(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.

(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.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Question

(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

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