Geoscience Reference
In-Depth Information
Fig. 7.6 Water stored in the
channel reach control
volume of length
Δ
x
.
The cross-sectional
areas are
A
ci
and
A
ce
at the inflow and at
the outflow end,
respectively. The
corresponding
average water depths
at these sections are
h
i
and
h
e
.
Fig. 7.7
The time of travel
t
t
of
the flood wave through
the reach is the time
between the centroids
of the inflow and
outflow hydrographs.
In the linear
Muskingum storage
function this is given
by
t
t
=
K
.
undergoes, as it travels through the reach. The moments, which are used in what follows,
are defined in Chapter 13.
The mean time of occurrence of a flood wave is the first moment about the origin,
denoted as
m
1
or
; this quantity is also referred to as the centroid or center of area of
the hydrograph. Therefore, the travel time is the difference between the mean time of
occurrence of the wave at the exit section and that at the inflow section of the reach,
that is
t
t
=
μ
m
i1
, as shown in Figure 7.7; as before, the subscripts e and i refer to
the outflow and inflow sections of the reach. In other words, that travel time is the time
between the centers of area of the inflow wave
Q
i
(
t
) and of the outflow wave
Q
e
(
t
), or
m
e1
−
0
0
∞
∞
tQ
e
dt
tQ
i
dt
t
t
=
−
(7.17)
∞
∞
Q
e
dt
Q
i
dt
0
0
