• Support PF! Buy your school textbooks, materials and every day products Here!

Windmill Power Problem

  • #1
I had trouble with this, probably because there are no numbers in it:

"The power P delivered by a windmill whose blades sweep in a circle of diameter D by a wind speed v is proportional to the square of the diameter and the cube of the wind speed. Show that this dependence on diameter and wind speed is what you would expect in the case of 100% efficient energy transfer by showing that the energy transferred per unit time is equal to

P = π/8 * ρ * D^2 * v^3. (ρ is the density of air, approx. 1.25 kg/m^3)

I have no clue how or where to start.
 
Last edited:

Answers and Replies

  • #2
HallsofIvy
Science Advisor
Homework Helper
41,833
955
Imagine a column of air passing through the circle "swept out" by the blades of the windmill at speed v. In unit time, that will be a cylinder with diameter D and length v. Calculate the volume of that cylinder and multiply by the density to get its mass. Now, what is the kinetic energy of that mass of air?
 

Related Threads on Windmill Power Problem

  • Last Post
Replies
10
Views
3K
  • Last Post
Replies
5
Views
7K
Replies
2
Views
1K
  • Last Post
Replies
5
Views
2K
  • Last Post
Replies
1
Views
2K
  • Last Post
Replies
2
Views
2K
Replies
1
Views
5K
  • Last Post
Replies
3
Views
429
  • Last Post
Replies
4
Views
611
  • Last Post
Replies
11
Views
737
Top