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  • A wind - powered generator converts wind energy into elecrtical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For

A wind - powered generator converts wind energy into elecrtical energy. Assume that the generator converts a fixed fraction of the wind energy intercepted by its blades into electrical energy. For wind speed \upsilon, the electrical power output will be most likely proportional to : 

Option: 1

\upsilon ^{4}

 


Option: 2

\upsilon ^{2}


Option: 3

\upsilon


Option: 4

\upsilon ^{3}


Answers (1)

best_answer

 

 \begin{array}{l} F=v\left(\frac{d m}{d t}\right)=v \frac{d}{d t} \ \ (\because m= \rho \times \text {volume}) \\ F=v \rho \frac{d}{d t}(\text {volume})=v \rho \times(A v)=A \rho v^{2} \end{array}

\text { Power }= \text { Force } \times \text { Velocity }=A \rho v^{2} \times v=A \rho v^{3} \Rightarrow P \propto v^{3}

Posted by

manish painkra

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