CONTENTS Flow measurement

Transcription

1 CONTENTS Flow measurement 1 Introduction Weirs Terminology pertaining to weirs Approach velocity at weirs End contractions Submerged weirs Nappe types Choice of weir Setting up of weirs Equations to determine flow through weirs Flow over weirs Parshall flumes Flow characteristics of the Parshall flume Equations for free flow in Parshall flumes Dimensions of Parshall flumes Installation of a Parshall flume Examples Crump weir Maintenance of weirs and flumes Orifices for determining flow in channels Flow speed Area methods for flow measurement in channels Flowmetering by means of floats Current meters Other methods Volumetric flow measurement Gravimetric flow measurement Co-ordinate methods Vertically upwards Horizontal References All rights reserved Copyright 2003 ARC-Institute for Agricultural Engineering (ARC-ILI) ISBN

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3 Flow measurement Introduction The increasing demand on existing water sources, continually increasing costs of irrigation schemes and accompanying development costs necessitate that existing water be used economically and effectively. Regular measurements provide valuable information to the irrigation farmer or irrigation board, that can be used very effectively to: evaluate the performance of a scheme or system; facilitate the fair division of water between irrigators and thereby reduce the risk of faulty divisions and shortages; ease the administration of division and distribution; show up possible shortcomings or problem areas in a scheme or system; build up a data base which can be used for future planning; serve as a source of reference for irrigation research and technology development; determine the time and extent of system maintenance; enable control of and over stream sizes and volumes; and simplify scheduling management. The following apparatus are suitable for measurement of irrigation water: Rectangular weir (with or without end contractions) Cipolletti weir V-notch Parshall flume Crump weir Water-meter (see Chapter 9: Irrigation accessories) Long throated flume and variations thereof Flow measurement with structures in open channels depends on the flow rate to flow depth relation, which is determined for each structure by means of calibration. Besides the physical structure to be installed in open channels, it is necessary to measure the flow depth at the structure so that the relation can be used to determine the flow rate. The flow depth can be measured with various instruments, which varies from measuring plates, which do not collect continuity data, to mechanical or electronic sensors with automatic registers. The sensors can be in contact with the water, such as submersible pressure sensors or float-and-counterweight mechanisms, or it can make a distance observation, as in the case of ultrasonic sensors. A further component sometimes found with measuring apparatus, is telemetric communication systems that make it possible to collect data from the automatic register per radio or modem over a relatively far distance. This makes it possible to monitor the measurement at distant points without physically visiting the measuring point. 2 Weirs The weir is one of the oldest, cheapest, most straightforward and reliable structures for the determination of flow in channels where sufficient water depth is available. A simple weir consists of a structure in wood, metal or concrete placed perpendicular to the flow in a channel. The structure has a sharp-edged opening or notch of specific shape and dimension through which the water can flow. Weirs are identified by shape as indicated below.

4 8.2 Irrigation Design Manual Figure 8.1: Typical weir shapes 2.1 Terminology pertaining to weirs Approach velocity at weirs Figure 8.2: Weir terminology The approach velocity of the water in the pool formed upstream of a weir should preferably be lower than 0,1 m/s. Therefore the cross-sectional area of the pool should be relatively large compared to the cross-sectional area of the stream flowing through the weir. Where it is not practically possible to keep the approach velocity within acceptable limits, relevant improvements to the specific flow equations should be made. Figure 8.3: Approach velocity at weirs

5 Flow measurement 8.3 The approach velocity can be determined by the following equation: v a Q y b (8.1) where v a approach velocity [m/s] Q flow through weir [m 3 /s] y water depth in channel before weir [m] b channel width [m] If the approach velocity (v a ) is known, the velocity head (h a ) can be determined by the equation: h a 2 va 2g (8.2) where h a velocity head [m] g gravitational acceleration (10 m/s 2 ) The total energy head of water (H) is determined by the equation: H h + 2 va 2g (8.3) where H total energy head of water [m] h overflow depth [m] By repeated calculations of h a and v a for improved values of the flow rate (Q), the approach velocity can be determined to the required accuracy thereby giving an acceptable flow rate. In most cases one repetition would be sufficient End contractions When the channel feeding the water to the weir is wider than the weir crest, the sides of the stream will narrow where it crosses the weir. The width of the stream flowing over the weir will be slightly narrower than crest width. The phenomenon is known as end contraction. To make allowance for end contractions, the overflow width in the basic equation must be modified as follows: L' L - 0,1nh (8.4) where L' effective length of weir [m] L measured length of weir [m] n number of end contractions h overflow depth [m]

6 8.4 Irrigation Design Manual Figure 8.4: End contraction at weirs Submerged weirs Free overflow occurs when the flow after the weir is not backed up. With flood run-off, the water level on the downstream side of the weir may rise above the weir crest height. This reduces the overflow capacity and is known as a submerged condition. Figure 8.5: Submerged weirs α h B h (8.5) where α degree of submergence [fraction] h upstream height of water level above crest height [m] downstream height of water level above crest height [m] h B

7 Flow measurement 8.5 Table 8.1: Reduction factors for different degrees of submergence for sharp-crested weirs α 0,2 0,4 0,6 0,8 0,9 Reduction in discharge 0,07 0,15 0,26 0,42 (unstable) 0,55 (unstable) Nappe types With water measurement it must be attempted to always achieve a ventilated nappe, thereby ensuring reasonable accuracy of the observed readings. When water flowing over the weir does not make direct contact, an air bubble will be formed below the nappe. A certain amount of the air will be drawn along with the overflowing water. If an air bubble is not sufficiently aerated, a vacuum will be formed which increases the curvature of the nappe and leads to an increase in discharge over the weir. The problem can be solved by installing an aeration tube downstream of the weir (see Figure 8.7). Figure 8.6: Different nappe types The following discharge correction should be made for the different nappe types: Depressed nappe: Increase measured discharge by 8-10% Drowned nappe: Decrease measured discharge according to Table 8.1 Clinging nappe: Decrease measured discharge by 20-30%

8 8.6 Irrigation Design Manual 2.2 Choice of weir Each type of weir has certain advantages under specific conditions. Generally, for accurate readings, a standard V-notch or a rectangular suppressed (parallel sides with no side contractions) weir should be used. The Cipolletti and rectangular weirs with full end contractions are especially suited for water division. Normally the observer has a reasonable idea of the quantities to be measured and taking the following into account, a choice can be made of the suitable weir for particular circumstances: The maximum expected water height above the weir must be at least 60 mm to prevent the nappe from adhering to the weir crest. Furthermore it is difficult to take accurate readings on the measuring scale if (h) is too low. The length of the rectangular and Cipolletti weirs must be at least equal to three times the water height above the weir crest. The V-notch is the most suitable for measurements smaller than 100 m³/h. The V-notch is as accurate as the other weir types for flows between 100 and m³/h provided that submergence does not occur. The weir crest must be as high above the channel floor as possible so that free overflow (of the nappe) will take place. The flow depth over the weir should not exceed 600 mm. 2.3 Setting up of weirs Figure 8.7: Setting up of weirs The structure must be sturdy and placed as close to perpendicular to the flow direction as possible, in a straight section of the channel. The inner face of the structure must be smooth and set up vertically to the water surface.

9 Flow measurement 8.7 The crest must be level in the case of rectangular and Cipolletti weirs. The sides of the V-notch must be equidistant from an imaginary vertical line drawn through the lower point of the V. The weir crest should be at least 2 mm thick (not sharp). The weir crest must preferably be higher than 2h and in any case never lower than 300 mm above the channel floor (see Figure 8.7). The distance between the sides of the notch and the channel sides must not be less than 2h and never less than 300 mm. The nappe should only touch the sharp crest of the notch and not the thicker part of the structure. Air should be able to circulate freely around the nappe. The measuring scale must be fixed at a distance 4h from the structure in a position where it can be easily read. If the cross-sectional area of the water flowing through the weir is A and the maximum expected height above the weir is h, the cross-sectional area of the water pool above the restriction must not be less than 8A for a distance of 20h from the structure. If the water pool above the structure is smaller than prescribed, the approach velocity may be too high and the measuring scale readings accordingly too low. The approach velocity will then have to be taken into account when determining Q. The measuring scale must be calibrated to accommodate the maximum expected water level above the weir. The structure must not let any water pass through the floor or sides. The channel section downstream of the structure must be sufficiently large to prevent high backing up of water. The accuracy of weirs decreases with a high percentage of silt in the water. 2.4 Equations to determine flow through weirs Many equations for determining flow through weirs have been developed, the best known being one by J B Francis dating back to the previous century. Since then observers have continued development on Francis' work, giving rise to refinement of the original values. A good hydraulics handbook may be consulted for detailed information on equations that have been developed concerning this subject. This chapter will deal with imperial as well as metric equations as both are in use.

10 8.8 Irrigation Design Manual The Francis equations without approach velocities are as follows: Table 8.2: Francis equations Weir type Metric equations Imperial equations Cipolletti Q 1,86Lh 1, 5 Q 3,367Lh 1,5 90 V-notch Q 1,38h 2,5 Q 2,50h 2, 5 Rectangular, submerged Q 1,84Lh 1, 5 Q 3,33Lh 1, 5 Rectangular with end contractions Q 1,84(L-0,2h)h 1, 5 Q 3,33(L-0,2h)h 1, 5 Units Q : [ m³/s] h : [metre] L : [metre] Q : [cusec] h : [feet] L : [feet] In the above equations: Q discharge h measuring scale reading of water depth L length of notch The Francis equations considering approach velocities are as follows: Table 8.3: Francis equations Weir type Metric equations Cipolletti Q 1,86L(h +1,5ha ) 2,5 2,5 90 V-notch Q 1,38 [(h + ha ) - ha ] 1,5 1,5 Rectangular, submerged Q 1,84L [(h + ha ) - ha ] Rectangular with end contractions 1,5 1,5 Q [ - ](L - 0,2h) 1,84 (h + h a ) h 1,5 a where: Q discharge [m³/s] L length of notch [m] h measuring scale reading of water depth [m] h a velocity head [m]

11 Flow measurement Flow over weirs Weir crests are mostly rectangular, therefore the following equation applies, where the approach velocity has little or no effect: 1,5 Q C L h (8.6) where Q discharge [m³/s] C discharge coefficient L crest width [m] h height or depth of discharge [m] The value of C will depend on the depth of overflow that is the breadth of the weir crest (t) and the discharge depth over the crest (h). In practice most crests fall between sharp and broad crested and the following adjustments must be made for a weir with discharge depth (h) and crest breadth (t). Sharp crest (h > 3t) C 1,822 Broad crest (h < 0,3t) C 1,45 Provided that the h/t ratio is between 0,3 and 3,0, the C-value can be interpolated between 1,45 and 1,822. These refined C-values for rectangular weirs replace the original C-values developed by T B Francis shown in Tables 8.2 and 8.3. Figure 8.8: Flow over broad-crested weirs

12 8.10 Irrigation Design Manual Figure 8.9: Graph to determine a C-value for a given h/t ratio For end contractions and approach velocities, the same terminology applies to both sharp-crested and broad-crested weirs. Discharge under submerged conditions is influenced minimally provided that the degree of submergence is less than 0,67. Equation 8.5 also applies to broad-crested weirs. α h B h (8.5) where α degree of submergence [fraction] h upstream height of water level above crest height [m] h B downstream height of water level above crest height [m] Table 8.4: Reduction factors for different degrees of submergence with broad-crested weirs α Reduction in discharge 0,2 0,0 0,4 0,0 0,6 0,0 0,8 0,01 0,9 0,15

13 Flow measurement 8.11 Example 8.1: A sharp-crested weir is installed in a river with approximately rectangular section (b 10,0 m) as shown below: Section B-B Determine the flow rate for a discharge height of: (a) h 0,5 m (b) h 1,5 m Section A-A Solution: (a) Considering end contractions: From equation 8.4: L' L - 0,1 nh 5-0,1 2 0,5 4,9 m From equation 8.6: 1,5 Q CL' h 1,822 4,9 0,5 3 3,15 m /s 1,5 Determine approach velocity from equation 8.1: v a Q yb 3,15 1,5 10 0,21 m/ Determine velocity head from equation 8.2: h a 2 va 2g 0,002 2 m

14 8.12 Irrigation Design Manual h a is negligibly small, accept Q 3,15 m 3 /s (b) Divide section into 3 parts No end contractions. From equation 8.6: Q 1 C L h 1,5 1, ,5 1,5 16,73 m 3 /s Q 2 1, ,5 1,5 3,22 m 3 /s Q total Q 1 + Q 2 19,95 m 3 /s Determine approach velocity from equation 8.1: v a Q y b 19,95 2,5 10 0,8 m/s Determine velocity head from equation 8.2: h a 2 va 2 g 0,03 m Recalculate Q total : Q 1,822 5 (1,5 + 0,03) 1,5 17,24 m 3 /s Q 1,822 5 (0,5 + 0,03) 1,5 3,51 m 3 /s Q total 20,75 m 3 /s

15 Flow measurement 8.13 Determine approach velocity: v a Q y b 20,76 2, ,82 m/s h a 2 v a 2 g 0,03 (same as previous calculation) Determine velocity head: Therefore the discharge remains constant Q total 20,75 m 3 /s 4 Parshall flumes

16 8.14 Irrigation Design Manual Figure 8.10: Parshall flume The Parshall flume works on the venturi principle to determine flow in open conduits. The flume consists of three main parts, namely: a converging section upstream; a throat section; and a diverging section at the end. The floor of the converging section is level in length and breadth, while the throat section slopes downwards and the diverging section slopes upwards. The Parshall flume is named after Ralph L Parshall, an irrigation engineer at the Colorado Agricultural College in the USA. He began with experiments to design an improved flow measurement device to replace the known weirs and other devices of the time in approximately The Parshall flume has three major advantages as a flow measuring device, namely: An exceptionally high degree of flow measuring accuracy, even under partially submerged conditions (see Table 8.5). Almost no build-up of silt and sand occurs. Due to the small drop in water level, it is suitable for channels with very flat floor slopes. All flumes should be installed level in all directions to maintain a high measurement accuracy. The disadvantages of a Parshall flume are the following: Relatively expensive to build as Parshall flumes are normally installed as permanent concrete structures on water schemes. Portable units of wood, metal, fibre cement and GRP are commercially available. The smaller the flume, the more important it is to maintain strict construction tolerances, making construction more difficult. Special care must be taken with installation, particularly on smaller flumes to provide accurate readings. All flumes must be installed level in all directions. The size of flume to be used for a particular purpose will be determined by the average maximum flow to be measured, the permissible head loss through a flume and the normal channel water depth. The final choice of flume is based on the throat width best suited to the channel dimensions and hydraulic properties. Generally the throat width of a Parshall flume should be approximately 0,3-0,5 times the upstream width of the water surface during channel design conditions. Metric units cannot be used as Parshall flumes are experimentally calibrated with imperial units. Dimensions for these flumes will be in imperial units for some time to come, therefore the same units will be used in this manual. 4.1 Flow characteristics of the Parshall flume Flow through a Parshall flume can occur in two ways, namely: Free-flow conditions, that is no submergence takes place. Submerged flow conditions where the water level in the diverging section is such that it retards free flow.

17 Flow measurement 8.15 Often two measuring plate readings (h en h B ) are given to distinguish between submerged and freeflow conditions. Both measuring plate datums are set to the average crest height of the Parshall flume. The water flow through the throat and diverging sections can occur in two ways: At high velocities it will be a thin layer approximately parallel to the downward sloping section of the throat (condition Q in Figure 8.10). With the backwater pushing up the water level in the throat section to form a ripple wave (conditions S in Figure 8.10). During condition S a marked decrease in outlet velocity occurs, decreasing erosion of the conduit walls and reducing the drop in water level. The degree of submergence may also be determined by using equation 8.5. Provided that the ratio does not exceed certain limits, the flow rate through the flume will not be influenced by a rise in the tail water level. The permissible degree of submergence for free flow varies with throat width as shown in Table 8.5 Table 8.5: Permissible levels of submergence for accurate flow determination Throat width 1-3 inches 6-9 inches 1-8 feet feet Free-flow limit 0,50 0,60 0,70 0,80 Small Parshall flumes All flumes smaller than 1 foot are considered small. For submerged flow conditions, Figures 8.12 and 8.13 are used to determine the reduction in flow due to submergence. This reduction is then subtracted from the free-flow reading (see Table 8.8). Medium Parshall flumes All flumes with a throat width between 1 and 8 feet, are considered medium. If submerged flow occurs according to Table 8.5, Figure 8.14 is used to determine flow reduction due to submergence, which is then subtracted from the free-flow reading. Figure 8.14 applies only to 1 foot throat width Parshall flumes and the flow reduction (see Figure 8.14) must be adjusted for larger Parshall flumes with correction factor M (see Table 8.6). Table 8.6: Correction factors Throat width [ft] Factor M Throat width [ft] Factor M ,00 1,76 2,45 3, ,7 4,31 4,9 5,45

18 8.16 Irrigation Design Manual Large Parshall flumes All Parshall flumes with throat width larger than 10 feet, are considered large. Table 8.7: Correction factors Throat width [ft] Factor M Throat width [ft] Factor M ,0 1,2 1,5 2, ,5 3,0 4,0 5,0 When submerged conditions occur with large Parshall flumes, the correction factors of Table 8.7 are used for throat widths larger than 10 feet. 4.2 Equations for free flow in Parshall flumes The following equations are used to determine the discharge of a particular flume. Table 8.8: Parshall flume equations Throat width of Parshall flume Imperial equations Metric equations 3 inches Q 0,992h 1,547 Q 0,3259h 1,547 6 inches Q 2,06h 1,58 Q 0,3812h 1, feet Q 4 Wh 0,026 1,522W 0,026 1,57 W Q 0,3716 W(3,281h ) feet Q (3,6875W + 2,5)h 1,6 Q 0,1895(12,0981W + 2,5)h 1,6 Units Q discharge [ft 3 /s] W throat width [feet] h free-flow depth [feet] Q discharge [m³/s] W throat width [m] h free-flow depth [m] The equations for submerged flow are more complicated and are not dealt with in this chapter.

19 Flow measurement Dimensions of Parshall flumes Table 8.9: Specified dimensions Description 6 inches 9 inches 1 ft 2 ft 3 ft 4 ft 6 ft 8 ft Lengths Widths Heights Measuring scale position Capacity [m 3 /h] A B C W E F H K G D X Y Min Max Figure 8.11: Dimensions of Parshall flumes

20 8.18 Irrigation Design Manual Figure 8.12: Flow determination for a 6 inch submerged Parshall flume Figure 8.13: Flow determination for a 9-inch submerged Parshall flume

21 Flow measurement 8.19 Figure 8.14: Flow determination for a 1-foot submerged Parshall flume 4.4 Installation of a Parshall flume The most important factor when installing a Parshall flume is determining the crest height relative to the floor of the channel in which it is to be placed. With careful planning it is possible to install the flume so that submerged conditions only occur in isolated cases. It is not always possible with flat sloped conduits. Whatever happens, the percentage of submergence should always be kept as low as possible. With weirs it is advisable to place a flume in a straight section of conduit to avoid the effect of crossflow. The installation of a Parshall flume as a permanent structure should be done by an expert. 4.5 Examples Example 8.2: Determine the flow through a Parshall flume for the following: 1-foot Parshall flume: h 0,16 m h B 0,1 m Solution: Free-flow determination: hb α h 0,625 Free-flow limit: 0,7 (from Table 8.5) Therefore free-flow conditions occur (0,625 < 0,7) From Table 8.8 for h 0,16 m is Q 0,042 5 m 3 /s 153 m 3 /h

22 8.20 Irrigation Design Manual Example 8.3: Determine the flow through a Parshall flume for the following: 1-foot Parshall flume: h 0,16 m h B 0,128 m Solution: Free-flow determination: h α B h 0,8 Free-flow limit: 0,7 (from Table 8.5) Therefore submerged conditions occur (0,8 > 0,7) From Figure 8.14 for h 0,16 m and α 0,8, Q 0,004 2 m 3 /s From Table 8.6 M 1 for a 1-foot Parshall flume From Table 8.8 for h 0,16 m Q 0,042 5 m 3 /s Actual flow: Q 0, , ,038 3 m 3 /s 138 m 3 /h Example 8.4: Determine the flow through a Parshall flume for the following: 2-foot Parshall flume h 0,671 m and h B 0,396 m Solution: Free-flow determination: α h B /h 0,396/0,671 0,59 Free-flow limit: 0,7 (from Table 8.5) 0,59 < 0,70, therefore free-flow conditions occur From Table 8.8 for h 0,671 m Q 0,770 m 3 /s m 3 /h Example 8.5: Determine the flow through a Parshall flume for the following: 3-foot Parshall flume. h 0,643 m and h B 0,566 m Solution: Free-flow determination: α h B /h 0,566/0,643 0,88 Free-flow limit: 0,7 (from Table 8.5) 0,88 > 0,70 therefore submerged conditions occur From Figure 8.14 for h 0,643 m and α 0,88 m, Q 0,083 8 m 3 /s From Table 8.6 for a 3-foot flume M 2,45 Total flow reduction is therefore 0, ,45 0,205 m 3 /s For free-flow conditions: Q 1,09 m 3 /s (from Table 8.8) Actual flow: Q 1,09-0,205 0,885 m 3 /s m 3 /h

23 Flow measurement Crump weir In the past the Crump did not come to its right in the irrigation industry because it tends to cause a back-up of water on the upstream side. The most important features of the Crump are as follows: Straightforward structure High accuracy Relatively insensitive to submerged conditions Flow curves can easily be determined for any width The Crump consists of two parallel walls with a specially shaped overflow wall on the downstream side. The wall top is sloped at 1:2 on the upstream side and 1:5 on the downstream side. The crest should preferably be protected by a galvanized steel angle profile. The walls may be of concrete or plastered brickwork. It is important that the inner distance between the walls remains constant as specified. In the absence of a solid foundation, the walls are to be founded or the complete structure may be built on a concrete slab. One disadvantage of the Crump is the straight side walls which lack stability and may fall over. A stilling basin is recommended to make readings easier and more accurate. A tube or small hole big enough to avoid blocking, must be provided between the flume and stilling basin. The best position with respect to height, is just below the crest of the overflow wall. The distance is specified below and is rather critical. A tube can also be placed beneath the overflow wall to facilitate drainage if the channel upstream of the wall needs to be dried out. If the channel is wider than the flume, side walls must be provided to gradually concentrate the water, the ideal angle being 1:3. This type of flume is very suitable for rectangular concrete channels because the parallel walls exist and all that remains is the building of the overflow wall. Dimensions The width of the Crump will be determined by the minimum and maximum flows to be measured. The wider the Crump is, the smaller the scale-reading will be for a specific flow. The absolute minimum reliable reading with a Crump is 50 mm, therefore the width of the Crump should be such that the minimum flow to be measured gives a reading of at least 50 mm. It is, however, preferable to choose the width so that the minimum flow will give a reading of 100 mm. The most generally used scale lengths are 300 mm and 500 mm. The maximum reading and therefore also the maximum flow measurable by a Crump will be determined by the scale length. Table 8.10 shows the flow for different widths and specific scale readings, thereby allowing determination of a width (B).

24 8.22 Irrigation Design Manual Table 8.10: Flow limits for different Crump widths Width Minimum flow [m 3 /h] Reading Maximum flow [m 3 /h] Measuring scale length Most of the Crump's dimensions are determined by the measuring scale length to be used (see Table 8.11). This applies to all Crump widths. Table 8.11: Crump dimensions Measuring scale length A C D E F I J Figure 8.15: Crump weir

25 Flow measurement 8.23 The other Crump dimensions as determined by the normal flow depth for maximum flow directly downstream of the proposed position of installation are as follows: Table 8.12: Crump dimensions depending on maximum flows Measuring scale length Maximum normal flow depth G L K Po 300 < 400 <450 < < 650 < 700 < Equations for flow determination in a Crump weir. For a horizontal Crump, the discharge equation is as follows: Q 7 135Bh 1,5 (8.6) where Q B h discharge [m 3 /h] width [m] flow depth [m] The degree of submergence is also determined with equation 8.5: α h B h (8.7) where α degree of submergence [fraction] h upstream height of water level [m] h B downstream height of water level [m] The downstream height begins to influence the upstream height when α > 0,75. Figure 8.16 may be used to determine the reduction in discharge for a given degree of submergence.

26 8.24 Irrigation Design Manual Figure 8.16: Reduction factors for different degrees of submergence for a Crump weir 6 Maintenance of weirs and flumes Regular maintenance of water measuring devices is required to ensure long, accurate performance and reduce or avoid costly repairs. The following aspects are important: Weirs: Keep the ponding area free of sediments and plant growth Ensure that there is no leakage through or around the device Regularly check the position of the weir plate relative to the crest Maintain the condition of the crest finish in good order Remove rust from steel sections by wire brush and coat with a bituminous paint Flumes: Remove sediments and accretions especially in approach and venturi sections If manufactured from steel, remove rust by wire brush and coat with a bituminous paint Avoid erosion immediately downstream of the device Recast the floor if the existing one is no longer level Regularly check the measuring scale position relative to the crest

27 Flow measurement Orifices for determining flow in channels An orifice is an opening where: the dimensions of the opening are small in relation to the water pressure above it; and the water pressure at the centre of the opening, for all practical purposes, is the same as the pressure at the edge of the opening. An orifice to be used for flow measurement is usually rectangular or circular in shape and placed perpendicular to the flow direction in a vertical structure in the channel. An orifice is under free-flow conditions when the water discharges in an air medium and submerged flow conditions when it discharges in a water medium. Flow measurement is possible under submerged as well as free-flow conditions. As with weirs, orifices have full contraction if the orifice edge is sharp and it is located far from the channel wall. One disadvantage of an orifice as a flow measurement device is that it is relatively easily blocked by silt or sand build up as well as flotsam in the flowing water. The discharge for a submerged orifice with full contraction as well as for free flow, is determined by the following general equation: Q CA 2 g h (8.8) where Q discharge [m³/s] A orifice area [m²] g gravitational acceleration (10 m/s 2 ) h difference in water levels [m] C discharge coefficient (0,61) C-value The C-value for short pipes and sluice openings can be determined as follows: Short pipes Figure 8.17: Short pipes

28 8.26 Irrigation Design Manual Table 8.13: Discharge coefficients for flow through short pipes L/D C 0,82 0,82 0,79 0,77 0,71 0,64 0,55 Sluice opening Figure 8.18: Rectangular sluice opening Table 8.14: Discharge coefficients for flow through sluices Wall thickness (T) [m] 0,1 0,2 0,4 0,75 1,5 3,0 4,0 C 0,62 0,64 0,65 0,72 0,77 0,80 0,81 Example 8.6: Determine the discharge through a sluice opening of 600 mm 200 mm. The difference in water level before and after the sluice 0,35 m. Wall thickness 0,1 m. Solution: Cross sectional area 0,6 0,2 0,12 m 2 From equation 8.8: Q CA 2gh From Table 8.14: C 0,62 Q 0,62 0,12 0,195 m 702 m 3 3 /h /s 2g 0,35

29 Flow measurement Flow velocity - area methods for flow measurement in channels 8.1 Flowmetering by means of floats With a lack of suitable measuring devices or where high measurement accuracy is not required, the flow rate in a channel may easily and quickly be determined, using a float and wrist watch. The accuracy of measurement will depend on the type of float used. Use something like an orange that floats quite deep, preventing wind to influence the flow velocity. The method of flow measurement is as follows: Determine the cross-sectional area of the channel Determine water flow velocity as follows: Mark a 10 m straight channel section Take the time for the float to travel the 10 m distance Repeat the process 5 times with the float in different flow paths Determine the average flow velocity v C f v f (8.9) where v C f v f flow velocity [m/s] correction factor float velocity measured [m/s] Table 8.15: Correction factors (C f ) to adjust measured float velocity Average flow depth [m] 0,3 0,6 0,9 1,2 1,5 1,8 2,7 3,7 4,6 6,1 C f 0,66 0,68 0,70 0,72 0,74 0,76 0,77 0,78 0,79 0,8 The channel discharge may be determined with equation Q Ak v (8.10) where Q discharge [m 3 /s] A k cross-sectional area of wetted channel section [m 2 ] v flow velocity [m/s] Example 8.7: Determine the discharge for a parabolic channel with a flow depth (y) 400 mm and top width (W) 2 m Time for float to travel 10 m: Time (1) 11 s Time (2) 12 s Time (3) 10 s

30 8.28 Irrigation Design Manual Solution: Float velocity ( v f distance ) time 10 ( )/3 0,91 m/s From Table 8.15: C f 0,67 From equation 8.9: v C f v f 0,67 0,91 0,61 m/s Cross sectional area of 2 yw parabola ( Ak ) 3 2 0, ,54 m From equation 8.10: Q A k v 0,54 0,61 0,33 m 3 /s 8.2 Current meters A current meter is an apparatus with which the flow speed at a specific point in an open channel (or river course) can be measured. It is used to measure the average flow speed at different distances from the wall of the channel, so that each measuring point represents a portion of the cross section area of the channel profile. Figure 8.19: Flow speed is measured at representative points in the cross section area

31 Flow measurement 8.29 The flow depths are also registered during the measurement and the collective information is usually used to determine the flow rate to flow depth relation for measuring structures. Figure 8.20: Flow depths are measured at the representative points in the cross-section area The flow rate in the different portions can be calculated by means of the continuity equation. vi + vi+ 1 di + di+ 1 qi 2 2 ( L L ) (8.11) i+1 where q i the flow rate for the partial cross section areas between measuring points i and i + 1 [m³/s] v i average flow speed at point i [m/s] d i depth of the water at point i [m] L i distance of a reference point to point i in the channel [m] The total flow rate in the channel can be determined by adding the flow rate of the different portions. i Q n i 1 q i (8.12) where Q the total flow rate in the channel [m/s] 9 Other methods Besides the methods described in this chapter, there are quite a number of other flow measuring methods which are often used in practice. 9.1 Volumetric flow measurement Volumetric measurement is one of the most straightforward and accurate methods of flow measurement. With this method the full flow is discharged into a container of known volume and the time taken to fill the container recorded. This method is often used to calibrate other measuring devices.

32 8.30 Irrigation Design Manual For flow measurement a stopwatch must measure to ± 0,1 second accuracy, therefore for an accuracy of ± 1%, it must be possible to fill the container in 20 seconds. Theoretically a flow of approximately 5 λ/s can be determined with a normal 20 λ bucket. In practice, however, a maximum flow of 3 λ/s may be determined. A maximum flow of 30 λ/s can be determined with a 200 litre oil barrel. Q V t (8.13) where Q V t flow [λ/s] container volume [λ] time to fill container [s] Example 8.8: Determine the flow [λ/h] for the following case: Container diameter 100 mm Container depth 200 mm Average filling time 20 s (five readings) Solution: Container volume From equation 8.11: V Q t 0, , λ/h -3 m 3 2 π D h 4 2 0,1 π 0, ,0016 m /s 9.2 Gravimetric flow measurement One litre of water weighs one kilogram. If the container volume is unknown, a quantity of water is discharged into a container while the time is recorded. The mass of water is derived by determining the mass of the full as well as the empty container. Q M t (8.14) where Q M t flow [λ/s] water mass [kg water] time to fill container [s]

33 Flow measurement Co-ordinate methods Vertically upwards If a pipe is erected vertically so that the water is ejected straight up, the flow can be determined if the jet height (h) and the pipe diameter (d i ) are known (see Figure 8.19). As it is difficult to measure the jet height above the pipe end, this method is not very accurate and an accuracy of 10% may be expected. This method will therefore only be used to make an estimate of the flow. Table 8.16 indicates the flow [λ/s] for pipe diameters up to 300 mm and jet heights to 1 m. Figure 8.19: Dimensions required to determine the flow in vertical pipes Table 8.16: The flow [λ/s] from vertical pipes Jet height Pipe diameter ,7 3,2 3,6 3,9 4,3 4,6 4,9 5,1 5,8 6,4 7,0 7,5 8,0 8,4 9,4 10,3 11,1 11,8 12,4 10,0 12,0 13,9 15,0 16, ,5 23,

34 8.32 Irrigation Design Manual Horizontal To determine the flow rate of pipes delivering horizontally, both the horizontal distance (x) and the vertical distance (y) from the same point at the pipe end to the same point on the jet must be measured. For convenience, the distance from the upper inside edge of the pipe to a point on the top of the jet is measured (see Fig. 8.20). As in the vertical method, this method is also very inaccurate. Table 8.17 indicates the flow [λ/s] for pipe diameters of 50, 100 and 150 mm for a horizontal distance (x) of 150 mm and a vertical distance (y) varying from 6 mm to 200 mm. Figure 8.20: Dimensions required to determine flow in horizontal pipes Table 8.17: The flow [λ/s] from horizontal pipes ( x 150 mm) Vertical distance (y) Pipe diameter ,1 14,3 12,7 10,1 8,6 7,6 6,9 5,9 5,2 4,7 4,3 4,0 3,6 3,2 2,9 2,6 2,3 1,

35 Flow measurement References 1. Department of Agriculture and Fisheries. Besproeiing watermeting. Bladskrif nr Department of Environmental Affairs Handleiding vir die beplanning, ontwerp en bedryf van riviervloeimeetstasies. 3. Department of Water Affairs Besproeiing. Handleiding vir ingenieurs en tegnici. 4. Department of Agriculture ARS Flume: A computer Model for estimating flow through long-throated measuring flumes. United States. 5. FAO irrigation and drainage paper 26/ Small structures. Rome. 6. Jensen, M. E Design and operation of farm irrigation systems. The American Society of Agricultural Engineers. 7. McGraw-Hill Publishing Company Open channel hydraulics. Ven te Chow. 8. Fish River Agriculture Development Centre. Watermeting vir die Visriviervallei-besproeiingsboer. Cradock.