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| | == Wind Power == | | == Wind Power == |
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| − | The power ''P ''of a wind-stream, crossing an area ''A ''with velocity ''v ''is given by <br> | + | The power ''P ''of a wind-stream, crossing an area ''A ''with velocity ''v ''is given by |
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| | <math>P=\frac{1}{2}\rho A v^3</math><br> | | <math>P=\frac{1}{2}\rho A v^3</math><br> |
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| | It varies proportional to air density <math>\rho</math>, to the crossed area ''A ''and to the cube of wind velocity ''v''. | | It varies proportional to air density <math>\rho</math>, to the crossed area ''A ''and to the cube of wind velocity ''v''. |
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| − | The Power ''P ''is the kinetic energy | + | The Power ''P ''is the kinetic energy |
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| − | <math>E=\frac{1}{2}mv^2</math> | + | <math>E=\frac{1}{2}mv^2</math> |
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| − | of the air-mass crossing the area ''A ''during a time interval | + | of the air-mass ''m ''crossing the area ''A ''during a time interval <br> |
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| − | <math>\dot{m}=A \rho \frac{dx}{dt}=A\rho v</math> | + | <math>\dot{m}=A \rho \frac{dx}{dt}=A\rho v</math>. |
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| | + | Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation |
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| | + | <math>P=\dot{E}=\frac{1}{2}*\dot{m}*v^2=\frac{1}{2}\rho A v^3</math> |
Revision as of 17:51, 16 May 2011
Wind Power
The power P of a wind-stream, crossing an area A with velocity v is given by
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): P=\frac{1}{2}\rho A v^3
It varies proportional to air density Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): \rho
, to the crossed area A and to the cube of wind velocity v.
The Power P is the kinetic energy
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): E=\frac{1}{2}mv^2
of the air-mass m crossing the area A during a time interval
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): \dot{m}=A \rho \frac{dx}{dt}=A\rho v
.
Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): P=\dot{E}=\frac{1}{2}*\dot{m}*v^2=\frac{1}{2}\rho A v^3
