Environmental Engineering Reference
In-Depth Information
economic development and the overall efficiency of eco-
nomic performance. Secular and global comparisons of
energy intensities of national economies lead to many in-
teresting questions about the magnitudes and causes of
indicated disparities.
Energy concentration (J/m 2 ) reveals the spatial density
of resources (be they fossil fuels or trees), a critical deter-
minant of extraction or harnessing methods and costs
and of associated infrastructural needs. When applied to
natural ecosystems the measure is a fine surrogate for
specific richness and diversity. In heavily managed ecosys-
tems, such as crop fields or fast-growing tree plantations,
it informs about harvest possibilities. In urban and indus-
trial areas it expresses the levels of intensification either in
terms of habitation densities or as energy incorporated in
structures and infrastructure of these areas. And in all
instances it reminds us of
1.8
Derivation of the Umov-Poynting vector for a wind
turbine. Based on Kapitsa 1976.
bance (v, be it a kinetic or a heat flow) and its energy
density (U, measured in J/m 3 ), which is limited by the
physical properties of the working medium. Figure 1.8
illustrates the concept for wind turbines. The vector vU
can be used to assess the limits of any energy converter.
The vector was originally suggested in 1874 by a Rus-
sian physicist, Nikolai A. Umov (1846-1915), and a de-
cade later an English physicist, John Henry Poynting
(1852-1914), described the propagation of electromag-
netic waves as a product of electric and magnetic fields
expressed in W/m 2 (Poynting 1885). Application of the
Umov-Poynting vector was favored by Pyotr L. Kapitsa
(fig. 1.9), a student of Rutherford and a Nobel laureate
in physics (1978), for being a fundamental and conve-
nient characteristic of energy converters. Kapitsa (1976,
10) argued that ignoring the restrictions of various en-
ergy fluxes revealed by the vector ''results in wasting
money on projects that can promise nothing'' in terms
of supplying high-power energy production needed by
modern societies.
Kapitsa recalled how the use of this rather simple mea-
sure refuted the Russian Academician A. F. Ioffe's idea of
inexorable limits to future
growth.
Power density (W/m 2 ) is perhaps the most revealing
variable in energetics, and in this topic it is used in two
different ways: either with the generated power prorated
over the area of an energy converter (perpendicular to
energy flow, and hence either vertical or horizontal),
or (much more often) with harnessed, generated, or
used power over the land or sea surface (prorated only
horizontally).
In the first instance, the measure is of fundamental
physical importance in determining the maximum perfor-
mance of individual energy converters in all cases where
the transformation of energy can be envisaged as pro-
ceeding within a certain volume with one form of energy
supplied into this volume across its surface and the trans-
formed energy leaving that surface. The flux of energy
through the working surface of such a converter is then
the product of the velocity of propagation of a distur-
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