FREE OVERFALL IN A HORIZONTAL SMOOTH RECTANGULAR CHANNEL

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1 International Journal of Civil Engineering and Technology (IJCIET) Volume 8, Issue 4, April 017, pp , Article ID: IJCIET_08_04_8 Available online at ISSN Print: and ISSN Online: IAEME Publication Scopus Indexed FREE OVERFALL IN A HORIZONTAL SMOOTH RECTANGULAR CHANNEL Gangesh Kumar Thakur PG Student, Civil Engineering Department, Sam Higginbottom University of Agriculture, Technology and Sciences, Allahabd, India Dr. V.C. Agarwal Professor & HOD, Civil Engineering Department, Sam Higginbottom University of Agriculture, Technology and Sciences, Allahabd, India ABSTRACT The experiments were conducted in hydraulics laboratory of civil Engineering Department, Shepherd Institute of Engineering and Technology, SHUATS, Allahabad.India. The effects on free overfall in smooth horizontal rectangular channel are studied. The characteristic include water depth, free overfall and brink depth at smooth horizontal Rectangular channel. The variation of y c with y e has been studied. In addition the relation between Q and y c, Q and y e has also been developed. The results are found to highly satisfactory and are close to results given by Rajaratnam, N. and Muralidhar, Rouse, Turan. Key words: Free overfall, Brink depth, Critical depth, Bed smoothness. Cite this Article: Gangesh Kumar Thakur and Dr. V.C. Agarwal, Free Overfall in a Horizontal Smooth Rectangular Channel. International Journal of Civil Engineering and Technology, 8(4), 017, pp INTRODUCTION The over-fall is known as the downstream portion of a rectangular channel, horizontal or sloping, terminating at its lower end. If tail water is not submerged, it is referred to as the free overfall. A vertical drop of a free overfall is a common feature in both natural and artificial channels. Natural drops are formed by river erosion while drop structures are built in irrigation and drainage channels as energy reducing devices especially where the flow is supercritical. The study of a free overfall is also important because of possible usage of it as a discharge-measuring device. The problem of the free overfall as a discharge measuring device has attracted considerable interest for almost 80 years and the end depth discharge relationship has been extensively studied by carrying out the theoretical and experimental studies at free overfall of a channel in order to establish a relationship between the critical depth, yc and the brink depth (end depth), ye. Rouse (1936) was the first to point out the editor@iaeme.com

2 Free Overfall in a Horizontal Smooth Rectangular Channel possibility of using the free overfall as aflow meter, which needs no calibration. Although the streamlines at the overfall is not parallel, the crest section is that of true minimum energy and hence is the actual section Hydraulics of Free overfall If the flow at an abrupt end of a long channel is not submerged by the tail water, it can be referred to as a free overfall. In channels with mild slopes, the approaching flow is subcritical (Fig. 1). At the upstream control section with critical depth h c, vertical accelerations are negligible and a hydrostatic pressure distribution can be safely assumed. At the brink section with depth h b the pressure distribution is no longer hydrostatic both due to the curvature of the flow and the aeration of the under nappe. Since there is a unique relationship between the critical depth and flow discharge, the ratio of the end- depth to the critical depth (EDR = h b /h c ) offers a possibility to predict the flow discharge and study erosion at the brink of a free overfall. For steep slopes, where the approaching flow is super-critical, flow discharge is a function of end-depth, channel slope, and channel roughness. Figure 1 (a) Typical free overfall; (b) Streamline pattern of a free overfall;. REVIEW OF LITERATURE Rouse (1936) conducted experiments in a horizontal mildly sloped channel for free over-fall confined nappe and concluded that the brink depth is a constant percentage of the computed critical depth of the parallel flow. He informed that end depth ratio, y e /y c =0.715 when Froude number is equal to one. He also calculated the ratio of brink depth and upstream flow depths, for variable upstream Froude number, (F 0 ).Dellur et al.(1956) he carried his experiment assuming two dimensional flow. He theoretically obtained EDR values by applying the momentum equation between the end section and upstream section. He considered pressure distribution hydrostatic. For evaluation pressure force at the end section they introduced a pressure coefficient C s; depending upon actual pressure distribution. The agreement between experimental EDR value and measured in both smooth flume and in rough one, and the theoretical is obtained by right c s value. The measurement of Dellur et al. allow one to establish the pressure distribution at the end section of rectangular channel deviate more and more from hydrostatic for increasing value of the ratio between slope s and critical value s c. C s value decrease from 0.6 to 0.3 changing from subcritical to super critical flow. Diskin(1961) applied the momentum approach assuming zero end pressure to calculate the EDR value of for horizontal rectangular free overfall. Replogle (196) carried out his investigation for rectangular channel based on several assumptions used in Diskin s momentum equation. For rectangular free over fall, he found for EDR. Markland (1965) was able to obtain the flow profile for various Froude numbers. Since Markland used a editor@iaeme.com

3 Gangesh Kumar Thakur and Dr. V.C. Agarwal finite difference method, round off errors were inevitably present. Markland was able to extrapolate a value of 0.70 which compares favourably to Rouse s values of Rajaratham and Muralidhar (1966) also reported the value as for confined nappe free overfall and for unconfined free overfall he reported Bauer and Graf (1971) gave a higher value of Ali and Sykes (197) calculated the value as by momentum equation and by free vortex theory. Kraijenhoff and Dommerholt (1977) investigated the end depth and the critical depth in a wide rectangular channel with variable slope and roughness. Their y e /y c value of was not significantly affected by either the mild slopes up to or by the bottom roughness. Supplementary experiments for the brink depth method in a rectangular channel are described including changes of channel slope and channel roughness. The ratio of the end depth and the critical depth y sub e /y sub c = Hager (1983) used energy momentum equations approach, he treated two dimensional free overfall taking account of streamline inclination and curvature. The EDR and flow discharge, determined from momentum consideration in the end is given below in equation (1) and () respectively. EDR= 9Fr n / (9Fr n + 4) (1) Q / (gb h b 3 ) =/ [5j b (1-j b )] () Where j b =5Fr n /(+5Fr n ). For subcritical approaching flow (i.e. Fr n =1), the above equation produces EDR= He also investigated the free surface profiles, upstream and downstream at the end section. Alastair et al. (1998) performed an experimental study of the free overfall in a rectangular channel with differing slopes and bed roughness. The relationship between the upstream critical depth and brink depth was explored and found to be influenced by both the slope and the channel bed roughness, with roughness having a greater effect at steeper slopes. Two empirical equations were proposed for calculating this relationship; the first equation requiring only the channel slope to be known and the second equation requiring knowledge of channel slope and Manning roughness coefficient, n. The accuracy of two equations when used in a method for flow measurements was compared. The first relationship, in which the effects of slope and roughness are aggregated, provided a useful estimate of channel discharge if only the channel slope is known. If both bed roughness and slope are known, then the second relationship could be used to calculate the channel discharge with greater accuracy. Turan (00) conducted several experiments in a sloping rectangular channel having smooth bed. The equation given by Alastair was reexamined by those additional data. He concluded that further experiments were needed in order to see the effect of bed roughness. Firat (004) experimentally studied the characteristics of the subcritical, critical and supercritical flows at the rectangular free overfall to obtain an empirical relation between the brink depth and the flow rate. A series of experiments were conducted by him in a tilting flume with wide range of flow rate and two bed roughness in order to find the relationship between the brink depth, normal depth, and channel bed slope and bed roughness. 3. MATERIALS AND METHODOLOGY 3.1. Analytical Studies of Free Over Fall Depth at the fall is called as brink or end depth. A slight distance upstream of this depth (say at x c ) is critical depth. Apply momentum equation between cc and ee. Neglecting frictional force and component of weight both being negligible. P c P e = ( ) editor@iaeme.com

4 Free Overfall in a Horizontal Smooth Rectangular Channel For a rectangular channel =, = At section ee pressure is atmospheric, hence P e =0, γ.. =.. = = = Or = = ( ) = ( ) Which is the theoretical relation between Now assuming channel to be a wide rectangular channel, apply Manning s equation at critical section and end section = 1 ( ) For wide rectangular channel R= y = 1 ( ) = 1. ( ) = 1. ( ) Or Or = = ( ) = ( ). 3.. Experimental Set-up Description The experiments were conducted in a metal rectangular flume 30cm in width and 1.6 m in length. Figure 3.1 shows the plan view of the channel. It had a steel bed and the sides of the channel were made of fiberglass. The base of the channel was made of well-polished steel which represents smooth bed. The weir capacity is enough to measure the maximum discharge used which is nearly13. lt/s. The sloping bed is regulated by a screw but channel bed is kept horizontally. By the screw the channel slope can be adjusted but the study is focused to only zero slope in smooth channel bedwater, regulated by valves, was supplied from a constant head tank through two 0 cm pipes. Water issuing out from the channel was collected in a basin connected to a return channel. An energy dissipater is used at the base of the over-fall to minimize the fluctuations caused by splashing resulting in a decrease in accuracy of readings in the manometer measuring discharge. Additionally, screen type energy dissipater is used at the entrance of the channel in order to reach uniform flow. The smooth channel was set to 10 different rotations. A point gauge mounted on rails along the channel allowed the normal depth, y c, to be measured. Yet, there is another point gauge at the brink section allowed the brink depth, y e, to be measured. In Figure 3 a cross sectional view of the channel demonstrating the gauge is given editor@iaeme.com

5 Gangesh Kumar Thakur and Dr. V.C. Agarwal Figure The Plan of the Experimental Set up Figure 3 The Channel Section (Section A-A) with pointer Gauge 3.3. Calculation of Discharge using Volumetric Method h(ᵞ) = h Specific weight of water on earth at 5degree centigrade is KN/m 3 h = 9.81()(N) And, h () = m 3 /s 4. RESULTS AND DISCUSSIONS 4.1. Experimental Findings The experiment for rectangular smooth open channel bed having zero slope were performed for 10 different rotation (to vary discharge) and discharge calculated which later is used to calculate the corresponding critical depth. The discharge ranges from m 3 /s to m 3 /s. Findings tabulated in table editor@iaeme.com

6 Free Overfall in a Horizontal Smooth Rectangular Channel Table 1 Rotation of valve to Discharge (m 3 /s) Critical Depth y c y e (cm) x c (cm) vary discharge (cm) Determination of Discharge The estimation of discharge capacity in a channel or river is most important fundamental problem in open channel flow. Without an accurate estimate of discharge, very little confidence can cause problems in subsequent design calculation or prediction. With due respect of time, little or no field data available especially for sudden flood flows; therefore the engineer must estimate a rough value to obtain a discharge relationship between brink depth and discharge. In India we don t have very much accurate and advance discharge calculator instrument. Also, in India especially in northern India we have flood situation and very good irrigation through small open rectangular channels. In such situation discharge can be predicted using volumetric method. This experimental study performed in the light of the effect of discharge on brink depth value Variation of y e with Discharge The relationship between brink depth and discharge is presented in fig 4. The best fit lines shown has been fitted through data. As seen as the discharge increases the brink depth also increases. For the slope tested the coefficient of best fit line placed through the data of smooth channel with zero slope are given in table 4.1 together their root mean square value is R² = The dashed line represent a very good agreement between experimental data and theoretical relationship showed by Dellur et al and Anderson. Ye (cm) graph -4.1 ye VS Q y = -0.09x x R² = Q(m3/s) Figure 4 Relation of brink depth with discharge editor@iaeme.com

7 Gangesh Kumar Thakur and Dr. V.C. Agarwal 4.4. Variation of y c with Respect to Q y c is influenced by Q. As Q is a function of Volume of water at critical depth. In fig 5 the quadratic best fit lines diverge as the slope increases and best fit line of y c appears to be increase with amount of discharge increase. The root square mean value R² = is compared with the result of Alstair (1998), Tarun (00) and Can Ersen (004). They have reported R² value , and respectively. figure 5 Discharge vs Critical Depth y c (cm) Q (^3/) Figure 5 Relation between discharge and critical depth Variation of x c with Respect to y c It will be practical way to know the x c position of critical depth (y c ) if an engineer know the discharge. Alternatively it also help engineer to decide the width of channel. Experimental study of Anderson have shown that the relative distance x c / y c is of the order 3 to 6 and is a function of channel slope. Anderson prediction appears to be better. The experiment conducted here, x c / y c = (4.17/3.618) = 6.67% which is 11. % more than the range given by Anderson. Since it is quite difficult to identify the exact location of y c theoretical, particularly when q is not known, it is customary to assume the brink depth as the yc, theoretical. Yet, the invalidity of this assumption, that is y c,theoretical is nearly equal to ye, has been proven in this study. x c (cm) graph-4.3 x c vs y c x c = 0.056y c y c R² = y c (cm) Figure 6 Variation of x c with respect to y c editor@iaeme.com

8 Free Overfall in a Horizontal Smooth Rectangular Channel 4.6. Relation between y e and y c A plot of brink depth against critical depth showed a trend of increasing distance with flow rate although the scatter of data was high. The obtained = which compares favorably to Rouse s value of Reploge carried out his investigation for rectangular channel based on several assumptions used in diskin momentum equation. For rectangular free overfall he found EDR (end depth ratio)= The brink depth ratio seems to be independent of upstream Froude number for subcritical flows. In other words, the relation between y e /y c shows different characteristics in subcritical and supercritical flow. It is constant for subcritical flow and polynomial for supercritical flow. The end depth ratio for horizontal rectangular channels with sub critical flow conditions at the upstream can be taken as Relationship between ye and yc with Best-Fit Line y e (cm) R² = y c (cm) Figure 7 Relation between critical depth and end depth 5. CONCLUSIONS In the present study following conclusions may be drawn- The ratio between the brink depth and theoretical critical depth y e /y c, is found to be. = channel bed slope is zero. Rouse experimental result for horizontal rectangular channel for subcritical flow are y e /y c = The experimental studies showed that =. = Experimental studies of Anderson. showed that = 3 6 and is a function of channel slope. Das and Goswami carried out experimental studies and concluded that 3 4. But it is experimentally observed that y e /y c varies with roughness and slope and therefore measurement of discharge and brink depth can t be universally accepted.. The statistical analysis of Das and Gowswami indicate that = 0.73 = 5.08 the above equation is tested in field trials in irrigation canal. And result reported Analytically by Anderson is = editor@iaeme.com

9 Gangesh Kumar Thakur and Dr. V.C. Agarwal the experimental study this is 3.31 % less than my experimentally obtained value of This slight variation observed in volumetric method is due to loss in infiltration in field canals. Another conclusion is that is constant for subcritical flow Sources and scope of Errors The time was measured with the help of stopwatch. So chances of noting time and pressing buttons cause human error. REFERENCES [1] Alastair, C.D. et al., Flow measurements in sloping channels with rectangular free overfall, J. Hydraulic Engng., ASCE, 1998, Vol. 14, No. 7, July [] Ali, K. H. M. and Sykes, A., Free vortex theory applied to free overfall, J.Hydraulic Div. ASCE, 197, Vol. 98, May [3] Bauer, S.W. and Graff, W.H., Free overfall as flow measurement device, J. Irrigation and Drainage Div., ASCE, 1971, Vol. 97, No. 1 [4] Delleur et al., Influence of the slope and roughness on the free overfall, J.Hydraulic Div. ASCE, 1956, Vol. 8, Aug. [5] Ferro, V., Flow measurement with rectangular free overfall, J. Irrigation and Drainage Div., ASCE, 199, Vol. 118, No. 6 [6] FIRAT, Can Ersen Effect of roughness on flow measurements in sloping rectangular channels with free overfall 004 [7] Gupta, R.D., et al., Discharge prediction in smooth trapezoidal free overfall- (positive, zero and negative slopes), J. Irrigation and Drainage Div., ASCE,1993, Vol. 119, No. [8] Keller, R.J. and Fong S.S., Flow measurement with trapezoidal free overfall, J.Irrigation and Drainage Div., ASCE, 1989, Vol. 115, No. 1 [9] Rajaratnam, N. And Muralidhar, D., Characteristics of the rectangular free overfall, J. Hydraulic Research, 1968, Vol. 6 No. 3 [10] Rajaratnam, N. And Muralidhar, D., Roughness effects on rectangular free overfall, J.Hydraulic Div. ASCE, 1976, Vol. 10 No. 5 [11] Rouse, H., Discharge characteristics of the free overfall, Civil Engineering, 1936, Vol. 6, No. 4 [1] Turan, Ç.K., Flow measurements in sloping rectangular channels with free overfall, M.Sc. Thesis METU, Ankara, December editor@iaeme.com