Flow trajectory analysis and velocity coefficients for fluid dynamics in tubes and holes

. The article is devoted to determining the values of the flow trajectory of the water flowing through various tubes and holes depending on the pressure in front of the hole, and the flow rate coefficient is determined based on the flow parameters. Using the value of the velocity coefficients, the velocity and the force generated as a result of the velocity, the condition of the flow trajectory and the effect of the flow on various obstacles are determined.


Introduction
The flow of liquid through holes and tubes has been studied and researched by many scientists.V.S.Kuznesov, V.V.Yazos determined the effectiveness of blocking the channel with a cylindrical throttle, studied the influence of the absolute pressure at the entrance to the channel from 221 kPa to 240 kPa, and developed calculation methods that were used in the experiment [1,2].V.M.Bigler, V.F.Yudaev analyzed the non-stationary flow of real fluids through a hole, calculated the change in speed during non-stationary flow, and calculated its hydrodynamic pressure and the equation of motion for the non-stationary state, and analyzed the dependence of the resistance coefficient value on the speed.S.L.Polokonnikov analyzed the symmetric situation of the stationary flow of the liquid with respect to its occurrence, and found a general solution to the parametrically analyzed problem.Speed was determined using D.Bernoulli's equation.Equations are developed and methods of solving this equation are analyzed.T.J.Simiev, Y.I.Ivanov, in their works, the way and methods of conducting experiments by organizing a laboratory device for the analysis of liquid flow through holes and tubes were considered [3][4][5].The flow of liquids through holes and pipes is considered the main problem of hydraulics and is important in solving practical problems.The study of the law of flow of liquids through holes and tubes during the emptying of technological devices, large capacities and other containers is used to solve many technical problems.It determines the flow rate, flow trajectory and consumption of fluids [6][7][8][9].
In this case, the flow parameters depend on the types and location of the hole and tube, so the holes are divided into thin-walled, thick-walled, perfect, and imperfect types.The velocity of the flowing liquid varies in different places of the hole.The velocity of a particle of fluid flowing through an orifice increases as it approaches the orifice and gradually decreases after the orifice [10][11][12].This increase in inertia effect continues beyond the hole, and reaches a maximum velocity at approximately the diameter of the hole, where a compacted surface appears [13].When compressed, the degree of compression of the crosssectional surface is expressed by If the compressed section remains inside a full hole, it is called a tube.Therefore, if the length is , it is actually called a tube.If the thickness of the wall has a small, negligible frictional resistance when the liquid flows out, we consider it a thin-walled hole, where the wall thickness is usually δ<0,2d.In order to have a fully compressed state, the speed at points A and B should be equal to each other, to have a fully compressed section, the hole should be larger than 3 times the diameter of the sides of the wall a>3d, b >3d.Let's study a thin-walled hole in a vertical wall, the flow rate and consumption of liquid in it are determined by the following formulas

𝜗 = 𝜑√2𝑔𝐻
Here  − speed coefficient.When a liquid flows through a tube, the velocity increases where the fluid flow is compressed inside the tube, which causes the kinetic energy of the flow to increase.As a result, the potential energy decreases, a vacuum is created inside the tube, and as a result, the ability to pass liquid through the hole increases, that is, the value of the consumption coefficient increases.In this case, the consumption coefficient is determined by the following empirical formula: (for a cylindrical outer tube): here -tube length, d -tube inner diameter, λ -coefficient of hydraulic friction resistance, α -a coefficient that takes into account the unevenness that regulates the distribution of the liquid in the cross section.
Coefficient of unevenness and friction, coefficients of local resistance are determined depending on the order of fluid movement and Reynolds number.But today, since there are no analytical formulas for determining the values of the above coefficients, graphical and empirical connections obtained through experience are used.When determining these parameters, it is an acceptable method to obtain the true values by conducting experiments.
Therefore, in the article, using the experimental results, the interdependence of the parameters was determined by constructing a graph.
We determine the speed coefficient using the flow trajectory graph.

2
x Hy

 
from the rate coefficient:     For a small hole, d < 0,1H, because when the pressure H is more than 10 times the diameter of the hole, a compressed surface appears in the flow. 1 We conduct an experiment in a special experimental setup to determine the geometric parameters of the flow.In the experiment, the speed of the flow of liquid at different pressures and the distance of the flow are determined.Based on the results, the speed coefficient is determined and the order of movement is determined.Depending on the velocity of the liquid and the size of the flow, the Reynolds number is determined.Using the Reynolds number, the consumption coefficient is determined from empirical formulas.In the graphs below, the coordinates of the flow are determined depending on the water pressure in the tank.Based on the obtained results, we make a graph for different sizes of tubes and holes.

Conclusion
By analyzing the obtained graphs, we determine the speed, consumption and flight length of water flowing into various pipes and holes.Using stream parameters, we get a link that represents the action.It can be seen from the graph obtained with the results of the experiment that the length of the flow increases with the decrease in the diameter of the hole and conoid tubes.
In addition, it is analyzed that the length of the current flight increases with the increase of pressure.Theoretical and practical results have changed proportionally to each other if the connections in the graph are based on the equation of motion.The reduction in the length of the current is due to the loss of energy there.
Based on the obtained results, the flow rate and the length of its flight are determined.According to these results, the effect of water on other bodies is determined.

Fig. 1 .
Fig. 1.A device for detecting the leakage of liquid from small-hole tubes.

-
consumption coefficient.If we use the equation of motion known in theoretical mechanics for a particle with mass m to determine the flow trajectory, we get the following relation: c xt   , 020 (2023) E3S Web of Conferences IPFA 2023 https://doi.org/10.1051/e3sconf/t-time, ʋc -m initial theoretical speed of a liquid particle with mass, i.e: 2 c gH  From this, the equation of the trajectory of a particle with mass is as follows: the flow rate formula is called the flow rate , In practice, the consumption coefficient is determined from the following empirical formula when low-viscosity liquids flow through a small hole: Reynolds number for an ideal fluid.If we know the speed coefficient, the flow trajectory is determined as follows: Coriolis coefficient that corrects uneven speed distribution α=(1,01 -1,1) ξ -local resistance coefficient.For tubes: /doi.org/10.1051/e3sconf/202345202010 10 452

Fig. 2 .
Fig. 2. Flow of liquid through a conoid hole with a diameter of 4 mm.

Figure 2
Figure2shows the graph of flow trajectories depending on water pressure for a canoeideal tube with a cross-sectional diameter of  = 4.

Fig. 3 .Fig. 4 .
Fig. 3. Flow of liquid through a conoid hole with a diameter of 8 mm.In Figure3, a graph of parameters representing the trajectory of flow constructed based on an experiment conducted in a canoidal tube with a diameter of  = 8  is plotted as a function of the pressure of the water in the tank relative to the tube.

Figure 4
Figure 4 shows the graph of the flow parameters of water flowing out of a hole with a diameter of  = 4  at different pressures, in which the flight length and height are determined depending on the pressure.

Fig. 5 .
Fig. 5. Liquid flow through a simple hole with a diameter of 8 mm.

Figure 5
Figure5shows the graph of flow parameters of water flowing through a hole with a diameter of  = 8 .Using the graph, we can obtain the equation of motion of water, using the equation of motion, we can also estimate the effect of the flow on the barrier, and determine the flow parameters[14][15][16].