Problem Statement: 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 2, and the number of blades n. Part [A] - Write this relationship in dimensionless form? Part [B] - A model windmill, of diameter 50 cm, develops 2.5 kW at sea level when V = 38 m/s and when rotating at 4600 rev/min. What power will be developed by a geometrically similar prototype (n is the same for both mills), of diameter 5 m, in winds of 10 m/s at 1800 m standard altitude?
Problem Statement: 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 2, and the number of blades n. Part [A] - Write this relationship in dimensionless form? Part [B] - A model windmill, of diameter 50 cm, develops 2.5 kW at sea level when V = 38 m/s and when rotating at 4600 rev/min. What power will be developed by a geometrically similar prototype (n is the same for both mills), of diameter 5 m, in winds of 10 m/s at 1800 m standard altitude?
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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Use image below to solve Parts A and B
![**Homework Part A and Part B**
**Problem Statement**: The power \( P \) generated by a certain windmill design depends upon its diameter \( D \), the air density \( \rho \), the wind velocity \( V \), the rotation rate \( \Omega \), and the number of blades \( n \).
**Part [A]** - Write this relationship in dimensionless form?
**Part [B]** - A model windmill, of diameter **50 cm**, develops **2.5 kW** at sea level when \( V = 38 \, \text{m/s} \) and when rotating at **4600 rev/min**. What power will be developed by a geometrically similar prototype ( \( n \) is the same for both mills), of diameter **5 m**, in winds of **10 m/s** at **1800 m** standard altitude?
**HINT** - Pay attention to the Numbers Highlighted AND BOLDED.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fc846a080-c87d-4490-a2a5-bc99fd5c8d6b%2F5fa25e41-07e8-4f5e-8b35-da30e815db3e%2Foo3ixnr_processed.jpeg&w=3840&q=75)
Transcribed Image Text:**Homework Part A and Part B**
**Problem Statement**: The power \( P \) generated by a certain windmill design depends upon its diameter \( D \), the air density \( \rho \), the wind velocity \( V \), the rotation rate \( \Omega \), and the number of blades \( n \).
**Part [A]** - Write this relationship in dimensionless form?
**Part [B]** - A model windmill, of diameter **50 cm**, develops **2.5 kW** at sea level when \( V = 38 \, \text{m/s} \) and when rotating at **4600 rev/min**. What power will be developed by a geometrically similar prototype ( \( n \) is the same for both mills), of diameter **5 m**, in winds of **10 m/s** at **1800 m** standard altitude?
**HINT** - Pay attention to the Numbers Highlighted AND BOLDED.
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