Power produced by the Wind Farm

[snowboarder82]

Hi all,
I'm studying for my and I've been trying to do one of the past exams from the University of Auckland. Unfortunately I'm not so clever so I'm asking for some help


Two design proposals for a wind park have been made. The first design uses 10 turbines, each with a height of 90m and a blade radius of 45m . The second design is comprised of 20 turbines, each of which has a height of 50m and blade radius of 30m. Assume that both designs use turbines that are optimized to the Betz Limit and that all complex effects are ignored.

a)
calculate the power produced for each design and recommend which design you should choose.

b)
Assume that the second design been chooses and that it has a 25MW maximum power output. What is the Coefficient of Performance of the turbines?



So what i think is that
Area A = Db where D is the diameter and b is the blade radius. But how can i calculate anything without velocity and air density?

For the part b) i think i need to do 25MW x 0.6


Please help me

 

[willem2]

This seems impossible with the problem as given. You can't calculate the power without the wind speed. It's possible you might give the answer as (a constant) * v^3, but there's no way to choose a design without knowing how expensive those windmills are.
Wind speed will depend on height, but that's probably a "complex effect" you should ignore.

For part b you also have to know the windspeed, so you can calculate the shaft power from the wind spped using the Betz limit, and the coefficient of performance of the turbine will be (electrical power)/(shaft power)

You can probably look up air density.

 

[Naty1]

Wind speed will depend on height, but that's probably a "complex effect" you should ignore.

not so see wikipedia: Wind farm