Design and Calibration of Submerged Open Channel Flow Measurement Structures: Part 3 - Cutthroat Flumes

Transcription

1 Uth Stte University Reports Uth Wter Reserch Lbortory Jnury 1967 Design nd Clibrtion of Submerged Open Chnnel Flow Mesurement Structures: Prt 3 - Cutthrot Flumes Gylord V. Skogerboe M. Leon Hytt Ross Ky Anderson Keith O. Eggleston Follow this nd dditionl works t: Prt of the Civil nd Environmentl Engineering Commons, nd the Wter Resource Mngement Commons Recommended Cittion Skogerboe, Gylord V.; Hytt, M. Leon; Anderson, Ross Ky; nd Eggleston, Keith O., "Design nd Clibrtion of Submerged Open Chnnel Flow Mesurement Structures: Prt 3 - Cutthrot Flumes" (1967). Reports. Pper This Report is brought to you for free nd open ccess by the Uth Wter Reserch Lbortory t DigitlCommons@USU. It hs been ccepted for inclusion in Reports by n uthorized dministrtor of DigitlCommons@USU. For more informtion, plese contct dyln.burns@usu.edu.

2 Design nd Clibrtion of Submerged Open Chnnel Flow Mesurement Structures Prt 3 CUTTHROAT FLUMES OWRR Project No. B-006-UTAH Mtching Grnt Agreement No Investigtion Period - April 1, 1965 to June 30, 1967 Prtil technicl completion report prepred for Office of Wter Resources Reserch United Sttes Deprtment of the Interior nd Uth Center for Wter Resources Reserch Uth Stte University Prepred by Gylord V. Skogerboe M. Leon Hytt Ross Ky Anderson Keith o. Eggleston Uth Wter Reserch Lbortory College of Engineering Uth Stte University Logn, Uth April 1967 Report WG31-4

3 ABSTRACT DESIGN AND CALIBRATION OF SUBMERGED OPEN CHANNEL FLOW MEASUREIUENT STRUCTURES PART 3, CUTTHROAT FLUMES Cutthrot flumes hving rectngulr or trpezoidl shpe hve been developed, nd their role in wter mesurement, long with the dvntges of their use re discussed. The dimensions nd criteri for constructing cutthrot flumes re given. The differences between free flow nd submerged flow conditions re discussed, long with the necessry criteri for determining which flow regime exists. The vlue of trnsition submergence is listed for ech of the rectngulr nd trpezoidl cutthrot flumes which were investigted in the lbortory. The free flow nlysis nd tbles re presented for the cutthrot flumes studied s re the three-dimensionl clibrtion curves which re used when submerged flow exists in the flumes. Exmples re given which illustrte the free nd submerged flow opertion. Proper instlltion nd mintennce procedures for cutthrot flumes re described, s well s techniques for mesuring flow depths which will yield stisfctory results. Skogerboe, Gylord V., M. Leon Hytt, Ross K. Anderson, nd Keith O. Eggleston. DESIGN AND CALIBRATION OF SUBMERGED OPEN CHAN NEL FLOW MEASUREMENT STRUCTURES: PART 3, CUTTHROAT FLUMES. Reserch Project Prtil Technicl Completion Report to Office of Wter Resources Reserch, Deprtment of Interior, nd Uth Center for Wter Resources Reserch. Report WG31-4, Uth Wter Reserch Lbortory, College of Engineering, Uth Stte University, Logn, Uth. April KEYWORDS - flow mesurement 'kflow mesuring flumes hydrullics hydrulic structures open-chnnel flow *subcriticl flow *submerged flow ii

4 ACKNOWLEDGMENTS The existence of this publiction is bsed on support in prt from funds provided by the United Sttes Deprtment of the Interior, Office of Wter Resources Reserch, s uthorized under the Wter Resources Reserch Act of 1964, Public Lw The project providing the informtion used in this report is prt of the progrm of the Uth Center for Wter Resources Reserch, Uth Stte University, Logn, Uth. Thnks nd pprecition for this support is here cknowledged. The coopertion nd services of the Uth Wter Reserch Lbortory were invluble in the publiction of this report. Sincere thnks re given Miss Donn Higgins for editing nd Mrs. Lind Willims for typing this mnuscript. Gylord V. Skogerboe M. Leon Hytt Ross Ky Anderson Keith O. Eggleston iii

5 TABLE OF CONTENTS Pge Approch to Study Development of Flume Dimensions of Rectngulr Cutthrot Flumes Definition of Flume Opertion Free Flow Opertion Submerged Flow Opertion Fundmentl Theory Appliction Principles Trpezoidl Cutthrot Flumes Dimensions Opertion Instlltion of Cutthrot Flumes Flume Instlltion to Insure Free Flow Flume Instlltion for Submerged Flow Mintennce of Cutthrot Flumes Summry References iv

6 Figure LIST OF FIGURES Pge 1 Rectngulr cutthrot flume Pln nd sectionl view of rectngulr cutthrot mesuring flume Illustrtion of flow conditions in rectngulr cutthrot flume Rectngulr cutthrot flume operting under free flow conditions Rectngulr cutthrot flume operting under submerged flow conditions Reltionship between 11"2 nd 11" Submerged flow clibrtion curves for 1-foot rectngulr cutthrot flume Submerged flow clibrtion curves for 1.5-foot rectngulr cutthrot flume Submerged flow clibrtion curves for 2-foot rectngulr cutthrot flume Submerged flow clibrtion curves for 2.5-foot rectngulr cutthrot flume n Submerged flow clibrtion curves for 3-foot rectngulr cutthrot flume Submerged flow clibrtion curves for 4-foot rectngulr cutthrot flume Submerged flow clibrtion curves for 5-foot rectngulr cutthrot flume Submerged flow clibrtion curves for 6-foot rectngulr cutthrot flume Pln, sectionl, nd end view of trpezoidl cutthrot mesuring flume Submerged flow clibrtion curves for V-shped or zero throt width trpezoidl cutthrot flume Submerged flow clibrtion curves for 6-inch trpezoidl cutthrot flume Submerged flow clibrtion curves for 12-inch trpezoidl cutthrot flume Reltion between flume size nd submergence for rectngulr cutthrot flumes Development of submerged flow clibrtion curves for 2.2 foot rectngulr cutthrot flume Illustrtion of the instlltion of 12-inch trpezoidl cutthrot flume to operte under free flow conditions v

7 LIST OF TABLES Tble Pge 1 Trnsition sub mergences for rectngulr cutthrot flumes Free flow clibrtion tbles for rectngulr cutthrot flumes Trnsition submergences for trpezoidl cutthrot flumes Free flow clibrtion tble for V-shped trpezoidl cutthrot flume 24 5 Free flow clibrtion tble for 6-inch trpezoidl cutthrot flume 25 6 Free flow clibrtion tble for 12-inch trpezoidl cutthrot flume -- 2& NOMENCLATURE Symbol Definition C coefficient in free flow eqution CO' 1 the dischrge intercept for prticulr submergence when h" - h; is equl to 0.1 h flow depth t specified loction in entrnce section of cutthrot flume hi> flow depth t specified loction in exit section of cutthrot flume hili minimum depth of flow in flume Q flow rte or dischrge S submergence, which is the rtio of downstrem to n upstrem depth where both depths re referenced to common elevtion Sl trnsition submergence W throt width t cutthrot flume neck " ~ submergence, S 7.3 (h - h b ) Ih m vi

8 APPROACH TO STUDY Procedure nd methods for more ccurte mesurement nd improved mngement of wter re continully being sought for better utiliztion of our wter resources. Mny devices nd structures hve been developed for mesuring wter, but mesuring flumes re one of the most widely ccepted nd used. The most common mesuring flume is the Prshll flume which is discussed in preceding report (Skogerboe, Hytt, Englnd, nd Johnson, 1967). Common to most flumes is the bsic geometry consisting of converging inlet section, throt, nd diverging outlet section. Occsionlly, the diverging outlet section is removed under free flow conditions nd the wter is llowed to jet directly from the throt section into the downstrem chnnel. This is not lwys permissible, however, becuse of possible erosion problems. In flt grdient chnnels, it my be desirble to instll flume to operte under conditions of submerged flow rther thn free flow in order to: (1) reduce energy losses, nd (2) plce the flume on the chnnel bed 10 minimize the increse in wter surfce elevtion upstrem from the flume. The purpose of the reserch effort reported herein ws to develop flume which would operte stisfctorily under both free flow nd submerged flow conditions. DEVELOPMENT OF flume Previous studies by Robinson nd Chmberlin (1960) nd Hytt (1965) indicte tht flume hving flt-bottom is stisfctory for both free flow nd submerged flow opertion. The dvntges of level flume floor, s opposed to the Prshll flume with n inclined floor in the throt nd exit sections, re: (1) it is esy to construct, (2) it cn be plced inside concrete-lined chnnel, nd (3) it cn be plced on the chnnel. bed. Ackers nd Hrrison (1963) recommend mximum convergence of 3:1 for flume inlet section. Experimentl work by the writers indicted tht this recommendtion hd nd consequently 3:1 convergence ws used in developing flt-bottomed flume. Studies regrding the length of the throt section, discussed in preceding report (Skogerboe, Hytt nd Eggleston, 1967), showed tht flow depths mesured in the exit section of the flume resulted in more ccurte submerged flow clibrtion curves thn clibrtions employing flow depth mesurements in the throt section. The wter surfce profile chnges rpidly in the throt section s compred with the exit section where the wter surfce profile is more nerly horizontl. Consequently, flow depth in the exit section of the flt-bottomed flume ws selected for mesurement. The erlier study by Hytt (1965) indicted tht when the divergence of the flume exit section exceeded 6 :1, flow seprtion would occur, nd mjor portion of the flow would dhere to one of the sidewlls. Although numerous divergences nd lengths of exit section were tested, the 6:1 divergence proved most stisfctory s blnce between flow seprtion nd fbriction costs. 1

9 Since the downstrem flow depth ws to be mesured in the exit section, there ppered to be no pprent dvntge in hving throt section. Consequently, testing ws initited with flt-bottomed flume hving only n entrnce nd n exit section. The flume performed very well. One distinct dvntge of removing the throt section ws improved flow conditions in the exit section. The converging inlet section tended to confine the flow into jet which trveled long the flume centerline, thus ssisting in the prevention of flow seprtion. The rectngulr flt-bottomed flume, which resulted from the testing progrm, is illustrted in Fig. 1. Since the flume hs no throt section (zero throt length), the flume ws given the nme "Cutthrot" by the writers. The most obvious dvntge of "cutthrot" flume is economy, since fbriction is fcilitted by flt-bottom nd removl of the throt section. Another dvntge is tht every flume size hs the sme wll lengths in both the entrnce nd exit sections, which llows the sme forms or ptterns to be used for ny flume size. The cutthrot flume cn operte either s free or submerged flow structure s indicted in this report. Submerged flow clibrtion curves nd free flow tbles re developed nd their use illustrted for the rectngulr nd trpezoidl cutthrot flumes studied. Discussion nd exmples regrding the prcticl spects of instlling, operting, nd mintining the structures re given. Fig. 1. Rectngulr cutthrot flume. 2

10 DIMENSIONS OF RECTANGULAR CUTTHROAT FLUMES The cutthrot flume consists of only converging inlet section nd diverging outlet section. Fig. 2 is pln nd sectionl view of rectngulr cutthrot flume. The one vrying dimension indicted in Fig. 2 is the flume size or throt width, W. The length of the converging nd diverging sections re the sme for ech flume size, s well s the loction of the points for upstrem depth mesurement, h, nd downstrem depth mesurement, hi>' Rectngulr cutthrot flume sizes of 1, 2, 3, 4, nd 6 feet were studied nd tested in the lbortory. Although wll height of 3 feet ws mintined for the flumes studied, the height used for ny prticulr structure would be dependent upon the stge-dischrge reltionship of the conveynce chnnel nd the desired flow conditions under which the flume would operte. The rectngulr cutthrot flumes studied in the lbortory were constructed of steel plte, but ny field structure could be constructed of wood, concrete, or ny other mteril depending on existing conditions, desired use, nd durbility. DEFINITION OF FLUME OPERATION The two most significnt flow regimes, or flow conditions, under which the flume my operte re free flow nd submerged flow. The distinguishing difference between the two is the occurrence of criticl depth, in the vicinity of the flume neck, for the free flow condition. This criticl flow control requires only the mesurement of flow depth t some loction upstrem from the point of criticl depth to obtin the free flow dischrge. Figs. 2 nd 3 show the loction selected for mesuring the upstrem depth, h, which is two-thirds the length of the converging section upstrem from the flume neck. When the flow conditions re such tht the downstrem, or tilwter, depth is rised to the extent tht the flow depths t every point through the structure become greter thn criticl depth, in chnge in the upstrem depth, then the flume is operting under submerged flow conditions. A flume operting under submerged flow requires tht two flow depths be mesured, one upstrem (h,,) nd one downstrem (hh) from the flume throt s shown in Fig. 2. The definition given to submergence, designted by S, is the rtio, often expressed s percentge, of the downstrem depth to the upstrem depth (S hh/h,,). Ofttimes, flumes designed initilly to operte under free flow conditions become submerged upon occsion, either due to unusul operting conditions downstrem or the ccumultion of moss nd/or vegettion in the chnnel. Cre lwys should be tken to note the operting condition of the flume in order to determine whether the free flow tbles or the submerged flow curves should be used. The vlue of submergence t which free flow chnges to submerged flow, or vice vers, is referred to s the trnsition submergence, symbolized by S,. At this trnsition stte, the given by the free flow tbles or eqution is exctly the sme s tht given by the submerged flow clibrtion curves or eqution, if such is known. Hence, if dischrge equtions re known for both the free nd submerged flow conditions, definite vlue of the trnsition submergence cn be obtined by setting the equtions equl to one 3

11 nother. Thus, the proper method for determining the operting conditions of flume is to compute the submergence fter mesuring h nd hu H the submergence is less thn the trnsition submergence, the flume is operting under free flow conditions. The flume is operting under submerged flow conditions when the submergence is greter thn the trnsition submergence. Stilling well for h StH ling well ~ for hb T L... T 3' 6' Converging Inlet Section Q II Diverging Outlet Section - ro h I. 2'.. I. 4.93'.. I.hb ~--~------~~ ~~~---- SECTION T-T Fig. 2. Pln nd sectionl view of rectngulr cutthrot mesuring flume.."",.. (e) ~ r-:s"z.-(b) Q Fig. 3. Illustrtion of flow conditions in rectngulr cutthrot flume. 4

12 Evlution of the lbortory dt for rectngulr cutthrot flumes rnging in size from 1 to 6 feet resulted in the trnsition submergences Tble 1. Trnsition submergences for rectngulr cutthrot flumes. Flum.e Trnsition Flum.e Trnsition Size, Subm.ergence, Size, Submergence, W S t W St If 790/. 3' 85% 1. 5' 81% % Zt 83% 51 87% Z.5 f 84% 6 ' 88% listed in Tble 1. When the submergence, hb/h", for ny given flume size exceeds the trnsition submergence given in Tble 1, the flow is subcriticl (submerged) nd the submerged flow clibrtion curves must be used to determine the dischrge. When the submergence vlue does not exceed the limit given in Tble 1, then criticl depth (free flow) occurs in the flume nd the free flow tble (Tble 2) should be used to obtin the dischrge. The difference between free flow, trnsition submergence, nd submerged flow wter surfce profiles for the cutthrot flume is illustrted in Fig. 3. The dischrge is constnt. Wter surfce profile illustrtes free flow, wheres profile b indictes the trnsition submergence condition. Both profiles nd b hve the sme upstrem depth of flow. Profile b hs Fig. 4. Rectngulr cutthrot flume operting under free flow conditions. 5

13 Fig. 5. Rectngulr cutthrot flume operting under submerged flow couditions. mximum submergence vlue for which the free flow condition cn exist in the flume. The submerged flow condition is illustrted by profile c, where n increse in the tilwter depth hs lso incresed the depth of flow upstrem from the flume. FREE FLOW OPERATION Under free flow conditions, the dischrge, Q, through cutthrot flume depends only upon the upstrem depth of flow, hu" Anlysis of the free flow dt collected in the lbortory for rectngulr cutthrot flumes resulted in the following bsic form of the free flow eqution Q Ch The vlue of C for ech size of flume my be obtined from the following eqution, C = 3.50 Wl where W is the throt width in feet. By combining Eqs. 1 nd 2, the free flow dischrge in second-feet (cis) cn be obtined for the rectngulr cutthrot flume sizes listed in Tble 1. The free flow dischrge for cutthrot flumes is listed in Tble 2 for hit vlues between 0.20 nd 2.60 feet. Exmple 1: For illustrtion of the use of Tble 2, 4-foot rectngulr cutthrot flume known to be operting free flow 6

14 Tble 2. Free flow clibrtion tbles for rectngulr cutthrot flumes. Upper Throt Width Hed h I' 1. 5' 2' 2.5' 3' 4' 5' 6' Feet Flow in cubic feet per second O I I t:'i (:'" ::: I ( o J t B I e t,. IB -; 45 O {, 38 ( zz l".5b I. 9Z l,.7o Ii t t~. 9(" O ,[ 5. ';'0 -; It) 8. (,~ O.Sf) (, 5. ~~ t, 7.3& ~.S9 O % 3. i 2 'f. 49 f" S 0.51> t l'z b 21 7 SO ') 41 O.=j ,0;.3 t; ') (,6 7

15 Tble 2 Upper Hed Feet Continued I Throt Width l' 2.5' 2' 2.5' I 3' 4' : Flow in cubic feet per second I I 5' 6' I ! O ) O o O O O O O O S' :;

16 Tble 2 Upper Hed Feet Continued I' 1. 5' 2' 2. 5' Throt Width I Flow in cubic feet per second 3' 4' 5' 6' ,80 11, , , I , ,04 10,09 12, , , , ,27 10, ,39 10, ,51 10, , , , , , , , , , , , , , , , , , , ,09 12, ,53 25, , , , , , , , , , , I 1 35, , , I ,62 17, , , ,92 14,95 18,03 24, (,

17 Tble 2 Continued Upper Throt Width Hed I h 1 ' 1. 5' 2' 2.5' 3' 4' 5' 6' Feet Flow in cubic feet per second I I I ' I L )

18 Tble 2 Conti,:!ued Upper Throt Width Hed h 1 ' 1. 5' 2' 2.5' 3' 4' 5' 6' Feet Flow in cubic feet per second , , , I , , , , , , ,27 64, , , (f, 65, , , " , ,80 44, , Of, l() (, , t) ,8(; ( ( , H \ (, ,. 'Ii' ~ S S ( S 7l I', '). 15 3'; l'i {,7 c IS 1; i Q , S ') ! 35,d I 72. (,0 2 I" ,,0 23. u K ~ I 11. ~..3 I,, S 3. S ~!-\, fp I"' () (,, , 1'.' II no lk l (I. 3 l ( ( ,,

19 Tble 2. Continued. I Upper Throt Width Hed h 1 ' 1. 5' 2' 2.5' 3' 4' 5' 6' Feet Flow in cubic feet per second i J Z , GO G (, 61. 7, 77.6(, l, ' {) I U (, I J Z i ()4.i 'I ' ' ( ( 3. ()'" , 'l '). 5(, 4,. (,'I 04.0') HO. 58 'I.24 I 12

20 nd with n upstrem depth of flow, h, equl to 1.77 feet is considered. Enter Tble 2 t the left side with vlue of h" equl to 1.77 feet, then under the column heded by throt width of four feet, observe the rte of flow which is cis. SUBMERGED FLOW OPERATION Fundmentl Theory Utilizing momentum principles, theoreticl submerged flow dischrge eqution could be developed for the rectngulr cutthrot flume. Such n eqution hs been written (Skogerboe, Hytt, nd Eggleston, 1967) for rectngulr flume ssuming uniform velocity distribution, hydrosttic pressure distribution, stedy flow, nd neglecting friction forces. The theoreticl eqution strengthens the results of dimensionl nlysis pplied to ny prticulr flume geometry. When dimensionl nlysis is pplied to submerged flow through specified flume geometry, three pi-terms re obtined. The first pi-term (lt1) is the Froude number evluted t the section of minimum flow depth, hnp The submergence, S, is the second pi-term (ltc)' The chnge in wter surfce elevtion, h" - h/), divided by the minimum flow depth, hu11 is the third pi-term ("3)' The logrithm of "2 plotted ginst "" (Fig. 6) yields the distribution of the lines of constnt submergence for the submerged flow clibrtion curves (Skogerboe, Hytt, nd Eggleston, 1967). The true distribution of the lines of constnt submergence is given by the curved line in Fig. 6 which best fits the dt, wheres, the stright line is n pproximtion of the reltionship over lrge rnge of submergence. The distribution of the lines of constnt submergence obtined from the stright line reltionship in 6 hs merit becuse of the pproximte submerged flow eqution which cn be obtined. The pproximte submerged flow eqution obtined from the stright line reltionship will usully produce resonble ccurcy for submergence vlues less thn 96 percent. The true distribution hs been used in developing submerged flow clibrtion curves for cutthrot flumes. Appliction Principles Submerged flow clibrtion curves for the rectngulr cutthrot flumes were obtined by prepring three-dimensionl plots of the prmeters describing submerged flow. Ech plot is mde on log-log pper with the dischrge, Q, s the ordinte; difference in upstrem nd downstrem depths of flow, h n - hi" s the bsciss; nd the submergence, h,/h" s the vrying prmeter. Lbortory dt were collected for rectngulr cutthrot flumes hving throt widths of 1, 2, 3, 4, nd 6 feet. The submerged flow clibrtion curves for these flumes re shown in Figs. 7, 9, 11, 12, nd 14. The clibrtion curves for the 1.5-, 2.5-, nd 5 foot flumes (Figs. 8, 10, nd 13) were obtined by interpolting between the curves developed from the collected dt. The distribution of the lines of constnt submergence follow the true distribution rther thn n pproximte distribution (Fig. 6). One incidentl point of interest is tht the slope of the lines of constnt submergence is the sme for ll the submerged flow clibrtion curves 13

21 -0,04 True -0,02 Note - True distribulion used lor cutthrot flumes, 0,0 o"----'----.l----.l j.o----' J' J'" 0' 0 ~ ci Fig. 6. Reltionship between 11' ~.nd 'l1' $' I/)... o Fig. 7. Submerged flow clibrtion curves for I-foot rectngulr cutthro flume. 14

22 (Figs. 7 through 14). The slope is 1.56, which corresponds to the power of hit in the free flow eqution (Eq. 1) for rectngulr cutthrot flumes. To obtin the dischrge under submerged flow conditions, the upstrem, h, nd downstrem, hlp depths of flow re first mesured. Next, using these depths, the submergence rtio, hb/h., is computed s is the difference in the depths, h" - h b With the two computtions completed, the proper set of clibrtion curves re selected, from which the dischrge is obtined. To illustrte the use of the submerged flow clibrtion curves, n exmple will be selected using 2-foot rectngulr cutthrot flume. Exmple 2: Assume the mesured vlues of hit nd hb in 2-foot flume re 1.94 nd 1.55 feet, respectively. The submergence rtio is computed to be 80 percent ( ) nd the difference in depths is 0.39 foot ( ). Checking Tble 1, the trnsition submergence rtio for the 2-foot flume is found to be 83 percent which is greter thn the 80 percent submergence mesured for this sitution. Hence, the flow condition is free flow nd the dischrge is obtined from Tble 2. Here, for n h" heding of 1.94 feet, the free flow dischrge is h - hb t fee t Fig. 8. Submerged flow clibrtion curves for 1.5-foot rectngulr cutthrot flume. 15

23 found to be cfs for 2-foot rectngulr cutthrot flume. Suppose now tht in the sme 2-foot flume, conditions chnge such tht h" nd hi> re mesured s 2.14 nd 1.93 feet, respectively. The submergence rtio is 90 percent nd the difference in depths is 0.21 foot. The clibrtion curve for the 2-foot flume (Fig. 9) is entered from below with n h" - hi> vlue of Then, move verticlly upwrd to the 90 percent submergence line. At this point of intersection, move horizontlly to the left nd red the dischrge s cis on the verticl scle. fii "I (.) o 2.0 l':'.2.lili.lli:.iill..l.'llli1.i:l: l1eif:l h-hb, feet 0.- Fig. 9. Submerged flow clibrtion curves for 2-foot rectngulr cutthrot flume. 16

24 30 20 '<- () 10 o Fig. 10. Submerged flow clibrtion curves for 2.5-foot rectngulr cutthrot flume. 17

25 ho - hb t fee t ;. 11. Submerged flow clibrtion curves for 3 foot rectngulr cutthrot flume. 18

26 iii ~ 0 10 I I i, h-hb, feet Fig. 12. Submerged flow clibrtion curves for 4-foot rectngulr cutthrot flume. 19

27 60 ;~--T-cT ho-hb, feet 13. Submerged flow clibrtion curves for 5-foot rectngulr cutthrot flume. 20

28 40 (j) '+ () I E=- ~ ho - hi> fee t Fig. 14. Submerged flow clibrtiou curves for 6-foot rectngulr cutthrot flume. TRAPEZOIDAL CUTTHROAT FLUMES Dimensions The trpezoidl cutthrot flume is similr to the rectngulr cutthrot flume in tht both consist of only converging inlet section nd diverging outlet section, with no throt section. 15 is pln, sectionl, nd end view of the type of trpezoidl flume investigted. In the testing progrm, only the flume width, W, ws vried with the length of the converging nd diverging sections nd the side slope kept s constnt vlue (Fig.' 15). Mesurement of the upstrem, h,,, nd downstrem, hi" depths of flow were mde t the points shown in Fig. 15. Steel plte ws used in construction, but other mterils could be used s discussed erlier in this report. Trpezoidl cutthrot flumes hving throt widths, W, of zero (Vshped), 6 inches, nd 12 inches were selected for lbortory investigtion. Development of intermedite sizes, or lrger sizes, ws not ttempted becuse of the gret diversity of possible trpezoidl geometries. To test such vriety of possible shpes ws considered beyond the resources of this study. 21

29 T L Q II PLAN 3' 6' L. Converging Diverging ] Section w ln~le~t~s_e_c_ti_o_n~ o_u_tl_et ~~ ~ ~~. Q II Ah I...1 2' 4.5' SECTION T-T.. hb END 5. Pln, sectionl, nd end view of trpezoidl cutthrot mesuring flume. 22

30 Opertion The previous discussion given to the free nd submerged flow opertion of the rectngulr cutthrot flumes pplies eqully well to the trpezoidl flumes. The rte of dischrge under the free flow condition depends only upon the upstrem depth of flow, h, wheres under submerged flow conditions, the dischrge requires the mesurement of the upstrem nd downstrem depths of flow, ho nd hi,' The trnsition from the free flow condition to the submerged flow condition occurs when chnge in the downstrem, or tilwter, depth results in n incresed upstrem flow depth. Tble 3 indictes the vlue of trnsition submergence for the trpezoidl cutthrot flumes which were studied. Tble 3. Trnsition sub mergences for trpezoidl cutthrot flumes. Flume Throt Width Zero or V -shped 6 inch 12 inch Trnsition Submergence, St 60% 76% 79% Hence, when the submergence rtio, hb/h, is less thn the vlue given in Tble 3 for prticulr trpezoidl cutthrot flume, the free flow tbles (Tbles 4, 5, nd 6) should be used, nd when ho/h" is greter thn St, the submerged flow clibrtion curves should be used for determining the dischrge. When the trpezoidl flumes re operting under free flow conditions, only the upstrem depth of flow, hn' is required for obtining the dischrge. Free flow equtions hve been developed from lbortory dt for the three trpezoidl cutthrot flumes listed in Tble 3. The free flow eqution for the V-shped flume is Q = 2.57 h For the 6-inch flume, the free flow eqution is Q = 3.98h The free flow eqution for the 12-inch flume is Q = 5.48 h Tbles 4, 5, nd 6, re the free flow clibrtion tbles corresponding to Eqs. 3, 4, nd 5, respectively. The tbles give the free flow dischrge in cfs for vlues of h" between 0.10 nd 2.09 feet. The submerged flow clibrtion curves for the trpezoidl cutthrot flumes were developed from the collected dt in the sme mnner s were the rectngulr flume curves. A three-dimensionl plot ws mde of the dischrge, Q, plotted s the ordinte; the difference in upstrem nd downstrem depths, hu - hi" plotted s the bsciss; nd the submergence, hl,/hn' plotted s the vrying prmeter. The distribution of the lines of constnt submergence is the true distribution rther thn the pproximte distribution s illustrted by the curved plot in Fig. 6. The 23 4

31 Tble 4. Free flow clibrtion tble for V~shped trpezoidl cutthrot flume. Upper Dischrge Upper Dischrge Uppe r Dischrge Upper Dischrge Upper Dischrg hed Q hed Q hed Q hed Q hed Q h cis h ds h cis h ds h cis feet feet feet feet feet O. II l J O S l O I l L ! l I O l O. 13 D O l l D l (, 0.19 O. 76 I O I O I o J G J J.42 D I O l l I. 91 I

32 Tble 5. Free flow clibrtion tble for 6-inch trpezoidl cutthrot flume. Upper Dischrge Upper Dischrge Upper Dischrge Upper Disch rge Upper Dischrge hed Q hed Q hed Q hed Q hed Q h cfs h cfs h cis h cf. h cfs feet feet feet feet feet L l O. II O l O l O O l O l I l l O l. 40 l l O l. 45 l l l l. 50 l l l l. 56 l l I l. 61 l I l I I I. 72 I I l I. II 5.03 I I I l I 95 I I l I ) S l l UL 04 O : I , t , l , S I , I. 28 6,

33 Tble 6. Free flow clibrtion tuble for 12-inch trpezoidl cutthrot flume. Upper Dischrge Upper Dischrge Upper Dischrge Upper Dischrge\ U""" r Di schr g e hed Q hed Q hed Q hed Q hed Q h cis h cfs h ds h cis h cfg fee! feet feet feet feet I I O Ib.38 O I I O. to lb.77 O I O I I l I I I 5.58 J J O. Z I l I I I I I I. 46 II. 77 I I I I I I I I I I I J J J I l & l I J I I J % I &6 I , I ! I l Z l I I I l J l I I l l I I I

34 II) '+o h hb t 0.20 feet Fig. 16. Submerged flow clibrtion curves for V-shped trpezoidl cutthrot flume. clibrtion curves developed for the V-shped, 6-inch, nd 12-inch trpezoidl cutthrot flumes re found in Figs. 16, 17, nd 18, respectively. As n illustrtive exmple of the trpezoidl cutthrot flume submerged flow clibrtion curves, the following exmple hs been selected. Exmple 3: Assume tht n h" nd h]) vlue of 1.50 feet nd 1.38 feet, respectively, re mesured in 6-inch trpezoidl cutthrot flume. The submergence rtio of 92 percent (1.38/ 1.50 = 0.92) nd the difference in depths of 0.12 foot ( = 0.12) re first computed. By first entering Tble 3, trnsition submergence of 76 percent is obtined for this prticulr flume, which is less thn the submergence rtio of 92 percent. Thus, submerged flow condition exists. Entering Fig. 17 from below with n h" - hh vlue of 0.12 foot, move verticlly upwrd until the submergence line of 92 is intersected. From this point of intersection, move horizontlly to the left nd red dischrge vlue of 8.25 cfs on the verticl scle. 27

35 Fig. 18. Submerged flow clibrtion curves for 12-inch trpezoidl cutthrot flume. 28

36 INSTALLATION OF CUTTHROAT FLUMES Any wter mesuring device must be properly instlled to yield dequte results. The first considertion prior to instlling flume is the loction or site of the structure. The flume should be plced in stright section of chnnel. If operting conditions require frequent chnging of the dischrge, the flume my be conveniently locted ner point of diversion or regulting gte. However, cre should be tken to see tht the flume is not locted too ner gte becuse of unstble or surging effects which might result from the gte opertion. After the site hs been selected for the flume, it is necessry to determine certin design criteri. The mximum quntity of wter to be mesured, the depth of flow necessry to obtin this dischrge, nd the llowble hed loss through the flume must be determined. For design purposes, the hed loss my be tken s the chnge in wter surfce elevtion between the flume entrnce nd exit. The downstrem depth of flow will remin essentilly the sme fter instlltion of the flume s it ws prior to instlltion, but the upstrem depth will increse by the mount of hed loss. The llowble increse in upstrem depth my be limited by the height of cnl bnks upstrem from the flume. Such limiting condition my require incresing the flume size, or operting the flume s submerged flow structure. Economic fctors ply deter.. mining role in the flume size selected. The following exmple is illustrtive of the instlltion fctors discussed bove. Exmple 4: Suppose the logicl rectngulr cutthrot flume size necessry to mesure mximum dischrge of 12.5 secondfeet under free flow conditions must be found. Presently, the mximum flow depth in the cnl is 0.95 foot nd the hed loss is not to exceed 3 inches (0.25 foot). Under these conditions, the mximum downstrem flow depth would be 0.95 foot nd the mximum upstrem flow depth 1.20 feet ( ). The submergence would be 79 percent (0.95 -; ). Checking Tble 1, we find tht the trnsition submergence for ll the rectngulr cutthrot flumes is equl to, or greter thn, 79 percent. Hence, nyone of the flumes could be selected. However, the trnsition submergence for the I-foot flume is 79 percent, nd cution should be used in selecting this flume size since ny future chnges in the cnl system could result in submerged flow conditions. To select the proper flume size, enter Tble 2 under 1.5-foot flume to obtin the vlue of h" corresponding to dischrge of 12.5 cfs. For this dischrge vlue, the upstrem depth is 1.74 feet which is greter thn the llowble mximum upstrem depth of 1.20 feet. Hence, the 1.5 flume will hve the cpcity to mesure the desired dischrge, but will produce too gret hed loss ( foot). Consequently, lrger flume size is necessry to. stisfy the imposed conditions. The 2- nd 2.5-foot flumes hve h vlues of bout 1.44 feet nd 1.24 feet, respectively, for dischrge of 12.5 cfs, both of which re greter thn the llowble depth of 1.20 feet. The 3-foot flume hs n upstrem depth of 1.18 feet for dischrge of 12.5 nd since this 29

37 vlue is less thn the restrictive depth of 1.20, it would be selected for use in this prticulr sitution. The 4-foot nd lrger flumes could lso be used but the economic fctors would mke their selection undesirble. Exmple 5: Suppose in the preceding exmple the present conditions re such tht plcement of 2-foot rectngulr cutthrot flume is necessity. Entering Tble 2 under ;2-foot flume, the upstrem depth which corresponds to the dischrge vlue of 12.5 cfs is bout 1.44 feet. The mximum downstrem depth of flow is given s 0.95 foot. The hed loss resulting from operting this flume under the imposed conditions is 0.49 foot ( = 0.49). The previous exmple sttes the hed loss must not exceed 3 inches, but plcing the 2-foot flume will exceed this by 0.24 foot ( ). Hence, to plce this prticulr flume into the cnl under these conditions, it will be necessry to rise the cnl bnks upstrem from the flume. The cnl bnks must be rised 0.24 foot plus whtever freebord llownce is considered desirble. As mentioned before, the only other lterntive would be the use of lrger flume which would produce resulting decrese in hed loss. Proper instlltion requires the flume be plced level in the chnnel. The flume should be ligned stright with the chnnel nd should be level longitudinlly nd lterlly. Note tht with time the tendency is for the flume to settle with the exit becoming lower thn the entrnce. For rectngulr cutthrot flume whose width, W, does not conform with the stndrd sizes listed in this report, the free flow dischrge tble or curve cn be obtined from Eqs. 1 nd 2. An exmple will illustrte the technique, Exmple 6: Assume free flow clibrtion is needed for. rectngulr cutthrot flume with width, W, of 2.20 feet. The vlue of C required in Eq. 1 cn be computed by substituting 2.20 for W in Eq. 2 C 3.50 (2.2)1. 02;; = 3.50 (2.224) Substituting 7.85 for C in Eq. 1, the free flow eqution becomes Q 7.85 h" 1.;36.7 From Eq. 7, the clibrtion tbles for the 2.2-foot flume cn be obtined. Thus, if the h" gge reding were 1.87 feet, then the dischrge, Q, could be computed. Q 7.85 (1.87) 1.;;U = 7.85 x 2.65 ::: cfs. The procedure to follow for obtining the submerged flow clibrtion curves for rectngulr cutthrot flume of width, W, is s follows. 1. Determine the throt width, W, t the flume neck. 2. Enter Fig. 19 on the left with the flume size, W, obtined in step 1 nd move horizontlly to the right cross the lines of constnt submergence. Note in Fig. 19 tht the lines of constnt submergence, up to. vlue of 88 percent, terminte on the flume size which hs corresponding vlue of trnsition submergence. 3. At the intersection of ech line of submergence, move verticlly downwrd nd obtin the C"., intercept corresponding to ech submergence. The Co'' intercept is the vlue of Q when h - hh is equl to 0.10 foot. 4. On log-log pper, enter the horizontl xis with n h" - hb vlue 30

38 Flume Size, W, feet.~ <> '" N o o '" ;:; o g '" Fig. 19. Reltion between flume size nd submergence for rectngulr cutthrot flumes. 31

39 of 0.10 nd move verticlly upwrd plotting ech C"'l s Q. List the vlue of submergence on ech plotted point. 5. Drw line with slope of 1.56 through ech plotted point to obtin complete set of clibrtion curves. The following exmple will further illustrte nd explin the bove procedure. Exmple 7: Assume now set of submerged flow clibrtion curves is desired for rectngulr cutthrot flume with width, W, of 2.20 feet. Fig. 19 is entered from the left with flume size of 2.2. Moving horizontlly to the right, the C O ' l vlues re obtined for ech submergence vlue nd re tbulted in the corner of Fig. 20. With the rnge of ordinte nd bsciss vlues obtined, comprble to those in Figs. 7 through 14, the C"'l vlues re plced on Fig. 20 by moving verticlly upwrd on the h" - hh line of The line of constnt submergence is drwn through ech C n ' l point t slope of 1.56 nd the corresponding submergence vlue is lbeled on the line. The complete fmily of prllel lines constitute the submerged flow clibrtion curves for the 2.2-foot rectngulr cutthrot flume. Mesurements my be mde in the flume by the use of stff gges or stilling wells. Only fir ccurcy is obtined from the use of stff gges. When used, stff gge should be set verticlly t the specified loction for h nd h" long the converging or diverging wll. The stff gge must be crefully referenced to the elevtion of the flume bottom. Use of stilling wells is recommended, however, for ccurcy. Stilling wells hve the dvntge of providing clm wter surfce compred with the fluctution or "bounce" of the wter surfce tht my exist within the flume. Stilling wells re lso necessry if continuous recording instruments re to be used. Under submerged flow conditions, two stilling wells plced djcent to ech other re very desirble nd fcilitte the use of double hed recording instrument for obtining continuous record with time of h" nd h b Flume Instlltion to Insure Free Flow If circumstnces llow, it is preferble to hve flow mesuring device operte under free flow conditions. The obvious dvntge is tht only n upstrem flow depth need be mesured to determine the dischrge. The procedure to follow for instlling cutthrot flume to operte under free flow conditions is listed below. 1. Ascertin the mximum flow rte to be mesured. 2. At the site selected for instlling the flume, locte the high wter line on the- cnl bnk nd determine the mximum depth of flow. 3. Using the free flow dischrge tbles (Tbles 2, 4, 5, nd 6), select the proper depth of wter tht corresponds to the mximum dischrge cpcity of the cnl. 4. Plce the floor of the flume t depth which does not exceed the trnsition submergence multiplied by htl (St x h"j below the high wter 32

40 line (Fig. 21). Generlly, the flume bottom should be plced s high in the cnl s grde nd other conditions permit to insure free flow. Exmple 8: The 12-inch trpezoidl flume shown in Fig. 21 hs trnsition submergence of 79 percent. The mximum dischrge in the cnl is 20 cfs, which for free flow conditions corresponds to n h" vlue of 1.90 feet. Multiplying h (1.90) by the trnsition submergence (0.79), gives depth to the flume floor of 1.50 feet (1.90 x 0.79 = 1.50). Therefore, the flume crest should be set no lower thn 1.50 feet below the en -u o ' h-hbl feet Fig. 20. Developmen.t of submerged flow clibrtion curves for 2.2-foot rectngulr cutthrot flumes. 33

41 originl mximum wter surfce (Fig. 21) tht existed prior to instlling the flume. The loss of hed through the structure will be the difference between 1.90 feet nd 1.50 feet, which is 0040 foot, s shown in Fig. 21. A lrger flume cn be used if the hed loss is too gret. Mximum wter surfce fter flume instlltion Mximum wter surfce before flume instlltion 1.50' ~--~----~ Originl cnol bottom Fig. 21. Illustrtion of the instlltion of 12-inch trpezoidl cutthrot flume to operte under free flow conditions. Flume Instlltion for Submerged Flow The existence of certin conditions, such s insufficient grde or the growth of moss nd vegettion, sometimes mkes it impossible or imprcticl to instll flume to operte under free flow conditions. Where such situtions exist, flume my be set in the cnl to operte under submerged flow conditions. The principl dvntge of submerged flow opertion is the smller hed loss which occurs in the flume s compred with free flow. This reduction in hed loss my men tht the cnl bnks upstrem from the flume do not hve to be rised to enble the sme mximum flow cpcity in the cnl tht existed prior to the instlltion of the flume. When the flt-bottomed cutthrot,flumes re instlled to operte under submerged flow conditions, the flume floor my be plced level on the cnl bottom. This plcement will llow quicker dringe of the cnl section upstrem from the flume, nd reduced seepge losses upstrem from the flume, prticulrly for the flow rtes which re less thn the mximum dischrge. The following is illustrtive of the procedure to follow in plcing cutthrot flume to operte under submerged flow conditions. 1. Estblish the mximum flow rte to be mesured. 2. On the cnl bnk, where the flume is to be instlled, locte the high wter line to determine the mximum flow depth. 3. Giving considertion to the mount of free-bord in the cnl t mximum dischrge nd mximum flow depth, determine how much higher the wter surfce cn be rised in the cnl upstrem from the flume loction. 4. Select the required size of flume from the submerged flow clibrtion curves by tril nd error. With the floor of the flume being plced t essentilly the sme elevtion s the bottom of the cnl, the mximum depth of flow (item 2) becomes hll1 nd the dditionl mount tht the wter surfce in the cnl cn be rised (item 3), becomes h" - h". Using this informtion, the submergence, h"/h,,, cn be computed. Knowing 34

42 h" hh nd hb/h.., the flume size cn be selected from the submerged flow clibrtion curves. The tril nd error procedure for selecting the size of flume cn be illustrted with the following exmple. Exmple 9: The site selected for rectngulr cutthrot flume is cnl with mximum dischrge of 28 cfs. The mximum depth of wter in the cnl corresponding to this flow rte is 1.8 feet. With the mount of existing freebord in the cnl, it is felt tht the wter surfce should not be rised more thn 0.2 foot, thereby resulting in mximum flow depth of 2.0 feet ( = 2.0) upstrem from the flume fter instlltion. Therefore, for purposes of selecting the flume size, hb = 1.8 feet h.. = 2.0 feet h.. ~ hb = 0.20 foot hb/h.. = 1.8/ = 90% As beginning point, enter the submerged flow clibrtion curves of 2-foot rectngulr cutthrot flume (Fig. 9). With the h.. - hh vlue of 0.20 foot, move verticlly to the submergence line of 90 percent, nd then red the dischrge to the left s 20.1 cfs. Since this flow rte (20.1 cfs) is less thn the mximum flow rte (28 cis), lrger flume is required. Entering the submerged flow clibrtion curves for 2.5-foot rectngulr cutthrot flume (Fig. 10) with h" - hb = 0.20 foot, move verticlly to the 90 percent submergence line, nd red the dischrge s 26.5 cis. Agin, the flow rte is less thn the design mximum flow rte of 28 cis, nd lrger cutthrot flume is required. Entering the submerged flow clibrtion curves for 3-foot rectngulr cutthrot flume (Fig. 11) with h.. - hh = 0.20 foot, move verticlly to the 90 percent submergence line, nd red the dischrge s 32.0 cfs. Since this flow rte (32.0 cis) is lrger thn the mximum flow rte in the cnl (28 cis), 3-foot rectngulr cutthrot flume my be used. Exmple 10: Suppose trpezoidl cutthrot flume were desired for plcement in the cnl insted of the rectngulr flume. The sme conditions s given in Exmple 9 exist. The solution to this problem is found by entering submerged flow clibrtion curves for the 12-inch trpezoidl cutthrot flume (Fig. 15) with h" - hh 0.20 foot. Move verticlly to the 90 percent submergence line nd then red the dischrge to the left s 20.7 cfs. This flow rte (20.7 cfs) is less thn the mximum flow rte expected in the cnl (28 cis), so lrger trpezoidl cutthrot flume would be required for this sitution. Since no clibrtion curves re vilble for lrger trpezoidl cutthrot flumes, plcement of the trpezoidl flume would be impossible unless the existing design conditions were ltered in some wy or testing ws conducted on lrger trpezoidl flumes. Worthy of note, 12-inch trpezoidl cutthrot flume hs dischrge cpcity greter thn the 2.0-foot rectngulr cutthrot flume (20.7 cfs s opposed to 20.1 cfs) for the sme given set of conditions. 35