Environmental Engineering Reference
In-Depth Information
quite large. Namely, U
¼
(5.18
10
9
m
2
0.22m)
1000
9.8
0.22
¼
2.46
10
12
J.
In terms of an average power P
dU/dt, this is 57MW. The annual market value of
the entirety of this potential power, at $0.14/kWh, would be 57
¼
10
6
10
7
3.15
10
6
. In an age of governments needing to raise taxes,
this might be an incentive to install water turbines.
This situation is present in numerous smaller scale examples. In New York City,
the TV host will speak of the danger, on a given day, at a particular beach, of rip
currents, to swimmers. Rip currents are tidal
flows of water through such
constrictions (between open sea and a tidal pool) as we have discussed. There are
many locations where sandbars or keys are located just off the mainland.
It would seem that constructing arti
cial entrapments of this sort, for example, a
sandbar (key) extended by levees (dams) to trap tidal
flows, augmented with water
turbines and grid connections, could be a new activity for the illustrious U.S. Army
Corp of Engineers, which has installed numerous bridges, levees, and other water-
related engineering projects in the United States.
10
6
)
1
(3.6
0.14
¼
$69.8
1.1.3.2 Geothermal Energy
Geothermal potential according to Table 1.1 is 32.2 TWwith a higher value, 44.3 TW,
from a different source [17]. The core of the earth is molten, and heat leaks out to the
surface. The energy release actually comes fromtwo sources. One is radioactive decay
of elements like uranium and thorium in the outer layers of the earth. The second is
the heat from the earths core that remains molten, at a much higher temperature.
While the trend is of cooling of the core from its primordial high temperature, it has
been mentioned that some heat input, a continual heating of the earths core, comes
from the motion of the moon, which continually distorts the shape of the earth, as
well as driving the tides.
From a physics point of view, the condensation energy in forming the earth from a
dispersed cloud of dust to a condensed sphere of radius R,
5 GM
2
E
¼
3
=
=
R
;
ð
1
:
16
Þ
is a benchmark value, easily calculated. Here G is the universal gravitation constant,
G
10
11
, so that, with M
10
24
kg, and R
10
6
m, we
nd
¼
6.67
¼
5.97
¼
6.37
10
32
J
E
¼
2
:
24
:
This energy, released as kinetic energy, is vast, comparable to the present rate of
consumption extended for 4.84
10
11
years! It is clear that most of this energy has
already been lost, mostly by radiation shortly after the condensation. If we were to
attribute this full energy to heating of the earth, we can estimate what the temperature
would have been. In a simple model of a solid or liquid, the thermal energy is
U
¼
3Nk
B
T
:
ð
1
:
17
Þ
10
24
kg to iron atoms, atomic mass
If we attribute all the mass M
¼
5.97
10
3
K.
The radiation power from the surface of the early earth at that temperature would be
10
27
kg, then N
10
49
atoms, and T
55.85
1.67
¼
6.4
¼
U/3Nk
B
¼
84.5
