Hydraulic resistances experimental and field studies of supply canals and pumping stations structures

Currently, many authors have studied the uniform axisymmetric pressure head laminar and turbulent movement of water in hydraulic smooth and rough (with uniform roughness) pipes of circular cross-section. The results obtained in the study of a plane-parallel turbulent flow in pressure canals allows here only to outline the structure of the corresponding dependencies and to clarify the simplest case of unpressurized fluid movement, when this movement can also be reduced to plane-parallel or, in other words, to movement in a canal of infinitely large width with a flat bottom. In all other cases, the only way to solve the problem is an experiment. The construction of numerous free-flow watercourses and machine canals of pumping stations requires scientifically based calculation methods.


Introduction
At present, numerous pumping stations have been created in the irrigation systems of the Republic of Uzbekistan, with the help of which about 50 billion m 3 of water are pumped per year for irrigation of more than 2 million hectares of irrigated land. The most important element of these pumping stations (PS) are water supply and water supply machine canals and structures of pumping stations (PS) [1][2][3][4][5][6][7]. Turning to the question of those engineering problems, in the solution of which the results of this work can be used, let us select, first of all, from the wide range of design cases related to free-flow canals, the main design case, which we will keep in mind in what follows (as, so to speak, " starting "). In most cases, the formulation of the above tasks boils down to the following -given: soil conditions and the amount of water flow. It is required to find such a slope of the water, at which the shape of its cross-section would be stable (i.e., indelible), and the area of the living section would be the smallest. It is known that such a problem, until recently, was solved by using the concept of "maximum permissible speed" , (referring to the uniform movement of water) [8][9][10][11][12][13][14]. The value of this speed was assigned (and is assigned at present) based on reference data from the type of soil (and, in some cases, depending on the depth of water in the canal). Knowing Vmax and the flow rate, it is easy to find the cross-sectional area and the slope of the canal (using formulas to determine the Shezy coefficient C or the coefficient of hydraulic friction λ and following the accepted value of the roughness coefficient 16,22]. The object of research in operation is the Amu-Bukhara machine canal (ABMC), in the area of the damless water intake from the Amudarya river bed. Sections of the ABMC machine canals, from the head structure to the ABMC-1 and ABMC-2 pumping stations, were taken as the object of hydraulic research [17-21].

Methods
In the process of research, experimental methods, methods of field observation, as well as generally accepted methods in hydraulics, methods of compiling mathematical models based on the laws of hydromechanics, and their numerical calculations were used.

Results and Discussion
The results obtained in the study of a plane-parallel turbulent flow in pressure canals allows us to outline the structure of the corresponding dependencies and clarify the simplest case of unpressurized fluid movement, when this movement can also be reduced to planeparallel or, in other words, to movement in an infinitely large canal [22,23,26]. The results of studying the turbulent uniform free-flow movement of water in smooth canals obtained by various authors for the coefficient R  in smooth gravity canals are similar in general form, which is obvious from (1): And it differs only in the values of the constants , , . decreasing constant in the formula (1) magnitude R  increases. An extensive study of the turbulent movement of water in free-flow canals of rectangular cross-section with uneven-grained (sandy) artificial roughness of the surface of the bottom and walls of the canal was carried out by the author of the work A.P. Zegzhda. The results of this study led the author to an addiction graph: For the quadratic area of resistance, the author obtained the dependence: Where  is absolute grain roughness (the diameter of the grains of sand, which were glued to the surface of the bottom and walls of the canal to create uneven grain roughness) Nikuradze for the area of quadratic resistance in pipes at one time received the dependence: The author of the work is A.P. Zegzhda, relying on the experimental data of Nikuradze, proposes a dependence of the form for free-flow flows: As you can see, the dependences obtained by various authors for the coefficient in free-flow canals with uniform artificial roughness have the form: And differ in the values of the constants , 3 , and 3 . Different values of the constant , , obtained in the works are due, from our point of view, mainly because these works do not fully take into account the effect on the size of the shape of the free cross-section of the canal [24,25,27,28,29].
The results of experiments in experimental and field studies of hydraulic resistances of supplying machine canals and structures of pumping stations, the corresponding experiments are presented on models of free-flow canals of a rectangular and trapezoidal cross-section. And also, to fill the experimental data, the corresponding series of Bazin's experiments were used on models of free-flow canals -rectangular, trapezoidal, and semicircular cross-sections with different roughness. Canals with two types of the roughness of the bottom and wall surfaces were investigated: close to smooth (smooth concrete), and a surface with gravel glued on it = 5 − 7 . In the above experimental canals of rectangular and trapezoidal cross-section, 4 series of experiments were combined. In each of them, 14 -16 experimental points were filmed, with a constant slope of the canal bottom = 0.001. At the same time, 14-16 (usually 16) different flows were passed through the canal; they varied in the range from 4 / up to 250 / . The Reynolds №s varied within = 6400 + 124000, and the Froude №s were < 1.0. The hydraulic radius varied in each series of experiments in the range from 1.72 to 19.45 cm. In each experiment, the flow rate, temperature, and flow depth were measured. In our case ( < 1.0), in all experiments, the normal depth of a uniform flow was determined. In the dissertation work, the criteria for recalculating the results of experimental studies on nature are used. At the same time, the geometric dimensions of the experimental canal were recalculated based on the parameters of a real object, taking into account the scale of modeling. Based on experimental studies of the distribution of vertical velocities of the water flow, as well as field data of machine canals ABMС (water consumption in ABMC -1 = 75 3/ and ABMC-2 is = 150 3/ ) in nature, the water speed on the machine canal is quite high and is equal to (=3÷4,5 m/s), the obtained materials of experimental and natural conditions gave similar results [30][31].
In addition, the following series of Bazin's experiments were processed: Series № 2 (duct with rectangular cross-section: the surface of the bottom and walls of the canal is smooth cement; series № 24 (canal with a semicircular cross-sectional shape; the surface of the bottom and walls of the canal is smooth cement; series № 6 (canal with a rectangular cross-sectional shape; the surface of the bottom and walls of the canal are boards; series № 26 and series № 4 (canal with a rectangular cross-sectional shape; the surface of the bottom and walls of the canal -gravel = 0.01 − 0.02; series № 27 (the canal has a semicircular cross-sectional shape; the surface of the bottom and walls of the canal -gravel = 0.01 − 0.02 .
Determination of the coefficient of hydraulic friction ʎ and the Reynolds №, for all series of Bazin's experiments, was also carried out according to the usual dependencies. At small values of the relative roughness, i.e., in the area of resistance close to smooth, the difference between ʎ for canals of a rectangular and semicircular cross-section is 12 -16%, with an increase ∆/ relationship between ʎ increases to 32 -44%.
Bazin's experimental data in canals with regular cross-sections of various geometric shapes (rectangular, trapezoidal, triangular, semicircular), as well as experimental data on the flow in rectangular and trapezoidal canals obtained in this work; the results of some published data on water flows in canals of various geometric shapes were summarized on the graph below in coordinates Whence for the quantity  the following cubic equation is obtained where,  is desired coefficient of hydraulic friction; пл  is flat flow hydraulic friction coefficient; R is hydraulic radius; χ is wetted perimeter. Equation (9) 2  1  2  1 1  2  3  3  4  27  2  27  9   2  1  2  1  1  2  3  3  4 27 When R/χ<4/27 discriminant less than or equal to zero. In this case, equation (9) has three real solutions, of which (as shown by the analysis), only a solution of the form satisfies the conditions of the problem under consideration: From the above, the following procedure for calculating the coefficient of hydraulic (Where, Re* h = v*h/v: v* -dynamic flow velocity), the value is calculated пл  for flat flow with depth h. Of given formulas for the solution of cubic equation (9) following the given value R/χ, the required value is found  .

Conclusions
1. Experimental data published in the literature on pressure losses in free-flow canals with a "regular" cross-section, as well as the data of our studies, as well as studies of other authors, show that the value of pressure losses in the above canals is not only a function of the Reynolds №, but also a significant degree (especially in canals with a rough wetted surface) depends on the shape of their cross-section.
2. From consideration of the collected experimental data on losses in the abovementioned free-flow canals, it follows that for several canals with different cross-sectional shapes but with the same slopes and the same roughness of the wetted surface, the curves on the graph ( Re ) will be arranged in the following order (from top to bottom); a very wide rectangular canal, a relatively narrow rectangular canal, trapezoidal and triangular canals, a semicircular cross-section canal.