# Chapter 4 Streamflow

This chapter reviews methods for measuring rates of runoff in channels, small streams and rivers. Estimating the total quantity of runoff by empirical methods or from models is discussed in Chapter 7.

## VOLUMETRIC METHODS

The simplest way to estimate small flows is by direct measurement of the time to fill a container of known volume. The flow is diverted into a channel or pipe which discharges into a suitable container, and the time to fill is measured by stopwatch. For flows up to about 4 l/s, a bucket of 10 l capacity is suitable and will fill in 2½ seconds. For larger flows, an oil drum of 200 l can handle flows up to about 50 l/s. The time to fill must be measured accurately, especially when it is only a few seconds. The variation between several measurements taken in succession will give an indication of the accuracy of results.

If the water flow can be diverted into a pipe so that it is discharged under pressure, the rate of flow can be estimated from measurements of the jet. If the pipe can be arranged to discharge vertically upwards, the height to which the jet rises above the end of the pipe can be measured and the rate of flow calculated from the appropriate formula as shown in Figure 19. Estimates of discharge can also be made from measurements of the trajectory from horizontal or sloping pipes, and from partly filled pipes, but these are less reliable (Scott and Houston 1959).

## VELOCITY/AREA METHOD

This depends on measuring the average velocity of flow and the cross-sectional area of the channel and calculating the flow from:

Q(m3/s) = A(m2) x V(m/s)

The metric unit m3/s is referred to as the cumec. Because m3/s is a large unit, smaller flows are measured in litres per second (l/s).

A simple way to estimate the velocity is to measure the time taken for a floating object to travel a measured distance downstream. The velocity is not the same at all places in the stream, being slower at the sides and bottom, and faster on the surface, as shown in Figure 20. Taking 0.8 of the surface velocity as measured by the float gives an approximate value for the average velocity. Alternatively, the velocity can be measured below the surface by attaching a submerged weight to a float. The float and weight move down the stream together at the velocity of the stream at the depth where the weight is suspended. At about half the stream depth, the velocity is approximately the same as the average velocity for the whole stream. Float methods are only suitable for straight streams or canals where the flow is fairly even and regular.

Another method is to pour into the stream a quantity of strongly coloured dye, and to measure the time for this to flow a measured distance downstream. The dye should be added quickly with a sharp cutoff, so that it travels downstream in a cloud. The time is measured for the first and last of the dye to reach the downstream measuring point and an average of the two times is used to calculate the average velocity.

In turbulent streams the cloud of dye is dispersed quickly and cannot be observed and measured, but other tracers can be used, either chemical or radio-isotopes, in what is called the dilution method. A solution of the tracer of known strength is added to the stream at a constant measured rate and samples are taken at points downstream. The concentration of the sample taken downstream can be compared with the concentration of the added tracer and the dilution is a function of the rate of flow which can be calculated.

More accurate determination of velocity can be obtained by using a current meter. The two main types are illustrated in Figure 21. The conical cup type revolves about a vertical axis, and the propeller type about a horizontal axis. In each case the speed of revolution is proportional to the velocity, and the number of revolutions in a given time is counted, either on a digital counter or as clicks heard in earphones worn by an operator. In shallow streams small current meters will be mounted on rods and held by wading operators (Plate 23). When measurements of floodflows are to be measured on big rivers, the readings are taken either from a bridge, or an overhead cableway is installed well above maximum flood level, and the current meter is lowered on cables into the river with weights to hold it against the riverflow.

A current meter measures the velocity at a single point, and several measurements are required to calculate the total flow. The procedure is to measure and plot on graph paper the cross-section of the stream and to imagine that it is divided into strips of equal width as shown in Figure 22. The average velocity for each strip is estimated from the mean of the velocity measured at 0.2 and 0.8 of the depth in that strip. This velocity, times the area of the strip, gives the flow for the strip and the total flow is the sum of the strips. Table 2 shows how the calculations will be done for data shown in Figure 22. In practice, more strips would be used than the number shown in Figure 22 and Table 2. For shallow water a single reading is taken at 0.6 of the depth instead of averaging the readings at 0.2 and 0.8 of the depth.

Sometimes the information required on streamflow is the maximum flood flow, and a rough estimate can be made using the velocity/area method. The maximum depth of flow in a stream can sometimes be deduced from the height of leaves and trash caught in vegetation on the bankside, or from the highest signs of scour or sediment deposits on the bank. Alternatively some device can be installed which is designed to leave a record of the maximum level. To prevent false readings from turbulence in the stream, some kind of stilling well is used - usually a pipe with holes on the downstream side. The maximum depth of water can be recorded on a rod painted with a water soluble paint, or from traces left at the highest level from something floated on the water surface in the tube. Materials used have included ground cork, chalk dust and ground charcoal. Knowing the maximum depth of flow, the corresponding cross-section area of the channel can be measured, and the velocity estimated by one of the methods described, bearing in mind that the velocity at high flood will usually be faster than the normal flow.

## RATING A GAUGING STATION

If a measurement of the flow is made by the current-meter method on different occasions when the river is flowing at different depths, these measurements can be used to draw a graph of amount of flow against depth of flow as shown in Figure 23. The depth of flow of a stream or river is called stage, and when a curve has been obtained for discharge against stage, the gauging station is described as being rated. Subsequent estimates of flow can be obtained by measuring the stage at a permanent gauging post, and reading off the flow from the rating curve. If the cross-section of the stream changes through erosion or deposition, a new rating curve has to be drawn up. To plot the rating curve, it is necessary to take measurements at many different stages of flow, including infrequently occurring flood flows. Clearly this can take a long time, particularly if access to the site is difficult, so it is preferable to use some type of weir or flume which does not need to be individually calibrated, and these are discussed in later sections.

## EMPIRICAL FORMULAS FOR ESTIMATING VELOCITY

The velocity of water flowing in a stream or open channel is affected by a number of factors.

· Gradient or slope. All other factors being equal, velocity of flow increases when the gradient is steeper.

· Roughness. The contact between the water and the streambank causes a frictional resistance which depends on the smoothness or roughness of the channel. In natural streams the amount of vegetation affects the roughness, and also any unevenness which causes turbulence.

· Shape. Channels can have the same cross-sectional area, gradient and roughness, but still have different velocities of flow according to their shape. The reason is that water close to the sides and bottom of a stream channel is slowed by the friction effect, so a channel shape which provides least area of contact with the water will have least frictional resistance and so a greater velocity. The parameter used to measure this effect of shape is called the hydraulic radius of the channel. It is defined as the cross-sectional area divided by the wetted perimeter, which is the length of the bed and sides of the channel which are in contact with the water. Hydraulic radius thus has units of length, and it may be represented by either M or R. It is also sometimes called hydraulic mean radius or hydraulic mean depth. Figure 24 shows how channels can have the same cross-sectional area but a different hydraulic radius. If all other factors are constant, then the lower the value of R, the lower will be the velocity.

All these variables which affect velocity of flow have been brought together in a very useful empirical equation called the Manning formula, which is:

where:

V     is the average velocity of flow in metres per second

R     is the hydraulic radius in metres (the letter M is also used to denote hydraulic radius, standing for Mean Hydraulic Depth)

S     is the average gradient of the channel in metres per metre (the letter i is also used to denote gradient)

n     is a coefficient, known as Manning's n, or Manning's roughness coefficient. Some values for channel flow are listed in Table          3.

Strictly speaking, the gradient of the water surface should be used in the Manning formula and this may not be the same as the gradient of the streambed when the stream is rising or falling. However, it is not easy to measure the level of the surface accurately and so an average of the channel gradient is usually calculated from the difference in elevation between several sets of points each 100 metres apart. Nomographs are available to assist solving the Manning formula, and an example is shown in Figure 25.

Another simple empirical formula for estimating velocity of flow is Elliot's open-ditch formula which is:

where:

V     is the average velocity of flow in metres per second

m     is the hydraulic radius in metres

h     is the channel gradient in metres per kilometre.

This formula assumes a value of Manning's n of 0.02 and so is only suitable for free-flowing natural streams with low roughness.

## GAUGING WEIRS

Gauging the flow in natural streams can never be precise because the channel is usually irregular and so is the relationship between stage and flow rate. Natural stream channels are also subject to change by erosion or deposition. More reliable estimates can be obtained when the flow is passed through a section where these problems have been reduced. This could be simply smoothing the bottom and sides of the channel, or perhaps lining it with masonry or concrete, or installing a purpose-built structure. There is a wide variety of such devices, mostly suitable for a particular application. A selection of those simple to install and operate are described here with reference to appropriate manuals for more expensive or complicated structures.

In general, structures across the stream which change the upstream level are called weirs, and channel-type structures are called flumes, but this distinction is not always followed. A more important distinction is between standard and non-standard devices. A standard weir or flume is one where if it is built and installed to a standard published specification, the flow can be directly obtained from the depth of flow by the use of charts or discharge tables, that is the flume is pre-calibrated. A non-standard weir or flume is one which needs to be individually calibrated after installation by using the velocity/area method as when rating a stream. There is such a wide range of standard devices available, that non-standard structures are best avoided except for one-off estimates of flood flows using the velocity/area method at a bridge, or ford, or culvert.

Most weirs are designed for free discharge over the critical section so that the rate of flow is proportional to the depth of flow over the weir, but some weirs can operate in the condition called submerged or drowned, where the level downstream interferes with the flow over the weir. Some types of weir can be corrected for partial submergence but this is an undesirable complication requiring additional measurements and more calculations so should be avoided where possible (Figure 26). Another variation best avoided is the suppressed weir, which is a weir set in channel of the same width as the critical section (Figure 27).

### Sharp-crested weirs

The two most common types are the V-notch and the rectangular notch as shown in Figure 28. There must be a stilling pool or approach channel on the upstream side to smooth out any turbulence and ensure that the water approaches the notch slowly and smoothly. For accurate measurements the specification is that the width of the approach channel should be 8 times the width of the notch, and it must extend upstream for 15 times the depth of flow over the notch. The notch must have a sharp edge at the upstream side so that the flow is clear of the downside edge as shown in Figure 29. This is called the end contractions, which are required for the standard calibration to be applicable.

To read the depth of flow through the notch a measuring scale is set in the stilling pool in a position where it can be easily read. The zero of the scale is set level with the lowest point of the notch. The scale should be set well back from the notch so that it is not affected by the drawdown curve as the water approaches the notch.

V-notch weirs are portable and simple to install in either temporary or permanent positions. The V shape means that they are more sensitive at low flows, but the width increases to accommodate larger flows. The angle of the notch is most commonly 90°, but calibration charts are available for other angles, 60°, 30° and 15°, if more sensitivity is required. Discharge values through small 90° V-notch weirs are given in Table 4.

For larger flows the rectangular weir is more suitable because the width can be chosen so that it can pass the expected flow at a suitable depth. Table 5 gives the discharge per metre of crest length and so can be applied to rectangular weirs of any size.

### Other sharp-crested weirs

In some weirs the characteristics of the V-notch and the rectangular notch are combined. The Cipoletti weir has a horizontal crest like a rectangular notch and sloping sides like a V-notch, but for simple installations there is no advantage over the rectangular notch (Figure 30).

The compound weir is sometimes used when a sensitive measurement is required of low flows through the V-notch, and measurements are also required of large flood-flows through the rectangular notch. The more complicated design and calibration mean that this type is usually confined to serious hydrological studies (Figure 31).

On streams or rivers with gentle gradients it may be difficult to install sharp-crested weirs which require a free overfall on the downstream side. The alternative is weirs which can operate in the partly submerged condition. An example is the USDA-ARS triangular weir shown in Plates 24 and 25. This is nearly a standard weir in the sense that rating tables are available (USDA 1979), but the rating is influenced by the velocity of approach and the calibration should be checked by current meter measurements. Another example, which might be called either a flume or weir, is shown in Plate 26 and also requires rating by current meter.

## MEASURING FLUMES

Several flumes have been developed in the USA for use in particular situations, and are widely used in spite of the awkwardness of the units of measurement. The design, construction and laboratory calibrations were all done in fps units, and until some laboratory undertakes the huge task of starting again in metric or SI units, the practical approach is to construct the flumes according to the original specifications in feet, and use the metric conversions of flow rates which have been computed by a consortium of hydraulic laboratories in The Netherlands (Bos 1976).

TABLE 4

Flow rates over a 90° V-notch weir (from USDI 1975)

 Head (mm) Flow (l/s) 40 0.441 50 0.731 60 1.21 70 1.79 80 2.49 90 3.34 100 4.36 110 5.54 120 6.91 130 8.41 140 10.2 150 12.0 160 14.1 170 16.4 180 18.9 190 21.7 200 24.7 210 27.9 220 31.3 230 35.1 240 38.9 250 43.1 260 47.6 270 52.3 280 57.3 290 62.5 300 68.0 350 100.0

TABLE 5

Flow rates over a rectangular weir with end contractions (from USDI 1975)

 Head (mm) Flow (l/s per metre of crest length) 3040 50 60 70 80 90 100 110 120 130 140 150 160 170 180 190 200 210 220 230 240 250 260 270 280 290 300 310 20 330 340 350 360 370 380 9.514.6 20.4 26.7 33.6 40.9 48.9 57.0 65.6 74.7 84.0 93.7 103.8 114.0 124.5 136.0 146.0 158.5 169.5 181.5 193.5 205.5 218.5 231.0 244.0 257.5 271.0 284.0 298.0 311.5 326.0 340.0 354.0 368.5 383.5 398.0

The reason for this approach is the complicated design of the different sizes of flumes, which were standardized after years of trial and error testing, and then calibrated. The different sizes of flume are not hydraulic scale models of each other, so it cannot be assumed that a dimension in the 4-foot flume will be twice the corresponding dimensions in a 2-foot flume. Some dimensions or proportions are constant for part of the range, but others vary for each size. As a result, each of the 22 variations in the range of Parshall flumes, and each of the H-flumes, must be regarded as a different device. They will have some features in common but each has its own manufacturing specification and its own calibration tables.

In spite of this complication, the flumes are widely used because of the advantages: they are purpose-built to meet a particular requirement; they are 'standard' measuring devices, that is when manufactured and installed according to the specification, they do not need calibration, and the rating can be taken directly from published tables. Like weirs, it is usually preferable for flumes to operate with free discharge downstream, but some types can operate satisfactorily in the partly submerged condition, i.e. when downstream conditions cause the water to back up in the flume and create some restriction of the flow. If the effect is predictable and quantifiable this is not a serious problem, but it does mean that the depth of flow must be measured at two points in the flume, as shown in Figure 32 and a correction factor applied to the rating tables.

### The Parshall flume

Named after the American irrigation engineer who developed it, this is technically described as a venturi, or standing-wave, or critical-depth flume. The main advantages are that there is only a small loss of head through the flume, it readily passes sediment or debris, it does not need special approach conditions or a stilling pond, and it does not need correction for up to 70% submergence. It is therefore particularly suitable for measuring flow in irrigation canals, or natural streams with a gentle gradient.

The basic principle is illustrated in Figure 32. The flume consists of a converging section with a level floor, a throat section with a downward sloping floor, and a diverging section with an upward sloping floor. This results in flow at critical velocity through the throat, and a standing wave in the diverging section.

In the 'free-flow' condition the water level at the outlet is not high enough to affect the flow through the throat and so the rate of flow is proportional to the level as measured at a specified point in the converging section (Plate 27 and Figure 32). The ratio of the downstream water level (Hb in Figure 32) to the upstream level Ha is called the degree of submergence, and an advantage of the Parshall flume is that no correction is required up to 70% submergence. If a greater degree of submergence is likely, then both Ha and Hb must be recorded, as in Plate 28.

The dimensions of flumes with throat width of 1 to 8 feet are shown in Table 6 and Figure 33. The flow rates of a 1-foot flume are shown in Table 7. The manuals listed in the section Further reading give dimensions and rating tables for larger and smaller flumes and correction factors for submergence over 70%.

TABLE 6

Construction dimensions for some Parshall flumes (from USDA-SCS 1965)

 Throat width W (feet) A (feet, inches) B C D 1 3-0 4-4 7/8 2-0 2-9 1/4 1½ 3-2 4-7 7/8 2-6 3-4 3/8 2 3-4 4-10 7/8 3-0 3-11½ 3 3-8 5-4 3/4 4-0 5-1 7/8 4 4-0 5-10 5/8 5-0 6-4 1/4 5 4-4 6-4½ 6-0 7-6 5/8 6 4-8 6-10 3/8 7-0 8-9 7 5-0 7-4½ 8-0 9-11 3/8 8 5-4 7-10 1/8 9-0 11-1 3/4

Dimensions as shown in Figure 33.

Dimension A = 2/3 (w/2 + 4)

For this range of throat width the following dimensions are constant.

E = 3-0, F = 2-0, g = 3-0, K = 3 inches, N = 9 inches, X = 2 inches, Y = 3 inches.

Table 7

Flow rates in a Parshall flume of throat width 304.8 mm (12 inches)

 Head (mm) (Ha in Figure 32) Flow (l/s) 30 3.3 40 5.2 50 7.3 60 9.6 70 12.1 80 14.9 90 17.8 100 20.9 110 24.1 120 27.5 130 31.1 140 34.8 150 38.6 160 42.6 170 46.7 180 51.0 190 55.4 200 59.8 225 71.6 250 84.0 275 97.1 300 110.8 325 125.2 350 140.1

A wide variety of materials has been used for making Parshall flumes. They can be prefabricated from sheet metal or timber, or they can be constructed in the field from brick and plaster using a prefabricated metal skeleton to ensure that the exact measurements are achieved (Plate 29). If a number of flumes are required, they can be cast in concrete using reusable shuttering. Spot measurements of the depth of flow may be read from a gauge post set in the wall of the flume or, if continuous records are required, a float-operated recorder can be installed in a stilling well at the specified position.

### H flumes

A group of special-purpose flumes, called H flumes were designed by the US Soil Conservation Service for measuring flows accurately and continuously from runoff plots or small experimental catchments. The design requirements were that the flume should measure low flows accurately but still have a good capacity for high flows, and not need a stilling pond. It is also required to be able to pass runoff containing a heavy sediment load. The practical solution to the American units is, as for the Parshall flumes, to construct in the original specifications in feet, and use the metric conversions of flow rate in Bos (1976).

There are three types of H flume. The smallest (HS) can record flows up to 22 l/s, the regular type (H) can take flows up to 2.36 m3/s, and the large type (HL) flows up to 3.32 m3/s. Each type can be built in a range of sizes which is defined by the maximum depth of flow (D), and the manufacturing dimensions are given as proportions of D, but the proportions, i.e. the shape of the flume, are different for each of the three types HS, H, and HL.

The HS can be built in four sizes, from 0.4 to 1.0 feet, the H type in eight sizes from 0.5 to 4.5 feet, and the HL in two sizes, 3.5 and 4.0 feet. There are thus fourteen possible manufacturing specifications and fourteen different calibration tables. As examples, the dimensions for the H type are shown in Figure 34, and the calibration for the H-type of size 1.5 ft (0.457 m) in Table 8.

H flumes can operate partly submerged and the correction is shown in Figure 35. The submergence downstream causes the water to back up in the flume and flow at an increased depth. The correction curve shows how much the measured depth in the flume should be reduced to give the equivalent depth for free flow with which to enter the calibration tables.

H flumes are usually prefabricated from sheet metal and may be used either for temporary installation using sandbags to form an approach channel, or for more permanent installation, using concrete or masonry as illustrated in Plate 30. Like the Parshall flume, spot measurements of depth of flow can be made from a gauge plate at a specified point on the wall of the flume, or a continuous record from a float-operated recorder. With all flumes there is a drawdown curve, that is the surface level falls as the water accelerates to the discharge point, and it is therefore essential that the measurement of depth of flow must be made at precisely the specified distance upstream from the control section.

H flumes have two other advantages. The water flows through the notch fast so there is no deposition of sediment in the flume. Also the outlet design with a backward sloping V does not get jammed by floating trash. If some vegetation does get caught in the V, the water backs up behind until the obstruction is floated over the top of the notch.

TABLE 8

Free-flow discharge through 1.5 ft H flume in l/s (from Bos 1976)

 ha (mm) 0 2 4 6 8 2040 60 80 100 150 200 250 300 350 400 450 0.270.91 1.75 3.43 5.38 12.5 23.3 38.2 57.7 82.3 112 148 0.321.00 2.08 3.60 5.60 12.9 23.8 38.9 58.6 83.4 114 150 0.371.09 2.21 3.78 5.83 13.2 24.3 39.6 59.5 84.5 115 0.421.18 2.35 3.96 6.06 13.6 24.9 40.3 60.4 85.6 116 0.481.28 2.49 4.15 6.29 14.0 25.4 41.0 61.3 86.7 118

TABLE 9

Flow rates in Washington flumes

 Depth of flow (mm) 30 40 50 60 70 80 90 Flow (l/s) 0.1 0.2 0.33 0.5 0.75 1.07 1.43

Flow in litres per second for depth of flow measured on scale in millimetres.

### Washington State College (WSC) flume

This is another critical-depth flume of a design rather similar to the Parshall which is particularly useful as a portable flume for spot measurements of small flows in unlined streams or channels (Chamberlain 1952). It can be prefabricated in fibre-glass (Plate 31) or thin sheet metal and installed in a few minutes. Dimensions are shown in Figure 36 and the rating in Table 9.

There are many larger versions and variations on the principle of the Washington flume. They are usually built in situ rather than prefabricated, and are particularly useful for swift-flowing mountain streams (Goodell 1950) or for semi-tropical conditions where high-load flash floods can be expected (Gwinn 1964). An intermediate size of Washington-type flume, designed for use in New Mexico, can measure flows up to 6 m3/s with heavy bedload (Aldon and Brown 1965). These are not standard flumes and have to be rated using the velocity/area method discussed in the section on Velocity/area method.

### Using existing structures

Existing structures can sometimes be used as control sections to give an estimate of peak flows through road culverts or bridge openings. For rectangular culverts, an approximate value can be calculated from the general formula for flow through a rectangular weir.

Q= c W H 3/2

where:

Q     is the flow in cubic metres per second

W     is the width of opening in metres

H     is the depth of flow in metres

c     is a coefficient of discharge which depends on the geometry of the culvert. A typical value is 0.6; more precise figures can be taken          from tables such as in USDA-ARS (1979)

Larger flows may be estimated at rectangular bridge openings using this method, or from current meter reading of velocity and the velocity/area method. For fast flows it may be necessary to attach a heavy weight to the current meter, or to mount it on a rod. If high-water marks can be seen at the bridge opening and also at a distance upstream where the flow is not affected by the bridge opening, the maximum flow can be calculated using a procedure established by the US Geological Service (Kindsvater, Carter and Tracey 1953).

## WATER-LEVEL RECORDERS

Sometimes a single measure of maximum depth of flow is sufficient to estimate maximum flood flow, and methods were described in the section on Velocity/area methods. If a hydrograph is required, i.e. a plot of rate of flow against time, then a continuous record of changes in water level is needed. For decades the standard method was a float whose rise and fall in a stilling well was recorded by a pen on a clockwork-driven chart. These recorders were flexible in that gearing could be used to cover large or small ranges of level, and the time-speed of the charts could also be varied by the gearing of the clockwork. The disadvantage was the susceptibility to accidental errors and malfunction. To name just a few, the pipe to the stilling well gets blocked or silted up, insects nest in the recorder housing, humidity or aridity makes the pen overflow or dry up, the chart may stretch or contract, the clock stops, the observer cannot get to the site to change the chart, and many other problems. Daily inspection is not always possible when sites are remote or have difficult access. In addition to the difficulties of getting good data, the analysis and computation of the charts are laborious.

Fortunately modern technology has greatly improved both the collection and the processing of data. Non-float level detectors can be based on electrical resistance/ capacitance, pressure on a sealed bulb or affecting the discharge of air bubbles and acoustic transducers. Most commonly used today is the pressure transducer in which the deflection of a membrane is sensed electrically. These can be connected to solid-state programmers, timers, and memory storage to provide any required type and frequency of recording, and the stored data can be plugged into a computer for rapid analysis.