Hydraulic Friction Coefficient Research Articles

Determination of the coefficient of hydraulic friction and factors reducing the value of hydraulic resistance along the length

The article discusses issues related to the determination of hydraulic resistances and the coefficient of hydraulic friction based on scientific research conducted relatively recently. Formulas for determining the coefficient of hydraulic friction by various authors and studies on determining the value of hydraulic resistances are presented, which propose a non-traditional method for determining the average speed along the pipeline section. The works studying the influence of liquid temperature and the introduction of polymer additives on the amount of hydraulic losses are analyzed.

ГІДРОДИНАМІКА ФІЛЬТРУВАННЯ ТЕПЛОВОГО АГЕНТУ КРІЗЬ СТАЦІОНАРНИЙ ШАР ГРАНУЛЬОВАНОЇ КРЕЙДИ

The experimental results of the hydrodynamics of filtration of the thermal agent in a stationary layer of granular chalk are given. As a result of the conducted experiments, new calculation dependencies were obtained for determining the hydraulic resistance of a layer of granular chalk depending on the filtering speed of the heat agent and the height of the material layer. Calculation dependencies for determining the coefficient of hydraulic friction were also proposed and its dependence on the Reynolds number was established. This will make it possible to determine pressure losses in the material layer during equipment design and the economic feasibility of modernizing production processes.

Coefficient of hydraulic friction of plastic pipes

Pressure systems are widely used in almost all areas of the public economy related to liquids. For example, at present, in the supply of drinking water to populated areas in the world, in heating systems, in agriculture, in cleaning water basins from muddy flows, in the mining industry, in construction, in the raising of muddy flows, in the chemical industry, in the process of moving muddy flows at the same speed, in pipeline systems of viscous muddy flows efficient systems are being used for transportation and many other purposes. Recently, plastic pipes have been widely used in production. Such pipes are cheap, light, and resistant to various decays, and their installation is relatively easy. One of the main problems in the hydraulic calculation of pressure systems is the determination of the coefficient of hydraulic friction. Recently, many scientists working in the field have been improving the hydraulic calculations of such pipelines. Yet, there is still a lot of theoretical and experimental research to be done. The article presents a method for determining the coefficient of hydraulic friction in plastic pipes in laboratory conditions.

Modification of dispersed systems and its effect of the internal corrosion of hydrotransports

Studies The impact of the modification of dispersed systems of kinematic and dynamic parameters of hydraulic windows, as well as wear in pressure pipes, taking into account the variability of the mechanical composition and the number of hydraulic windows. It is recommended for the modifying additives of the GosIpol resin for dispersed systems and its movements in the cylindrical pipes. The current model that takes into account the concentration of turbidity in the stream and the structural composition of dispersed systems, developed methods of calculation in the process of hydrotransport of modified dispersed systems. The method of calculating the rate of internal corrosion of hydrotransports, specific pressure losses for fluid and solid flow and the effect of variability of the mechanical composition of particles and concentration of turbidity to the flow rate and power of the modified dispersion system is justified, the dependence of the hydraulic friction coefficient from the flow movement mode, taking into account the variability of the solid flow concentration in modified dispersed systems of hydrotransport.

Численное моделирование явления гидроудара с учетом гидравлического трения трубопровода методом контрольных точек

The calculations of dynamic processes in the pipeline are necessary for modeling the processes of fluid movement in the pipeline, for example, for predicting loads on the pipeline when compression and rarefaction waves move in it. These tasks are reduced to solving systems of partial differential equations. The calculation of the phenomenon excluding hydraulic friction can be carried out by the method of characteristics, however, the calculation, taking into account the friction forces, is complicated for known methods, such as the finite difference method and the final element method. The article provides a brief description and an example of using the control point method for the task of modeling the water hammer phenomenon, taking into account the hydraulic friction forces of the pipeline. The main idea of the proposed method is to reduce the solution of these systems of equations to solving linear programming problems. The purpose of this work is to solve the problem of water hammerwith friction by the control point method. This method, developed jointly with A.S. Maksimov by the authors of this article at the Melentiev Energy Systems Institute, has shown good results in solving systems of partial differential equations of a periodic heat exchanger with ceramic ball filling. Moreover, heat transfer inside these elements was taken into account. With large values of thermal conductivity coefficients, this system is also rigid, which complicates its solution by the control volume method, but the control point method has shown good results. This gives reason to consider it promising in calculations of hydraulic friction. The results of modeling a hydraulic shock to a pipe filled with an incompressible liquid at different friction coefficients have been obtained. The results make it possible to make a numerical assessment of the effect of the o hydraulic friction coefficient on the attenuation of oscillatory processes during a hydraulic shock.

The problem of hydraulic calculation of pressure distribution pipelines

Most production technologies require a uniform flow path of liquid from pressure distribution pipelines. To achieve this goal, it is proposed to introduce polymer additives into the liquid flow or to use converging distribution pipelines with a continuous longitudinal slot in the wall. To reduce the uneven operation of the distribution pipeline during discrete liquid dispensing, it is proposed to use cylindrical output rotary nozzles with a lateral orthogonal entry of the jet into the nozzle. The problem is the lack of methods for accurate hydraulic calculation of the operation of distribution pipelines. Adequate calculation methods are based on differential equations. Finding the exact solution of the differential equation of fluid motion with variable path flow rate for perforated distribution pipelines is urgent, because it still does not exist. The available calculation methods take into account only the right angles of separation of the jets from the flow in the distribution pipeline. These methods are based on the assumption that the coefficient of hydraulic friction and the coefficient of resistance of the outlets are constant along the flow. A calculation method is proposed that takes into account the change in the values of these resistance coefficients along the distribution pipeline. The kinematic and physical characteristics of the flow outside the distribution pipeline are also taken into account. The accuracy of calculating the value of the flow rate of water distributed from the distribution pipeline has been experimentally verified. The error in calculating the water consumption by the method assuming that the values of the resistance coefficients are unchanged along the distribution pipeline reaches 18.75 %. According to the proposed calculation method, this error does not exceed 6.25 %. However, both methods are suitable for the design of pressure distribution pipelines, provided that the jet separation angles are straight. Taking into account the change from 90° to 360° of the angle of separation of the jets from the flow in the distribution pipeline will expand the scope and accuracy of calculation methods.

Optimization of Long-distance Oil Pipeline Production Operation Scheme

XX oil pipeline is responsible for transporting crude oil from XX to XX refinery. According to the actual operating conditions of the pipeline, it is known that the pipeline operation scheduling plan is manually formulated based on experience, resulting in a large amount of waste of fuel energy and electrical energy. In order to improve the economic benefits of pipeline operation and reduce system energy consumption, it is of great practical significance to optimize the pipeline operation scheduling scheme. In order to reduce the deviation between theoretical calculation and actual data, the total heat transfer coefficient and hydraulic friction coefficient of the pipeline are corrected and fitted according to the principle of least square method, which effectively improves the accuracy of the calculation method. Take the minimum total energy consumption cost of the entire pipeline as the objective function, take the outbound temperature and pump combination scheme of the entire pipeline as the decision variables, and take the inbound temperature, outbound temperature, flow rate, heating furnace heat load, and pump unit characteristics as constraints Conditions, the establishment of the XX oil pipeline production operation scheduling program optimization mathematical model. The model is an optimization design problem including discrete variables and continuous variables, which is solved by dynamic programming according to the structural characteristics of the model. The optimization results show that energy consumption in winter and summer has been reduced by 23% and 18%, respectively.

Исследование изменения коэффициента гидравлического трения материалов напорных труб при различных температурах

Снижение затрат электроэнергии на механическую транспортировку воды по напорным трубопроводам за счет уменьшения гидравлического сопротивления внутренних стенок труб носит актуальный характер. Это обстоятельство предопределяет необходимость проведения соответствующих гидравлических испытаний альтернативных материалов, которые могут быть использованы при проектировании и строительстве трубопроводных систем. Целью исследований является выявление характера изменения величины гидравлического трения в зависимости от температурных условий транспортируемой воды и окружающей среды в определенных диапазонах с последующей возможностью управления процессом транспортировки при минимуме затрат на электроэнергию. Достижение поставленных целей осуществляется путем опытного и расчетно-аналитического подходов к определению динамики изменения гидравлических показателей трубопроводов из различных материалов. Представлен комплексный анализ экспериментальных и расчетных данных, полученных с помощью запатентованных автоматизированных комплексов, по определению коэффициентов гидравлического трения для полиэтиленовой трубы и трубы из непластифицированного поливинилхлорида и динамики изменения этих коэффициентов в зависимости от температуры транспортируемых вод и температурных условий прокладки трубопроводов. Reducing the cost of electricity for the mechanical transportation of water through pressure pipelines by reducing the hydraulic resistance of the inner walls of the pipes is of current importance. This circumstance predetermines the need for appropriate hydraulic testing of alternative materials that can be used in the design and construction of pipeline systems. The aim of the study is to identify the nature of the change in the value of hydraulic friction depending on the temperature conditions of the transported water and the environment in certain ranges, with the subsequent possible control of the transportation process with a minimum of energy costs. The set goals are achieved by experimental computational and analytical approaches to determining the dynamics of changes in the hydraulic parameters of pipelines made of various materials. A comprehensive analysis of the experimental and calculated data obtained using patented automated systems for determining the coefficients of hydraulic friction for a polyethylene pipe and a pipe made of unplasticized polyvinylchloride, and the dynamics of changes in these coefficients depending on the temperature of the transported water and the temperature conditions of pipeline laying is presented.

Influence of the temperature factor on the hydraulic resistance of pressure pipes

The assessment of the temperature factor influence on the pressure pipeline hydraulic operation mode is very relevant, since it is considered primarily as an opportunity to reduce the cost of mechanical water transportation. Smaller pressure pipe hydraulic resistances save the electrical energy consumption, and the temperature factor has an additional positive effect on the energy saving process. The purpose of the research is to identify the nature of changes in the hydraulic friction value in relation to the temperature conditions of the transferred water temperature and environmental conditions in the designed ranges, with the subsequent possible control of the transportation process with minimum electrical energy consumption. The method of achieving these goals is an experimental and analytical approach aimed at determining the dynamics of changes in the hydraulic parameters of pipelines made of various materials. The tasks of experimental bench studies include the development of a method for calculating the values of hydraulic friction coefficients for pressure pipelines. The results of hydraulic experiments and comprehensive analysis of the experimental and calculated data for determining the hydraulic friction coefficients for polyethylene pipe are presented. The calculated values of the hydraulic friction coefficient were compared with the experimental ones, which enabled identification of their sufficiently high convergence. The conclusions show a positive effect of reducing hydraulic resistances depending on the increase in the temperature of the transported water.

Substantiation of the influence of the channel shape and the roughness of machine canals on the pressure loss of irrigation pumping stations

To take into account the influence (on the value of head losses) of the channel cross-sectional shape and the presence of a flow with a free surface in it, additional correction factors are introduced (when using the concept of hydraulic radius), as well as new dependencies and formulas for determining the coefficient of hydraulic friction are presented, taking into account the influence of the morphometric elements of the channel on the hydraulic resistance of the machine channels of pumping stations. The article presents the results of hydraulic studies in free-flow and pressure water pipelines, the results of which showed that the dependencies obtained for calculating hydraulic resistance in round pressure pipes cannot be extended without appropriate adjustments to the pressure-free channels (provided that the pipe diameter is replaced in the corresponding calculations D-value 4R, where R-hydraulic radius). This position is justified by the presence of a number of factors that distinguish the pressure movement of liquid in pipes from its free-flow movement in the channels, where there is a free flow surface, a wider range of roughness of the channel bottom and walls, a different (than in pipes) distribution of tangential stresses along the wetted perimeter, the possibility of two different flow states (depending on the slope of the channel bottom). The work also considers the general equation of fluid motion in free-flow channels and the functional dependences of the hydraulic friction coefficient on the Reynolds number, relative roughness and on the shape of the free section of the channel; resistance formulas, first for the simplest channels with respect to the cross-sectional shape (round and infinitely wide rectangular), and then for channels with a more complex cross-sectional shape.

Hydraulic Friction Coefficient at Hydraulic Mixing Movement in Pressure Pipelines

Hydraulic Friction Coefficient at Hydraulic Mixing Movement in Pressure Pipelines

The influence of the shape the living section of the pressureless machine channel and the roughness of its wetted surface on the hydraulic resistance

Turning to the question of those engineering problems, the solution of which can be used the results of this work, let us first of all select from the wide range of design cases related to pressureless channels, the main design case, which we will keep in mind in the future (as, so to speak, «starting»). Concerning the indicated main design case, we agree to consider the non-pressure movement of water in the prismatic channel (operating in summer conditions) along which uniform turbulent movement of water occurs, which is almost pure in the absence of waves and other phenomena that violate the uniform motion regime, assuming that if such phenomena are taking place, then they should be taken into account the introduction into the calculations of the relevant adjustments. The statement of the above problems in most cases boils down to the following, it is necessary to find a water slope such that its cross-sectional shape is stable (indelible) and the living cross-sectional area is smallest. It is known that such a problem, until recently, was solved by using the concept of “maximum permissible speed” V max (related to the uniform movement of water). The magnitude of this speed was assigned (and is currently assigned) based on reference data on the type of soil (and in some cases depending on the depth of the water in the channel). Knowing V max and the flow rate, one can easily find the cross-sectional area, as well as the channel slope (using formulas to determine the Shezi coefficient «C» or hydraulic friction coefficient λ and following the accepted value of the roughness coefficient). In engineering practice, when hydraulic calculations of the channels under consideration, we usually use the Shezy coefficient «C». Meanwhile, there is a shared opinion by us that, when performing the above calculations, it is more advisable to use the coefficient of hydraulic friction λ.

Influence of the shape of the pressureless trapezoidal channel and roughness on the pressure loss of the machine channels of the pumping stations

In this work, we consider the general equation of fluid motion in pressureless channels and the functional dependences of the coefficient of hydraulic friction on the Reynolds number, relative roughness, and the shape of the live section of the channel, as well as the resistance formulas for the simplest channels with respect to the cross-sectional shape (round and infinitely wide rectangular), and then for channels with a more complex cross-sectional shape. To take into account the effect (on the pressure loss) of the channel cross-sectional shape and the presence of a flow with a free surface in it, additional correction factors are introduced (using the hydraulic radius concept). In conclusion, it is concluded that the values of the mentioned correction factors can and should be refined only as a result of the relevant experiments. The work also examined the patterns of hydraulic resistance in engine channels of the correct form of a live section with uniform turbulent fluid motion. Formulas of hydraulic resistance in the machine channels of a simple and complex outline of a live section are given.

Water jet cutting resistance

The main purpose of the study was establishing the coefficient of hydraulic resistance of two-phase flow using in water jet cutting. In waterjet cutting (JWC) and in abrasive waterjet cutting (AJWC), a two-phase flow consist of water and abrasive solid particles, moves at a high mean velocity (more than 8.0 m/s). Such flows differ from natural and well-studied flows in hydraulic transport. The aim of this work is to investigate experimentally the additional pressure losses during transportation of the abrasive. For the experimental research were used. The supply of fire extinguishing agents is carried out along the sleeve lines, and, as is known, there are pressure losses. In this regard, the problem arises, at what maximum distance from the pumping unit is possible to supply fire extinguishing agents in the form of water and a mixture of water and abrasive particles, and how pressure losses occur in this case, because the flow rates and working pressure of fire extinguishing systems with waterjet cutting are high enough (the working pressure is 30 MPa). The loss of pressure during transportation depends on the flow rate, its viscosity, pipeline characteristics, etc. The results of field studies to determine the basic kinematic characteristics of the two-phase flow are presented. The combination of these parameters is largely characterized by the coefficient of hydraulic friction, which is insufficiently studied for the systems under consideration. As a result of the obtained experimental data, based on the Darcy-Weisbach equation, the coefficient of hydraulic friction was determined, the value of which was 0.019. The coefficient of local resistance was 0.45.

The effects of morphometric elements of the channel on hydraulic resistance of machine channels of pumping stations

Presents the results of hydraulic studies in pressureless and pressure water conduits, the results of which showed that the dependences obtained for calculating the hydraulic resistance in round pressure pipes cannot be distributed without the corresponding adjustments of pressureless channels (provided that the diameter of the pipe is replaced in the corresponding calculations with a value where hydraulic radius). In particular, it follows (and this is confirmed by the data of the corresponding experimental studies published in the literature) that in the case of pressureless channels, the pressure loss coefficient, and therefore the pressure loss, depends not only on the relative roughness and Reynolds number, but also on the shape of the cross section the channel. Moreover, if for hydraulically smooth pressureless channels this dependence can be considered to a first approximation clarified, then for channels whose wetted surface is characterized by the presence of a certain roughness, the question of its influence, as well as the shape of the channel cross section on the pressure loss, is far from roughly approximate solution. The paper also considers the general equation of fluid motion in pressureless channels and the functional dependences of the coefficient of hydraulic friction on the Reynolds number, relative roughness, and on the shape of the living section of the channel; resistance formulas are first for the simplest with respect to the cross-sectional shape of the channels (round and infinitely wide rectangular), and then for channels with a more complex cross-sectional shape. To take into account the effect (on the pressure loss) of the channel cross-sectional shape and the presence of a flow with a free surface in it, additional correction factors are introduced (using the hydraulic radius concept) as well as new dependencies and formulas for determining the hydraulic friction coefficient are given, s taking into account the influence of morphometric elements of the channel on the hydraulic resistance of the machine channels of pumping stations.

Research of the dependence of the hydraulic friction coefficient of the liquid (λ) on the reinolds number (Re) applicable to the hydraulic drive

AnnotationExperimental studies of the dependence of the coefficient of hydraulic friction λ on the Reynolds number Re at the stand “Hydraulics” in relation to the hydraulic drive. The formula for determining the coefficient of hydraulic friction for a turbulent regime of fluid motion is refined. Based on the results of studies, a graph of the dependence of the coefficient of hydraulic friction λ on the Reynolds number Re with an analysis of the four zones of this dependence is constructed.

Затраты энергии в высокотемпературном сверхпроводящем трёхфазном кабеле переменного ток

The basic circuit diagrams of cryogenic installations that can ensure the necessary temperature operation conditions of power cables on the basis of high-temperature superconductors are considered. Formulas for calculating the energy consumed for cooling the cable by means of closed- and open-type cryogenic installations are determined. The hydraulic losses determining the energy expenditures for pumping the cryoagent in the cable cryostat with corrugated shells are analyzed. The components of the power required to compensate for the losses in transmitting electric energy via a superconducting cable are determined. As a result, a procedure for calculating energy expenditures for cryogenic installations in different cycles of their operation is proposed. The hydraulic friction coefficient in the flexible cryostat shells is determined. The available empirical relations for estimating the hydraulic friction coefficient in a flexible cryostat are compared with one another.

THEORETICAL CALCULATION OF THE VALUE OF THE VON KARMAN CONSTANT

The article considers various approaches to assessing the physical essence of the von Karman constant characterizing the vertical distribution of the flow velocity. On the one hand, the von Karman constant is a proportionality coefficient between the length of the mixing length and the depth; on the other hand, it characterizes the tilt angle of the vertical velocity profile. It is considered that this parameter is universal, that means it is constant as long as the averaged velocity distribution is constant. However, depending on estimation way of this constant, its values under the same conditions may differ to 2 orders. Two methods for estimating the von Karman constant are considered. In the first case, determination of the von Karman constant is on the grounds of direct measurements of the maximum and average flow velocities, depth and slope of the water surface in a particular area. Propagation of the obtained value to other objects will lead to errors. In the second case, the parameter is defined as a function of the coefficient of hydraulic friction. The authors showed that the von Karman constant is a function of the coefficient of turbulent exchange (viscosity) and indirectly is a function of the depth. As a result of the calculations, it was shown that the maximum values of the von Karman constant observed on the bottom. Additionally, the authors propose a new version of the calculation of the von Karman constant through the tension shift for a turbulent flow. It is concluded that since for velocities <1 meter per second the changes in the von Karman constant values from 0.27 to 0.38 the maximum velocity with variation do not exceed 3%, which fits into the accuracy of the velocity measurements, it is practically impossible to estimate the value of von Karman constant by first method for flat rivers even with multiple measurements with standard hydrometric equipment. Keywords: the von Karman constant; coefficient of turbulent exchange (viscosity); Reynolds number; coefficient of hydraulic friction; velocity distribution diagram; turbulent mode

Transportation of river sediments in cylindrical pipeline

This article deals with the hydraulic transport of river sediments in a cylindrical pipeline. To describe the nature of hydraulic phenomena, experiments were provided for single-phase and two-phase flows in field and laboratory condition. According to the results of the experiments, the main hydraulic parameters of the proposed jet device for hydro transportation of river sediments were determined. Based on the processing of the available data, as well as the data of specially commissioned experiments, the dependencies of flow rates, speed, jet constraining and resistance when the pulp flow from the jet apparatus has expired on the Reynolds number, are valid for certain limits of Reynolds number change. As a result of special experiments, the dependences of local resistance coefficients on the Reynolds number for some practically important cases (when the net flow and pulp from the jet apparatus pipeline have elapsed), valid within certain limits of change of Reynolds numbers, are established. The design parameters of the jet apparatus for the purification of water bodies from river sediments are substantiated, the design formulas for determining the hydraulic parameters of the proposed jet apparatus are proposed. A calculation formula for determining the flow rate of the slurry jet apparatus is proposed. As a result of special experiments, the dependences of the coefficient of hydraulic friction on the Reynolds number for various saturations of flow with a suspension are established. The article offers a new method for determination critical velocity two-phase current, and proposed method is valued with given laboratory condition.

Гідродинаміка руху теплового агента під час фільтраційного сушіння Miscánthus giganteus

Наведено результати експериментальних досліджень гідродинаміки руху теплового агента крізь стаціонарний шар подрібненого Miscánthus giganteus. Визначено основні параметри шару miscánthus giganteus та вибрано еквівалентний діаметр каналів між частинками de. Подано основні технічні характеристики miscánthus giganteus. Проведено експериментальні дослідження гідродинаміки фільтрування теплового агента крізь стаціонарний шар miscánthus giganteus. Наведено експериментальні дослідження гідродинаміки шару miscánthus giganteus від фіктивної швидкості теплового агента. Отримано рівняння, яке описує складну залежність між напором і швидкістю, зумовлену пружними властивостями miscánthus giganteus. Отримане рівняння дає змогу прогнозувати енергетичні затрати на створення перепаду тиску під час сушіння в стаціонарному шарі Miscánthus giganteus у межах зазначених похибки і меж висоти шару та фіктивної швидкості. Представлено коефіцієнт опору шару miscánthus giganteus у вигляді безрозмірних комплексів як функцію числа Рейнольдса. Визначено коефіцієнт гідравлічного тертя l. Проаналізовано абсолютне значення відносної похибки між теоретично розрахованими значеннями та експериментальними даними. Одержано критеріальні залежності, які дають змогу використати отримані результати для проектування нового сушильного обладнання за подібних гідродинамічних умов.