Geoscience Reference
In-Depth Information
1
q
L+
0.5
t
p+
0
D
+
0
1
2
3
4
5
6
t
+
=(t/t
s
)
Fig. 6.10 Hydrograph at the lower end
x
=
L
of a plane (heavy line), resulting from a uniform rainfall of
duration
D
+
, obtained with the kinematic wave approach (with
a
=
2
/
3). The rate of flow is
scaled with the equilibrium rate of flow
q
s
L
=
(
iL
) and the time is scaled with the time to
equilibrium given by Equation (6.20), so that
qL
+
=
(
qL
/
q
s
L
)
,
t
+
=
(
t
/
t
s
) and
D
+
=
D
/
t
s
.In
this example
D
+
=
0
.
6 and
t
p
+
=
0
.
483.
should be recast as
t
+
=
D
+
+
(
a
+
1)(
q
L
+
)
a
/
(
a
+
1)
−
1
(1
−
q
L
+
)
(6.34)
As an example, this outflow sequence is shown in Figure 6.10 for a rainfall duration
D
=
0
.
6
t
s
; in this case (6.33) yields
t
p
+
=
.
0
483.
Effect of raindrop impact
In the analysis so far it was assumed that
K
r
in (6.8) is unaffected by the impact of
the raindrops on the water surface. Under conditions of turbulent flow this assumption
may be a good approximation but, as seen in Table 5.2, under conditions of laminar
flow the additional resistance may be considerable. This effect can be incorporated in
the recession analysis as follows. Let
K
rr
denote the parameter in Equation (6.8) under
conditions of rainfall impact, and
K
rn
the same parameter in the absence of rain. Both
parameters can be determined, for example by means of Equations (5.33) and (5.32),
respectively. Equation (6.24) must now be adjusted to
1)
K
rn
h
a
t
i
)
h
a
+
1
x
=
(
a
+
+
(
K
rr
/
(6.35)
which, at
x
=
L
becomes, instead of (6.26),
q
a
/(
a
+
1)
L
1)
K
1
/
(
a
+
1)
rn
=
+
+
(
K
rr
/
K
rn
)
q
L
/
L
(
a
t
i
(6.36)
As before, this result yields immediately the outflow hydrograph, i.e.
t
=
t
(
q
L
), as follows
=
(
a
−
1
[
iL
iq
a
/
(
a
+
1)
L
1)
K
1
/
(
a
+
1)
rn
t
+
−
(
K
rr
/
K
rn
)
q
L
]
(6.37)
