Experimental evaluation of hydraulic resistance of pipelines from modern polymer materials

: The aim of the studies was to test the hydraulic pressure losses along the length, local pressure losses, absolute and relative roughness values of the pipeline walls made of modern polymer material. The article presents the results of the experimental studies of hydraulic resistance of pipelines from modern polymer materials, the method of theoretical determination of resistance coefficients in the VALTEC ISO 21003 metal polymer pipeline, the classification and method of determining the values of local hydraulic resistance coefficients of T-Junctions are given, the dependence for determining the Darcy  hydraulic friction coefficient associated with the value of the equivalent hydraulic roughness coefficient of the inner surface of pipes and the Reynolds number. The experimental data of the hydraulic coefficient of friction Darcy λ was compared with the known theoretical relationships of A.D. Altschul, Colbrooke for smooth pipes, Colbrooke and White, an alternative to the Colbrooke-White, Offengenden equation for low-shear pipes and pipes from polymer materials with Reynolds numbers Re > 10 4 . Dependence of hydraulic coefficient of friction on relative equivalent roughness of pipeline walls and Reynolds number, specific energy loss per one linear meter on total flow rate in system of hydraulically short pipeline is obtained. The empirical dependence of values of coefficients of local resistance ζ=f(Q2/Q3) from a ratio of the divided expenses of Q2/Q3 of the equal-pass T-Junction α=90 0 the pipeline to a branch up, on pass in the direct T-Junction and division of streams at various internal pipeline diameters of VALTEC.


Introduction
When designing and hydraulic calculation of pipelines from modern polymer materials, two types of head losses are taken into account: • pressure losses along the length (water friction against pipeline walls); • local head losses (overcoming resistance in pipeline fittings: in shaped parts and pipe elements, in confusers and diffusers, in taps, turns and T-Junctions (when mixing and separating flows), in check valves, ball valves, valves and other elements.
The total hydraulic losses are expressed by the algebraic sum of the above head losses. Friction losses are determined by theoretical formulas or as a result of experimental studies. Local head losses are determined by reference or experimental data for a particular local resistance. Hydraulic calculation of pipelines from polymer materials requires taking into account a large number of a number of placed elements in the pipe fittings, which cause the occurrence of total local resistances. The kinematic structure of the flow behind these local resistances is complex, which means that in calculations the use of reference data is not always possible and correct.
In hydraulically short pipelines, quantitative head losses in local resistances can be 10÷15% from the total head losses.
The ubiquitous use of composite materials and new pipe manufacturing technologies contribute to the widespread use of polymer pipes. Reduction of total head losses along with accurate determination of their values is an urgent problem during transportation of liquids by pipelines. In the hydraulic calculation of pipelines of water, gas and heat supply systems made of polymer and metalpolymer pipes, it is necessary to determine the value of friction losses and local head losses.
The current state of the problem. The study of hydraulic resistances of polypropylene pipes and fittings is devoted to the work of I.Cisowska, A.Kotowski [1], experimental tests of head losses in plastic fittings, article T. Siwiec, D.
The determination of head losses along the length is based on such a parameter as the Darcy coefficient  determined by the Darcy-Weisbach equation [5] and dependent on the value of the coefficient of equivalent hydraulic roughness of the inner surface of pipes  э =k e and the Reynolds number. The value of equivalent hydraulic roughness  э =k e can only be determined experimentally [6]. It is not allowed to use in calculations the absolute roughness of pipes measured by a profilometer, which is usually given in the manufacturer's certificate [7].
Friction resistance coefficients of polymer (plastic) pipes can be determined by formulas proposed by J.S. Offengenden [10]. In most cases, plastic pipes are small-haired ( э =k e < 0.03mm). The smallest absolute roughness is fluoroplastic pipes, the largest is fiberglass and phaolite pipes. In plastic pipes, micro-and macrovolarity is observed due to the technology of their manufacture. In the first approximation with Reynolds numbers (with an error of up to 25% or more) for hydraulic calculation of plastic pipes it is possible to use the formula Colbrooke [8], Colbrooke-White [3] or alternative to the equation Colbrooke-White [9] with substitution of values of  э =k e given in tables of reference for calculations of hydraulic and ventilation systems [10]. For polyethylene (unstabilized), fluoroplastic and polypropylene pipes the value of  э is not determined, since for them the coefficient λ can be found by formulas for smooth pipes [10].
Tables of reference book [10] show data on the value of equivalent surface roughness for polyethylene pipes equal to  э =k e =0,007 mm (multilayer pipes for water supply and heating systems with internal polyethylene layer). The sources [10,11,12] give recommendations on the selection of equivalent roughness of the inner surface of pipes made of polymer materials with roughness values of э=ke  0,01 mm, and copper and brass pipes with values of э=ke э  0,11 mm [11,12].
In the reference literature for plastic pipes (polyethylene, vinyl plastic), it is recommended to take equivalent roughness values equal to the values for allstretched pipes made of brass, copper or lead (technically smooth) -э=ke =0,0015÷0,0005 mm , polyethylene pipes (2-20 mm) =0,003 mm [10]. According to manual [7], the equivalent roughness of the metal polymer pipeline is -, which makes them comparable in smoothness with new copper and glass pipes [7]. At the same time, it is indicated that the roughness of steel and copper pipes increases during operation, and in metal-plastic pipes this indicator remains unchanged for the entire service period [7].
In a pressure head turbulent stream for Reynolds numbers = 10 4 ÷ 10 5 values of coefficients of local resistance ζ depend generally on geometrical characteristics of a stream, Reynolds number practically doesn't affect values of these coefficients. According to the recommendations of A.D. Altschul for local pipeline resistances in which flow narrows, with its subsequent expansion, the auto-model zone begins with Reynolds numbers > 10 4 [14], therefore, in copyright studies of losses on local resistances, auto-model by Reynolds number took more 10 4 . Therefore, in the hydraulic calculation of the metal polymer pipeline and its design, it is required to use the values of experimental coefficients of local head loss and length to accurately account for losses, which is an urgent task.
Chalecki, P. Wichowski [36,37]. The design of the T-Junctions is very diverse, the studies were carried out as a result of the selection and comparison of the resistance coefficients of the T-Junctions based on the classification below ( Fig. 1). Lateral branch: see table and curves Straight pass: see table and curves For T-Junctions of type For T-Junctions of type where п reference data [10].
Experimental metal polymer pipeline VALTEC ISO 21003 was installed in the hydraulics laboratory RSAU-Moscow Timiryazev Agricultural Academy (Fig.2), the pipeline was fixed with plastic ties to the base. The material and diameter of the pipeline was chosen due to its resistance to salt deposits and fouling with iron oxide during operation, as presented in work [4], as well as  Length of stabilization l section is determined by formula: For turbulent motion, the initial length of the section for all regions of resistance can be determined by the formula of V.S. Borovkov and F.G.

Mayranovsky [13]
: According to the formula E.A. Gizh, the length of the initial section in the pipes during turbulent mode depends on d, coefficient λ and is taken into account by the formula: where λis the Darcy coefficient in a uniform flow. Procedure for calculation of experimental data: In the pressure tube with diameter d and flow rate Q, the cross-sectional area ω and the flow rate of water V were determined: In each series of experiments, the water temperature of the hydrometric tray was measured with a thermometer. By measurements, the kinematic viscosity coefficient of water and the Reynolds number were determined: where Vis the average flow rate, m/s; dpipe diameter, m; ωthe area of live section of a pipe, m 2 ; Qwater flow rate, m 3 /s; νcoefficient of kinematic viscosity,    Altschul [14], Colbrooke [6.8], Colbrooke-White [3] or alternatives to the Colbrooke-White equation [9] and J.S. Offengenden points. Theoretical calculation for polymer pipelines can be made according to formulas of other researchers [26,27,28,29,30] using obtained values of absolute and relative roughness of pipeline walls.
The error of hydraulic measurements was calculated according to GOST R ISO [25]. The main hydraulic parameters defined in the experiment − hydraulic coefficient of friction λ and coefficient of local resistances ζ, which are calculated indirectly and require careful determination of errors of experimental data.
Formulas for determining the values of  and ζ: Systematic and random errors of the experimental value of the hydraulic friction coefficient] and the coefficient of local resistances were calculated in the work. In the formula for calculating the bias of the Darcy coefficient, the parameters measured in the experience were substituted: The random component of the Darcy coefficient error was calculated by the formula: The total relative error of determining the Darcy coefficient was calculated using the formula: and with a confidence probability of 95% was ±4,05% .
The random error component of the local resistance coefficient was calculated using the formula: The total relative error of determining the coefficient of local resistances was calculated using the formula: and with a confidence probability of 95% was ±3%.
As in article [4], based on experimental data, reliable statistical dependencies of specific energy loss on consumption are obtained (Fig. 5).   The results of accuracy of hydraulic experiments were established according to the requirements of GOST R ISO [25]. Experimental studies were carried out under conditions of repeatability and reproducibility. Since the systematic and random components of the error of determining resistance coefficients were comparable, the total relative errors of the Darcy coefficient and local resistances were calculated, which amounted to ± 4.05% and ± 3%, respectively (for a confidence probability of 95%).

Conclusions
Based on the performed experiments, head losses along the length in the

Funding
This study received intra-university grant support for research projects within the framework of the academic strategic leadership program "Priority 2030"

Russian State Agricultural University -Moscow Timiryazev Agricultural
Academy.

Data Availability Statement
Data will be available on request.