7.4 Parshall flumes Description

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1 measuring ha will be in a zone of flow separation. As already mentioned in Section 7.2.3, the ratios b,/b, and bjl, are also expected to influence the head-discharge relationship. Bennett (1 972) calibrated a number of cutthroat flumes having other overall lengths than m. He reported large scale effects between geometrically identical cutthroat flumes, each of them having sufficiently large dimensions (b, ranged from 0.05 to m). Those scale effects were also mentioned by Eggleston (1967), Skogerboe and Hyatt (1969), and Skogerboe, Bennett, and Walker (1972). In all cases, however, the reported large scale effects are attributed to the improper procedure of comparing measurements with extrapolated relations. As a consequence of the foregoing, no head-discharge relations of cutthroat flumes are given here. Because of their complex hydraulic behaviour, the use of cutthroat flumes is not recommended by the present writers. 7.4 Parshall flumes Description Parshall flumes are calibrated devices for the measurement of water in open channels. They were developed by Parshall (1 922) after whom the device was named. 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. Because of this unconventional design, the control section of the flume is not situated in the throat but near the end of the level crest in the converging section. The modular limit of the Parshall flume is lower than that of the other long-throated flumes described in Section 7.1. In deviation from the general rule for long-throated flumes where the upstream head must be measured in the approach channel, Parshall flumes are calibrated against a piezometric head, ha, measured at a prescribed location in the converging section. The downstream piezometric head h, is measured in the throat. This typical American practice is also used in the cutthroat and H-flumes. Parshall flumes were developed in various sizes, the dimensions of which are given in Table 7.3. Care must be taken to construct the flumes exactly in accordance with the structural dimensions given for each of the 22 flumes, because the flumes are not hydraulic scale models of each other. Since throat length and throat bottom slope remain constant for series of flumes while other dimensions are varied, each of the 22 flumes is an entirely different device. For example, it cannot be assumed that a dimension in the 12-ft flume will be three times the corresponding dimension in the 4-ft flume. On the basis of throat width, Parshall flumes have been some what arbitrarily classified into three main groups for the convenience of discussing them, selecting sizes, and determining discharges. These groups are very small for 1 -, 2-, and 3-in flumes, small for 6-in through 8-ft flumes and large for IO-ft up to 50-ft flumes (USBR 1971). 224

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3 Very small flumes (1, 2, and 3 ) The discharge capacity of the very small flumes ranges from 0.09 I/s to 32 I/s. The capacity of each flume overlaps that of the next size by about one-half the discharge range (see Table 7.4). The flumes must be carefully constructed. The exact dimensions of each flume are listed in Table 7.3. The maximum tolerance on the throat width b, equals m. The relatively deep and narrow throat section causes turbulence and makes the h, gauge difficult to read in the very small flumes. Consequently, an h,-gauge, located near the downstream end of the diverging section of the flume is added. Under submerged flow conditions, this gauge may be read instead of the h,-gauge. The h, readings are converted to h, readings by using a graph, as will be explained in Section 7.4.3, and the converted h, readings are then used to determine the discharge. Small flumes (6,9, I, I, 2 up to 8 ) The discharge capacity of the small flumes ranges from m3/s to 3.95 m3/s. The capacity of each size of flume considerably overlaps that of the next size. The length of the side wall of the converging section, A, of the flumes with 1 up to 8 throat width is in metres: b, A = (7-3) where b, is the throat width in metres. The piezometer tap forsthe upstream head, h,, is located in one of the converging walls a distance of a = 3 A upstream from the end of the horizontal crest (see Figure 7.9). The location of the piezometer tap for the downstream head, h,, is the same in all the small flumes, being 51 mm (X = 2 inch) upstream from the low point in the sloping throat floor and 76 mm (Y = 3 inch) above it. The exact dimensions of each size of flume are listed in Table 7.3. Large flumes (1 O up to 50 ) The discharge capacity of the large flumes ranges from O. 16 m3/s to m3/s. The capacity of each size of flume considerably overlaps that of the next size. The axial length of the converging section is considerably longer than it is in the small flumes to obtain an adequately smooth flow pattern in the upstream part of the structure. The measuring station for the upstream head, ha, however, is maintained at a = b,/ m upstream from the end of the horizontal crest. The location of the piezometer tap for the downstream head, h,, is the same in all the large flumes, being 305 mm (12 in) upstream from the floor at the downstream edge of the throat and 229 mm (9 in) above it. The exact dimensions of each size of flume are listed in Table 7.3. All flumes must be carefully constructed to the dimensions listed, and careful levelling is necessary in both longitudinal and transverse directions if the standard discharge table is to be used. When gauge zeros are established, they should be set so that the ha-, hb-, and h,-gauges give the depth of water above the level crest - not the depths above pressure taps. 226

4 surface, S surface FF SECTION A-A converging throat diverging section section section 'I - I III- i-. A Figure 7.9 Parshall flume dimensions If the Parshall flume is never to be operated above the 0.60 submergence limit, there is no need to construct the portion downstream of the throat. The truncated Parshall flume (without diverging section) has the same modular flow characteristics as the standard flume. The truncated flume is sometimes referred to as the 'Montana flume' Evaluation of discharge The upstream head-discharge (ha-q) relationship of Parshall flume of various sizes, as calibrated empirically, is represented by an equation, having the form Q = Kh," (7-4) where K denotes a dimensional factor which is a function of the throat width. The power u varies between and Values of K and u for each size of flume are given in Table 7.4. In the listed equations Q is the modular discharge in m3/s, and ha is the upstream gauge reading in metres. The flumes cover a range of discharges from 0.09 l/s to m3/s and have overlap- 227

5 ping capacities to facilitate the selection of a suitable size. Each of the flumes listed in Table 7.4 is a standard device and has been calibrated for the range of discharges shown in the table. Detailed information on the modular discharge for each size- of flume as a function of h, are presented in the Tables 7.5 to 7.1 I. Table 7.4 Discharge characteristics of Parshall flumes Throat Discharge range Equation Head range Modular width b, in m3/s x IOT3 Q = K hau in metres limit in feet or inches minimum maximum (Q in m3/s) minimum maximum hb/ha 1" 2" 3" 6 9" hal." hal." ha1." ha"" I' 1 ' 6 2' 3' 4' 5' 6' 7' 8' I hal.60' in m3/s 10 12' 15' 20' 25' ' hal hal ha' hal O ,

6 Table 7.5 Free-flow discharge through 1 Parshall measuring flume in I/s computed from the formula Q = hal.55 Head ha (ml,000.o0 I.O02.O03.O04,005,006.O07.O08,009.o I o O O o O O os O I I I I I I I I I Table 7.6 Free-flow discharge through 2 Parshall mesuring flume in l/s computed from the formula Q = Head ha (ml,000.ooi.o02.o03.o04.o05.o06.o07.o08.o09.o 1.o O O o O O7 I.96.O O I I I I I I I I I I I.O I.35 I I I o I I O I I o I I.so I

7 Table 7.7 Free-flow discharge through 3" Parshall measuring flume in I/s computed from the formula Q = ha'.550 Upperhead ha (d.o00.o01.o02.o03.o04.o05.o06.o07.o08.o09.o3.o4.o5.o6.o7.o8.o9.io.i I.12.I3.I I7.I I I I I I I O2 1.o2 1 s o I , O o

8 Table 7.8 Free-flow discharge through 6 Parshall measuring flume in I/s computed from the formula Q = ha'.580 Upperhead ha (m),000.o01,002.o03,004,005,006,007.o08.o09.o3.o4.o5.o6.o7.o8.o9.10.i 1.I2.I3.14.I5.I6.I7.I I I I I I I I 58. I SS.! I I I I

9 Table 7.9 Free-flow discharge through 9 Parshall measuring flume in I/s computed from the formula Q = Upper- head ha ( 4.O00.O0 1.O02.O03,004.O05.O06.O07.O08.O09.O3.O4.o5.O6.O7.O8.O9.IO.II.I2.I3.14.I5.I I so.si I I I I I I

10 Table 7.10 Free-flow discharge through Parshall measuring flumes 1-to-8 foot size in I/s computed from the formulae as shown in Table 7.4 Upper- Discharge in I/s for flumes of various throat widths head ha (") feet feet feet feet feet feet feet feet feet I O I I I , I I02 I04 I06 IO8 I10 I12 I I4 I I I22 I24 I26 I I34 I I40 I I46 I I I I

11 Table 7.10 continued Upper- head ha (" I 8 Discharge in I/s for flumes of various throat widths feet feet feet feet feet feet feet feet feet I66 I68 I70 I I I84 I I I I I I I I I I I I 329. I O I I I I I.o I 560. I

12 Table 7.10 continued Upper- Discharge in l/s for flumes of various throat widths head h, (" feet feet feet feet feet feet feet feet feet I I I I 256. I I I I I I I 897. I I I I048 I069 I090 IIII 1 I33 I I I I98 I220 I242 I I I I I I52 I I I I I I57 I I I I I070 I088 1 IO7 1 I26 I145 I I64 I I84 I I I274 I299 I I506 I532 I559 I I I I I I I 820. I 832. I I I068 I084 I I66 I I83 I I250 I267 I284 I I I342 I I I I508 I I572 I I659 I520 I I I I767 I I I948 I I779 I

13 Table 7.10 continued Upper- Discharge in I/s for flumes of various throat widths head ha (") feet feet feet feet feet feet feet feet feet I I I I007 I I I26 1 I39 1 I I I94 I I249 I I320 I I I I I720 I I703 I725 I748 I I I I I

14 Table 7.1 I Free-flow discharge through Parshall measuring flumes IO to 50 feet size in m3/s. Computed from the formulae as shown in Table 7.4 Upper- Discharge per m3/s for flumes of various throat widths head ha (") feet feet feet feet feet feet feet feet O0 105 I IO I I I50 I55 I I o. I58 O. 173 O I I I.o I.O58 I.O I.266 I I I.65 I.69 o O3 1.O6 1.O I.26 I.29 I.33 I.36 I I I I I I.92 I O4 1.O I I I.90 I I.O I.78 I.83 I I o0 I.o ' I I O3 I.O I I s o 1.57 I.63 I I.90 I o2 1.O I O I I I 237

15 Table 7. I 1 continued Upper- head h, Discharge in m3/s for flumes of various throat widths (" feet feet feet feet feet feet feet feet I I I I I I I

16 Table continued Upper- Discharge in m3/s for flumes of various throat widths head ha (" feet feet feet feet feet feet feet feet O00 I010 I I I Ill I I40 I150 I I60 I I70 I180 I I90 I I230 I I I I I390 I I I I490 I I I I I I I I I I I I I ' I

17 Table 7. I 1 continued Upper- Discharge in m3/s for flumes of various throat widths head ha (") feet feet feet feet feet feet feet feet I I660 I I I 29. I I I I I I I I I I I I I

18 7.4.3 Submerged flow When the ratio of gauge reading h, to ha exceeds the limits of 0.60 for 3-, 6-, and 9-in flumes, 0.70 for 1- to 8-ft flumes and 0.80 for 10- to 50-ft flumes, the modular flume discharge is reduced due to submergence. The non-modular discharge of Parshall flumes equals Qs = Q-QE (7-5) where Q equals the modular discharge (Tables 7.5 to 7.11) and QE is the reduction on the modular discharge due to submergence. The diagrams in Figures 7.10 to 7.16 give the corrections, QE, for submergence for Parshall flumes of various sizes. The correction for the 1-ft flume is made applicable to the 1.5-ft up to 8-ft flumes by multiplying the correction QE for the I-ft flume by the factor given below for the particular size of the flume in use. Size of flume correction b, in ft b,inm factor I S I o 1.4 I Similarly, the correction for the 10-ft flumes is made applicable to the larger flumes by multiplying the correction for the 10-ft flume by the factor given below for the particular flume in use. Size of flume correction b, in ft b,in m factor IO I.o If the size and elevation of the flume cannot be selected to permit modular-flow operation, the submergence ratio h,/h, should be kept below the practical limit of 0.90, 24 1

19 LPSTREAM HEAD ha in metres Figure 7.10 Discharge correction for submerged flow; 1 Parshall flume CORRECTKM 0. in L h Figure 7.1 I Discharge correction for submerged flow; 2 Parshall flume 242

20 UPSTREAM HEAD ho in metres 100.?O.so O7 M.O3.O1 DI O.? ao Figure 7.12 Discharge correction for submerged flow; 3" Parshall flume CORRECTION OE in L/s UPSTREAM HEAD h.in <O0.I O ?O.lo.O7 05.O3 O a o CORRECTION O, in L/s Figure 7.13 Discharge correction for submerged flow; 6 Parshall flume 243

21 UPSTREAM HEAD ha in metres too io.ao.lo 07 B.o3.oa Q. R R W L FLUME.o a ? a i s 7 10 ao io so 70 im CORRECTIOC( 0. in L/S Figure 7.14 Discharge correction for submerged flow; 9 Parshall flume Figure 7.15 Discharge correction for submerged flow; I Parshall flume, correction QE (m3/s) 244

22 CORRECTON in mh Figure 7. I6 Diagram for determining correction to be subtracted from free-discharge flow to obtain submerged flow discharge through 10 Parshall flumes since the flume ceases to be a measuring device if submergence exceeds this limit. It is recommended to use a long-throated flume (Section 7.1) instead of a non-modular Parshall flume. As mentioned, turbulence in the relatively deep and narrow throat of the very small flumes makes the h,-gauge difficult to read. If an h,-gauge is used under submerged flow conditions, the h,-readings should be converted to h,-readings with the aid of Figure 7.17, and the converted h,-values are then used to determine the submerged discharge with the aid of Figures 7.10 to Accuracy of discharge measurement The error in the modular discharge read from the Tables 7.5 to is expected to be about 3%. Under submerged flow conditions the error in the discharge becomes greater, until at 90% submergence the flume ceases to be a measuring device. The method by which this discharge error is to be combined with errors in h,, h,, and the flume dimensions are shown in Annex Loss of head through the flume The size and elevation of the crest of the flume depend on the available loss of head through the flume Ah( N AH). Since for the Parshall flume h, and h, are measured at rather arbitrary locations, the loss of head through the flume Ah is not equal to 245

23 .- o. 3( OX o 10 O O o v HEAO (metres) Figure 7.17 Relationship of h, and hb gauges for I", than 50 percent (after Parshall 1953) 2" and 3" Parshall flumes for submergences greater Figure 7.18 Section of Parshall flume the difference between ha and hb but has a greater value (Figure 7.18). The head loss Ah can be determined from the diagrams in Figures 7.19 and 7.20 for small and large flumes. For very small flumes no data on Ah are available Limits of application The limits of application of the Parshall measuring flumes essential for reasonable accuracy are: a. Each type of flume should be constructed exactly to the dimensions listed in Table, 7.3; 246

24 b. The flume should be carefully levelled in both longitudinal and transverse directions; c. The practical range of heads h, for each type of flume as listed in Table 7.4 is recommended as a limit on h9; d. The submergence ratio h,/h,should not exceed to 8' F SH4LL FL PERCENTAGE OF SUBMERGEN( 4EAD LOSS C AH THROUGH FLUME in metres L 0.10 o O Figure 7.19 Head-loss through Parshall flumes. I' up to 8' Parshall flumes 247