CHAPTER 8 Discharge Equation For Inclined Sluice Gate

Transcription

1 CHAPTER 8 Discharge Equation For Inclined Sluice Gate 8.1 Abstract Generally, sluice gates are used to regulate flow in open channels. The discharge coefficient of a sluice gate is a function of geometric and hydraulic properties. For free flow conditions; the discharge coefficient is related to upstream flow depth and gate opening, whereas for submerged flow, it also depends on tail water depth. Flow through the gnle opening has been the subject of investigation for many academicians and researchers. The main objective of this chapter is to report an investigation done on flow through inclined sluice gate and establish relationships for the discharge through the gate for free-flow and submerged-flow conditions independently. For free-flow condition, the discharge is expressed as a function of head causing flow, gate opening and inclination of the gate. For submerged-flow condition, the discharge is expressed as a function of head cuiising flow, inclinatiun of the gate, gate opening and tail water depth. Experiments were carried on different gate inclinations such as 0" (normal to flow), 15", 30", and 45" with respect to the vertical plane on upstream side for different gate openings. 8.2 Introduction Flow metering is an integral part of water management especially in the field of irrigation and environmental engineering. Due to the increased pressure on demand from every phase of human activity, the water is being treated as scarce commodity; it needs proper regulation and restricted usage so that the ecological balance is maintained. The water is being supplied for irrigation through canals. In canals, a sluice gate is often used as a flow-controlling and measuring device. 81

2 The conventional sluice gate discharge equation is written in the form Q^C.ab^l^ (8-1) In which Q is the sluice gate discharge; a is the sluice gate opening; b is the sluice gate length or width of rectangular channel; y is the upstream water depth; g is gravitational acceleration; and Cj is the discharge coefficient of the gate. Many investigators have studied flow below vertical sluice gates located across the full width in rectangular channel. Henry [65] derived a plot showing variation of discharge coefficient with y/a under free-flow, and with y/a and y,/a for submerged-flow conditions, where y, is the tail water depth. Later, Rajaratnam and Subramanya [40] confirmed Henry's investigations. Ramamurthy, et. al. [43] have carried out experimental investigation on flow past gate with cylindrical lip for submerged-flow condition and reported a higher discharge coefficient for such gates. Using the concept of elementary discharge coefficient, C«, Swamee, et. al. [65] proposed equation for free-flow in terms oi y/a and for submerged flow in terms of>'/a for different ^^/a ratios. Available literature mainly pertains to flow through normal sluice gate with bottom edge sharp or cylindrical. Literature on inclined sluice gates was not available. Thus, there is a need to analyse the discharge characteristics of these types of gates and exploit the advantages of these gates for the best use of sluice gates in practical conditions. In this direction, it is an attempt to experimentally obtain the data on flow conditions below the inclined sluice gates and analyse the same. In the present investigation, the flow through the inclined sluice gates is studied. Independent expressions for discharge for free-flow and submerged-flow conditions are obtained for the inclined gates by conducting experiments on normal. 15, 30 and 45 inclinations of sluice gules with respect to the vertical plane (normal to the bed of the rectangular channel). Most of the researchers have used weir to calibrate the sluice gate (or measure actual discharge) in a channel, which limits the accuracy of the results. In the present work, the discharge was measured by volumetric measurement. 82

3 8.3 Formulation of the Problem The discharge cocrficicnt of a sluice gate depends on the conditions of flow through the gate such as free flow and submerged flow. Hence, an explicit equation for discharge coefficient has to be obtained as a function of y & 'a' for free-flow condition, and 'y', 'a' and 'y,' for submergedflow condition. The expression for discharge coefficient for the normal gate can be obtained for free-flow and submerged-flow conditions as For free flow, C,=Aa.y) (8-2) For submerged flow, C, = /(a.y,y.) (8.3) The discharge coefficient is a function of various factors such as head causing flow, gate shape, surface tension, viscosity, Froude's number, Reynold's number and inclination of gate with free water surface in channel. In the present experimental work, as the gates are inclined to the bed of the channel, the uniform flow condition does not exist and the streamlines converge more rapidly for higher inclinations as compared to streamlines in case of (conventional) normal gate. Hence, the inclined gates are likely to improve their discharging capacity. The pattern of streamline flow lines near the gates is as shown in Fig Therefore, a new parameter '^' as a function of gate inclination with respect to the normal 'a' (in radians) has been introduced in the equation as For free flow, C, = (1+J^)f(a,y) (8.4) For submerged flow, C,'-(l-^/f)f(a,y.y,) (8.5) The schematic definition sketch for submerged flow is as shown in Fig K.<

4 (a) Vertical gate (b) Upstream Inclined gate Fig.8.1 Strcani-Flow patterns Tor Sluice gates f- J Slultt <Jc*.ltf I Tftllgrvit B > rrrrrrrrr7 M ff f % /'//f ^:xm^~^»f/*f*//f**f^ Fig.8.2 Definition Slcetclt for submerged flow 8.4 Experiments The sluice gate was of 5mm thick MS s\i&ex. The lower edge was chamfered at 45 downslrcam in upward direction, with 1mm flat edge. The gates were raised or lowered in the slot provided in the channel to a desired gate height opening. Experiments were carried out on sluice gates fixed normal to the flow direction, 15, 30, and 45 inclinations with vertical plane for 10 to SQ mm gate openings with a step of 10 mm increment in opening. Experiments were conducted for the range ol variables shown in Table

5 8.5 Analysis of Experimental Data The actual discharge is plotted against the head for the gate opening (a = 40 mm) for all the positions of sluice gate (free-flow condition) (Fig.8.3). This indicates that, there is a relative increase in discharge for a particular head, with the increase in the gate inclination. It can be concluded that unlike the conventional sluice gates, smooth convergence of flow lines for flow under the inclined sluice gate increases the sluice discharge coefficient. Retaining the functional form of C^ as given by Swamee [65] for normal gale, a general expression for C^ fur inclined sluice gate is obtained through regression analysis as follows. For free-flow conditions ( y + 15aj \0.072 (8.6) where a is the gate inclination with respect to the (conventional) normal gate :^ ^ \ g) I o.oioh t3 ^ O.(XX) f f 0*» o. %.0 * * <fi %i * Head (m) Nomal «15 degree inclination A 30 degree inclination o 45 degree inclination Fig. 8.3 Actual discliargc Vs Mead (For a =40 mm)

6 Table 8.1: Range of variables studied Normal Gate Inclination Variable «r-0* a-15* a-30* a-45* 1 a) Free flow Gate liciglil opening 'a' (in) O.OI Flow cicptu on u/s of sluice gate y (m) ,00148 Actual discharge 'Q'" (mvs) Number of runs (b) Submerged flow Gate height opening 'a' (m) Flow depth on u/s of sluice gate y (m) Tail water depth y (m) Actual discharge 'Q' (mvs) Number of runs For submerged flow conditions: An additional factor y,/y' is introduced as a third parameter along with 'a ' and 'y' as \0,07J C, =0.645(i + 0.I52a"j-^^^^ ^ V + 15a U^ <y. \ (8.7) The Variation of /^ with a for inclined sluice gates for both the cases are as shown in Fig 8.4. The discharge values are computed, for the measured head, gate opening, upstream flow depth and tail water depth for the corresponding 86

7 flow conditions using Eqs. 8.1, 8.6 and 8.7. Figs. 8.5 and 8.6 show plot of computed discharge versus actual discharge for free-flow and submerged flow conditions respectively , '^O.OS 0.06 ^ Free Flow ti' P =0.224 a ' ",.. ' - ",.-^,^ Submerged Flow /3 =0.152 a"' y^ _.ik l.o a FiB.8.4 /J VM. a The computed discharges are well within ±10% of actual discharge for free-flow condition. Fig. 8.5 indicates a good agreement of established Actual Discharge (rt?/s) fig. 8.5 Actual Discliarge Vs Cbiipjlcd Discliarge (Free flow) 87

8 Eq. 8.6 except at very low discharge values. This may be due to the effect of viscosity and surface tensior\ properties of fluid and further, for small head, the sluice gate acts as a large orifice. From Fig. 8.6, it can be observed that, majority of discharge values (except very few points) lie within ±10% error line. For smaller discharges with small gate opening, the computed discharges are closer to -10% error line, whereas for higher discharges and higher gate openings, the majority of estimated values are within ±10% error line for all the inclined gate positions Actual cliscliargc (m /s) Fig. 8.6 Actual discharge Vs Computed discharge (Submerged flow) The percentage increase in discharge with inclinations when compared to normal sluice gate is shown in Table

9 Tabic 8.2: Variation in relative Increase In % discharge with ' oi Inclination with the vertical plane a=15* a-30* a-45* For free-flow condition For submerged-flow condition Practical Applications The conventional sluice gate can be fixed inclined in a rectangular channel to improve its discharge capacity. The arrangement will also help to reduce afflux especially for higher discharges in an existing channel as it can discharge at a relatively quicker rate. The property of inclined sluice gates can be used in designing canal most economically because inclined gates requires lesser free board in the channel. 8.7 Conclusions Equations Eqs. 8.6 and 8.7 can be used to compute discharge. The computed discharges as obtained by these equations are within 10% error. The property of improvement in discharge capacity of gates with inclination may be effectively used, in economical design of the channels by reducing the free board requirements, as the afflux magnitude is reduced. It is possible to fix the gate in any desired inclination even under general field conditions. Mcnce they find applications in various fields of engineering such as irrigation, chemical and environmental for flow measurement and control. Following conclusions are drawn based on the analysis of experimental data. 1. The variation of computed discharge using the equations derived here (Eqs. 8.6 & 8.7) with the actual discharge is observed to be within ±10 % error. However, majority of points lies on 45 line indicating the accuracy of the equation. 89

10 2. Higher discharge is possible for the same head, with the increase in gate-inclination towards upstream side. The inclination will also help in reducing afflux in a pre-designed canal, thereby higher discharge may be allowed in the canal. 3. With the reduction of afflux, the requirement of free board for the channel is reduced and hence sections can be designed more economically. 4. It is possible to fix gate in any desired inclination even under general field conditions. Hence it finds use in various fields of engineering such as irrigation, chemical and environmental for flow measurement and control. A paper based on the content of above chapter has been presented at the international seminar on earth resources management held at Kuvempu University, Shimoga,28-30, Jan

11 Plate 7 Flow Through Inclined Sluice Gate