The power P generated by a certain windmill design depends upon its diameter D, the air density p, the wind velocity V, the rotation rate 0, and the number of blades n. (a) Write this relationship in dimensionless form. A model windmill, of diameter 50 cm, develops 2.7 kW at sea level when V= 40 m/s and when rotating at 4800 r/min. (b) What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 12 m/s at 2000 m standard altitude? (c) What is the appropriate rotation rate of the prototype?

The power P generated by a certain windmill design depends upon its diameter D, the air density p, the wind velocity V, the rotation rate 0, and the number of blades n. (a) Write this relationship in dimensionless form. A model windmill, of diameter 50 cm, develops 2.7 kW at sea level when V= 40 m/s and when rotating at 4800 r/min. (b) What power will be developed by a geometrically and dynamically similar prototype, of diameter 5 m, in winds of 12 m/s at 2000 m standard altitude? (c) What is the appropriate rotation rate of the prototype?

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

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The power P generated by a certain windmill design
depends upon its diameter D, the air density p, the wind
velocity V, the rotation rate 0, and the number of blades n.
(a) Write this relationship in dimensionless form. A model
windmill, of diameter 50 cm, develops 2.7 kW at sea level
when V= 40 m/s and when rotating at 4800 r/min. (b)
What power will be developed by a geometrically and
dynamically similar prototype, of diameter 5 m, in winds
of 12 m/s at 2000 m standard altitude? (c) What is the
appropriate rotation rate of the prototype?

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