Liu, Henry, 1936-

Robinson, A. R. (August Robert), 1921-

English

Robinson, A. R. (August Robert), 1921-, author

Liu, Henry, 1936-, author

Colorado State University, publisher

Mountain Scholar (Digital Collections of Colorado and Wyoming)

-rA 1 c~ e,£1?~3.- LI j COPY 2 JI == DISCUSSION of "UNIFICATION OF PARSHALL FLUME DATA" by A. R. Robinson and Henry Liu AUG 16 '71 fQOl'~i~ &tl'.Ua.,ti iWu CER62ARR21 b;:;., (,,l ,f R ~ I tiRJ-6fo ~-S~6 . :. f" DISCUSSION of ., fU COPY "UNIFICATION OF PARSHALL FLUME by DATA"!_/ A. R. Robinson and Henry Liu 21 CER62ARR21 Published in t he Journal of the Irrigation and Drainage Division, Pr' oceedings of the American Society of Civil Engineers, Vol. 87, No . IR4, DecerLber, 196 1, Paper No. 13. Agricultural Engineer, Northern Plains Branch Soil and \ 'Vater Conservation Research Division, Agricultural Research Service and Colorado Agriculturcl Experiment Station; and Graduate Assistant, Civil Engineering Depart-ment, Colorado State University, Fort Collins, Colorado. 11 1111 1 H!llll!lllll HI !Ill U18401 0593550 / ,, I I DISCUSSION of "UNIF ICATION OF PARSHALL FLUIVIE DATA"}./ by A. R. Robinson and Henry Liu Y The paper by Mr. Davis represents a contribution to the understanding of the o Jeration of the Parshall Measuring :Flume. The dimensionless approach in the development of the unified equation is unique and t he excellent agreement with existing data for all sizes of Parshall flumes is gratifying. However, it should be pointed out that equation 16 is a semi-empirical equation since experimental data has been used to deter mine the constants . Published in t he Journal of the Irrigation and Drainage Division, Proceedin,,s of t he American Society of Civil Engineers, Vol. 87, No. IR4, December, 19 61 , Paper No. 13. Agricultural E ngineer, Northern P l ains Branch, Soil and \\'ater Conservation Research Divis ion, Agricultur al Research Service and Colorado Agricultural Experiment Station; and Graduate Assistant, Civil E n :rineering D~partment. Colorado State Uni-versity, Fort Collins, Colorado. :.. - I z The general form of the equation results from use of the energy and continuity equations be t ween points 1 and 2 . The general form of equation ( 1) and the specific form of equation ( 9) also results from the energy a..'1d continuity relationships. Equation ( 9) in its broadest sens,., also requires either the assum ption that ( 41) in the derivation or the actual relationship between y 1 and Yz • As M r. Davis has pointed out critical depth occurs in the contra ction section upstream from the throat section. This makes it difficult to determine the location and magnitude of critical depth. Using the energy relationship . the development of equation (9) will show t hat t he e xp onent of y 1 should be 1. 5 . From Table 1 - - -the values of n are always different than 1. 5 which m eans tha t K p is a function of depth y1 for a g iven size of flum e. For the 6-inch flume. so that 1. 58 Q= 4.12 b y 1 1/2 = K g p 0.08 KP = O. 72 8 Yt 1. 50 b Y1 { 42) ( 43} L Figure 2 is actually the relationship between KP and y 1 for different sizes of flumes . In other words , an equation similar to eq. 43 exis ts for each size of flume . KP is also a function o! the throat width b as shown by the displacement of each curve in figure 2. 3 An exam ination of T able 1 and figure 2 raised a question as to the validity of t he original calibration data. Since the sidewall angle (J as well as the drop-down angle <f, are constant for all sizes of flume s , one would e =-..-pect a definite trend in t he values o! K~ and n for the different flumes because of geometric simila rity . .... This should be definitely true for tl e "foot" flum es and should apply also !or t he "inch'' ones despite the s light difference in geometrical relationships . A family of curves possibl yW]~re~s~z __ n slope ---with increased throat width would be expected. Since equa tion 16 has been developed for flumes with constant contraction and drop-dovm angles it should not be applied to those with dif e r ent angl es . Experimental verification ls needed to det e r mine the effe ct of changing t he sidewall anel e . \Vith equation· 16, the allowable change of dilnensions from that of the s t andard ones are throat width b and gage location X 1 only . L! . - I . , , 4 -.-Actually the close fit of eq. 16 to the published data for the Parshall flume i s not surprising in view of the relatively small spread in values of Ke and n as shown in Table 1. An equation of the form (44) can be used for flumes up to 8 feet with deviation only slightly greater than those given in eq. 16. The importance of equation 16 lies in the inclusion of the variable distances X and y in the discharge formula . V:ith this relationship, the point of measuring upstream head can be changed frorr1 the standard one and a nevi rating t able determined. It is hardly foreseeable t hat intermediate sizes of Parshall flumes, other than those now in published literature, are needed. There is a probable need for flumes in excess of the l argest size {50 feet) which is presently available . Equation 1 G applies. only to the free flow condition v.ith the flow passing through critical depth within the flume . A rigorous equation for flow under submerged conditions does not presently exist. - l I .. ... I I I I 5 Instead, empirical r elationships using plots are utilized to determine the flow under these conditions. Special care should be used in installing the flumes so that the free fl.ow condition exists for most or the flows. The elevation of the flume above the bottom of the channel must be set so that there is a subn1ergence of less than 50 percent for the "inch" flumes and 60 percent for the "foot" flumes. The increase in elevation of the crest will raise the water surface upstream and restrict the . use of Parshall flumes in channels with very flat slopes. Tests at Colorado State University by the Agricultural Research Service have sho wn that trapezoidal measuring flumes are at times superior in operation to the Venturi" or Parshall type flumes. Advantages which were noted include: 1) Trapezoidal flumes operate under higher degrees of submergence tha n will the rectangular flume without corrections being necessary to the standard rating. 2) Tlie-t:rapezoidal shape fits the common canal section more closely ~han does the rectangular flume. For the lined section this simplifies the transition design and construction. - I ~-.-J - ' , I . .. 3) A large range of flows can be measured with a relatively small change in depth thus minimizing the amount of freeboard needed on the canal. ·s . ! 

Discussion of Unification of Parshall flume data

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Discussion of Unification of Parshall flume data

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