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24 Jun 2024, 21:43
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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:
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).
• 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:
\(P = kl^2v^3\)
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).
150,000 watts
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
35%
(medium)
Question Stats:
74% (03:18) correct
26%
(03:19)
wrong
based on 151
sessions
History
Date
Time
Result
Not Attempted Yet
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?
| 23,000 watts | |
| 65,000 watts | |
| 150,000 watts | |
| 800,000 watts | |
| 1,300,000 watts |
ShowHide Answer
Official Answer
150,000 watts
The median of the rated output speeds for Models M-Q: Does not exceed 15 m/s
The mean of the rated output speeds for Models M-Q: Does not exceed 15 m/s
The least wind speed at which a Model Q turbine generates more than 5,000,000 watts of power: Does not exceed 15 m/s
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
95%
(hard)
Question Stats:
67% (02:45) correct
33%
(02:46)
wrong
based on 837
sessions
History
Date
Time
Result
Not Attempted Yet
For each of the following speeds select Exceeds 15 m/s if the information provided indicates that the speed exceeds 15 meters per second. Otherwise, select Does not exceed 15 m/s.
| Exceeds 15 m/s | Does not exceed 15 m/s | |
| The median of the rated output speeds for Models M-Q | ||
| The mean of the rated output speeds for Models M-Q | ||
| The least wind speed at which a Model Q turbine generates more than 5,000,000 watts of power |
ShowHide Answer
Official Answer
The median of the rated output speeds for Models M-Q: Does not exceed 15 m/s
The mean of the rated output speeds for Models M-Q: Does not exceed 15 m/s
The least wind speed at which a Model Q turbine generates more than 5,000,000 watts of power: Does not exceed 15 m/s
The average wind speed for Site S last year: Yes
The maximum wind speed for Site S last year: No
The least wind speed at which a Model O turbine produces its maximum amount of power: Yes
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
65%
(hard)
Question Stats:
63% (01:42) correct
37%
(01:47)
wrong
based on 859
sessions
History
Date
Time
Result
Not Attempted Yet
For each of the following wind speeds, select Yes if the information provided indicates that all models of turbines from among Models M-Q would produce power at that speed. Otherwise, select No.
| Yes | No | |
| The average wind speed for Site S last year | ||
| The maximum wind speed for Site S last year | ||
| The least wind speed at which a Model O turbine produces its maximum amount of power |
ShowHide Answer
Official Answer
The average wind speed for Site S last year: Yes
The maximum wind speed for Site S last year: No
The least wind speed at which a Model O turbine produces its maximum amount of power: Yes
Official Mock 6 DI question
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22 Jul 2024, 02:22
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bhavyatayal1833
Question 1.
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?
Average wind speed for site S = 6.8 (tab 3)
Efficiency of model M = 0.4
Blade length of model M = 35
\(Power = kl^2v^3\)
\(Power = 0.4 * 35^2 * 6.8^3 = 150,000\) approx (using calculator)
ANSWER: 150,000 watts
Question 2.
For each of the following speeds select Exceeds 15 m/s if the information provided indicates that the speed exceeds 15 meters per second. Otherwise, select Does not exceed 15 m/s.
The median of the rated output speeds for Models M-Q
Integer part of Rated output speeds are 12, 13, 14, 15, 16. Median will be 14.0
ANSWER: Does not exceed 15 m/s
The mean of the rated output speeds for Models M-Q
Use the method of deviations.
Deficit from 15 = 2.3 + 1.5 + 1
Excess from 15 = 0.2 + 1.1
Certainly deficit is higher so mean will be less than 15. We don't need to calculate what exactly it is.
ANSWER: Does not exceed 15 m/s
The least wind speed at which a Model Q turbine generates more than 5,000,000 watts of power
Efficiency = .46
Blade length = 58
\(5000,000 = 0.46 * 58^2 * v^3\)
v = 14.78 (Use calculator)
ANSWER: Does not exceed 15 m/s
Question 3.
For each of the following wind speeds, select Yes if the information provided indicates that all models of turbines from among Models M-Q would produce power at that speed. Otherwise, select No.
The average wind speed for Site S last year
The average of site S last year has been given to be 6.8. Every turbine's cut-in speed is less than that. So at 6.8, each turbine will start producing power.
ANSWER: Yes
The maximum wind speed for Site S last year
Maximum wind speed for site S last year was 23.7. Cut put speed for P is 20.3. So P will not produce power at 23.7 speed. Hence not all models of turbine will produce power at this speed.
ANSWER: No
The least wind speed at which a Model O turbine produces its maximum amount of power
Model's O's rated output speed is 13.5. It produces its maximum output at 13.5 or higher (uptill 25 which is its cut out speed).
13.5 lies between every turbine's cut in speed and cut out speed. So each turbine will produce power at 13.5
ANSWER: Yes
Calculating mean using deviations is discussed here: https://anaprep.com/arithmetic-usefulness-of-deviations/
03 Jul 2024, 21:56
Kudos
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Purnank
Q3, 3rd statement "The least wind speed at which a Model O turbine produces its maximum amount of power"
The first passage has given "The rated output speed is the wind speed at which the turbine generates the greatest amount of power"
So, The least wind speed at which a Model O turbine produces its maximum amount of power = 13.5, which is given in the 2nd table, YES is the answer.
