Parshall Flume Discharge Relation under Free Flow Condition

Transcription

1 Journal omepage: ttp:// INTERNATIONAL JOURNAL OF ADVANCED RESEARCH RESEARCH ARTICLE Parsall Flume Discarge Relation under Free Flow Condition 1 Jalam Sing, 2 S.K.Mittal, and 3 H.L.Tiwari 1 PG Scolar, Civil Engineering, MANIT, Bopal (M.P.), 2 Professor, Civil Engineering, MANIT, Bopal (M.P.), 3 Asst. Professor, Civil Engineering, MANIT, Bopal (M.P.) Manuscript Info Manuscript History: Received: 15 May 2014 Final Accepted: 22 June 2014 Publised Online: July 2014 Key words: Flumes, Water measurement, Parsall Flume, Troat widt, Free flow, MATLAB Abstract Parsall flumes are well accepted and extensively used for management of water used in irrigation. In te present study experimental work as been carried out on Parsall flumes aving troat widt of m, m, m and m under free flow condition. Coefficient of Parsall flume (K) and exponent (n) were determined troug MATLAB programming and a unique discarge rating equation as been developed for Parsall flumes. Tis equation is simple and can be applied for field condition. *Corresponding Autor Jalam Sing Copy Rigt, IJAR, 2014,. All rigts reserved. Introduction One of te important problems in irrigation system is measurement of irrigation water tat flows in small cannels. Several devices ave been used for measuring irrigation water including weir, Venturi flume, Cuttroat flume, Parsall flumes, etc. However, Parsall flume is one of te effective flow measuring devices for small irrigation cannels. Parsall flumes can measure discarges wit comparatively small ead loss wit low ead tan weirs. Tere is one more advantage of Parsall flume is tat it can operate successfully wit sediment laden flow. A Parsall flume consists of a converging section, a troat section and diverging section [10]. Te crest of te troat section is tilted downstream. In oter words, tere is a sill between te orizontal crest, converging section and te crest of te troat section. Fig. 1 depicts te scematic diagram of a Parsall flume. Upstream ead () was measured at specific location (Fig.1). Under free-flow condition, te flow at on upstream division will be subcritical wile it becomes critical at around te troat and finally may become supercritical at te downstream portion of te flume. Hence for a Parsall flume, a unique relation must be present between te discarge and te ead causing flow. Calibration of te flume in field is difficult in most of te cases. Terefore it is required to develop a relationsip between ead and discarge to calibrate flumes in te field. In 1917, Cone [6] developed a flume wic is working on Venturi principle of flow applied in open cannel and known as Venturi flume. He carried out experimental work in te small flumes and resulted wit tat te Venturi flume seems to fulfil te conditions of being trouble free from sand, silt, or floating tras and requires small loss of ead for making te measurement. In 1928, Parsall [10] modify te Venturi flume by reducing te angle of convergence and divergence section, providing depression on troat section towards diverging section along wit increase lengt of troat. In is study e tested Parsall flumes varying 1 foot to 8 feet. Parsall express discarge relation for free flow condition by following expression [10]. n Q J H (1) 906

2 Wit J = 4W and n = 1.55 W , tus te equation (1) is written as follows Q= 4WHa W (2) In equation (2), Q is te discarge in ft 3 /s, W is te troat widt in feet and Ha is te upstream ead measured at 2/3 of te convergence section in feet. He found tat Parsall flume is working efficiently and ead loss is four times lesser tan weir. In 1967, Skogerboe et al. [12] studied te parameters wic describe submergence in flow measuring flumes and it was developed by a combination of dimensional analysis. Validity of te parameters was verified by te teoretical submerged flow equation developed from momentum relationsips. In 1990, Abt and Staker [1] attempted experiment for a 7.62-cm Parsall flume in a cannel and measure flow rates wit lateral flume crest slopes of 0, 3.6, 6.5, 9.0, 13.3, -3.8, -4.8, -7.2, and -11.8%. Te results of tis study sowed tat te Parsall flume as error approximately 7% at a lateral slope of ±10%. In 1994, Blaisdell [3] conducted an experiment wit different size of Parsall flumes and analysis of results wit Parsall s experiment data was carried out. Study resulted wit conclusion tat equation given by Parsall and tese investigators ave same accuracy witin practical limit. In 2009, Tornton et al. [13] conducted an experiment for 15 different Parsall Flume configurations. Tey found in tis study tat single Parsall flume can be used to measure flow witin ±5% accuracy for bot supercritical and subcritical flow regimes for a specified range of flows. A single relation between discarge and upstream ead is not available in literature. Te objective of present study is to develop a single relation between discarge and upstream ead for different troat widt Parsall flumes under free flow condition. Wit tis objectives experiment work was carried out on four Parsall flumes aving troat widt of m, m, m and m. MATERIAL AND METHODS In present study, four different sizes of Parsall flumes aving troat widt of m, m, m and m were used. Te dimensions of Parsall flume used in tis study are given in Table 1. Te flumes were installed in a flat bed recirculatary rectangular cannel aving a size of 9.45 m 0.60 m 0.55 m at Fluid Mecanics Laboratory of Maulana Azad National Institute of Tecnology, Bopal. Fig.2 depicts te scematic diagram of experimental setup. It sows tat Parsall flumes were installed in a rectangular cannel. Te water supply was done by a centrifugal pump to te cannel wic delivered water from sump to cannel. Te eads at te upstream location was measured by a vernier type pointer gauge wit an accuracy of ±1 mm and velocity was measured using Prandtl Pitot tube. Te discarge is calculated by velocity area metod. Te values of measured eads and discarges are given in Appendix A. In free-flow condition, discarge troug Parsall flume depends on upstream ead at a specific position (Fig.1) of te Parsall flume. Hence, discarge can be expressed as: Q f (, W, g) (3) Q C 2 g W n (4) d Q K n were ( K Cd 2 g W ) (5) Were Q is te discarge troug Parsall flume, W is te troat widt of te Parsall flume, K is te coefficient of Parsall flume wic is te function of troat widt, is te upstream ead measured at 2/3 of convergence section, n is te exponent of and g is acceleration due to gravity. 907

3 Equation (5) can be normalized by taking logaritmic bot sides. Log Q Log ( K n ) (6) Log 10 Q Log K n Log (7) If Log Q =Y, Log K = A and Log = X tan Equation (7) can be written as Y A n X (8) DISCHARGE RELATIONSHIP FOR SMALL PARSHALL FLUMES Observations for discarges and eads on four Parsall Flume of different sizes are made. All 37 observations are given in Appendix A. Regression analyses for all tese observations were performed for matematical relations given by equation (8). Te values of coefficients K, exponent n and coefficient of determination R 2 for all tese equations are given in Table 2. Wit tese values equation (5) can be written for different flume as: For m Parsall flume, For m Parsall flume, For m Parsall flume, For m Parsall flume Q r (9) Q r (10) Q r (11) Q r (12) Table 2 sows tat equation (9) developed wit R 2 = 0.995, 0.673, and respectively for equation (10), (11) and (12). It also sows tat exponent n varies from to Relationsip between actual discarge and corresponding ead was sown in fig. 3. DEVELOPEMENT OF UNIFIED EQUATION FOR SMALL PARSHALL FLUMES In 1928, Parsall [10] ad correlate te coefficient of Parsall flume (J) wit te function of troat widt, W (J = 4W) in fps system. On te similar line, present analysis as been carried out, in wic J = K = 2.78 W for m and m Parsall flumes. Te value of K = 2.78 W is obtained by it and trial to matc wit te experimental value of K. It is found tat te computed value of K and troug it and trial are more or less same (Table 3). Similarly J = K = 2.50 for m and m Parsall flumes (Table 4). Te corresponding value of exponent n kept as 1.5 and 1.55 respectively. Tese values of K and n are given in Table 3 and Table

4 From Table 3 and Table 4, equation (5) can be written as 1.5 Qp 2.78 W (13) 1.55 Qp 2.50 W (14) Te experimental data were plotted in Fig. 4 along wit te fitted equation 13 and equation 14. Fig. 4 sows a good agreement of experimental data wit te fitted equations. Now considering te average value of K as 2.72 W and keeping n = 1.55, after dividing by W, a curve was plotted in Fig. 5, wic sows te variation of discarge intensity Q 2.72W (15) p COMPARISON OF EXPERIMENTAL DATA WITH USDA METHOD In order to compare te accuracy of equation 15 wit te discarge calculated by USDA, te comparison discarge calculated by Equation 15 and discarge calculated by USDA is sown in Fig. 7. It is clear from fig.8, te proposed equation establised as compare to USDA witin ±10 % error. CONCLUSIONS D E F A C W B Fig. 1: Plan and Sectional view of Parsall Flume 909

5 Supply Pipeline Pointer gauge Control Valve Pump Vertical Screens Adjustable Gate Parsall Flume Test cannel Sluice Gate Sump Fig.2: Scematic diagram of Experimental Setup Table 1: Dimensions of Parsall Flumes used in Experiments (All dimensions are in meter) W A B C D E F Table 2: Regression analysis of Experimental data W, meter K n R Fig. 3: Relationsip between Actual discarge and upstream ead for Parsall flumes. 910

6 Table 3: Coefficient of Parsall flume and Exponent for Proposed equation Troat widt, W Coefficient of Parsall flume, K Exponent, n R 2 experimental 2.78 W experimental n m m Table 4: Coefficient of Parsall flume and Exponent for Proposed equation Troat widt, W Coefficient of Parsall flume, K Exponent, n R 2 experimental 2.50 W experimental n m m Fig. 4: Relationsip between discarge dept for Parsall flumes Fig. 5: Relationsip between discarge intensity and upstream dept for Parsall flumes 911

7 Fig.6: Relationsip between actual discarge and Predicted discarge for Parsall flumes Fig.7: Comparison of discarge calculated by USDA and Predicted discarge for Parsall flumes 912

8 Fig. 8: Relationsip of discarge calculated by USDA and Predicted discarge for Parsall flumes Based on experimental work carried out, following conclusions are drawn: A universal relationsip of discarge and ead is not available in literature for te small Parsall flume aving troat widt up to m. Suc a relationsip is necessary for te measurement of less discarge in field condition. Wit tis concept, a semi-empirical formula as been developed as given as below: Q p W From experimental results and proposed equation (15) te introduced is witin ± 10 %. It is also concluded tat results obtained using Eq. (15) and USDA equations; te error is witin ± 10 % APPENDIX A: Free Flow Observations for Parsall Flumes Troat widt,w Test Upstream Head, (), m Actual discarge,(qa), m 3 /s m m m

9 0.229 m REFERENCES [1]. Abt, Steven R. and Staker Kennet J. (1990) Rating Correction for Lateral Settlement of Parsall Flumes Journal of Irrigation and Drainage Engineering, ASCE, Vol. 116, No. 6 pp [2]. Amanda L. Cox, Cristoper I. Tornton, Steven R. Abt, (2013. Supercritical Flow Measurement Using a Large Parsall Flume, Journal of Irrigation and Drainage Engineering, ASCE, 139(8) pp [3]. Blaisdell, Fred W.(1994) Results of Parsall Flume Tests Journal of Irrigation and Drainage Engineering, ASCE, Vol. 120, No. 2 pp [4]. Boman, B. and Sukla, S. (2006) Water measurement for Agricultural Irrigation and Drainage System Circular 1495, pp 1-12 [5].Clemmens, A.J., Wal, T.L., Bos, M.G. and Replogle (2001) Water Measurement wit Flumes and Weir International Institute for Land Reclamation and Improvement / ILRI, publication 58 [6]. Cone, V.M. (1917) Te Venturi Flume Journal of Agricultural Researc, Vol. 9 No. 4 pp II5- I29 [7]. Inglis, C. C Notes on standing wave flumes and flume meter falls Government of Bombay, Public Works Department Tecnical Paper No. 15 [8]. Keller, Robert J., Fong, Soon S. (1989) Flow Measurement Wit Trapezoidal Free Over fall Journal of Irrigation and Drainage Engineering, ASCE, Vol. 115 No. pp [9]. Kilpatrick, F. A. and Scneider, V. R. (1983) Use Of Flumes in Measuring Discarge Book 3 [10]. Parsall, R. L. (1928). Te Improved Venturi flume. Bulletin 336, Colorad Experiment Station, Colorado Agricultural College, Fort Collins, CO. [11]. Robinson, A.R. and Humperys, A.S. (1968) Water control and measurement on Farm ARS, Kimberly, Idao, pp [12]. Skogerboe, Gaylord V.; Hyatt, M. Leon; and Eggleston, Keit O. (1967). "Design and Calibration of Submerged Open Cannel Flow Measurement Structures: Part 1 - Submerged Flow" Reports. Paper

10 [13]. Tornton, Cristoper I., Smit, Brian A., Abt, Steven R. F. and Robeson, Micael D. (2009) Supercritical Flow Measurement Using a Small Parsall Flume Journal of Irrigation and Drainage Engineering, ASCE, Vol. 135, No. 5 pp [14]. Wrigt, Steven J., Tullis. Blake P. and Long, Tamara M. (1994) Recalibration of Parsall Flume at Low Discarges Journal of Irrigation and Drainage Engineering, ASCE, Vol. 120, No. 2 pp