Energy Dissipation Through Pool Downstream Vertical Gates

The hydraulic jump downstream gates leads to increase the length of stilling basin for protection hydraulic structures from failures. In this paper, a new technique to increase energy dissipation between upstream and downstream through vertical gate with submerged hydraulic jump using a cylinder putting in pool is locating on stilling basin. This cylinder has different openings in solid and hollow cylinder with constant diameter and different heights. The results showed that in case of solid cylinder, the relative total energy dissipation is directly proportional to the initial Froude number and inversely proportional to the upstream and sequent Froude number. And vice versa in case of hollow cylinder, i.e. the relative total energy dissipation is inversely proportional to the initial Froude number and directly proportional to the upstream and sequent Froude number. Also, the maximum values of relative total energy dissipation occur when all the openings are open but the minimum values of it occurs when all the openings are close. Regardless of whether the cylinder is solid or hollow. Finally, in case of hollow cylinder, the relative height 2.4 gives the maximum values of relative total energy dissipation but the value of 1.0 gives the minimum ones. The main output of this paper that presence of openings in the cylinder has a clear effect on the energy dissipation.


INTRODUCTION
A lot of research has studied theoretically and experimentally the energy dissipation through hydraulic structures to get maximum energy dissipation and minimum hydraulic jump. For energy dissipation below flow regulartors, Ead and Rajaratnam (1998) presented a novel design idea. It was proposed to use a double-leaf gate design rather than a single-leaf sluicegate.The investigation of Screen-type energy dissipation for hydraulic structures was done in (2000) by Rajaratnam, N., and Hurtig K. Cakir P. (2003) performed studies on screens to see how effective they are in dissipating energy. They also found that the amount of energy wasted was not greatly affected by the thickness of screens. The results of studies on the usage of vertical screens showed that variations in the number of screens and the shape of the square aperture had an effect, but the thickness of the screen had no effect on energy loss. Lozano et al. (2009) studied sluice gates in irrigation canals under submerged conditions. The effect of the contraction coefficient was studied and the energy loss was found to be insignificant for large submergences. No attempt was made to explicitly relate the effect of energy loss on the discharge coefficient. Hong et al. (2010) investigated the force and drop length downstream of a vertical drop with a positive slope. Equations were given to estimate the force and drop length, and it was demonstrated that as the bed slope grew, so did the drop length and force on the downstream bed. An equation for the discharge coefficient of sluice gates in rectangular channels under orifice-flow conditions (both free and submerged) was developed by Habibzadeh A. et al.

EXPERIMENTAL WORK
The experiment was conducted in the Hydraulic Engineering Laboratory at Benha University's Faculty of Engineering. The employed flume has the dimensions given in Figure 1 where: width is 0.4 m, height is 0.6 m, and length is 15.0 m. sample of experimental models hollow and solid cylinder with opening as shown in Figure 1. To measure the discharge that fed the flume, a flow meter was mounted. Table 1 defines the experimental results.

DIMENSIONAL ANALYSIS
The dimensional analysis method for the experimental parameters was applied; Figure 3 shows the many factors that may be defined as functions of the following independent variables to effect the energy dissipation through the gate: = f (y u , y 1, y 2, y d , a, B, H, w, h, o, d, L, V, g , , μ) (1) By using (B, g and ) as repeated variables the Buckingham theorem is applied, the number of groups = 16-3 = 13 П.
The following fundamental relationship can be obtained: In which R n is Reynolds number, which assumed to be neglected, Eq. (2) may be rewritten as; ( Where: : Loss of total Energy = E u -E d , : Energy at the gate's upstream, : Energy at the gate's downstream, H: height of the pool, y u : water depth at upstream of gate, y 1 : initial hydraulic depth of the water, y 2 : depth of water at the subsequent hydraulic depth, y d : depth of the water at the gate's downstream, d: the cylinder diameter, w: width of the pool, o: No. of openings in the cylinder, h: height of the cylinder, L: the pool distance from gate, a: gate opening , B: width of the flume, g: the gravitational acceleration , ρ : Water density, V: water velocity, μ: the fluid's dynamic viscosity, F n : Froude Number.

Effect of No. of openings (o) in a hollow cylinder on energy dissipation
The effect of number of openings (o) in a hollow cylinder on dissipation of energy was investigated experimentally. The number of openings (o) = 1, 2 and 3 respectively are considered. The relationship between relative total energy dissipation (ΔE T /E u ) versus Froude number are shown in Figures. (8), (9) and (10). This figures clarify that the relative total energy dissipation is inversely proportional to the initial Froude number (F 1 ) and directly proportional to the upstream Froude number (F u ) and sequent Froude number (F 2 ), this means that the relative total energy dissipation increases with increasing upstream Froude number and final Froude number and decreases with increasing initial Froude number. Also, these figures show that the maximum values of relative total energy dissipation are obtained when all opening are open and the minimum ones are obtained when all openings are close. Figure 11 confirms this result which showed relationship between relative total energy dissipation (ΔE T /E u ) and different No. of openings (o) in solid cylinder at F u = 0.12. Also, this figure illustrates that the relative total energy dissipation in case of all openings are open is higher which a percentage 9% comparing with the case of all openings are close at the considered value of F u = 0.12  (14) show the relationships between the relative total energy dissipation (ΔE T /E u ) and upstream, initial and sequent Froude number respectively. From these figures, it can be concluded that, the maximum values of relative total energy dissipation are obtained from the case of (h/H = 2.4) and the minimum ones are obtained from the case of (h/H = 1). This means increasing of the height of the cylinder leads to increasing of energy dissipation. Also, this figure clarifies that the case of (h/H = 2.4) gives relative total energy dissipation more than the case of (h/H = 1) with a percentage 6% for the case of F u = 0.12. Figure 15 confirms this result which showed relationship between relative total energy dissipation (ΔET/Eu) and different relative height (h/H) at F u = 0.12

Energy Dissipation
To study the effect of the existence of the cylinder, as well as the effect of the cylinder body being solid or hollow, the case of the cylinder that gives the highest energy dissipation was chosen, which is that all openings are open, whether the cylinder is solid or hollow and compared them to the case without cylinder, when the values of upstream Froude number Fu = 0.1, 0.12 and 0.14 as shown in Figures (16), (17) and (18). These figures illustrate that the case of hollow cylinder dissipates the energy more than the case of solid cylinder and existence of the cylinder whether solid or hollow gives values of energy dissipation more than the case of without cylinder. From figure (18), it can be concluded that the existence of the solid cylinder dissipates the energy with a percentage 15% more than the case of without cylinder and 19% for the case of hollow cylinder at F u = 0.14

COMPARISON of MEASURED DATA WITH OTHER STUDIES
It is important to compare of relative total energy dissipation for the different cases of this study with other searches. Fig. (19) Comparison of measured relative total energy dissipation (ΔE T /E u ) and initial Froude number (F 1 ) from others studies likes Rajaratnam (2000), Rasoul (2019) and Ujjawal (2023). From this figure obvious that the experimental data for this cases are acceptable compared to the equations collected from review. Figure 19: Comparison of measured relative total energy dissipation (ΔE T /E u ) and initial Froude number (F 1 ) from others studies.

CONCLUSION And RECOMMENDATION
The experimental study of energy dissipation led to the following conclusions: 1-For the solid cylinder, the relative total energy dissipation (ΔE T /E u ) increases with increasing initial Froude number (F 1 ) and decreases with increasing upstream Froude number (F u ) and sequent Froude number (F 2 ). 2-For the hollow cylinder, the relative total energy dissipation (ΔE T /E u ) decreases with increasing initial Froude number (F 1 ) and increases with increasing upstream Froude number (F u ) and sequent Froude number (F 2 ). 3-The maximum values of relative total energy dissipation are obtained when all openings are open and the minimum ones are obtained when all openings are close regardless of whether the cylinder is solid or hollow. 4-For the hollow cylinder, increasing the relative height of the cylinder (h/H) leads to increasing the relative total energy dissipation. 5-Existence of the cylinder in the pool whether solid or hollow gives values of energy dissipation more than the case of without cylinder. 6-The hollow cylinder dissipates the energy more than the solid cylinder. 7-In case of hollow cylinder, the relative height 2.4 gives the maximum values of relative total energy dissipation but the value of 1.0 gives the minimum ones. 8-Present study agree well with other searches and give good result. The following points are recommended for future studies: 1-The effect of changing gate opening. 2-The effect of dimensions of pool.
3-Appling this result on scour downstream hydraulic gats.
4-Appling this research on program hydraulic.