Water Conduits Research Articles

Modeling of Explosive Pingo-like Structures and Fluid-Dynamic Processes in the Arctic Permafrost: Workflow Based on Integrated Geophysical, Geocryological, and Analytical Data

Understanding the mechanisms responsible for the origin, evolution, and failure of pingos with explosive gas emissions and the formation of craters in the Arctic permafrost requires comprehensive studies in the context of fluid dynamic processes. Properly choosing modeling methods for the joint interpretation of geophysical results and analytical data on core samples from suitable sites are prerequisites for predicting pending pingo failure hazards. We suggest an optimal theoretically grounded workflow for such studies, in a site where pingo collapse induced gas blowout and crater formation in the Yamal Peninsula. The site was chosen with reference to the classification of periglacial landforms and their relation to the local deformation pattern, according to deciphered satellite images and reconnaissance geophysical surveys. The deciphered satellite images and combined geophysical data from the site reveal a pattern of periglacial landforms matching the structural framework with uplifted stable permafrost blocks (polygons) bounded by eroded fractured zones (lineaments). Greater percentages of landforms associated with permafrost degradation fall within the lineaments. Resistivity anomalies beneath pingo-like mounds presumably trace deeply rooted fluid conduits. This distribution can be explained in terms of fluid dynamics. N–E and W–E faults, and especially their junctions with N–W structures, are potentially the most widely open conduits for gas and water which migrate into shallow sediments in the modern stress field of N–S (or rather NEN) extension and cause a warming effect on permafrost. The results obtained with a new workflow and joint interpretation of remote sensing, geophysical, and analytical data from the site of explosive gas emission in the Yamal Peninsula confirm the advantages of the suggested approach and its applicability for future integrated fluid dynamics research.

Symbolism of Sacred Art in Water Conduits

Nepal is a country with abundance of traditional art, architecture and culture. Almost every monument comprises faith, belief, devotion and sacredness which are initiated to be expressed through symbolic representation. Historicity of water conduit of Kathmandu valley can be traced back to early Cristian Era. They were installed to fulfill basic need of water. Flowing water is compared to goddess Ganga. Thus, every water conduit is equated to goddess Ganga with depiction of a crocodile, her vehicle. Cent percent water conduits of the valley consists of sculptural art associated to Hindu or Buddhist deities and a few with architectural monuments. It also comprises sculptural art of several creatures as; serpent, fish, frog, chameleon, mongoose. These deities, monuments and creatures are found to be a symbolic expression of theme associated with religious belief and faith. In this context, finding out the theme of an art expressed in a water conduit, chief feature of sacred sculptural art of water conduits and symbolic representation of sculptural art of water conduits of Kathmandu valley have been focused as an objective of this research. This qualitative research is based upon historical fact. Thus, the facts are collected from historical monuments through survey, interview, collection of photographs and are analyzed in a descriptive way. Related literary sources have been consulted as a secondary source. From several references, it is to be considered that water conduits of the valley have been basically set up for social and religious utility with installation of several deities according to their faith. Art of each conduit as well as image portrays specific features belong to related historical age. Besides this, each sculptural art depicted on the conduit conveys symbolism of goddess Ganga and several pilgrimages composed within a precise pious abode.

Modeling of scale-dependent perforation geometrical fracture growth in naturally layered media

In this study, the discrete lattice simulation of multi-scale fracture growth in layered media is conducted and validated against fracturing laboratory observation and field micro-seismic monitoring. The results reveal that the perforation can substantially influence hydraulic fracture initiation and extension. The vertically-oriented-perforation induced fracture will effectively initiate with moderate near-wellbore complexity, promoting fracture crossing at bedding interfaces. The interlaced design of perforation cluster can alleviate the stress shadow effect and facilitate uniform fracture propagation. The far-field fracture complexity are related to the bedding interfacial properties: more tensile interfaces tend to arrest induced fractures and restrict their vertical growth, while more fracturing fluid will be diverted into the permeable interfaces of lower shear strength. The complex fracture networks has the potential to trigger fault reactivation or serve as conduits for underground water, thus causing induce seismicity or aquifer contamination. The findings can enrich the understanding of multi-scale fluid-solid coupling mechanisms and further help us prevent geological hazards.

Alternative Arrangement for Roof Tops Rural Housing Catching Rain Water in the Semi-Arid

Harvesting rainwater for human consumption through rooftops is becoming an increasingly common practice, especially in regions where there are no community water supplies, such as much of the Indian semi-arid region. The water collection systems installed in this region are based on the construction of cisterns to collect water collected through roofs. In order to contribute to the improvement of the performance of these systems, this work aimed to study the problems preventing the proper functioning of this important water supply and to propose design solutions adapting appropriate technologies for the rural population of the Indian hemisphere, Arid region. The starting point was a field study conducted in the rural community of Namakkal Taluk in Tamil Nadu between 2020 and 2021. The results showed that 80% of the residential buildings surveyed have a water intake system, but only 16% store enough water for a year-round supply. It was found that this low rate is mainly due to unreliable conditions for installation and maintenance of water conduit subsystems (gutters and channels). Based on this finding, and taking into account functional and aesthetic-formal aspects, five alternative devices for rainwater harvesting systems, consisting of roofs, gutters and channels, were developed. In order to simplify and, as a result, reduce the cost, the gutter supports were eliminated, which gave a performance advantage over conventional systems.

Расчет времени охлаждения надземного водовода с теплоизоляцией в условиях отрицательных температур

Objective: transport infrastructure facilities include a variety of water supply systems. In the event of an emergency, after stopping the movement of water in the pipeline, it is cooled first, and then there is a risk of freezing and destruction of water pipelines. This work is devoted to the calculation of the cooling time of water in the above-ground water conduit with thermal insulation from the specified temperature value in the initial state to the freezing temperature. Methods: when building a mathematical model of the water cooling process, an approach is used based on averaging the equations of hydrodynamics by the volume of water in the pipeline and averaging the equations of thermal conductivity in the wall of the pipeline and in the layer of the heat insulator by the polar angle. To obtain a quasi-stationary form of equations, a comparative analysis of the rates of thermal processes in different layers of the water conduit is used. Results: a new mathematical model for cooling the water pipeline is formulated — a model of average temperatures. The applicability of the quasi-stationary form of the equations of the model is justified and its analytical solution is found. Explicit formulas are obtained for cooling time of water conduit as a function of its parameters. Cooling time was calculated in a wide range of parameters. The results of model calculations are compared with calculations according to traditional semi-empirical formulas. Practical importance: the formulas obtained in the work can be used to estimate the cooling time of water in an above-ground water pipeline with heat insulation to the freezing temperature in the case when the ambient temperature drops to negative values.

Hydrogeological structures of karst features using hydrographs in an underground river basin formed in a peak cluster depression, southwest China

Understanding of the hydrological behaviors in different karst features is crucial for evaluating the hydrological storage and transfer functions of a karst system. In this study, the Maocun karst underground river system, characterized by typical karst features, was selected as the research area in the southwest region of China. The main objectives of this research are to analyze the hydrogeological structure characteristics of each karst feature and assess water storage capacity in different aquifer media. Frequency distribution curve (FDC) of electrical conductivity (EC) values revealed that recharge sources in the five karst features differed and varied according to the amount of precipitation. All hydrographs of water levels in five karst features were divided into three periods due to the presence of triple aquifer media in the basin. The spatial structure of each feature was interpreted by analyzing the variation characteristics of recession exponential coefficients (λ). Additionally, the ratios of fissure water, fracture water, and conduit water sources were calculated based on the recession curves of water levels. Results showed that fast water flow had the highest proportion in the relatively open subsystem located upstream, while fracture water flow had the lowest proportion. The slow water flow was the main pattern of water storage in the basin. Values of EC in water decreased with a well-connected spatial structure and high hydraulic conductivity. There were significant differences in the values of EC among conduit water, fracture water, and matrix water. These values were calculated using mathematical relationships between EC and water level hydrographs. The results indicated that the EC values in matrix water exceeded 200 μS/cm, while EC values in conduit water/channel water were below 100 μS/cm. Finally, hydrogeological conceptual models were constructed for five karst features based on the depletion characteristics of the aquifer media during each recession period. These characteristics were interpreted using variation curves of EC and hydrographs of water levels. These findings not only elucidated the characteristics of hydrogeological structures in multiple karst features, but also had significant implications for the assessment of karst water sources.

System‐Wide Effects of Local Bed Disturbance on the Morphological Evolution of a Bifurcating Channel Network

AbstractDeltaic channel networks are important conduits for water and material supplies to the fluvial and coastal communities. However, increasing human interventions in river deltas have altered the topology and geometry of channel networks as well as their long‐term evolution. While the morphological evolution of a single channel has received extensive studies, the system‐wide morphological responses of channel networks to local disturbances remain largely unclear. Here we investigate the morphological responses of a bifurcating channel network subject to local disturbance of channel deepening due to dredging and sand mining through idealized simulations, and further compare the results with the reference scenarios of a single channel and theoretical analysis of the phase plane. The results show that the infilling of the local deepening is associated with the erosion of the entire branch, which also causes system‐wide effects on the siltation of the other branch. The morphological responses of the bifurcating channel network consist of a relatively short stage for the infilling of the local deepening followed by a relatively long stage for recovering the equilibrium configuration of the river bifurcation. The system‐wide effects of the local disturbance arise from the altered water surface slope and water partitioning downstream of the bifurcation due to the local deepening. Also, the prolonged recovery of the equilibrium configuration is consistent with theoretical analysis, which reveals a slow evolution of the bifurcation when approaching the equilibrium. Our results can help understand the long‐term morphological responses of large‐scale complex channel networks and inform water managements under increasing human interventions.

Stability analysis of the rock zone between the tunnel face and the fault fracture zone

Abstract Water and mud inrush is one of the main safety accidents that occur during tunnel construction in water-rich karst regions. Often, faulting occurs in front of the tunnel face, creating a conduit for water and inrush disasters can easily occur. Accurately predicting the safety distance between the tunnel face and the fault fracture zone allows for effectively avoiding water and mud inrush disasters during construction. First, an analytical model of the safety distance of water and mud inrush prevention is proposed, in which the rock zone between the tunnel face and the fault fracture zone is considered a thick rectangular plate with simple support on four sides. Subsequently, the proposed model is successfully verified through comparison with two existing models and engineering cases. Finally, the influence of main model parameters on the safety distance is further determined. This study shows that: (i) The safety distance increases with the increase in the cross-sectional height and width, and the burial depth of the tunnel; (ii) The safety distance increases with the increase in the effective gravity of the rock inside the fault fracture zone and the height of the groundwater table, and decreases in the dip angle of the fault; (iii) The safety distance increases with the increase in fault width, and the fault length has little influence on the safety distance.

Incised valleys drive distinctive oceanographic processes and biological assemblages within rhodolith beds

Continental shelves encompass gently sloped seascapes that are highly productive and intensively exploited for natural resources. Islands, reefs and other emergent or quasi-emergent features punctuate these shallow (<100 m) seascapes and are well known drivers of increased biomass and biodiversity, as well as predictors of fishing and other human uses. On the other hand, relict mesoscale geomorphological features that do not represent navigation hazards, such as incised valleys (IVs), remain poorly charted. Consequently, their role in biophysical processes remains poorly assessed and sampled. Incised valleys are common within rhodolith beds (RBs), the most extensive benthic habitat along the tropical and subtropical portions of the mid and outer Brazilian shelf. Here, we report on a multi-proxy assessment carried out in a tropical-subtropical transition region (~20°S) off Eastern Brazil, contrasting physicochemical and biological variables in IVs and adjacent RBs. Valleys interfere in near bottom circulation and function as conduits for water and propagules from the slope up to the mid shelf. In addition, they provide a stable and structurally complex habitat for black corals and gorgonians that usually occur in deeper water, contrasting sharply with the algae-dominated RB. Fish richness, abundance and biomass were also higher in the IVs, with small planktivores and large-bodied, commercially important species (e.g. groupers, snappers and grunts) presenting smaller abundances or being absent from RBs. Overall, IVs are unique and vulnerable habitats that sustain diverse assemblages and important ecosystem processes. As new IVs are detected by remote sensing or bathymetric surveys, they can be incorporated into regional marine management plans as conservation targets and priority sites for detailed in situ surveys.

A Generalized Area‐Based Framework to Quantify River Mobility From Remotely Sensed Imagery

AbstractRivers are the primary conduits of water and sediment across Earth's surface. In recent decades, rivers have been increasingly impacted by climate change and human activities. The availability of global‐coverage satellite imagery provides a powerful avenue to study river mobility and quantify the impacts of these perturbations on global river behavior. However, we lack remote sensing methods for quantifying river mobility that can be generally applied across the diversity of river planforms (e.g., meandering, braided) and fluvial processes (e.g., channel migration, avulsion). Here, we upscale area‐based methods from laboratory flume experiments to build a generalized remote sensing framework for quantifying river mobility. The framework utilizes binary channel‐mask time series to determine time‐ and area‐integrated rates and scales of river floodplain reworking and channel‐thread reorganization. We apply the framework to numerical models to demonstrate that these rates and scales are sensitive to specific river processes (channel migration, channel‐bend cut‐off, and avulsion). We then apply the framework to natural migrating and avulsing rivers with meandering and braided planforms. Results show that our area‐based framework provides an objective and accurate means to quantify river mobility at reach‐ to floodplain‐scales, which is largely insensitive to spatial and temporal biases that can arise in traditional mobility metrics. Our work provides a framework for investigating global controls on river mobility, testing hypotheses about river response to environmental gradients, and quantifying the timescales of terrestrial organic carbon cycling.

Unintentional designs in ecology: The case of river Periyar in Kerala

AbstractThis paper moves across the ecological assemblages of the Periyar basin in Kerala. It argues that the connectivities and unintentional designs that emerge bespeak the Anthropocene in its regional and political peculiarities. The river has never been a conduit of water alone. The narrative builds broadly on ecological relations entrenched in history, most visibly as hydrological regimes. Such regimes are significant because of the riparian densities that articulate the geo‐morphology. The different entanglements in ecology, as well as the successive productions of natures, gain significance as ‘recognitions’ during rupture events like the large floods. In contemporary contexts, the versatile flows of capital dissolve markers and boundaries and reconfigure regions in terms of capital. Vikasanam or new urban reforms, apart from political policies, are also ecological designs that normalise exceptions, otherwise reserved for special economic zones. The frictions with new materiality, post dam floods and hydrological controls, during developmental and neoliberal post developmental phases, become moments of recognition, making and unmaking sense of place.

Optimal balancing of xylem efficiency and safety explains plant vulnerability to drought.

In vast areas of the world, forests and vegetation are water limited and plant survival depends on the ability to avoid catastrophic hydraulic failure. Therefore, it is remarkable that plants take hydraulic risks by operating at water potentials (ψ) that induce partial failure of the water conduits (xylem). Here we present an eco-evolutionary optimality principle for xylem conduit design that explains this phenomenon based on the hypothesis that conductive efficiency and safety are optimally co-adapted to the environment. The model explains the relationship between the tolerance to negative water potential (ψ50 ) and the environmentally dependent minimum ψ (ψmin ) across a large number of species, and along the xylem pathway within individuals of two species studied. The wider hydraulic safety margin in gymnosperms compared to angiosperms can be explained as an adaptation to a higher susceptibility to accumulation of embolism. The model provides a novel optimality-based perspective on the relationship between xylem safety and efficiency.

Biohybrids: Textile fibres provide scaffolds and highways for microbial translocation.

Introduction: Living materials (biohybrids, textile-microbial hybrids, hybrid living materials) have gained much attention in recent years with enormous potential for applications in biomedical science, the built environment, construction and architecture, drug delivery and as environmental biosensors. Living materials contain matrices which incorporate microorganisms or biomolecules as the bioactive components. A cross-disciplinary approach, operating at the intersection of creative practice and scientific research, incorporated textile technology and microbiology to demonstrate textile fibres providing microbial scaffolds and highways during this study. Methods: The study evolved from previous research which showed bacteria utilising the water layer surrounding fungal mycelium for motility, termed the 'fungal highway', which led to the investigation of the directional dispersal of microbes across a range of fibre types (natural and synthetic). The application of the study centred around the potential for biohybrids to be used as a biotechnology to improve oil bioremediation through seeding of hydrocarbon-degrading microbes into polluted environments via fungal or fibre highways, therefore treatments in the presence of crude oil were tested. Furthermore, from a design perspective, textiles have huge potential to act as a conduit for water and nutrients, essential to sustain microorganisms within living materials. Using the moisture absorption properties of natural fibres, the research explored how to engineer variable liquid absorption rates using cellulosics and wool to produce shape-changing knitted fabrics suitable for adaptation to oil spill capture. Results: At a cellular scale, confocal microscopy provided evidence to show that bacteria were able to utilise a water layer surrounding the fibres, supporting the hypothesis that fibres can aid bacterial translocation through their use as 'fibre highways'. A motile bacterial culture, Pseudomonas putida, was shown to translocate around a liquid layer surrounding polyester, nylon, and linen fibres, yet no evidence of translocation was apparent on silk or wool fibres, suggesting microbes elicit different responses to specific fibre types. Findings showed that translocation activity around highways did not diminish in the presence of crude oil, known to contain an abundance of toxic compounds, in comparison to oil-free controls. A design series demonstrated the growth of fungal mycelium (Pleurotus ostreatus) through knitted structures, highlighting the ability for natural fabrics to provide a scaffold to support microbial communities whilst retaining the ability to undergo environmentally responsive shape-change. A final prototype, Ebb&Flow, demonstrated the potential to scale up the responsive capacities of the material system using locally produced UK wool. The prototype conceptualised both the uptake of a hydrocarbon pollutant by fibres, and the translocation of microbes along fibre highways. Discussion: The research works towards facilitating the translation of fundamental science and design into biotechnological solutions that can be used in real world applications.

Simulation of the Operation of a Borehole Groundwater Intake with an Annular Prefabricated Conduit

Among the considered options for schemes of prefabricated water conduits of borehole water intakes, the main ones are linear and ring schemes. The article presents a comparative analysis of the linear and ring schemes for the placement of prefabricated water conduits when choosing an option for designing a group well water intake with a circular arrangement of wells. It is founded that a small water intake with individual radial connections to the prefabricated unit can have advantages in reducing energy consumption for water transportation as compared to a water intake with an annular prefabricated conduit, which in any case should be justified by a feasibility comparison of options, which is based on hydraulic calculation water supply systems. Equations have been obtained for calculating the pumping rates of water intake wells with linear prefabricated conduits. It is shown that in an annular prefabricated conduit, in contrast to a linear one, in which the direction of movement of water flows is unambiguously known, there is always a point of separation of two flows directed along the ring to the prefabricated unit clockwise and counterclockwise, which makes it difficult to calculate such water intakes. Moreover, the position of this point depends on the number of water intake wells involved in the work and the parameters of the pipes connecting the sections of the water conduit. The absence of algorithms for calculating the ring prefabricated conduit with non-fixed flow rates at the well connection points complicates the hydraulic calculation, and, hence, finding the optimal water intake option. The article presents an algorithm for the hydraulic calculation of a water intake with a single-ring prefabricated conduit, which is based on the equation for the equality of pressure losses when water moves from the point of separation of two flows to the prefabricated unit along various paths and the continuity equation. The resulting algorithm can be easily extended to any number of wells. A numerical example of the hydraulic calculation of a group water intake, consisting of eight wells connected to an annular prefabricated, is considered.

The Canal Top Solar Power Generation Project

Abstract: Solar energy is one of the most abundant sources of renewable energy for the future. This solar energy can be uprooted by PV system. Negative environmental impact of reactionary energy consumption highlights the part of renewable energy sources and give them a unique occasion to grow and ameliorate. Among renewable energy sources solar energy attract further attention and numerous studies have concentrated on using solar energy for electricity generation. Then, in this study, solar energy technologies are reviewed to find out the stylish option for electricity generation. Using solar energy to induce electricity can be done either directly and laterally. In the direct system, PV modules are employed to convert solar irradiation into electricity. In the circular system, thermal energy is exercised employing concentrated solar power (CSP) shops similar as Linear Fresnel collectors and parabolic trough collectors. In this design electricity generation in Pune from solar energy by furnishing solar panels on top of conduit is bandied. And we prepare model for the design in Pune. We also bandied about the developments in Pune due to this solar power design and how the electricity is distributed in Pune and how the conduit water is used for agrarian purposes. This solar power generation from the top face of conduit design has several benefits similar as16.2 million units of power generated annually, 90 million liters of water is conserved annually, 25 acres of land conserved, lower algae growth in the conduit water, minimize evaporation from conduit, produce Eco-friendly power using solar panels as a cover and save land

Unveiling the nitrogen transport and transformation in different karst aquifers media

Karst aquifers, a significant source of drinking water worldwide, are vulnerable to anthropogenic pollutants because of their special hydrogeological conditions. However, distinguishing the nitrogen transformation process is difficult owing to the heterogeneity of karst media. Therefore, the process of nitrogen transformation in different karst aquifer media remains poorly understood. In this study, multiple stable isotopic and physicochemical indicators are combined, the sources of water and nitrogen are analysed, and the degree of openness and redox conditions of different media are discussed to elucidate the nitrate sources and N transformation in groundwater with different degrees of openness. Water isotopes indicate local meteoric groundwater origin. However, different karst aquifer media have different degrees of openness, resulting in the highest deuterium–oxygen isotope values in surface water, followed by conduit water, fissure water, and isolated cave water. Based on the evidence from isotope and physicochemical indicators, different karst aquifer media have different redox processes. Isolated cave water environments were under anoxic conditions dominated by sulfate reduction reactions. Fissure water was under temporary anoxic or sub-anoxic conditions dominated by denitrification reactions. Conduit water and karst surface water were between micro-oxygen and oxidising conditions, and nitrification was the key process. This phenomenon was observed because the diversity of karst media produces different conservation conditions and openness. The nitrate isotope and Bayesian mixing model indicate that the main sources of nitrate in karst groundwater in the study area are mostly associated with manure and sewage wastes, and a few are from soil organic nitrogen, atmospheric deposition, and chemical fertilizer. This study helps identify the migration and transformation patterns and processes of nitrogen in different karst aquifer media, providing a scientific basis for the restoration and remediation of contaminated karst groundwater.

Archaeoparasitological characteristics of drains in the Phanagoria city of the Khazar period (VIII-IX centuries AD)

This article reports the parasitic contamination of water-collecting drains in the Greek city of Phanagoria, dated back to the Khazar period (8th-9th centuries AD).Helminths of the Opistorchiidae and Diphyllobothriidae families were found in soil samples obtained from water conduits. Based on the life cycle of these parasites and the historical and archaeological context, the authors argue that both humans and animals could have become infected with them through eating fish from freshwater rivers and reservoirs of the Taman Peninsula, or, more likely, from more distant rivers. Taenia eggs discovered in the samples indicate that the dietary habits of the people who lived in Phanagoria in the Middle Ages included the consumption of insufficiently thermally processed meat of pigs, cattle, and small cattle.Numerous eggs of the genera Trichuris and Ascaris identified in the studied samples taken from water conduits could belong to humans and domestic animals (pigs). This fact suggests a settlement with poor sanitary conditions. A similar route of transmitting both geohelminths and various intestinal infections might indicate a high risk of infection with gastrointestinal infectious diseases in the population of medieval Phanagoria.The study showed that wastewater and rainwater were collected in watercourses and went to a cistern without prior treatment. Its use for drinking water is, therefore, highly improbable; it is more likely that this water source was used to water plants and livestock, providing the means by which geohelminths persisted in domestic animals and humans.

Around certain critical cases in stability studies in hydraulic engineering

It is considered the mathematical model of a benchmark hydroelectric power plant containing a water reservoir (lake), two water conduits (the tunnel and the turbine penstock), the surge tank and the hydraulic turbine; all distributed (Darcy-Weisbach) and local hydraulic losses are neglected,the only energy dissipator remains the throttling of the surge tank. Exponential stability would require asymptotic stability of the difference operator associated to the model. However in this case this stability is “fragile” i.e. it holds only for a rational ratio of the two delays, with odd numerator and denominator also. Otherwise this stability is critical (non-asymptotic and displaying an oscillatory mode).

Determination of head loss in water pipes

This article is devoted to the problems of water supply to the population, which are associated with the current water management situation, such as the shortage of water resources, the decline in the quality of surface and groundwater, the technical condition of pipelines. In this situation, there is a need to eliminate or mitigate the current situation, so the study of hydraulic friction losses in water conduits is of national economic and scientific importance.The article deals with the issues of determining the pressure loss in water pipes under various modes, the causes of clogging of pipelines in water supply systems and the basic formulas of engineering hydraulics under conditions of insufficient water supply to the population. Solving the problem will increase the reliability of pipeline operation, meet the requirements of the population, and meet the minimum of the reduced costs for construction and operation.

METHOD FOR CALCULATION OF DISPERSIONS OF DEPENDENT VARIABLES OF A STOCHASTIC MODEL OF QUASI-STATIONARY OPERATING MODES OF THE MAIN WATER PIPELINE

The subject of research in the article is a stochastic model of quasi-stationary modes of operation of water supply and distribution systems, which adequately describes the actual operating modes of the water supply system for a given time interval and can be used as a basic model for setting and solving problems of optimal stochastic control of the development and operation of supply and distribution systems. water. The goal of the work is to develop a method for calculating estimates of the dispersions of dependent variables depending on the given values of mathematical expectations and dispersions of independent variables for a stochastic model of quasi-stationary modes of operation of the main water conduit as a subsystem of the water supply and distribution system. To achieve this goal, it is necessary to solve the following tasks: to build a deterministic equivalent of a stochastic model of quasi-stationary modes of operation of the main water conduit; calculate estimates of mathematical expectations of dependent variables; calculate estimates of variances of dependent variables. To calculate estimates of the variances of dependent variables depending on the variances of independent variables, we will use the method of statistical linearization. To obtain estimates of mathematical expectations of dependent variables, the deterministic equivalent of the stochastic model of quasi-stationary modes of operation of the main water conduit is solved by the modified Newton method. The following results are obtained: a method for calculating estimates of the dispersions of dependent variables for a stochastic model of quasi-stationary modes of operation of the main water conduit. Conclusions: the paper proposes an approximate method for calculating the statistical properties of dependent variables depending on the statistical properties of the parameters and independent variables of the stochastic model of quasi-stationary modes of operation of the main water conduit. The proposed method is based on the construction of a deterministic equivalent of a stochastic model of quasi-stationary modes of operation of the main water conduit and its use for calculating estimates of variances of dependent variables depending on the given values of mathematical expectations and variances of independent variables. Compared with the simulation method, the proposed approximate method does not require significant time and computational resources. The use of the proposed method was demonstrated by an example.