Geoscience Reference
In-Depth Information
10.2
Suppose that recession outflow data for a certain basin can be described by Equation (10.157)
with
b
=
2
.
Derive the recession outflow hydrograph as a function of time, i.e.
Q
=
Q
(
t
), for this
case. Use two parameters in this function, namely
a
of (10.157) and
Q
0
,
that is the flow rate at
t
=
0
.
10.3
(a) Suppose that for a design project it is necessary to express the base flow recession as an
exponential equation in the form of (10.153). Determine the value of
K
(in days) for Tonkawa
Creek (see Figure 10.31) for which it is known that, for
b
=
3 in Equation (10.157),
a
=−
2
.
74
×
10
−
5
sm
−
6
, and for
b
=
1 in Equation (10.157)
a
=−
3
.
24
×
10
−
7
s
−
1
. (b) Determine the value
of
K
r
in Equation (10.154) for this basin.
10.4
Solve the previous problem, 10.3 (a) and (b), for Salt Creek (see Figure 10.33) for which it is
known that for
b
=
3 in Equation (10.157),
a
=−
3
.
90
×
10
−
5
sm
−
6
, and for
b
=
1 in Equation
(10.157)
a
=−
3
.
82
×
10
−
7
s
−
1
.
10.5
(a) Derive Equation (10.160) from (10.64) by using the geomorphic relationship (10.158). (b)
Derive from (10.160) the corresponding values of
a
1
and
b
1
for (10.157), as given by (10.161).
10.6
Derive Equation (10.162) from (10.85) with (10.86) using the geomorphic relations (10.158) and
(10.159). (b) Then use (10.162) to derive (10.163) for
a
2
and
b
2
.
10.7
(a) Derive Equation (10.164) from (10.116) by making use of the geomorphic relationships
(10.158) and (10.159). (b) Then derive the corresponding values of
a
3
and
b
3
of (10.157), as
given by (10.165).
10.8
Calculate the value of
a
+
in Equation (10.169) for the case
b
=
3 by scaling (10.157) and (10.161)
with (10.168). Compare this dimensionless number with that obtainable with the interpolation
formula (10.170).
10.9
Combine Equations (10.165) and (10.161) to derive expressions for the effective hydraulic con-
ductivity
k
0
and for the effective unconfined aquifer thickness
D
in terms of
a
1
and
a
3
. Assume
that the drainable porosity
n
e
is known.
10.10
The recession flow data for Tonkawa Creek shown in Figure 10.31 yielded the parameters
a
3
=−
3km
2
,
3
.
24
×
10
−
7
s
−
1
and
a
1
=−
2
.
74
×
10
−
5
sm
−
6
. This watershed has an area
A
=
67
.
total stream length
L
=
70
.
1 km and an average surface aquifer thickness
D
=
1
.
6 m. Calculate
effective values of the hydraulic conductivity
k
0
and of the drainable porosity
n
e
.
10.11
By combining (10.161) with (10.163), derive expressions for the regional values of
k
0
and
n
e
,
which can be used with the results of hydrograph analyses in which the slopes of the logs of
dQ
/
dt
versus those of
Q
,
are
b
=
3 and
b
=
3
/
2 (cf. (10.174)). Assume that the mean near-
surface aquifer thickness
D
is known.
10.12
Select a stream gauging station in your region of interest, preferably with a drainage area
A
smaller than 200 km
2
. Obtain the daily flow data during periods of recession, for a number of
years sufficient to produce an adequate data base. Plot these data, according to Equation (10.156)
with logarithmic scales as illustrated in Figure 10.31. Estimate the length of all stream channels
