Flow over oblique Side Weir

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1 Damascus University Journal Vol. (8) - No. () 0 Al-Tali Flow over olique Side Weir Eng. Azza N. Al-Tali * Astract In this paper, an olique side weir was studied y nine models installed at the entrance of side channel at an angles (30 0,45 0,60 0,75 0 and 90 0 ) respected to side channel wall and installed at two directions, with flow direction and opposite it. The models were tested y five different flows passing over them so, the numer of runs is 45. The hydraulic characteristics of flow over vertical and olique side weir were studied, and the results show increasing of discharge over side weir when installed at an olique direction and the average increases when their inclination at left direction was greater (6%) than that right direction. Equations were predicted for calculation of discharge coefficient (C d ) and coefficient of energy loss (k) for two directions and the water surface profile for vertical and olique side weir in two directions is plotted. Keywords: Olique side weir- discharge coefficient- energy loss coefficient * Univ. of Mosul, Coll. of Eng., Dept. of Water Resources, Eng. P.O. Box 44, Mosul, Iraq 5

2 Flow over olique Side Weir. Introduction Most of side weirs serve mainly to measure discharge in side channel, so flow direction discharge control and other means due to the use of various geometric and hydraulic shapes of side weir, and there is much research work has een done from different types of side weir. [] Ramamurthy et.al.(978) studied modification to the geometry of the main open channel is suggested as a means to otain uniform flow over side weir discharging in to asins. [] Ramamurthy et.al.(986), [3] Uyumaz & Smith (99) and [4] Yilmaz (00), analyzed flow over side weir theoretically. [5] Ramamurthy et.al.(990) skipping the assumption of critical condition, assumed no energy loss long the depth averaged stagnation dividing stream line surface to otain an expression for the momentum transfer rate from the main to the side channel. They proposed a model for upstream Fruod numer <0.75 which relates discharge of main channel to upstream Fruod numer and water depth of main channel. Their predictions agree well with their data. [6] Borghei et.al.(999),there studied relate the discharge coefficient with the main channel's upstream Froud numer and geometric parameters of the channel and the side weir. [7] Samani A.R.(00) studied flow over olique weir through analytical models of flow are ased on energy conservation for the upstream and downstream of weir momentum conservation and continuity equations and show that flow discharge over and olique weir is greater than that over a straight or plain weir for the same water head due to its extra length with respect to the channel width. The primary ojective of this paper is to calculate the hydraulic characteristics for flow over vertical and olique side weir inclined with and opposite direction as well as predicted an equation to calculate coefficient of discharge and energy loss. in the main channel was measured y sharp crested weir (standard weir) at (35cm) distance from the end of main channel with (0*30*0.) cm dimensions, the side weirs were made of wood with (*5*0.)cm dimensions installed at the entrance of the side channel inclined at an angles (30 0,45 0,60 0, 75 0 and 90 0 ) respect to side channel wall in two direction, with flow direction (inclined to the left) and opposite it (inclined to the right) figure (),with five different discharge range from ( ) l/s,so the numer of runs was (45). The discharge at the main channel was found from eq.() using volumetric method, Q=0.58*H.5 () Were, Q: discharge (l/s), H: head over standard weir Side channel was closed and measured the total discharge Q then let flow pass at the side channel then measured the discharge of main channel Q, the difference etween Q & Q gives the discharge of side channel Q 3.. Experimental setup Tests were conducted at hydraulic laoratory of College of Engineering, Mosul University. In a rectangular flume shown in figure (), it is (0m) long, (30cm) width and (45cm) height.the side channel was (m) long, (5cm) width and (30cm) height. The discharge 6 Fig. () Channel Cross Section

3 Damascus University Journal Vol. (8) - No. () 0 Q, E, F, y Q, E, F, y B Al-Tali Where x= longitudinal distance in main channel upstream and downstream side weir in cm, y=distance along the width of the ranch channel in cm, and z= water depth aove the ranch channel in cm θ θ Q 3, E 3, F 3, y 3 3 θ=90 o, 75 o, 60 o, 45 o, 30 o eft direction Right direction Fig. () details of laoratory measurements y y y3 Q Q Q3 Tale : Sample of laoratory measurements and calculated used in equation estimated. Tale : sample of laoratory measurements for water surface profile over side weir installed vertically at (90 o ) and inclined at (30 o eft), all dimension in. Where H wm ; water depth over the standard weir when ranch channel opened, H wt ; water depth over the standard weir when ranch channel closed, y ; total water depth, y ; main channel water depth, h ; water depth over the side weir, y 3 ; water depth at side channel, Q total discharge, F Froude numer upstream side weir, 7

4 Flow over olique Side Weir Q discharge of main channel, Q 3; discharge of side channel, weir side weir width, and k coefficient of energy loss calculated from (3). 3. Energy loss coefficient The discharge passing through the side channel can e calculated y the equation: Q 3 =Q -Q..() Were; Q :total discharge, Q :main channel discharge, Q 3 :side channel discharge The conservation of energy implies etween upstream and down steam channel given in the equation elow [8] Chow, 959: Q E (-k)=q E +Q 3 E 3...(3) Were; E : total energy, E : energy of main channel, E 3 : energy of side channel, k: energy loss coefficient The energy loss coefficient can e written as a function of parameters as following: k=f (Q, Q, E, E, ρ)....(4) Were; ρ: water density Using П-theorem the equation (4) can e written as following: k=f`( E Q, E Q ).....(5) Equation (5) can e used for coefficient of energy loss calculation and can e written as following: E C Q C3 k=c + ( ) + ( )....(6) E Q Using statistical programming (SPSS V.7) the parameters C to C 3 for (6) were estimated to adjust model parameters and excitations until the fit etween (k) calculated from (3) and (6) are optimized in the weighted least square sense, so k can e calculated for inclined side weir (left & right direction) from the following equations: For weir inclined with flow direction (left direction) use the following equating with correlation (R =0.97) E.8 Q k= ( ) + ( ).....(7) E Q k cal For weir inclined opposite flow direction (right direction) use the following equating with correlation (R =0.98) E Q 0.53 k= ( ) + ( )....(8) E Q Figure (3) shows the compared etween energy loss coefficients calculated from equations (7 & 8) and measured experimentally. It is clear that the average parentage error not exceed 4%. The predicted k values for all angles at left direction versus upstream Froude numer (F ) are shown in figure (4).from this figure (k) values increase with increasing F and large values of k oserved when side weir inclined at 30 0 with side channel sides, while the lower values shown when side weir installed at k value of weir inclined at (30 0 ) is greater 44% than that at (90 0 ). All these vales for all angles inclined at left and right direction are shown in figure (5). From figure the larger values of (k) oserved when side weir installed inclined towards left direction for all angles y (.5%) respected to that inclined towards right direction. R k mesured Fig. (3) Comparison etween calculated (k ) and measured (k) 8

5 Damascus University Journal Vol. (8) - No. () Al-Tali 0. k F Water depth Side weir position Distance k Fig. (4) Relation etween (k ) and (F ) for all angles of models R k = 0.98F R = k = 0.80F R = F Fig. (5) Relation etween (k ) and (F ) for two direction models 4. Water surface profile Water depth Fig. (6) Water surface profile for model installed 90 0 with channel side walls Side weir position Distance Fig. (7) Water surface profile for model installed 30 0 with channel side walls (left direction) The water surface profile were plotted at figures ( 6 to 8 ) using measured data collection at grid points from main to side channel for side weir installed at 90 0, 30 0 inclined towards left and right direction respectively for (6.5)l/s discharge. From water surface profile the figures indicate the volume of water passing from side weir at left and right direction are greater than that installed at 90 0,this mean increasing of discharge passing through side channel at the same water depth height. Water depth Side weir position Distance Fig. (8) Water surface profile for model installed 30 0 with channel side walls (right direction) 9

6 Flow over olique Side Weir 5. Discharge coefficient The discharge coefficient of olique side weir (C d ) is a function of many parameters such as the discharge of side channel (Q 3 ), the side channel water depth (y 3 ),the total water depth (y ),the width of side channel (),the length of olique side weir (), the gravitational acceleration (g), and water density (ρ),so the discharge coefficient can e written as following: C d =f(q 3, y 3, y,,, g, ρ ).(9) The variation of parameters appeared in equation (9) can e measured experimentally; some of the proposed formulas for (C d ) are as following: P C d = F y B [6](Borghei et.al.,999).(0) + F 0.5 = 0.485( ) [9] (Hagar,987).() 3F C d + Were; P: side weir height, B: width of main channel Most investigators accept the upstream Froud numer as the main variale in the formula. [0] Ramamurthy and Carallada (980) showed the influence of /B as another non dimensional parameter. [6]Borghei et.al.,(999) showed the influnce of P/y as well as /B and F as non dimensional parameters. Using П-theorem the equation (9) can e written as following: y 3 C d =f`(f 3,, ).() y Were; F 3 : Froud numer at side channel Equation () can e used to calculate (C d ) and can e written as following: y C = C + F +..(3) d C 3 C3 ) C4 3 + ( ) ( y Using statistical programming (SPSS V.7) the parameters C to C 4 for (3) can e calculated to adjust model parameters and excitations until the fit etween (C d ) oservations and estimated are optimized in the weighted least square sense, so equation (3) can e written as following: y C d =.38 + F3 + ( ) + ( )..(4) y Equation (4) can e applied for olique side weir (left direction) with correlation (R =0.88) 0.37 y C d =.08 + F3 + ( ) + ( )..(5) y Equation (5) can e applied for olique side weir (right direction) with correlation (R =0.84) To compare the computed c d from equations (4&5) and the measured one, figure (9) presents that the average percentage error not exceed 0%. The measured y /y (y is main channel water depth) with respect to Q 3 /Q for all angles inclined at left direction are shown in figure (0). From figure the values of y /y increase with increasing values of Q 3 /Q and the large values of the two parameters oserved when side weir inclined at 30 0 while the lower values oserved when side weir installed at 90 0 (horizontally). These two parameters for all side weir angles located at left and right direction where shown in figure (). From figure the ratio of y /y is greater when side weir installed at left direction greater than that inclined to the right direction. cd cal R cd mesured Fig. (9) Comparison etween calculated (C d ) and measured (C d ) 0

7 Damascus University Journal Vol. (8) - No. () 0 Notation: Al-Tali q 3/q ym/yt y/y y/y y/y q/qt R y/y =.0078Q3/Q R = y/y =.063Q3/Q R = Q3/Q 6. Conclusions: Q 3 /Q Fig. (0) Relation etween (y /y ) and (Q 3 /Q ) for all angles of models Q 3 /Q Fig. () Relation etween (y /y ) and (Q 3 /Q ) for two dimension models An experimental data were curried out for an olique side weir with different angles, the results show increasing of discharge greater than 6% with respect to vertical one. Equations to calculated coefficient of discharge (C d ) and coefficient of energy loss (k) were predicted and compared with other studies. B weir C d E E E 3 F F 3 g H h H wm H wt k P Q Q Q Q 3 x y y y y 3 z ρ width of main channel width of side channel side weir width discharge coefficient total energy energy of main channel energy of side channel Froude numer upstream side weir Froud numer at side channel gravitational acceleration head over standard weir water depth over the side weir water depth over the standard weir when ranch channel opened water depth over the standard weir when ranch channel closed coefficient of energy loss length of olique side weir side weir height flow discharge total discharge discharge of main channel discharge of side channel longitudinal distance distance along the ranch channel total water depth main channel water depth side channel water depth water depth aove the ranch channel water density

8 Flow over olique Side Weir References: [] Ramamurthy,A.S., Suramanya,K., and Carallada,., (978). "Uniformily discharge lateral weir." J.Irrig. and Drain.Div., ASCE, 04(), [] Ramamurthy,A.S., Tim,U.S., and Sarraf,S., (986). "Rectangular lateral orifices in open channels"j.envir. Engrg., ASCE, (), [3] Uymaz,A., and Smith,R.H. (99). "Design procedure for flow over side weirs." J.Irrig. and Drain.Div., ASCE, 7(), [4] Yilmaz M. (00). "Numerical Analysis for ateral Weir Flow." Journal of Irrigation and Drainage Engineering, ASCE, 7(4), [5] Ramamurthy,A.S., Tran,D.M., and Carallada,., (990). "Dividing flow in open channels." J.Hydr.Engrg., ASCE, 6(3), [6] Borghei,S.M.,Jalili,M.R.,and Ghodsian,M. (999). "Discharge coefficient for sharpcrested side weir in sucritical flow." J.Hydr.Engrg., ASCE, 5(0), [7] Samani A.R.,(00). "Analytical approach for flow over an olique weir", Scientia Iranica, 7(), [8] Chow V.T. (959)."Open Channel Hydraulics." McGraw Hill, New York, pp [9] Hager,W.H.(987)."Experimental investigation of flow over side weirs." J. Hydr. Engrg., ASCE, 3(4), [0] Ramamurthy,A.S., and Carallada,. (980). "ateral weir flow model." J.Irrig. and Drain.Div., ASCE, 06(),9-5. Received 4//0

9 Damascus University Journal Vol. (8) - No. () 0 Al-Tali 3

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