Maximizing Current Output from a Windmill Generator

[Hafid Iqbal]

A 120-V generator is run by a windmill that has blades 2.0 m long. The wind, moving at 12 m/s, is slowed to 7.0 m/s after passing the windmill. The density of air is 1.29 kg/m³. If the system has no losses, what is the largest current the generator can produce?
(Hint : How much energy does the wind lose per second?)

Thank you very much...

 

[SammyS]

What have you tried?

Where are you stuck?

We shouldn't try to help until we have seen that you have tried.

 

[Hafid Iqbal]

What have you tried?

Where are you stuck?

We shouldn't try to help until we have seen that you have tried.

\Delta \ KE = -\frac{1}{2}.m.(v_2^2-v_1^2)=-\frac{1}{2}.\rho.V.(7^2-12^2)=61.275V (V = Volume of air)

\frac{\tau}{\epsilon} = \frac{N.B.I.A}{N.B.A. \omega} = \frac{I}{ \omega } \ \rightarrow \ \tau= \frac{\epsilon.I}{\omega}=\frac{P}{\omega}

\tau=\frac{\Delta KE}{\omega.t} \ = \ \frac{61.275V}{\omega.t}

And I stuck from that point. Here is my problems :
1. I don't understand what is the use of blades' length
2. How to find volume of air?
3. Is it true angular speed not given?

 

[gneill]

It could be that they want you to assume that the cross sectional area of the airstream is defined by the span of the blades as they rotate.

 

[Hafid Iqbal]

It could be that they want you to assume that the cross sectional area of the airstream is defined by the span of the blades as they rotate.

I still can't get the answer... :(
Anyway, the book says its answer is 77 Ampere

 

[gneill]

I still can't get the answer... :(
Anyway, the book says its answer is 77 Ampere

Start with determining the volumetric rate (m³/s) at which air is passing the windmill cross section. Then turn that into mass rate by multiplying by density. What do you get?

 

[Hafid Iqbal]

Start with determining the volumetric rate (m³/s) at which air is passing the windmill cross section. Then turn that into mass rate by multiplying by density. What do you get?

How to find volumetric rate sir? If I multiply it by density, i wiil get mass rate...

 

[gneill]

How to find volumetric rate sir? If I multiply it by density, i wiil get mass rate...

Volume has units of m³. Cross sectional area has units of m². Velocity has units of m/s...