
32.59
Repower MM92
6720
2
0.21
20.57
Siemens
6793
2.3
0.23
23.40
Goldwind
7000
2.5
0.25
24.68
Mitsubishi MW95
7088
2.4
0.23
23.40
Gamesa G97
7390
2
0.19
18.70
Vestas V100
7854
2.75
0.24
24.20
Vestas V110
9503
2
0.15
14.55
Vestas V112
9852
3
0.21
21.05
b) From the table above, it ant be necessarily said that bigger turbines are more efficient. Infact the most efficient turbine is the Siemens model which is the fourth smallest in the list.
However, the newer models can be significantly more efficient. For example, for the Vestas V90, the newer model has an efficiency of 32.56% while the older one was only 19.55% efficient.
Turbine
Area
Power (MW)
Efficiency
% Efficiency
Suzlon 950
3217
0.95
0.20
20.41
Suzlon S64
3217
1.25
0.27
26.85
GE 1.5s
3904
1.5
0.27
26.55
Siemens
4536
2.3
0.35
35.04
GE 1.5sle
4657
1.5
0.22
22.26
Vestas V82
5281
1.65
0.22
21.59
Siemens
5333
2.5
0.32
32.40
Gamesa G87
5945
2
0.23
23.25
Suzlon S88
6082
2.1
0.24
23.86
Clipper Liberty
6221
2.5
0.28
27.77
Vestas V90
6362
1.8
0.20
19.55
Vestas V90
6362
3
0.33
32.59
Repower MM92
6720
2
0.21
20.57
Siemens
6793
2.3
0.23
23.40
Goldwind
7000
2.5
0.25
24.68
Mitsubishi MW95
7088
2.4
0.23
23.40
Gamesa G97
7390
2
0.19
18.70
Vestas V100
7854
2.75
0.24
24.20
Vestas V110
9503
2
0.15
14.55
Vestas V112
9852
3
0.21
21.05