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Hydrological measurements: 8. + 9. streamflow measurements


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  • 1. 8Streamﬂow measurements8.1 IntroductionStreamﬂow measurement is a way to obtain information about the discharge of a river; variousmethods can be applied. Often it is hard to measure discharge itself and therefore it is derivedfrom measuring other parameters. Examples are: combining measurements of velocity and cross-sectional area into discharge, changes in electro-magnetic properties of the stream as a functionof discharge, or change in concentration of a substance that is released into the stream.Good water management is founded on reliable streamﬂow information and the ﬁnal reliabilityof the information depends on the initial ﬁeld measurements. The hydrologist making thesemeasurements has therefore the responsibility of ensuring that raw data of acceptable quality iscollected. The successful processing and publication of the data depend largely on the qualityof the ﬁeld measurements.There are many diﬀerent uses of streamﬂow data within the broad context of water management,such as water supply, pollution control, irrigation, ﬂood control, energy generation and industrialwater use. The importance placed on any one of these purposes may vary from country tocountry. In India and China, for example, emphasis may be placed upon irrigation and ﬂoodcontrol whereas in the United Kingdom water supply may be given priority; the emphasis foranyone may also change over short or longer periods of time. Basically the streamﬂow data iseither required as inﬁnite integration over time (= runoﬀ) or as instantaneous values for purposes.Continuous measurements of streamﬂow are often derived from continuous stage measurements,as stage is easier to measure than ﬂow. The streamﬂow in that case is obtained through a stagedischarge relationship (=the rating curve) based on occasional measurements. Nevertheless somemethods exist which under speciﬁc condition are capable of continuously measuring streamﬂow.Various ways exist to measure discharge instantaneously. Both, continuous measurements andinstantaneous measurements will be discussed in this chapter.
  • 2. 84 8. Streamﬂow measurements8.2 Velocity Area Method8.2.1 PrinciplesThe velocity area method is a method to obtain a near instantaneous value of the dischargeof a river. The discharge Q of a river is being measured by means of measuring velocities(ui ), representative for the part Ai of the area (A), in a suitable cross-section. The method ofapproach is: A n Q= udA ≈ ui · ∆Ai (8.1) Fig. 8.1: Example ‘velocity-area-method’A common approach is to select a number of verticals within the cross-section. In each of theseverticals the velocity is being measured at a pre-determined depth (see Fig. 8.1). There arevarious methods to determine the discharge from the measured geometry and velocity measure-ments. It should be realized that the cross-sections are usually more stretched (B >> h) thenshown in Figure 8.1. An elaborate study in ISO-connection has shown that it is preferred tohave many verticals in the cross-section rather than many measuring points in each vertical.This goes for regular velocity proﬁles, not for tidal rivers, even if no density ﬂows occur in thetidal river. For a tidal river, the time interval during which one vertical is being measured isnot negligible compared to the tide period. In this case options are: • When no density ﬂows occur the moving-boat method with ﬂow at a ﬁxed depth could be applied (see subsection 8.2.6) • When density ﬂows do occur the moving-boat method with an acoustic doppler ﬂow instru- ment (ADCP), applying measurement over the vertical, could be applied (see subsection 8.2.3) • Use of a reference vertical. By means of elaborate measuring, a correlation between the velocity in the vertical and the mean velocity in the whole cross-section is established.An example of using the reference vertical methodFor the Mekong River the secretariat of the Interim Mekong committee has worked out thereference vertical method (referred to as ’the velocity index method’) for a couple of cross-sections. In Figure 8.2 an example is given of the correlation between the mean velocity in theindex vertical (= reference vertical) and the mean velocity in the cross-section.
  • 3. 8.2. Velocity Area Method 85In this case the choice of measuring method has a political background. The Mekong is a borderriver between Thailand and Laos. A measurement over the whole cross-section, approved by bothcountries, requires a lot of diplomatic preparations. The data obtained by measurements overthe whole cross-section are being used to make routine measurements possible without havingto cross the border. Given the fact that the Mekong secretariat is established in Bangkok, it isnot a surprise that the reference vertical in Figure 8.2 is situated in Thailand. Nonetheless, it isstill necessary to check the validity of the correlation from time to time. After all, morphologicalchanges in the considered reach can occur. Fig. 8.2: The use of reference vertical by VientianeIn general three main sources of errors associated with the velocity area method, as depictedin Figure 8.1, can be distinguished. Assumed is the use of a propeller current meter (OTT) todetermine the velocities. Error I: The error in the determination of the velocity ui. This error is small when for more than a minute the velocity is being measured. Error II: The error as a result of the limited number of measuring points in a vertical. The local discharge per unit width holds an error. Error III: The error as a result of the limited number of verticals. This gives a great contribution to the error made in the discharge as a result in the approach of the integral given in Equation 8.1.Elaborate measurements of various rivers have been analyzed. In Figure 8.3 and 8.4 the resultsare summarized.
  • 4. 86 8. Streamﬂow measurements Fig. 8.3: Inﬂuence number of points in the vertical Fig. 8.4: Inﬂuence number of verticals in the cross-sectionNotes 1. The results as depicted in Figure 8.4 depend on the applied interval between the verticals. The easiest way is to choose the distance between the verticals equally. More accurate is to choose the distance between the verticals in such a way that every vertical equally contributes to Q, hence Q(y) = q(y)∆y is constant. 2. Especially for small watercourses it is usual to limit the number of measuring points in the vertical. • Three point measurement (measured away from the water surface): 1 u = (u0.2 + u0.6 + u0.8 ) (8.2) 3 or 1 u = (u0.2 + 2u0.6 + u0.8 ) (8.3) 4
  • 5. 8.2. Velocity Area Method 87 • One point measurement: Measured velocity on half of the water depth multiplied by 0.95. 3. In watercourses with high velocities it is often diﬃcult to measure below the water surface. Thus the mean velocity in a vertical can not be determined accurately. It is therefore advisable to multiply the measured velocities at the surface by a factor 0.84 ` 0.90 to a obtain the mean velocity in the vertical.8.2.2 Site selectionAs discharge potentially varies along the reach of a river or canal the location is generally deﬁnedby the site where the discharge is required. Nevertheless, on a smaller scale the variation ofdischarge might well be negligible. In that case a reach or cross section is preferred having thefollowing characteristics. • A straight reach with the threads of velocity parallel to each other. • A stable streambed free of large rocks, weeds or other obstacles that create turbulence • A ﬂat streambed proﬁle to eliminate vertical components of velocity.8.2.3 Instruments to measure point velocityThe velocity area method uses point information of ﬂow velocity in the considered cross-section.Various instruments have been designed to obtain these velocities. The following instrumentswill be discussed: • Pendulum • Cub current meter • Propeller current meter • Electromagnetic current meter • Doppler current meter • FloatThe pendulumThe pendulum current meter, developed by the Delft Hydraulics Laboratory, consists of a resis-tance body suspended on a cable. When lowered in ﬂowing water the ‘pendulum’ experiences ahorizontal force due to the ﬂow pressure. This causes the suspension cable to deviate from thevertical and the magnitude of the deviation is a measure of the ﬂow velocity at the location ofthe pendulum. The velocity is measured, by means of the resistance force being a function ofthe velocity, namely
  • 6. 88 8. Streamﬂow measurements Fig. 8.5: Pendulum 1 FN = CN ∗ ρu2 A (8.4) 2The structure for suspending the resistance body can be ﬁxed to a rail of a boat, the parapet of abridge, to a trolley, or can be held by hand in the case of the smaller types. Generally, the cableto which the body is attached can be reeled by a winch provided with an indicator showing thelength of cable released. Obviously the bending of the submerged part of the cable due to ﬂowpressure has to be taken into account. At every measuring point, the resistance body shouldbe given time to become adjusted to the ﬂow before the reading is taken. The instrument willalso facilitate reading of the ﬂow direction with respect to a ﬁxed orientation in the horizontalplane. This may be of importance when the ﬂow direction changes with depth. To cover a widevelocity range, the pendulum current-meter is provided with a series of resistance bodies. By acareful choice of body, velocities ranging from 0.05m/s to 3.5m/s can be measured. The choiceof resistance bodies should be such that the readings can be made with maximum accuracy.To this end, the angle with the vertical should not become too small and it may sometimes benecessary to change resistance bodies during a series of measurements in the vertical.In order to determine velocities and corresponding depths from the ﬁeld data, a number ofdiagrams are needed. They are based on the equation: ¯ u2 = coeﬃcient ∗ tan(φbody ) (8.5)The coeﬃcient as well as the correction for bending of the submerged part of the cable dependson the characteristics of the resistance bodies, the drag coeﬃcient and the diameter of thecable. They have to be determined by calibration. The manufacturer of the instruments usuallysupplies the diagrams.
  • 7. 8.2. Velocity Area Method 89Cub- and propeller- type current metersBoth cub- and propeller- types of current meters have the same basic principle, which is theproportionality between the local ﬂow velocity and the resulting angular velocity of the rotorof the instrument. An electrical circuit closed intermittently by contact points measures thenumber of the revolutions of the rotor. The interruptions are transmitted to an acoustic orelectric counter.The cub current meter can be held in the stream either by a rigid rod or by suspension froma cable. Rigid rod suspension enables placement of the meter at exactly the required point ofmeasurement. In deep streams, however, cable suspension has to be used. A suitably shapedcounterweight is than attached to ensure that the cable deviates from the vertical as littleas possible. The counterweights must be interchangeable so they can be adapted to the ﬂowvelocity. They vary from 25 kg where ﬂow velocities are lower than 1 m/s to 100 kg for ﬂowvelocities exceeding 1.5m/s.Calibration of these types of current meters is carried out by experimental determination of thecurves representing the relationship between the velocity of ﬂow and the propeller or rotor speed,usually expressed in revolutions per second. Current meters may be calibrated individually or agroup rating may be supplied by the manufacturer for a particular type of meter. A calibrationcurve, a formula, or a rating table is supplied by the manufacturer and the actual limits ofvalidity are also indicated. Usually a current meter is calibrated by moving the complete currentmeter, at accurately known speeds, through stagnant water in a ﬂume of adequate dimensions.Although it remains questionable whether this is identical with the reverse situation where thewater moves and the meter is at rest, this method of calibration is generally accepted.Cub current meter The cub current meter has a vertical axis; attached to the axis are anumber of cubs. The water ﬂows into one cub pushing the cub backward and thus turning theaxis round. Now the opening of another cub is pointing towards the side from which the wateris ﬂowing, the water ﬂows into this cub pushing this cub backward turning the axis furtherround. The rotors of the cubs are replaceable in the ﬁeld without aﬀecting the rating. The cubcurrent meter operates at lower velocities then the propeller-type meter. A single rotor servesfor the entire range of velocities. Due to its shape, a cup current meter should not move in avertical direction during the measurements, because the ﬂow at a cup can be disturbed by theturbulence form the other cups. Therefore, this type cannot be used for an integration method.Compared to the propeller current meter (see below) the cub current meter is more sensitive tovertical components in the velocity and to the bobbling of a boat.Propeller current meter The propeller current meter (OTT) has a horizontal axis to whicha propeller is attached. The ﬂow makes the propeller turn and thus the axis. The propeller isless likely to become entangled with debris than the cub current meter. Propeller current metersare not so susceptible to vertical currents as cub current meters and therefore give better resultswhen used for measurements from boats.
  • 8. 90 8. Streamﬂow measurements Fig. 8.6: Cub current meter Fig. 8.7: Propellor current meterElectromagnetic current meterThe electromagnetic current meter employs the Faraday principle of electromagnetic inductionwhereby a magnetic ﬁeld (in the velocity sensor) induces an electropotential in a moving conduc-tor (the water). An alternating current is passed through a coil in the velocity probe, which inturn sets up an alternating ﬁeld in the probe head and surrounding water. Movement of waterpast the probe causes an electric potential in the water, which is detected by two electrodesin the probe. This potential is than ampliﬁed and transmitted through the connecting cableto the display unit where the velocity signal is digitized and displayed in meters per second atpreset intervals in the range 2-60 seconds as required. Maintenance of the meter is minimal andconsists of keeping the velocity probe’s electrodes clean at all times. Because of the principleof electromagnetic induction the meter will not operate successfully in very low conductivitysolutions.
  • 9. 8.2. Velocity Area Method 91 Fig. 8.8: Electromagnetic current meterDoppler current meterAn instrument, that measures the ﬂow velocity by means of the Doppler eﬀect, is the AcousticDoppler Current Proﬁler or ADCP. ADCP’s are used to measure discharges in open channels,according to the velocity-area method. There are either downward looking ADCP’s, measuringvelocity proﬁles from near the water surface to the bed, or upward looking ADCP’s, installedon the bed. An example of a downward looking installation is the vessel mounted ADCP, whichis in use since the mid-1980’s.The Doppler eﬀect is a change in the observed sound pitch that results from relative motion.Doppler shift is the changed frequency observed from a moving sound source, compared to thestagnant situation. v Fd = Fs (8.6) cWith: Fd is the Doppler shift frequency (Hz) Fs is the frequency of the sound under stagnant condition(Hz) v is the relative velocity between the sound source and the sound receiver (m/s) c is the speed of sound (m/s)ADCP’s use the Doppler eﬀect by transmitting sound at a ﬁxed frequency and listening to echoesreturning from sound scatters in the water. These sound scatters are small particles (suspendedload) that reﬂect the sound back to the ADCP. Scatters are everywhere in rivers. They ﬂoatin the water and on average they move at the same horizontal velocity as the water (Note thatthis is a key assumption!). Sound scatters in all directions form scatters. Most of the soundgoes forward, unaﬀected by the scatters. The small amount that reﬂects back is Doppler shifted.
  • 10. 92 8. Streamﬂow measurementsWhen sound scatters move away from the ADCP, the sound you hear is Doppler shifted to alower frequency proportional to the relative velocity between the ADCP and the scatter. Whenthe sound reaches the sound scatters the sound is Doppler shifted, then the sound reﬂects backtowards the ADCP, so when it reaches the ADCP the Doppler shift is double, changing to: v Fd = 2Fs (8.7) cFinally the Doppler shift only works when sound sources and receivers get closer to or furtherfrom one another, this is radial motion. Limiting the Doppler shift to the radial componentgives v Fd = 2Fs cos(A) (8.8) cThe ADCP measures only the velocity component parallel to the acoustic beams. The angle Ais the angle between the beam and the direction of ﬂow (see Fig. 8.9). Fig. 8.9: Relative velocity vectorAcoustic Doppler Current Proﬁler is an accurate description of how the instrument determinesﬂow velocities in a vertical proﬁle: 1. Acoustic, as it uses sound waves to sense ﬂow velocities; 2. Doppler, because it uses Doppler eﬀect which is directly proportional to the ﬂow velocity; 3. Current. The ADCP needs three beams to determine the three vector components of water ﬂow. The four-beam conﬁguration provides two vertical vectors that the ADCP uses to check data integrity; 4. Proﬁler. The instrument measures ﬂow velocities in a large number of points (depth cells) in the vertical by ’range-gating’ the back scattered signal in time.The ADCP makes a velocity proﬁle for many depth cells, which can be from 5 cm in height ormore (depending on the frequency). Figure 8.10 shows a four beam conﬁguration measuring in14 cells. Each depth cell is comparable to a single current meter. Therefore an ADCP velocityproﬁle is like a string of current meters uniformly spaced. Thus, we can make the followingdeﬁnitions by analogy:
  • 11. 8.2. Velocity Area Method 93 Fig. 8.10: ADCP current proﬁler • Depth cell size = distance between current meters • Number of depth cells = number of current metersThere are two important diﬀerences between the string of current meters and an ADCP velocityproﬁle. The ﬁrst diﬀerence is that the depth cells in an ADCP proﬁle are always uniformlyspaced, while current meters can be spaced at irregular intervals. The second is that the ADCPmeasures average velocity over the depth range of each depth cell while the current metermeasures current only at one discrete point in space.Use of the instrument The ADCP is able to determine ﬂow-velocity magnitude and directionat selected depths in the vertical. It is also able to determine the relative location of theinstrument and to measure water depths. The transducer head is normally mounted about 0.2mto 0.5m below the water surface. The transducer should be mounted to minimize pitch, roll andwave bobbling of the head. The head should also be mounted so that cavitation will not occuraround the transducers. The vessel is positioned a measurable distance from the edge of thestream in the water that is deep enough for the instrument to operate. The instrument is turnedon, and the vessel on which the instrument is mounted traverses the channel. Depending on thedesign and the software, the instrument can provide continuous values of water depth, velocitymagnitude and direction and vessel position. Estimates of distances to the channel edges fromthe closest point at which the instrument can measure are made by the operator and enteredinto the program. Algorithms can be used to estimate velocities and ﬂow in the unmeasuredareas near the top, bottom and sides of the channel so that the total measured discharge in thechannel is available when the traverse of the channel is complete.The vessel on which the transducer head is mounted must be moved slowly enough during ameasurement so that cavitation does not occur around the transducer head. The uncertaintyof any set of velocity measurements is directly related to the speed of the vessel moving acrossthe channel and the measurement rate of the instrument. Despite vessel speed limitations, it is
  • 12. 94 8. Streamﬂow measurementspossible to obtain an accurate discharge measurement in a 200 meter-wide channel in about 5to 10 minutes.The vessel is not required to move in a straight line across the channel or to move perpendicularto the ﬂow direction. It is only necessary to traverse the cross-section from one bank to theother. The instrument can be moved in a very irregular path across the channel and can ﬁnishat a point some distance upstream or downstream form the starting point. The instrument isable to compensate for these irregularities in the traverse of the channel because of its ability todetermine continuously vessel position.Measurement characteristics and limitations Some parts of the channel cross-sectioncannot be measured with the ADCP instrument. One area void of measurement is near thesurface. The transducer head must be mounted slightly below the water surface, and there isalso a minimum distance required for the instrument to respond to returned acoustic signals.This depth in which no measurements are obtained can be 0.5m or more. When the acousticsignal is transmitted, the signal produces unwanted side-lobes. Some of these side-lobes travelin a vertical direction, while the primary signal is travelling at a set angle to the vertical. Theside-lobe signal, therefore, reaches the channel-bed before the primary signal. The reﬂected side-lobe signals thus return to the transducer from the bed before the near-bed primary signal andare much stronger than those returned from sediment particles in the water, thus overshadowingreturn signals from the primary signal before it completes its top-to-bottom excursion. Thepercentage of the depth at the bottom of the channel that cannot be measured, Dp , is therefore,approximately equal to: Dp = 100(1 − cosφ) (8.9)where φ is the angle of the acoustic beam from the vertical.Thus, for an angle of the acoustic beam to the vertical of 30◦ , approximately 13% of the depthat the bottom of the channel cannot be measured. For an angle of 20◦ , this decreases to about6%.Depths near the banks are commonly too shallow for the instrument to operate properly or forthe vessel on which the instrument is mounted. Therefore, part of the ﬂow near the banks cannotbe measured, and must be estimated. In large, deep channels, unmeasured ﬂows are relativelysmall. Unmeasured ﬂows are important in small streams, however where a large percentage ofthe ﬂow may have to be estimated.Instruments are currently capable of measuring velocities in depths as shallow as about 5m. Forbest results, the transmitted signal frequency for shallow water should be relatively high whilemeasurements made in deeper water should be made using lower frequencies. High-frequency(short-wavelength) transmissions provide for detailed velocity deﬁnition throughout the watercolumn but do not penetrate as far through a water column as a low-frequency (long wavelength)transmission. Common frequencies range from 300 to 2400 kilohertz.Velocities can be measured in depth cells as small as 0.1m. The uncertainty of the measurementincreases with decreasing depths, velocities and depth cell size. Velocities as slow as 0.05m/scan be measured but the uncertainty tends to increase for these slow velocities. A number of
  • 13. 8.2. Velocity Area Method 95 Fig. 8.11: Floatscomparisons have been made between measurements using the ADCP and measurements usingvertical-axis or acoustic current-meters or ultrasonic velocity-meters. Diﬀerences generally rangefrom about ± 2% to about ± 5%, but this can vary depending on ﬂow and channel conditions(Gordon [1989]).FloatsFloats are the simplest tools for measurement of ﬂow velocity. The time it takes the ﬂoat todrift over a known distance between two previously ﬁxed transversal lines is a measure of theﬂow velocity. Examples of surface ﬂoats and subsurface ﬂoats are shown in Figure 8.11.Two disadvantages of surface ﬂoats are that they measure the ﬂow velocity at the water surfaceonly and that they are inﬂuenced by the wind. Better information on the mean velocity in thevertical can therefore be obtained using subsurface ﬂoats.The various types of ﬂoats have conversion factors varying from 0.85 to 0.95; these values,for conversion of the ﬂoat velocity to mean ﬂow velocity, have been obtained by simultaneousmeasurements on ﬂoats and propeller current-meters. Floats in particular are of practical usefor streamﬂow measurements during ﬂoods.8.2.4 Current meter measurements by wadingCurrent meter measurements by wading are preferred if conditions permit. Wading measure-ments with the current meter supported on a graduated wading rod, which rests on the bed ofthe stream are normally more accurate than those from cableways or bridges as the operatorhas more control over the general gauging procedure.A measuring tape or tag line is stretched across the river at right angles to the direction ofﬂow; the spacing of verticals is determined by the required accuracy. The positions of successiveverticals used for depth and velocity are located by horizontal measurements from a referencemarker (initial point) on the bank, usually deﬁned by a pin or a monument. The gauging startsat the water edge of the near bank, where depth and velocity may or may not be zero. At eachchosen vertical the depth is measured and the value used to compute the setting or settings ofthe current meter depending on the method to be used (usually 0.6 or 0.2 and 0.8 depth).
  • 14. 96 8. Streamﬂow measurements Fig. 8.12: Current meter by wadingThe position of the operator is important to ensure that the operator’s body does not aﬀectthe ﬂow pattern when approaching the current meter. The best position is to stand facing oneof the banks, slightly downstream of the meter and an arm’s length from it. The rod is keptvertical throughout the measurement with the meter parallel to the direction of ﬂow (see Fig.8.12).8.2.5 Suspension systemsAn alternative to wading is lowering the ﬂow measurement equipment by means of a cable froma supporting structure. In general it can be stated that proper positioning of the equipmentfrom a cable in vertical and horizontal direction causes much more problems than with wading.To avoid dragging of the suspended cable with the current, usually a weight is attached to thecable or current meter.The cable with the current meter can for instance be moved by means of a cableway that crossesthe river. Alternatively river crossing bridges are used to lower the measuring equipment.Current meter measurements from cablewaysCableways are normally used when the depth of ﬂow is too deep for wading, when wading in aswift current is considered dangerous, or when the measuring section is too wide to string a tagline or tape across it.There are two basic types of a cableway: 1. Those with an instrument carriage controlled from the bank by means of a winch, either manually or electrically operated (Fig. 8.14); 2. Those with a manned personnel carriage, commonly known as a cable car, in which the operator travels across the stream to make the necessary observations; the car may be pulled manually across the river by means of a cable car puller, or it may be electrically operated
  • 15. 8.2. Velocity Area Method 97 Fig. 8.13: Schematic arrangement of unmanned cableway and suspension assemblyThe general gauging procedure is similar, except that in the case of the non-manned cableway theinstrument carriage, suspended from the track cable, moves the current meter and sinker weightacross the stream between the cable supports. The operator remains on the bank and operatesthe gauging winch, which is provided with both distance and depth counters for placing thecurrent meter at the desired position. The electrical pulses from the current meter are returnedthrough the core conductor of the suspension cable and registered on a revolution counter. Themanned cableway, on the other hand, is provided with a support for a gauging reel, a guidepulley for the suspension cable, and a protractor for reading the vertical angle of the suspensioncable.Line suspension from bridgesFrom higher bridges and for greater depths, the current meter and weight are suspended on acable. The cable is controlled by a gauging reel mounted on a bridge crane or on a bridgeboard(see Fig. 8.14). A handline may be used with the smaller weights. The gauging procedure isessentially the same as that for measurements from a cable car.Sinker weightsThe size of the sinker weight, attached to the current meter by means of a hanger bar, requiresbeing suﬃciently heavy to maintain the current meter suspension cable in an approximate ver-tical position. It is usually decided on by experience, common weights in operation vary fromabout 7 to 150 kg depending on the velocity and depth of ﬂow. On the Qintong River in theZhjiang Province of China, for example, depths are as much as 70 meter and velocities are ofthe order of 7 m/s, and a sinker weight of 750 kg is required. This, however, is an exception butweights of 250 kg are common in the Yangtze River catchment. Also in the Yangtze catchmentthe Bureau of Hydrology in China has introduced a combined sediment sampler and current me-ter equipped with an ultrasonic depth sounder. The facility of the ultrasonic transducer enablesdepth to be measured without the necessity of having to make air-line and wet-line correctionsalthough the weight of the sampler requires to be suﬃcient to place the device at the appropriatelocation in the vertical to make the velocity measurements.
  • 16. 98 8. Streamﬂow measurements Fig. 8.14: Line suspension from bridgeSinker weights are designed to a streamline form and furnished with tail ﬁns to orient themparallel with the current so as to cause the minimum interference to the ﬂow.8.2.6 Moving boatFrequently on larger streams and in estuaries conventional methods are impractical and involvecostly and tedious procedures. This is particularly true during ﬂoods when facilities may beinundated or inaccessible, at remote sites where no facility exist, or at locations where unsteadyﬂow conditions require that measurements be made as rapidly as possible. In other cases ﬂoat-ing obstacles or river traﬃc require that measurements be made as rapidly as possible. Theinstruments that are most used with moving boat ﬂow measurements are the ADCP and thepropeller current meter (see subsection 8.2.3).The moving boat technique is applicable to rapid measurements of rivers. In tidal rivers orestuaries, where density currents occur, the technique using a propeller current meter, withonly limited information in the vertical, can not be applied. The river water in the upperlayer can ﬂow seawards while in the underlayer seawater will ﬂow inland. The ADCP, on thecontrary, is more suitable under these conditions. Traditionally the term moving boat is mainlyassociated with the measurements using the propeller current meter and will be as such used inthe remainder of this chapter.The moving boat technique is based on the velocity area method of determining discharges.According to this method the total area of the cross-section is divided in sub-areas for which arepresentative velocity is determined. The principal diﬀerence between a conventional measure-ment and the moving boat measurement is in the method of data collection. The mean velocity,in the segments of a cross-section of the stream in case of a conventional technique, is deter-mined by point velocities or by an integrated mean velocity in the vertical. The moving boattechnique measures the velocity over the width of a segment by suspending the current meter
  • 17. 8.2. Velocity Area Method 99 Fig. 8.15: Vector diagramat a constant depth during the traverse of the boat across the stream. The measured velocityand the additional information of the depth sounding gives the required data for determiningthe discharge.The velocity measurement taken at each of the observation points in the cross-section is a vectorquantity, which represents the relative velocity of water past the current meter. This velocityvr is the vector sum of vw , the component of the time integrated stream velocity perpendicularto the boat path in the interval, and vb , the velocity of the boat with respect to the streambedalong the selected path. As this vector sum is the relative velocity of the water past the currentmeter assembly. The vector diagram, Figure 8.15, demonstrates this relationship.Three types of data are required: 1. Location of observation points across the stream 2. Stream depth 3. Stream velocityDuring the traverse an echo-sounder normally records the geometry of the cross-section and acontinuously operating current meter senses the combined stream and boat velocities. A thirdset of data is needed to determine the location of the boat in the cross-section. This can bedone by various methods. One method is to measure the angle between the boat and the cross-section that is traversed. Due to the current the boat will drift from the section if not correctedby steering. As a result the boat will move in an angle with the traversed path. The anglecan be measured and results, in combination with the measured velocity, in a position of theboat (method 1). Alternatively the location is directly measured relatively to a grid or beacons(method 2).The two methods are described as being representative for the diﬀerent approaches. Combi-nations of the described techniques are of course possible. In method 1 (as it is called in thefollowing) the current meter is located at a ﬁxed depth below the water surface. The determina-tion of the location of the observation points in the cross-section is based on observations of the
  • 18. 100 8. Streamﬂow measurements Fig. 8.16: Possible layout of equipment on board of a boatangle between the section and the orientation of the current meter. In (the afterwards called)method 2 the current meter is freely suspended while the location of the observation points isdirectly measured with for example sextant readings.In the following a more detailed description is given of the two methods, the way of measurementand the principle of the calculation procedure.Method 1Equipment and measurements A specially equipped boat is used as indicated in Figure8.16. A vane with an indicating mechanism is mounted on the bow. The angles (α) betweenthe direction of the vane and the cross-section are read via a pointer mounted in line with thevane. A sighting device attached to the free swivelling dial provides a means of aligning theindex point on the dial with the cross-section.The propeller current-meter (OTT) is mounted on the leading edge of the vane, whereas anelectronic counter is used as pulse indicator. A stopwatch is used to time interval measurements.Finally an echosounder is installed for depth registration.A crew of four persons is required: 1. A boat operator. 2. An angle observer. 3. A revolution counter operator. 4. A note keeper, echosounder operator, stopwatch operator.After selection of the site and installation of the reference marks or beacons that deﬁne theorientation of the cross-section, the width of the stream and the location of the beacon(s) nearthe river are determined for example by triangulation. For rivers with a width of more thanabout 600 meter alignment reverends are used on both banks (see Fig. 8.17).The location of the water line is ﬁxed in relation to a nearby beacon. Using method 1, the exactlocations of the starting and ﬁnishing position of the boat have to be determined (A and B).
  • 19. 8.2. Velocity Area Method 101 Fig. 8.17: Stream, boat and beaconThis can be done by rangeﬁnder observations or sextant readings. If a third reference point onthe bank(s) is available Buoys can be located in A and B. Starting in A the revolution counterand vane direction indicator are read and the echosounder registration is marked simultaneously.The observations can be done at regular time intervals for calculation purposes (20 or 30 sec); itis not essential for the method itself. However, a minimum of 25 ` 30 observations is required. aFor this purpose and, the boat velocity is estimated more or less equal to the water velocity.Computation The boat velocity is calculated by: vb = vr · cos(α) (8.10)With: vb boat velocity (m/s) vr measured relative water velocity (m/s) α angle between cross section and the longitudinal axes of the boat (degrees)∆L is the distance covered in the time interval ∆t with: ∆L = vb ∆t (8.11)The total distance L between A and B is calculated as the sum of the distances ∆L: n L= vb ∆t (8.12)with n = number intervals.Knowing the real distance between A and B (Lr ) a correction factor kl can be determined: Lr kl = (8.13) LThe water velocity is calculated leading to vw = vr · sin α (8.14)where vw = water velocity,and the partial areas and discharges as: ∆A = ∆L · d (8.15)
  • 20. 102 8. Streamﬂow measurements ∆Q = ∆A · vw (8.16)where d = average depth between two observation points.The total area and discharge between A and B (n intervals) is calculated according to AAB = ∆A (8.17) n QAB = ∆Q (8.18) nThe corrections for the areas and partial discharges between the points A and B and the banksare made assuming a straight bottom slope between the water line and the depth in A or B andusing a parabolic velocity distribution. Taking into account these corrections, the total area anddischarge Atot and Qtot are calculated.Two more adjustments are made: 1. Adjustment for the mean velocity in the vertical (kv ). It is assumed that in larger streams the relation between the velocity on the depth of the current-meter and the mean velocity in the vertical can be considered as fairly constant. In order to arrive at a representative average value of kv several vertical velocity distributions have to be determined in strate- gically placed verticals. kv is calculated as a weighed average with weights in proportion to the discharge in the segments. As the coeﬃcient depends on the average water depth, these kinds of measurements have to be repeated at several stages in a non-tidal river and at various moments in a tidal river or estuary. It is, however, not necessary that kv is determined for each diﬀerent discharge measurement. kV normally ranges between 0.85 and 0.92, and depending on the required accuracy of the measurement it seems that a good estimation is obtained using kv = 0.90. 2. Width adjustment. The correction factor kl is used to correct both the calculated area (Atot ) and discharge (Qtot ).Summarized the real area (Ar ) and discharge (Qr ) are calculated with the following formula: Ar = kl · Atot (8.19) Qr = kv · kl · Qtot (8.20)Method 2Equipment and measurements No special equipment with reference to the conventionaltechniques is required in the most basic execution form of method. The current-meter is freelysuspended in the same way as for a conventional discharge measurement and distances aredetermined by rangeﬁnder or sextant. However, it is recommended to use an echosounder for
  • 21. 8.2. Velocity Area Method 103 Fig. 8.18: Stream, boat and beacons for sextant readingsimultaneous depth registration and special counting device for revolutions and time intervalobservations; the objective of the special counter is to ’freeze’ for a moment the observationsthat have to be copied. Two counters that operate alternatively or one counter with a specialmemory system can do this. Due to computational diﬃculties in cases that observation errorsare made, a one counter system with a memory is highly recommendable. A crew of four personsis required: 1. A boat operator 2. A sextant or rangeﬁnder observer. 3. A revolution, time interval observer. 4. A note keeper, echosounder operator.Field practice showed that for experienced groups, dependent; however, on the facilities oﬀeredby the counting device, a crew of three persons is suﬃcient. As far as the site selection isconcerned reference is made to the description given above for method 1. The reference pointson one bank consist of 3 beacons, two for alignment of the launch and two as a base for thesextant readings. For rivers over about 600 meters wide these reference marks are installed onboth banks(see Fig. 8.18). No special measurements as described in method 1 are required tolocate points A and B.Computation The computational procedure is slightly diﬀerent for method 1. ∆L resultsdirectly form the location determined by the sextant readings and vb is calculated with ∆L vb = (8.21) ∆tWith: vb boat velocity (m/s) ∆L the distance between the observation points (m) t the time interval between two readings (s)The water velocity is determined by vw = 2 2 vr + vw (8.22)
  • 22. 104 8. Streamﬂow measurements Fig. 8.19: Vertical velocity distributionWith: vr the measured relative water velocity (m/s) vw the water velocity (m/s)The mean velocity adjustment is made directly after the computation of vw (and before calcula-tion of the partial discharges) by way of a unitary-velocity distribution in the vertical, relatingthe relative depth with the relative velocity.With: vw mean water velocity (m/s) h depth of the current meter (m) htot total depth (m)8.3 Dilution gauging8.3.1 PrinciplesDilution gauging is, as is the velocity area method, a method to obtain a near instantaneousvalue of the discharge of a river. The principle of dilution gauging is simple. Added to a constantunknown discharge Q, is a smaller discharge ∆Q(t) that exists of a watery solution of a substanceof which the concentration (t) is measurable. From the known data, ∆Q(t) and φ(t) the valueof Q is derived.8.3.2 Constant rate injection methodConstant rate injection is the simplest case of the dilution gauging. The injection consists of aconstant discharge ∆Q, with concentration 1 that is added to the river discharge Q, during along enough time period. If on the reach L (see Fig. 8.20) there is suﬃcient mixture, than aftera certain time period a constant concentration 0 will be measured at the end of the reach. From
  • 23. 8.3. Dilution gauging 105 Fig. 8.20: Dilution gauging for reach Lthe mass-balance of the concentrations, it follows by approximation (when ∆Q << Q): ∆Q φ0 = φ1 (8.23) QFor a good measurement a couple of conditions have to be met, the most important are describedbelow. Also Andr´ and Molinari [1979] pays attention to this kind of measurements. eRequirements of the tracer • Naturally, the tracer has to dissolve in water • The concentration of the tracer still has to be measurable after a suﬃcient dilution (∆Q << Q). • No density ﬂows may occur. Almost all solutions meet this requirement. Even NaCl- solutions do because of ∆Q << Q possible. • The tracer may not attach to ﬂoating sediment. Therefore the colouring agent Rhodamine (concentration determination with colorimeter) is normally not suitable. Only suitable is Rhodamine WT (= ‘watertracer’). • The unmarked water should have low concentrations of the tracer. This is why NaCl is not always suitable.Requirements of the river reach • Within the reach (see Fig. 8.20) no water ﬂows into nor out of the river • Within the reach length L the mixture has to be as good as possible. • During the measurement steady ﬂow (Q=constant) needs to occurThe length L can be roughly determined with an experimental equation (Eq. 8.24): B2 L > 0.13K (8.24) aWith:
  • 24. 106 8. Streamﬂow measurements φ Fig. 8.21: φ0 = f (ξ) √ C(0.7C + 2 g) C K= for 4.8 < < 16 (8.25) g gWith: C Chezy roughness (m1/2 /s B river width (m) a river depth (m)van Mazijk [1996] has analytically examined the relationship between the concentration nearthe banks and the average concentration when the injection takes place at one bank (see Fig.8.21). It is assumed that complete mixture occurs when the concentration on the opposite bank(φ), is 95% of the average concentration in the whole cross-section (φ0 ).For the accompanying length L0.95 it is found that: L0.95 uB ¯ = 0.4 (8.26) B K2Whereby K2 is the transversal dispersion coeﬃcient with K2 ≈ αau∗Together with Equation 8.26 applies, 0.4 C B 2 L0.95 = √ (8.27) α g abecause
  • 25. 8.3. Dilution gauging 107 Fig. 8.22: Determining reach length u ¯ C =√ (8.28) u∗ gFor a rectangular proﬁle applies α ≈ 0.15 and for an arbitrary proﬁle applies α ≈ 0.6 (see alsode Vries, 1984). For Equation 8.26 and 8.27 generally goes: B2 L>β (8.29) a 0.4 CWith β = a √ gBoth Equation 8.29 and 8.27 give a functional relation between the dimensionless parameter √β = aL/B 2 and C/ g (Fig. 8.22). Because the dilution gauging is mostly used for irregularwatercourses (α = 0.4), it appears that both criteria for the length L of the river reach dotally. The length L does not need to be chosen longer then necessary. After all the timespan θover which one has to inject depends on the length L. It appears that θ = 10 ` 15 minutes is asuﬃcient. This could be checked with a test-measurement.Execution of the measurementFor the constant rate injection method, it is important to keep ∆Q constant. This is possible byinjecting the tracer into the river with an adjustable pump. It is also possible to use the principleof the bottle of Mariotte (1620-1684) (see Fig. 8.23) This is the principle that is also used fordrinking water bottles in birdcages. When the water level starts to lower, automatically air is letinto the bottle, as much as to keep the ﬂow opening under a constant pressure. The discharge
  • 26. 108 8. Streamﬂow measurements Fig. 8.23: Bottle of Mariotte∆Q depends on the pressure at the ﬂow opening and thus is independent of the amount of ﬂuidleft in the bottle.The concentration depends on the used tracer. For colouring agent (e.g. rhodamine WT orﬂuorescent) a colorimeter is being used. For salt solutions (e.g. cooking salt) the conductivityis being measured.Comment:For the sake of completeness, the use of radioactive tracers will also be mentioned. The necessaryexpertise and often-rigorous safety rules make the use of this kind of tracer troublesome.It is wise to verify that a uniform dilution of the added concentration occurs at the measurementsite. Obviously the necessary length of the reach is shortest if one injects in the centre of thewatercourse. Because this is not always possible, Figure 8.22 assumes adding of the concentrateand measurement of the dilution from the banks. Dilution gauging works best in strong turbulentwater (and thus good mixture). For mountain creeks this method is ideal. In fact, other methodsbased on velocity measurements in mountain creeks are usually less suitable, due to the irregularcross-sections. The method of dilution gauging is also very suitable for the determination of thecapacity of pumping stations (the pump will take care of the necessary mixture).8.3.3 Sudden or Gulp injection methodAs a variant on the discussed method of the constant rate injection, the method of sudden or Gulpinjection has to be mentioned. By this method on t = 0 a tracer mass (M ) is instantaneouslyinjected in the river. On a distance L downstream (where the concentrate is assumed uniformlydiluted) the mass concentration is being measured. The following formula applies here:
  • 27. 8.4. Ultra-sonic streamﬂow measurement 109 Concentration Wave 0.8 Maisbich, 01-05-2004 Q=3.6 L/s 0.7 0.6 Concentration (g/L) 0.5 0.4 0.3 0.2 0.1 0 0 100 200 300 400 500 600 700 800 900 Time (s) Fig. 8.24: Example of a concentration wave from a sudden injection of 500 gram of salt ∞ M =Q (φ(t) − φ1 )dt (8.30) 0Where φ1 is the possible existent natural concentration in the watercourse, which can be de-termined upstream from the injection point. Theoretically φ1 can be a function of time. Thecondition that φ1 << φ does apply. When M is known and both φ(t) en φ1 (t) are measured,the discharge Q in Equation 8.30 is the only unknown.8.3.4 Range and accuracyThe dilution gauging is preferably suitable for small watercourses with a lot of turbulence as wellas for pumping stations. Nevertheless, accurate measurements were achieved with discharges upto 2000 m3 /s. With precise execution the relative error in the discharge can be in the order of1%.8.4 Ultra-sonic streamﬂow measurementUltrasonic streamﬂow measurement is a method to determine an instantaneous value of thedischarge of a river.8.4.1 TheoryWhen there is no ﬂow in a watercourse (v = 0), the time TAB it takes for an acoustic pulse togo from A to B is the same as the time TBA to go from B to A. The time TAB and TBA equalsL/c, where L is the distance between A and B, and c is the speed of sound in water (about 1500m/s).
  • 28. 110 8. Streamﬂow measurements Fig. 8.25: Speed of sound in ﬂowing waterWhen there is ﬂow in the watercourse (v = 0), than the sound from A to B will have an extravelocity vcosφ (see Fig. 8.25). The total dynamics of the sound which goes from A to B will bec + vcosφ , hence L = (c + vcosφ) TAB (8.31)A sound pulse from B to A is slower (with a fraction vcosφ ), so the dynamics of the soundwhich goes from TBA is equal to c − vcosφ, and hence L = (c − vcosφ) TBA (8.32)From these equation follows (elimination of c): L 1 1 v= − (8.33) 2cosφ TAB TBAThe ﬂow velocity can be calculated from Equation 8.33 if L and are known, and TAB and TBAhave been measured. However when put into practice two important problems occur: • To derive Equation 8.33 from Equation 8.31 and 8.31, it is assumed that the speed of sound for both measurements (from A to B and vise versa) is exactly the same; this however is often not the case. • The streamﬂow direction is never exactly along the river centre.Both problems will be discussed.The motion of sound is not a real constant, but depends on diﬀerent conditions of the water: • The water temperature and water pressure. • The salinity (=salt concentration in the water). • The concentration, size and distribution of air bubbles.Because the measurements are made in two directions along the same sound path, the conditionsfor both are similar. Furthermore, from a good ﬂow measurement utility, one has to expect itwill measure both measurements simultaneously (otherwise conditions could change).
  • 29. 8.4. Ultra-sonic streamﬂow measurement 111 Fig. 8.26: Flow with lateral componentIn Equation 8.31, vcosφ is the component of the streamﬂow velocity assuming the directionof the streamﬂow velocity along the river centre. In an arbitrary watercourse (normally) thisdirection is not along the river centre, but makes an angle δ with the line following the censer(see Fig. 8.26).The component v1 is now equal to vcosδ and the component vd is vsinδ. The streamﬂow-component along AB is now vcos(φ + δ). Hence Equation 8.33 still applies, on condition that φis replaced by (φ + δ): L 1 1 v= − (8.34) 2cos(φ + δ) TAB TBAUsing simple geometry1 we get: L 1 1 vcosφcosδ − vsinφsinδ = − (8.35) 2 TAB TBAFor a second measuring line CD (see Fig. 8.27) under the same angle with the centre line, butmirrored, it follows that: L 1 1 vcosφcosδ − vsinφsinδ = − (8.36) 2 TDC TCDFrom adding Equation 8.35 with 8.36 we get: 1 L 1 1 1 1 vcosδ = − + − (8.37) 2 2cosφ TDC TCD TAB TBAThe left side of this equation is the component of the ﬂow velocity along the river centre, vl , andthe right side of this equation is the average of Equation 8.33, for two measuring lines AB andCD. Lateral components can thus be eliminated using the ’measuring-cross’. Using Equation8.35 and 8.36 also the component vd can be calculated. 1 L 1 1 1 1 vsinδ = − − + (8.38) 2 2sinφ TDC TCD TAB TBA 1 cos(φ ± δ) = cos φ · cos δ ± sin φ sin δ
  • 30. 112 8. Streamﬂow measurements Fig. 8.27: Measuring cross8.4.2 Site selectionWhen making a decision as to whether or not a site is suitable for an ultrasonic streamﬂowgauge the following basic factors need to be true: 1. A reliable source of power is available; a portable system is now marketed, however, which is battery operated. 2. The channel width is in the range 20-300m, although the system operates outside this range, this range is normally considered economically feasible. 3. The channel is free of weed growth at all times as weeds disperse the beam. 4. Generally, as a guide, sections having concentrations of over 1000 mg suspended solids/litre, for signiﬁcant periods of time are avoided. Suspended solids may have a signiﬁcant eﬀect on the signal attenuation caused by both reﬂection and scatter from sediment particles suspended in the stream. 5. Other causes of attenuation need also be avoided; attenuation of the acoustic signal may also be caused by reﬂection and scatter from entrained air usually caused by rapids or waterfalls. 6. Upstream inﬂows to the river at diﬀerent temperatures or high salt content are not advis- able; they may cause the beam to be refracted. 7. The measuring reach is one, which is preferably straight and uniform, and at cross-sections in the reach, between the upstream and downstream transducers, the velocity distribution is similar. 8. The bed is stable. 9. Wide shallow rivers are avoided, otherwise the beam may reﬂect from the surface or channel bed and cause gross uncertainties.
  • 31. 8.4. Ultra-sonic streamﬂow measurement 1138.4.3 InstrumentationIf there was no sound absorption in water, the highest possible operating frequency could beused as this increases the system timing accuracy and allows closer spacing between the acousticpath and the surface or bottom of the channel. However, sound absorption by particulatematter and entrained air increases with increasing frequency. While increasing transmitter powerhelps somewhat, there is an upper limit achievable and a compromise is therefore reached indetermining the operating frequency. Generally the frequency range used in ultrasonic systemsvaries between 200 and 500 kHz, the lower frequencies being used in wide rivers. Manufacturers,however, are able to modify their systems in order to use the appropriate frequency for the givenconditions of the site.As stated earlier, special problems arise for the paths nearest to the surface and bed (the reasonto avoid shallow rivers). If the transducers are too near these boundaries, reﬂected signalsfrom the boundary can interfere with the direct transmission and causes inaccuracies in thetime measurement. Sound is reﬂected from the water surface and, to a lesser extent, from thechannel bed. The bed may even be a net absorber of sound. As an acoustic wave propagatesacross a river it will intersect with the water surface and be reﬂected, suﬀering a 180 phasechange in the process. The secondary wave will proceed across the river and arrive at theopposite bank. The target transducer will sense its arrival later than the direct wave, and thediﬀerence in arrival time will be a function of the diﬀerence in the respective lengths of the directand indirect paths. Errors in signal timing will occur if the secondary signal interferes with theﬁrst cycle of the direct signal. To avoid this eﬀect, the diﬀerence in the two paths should exceedone acoustic wavelength (speed of sound divided by the frequency). This will be achieved if thedepth of water above the acoustic path exceeds that given by the equation: L H = 24 (8.39) fWith: H is the minimum depth (m) L is the path length (m) f is the transducer frequency (Hz)A similar restriction may apply to the channel bed, particularly if it is smooth and, hence,reﬂects rather than absorbs an acoustic signal.Single/multiple path systemsIn the single path system, measurement of velocity is made at one depth only with the pair oftransducers normally set at 0.6 of the most frequently occurring depth. If the transducers aremovable, they are used to calibrate the system by taking line velocity measurements throughoutthe depth as in the vertical velocity distribution method. Instead of using verticals, horizontalpaths are scanned at an inﬁnite number of ’verticals’. If the transducers are ﬁxed, a relation isestablished between ﬂow, as measured by current meter, and the ultrasonic line velocity. The
  • 32. 114 8. Streamﬂow measurementsFig. 8.28: Diagrammatic illustration of multi-path ultrasonic system (Also shown is an ultrasonic depth gauge)single path system is normally used when the variation in stage is small for a larger percentageof the time.The more common multi-path system incorporates several pairs of transducers to provide veloc-ity measurements at various water depths and is particularly suitable for rivers having a widerange in stage or with irregular velocity distributions.MaintenanceWorking with an ultra sonic streamﬂow measurement system requires little maintenance. Yearly,the transducers need to be cleaned and the altitude-measurement must be checked. Periodicallythe ﬂoat shafts and supply shaft of the altitude-measurer, needs to get ﬂushed and cleaned(removal of obstacles, bank growth and such more). Obviously, it needs to be checked regularlyif the, in the discharge measurement system, imported proﬁles and correction-factors still agreewith reality. It speaks for it self, the facilities need maintenance too.8.4.4 AccuracyThe streamﬂow velocity is determined by: the angle (φ ), the distance L and the time periodsTAB and TBA (see Eq. 8.33). The accuracy with which the streamﬂow velocity is determinedis also determined by the accuracy of these components. Without going into any details thefollowing can be said about the accuracy.The accuracy of the determined time periods (TAB and TBA ) is for the standard 200 kHz-transducers better than 15 ns (1ns = 10−9 s). Converted to the velocity this means accuracywithin circa 0.5mm/s for a measuring line length of 50m. For longer measuring lines the accuracygets proportionally better (e.g. for L = 250m the accuracy is better than 0.1mm/s). The otherway around, for smaller lengths the accuracy gets proportionally worse (better than 2.5mm/sfor L = 10m). For very small measuring lines the accuracy can be improved 5 times by usingspecial transducers.The measuring line L can normally be established within the 0.5% accuracy. The maximumerror for the velocity measurement as a result of the accuracy of L is than also 0.5%.
  • 33. 8.5. Electromagnetic streamﬂow measurement 115The angle can be established within 0.1% accuracy. For a measuring line angle of φ = 45◦ , thismeans the maximum error in the streamﬂow velocity determination is 0.2%.8.4.5 Existing installationsDespite the high initial costs of measurement equipment and measurement facilities, Rijkswa-terstaat expands the use of ultrasonic streamﬂow measurements. This because the methodgives: • Continuous information about the discharge and therefore is suitable for operational wa- termanagement. • Exact information, as well for high discharges as low discharges, and thus can be used for a broad scale of purposes. • Reliable information, due to internal controls. • Digital information and thus can be used for modern means of data transport and data processing.Finally the equipment is maintenance friendly and the exploitation costs are low.8.5 Electromagnetic streamﬂow measurement8.5.1 TheoryAccording to Faraday’s law of electromagnetic induction, the motion of water ﬂowing in a rivercuts the vertical component of the earth’s magnetic ﬁeld and an electromotive force (emf) isinduced in the water. This emf can be sensed by electrodes (’probes’) on each side of theriver and is found to be directly proportional to the average velocity of the ﬂow in the cross-section. Therefore, unlike the ultrasonic method (see section 8.4) which measures velocity acrosspaths, the electromagnetic method performs integration over the entire cross-section. However,although measurements have been conducted using the earth’s magnetic ﬁeld, usually in tidalestuaries, these have had a large uncertainty due to the fact that the emf induced by the earth’sﬁeld is too small to be distinguished from other electrical interference. This interference normallycreated by 240 V mains, electrical motors and other ambient electrical noise present in someform or another in the ground. Therefore, to induce a measurable potential in the electrodes,a vertical magnetic ﬁeld is generated by means of a coil buried in the riverbed, or placed overit, through which an electric current is driven. The potential generated is proportional to thewidth of the river (m) multiplied by the magnetic ﬁeld (T) multiplied by the average velocity ofﬂow (ms−1 ).The electromagnetic technique has been used for many years for gauging full pipes where thearea of ﬂow is constant. The basic principle is shown schematically in Figure 8.29. The pipeﬂow meter is manufactured in units of practically any required diameter sizes, the largest inpractice being about 2 meter diameter. The coil is incorporated in the form of a saddle around
  • 34. 116 8. Streamﬂow measurements Fig. 8.29: Basic principle of ﬂuid ﬂow measurement in pipes by electromagnetic inductionthe pipe section and the electrodes are inserted in the pipe wall ﬂush with the inside wall.In streamﬂow measurement, however, the stage varies and therefore the cross-sectional area ofﬂow is not constant. In addition, stream channels are much wider than pipes and hence theelectromagnet forms a large part of the cost; velocities in rivers are normally much slower thanin water ﬂowing in full pipes since the former are ﬂowing under gravity whilst full pipes arenormally under pressure. In addition, electrical interference is generally higher near rivers thanin pipes, particularly at the mains distribution frequency. All of these factors make open channelelectromagnetic gauging much more complex then those in full pipes.Referring to Figure 8.29 Faraday’s law of electromagnetic induction relates the length of aconductor moving in a magnetic ﬁeld to the emf generated, by the equation: E = B¯b v (8.40)With: E is the emf generated (V) B is the magnetic ﬂux density in teslas (T) v is the average velocity of the conductor in the cross-section (ms−1 ) b is the length of the conductor and is equal to the river width (m)Now in the case of an operational gauge having an insulated bed and a square coil just widerthan the channel, the voltage generated is approximately 0.8 times that given by Equation 8.40.This reduction in voltage is caused by the shorting eﬀect of the water upstream and downstreamform the magnetic ﬁeld. Numerically the empirical relation (±3%) is: E ′ ≈= v bH ¯ (8.41)
  • 35. 8.5. Electromagnetic streamﬂow measurement 117Where E ′ is the electrode potential (µV) and H is the average magnetic ﬁeld strength in amperesper meter. (Note: the physical relationship between B and H in free space, air or water is givenby: B = H4π107 (8.42)In the ideal case where the magnetic ﬁeld strength is constant over the entire wetted section,the discharge, Q (m3 s−1 ), is given by: Q = vbh (8.43)With h the water depth. From Equation 8.41 and 8.42 follows the equation for the discharge: E′h Q= (8.44) HOperationally this equation may take the form: n E′h Q=K (8.45) Iwhere I is the coil current in amperes and K and n are constants. If the coil is mounted abovethe channel the water near the bed will move in a less strong magnetic ﬁeld relative to that nearthe surface. Normally the relation is expressed in the form: E′ Q = K1 + h + K2 h2 (8.46) HThe current meter calibration graph may take several forms; it may be a single straight linewhen transposed logarithmically, or have several straight lines with inﬂexions or it may becurvilinear. It can be seen that the discharge from Equation 8.44 and 8.45 or 8.46 is obtainedby the velocity-area principle in which the velocity is inferred from the electrode potential andmultiplied by the cross-sectional area of ﬂow. The area is a function of the recorded water leveland the equations contain dimensional constants established empirically. The river width factordoes not appear in the equations and is accounted for in the design of the coil, which extendsthe full width of the channel, and in the empirical calibration.8.5.2 Site selectionThe following are the main considerations in selecting a site for an electromagnetic gauge: 1. Due to cost considerations, the maximum width of the river is in the order of 30m. This limit is mainly set by the need to insulate the channel with a membrane. 2. A site survey is carried out to measure any external electrical interference (e.g. power cables, radio stations, electric railways). Areas of high electrical interference are preferably avoided. 3. A 2kW source of electrical energy is available. For continuous operation a power supply of 110-240 V is necessary but the system can operate on a 12 V supply for short periods,
  • 36. 118 8. Streamﬂow measurements 4. The site requires adequate on-bank working space for handling the membrane and cable. 5. There is good access to the site for installation, operation and maintenance. 6. The site characteristics are such that the calibration of the station can be checked by current meters. 7. Sites are selected where there is no spatial variation of water conductivity. The accuracy is degraded if the spatial conductivity is not uniform across the section. Temporal variations are unimportant provided the spatial uniformity of the conductivity is maintained. This requirement makes an electromagnetic gauge unsuitable for channels where fresh water ﬂows over saline water, which often occurs in small estuaries. Provided these requirements are met, the quality of the water, ranging from mountain streams to foul sewage, will not aﬀect the operation of the gauge and, similarly, the conductivity of the water will not aﬀect the operation of the gauge.8.5.3 Design and constructionThe electromagnetic gauging station consists of (see also Fig. 8.30): 1. A ﬁeld coil installed below or above the cannel; 2. A pair of electrodes one on each side of the channel; 3. An insulating membrane; 4. An instrumentation unit including a coil power supply unit; 5. A water-level measuring gauge; 6. A reference gauge and station benchmark.The coilThe coil is wound with a determined number of turns of wire which will depend on: the accu-racy required, the river width, the minimum velocity and the coil power supply, but normallya coil of between 50 and 300 turns is required. The ﬁeld to be generated by the coil is madeof suﬃcient magnitude to cause the induction of a measurable voltage between the two elec-trodes at the minimum water velocity. For a rectangular channel the relationship between theelectrode voltage and the electromagnet is 500mVm-1s-1 water velocity for a 1000 A turn (AT )coil. To establish a minimum number of ampere-turns to be provided, the measurable voltage,which is typically 0.5mV, is related to the minimum voltage obtained at the minimum velocity.For example, consider a typical river situation where the minimum velocity to be measured is0.03ms−1 and the resolution of measurement required is 5%. This accuracy of 5% correspondsto a velocity of 0.0015ms−1 . If this velocity corresponds to a minimum voltage measurement of0.5mV an electromagnet is required with: 0.5 1 1000 · · AT ≈ 660AT (8.47) 500 0.0015
  • 37. 8.6. Flood surveys 119 Fig. 8.30: Schematic view of electromagnetic gauge with coil installed below channel bed8.6 Flood surveysTo handle the damage that ﬂoods can cause it is essential to be able to quantify its magnitude.This is in terms of the maximum discharge and/or ﬂood levels as well as the ﬂood volume. Thiswould need ﬂood surveys to link stage and discharge. Measuring discharge under extreme ﬂowconditions is not easy. Typical methods that can deliver estimates of stage and discharge undereven the most extreme ﬂood conditions are the slope area method and measurements by ﬂoats.8.6.1 FloatsContrary to what most hydrologists and hydrometrists wish to believe ﬂoats are the most reliableand scientiﬁcally most appropriate instruments for measuring discharges during peak ﬂows. Thehydrometrist often considers ﬂoats below his/her professional standard and thinks incorrectlythat his / her current meter is the most accurate instrument for determining peak discharges.Floats, well positioned, and with a resistance body at the right depth (see Fig.8.31) are best forthe following reasons: • Floats move at the same velocity as the surrounding water (provided they are made as in Figure 8.31) and integrate the velocity in the longitudinal direction; they thus provide an accurate sample of the real mean velocity. Current meters, that integrate the velocity over time at a ﬁxed position, may be aﬀected by local accelerations (e.g. due to bed forms). Moreover, current meters do not always measure the point velocity accurately. • Floats are stagnant in relation to the moving water, thus the vertical position of the resistance body in the ﬂow is correct. The vertical position of a current meter in the
  • 38. 120 8. Streamﬂow measurements Fig. 8.31: Float with resistance body and the location of the resistance body in the vertical stream, on the other hand, is not certain. Often velocities are so high that the instrument just ’takes oﬀ’ after touching the water surface. • A ﬂoat measurement can be carried out in a shorter period of time than a current meter measurement, which is an advantage under rapidly changing conditions. • Floats are cheap compared to current meters; it is not a disaster if one gets lost. • At the peak of the ﬂood, the river is full of debris; use of a current meter then is completely impossible. If no professional ﬂoats are available, it is easy to improvise.If one arrives at the site unprepared, it is always possible to clock the velocity of ﬂoating debris.The larger the debris (e.g. trees) the better they describe the mean velocity in the vertical. Aﬂoat measurement is brieﬂy described underneath.A straight reach is selected of 100m length (see Fig. 8.32). The width is divided into approx-imately eleven equal distances in which ten measuring points are established. If there are noconstraints in time or resources, try as many points as possible. At each measuring point a ﬂoatis used with a resistance body at 60% of the average depth at that point.Beacons, placed on both banks in a line perpendicular to the ﬂow, mark two measuring sectionsat the upstream and downstream end of the measuring reach. On each bank of a measuringsection the two beacons should stand with suﬃcient distance between them to allow the observerto determine his position from a boat (if a boat is used). At night the ﬂoats and the stacksshould carry lights. A ﬂoat measurement is carried out by launching a ﬂoat at a particular pointin the cross-section. The positioning can be done from a cable mounted across the river, frommarkings on a bridge (if present) or if necessary by sextant. The ﬂoat should be launched (from
  • 39. 8.6. Flood surveys 121 Fig. 8.32: Layout of ﬂoat measurementa bridge or from a boat) at least 10 m upstream from the cross-section where the measurementstarts, to allow the ﬂoat to adjust itself to the ﬂow velocity. When a boat is used, the observershould stay with the ﬂoat, keeping next to it. When the ﬂoat enters the measuring section, theobserver starts the stopwatch; he/she then follows the ﬂoat until the measuring cross-section100 meters downstream where he/she stops the stopwatch. He/she notes down the time and (ifusing a boat) recovers the ﬂoat to return and repeat the measurement at the next observationpoint. The advantage of a boat moving with the ﬂoat is that only one observer is needed perﬂoat and no communication problems occur. The disadvantage is that the determination ofthe moment in which the ﬂoat passes the section is less accurate If no boat is available, ﬂoatsshould be launched from a bridge, and followed along the bank. More observers could work atthe same time, and one observer could clock more than one ﬂoat. The advantage of this methodis a greater degree of accuracy when starting and stopping the stopwatch; the disadvantage,however, is the more complicated communication and that the ﬂoats are lost.A ﬂoat measurement over a distance of 100 meters has a relative error, in the measurementof the velocity, of 1%. A current meter does not have that degree of accuracy. Moreover, byfollowing the ﬂow trajectory, the velocity is correctly averaged in the longitudinal direction.The only problem remains getting the average over the cross-section. The variation over thecross-section may be substantial. The variation over the width appears to be the largest sourceof errors. Therefore, one should select at least ten measuring positions in the cross-section.This still leaves the problem of determining the cross-sectional area. Only if one has an echo-sounder at one’s disposal (it might get lost) and the river is navigable the cross-sectional area
  • 40. 122 8. Streamﬂow measurementscan be determined. Normally, however, determining the cross-sectional area has to be left forthe ’morning after’ program.8.6.2 Slope area methodThe slope area method is a method to estimate the discharge of a river. Application of the slope-area method, which is much less accurate than the other methods should only be considered asan ad hoc method if the other methods are not feasible, for example when ﬂoods occur.Flood marksFor the slope area method the cross-sectional area, the hydraulic radius and water slope, whichoccurred during the ﬂood, need to be determined. Immediately after the ﬂood peak has passedone should go to the ﬁeld and search for ﬂood marks. Flood marks can be found in the colorof mud on bridges, pillars, or (in case of extreme ﬂooding) on the walls of buildings. Also thepresence of small ﬂoating debris in trees and bushes are good indications of the ﬂood level. Oneshould take into account that bushes bend under the force of the ﬂow and that, considerablewaves could have occurred. Both actions indicate higher ﬂood levels than actually occurred.Flood marks on the banks, where wave action and run-up form surge are at a minimum, aregenerally preferable to those in bushes and trees. However, they disappear fast.The ﬁrst action, which has to be taken, is to paint the observed ﬂood marks on walls and trees,where possible accompanied by the date of occurrence of the ﬂood. A record of ﬂood marks onthe wall of a solid structure is an important future source of information.Try to get as many reliable ﬂood marks as possible along the river. Also in areas which at thetime are not yet developed. A good survey of ﬂood marks of an extreme ﬂood is an invaluableasset for the planning of future projects.Sometimes ﬂood marks are diﬃcult to ﬁnd, principally because one is too late and rains havecleared the coloring, or winds have cleared the debris from the trees. A good method then isto install a leveling instrument at the suspected ﬂood level and to look through the instrumenttowards diﬀerent objects. If the instrument is indeed at the approximate ﬂood mark position,then the accumulation of, sometimes insigniﬁcant, marks may help to verify the ﬂood level.If one is really too late to ﬁnd back any traces of the ﬂood, one should gather information frompeople living in the area. Needless to say that such information is much less reliable.Finally, where possible, take photographs of ﬂood marks, or of people indicating a ﬂood mark.ComputationFor a good slope area computation one should look for a fairly straight stable clean channel,without pools, rapids, island or sharp curves. No bridges or other obstructions should be down-stream of the reach.The reach to determine the cross-sectional area should be about ten times the width of theriver; one should survey approximately ﬁve to ten cross-sections. The ﬂood mark survey shouldbe over a long enough distance to determine the water level and slope accurately. Taking intoaccount the error of reading, this will often amount to a distance of several kilometers.
  • 41. 8.6. Flood surveys 123 Fig. 8.33: Slope areaThe following procedure is used to determine the discharge: ﬁrst, area Aj and hydraulic radiusRj of parts of the cross-section are determined. The parts are selected in such a way that theroughness coeﬃcient Cj in a part can be considered as a constant. The river slopes for all thediﬀerent parts of the cross-section are considered to be equal. For every section applies Ch´zy e(Eq. 8.48).The hydraulic calculations are based on Chzy’s formula: 1/2 Qj = uj Aj = Cj Aj Rj i1/2 = Kj i1/2 (8.48)With: 1/2 Kj = Cj Aj Rj (-) Cj Ch´zy coeﬃcient (m1/2 ) e Rj Hydraulic radius (m) Aj Cross sectional area (m2 ) i bedslope (-)The factor Kj , the so-called conveyance, contains the geometrical quantities. When using theManning sand roughness (n), Cj reads, 1/6 Rj Cj = (8.49) njBy estimating the values of Kj the discharge can be calculated with: j 1/2 Q=i Kj (8.50)In the above method the greatest diﬃculty lies in the determination of channel roughness. It isvery diﬃcult for even an experienced surveyor to arrive at an objective value. Indicative valuesfor channel roughness are provided in Table Simpliﬁed slope area methodA remarkable method developed by H.C. Riggs Riggs [1976] may be used to overcome thediﬃculty of subjectivity. Riggs postulates that in alluvial streams slope and roughness are
  • 42. 124 8. Streamﬂow measurementsrelated. In more popular terms this means that the river adjusts its roughness (through bedforms) to the slope, or that the river adjusts its slope (through meandering) to the roughness.Experiments have shown that there indeed is a relation between roughness and slope, althoughthe relation shows considerable scatter. However, Riggs showed that the error in the relationbetween slope and roughness is less than the error made by experienced surveyors in estimatingthe roughness.The equation of the simpliﬁed method reads: logQ = 0.188 + 1.33log(A) + 0.05log(S) − 0.056(logS)2 (8.51)In this equation the value of A should be representative for the reach under study. The cross-sectional area A should be determined on the basis of ﬁve to ten cross-sections: Ai A= (8.52) Nwhere N is the number of sections surveyed . The equation was tested in 64 rivers in the USAwith discharges ranging from 2m3 /s to 2500m3 /s, and with Ch´zy coeﬃcients ranging from 14 eto 65 m 1/2 /s. The method is extremely useful, also as a check on the previously mentioned slopearea method.8.7 Structures8.7.1 PrinciplesOn small rivers it is often convenient to measure ﬂow by means of a weir or ﬂume. Suchstructures have the advantage that they are less sensitive to the downstream conditions, thechannel roughness and the inﬂuence of backwater than the velocity-area method for example.The philosophy of the method is founded on the premise that the relation of discharge to waterlevel is found empirically or is based on physical principles.The water level, or head, is measured at a prescribed distance upstream of the structure. Forthe simple, and usual case, where the downstream water level is below some limiting conditionand where it does not aﬀect the upstream head, there is a unique relation between head anddischarge. This condition is termed the free-ﬂow or modular condition. If, however, the tailwaterlevel aﬀects the ﬂow, the weir is said to be drowned, or submerged, and operates in the non-modular condition. For this condition an additional downstream measurement of head is requiredand a reduction factor must be applied to the modular or free-ﬂow discharge equation. Whenthe ﬂow in the non-modular condition increases until the weir is almost or wholly submerged,the structure no longer performs as a measuring device.There is a signiﬁcant degradation in the accuracy of discharge measurements in the non-modularﬂow condition. This degradation is due mainly to the diﬃculty in measuring the downstreamhead because of turbulence and the uncertainty in the coeﬃcient of discharge in the non-modularrange.
  • 43. 8.7. Structures 125 Tab. 8.1: Values of Manning’s n and Chzy’s C
  • 44. 126 8. Streamﬂow measurementsIn order to increase the range of a structure in the free-ﬂow condition, it is sometimes convenientto raise the design height; otherwise for a weir the device may be used as a section control inthe non-modular condition, and rated by a current meter in this range.The installation of a measuring structure in a river requires major civil engineering work andeach device needs to be designed as such with due attention to foundations. Ground conditionsmay require sheet piling and cut-oﬀs to prevent the seepage of water under or around thestructure or risks to stability. If provision for energy dissipation downstream is not includedin the construction, for example, there may be a tendency to scour depending on the groundconditions. If this becomes excessive the stability of the structure will be in danger. If thestructure, however, is founded on rock, for example, such problems may not be severe butnevertheless due attention may still be required with regard to energy dissipation. The energydownstream of a structure is normally dissipated by a hydraulic jump and generally design andconstruction considerations involve the installation of a stilling basin and a suitable elevationfor the ﬂoor of the basin.The capital cost of installing a measuring structure is much greater than the capital cost ofinstalling a velocity-area station but the operational costs of a structure are very much lower.This is due to the calibration costs in manpower in establishing the stage-discharge relation fora velocity-area station. The advantage, in this respect, of a standard measuring structure isthat records of discharge are obtained immediately on completion of the installation.A weir or a ﬂume is basically a section control designed and built to speciﬁc criteria. The ratingequation for a stage discharge relation and measuring structure, therefore, take the same form,which is: Q = Chn (8.53)Ideally the ﬂow conditions upstream of a measuring structure are governed by the geometry ofthe structure and the approach channel, and by the physical properties of the water. They arenot aﬀected by the ﬂow conditions in the channel downstream or by the roughness and geometryof the channel upstream.At the control section critical ﬂow conditions occur, where for a given discharge the depth issuch that the total head is a minimum. The total head is the total energy of the ﬂow per unitweight of water and, by Bernoulli’s theorem; this is the sum of the potential head, the pressurehead and the velocity head. It is generally referred to the crest of the structure as a datum.In presenting the theoretical analysis for the establishment of the discharge equation the broad-crested weir is used (see Fig. 8.34). Taking the critical section to occur where the ﬂow is parallelnear the end of the crest of the weir, then the Bernoulli equation gives: u2 H =d+ (8.54) 2gWith:
  • 45. 8.7. Structures 127 Fig. 8.34: Schematic illustration of principle and theory of ﬂow over broad crested weir H the total head (m) g the acceleration due to gravity (m/s2 ) u the velocity on the streamline (m/s) d depth of ﬂow over the crest (m) h depth of ﬂow in front of the weir (m)If the approach channel is deep, the total head H is the same for all streamlines and it followsfrom Equation 8.54 that the velocity at the critical section is constant with depth and equal tou, the mean velocity. The discharge over a width b is: Q = bdu (8.55)and substituting from Equation 8.54 Q = bd 2g (H − d) (8.56)Diﬀerentiating Equation 8.56, treating H as a constant and putting dq/dd=0 gives the followingequation for critical ﬂow conditions 2 dc = H (8.57) 3or 2/3 2 √ Q= b gH 3/2 (8.58) 3Equation 8.58 is derived from theoretical concepts and calibration of a structure imposes on theequation a coeﬃcient of discharge. The equation than becomes: 2/3 2 √ Q= Cd b gH 3/2 (8.59) 3
  • 46. 128 8. Streamﬂow measurementsSince the total head H cannot be measured in practice, an iterative procedure is necessary tocompute the discharge from Equation 8.59. In order to avoid this cumbersome procedure thedischarge equation can be presented as 2/3 2 √ Q= Cd Cv b gH 3/2 (8.60) 3This is the basic equation for measuring structures with: Cv the dimensionless coeﬃcient for the velocity of approach (-) Cd the coeﬃcient of discharge (s/m1/2 )From an inspection of Equations 8.59 and 8.60 it can be seen that: 2/3 H Cv = (8.61) hThe Bernouilli equation relates H and h as follows: u2 Q2 H =h+ =h+ (8.62) 2g 2gA2The energy head H and measured water level in front of the structure will be practically equalif u is negligible. For a large range of discharges this will be the case if A is large. This isthe reason that a stilling basin of water upstream of the structures often is part of installationrequirements.With each of the discharge equations for measuring structures, limitations are imposed as totheir use in practice. Such limitations concern in range in head under which a laboratorycalibration was made, the distance upstream to the head measurement section, the limits oncertain ratios such as h/P , where P is the height of the weir, and others which will be presentedlater. The values and uncertainties of the coeﬃcients of discharge and velocity are dependenton maintaining these limitations in the ﬁeld installation. If the limitations are relaxed for anyreason the measuring structure may still produce a record of streamﬂow but the uncertaintyof the measurement will be impaired. In most, if not all, of these cases no data are availableto give values of uncertainties in the coeﬃcients, and therefore in the discharge measurementswhere the speciﬁed limitations have been relaxed. The only resort in these circumstances is toﬁeld calibration.8.7.2 Description of structuresMeasuring structures may be divided into the following categories: • Thin/sharp crested weirs • Broad crested weirs • Flumes • Compound measuring structures • Non-standard weirs
  • 47. 8.7. Structures 129As an overview the main concept in each category of structures will be discussed, with therelevant discharge formulae. For more details or speciﬁc designs numerous handbooks exist andmust be consulted for speciﬁc installations or ﬂow conditions.For the various discharge formulae provided below the following conventions were adopted. Q discharge (m3 /s) g acceleration due to gravity (m/s2 ) C coeﬃcient of discharge (-) b length of a notch or weir and breath of a ﬂume (m) h gauged head (m) P level of top of weir above the bottom (m)Thin/Sharp crested weirsA number of sharp crested weirs are depicted in Figure 8.35. The sharp crested weirs are eitherrectangular or formed as a V with a certain angle. The rectangular weirs can be contracted orsuppressed. For all thin plate weirs it is essential that the plates (or angle iron) are kept cleanand smooth so that the nappe does not cling to the downstream side. Fig. 8.35: Examples of thin plate weirsV-notch The most common V notch has an angle of θ = 90◦ . In that case the dimensionacross the top is twice the vertical depth. The discharge formula reads.
  • 48. 130 8. Streamﬂow measurements 8 θ Q= 2gCd tan h5/2 (8.63) 15 2approximated by Q = 1.34h2.5 (8.64)Other V-notches are the ‘half’ and ‘quarter’ V-notch, with tan(θ/2)=0.5 and tan(θ/2)=0.25respectively.Rectangular contracted or compressed notch The width, b, of the notch does not com-pletely extend over the full width, B, of the river. The vertical sides of the cross-section at thenotch are thin plated as well. The general discharge equation reads: 2 Q= 2gCbh3/2 (8.65) 3A more useful equation that awards the calculation of the coeﬃcient of discharge is: h √ Q = 0.554(1 − 0.0035 )(b + 0.0025) g(h + 0.001)3/2 (8.66) PRectangular surpressed notch This is a notch without side contraction (in contrary to acontracted or compressed notch). It also applies when a weir is subdivided into sections thatare separated by training walls. The general formula reads: h Q = 2.95(0.602 + 0.0832 )bh3/2 (8.67) PWith h/P = 0.25 the equations turns into the Rehbock formula: Q = 1.84bh3/2 (8.68)The Kriel factor In all standard formulae for thin-plate weirs it is assumed that they arereally ‘thin plated’ i.e. the thickness of the crest is only 1-2 mm. Often many of the crests areconsiderably thicker as they are made from commercial irons, and because of this a correctionfactor has to be introduced. The calculated discharge for rectangular notches is multiplied bythis so-called Kriel factor when the head is below 0.6m. 0.012Kriel factor: 1 + h0.8 for h <0.6m.Broad Crested WeirsWith broad crested weirs the critical ﬂow conditions are achieved by raising the bottom of thestream according to a certain proﬁle. Diﬀerent shapes of crests have been designed with diﬀerentnames often related to the shape and speciﬁc discharge formulae.Sometimes broad crested weir formulae are also applied when the ﬂow through ﬂumes and thesharp crested weirs contained within a gauging structure exceeds the design capacity. The most
  • 49. 8.7. Structures 131common method in that case is to assume that the cut-oﬀ wall acts as a broad crested weir.The accuracy of the ﬂows calculated in this way is low.Some typical broad crested weirs and discharge formulae are described below. Fig. 8.36: The triangle proﬁle (Crump) weirThe triangle proﬁle (Crump) weir The weir has a slope 1:2 on the upstream face and 1:5on the downstream face.Discharge formula: √ Q = 0.633 gbH 3/2 (8.69)The ﬂat V weir The ﬂat V weir has the same section as the triangular proﬁle weir, 1:2upstream slope and 1:5 downstream slope, but in elevation has a crest slope of 1:10, 1:20 or1:40 so that it takes the form of a shallow V when viewed in the direction of ﬂow. With thisgeometry, it is therefore sensitive to low ﬂows but at the same time has a wide ﬂow range.A diagrammatic illustration of the basic weir form is shown in Figure 8.37. The discharge overa ﬂat V weir may be within the V, above the V and within vertical side walls, or above the Vand within trapezoidal side walls. To allow for these conditions, a shape factor, Z, is includedin the discharge equation. The equation of discharge is: 4 √ Q = Cd Cv gmZh5/2 (8.70) 5In terms of total head the discharge equation is: 4 √ Q = Cd gmZH 5/2 (8.71) 5
  • 50. 132 8. Streamﬂow measurements Fig. 8.37: The ﬂat V weirwhere m is the cross-slope 1:10, 1:20 or 1:40. Other cross-slopes, less than 1:10, are unusual andundesirable (1 vertical : m horizontal). To calculate Z, if h′ is the height of the V (diﬀerence increst elevation), then for the V full conditionhh′ = 1 and Z = 1.0when h is greater than h′ (ﬂow above the V full condition) within vertical side walls: 5/2 h′ Z= 1.0 − 1.0 − (8.72) hwithin trapezoidal side walls: 5/2 n b Z h5/2 1− h− (8.73) m 2mwhere n is the channel side slope (1 vertical: n horizontal). The discharge equations then becomefor ﬂow within vertical side walls: 5/2 4 √ h′ Q = Cd Cv gmh5/2 1.0 1.0 − (8.74) 5 hand for ﬂow within trapezoidal side walls: 5/2 4 √ n b Q = Cd Cv gm h5/2 1− h− (8.75) 5 m 2mNote that when n=0 (vertical sidewalls), Equation 8.75 reduces to Equation 8.74 and when n =m (ﬂow within the V) Equation 8.75 reduces to Equation 8.70.
  • 51. 8.7. Structures 133The rectangular proﬁle weir Of all the pre-calibrated broad crested weirs in operationaluse today there has probably been more research carried out on the rectangular proﬁle weirthan on any other. This has not been because of the merit of the weir as a gauging structurebut rather due to the hydraulic considerations in the variable coeﬃcient range. Indeed, reportedinstallations of the weir have been few compared to other types of weir. However, there are manyexisting rectangular proﬁle weirs, which are used for operational purposes such as irrigationdevices or for compensation water measurement from reservoirs, which were built before theInternational Standard on the weir was published. Some of these weirs might conform, evenapproximately, to the limitations given later although degradation in the uncertainty in dischargehas to be accepted. The weir is one of the easiest to construct in the ﬁeld, the main requisitebeing that it has to have sharp right-angle corners. The main disadvantages of the weir are thatsilt and debris collect behind the structure and it has a low modular limit. A diagrammaticillustration of the weir form is shown in Figure 8.38. Fig. 8.38: The rectangular proﬁle weirThe equation of discharge is: 3/2 2 √ Q= C gbH 3/2 (8.76) 3The coeﬃcient of discharge C is a constant value of 0.86 in the rangeh hp ≤ 0.5 and L ≤ 0.3where L(m) is the length of the weir in the direction of ﬂow.For computer processing C may be obtained from the following equation:
  • 52. 134 8. Streamﬂow measurementsC = 0.888−0.093y+0.133y 2 −0.021y 3 −0.151x+0.102xy−0.065xy 2 +0.310x2 +0.028x2 y−0.102x3 (8.77)With: x = h/L y = h/P 4Other practical limitations for the use of Equation 8.76 are: h should not be less than 0.06m; b should not be less than 0.3m; P should not be less than 0.15m; L/P should not be less than 0.15 nor greater than 7.0; h/P should not be greater than 2.5 (variable coeﬃcient range); h/L should not be greater than 2.4 (variable coeﬃcient range)The location of the head measurement section is at 3-4 times Hmax upstream from the weirblock.FlumesA ﬂume is a ﬂow measurement device, which is formed by a constriction in a channel. Theconstriction is a narrowing in the channel mostly combined with a hump.Flumes are in particular recommended in streams where siltation of a weir is expected to be amayor problem. However, it should be realized that the construction is complex (and costly)and that attention must be given to the appropriate rating.It is essential to construct the ﬂumes to the dimensions as speciﬁed in the standard designs. Forthe same reason the heads should be measured at the positions speciﬁed.A typical design of a ﬂume is provided in Figure 8.39, which has rectangular cross-sections.There are variations to this design with diﬀerent cross-sectional shapes such as U-shaped trape-zoidal shaped cross-sections.An example of a short throated ﬂume is the Parshall ﬂume. It has a rectangular cross-sectionand comprises three main parts; a converging inlet section with a level ﬂoor, a throat sectionwith a downward sloping ﬂoor and a diverging outlet section with an upward sloping ﬂoor (seeFig. 8.40). The control section of the ﬂume is not located in the throat as on the previousﬂumes mentioned but near the end of the level ﬂoor, or crest in the converging section.Flumes are supposed to operate under free ﬂow conditions, i.e. the ﬂow is unaﬀected by thedownstream water level and only the upstream level (h1 ) needs to be measured. If the down-stream water level hb exceeds a certain level, free ﬂow conditions no longer exist and the ﬂumeis said to be submerged. The level that must not be exceeded depends on the size of the ﬂume,and is for 1ft to 8ft (0.30m to 2.4m) ﬂumes 0.7h1 and for 10ft to 50ft (3.0m to 15.2m) ﬂumes0.8h1 . If the ﬂume becomes submerged, hb must be measured and the ﬂow adjusted accordingly.
  • 53. 8.7. Structures 135 Fig. 8.39: Typical design of a ﬂumeIn case of high risk of submergence a tapping for measuring the downstream water level isused. Diﬀerent sizes of Parshall ﬂumes, related to the design discharges to be measured, can beapplied. Their typical dimensions and discharge formulas have been well investigated (see Tab.8.2 and 8.3. A Parshall ﬂume is typically identiﬁed by the width of the throat. One will talk ofan 8ft Parshall ﬂume.The discharge equation of a Parshall ﬂume is: Q = Khn 1 (8.78)where K and h are derived from the table to the applicable ﬂume.At some gauging stations there is a combination of ﬂumes and sharp-crested weirs. The head isthen not measured at the prescribed point in the ﬂume, but upstream of the ﬂume. Experimentsat some ﬂumes have indicated that the relation between the head in the ﬂume and the upstreamhead is ± 0.83. When the upstream pool level is measured 0.83 is therefore used as a conversionfactor.
  • 54. 136 8. Streamﬂow measurements Tab. 8.2: Dimensions for Parshall ﬂumes Tab. 8.3: Discharges for Parshall ﬂumes
  • 55. 8.7. Structures 137 Fig. 8.40: Diagrammatic illustration of the Parshall ﬂumesCompound measuring structuresCompound structures are combinations of measuring devices in one and the same structure. Thiscan be any combination of sharp-crested weirs, broad crested weirs and ﬂumes. The appliedcombination is usually doctored for speciﬁc reasons and applies under speciﬁc conditions. Twomain reasons can be mentioned for compound stations: 1. The structure has to be accurate for both low and high ﬂows. Accurate low ﬂow mea- surements need suﬃcient head above the structure. This is obtained by narrowing the proﬁle. To the contrary, ﬂood ﬂows would need a suﬃcient cross-sectional area (width) over the structure. The ideal solution is a structure where the cross-sectional width in- creases with increasing discharge. A triangular shape of the cross-sectional area of the measuring structure fulﬁlls this requirement. That is the reason that for low to moderate ﬂows the V-notches are applied. For constructional reasons a V-notch is not suitable for
  • 56. 138 8. Streamﬂow measurements large ﬂows. The alternative is a stepwise increasing proﬁle, where each step has a sharp crest. The typical lay-out for a compound station that measures low and high ﬂow in that case is a V-notch for the lower stages, and a stepwise proﬁle that takes over at higher stages, see Figure 8.41 and Figure 8.42. The various sections so created can be separated by training walls. Note that the rating equation for a compound station is also a compound of equations for the diﬀerent stages. Usually the zero stage is at the lowest notch, or the bottom of the notch in case of a V-notch. For every stage where a next notch will have discharge the rating equation changes with the contribution of this notch. Fig. 8.41: Compound gauging weir under construction (Zimbabwe, Mupfure catchment) 2. The structure needs to pass a considerable sediment load. In case of considerable sediment loads a ﬂume is the right solution. Flumes are not easy to construct and get easily drowned. Combining a ﬂume with a weir in one and the same structure provides the opportunity to pass high ﬂows, create more head and pass the sediment load. Stand alone large ﬂumes have been constructed. They can handle large ﬂows and large sediment loads. To compensate for the poor accuracy with low ﬂows, a V-notch can be added, down or upstream of the ﬂume. In general structures placed in series (one behind the other) are referred to as composite stations. They are not much favored, as the diﬀerent stages that are measured at such a composite station are reason for confusion. Together with the measurement of actual stages it must be clearly indicated to which structure they apply. At some composite stations stages are measured for each structure separately, but also sometimes the measurement of stages is combined through complicated plumbing arrangements.
  • 57. 8.7. Structures 139 Fig. 8.42: Discharging compound gauging weir (Zimbabwe, Sebakwe river)Non-standard structuresMost non-standard structures are structures that have been developed for other purposes thandischarge measurements, but provide an opportunity to determine the discharge. The dischargerelation in that case might not have been standardized and therefore should be carefully estab-lished. Examples of such structures are conducts, oriﬁces, sluices and spillways. Also a volumechange of a reservoir can be used for discharge estimation of a river or catchment. Obviouslyreleases, seepage and evaporation from the reservoir have to be considered. Depending on themoment (no releases) or the timescale (hours, days) these could be negligible.Generally, spillways have the advantage that only the upstream level is required, which is thereservoir level. It might well be that the levels of a reservoir are closely monitored anyway, asto keep track of the reservoir’s volume. The general equation for discharge over spillways is: Q = Cbh3/2 (8.79)With: h 0.07C for circular weirs = 2.03 RandC for parabolic weirs = 1.86h0.01Practical limits are: h should not be less than 0.05m h/p1 should not be less than 3 (p1 height of weir above upstream bed) h/p2 should not be less than 1.5 (p2 height of weir above downstream channel)
  • 58. 140 8. Streamﬂow measurements b/h should not be less than 2 h2 /h should be less than 0.3 (h2 downstream head above crest level) h should be measured at a distance 2 to 3 times hmax upstream from the weir face Fig. 8.43: Round crested weirsThe equations provided apply to spillways with vertical upstream faces. For sloping upstreamfaces correction factors for the discharge have to be applied.
  • 59. 9Tracer HydrologyThe following articles, which are online available on Blackboard, give a good overview on thefundamentals of tracer hydrology.9.1 General overview on tracer hydrologyLeibundgut, C., Seibert, J., 2011. Treatise on Water. Oxford: Academic Press, Ch. Tracer Hy-drology, pp. 215–2369.2 ApplicationsWenninger, J., Uhlenbrook, S., Tilch, N., Leibundgut, C., 2004. Experimental evidence of fastgroundwater responses in a hillslope/ﬂoodplain area in the Black Forest Mountains, Germany.Hydrological Processes 18, 3305–3322Uhlenbrook, S., Frey, M., Leibundgut, C., Maloszewski, P., 2002. Hydrograph separations in amesoscale mountainous basin at event and seasonal timescales. Water Resources Research 38Gonzales, A. L., Nonner, J., Heijkers, J., Uhlenbrook, S., 2009. Comparison of diﬀerent base ﬂowseparation methods in a lowland catchment. Hydrology and Earth System Sciences 13, 2055–2068Uhlenbrook, S., Didszun, J., Wenninger, J., 2008. Source areas and mixing of runoﬀ componentsat the hillslope scale - a multi-technical approach. Hydrological Sciences 53, 741–753
  • 60. 142 9. Tracer Hydrology