Maximizing Current Output from a Windmill Generator

  • Thread starter Hafid Iqbal
  • Start date
In summary: Volume has units of m3. Cross sectional area has units of m2. Velocity has units of m/s...Volume (m3) = Cross sectional area (m2) * Velocity (m/s)Volume (m3) = Cross sectional area (m2) * Velocity (m/s)Volume (m3) = Cross sectional area (m2) * Velocity (7.0m/s)Volume (m3) = Cross sectional area (m2) * Velocity (7.0m/s)
  • #1
Hafid Iqbal
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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...
 
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  • #2
What have you tried?

Where are you stuck?

We shouldn't try to help until we have seen that you have tried.
 
  • #3
SammyS said:
What have you tried?

Where are you stuck?

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

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

[itex]\frac{\tau}{\epsilon} = \frac{N.B.I.A}{N.B.A. \omega} = \frac{I}{ \omega } \ \rightarrow \ \tau= \frac{\epsilon.I}{\omega}=\frac{P}{\omega}[/itex]

[itex]\tau=\frac{\Delta KE}{\omega.t} \ = \ \frac{61.275V}{\omega.t}[/itex]

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?
 
  • #4
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.
 
  • #5
gneill said:
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
 
  • #6
Hafid Iqbal said:
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?
 
  • #7
gneill said:
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...
 
  • #8
Hafid Iqbal said:
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...
 

1. How is velocity different from speed?

Velocity is a vector quantity that includes both the magnitude (speed) and direction of motion. Speed, on the other hand, is a scalar quantity that only describes the magnitude of motion.

2. What does the given velocity change from V = 12 m/s to v = 7 m/s represent?

This represents a decrease in the velocity of an object from 12 meters per second to 7 meters per second.

3. Can velocity change without a change in speed?

Yes, velocity can change without a change in speed if the direction of motion changes. For example, if an object is moving in a circular path at a constant speed, its velocity is constantly changing because the direction of motion is constantly changing.

4. How is velocity measured?

Velocity is typically measured in meters per second (m/s) or other units of distance divided by time.

5. What factors can affect an object's velocity?

An object's velocity can be affected by changes in speed, direction, or both. Other factors such as gravity, friction, and air resistance can also impact an object's velocity.

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