(a) By considering the ratio of the areas A, and A, of Fig. 8.5, show that the optimum power extraction (according to linear momentum theory) per unit of area A, is 8/9 of the incident power in the wind. (b) Prove that the torque produced by a wind turbine rotor of radius R can be expressed as T=(/2) pC,R³u,2 12.

Elements Of Electromagnetics
7th Edition
ISBN:9780190698614
Author:Sadiku, Matthew N. O.
Publisher:Sadiku, Matthew N. O.
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(a) By considering the ratio of the areas A, and A, of Fig. 8.5,
show that the optimum power extraction (according to linear
momentum theory) per unit of area A, is 8/9 of the incident
power in the wind.
(b) Prove that the torque produced by a wind turbine rotor of
radius R can be expressed as T=(x/2) pC,R³u,? / 2 .
Transcribed Image Text:(a) By considering the ratio of the areas A, and A, of Fig. 8.5, show that the optimum power extraction (according to linear momentum theory) per unit of area A, is 8/9 of the incident power in the wind. (b) Prove that the torque produced by a wind turbine rotor of radius R can be expressed as T=(x/2) pC,R³u,? / 2 .
Power in the wind.
A,
A2
U2
Upstream
Turbine Downstream
(as actuator
disc)
Fig. 8.5
Lanchester-Betz-Zhukowsky model of the expanding airstream through the turbine rotor,
modeled as an actuator disk.
イ
Transcribed Image Text:Power in the wind. A, A2 U2 Upstream Turbine Downstream (as actuator disc) Fig. 8.5 Lanchester-Betz-Zhukowsky model of the expanding airstream through the turbine rotor, modeled as an actuator disk. イ
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