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BETZ’ LAW OF FLUID DYNAMICS 271

scheduled. Wind power forecasting methods include sophisticated satellite data and
ground-mounted wind-measurement instrumentation.

WIND FARM ECONOMICS

Critical factors associated with wind power generation economics are site location, land
acquisition costs, land-use considerations, environmental-impact consideration, and most
important, the availability of transmission lines. Even though the construction of wind
farms in off-shore locations in general costs considerably more, owing to considerably
consistent and stronger winds, the cost of energy production becomes much lower.

WIND POWER POTENTIAL

Presently, there are thousands of wind turbines operating throughout the world, pro-
ducing a total of 73,904 MW of electric power; Europe alone accounts for 68 percent
of this. Wind power is one of the fastest growing renewable-energy industries, and
world wind generation capacity quadrupled between 2000 and 2006.
World Wind Energy Association records indicate that worldwide wind energy pro-
duction by 2010 is expected to increase from the present 80 GW to 160 GW, which
represents a yearly growth rate of 20 percent. At present, Denmark generates one-fifth
of its electricity with wind turbines. In recent years, Germany has become the leading
producer of wind power, with a total output of 38.5 MWh, which represents 6.3 percent
of the country’s electric power production. By 2010, Germany’s official target is to
meet 12.5 percent of its electricity needs through the use of wind power. As of now,
Germany has 18,600 wind turbines, mostly located in the north of the country. In
2005, the government of Spain also approved a new national goal for increasing wind
power capacity to 20,000 MW by 2010. In the past decade, the United States has
added significantly more wind energy to its grid than any other country in the world.
U.S. wind power capacity in 2007 reached 16.8 GW.

Betz’ Law of Fluid Dynamics

Betz’ law of fluid dynamics formulates the maximum flow of possible energy that can
be derived by means of an infinitely thin rotor, such as a wind mill, from a flowing
fluid (in this case air) at a certain speed. To calculate the maximum theoretical effi-
ciency of a windmill, we must pretend that the propeller of the wind turbine is con-
structed from a thin rotor made of a disk with surface area S that withdraws energy
from the fluid or air passing. At a certain distance behind this disk, the fluid or the air
flows with a reduced velocity (Fig. 8.1).
If we designate v as the speed of the fluid entering the tube in front of the disk and
1
v as the speed of the fluid downstream, then the average or mean flow velocity
2
through the disk v avg will be
1
v = v ( + v )
avg 1 2
2