A certain renewable energy company is planning to construct a wind farm at Site S. Some of the most important...
GMAT Multi Source Reasoning : (MSR) Questions
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Turbine Characteristics
Turbine Models
Wind Speeds
A certain renewable energy company is planning to construct a wind farm at Site S. Some of the most important characteristics of the wind turbines they researched for the site are described below.
- The cut-in speed is the least wind speed required to turn the blades of the turbine and generate power. The turbine will not generate power at speeds less than the cut-in speed.
- The rated output speed is the wind speed at which the turbine generates the greatest amount of power. The turbine will generate no additional power at speeds exceeding the rated output speed.
- The cut-out speed is the wind speed at which there is risk of damaging the turbine should the blades continue to rotate. At speeds exceeding the cut-out speed, a braking system automatically stops the blades from rotating, and no power is generated.
- The amount of power P, in watts, generated by a turbine operating at any wind speed from its cut-in speed to its rated output speed is given by:
\(\mathrm{P = kl^2v^3}\)
where k is an efficiency coefficient that varies for different models of turbines, l is the turbine blade length in meters (m), and v is the wind speed in meters per second (m/s).
Ques. 1/3
According to the information provided, which one of the following is nearest to the amount of power one Model M turbine would have generated at the average wind speed for Site S last year?
Solution
Owning the Dataset
Understanding Source A: Text - Turbine Characteristics
| Information from Dataset | Analysis |
|---|---|
| ""The cut-in speed is the least wind speed required to turn the blades of the turbine and generate power. The turbine will not generate power at speeds less than the cut-in speed."" |
|
| ""The rated output speed is the wind speed at which the turbine generates the greatest amount of power. The turbine will generate no additional power at speeds exceeding the rated output speed."" |
|
| ""The cut-out speed is the wind speed at which there is risk of damaging the turbine...a braking system automatically stops the blades from rotating, and no power is generated."" |
|
| ""(mathrm{P = kl^2v^3})"" where (mathrm{k}) = efficiency coefficient, (mathrm{l}) = blade length (m), (mathrm{v}) = wind speed (m/s) |
|
| ""A certain renewable energy company is planning to construct a wind farm at Site S"" |
|
- Key Finding: Turbines operate within specific wind speed ranges
- Power generation starts at cut-in speed
- Power maximizes at rated output speed
- Turbines stop at cut-out speed for safety
Understanding Source B: Table - Turbine Models
| Information from Dataset | Analysis |
|---|---|
| Cut-in speeds: Model M (1.9 m/s) to Model Q (4.8 m/s) |
|
| Rated output speeds: Model P (12.7 m/s) to Model Q (16.1 m/s) |
|
| Cut-out speeds: Model P (20.3 m/s) to Model N (34.2 m/s) |
|
| Efficiency coefficients: Model O (0.38) to Model Q (0.46) |
|
| Blade lengths: Model N (22m) to Model Q (58m) |
|
- Key Finding: The five turbine models show substantial variation in all characteristics
- Trade-offs exist between low cut-in speeds (Model M) and high efficiency/blade length (Model Q)
Understanding Source C: Graph with Text - Wind Speeds at Site S
| Information from Dataset | Analysis |
|---|---|
| ""The average wind speed last year was 6.8 m/s"" |
|
| ""The maximum wind speed was 23.7 m/s"" |
|
| Peak frequency at 5-7 m/s range (11.6% at 5-6 m/s, 11.5% at 6-7 m/s) |
|
| Winds below 3 m/s occur about 8.1% of time (1.4% + 2.5% + 5.2%) |
|
| Winds above 15 m/s occur less than 5% of time |
|
- Key Finding: Site S has consistent moderate winds averaging 6.8 m/s
- Favors turbines with low cut-in speeds like Model M
- Model P's low cut-out speed would cause shutdowns during peak winds
Overall Analysis
- Site S experiences moderate, consistent winds that would allow all five turbine models to generate power during typical conditions
- Model M advantage: Low cut-in speed (1.9 m/s) maximizes operational time by capturing power even during calm periods
- Model P limitation: Would shut down during the site's strongest winds (23.7 m/s)
- Since winds strong enough for maximum power generation occur less than 5% of the time, models with lower cut-in speeds offer more total operational hours than models optimized for high-wind conditions like Model Q
Source Analysis
Source A - Turbine Characteristics
- Provides the power generation formula (mathrm{P = kl^2v^3}), where:
- P = power in watts
- k = efficiency coefficient
- l = blade length in meters
- v = wind speed in m/s
- Defines operational ranges:
- Cut-in speed: minimum for power generation
- Rated output speed: maximum power
- Cut-out speed: safety shutdown
Source B - Turbine Models
- Model M turbine specifications:
- Cut-in speed: 1.9 m/s
- Rated output speed: 14.0 m/s
- Cut-out speed: 28.9 m/s
- Efficiency coefficient (k): 0.40
- Blade length (l): 35 meters
Source C - Wind Speeds
- Average wind speed at Site S last year: 6.8 m/s
Information Integration
- The average wind speed (6.8 m/s) falls within Model M's operational range since (mathrm{1.9 leq 6.8 leq 14.0}) m/s
- This means the turbine would generate power according to the formula (mathrm{P = kl^2v^3})
Statement Evaluations
Statement 1 Analysis
""0,023,000 watts""
- Analysis: This value of 23,000 watts is significantly lower than the calculated power output
- Evidence Available: Using the power formula P = kl²v³ with k=0.40, l=35m, v=6.8m/s gives approximately 154,032 watts
- Conclusion: NOT SUPPORTED - The calculated value is about 6.7 times higher than this option
Statement 2 Analysis
""0,065,000 watts""
- Analysis: This value of 65,000 watts is substantially lower than the calculated power output
- Evidence Available: The step-by-step calculation yields P = 0.40 × 1,225 × 314.432 = 154,031.68 watts
- Conclusion: NOT SUPPORTED - The calculated value is approximately 2.4 times higher than this option
Statement 3 Analysis
""0,150,000 watts""
- Analysis: This value of 150,000 watts is the closest to the calculated power output of approximately 154,032 watts
- Evidence Available: Step-by-step calculation shows: l² = 35² = 1,225; v³ = 6.8³ = 314.432; P = 0.40 × 1,225 × 314.432 = 154,031.68 watts
- Conclusion: SUPPORTED - This option represents the nearest value to the calculated result among all given choices
Statement 4 Analysis
""0,800,000 watts""
- Analysis: This value of 800,000 watts is significantly higher than the calculated power output
- Evidence Available: The calculated power of approximately 154,032 watts is much lower than this option
- Conclusion: NOT SUPPORTED - This value is about 5.2 times higher than the calculated result
Statement 5 Analysis
""1,300,000 watts""
- Analysis: This value of 1,300,000 watts is extremely high compared to the calculated power output
- Evidence Available: The power formula calculation gives approximately 154,032 watts, which is far below this option
- Conclusion: NOT SUPPORTED - This value is approximately 8.4 times higher than the calculated result
Answer Selection
- The calculated power of approximately 154,032 watts is nearest to 150,000 watts among the given options
- The other options (23,000, 65,000, 800,000, and 1,300,000 watts) are significantly different from our calculated value
150,000 watts
Answer Choices Explained
A
0,023,000 watts
B
0,065,000 watts
C
0,150,000 watts
D
0,800,000 watts
E
1,300,000 watts
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