Task 2The performance of a wind turbine is believed to depend on the following parameters:Wind speedU●●●●Angular velocity of rotorRotor diameterChord lengthPitch of bladesDensity of air flowPower generatedWΦCрPW• Viscosity of airH(Note: The pitch of the blade is the distance it would advance through the fluid per revolution, withoutslip.)a) Find a full set of dimensionless parameters which define the operation of the unit.Wind tunnel power tests have been performed on a blade set with the following characteristics:Wind speed19 m/sAngular velocity of rotor524 rad/sRotor diameter0.25 mChord lengthPitch of bladesDensity of air flowPower generatedViscosity of air0.025 m0.216 m1.2 kg/m³44 W1.8 x 10-5 Pa.sDesign Engineers intend to use these results to find the power output of an identical unit when scaledup to a rotor diameter of 40 m, also using air, and conserving all dimensionless parameters.b) What air speed and rotor speed would be needed to achieve this?c) What power would the larger rotor set generate?

To find a full set of dimensionless parameters, we can use the Buckingham-Pi theorem, which states…

The performance of a wind turbine is believed to depend on the following parameters: Wind speed U Angular velocity of rotor Rotor diameter Chord length Pitch of blades • Density of air flow Power generated Viscosity of air H (Note: The pitch of the blade is the distance it would advance through the fluid per revolution, without slip.) ● ● ● ● ● ● ω e va a W a) Find a full set of dimensionless parameters which define the operation of the unit.

The performance of a wind turbine is believed to depend on the following parameters: Wind speed U Angular velocity of rotor Rotor diameter Chord length Pitch of blades • Density of air flow Power generated Viscosity of air H (Note: The pitch of the blade is the distance it would advance through the fluid per revolution, without slip.) ● ● ● ● ● ● ω e va a W a) Find a full set of dimensionless parameters which define the operation of the unit.

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Task 2
The performance of a wind turbine is believed to depend on the following parameters:
Wind speed
U
●
●
●
●
Angular velocity of rotor
Rotor diameter
Chord length
Pitch of blades
Density of air flow
Power generated
W
Φ
C
р
P
W
• Viscosity of air
H
(Note: The pitch of the blade is the distance it would advance through the fluid per revolution, without
slip.)
a) Find a full set of dimensionless parameters which define the operation of the unit.
Wind tunnel power tests have been performed on a blade set with the following characteristics:
Wind speed
19 m/s
Angular velocity of rotor
524 rad/s
Rotor diameter
0.25 m
Chord length
Pitch of blades
Density of air flow
Power generated
Viscosity of air
0.025 m
0.216 m
1.2 kg/m³
44 W
1.8 x 10-5 Pa.s
Design Engineers intend to use these results to find the power output of an identical unit when scaled
up to a rotor diameter of 40 m, also using air, and conserving all dimensionless parameters.
b) What air speed and rotor speed would be needed to achieve this?
c) What power would the larger rotor set generate?

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