Difference between revisions of "Wind Energy - Physics"

Revision as of 17:51, 16 May 2011

The power P of a wind-stream, crossing an area A with velocity v is given by

$P={\frac {1}{2}}\rho Av^{3}$

It varies proportional to air density $\rho$ , to the crossed area A and to the cube of wind velocity v.

The Power P is the kinetic energy

$E={\frac {1}{2}}mv^{2}$

of the air-mass m crossing the area A during a time interval

${\dot {m}}=A\rho {\frac {dx}{dt}}=A\rho v$ .

Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation

$P={\dot {E}}={\frac {1}{2}}*{\dot {m}}*v^{2}={\frac {1}{2}}\rho Av^{3}$

@@ Line 1: / Line 1: @@
 == Wind Power  ==
-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
 &nbsp;<math>P=\frac{1}{2}\rho A v^3</math><br>
@@ Line 7: / Line 7: @@
 It varies proportional to air density <math>\rho</math>, to the crossed area ''A ''and to the cube of wind velocity ''v''.&nbsp;
 The Power ''P ''is the kinetic energy
 <math>E=\frac{1}{2}mv^2</math>
-of the air-mass crossing the area ''A&nbsp;''during a time interval
+of the air-mass ''m ''crossing the area ''A&nbsp;''during a time interval <br>
-<math>\dot{m}=A \rho \frac{dx}{dt}=A\rho v</math>
+<math>\dot{m}=A \rho \frac{dx}{dt}=A\rho v</math>.
+Because power is energy per time unit, combining the two equations leads back to the primary mentioned basic relationship of wind energy utilisation
+<math>P=\dot{E}=\frac{1}{2}*\dot{m}*v^2=\frac{1}{2}\rho A v^3</math>