is measured at a
constant altitude, a factor k is used
to take account of the velocity distribution and to calculate the mean velocity
. The discharge QUS
measured with the ultrasonic system is therefore given by:
Torsten Dose
Section of Hydraulic Engineering, Department of Civil Engineering,
University of Wuppertal, Germany
Gerd Morgenschweis
Ruhr River Association, Essen, Germany
IGAW, Pauluskirchstr. 7, 42285 Wuppertal, Germany
Tel.: +49 202 439
4194, Fax: +49 202 439 4196, E-mail: dose@uni-wuppertal.de
Abstract: This paper deals with the measurement of discharge in a regulated river. Two different systems were installed to measure discharge: an ultrasonic flow meter operating as a reference system and a pressure-difference system. After describing both methods, the author will compare the computed discharge values as a function of water level and water surface slope with the discharge measured by the ultrasonic system. In addition, the application of a rating curve will be demonstrated. The investigation comes to the conclusion that the pressure difference system is able to compensate the tailback effects of a downstream weir as well as of rapid changes in discharge. Measurement accuracy is the most important factor limiting the determination of discharge at lower measurement values of the water surface slope.
Keywords: discharge measurement, water gauge, bubble procedure, ultrasonic system, tailback, pressure-difference system
The Ruhr River Association
(Ruhrverband) in Germany runs a
complex water management
system in one of the most densely populated and highly industrialised regions of
Europe. One major task is to provide drinking water for about 5.2 million
residents and to supply local industry with process water. At present a system
of 14 reservoirs with a total storage capacity of 474×106
m3 enables the Ruhr River Association to maintain a fixed minimum
runoff at critical cross-sections and to replenish the water, which is taken
directly from the river for the purpose of groundwater recovery, during dry
seasons. A second reason for operating this reservoir system, which is by far
the largest of its kind in the Federal Republic of Germany, is to prevent
flooding of the cities along the lower reach of the River Ruhr and its main
tributary, the River Lenne, by making use of the retention capacity of the
reservoirs.
This water quantity management scheme is supported by an overall
hydrological information system. As part of this system, an online flood
forecasting model based on a network of 98 gauges and discharge measuring
stations has been established. A traditional and simple way to gather
information on current discharge is to measure the water level with gauges and
to compute the runoff by using a rating curve. This relationship has to be
determined and verified by the direct measurement method, i. e. by
multiplying the flow area with the mean velocity. The latter can be measured by
an ultrasonic flow meter, an ADCP (acoustic Doppler current profiler), or any
other technique for measuring the velocity at the cross-section.
Several requirements must be met when setting up a measuring site
suitable for water level gauging: When selecting a gauging site, care must be
taken that no large changes are to be expected in the river bed. Moreover, the
reach should have a uniform slope. Sites at which changes between subcritical
and supercritical flow may occur are not suitable for discharge determination.
Furthermore, sites with divided channels, variable backwater, strong wave action
or ice hazards should be strictly avoided. The site should be easily accessible
and all potential water levels should be within the measurement range. Finally,
it is of fundamental importance that changes in discharge correspond to distinct
changes in water levels.
Heavily modified water bodies, in particular river reaches regulated by dams or weirs, could cause problems for a measuring site. Even at sites which are usually characterised by free flow, variations in the rating curve are observed during high water because of backwater influences. Under such conditions, a single water level gauge is not suitable; instead, a velocity measurement system is additionally required.
For the problem stated above, the present paper proposes a solution
that dispenses with a permanently installed velocity meter; instead, two gauges
are set up at a distance of about 200 m in the direction of the current.
Measurements were made at the Fröndenberg/Ruhr station in a straight reach
influenced by a regulated weir. The discharge observed over a total time period
of two years ranged from about 8 m3/s to more than 200 m3/s.
Two different
systems were installed to independently measure the discharge at the same area
of the site: an ultrasonic flow meter and a water level gauging system based on
the bubble procedure.
The ultrasonic flow meter
determines the velocity of the flow with the travel-time method. Two transducers are used to send signals from one riverbank to the other
over a distance of L=78 m at a
practical angle f=25°
against the direction of flow (Figure 1). Each transducer switches between
generator and receiver.
In the case where a sound pulse is
transmitted through water in motion, the propagation velocity c is equal to the sum of the sound
velocity c0 and the
component of the average flow velocity perpendicular to the cross-sectional
area. As a con-se-quence, the travel times t1
and t2 differ from each
other in both directions.
The flow area A can be determined with the water level height measured by a
pressure sensor. Because the velocity
is measured at a
constant altitude, a factor k is used
to take account of the velocity distribution and to calculate the mean velocity
. The discharge QUS
measured with the ultrasonic system is therefore given by:
QUS=vmA=kvA,
(1)
The ultrasonic system is used as a reference for calibration and for proving the accuracy of the pressure-difference system.
The alternative system that is the subject of this investigation consists of two measurement tubes with bubble orifices placed in the direction of flow with a distance of 208 m between them (figure 2). The pressure of the water column above the end of the tube is proportional to the water level.
Tube 1 is linked
to a pressure probe measuring the absolute water height h above the bubble orifice. Another high performance pressure probe
is connected to both tubes to measure the difference in water level between the
two orifices Dh. The
configuration satisfies the applicable German regulations [DVWK, 1990].
The measured
water level difference Dh divided
by the distance between the orifices L results
in the slope of the water surface IW.
This is the information we need to obtain precise results as will be shown in
the next chapter.
(2)
To compute the
discharge with h and IW, we consider the control
volume between both cross-sections (figure 3). We can state the momentum
equation and reduce it to equation 3 [Helmig,
1996] below:
(3)
The partial time derivatives are substituted by the difference quotient.
The mean velocity inside the control volume is calculated as
, analogous to
. Using the general loss equation together with the empirical
equation from Colebrook-White
(equation 4) and the continuity equation, we obtain equation 5, which can
be solved for the mean velocity. This equation contains time-dependent terms for
improvements when calculating unsteady flow.
(4)
(5)
The roughness coefficient ks
is computed by a reverse algorithm using the discharge measured with the
ultrasonic system. Calculating the mean value of ks finishes the calibration process, which was ks = 163 mm for a time period
of 100 days. All three data sets are collected every 15 minutes and are shown in
figure 4: QUS, h, Dh.
The results of
the calculation are presented for a time period of 30 days. The relative
disparity between the measured discharge and the results determined by an
approximated rating curve (figure 5) are shown in figure 6, while figure 7
illustrates the difference between the discharge calculated from the water level
and the water surface slope, respectively. Obviously the results computed with
equation 5 are of much better quality than those obtained with the conventional
method. The mean value of the relative difference is 2.2 %.
Another example is shown in Figure 8. Even the oscillating discharge, with a period of about 2.5 h caused by a water power plant, is measured accurately.
The
pressure-difference system has proven to be a very strict and reliable method
for quantifying the discharge in regulated reaches. Although a great distance is
required between the two orifices – depending on the range of discharge and
the influence of backwater – the system is much simpler and cheaper than a
permanently installed flow meter, which additionally requires a water level
gauge.
It is very
important to measure the water surface slope precisely since it has a
significant impact on the results at low discharges. For this reason, we
selected the bubble procedure, which is suitable for water differences of less
than one millimetre. Fortunately, a minimum discharge is guaranteed in many
regulated rivers (Cf.
Introduction).
The system is
demonstrably convenient in application. In particular, the difference measure-ment
is independent of physical water properties such as density, salinity
(conductivity), temperature and suspended matter. The latter often causes
problems with flow meter systems.
Further
investigations have to be carried out to determine the roughness coefficient on
the basis of a small number of control measurements. Moreover, additional
applications are needed for purposes of comparison.
This paper is based on investigations carried out as a consultancy project for the River Ruhr Association. The technical configuration was installed by Quantum Hydrometrie (ultrasonic system) and Ott Hydrometrie (pressure-difference system).
Morgenschweis,
G., Franke, P., “Experience with ultrasonic flow meters in the bottom outlet
of the Bigge dam, Commission internationale des grands barrages, Beijing, 2000,
Q.79 – R.7.
Helmig, R., “Einführung in die Numerischen Methoden der Hydromechanik”, Institut für Wasserbau der Universität Stuttgart, Heft 86, 1996.
DVWK Guidelines,
“Manual for Water Level Gauging and Discharge Measurements”, 1990, Verlag
Paul Parey.
Fig.4 Measured data
Fig. 5 Approximated rating curve
Fig. 6 Difference between measured and calculated discharge using figure 5
Fig. 7 Difference between measured and calculated discharge using equation 5
Fig. 8 Comparison of ultrasonic measurement and calculated discharge Q = f(h,Iw)