The power P generated by a certain windmill design dependson its diameter D , the air density ρ , the wind velocity V , therotation rate Ω , and the number of blades n . ( a ) Write this relationship in dimensionless form. A model windmill, of diameter50 cm, develops 2.7 kW at sea level when V = 40 m/s andwhen rotating at 4800 r/min. ( b ) What power will be developedby a geometrically and dynamically similar prototype, ofdiameter 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 dependson its diameter D , the air density ρ , the wind velocity V , therotation rate Ω , and the number of blades n . ( a ) Write this relationship in dimensionless form. A model windmill, of diameter50 cm, develops 2.7 kW at sea level when V = 40 m/s andwhen rotating at 4800 r/min. ( b ) What power will be developedby a geometrically and dynamically similar prototype, ofdiameter 5 m, in winds of 12 m/s at 2000 m standard altitude?( c ) What is the appropriate rotation rate of the prototype?

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter5: Analysis Of Convection Heat Transfer

Section: Chapter Questions

Problem 5.9P: When a sphere falls freely through a homogeneous fluid, it reaches a terminal velocity at which the...

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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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