Geoscience Reference
In-Depth Information
(a)
The basic formula,
Q
p
=
CIA
, can be used to determine storm outflow from confined
aquifers.
(b)
But its main application is in the design of highway culverts, sewers and other smaller
structures.
(c)
It is commonly used to compute the spillway design flood on larger basins in conjunction
with the 1000 y rainfall.
(d)
The runoff coefficient,
C
,
tends to be smaller for rural areas than for urban areas.
This method is more appropriate for flood prediction from areas larger than 10 km
2
than
for smaller areas, because it is based on the assumption that watershed characteristics can
be averaged.
(e)
(f)
It is based on the implicit assumption (among some others) that the input (rain) is merely
translated by means of a time lag to produce the output (runoff).
(g)
It can also be justified on the basis of the kinematic wave equation with a linear rating curve,
so that the velocity,
V
,
is independent of water depth.
(h)
It has the advantage of not requiring any information at all on the surface characteristics of
the watershed.
(i)
It is based on the assumption that the infiltration and other losses are a fraction of the
rainfall.
12.13
In a manner similar to Example 12.6, derive the mathematical expression for the unit response
function,
u
(
t
)
,
of a system consisting of a width function in the shape of a right-angled triangle
(representing translation effects) placed in sequence with a linear storage element representing
storage effects. (This case is shown graphically in Figure 12.15.) Thus, (a) give the equation
describing
A
r
(
t
), and (b) use this in the convolution integral with the unit response (12.28); the
parameters of the system are
K
and
t
c
.
12.14
Derive the unit response function (12.37) of the system illustrated in Figure 12.18 by showing
(and solving) the convolution operation needed to obtain (12.37) from the second of (12.36).
12.15
What would be the unit response function,
u
(
t
)
,
if the system shown in Figure 12.18 had four
(instead of three) subareas, such that
α
1
+
α
2
+
α
3
+
α
4
=
1?
12.16
Show that the first moment about the origin of the unit response function (12.41) is (12.42), i.e.,
m
u
1
=
nK
. (The moments are defined in Chapter 13.)
12.17
Show that the second moment about the mean of the unit response function (12.41) is (12.43), i.e.
m
u
2
=
nK
2
. Make use of the fact that the second moments about the mean and about the origin
are related as shown in Equation (13.12).
12.18
Determine the value of the power
m
in Equation (12.48) for storage in a reach of an open channel
with triangular cross section. Hint. Follow the same reasoning as that leading to Equation (12.53).
12.19
Prove Equation (12.55) by carrying out the integration outlined in the text.
12.20
Prove Equation (12.56) by carrying out the integration outlined in the text.
12.21
In the analysis of the outflow record from the downstream end of a lake during a drought period
(when the inflow
Q
i
is zero), it is found (surprisingly) that
t
versus
Q
−
1
/
3
e
plots as a straight
