Geoscience Reference
In-Depth Information
can sometimes be problematic, leading to the
installation of a concrete structure (e.g. flume or
weir) to maintain stability.
One of the difficulties with the stage vs discharge
relationship is that the requirement of frequent
measurements of river discharge lead to many mea-
surements taken during periods of low and medium
flow but very few during flood events. This is for
the double reason that: floods are infrequent and
unlikely to be measured under a regular monitoring
programme; and the danger of streamflow gauging
during a flood event. The lack of data at the extreme
end of the stage vs discharge curve may lead to
difficulties in interpreting data during peak flows.
The error involved in estimating peak discharge
from a measured stage vs discharge relationship will
be much higher at the high flow end of curve.
When interpreting data derived from the stage
discharge vs relationship it is important that the
hydrologist bears in mind that it is stream stage that
is being measured and from this stream discharge is
inferred (i.e. it is not a direct measurement of stream
discharge).
able if there is an area prior to the gauging structure
that slows the river down: a stilling pond.
The second part of using a gauging structure is
to isolate a cross-sectional area. To achieve this a
rigid structure is imposed upon the stream so that
it always flows through a known cross-sectional area.
In this way a simple measure of stream height
through the gauging structure will give the cross-
sectional area. Stream height is normally derived
through a stilling well, as described in Figure 5.9,
except in this case there is a regular cross-sectional
area.
Once the velocity and cross-sectional area are kept
fixed the rating curve can be derived through a
mixture of experiment and hydraulic theory. These
relationships are normally power equations
dependent on the shape of cross-sectional area used
in the flume or weir. There is an international
standard for manufacture and maintenance of weirs
(ISO 1438) that sets out theoretical ratings curves
for different types of structures. The general formula
for a V notch weir is shown in equation 5.3.
(5.3)
θ
25
.
Q
=
053
.
.
2
g C
. .tan
.
h
Flumes and weirs
2
Flumes and weirs utilise the stage-discharge
relationship described above but go a step further
towards providing a continuous record of river dis-
charge. If we think of stream discharge as consisting
of a river velocity flowing through a cross-sectional
area (as in the velocity profile method) then it is
possible to isolate both of these terms separately.
This is what flumes and weirs, or
stream gauging
structures
, attempt to do.
The first part to isolate is the stream velocity.
The way to do this is to slow a stream down (or, in
some rare cases, speed a stream up) so that it flows
with constant velocity through a known cross-
sectional area. The critical point is that in designing
a flume or weir the river flows at the same velocity
(or at least a known velocity) through the gauging
structure irrespective of how high the river level
is. Although this seems counter-intuitive (rivers
normally flow faster during flood events) it is achiev-
where
Q
is discharge (m
3
/s);
g
is the acceleration due
to gravity (9.81 m/s
2
); C is coefficient of discharge
(see Figure 5.10);
is the angle of V-notch (°);
h
is the height of water or stage (m). The coefficient
of discharge can be estimated from figure 5.10 for
a certain angle of V-notch. For a 90° V-notch the
coefficient of discharge is 0.578 and the rating
equation becomes:
Q
= 1.366
h
2.5
(5.4)
There is a similar type of equation for rectangular
weirs, based on the width of the rectangular exit and
another version of the coefficient of discharge
relationship.
The shape of cross-sectional area is an important
consideration in the design of flumes and weirs. The
shape of permanent structure that the river flows
