Environmental Engineering Reference
In-Depth Information
Figure 6-17. Comparison of wake flow conditions over flat and complex terrain.
(a) Flat terrain (b) Complex terrain, where the wind speed and static pressure outside the
wake are changed by a hill
The total head at the same downwind distance in each site can be written as
h
f
=
p
f
+ 0.5 r
U
f
(1 -
d
f
)
2
(6-11a)
h
c
=
p
c
+ 0.5 r
U
c
(1 -
d
c
)
2
(6-11b)
where
h
f
, h
c
= total head in the wake, for flat and complex terrain, respectively (N/m
2
)
p
f
,
p
c
= local static pressure, for flat and complex terrain, respectively (N/m
2
)
Now, outside the wake, the wind speeds and static pressures are coupled by the nondissipa-
tive Bernoulli equation to give
+ 0.5 r
U
f
=
p
c
+ 0.5 r
U
c
p
f
(6-12)
If we assume that the dissipation at a given downwind distance is the same for both the flat
and complex terrains, then the total head in each wake is also the same, and
h
c
= h
f
.
This
provides a simple result:
U
c
(-2
d
c
+
d
c
) =
U
f
(-2
d
f
+
d
f
)
which, for small values of
d
c
and
d
f
, linearizes to
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