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
The power of a wind-stream is transformed into mechanical energy by a wind turbine through slowing down the moving air-mass which is crossing the rotor area. For a complete extraction of power, the air-mass would have to be stopped completely, leaving no space for the following air-masses.
Unit abbreviations
m = metre = 3.28 ft.
|
HP = horsepower
|
s = second
|
J = Joule
|
h = hour
|
cal = calorie
|
N = Newton
|
toe = tonnes of oil equivalent
|
W = Watt
|
Hz = Hertz (cycles per second)
|
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): 10^{-12}
= p pico = 1/1000,000,000,000
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): 10^{-9}
= n nano = 1/1000,000,000
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): 10^{-6}
= µ micro = 1/1000,000
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): 10^{-3}
= m milli = 1/1000
Failed to parse (PNG conversion failed; check for correct installation of latex and dvipng (or dvips + gs + convert)): 10^{3}
= k kilo = 1,000 = thousands
10 6 = M mega = 1,000,000 = millions
10 9 = G giga = 1,000,000,000
10 12 = T tera = 1,000,000,000,000
10 15 = P peta = 1,000,000,000,000,000
