Investigation of Effective Parameters on Discharge Coefficient of Compound Arched Circular-Rectangular Sharp-Crested Weirs

The compound sharp-crested weirs are composed from several notches and those are designedin different shapes. One of the hydraulic advantagesof compound weirs is that atlowflow rate, the bottomnotchacts assimpleweir andwith the creation of morehydraulicheadonits upstream, due to theshape of thenotch, make dischargemeasurement withappropriatesensitivity. In high flow rates, the upper notch prevents of increasing upstream water level and backwater and discharge measurement is possible with acceptable accuracy. The compound sharp-crested weirs can be used as an appropriate solution for discharge measurement with reasonable accuracy and sensitivity of the extensive range of flows. Relations are derived from this kind of weirs hassufficientaccuracy withobservation of design criteriaandconstructionstandards. The purposeofthisresearch was a laboratory investigation of geometricandhydraulic effective parameterson discharge coefficient of compound arched circular- rectangular sharp-crested weirs in two cases of full width of channel and partially contracted weirs and compare the values of the discharge coefficient of compound and simple rectangular weirs.

Considering the geometric, kinematic and dynamic variables affecting the free flow of sharp-crested weirs, there are 11independent variableswiththree main quantities (length, massandtime). Usingdimensional analysis with π-Buckinghammethod,it can bederived thedimansionlessrelationship. In order to assess theeffect of various parametersonthe coefficient ofCd,thedimansionlessdiagramsare used. Inthe state of(h≤h0), discharge relationship usedinsimplecircular weir. In thestate of(h>h0), discharge of compound weir is computeted from the linear combination of discharge relationships in circular and rectangular weirs. Experimentsare conducted inthe hydraulic engineering models laboratory, Department of Water Engineering, University of Tabriz, in a rectangular glass-metal flume of 9 m length, 25 cm width and 50 cm height. Aftersetting up the weirs in a relevant place of flume andestablish thesteady flow,experiments were performedinthefree flowon36 models of weirs.

In this research, theeffects ofrectangularnotch width, the height of weir crest, the height ofcirculararch notch were investigated forchanges of headwithdimensionless ratios of h/P,h/R,h/h_0, h/Bon discharge coefficient. The results showthat fora known headover the weir, discharge coefficient increase about 2 to 10percent with the development of the rectangular notch width of compound and simple rectangular sharp-crested weirs. For a given head over the weir, discharge coefficient decrease approximately 1 to 5percent by increasing the height of the weir crest of compound and simple sharp-crested weirs. Fora given head over weir in low head values, discharge coefficient increase approximately 35percent by reducing the height of circulararch notch in the compound weirs than simple rectangular weirs. Based on statistical indicators, computational and observation discharge coefficient values in most compound and simple weirs, acceptable coincidence with each other. The meanvalues of thecoefficient of determination (R2) androot mean square error(RMSE) are 0.630and0.061,respectively. Among the effective factors that indicate the difference, it can be referred to the theoretical equation in the compound state that is obtained by assuming a linear combination of simple weirs. The effect of the lateral walls of the flume, the measurement accuracy of hydraulic head and discharge, the conditions of flow entrance, the extension of the range of empirical equations proposed in literature for discharge coefficient of simple weirs, Other factors contributing to the difference between the estimated and observed values of discharge coefficient. Inthistypeofweirs,the least amount ofdiscontinuityin thetransition region of simple to compound state in head-discharge relationship can be seenin thewide rangeofdischargescomparedwithother kinds ofcompound weirswithhorizontalorslopingcrests.

In this research, a seri of experiments conducted to investigate Cd of the compound arched circular-rectangular sharp-crested weirs in both full width of the channel and partially contracted. The advantage of these weirsisdischarge measurement ina wide range. According to the parametersaffecting theweir, Cd has changed from 0.54 to 0.89 range in the compound weirs and 0.55 to 0.66 range in the simple rectangular weirs. Bychanging the weir specifications, Cd increase about 35 percentthan thesimplerectangular weir. Forchanges of the head by usingthe experimental data, the discharge continuityofthistypeofweir is far more thanthecompound weirs withhorizontal orinclined crests. Based on theevaluation criteria, using alinear combinationofthe discharge relationshipof circularandrectangularsharp-crested weirs, be able to estimate Cd of the compound weirs withacceptable accuracy.