Environmental Engineering Reference
In-Depth Information
the formula:
Q
h
=
f
1
hbu
o
-
f
2
Q
t
(7)
where:
Q
h
= rate of horizontal water exchange (m
3
s),
f
1
,
f
2
= empirical coef-
ficients depending on the geometry of the basin,
h
= depth of entrance (m),
b
= width of entrance (m),
u
o
=mainflowvelocityinfrontoftheentrance
(m
/
s),
Q
t
= filling discharge due to rising tide (=
hbu
t
)(m
3
/
/
s),
u
t
= tidal in-
and outflow velocities in the entrance (m
s).
This formula is valid for rivers (
Q
t
= 0) and in tidal areas during flood;
Q
h
almost is negligible during ebb [33]. Hence, substitution of
h
=
h
o
-
/
η
cos
ω
t
and
u
o
=
u
o,max
sin
ω
t
(
η
tidal amplitude,
ω
tidal period) and integration over
the flood period (
t
=0to
T
/
2) yield the total volume per tide by horizontal
exchange:
V
h
=
f
1
h
o
b
u
o,max
π
T
-
f
2
V
t
(8)
where:
V
h
= total volume of water exchange per tidal cycle by horizontal ex-
change flow (m
3
),
h
o
= depth in the entrance relative to MSL (m),
T
=tidal
period (s),
V
t
= tidal prism of harbor basin (m
3
).
The coefficients
f
1
and
f
2
generally are within the ranges 0.01-0.03 and
0.1-0.25 respectively and can be estimated based on existing knowledge from
comparable situations. In some cases it may appear useful to determine more
accurate values via hydraulic model investigations. Delft Hydraulics has de-
termined these for several large harbors (Rotterdam, Antwerp). In case the
equation yields a negative value for
V
h
it means that the horizontal exchange
does not contribute to the total water exchange, in which case
V
h
=0.
3.3
Water Exchange due to Density Currents
Water exchange is also caused by density differences between the water inside
and outside the harbor basin (Fig. 3). This mechanism is very effective and,
besides, it affects the entire basin while the two others are restricted to the
area near the entrance. The tidal filling or emptying of the harbor basin re-
duces the water exchange due to the density currents. Bearing in mind that
2
u
t
h
2 represents the filling or emptying discharge rate, Fig. 3 shows that the
density-induced water exchange under all circumstances is reduced in the
same way.
Hence the rate of exchange by density currents (no influence of horizontal
exchange assumed) can be described by:
/
Q
d
=(
u
o
-
u
t
)
hb
/
2
(9)
