Geoscience Reference
In-Depth Information
7.9
A hydrograph at the downstream end of a river section (after a period of heavy rain over upland
catchments) was recorded as follows.
Ti
e (h)
0
2
4
6
8
10
12
14
16
18
20
Rate of flow
(m
3
1.5
1.4
16.9
54.1
72.8
62.4
46.3
31.7
20.7
13.9
9.6
s
−
1
)
Assume that there were no intermediate inflows (nor losses) in this river channel. From previous
events, the travel time in this reach is known to be 4 h, and the storage-weighting factor is
X
=
0
.
25.
(a) Determine the flood hydrograph at the upstream end of the reach for this event by means of
the Muskingum method. Hint: start computations at
t
=
20 h and go backwards. (b) If the width
of the river is 15 m and the water depth (at the downstream end) at the time of peak is 3.5 m,
what is the average velocity of the water (at the downstream end) at the time of peak? (Assume
a rectangular cross section.) (c) From the available information, give an estimate of the length of
the river reach.
7.10
Using the following hydrograph of a historical flood event at the entrance and exit sections of a
river reach:
Day
Q
i
inflow
Q
e
outflow
Day
Q
i
inflow
Q
e
outflow
(at noon)
(m
3
s
−
1
)
(
3
s
−
1
)
(at noon)
(m
3
s
−
1
)
(
3
s
−
1
)
1
668
611
9
2109
2895
2
1685
785
10
1668
2256
3
4647
1951
11
1325
1776
4
7906
4641
12
1098
1402
5
7864
7102
13
962
1125
6
5547
7392
14
869
966
7
3792
5657
15
781
854
8
2721
4098
16
708
811
(a) Determine the routing coefficients,
c
0
,
c
1
and
c
2
, of Equation (7.37) by multiple regression.
(b) Estimate the Muskingum parameters,
K
and
X
, from these coefficients. (c) Use these coefficients
to route the inflow through the reach, and compare the result with the measured outflow.
7.11
Assume that the following flood hydrograph was observed at the upstream end of a 40 km long
river reach.
i
e (h)
0
2
4
6
8
10
12
14
16
18
20
Discharge
rate (m
3
0
16.7
53.7
72.2
61.9
45.9
31.4
20.5
13.7
9.49
0
s
−
1
)
(a) If you know that the channel is uniform with a rectangular cross section and that the wetted
cross-sectional area at the peak discharge (i.e. after 6 h) is 42.0 m
2
, show that the celerity of the
flood wave is approximately 10 km h
−
1
(i.e. 2.78 m s
−
1
). (b) Assume that the celerity remains
