Geoscience Reference
In-Depth Information
7.4
The following hydrographs,
Q
i
and
Q
e
, respectively, were measured at the entrance and exit sections
of a reach on the Conecuh River in Alabama between Andalusia and Brooklyn in March-April of
1944 (Carter and Godfrey, 1960).
Date
Q
i
Q
e
Date
Q
i
Q
e
(m
3
s
−
1
)
3
s
−
1
)
(m
3
s
−
1
)
3
s
−
1
)
(at noon)
(
(at noon)
(
1944 March 16
120.64
118.38
29
982.70
1013.86
17
216.65
158.59
30
1280.06
1022.35
18
314.35
205.89
31
1390.51
994.03
19
472.94
272.44
1944 April 1
1169.62
1090.32
20
611.71
481.44
2
957.22
1263.07
21
594.72
518.26
3
580.56
1135.63
22
753.31
549.41
4
416.30
849.60
23
1302.72
719.33
5
322.85
583.39
24
1699.20
965.71
6
263.09
387.98
25
1634.06
1263.07
7
221.75
291.70
26
1356.53
1449.98
8
176.43
241.57
27
977.04
1469.81
9
172.19
218.35
28
614.54
1180.94
(a) Determine the routing coefficients,
c
0
,
c
1
, and
c
2
, of Equation (7.37) by multiple regression. (b)
Estimate the values of the Muskingum parameters,
K
and
X
, from these coefficients. (c) Using the
coefficients obtained in (a), route the inflow through this reach, and compare the routed outflow
with the measured outflow. Present this comparison graphically.
7.5
Consider the 1944 event listed in Problem 7.4. (a) Determine the values of the Muskingum param-
eters,
K
and
X
, by the technique illustrated in Example 7.2. (b) Route the measured inflow
through this reach, and compare the routed outflow with the measured outflow. Present the results
graphically.
Consider the hydrographs listed for Problem 7.4. For a design peak inflow rate,
Q
i
=
3000 m
3
s
−
1
,
predict the design peak outflow rate by the following two methods. (a) As a first approximation,
assume strict linearity and similarity between the design flood wave and the 1944 event. (b) Assume
that the river has a constant and large width, that its bed slope is
S
0
=
7.6
0.002, that its GM roughness
is
n
0.04, that the length of the reach is 35 km, and that the Muskingum parameters for the 1944
event are
K
r
=
=
0.2; find the design values of the parameters by using Equations
(7.57) and (7.58). (c) With these design values, calculate the design peak outflow,
Q
e
resulting
from an inflow hydrograph
Q
i
whose values are 1.766 times those listed in Exercise 7.4. Compare
this result with that obtained in (a).
2 days and
X
r
=
7.7
Making use of the data given in Problems 7.4 and 7.6, give an estimate of the cross-sectional area
of the flow,
A
c
, at the time of the outflow peak at Brooklyn in 1944.
7.8
The Muskingum flood routing method is a finite difference implementation of the diffusion equa-
tion. Determine the numerical value of
K
, in the Muskingum storage equation, for the flow situation
described in Problem 5.14, if the length of the channel section is
L
=
2.5 km.
