Graphical Interpretation Research Articles

Natural convection laminar flow between two vertical walls with a nonlinear variation of density and viscosity with temperature

AbstractUnder the combined influence of buoyancy force and constant pressure gradient, the free convection flow and heat transmission inside a channel placed vertically and consisting of two parallel walls are examined. Through the application of the Runge–Kutta fourth‐order approach and the shooting procedure, the modeled equations of the problem including nonlinear density–temperature and quadratic viscosity–temperature change at constant but different wall temperatures are numerically solved. For distinct values of the embedded parameters, the fluctuations in fluid's velocity and temperature are examined. For various situations of linear, quadratic, and nonlinear dependence of density on temperature, numerical values for heat transmission rate, volume flow rate and skin friction are determined and tabulated. The fluctuations of the Nusselt number with the Grashof number corresponding to thermal expansion coefficients are depicted through graphical interpretations. It was found that the combined effect of thermal expansion coefficients raises the values of the physical entities, Nusselt number, volume flow rate, and heat transmission rate. For the lower Reynolds number values, the Nusselt number value stays around one, indicating the same impact of conduction and convection on heat transmission.

Proposition for the graphic representation, interpretation and evaluation of the degree of terrain resolution in virtual reconstructions

The Seville Principles gather in their definitions the 3D representation of heritage assets in their context, that is, elements such as the surroundings and landscape, for both virtual reconstructions and virtual recreations. Currently, there are few virtual reconstructions that implement the historical-archaeological evidence scale to show the veracity of the work that has been carried out. Moreover, none of the existing propositions of historical-archaeological evidence scales consider the veracity of the represented terrain. Authors assign a neutral colour to the terrain, different from those applied to the evidence levels, in order to differentiate the former from the latter.The present study proposes the development of a methodology to implement a resolution scale that graphically represents, interprets and evaluates the setting of the terrain associated with virtual reconstructions. To this end, a literature review was conducted on the existing methodologies for the creation of Digital Terrain Models (DTM). The evaluation of the analysed information was key for the selection of the resolution levels, which was followed by the selection of the colours associated with each resolution level, taking into account the subjective connotations of colours.

Effect of extrusion process parameters on pellet crumbliness in fish feed production

The article presents the results of studying the pellets crumbliness index of a pilot batch of extruded compound feed for pike-perch. The regimes of extruded pellets fish compound feed production with minimal crumbling were defined using a mathematical model. A 3-factorial central composite design was implemented to obtain a mathematical model of the process of extrudate resulting in the second-degree polynomial. The process influencing factors include the feed mixture moisture W (%), extrusion temperature T (°C) and steam pressure P (MPa). Experimental studies were conducted according to the experimental plan. The experimental data obtained were entered into the planning matrix. Experimental data was processed in a program prepared in Microsoft Excel. As a result, an adequate second-order mathematical model describing the dependence of the crumbliness index on the feed mixture moisture before extrusion, extrusion temperature and steam pressure was obtained. The mathematical model adequacy was tested based on Fisher's variance ratio. The Fisher criterion is an important statistical tool for verifying the adequacy of the model and analyzing the variance. The analysis of the obtained model and its graphical interpretation are presented. A good extrusion process mathematical model was developed. The fundamental principles of feed mixture processing on a single-screw extruder and the choice of its rational parameters ensure the production of extruded compound feed pellets for pike-perch with minimal crumbling were studied. A minimal crumbling is provided at the following values of the factors - feed mixture moisture before extrusion is 32%, extrusion temperature is 132 °C, and pressure is 0.4 MPa. In the selected levels of factors, the calculated value of extruded pellets crumbling was 1.02%.

Cosine Similarity Measures of (m, n)-Rung Orthopair Fuzzy Sets and Their Applications in Plant Leaf Disease Classification

A fuzzy set is a powerful tool to handle uncertainty and ambiguity, and generally, the notions of symmetry and similarity are also exhibited in the fuzzy set theory. The class of (m, n)-rung orthopair fuzzy sets through two universes are more flexible and efficient than the q-rung orthopair fuzzy sets when discussing the symmetry and similarity between multiple objects. This research article comprehensively investigates ten similarity measures that employ cosine and cotangent functions for comparing (m, n)-rung orthopair fuzzy sets, which are a superclass of q-rung orthopair fuzzy sets. Moreover, the proposed weighted similarity measures are applied to real-world problems in building material analysis. A comparative analysis is conducted between the proposed measures and the existing cosine and cotangent measures of q-rung orthopair fuzzy sets, showing that the proposed measures are more efficient than existing ones. Additionally, a numerical example demonstrates the practical and scientific applications of these similarity measures in classifying plant leaf diseases. The sensitivity analysis shows that the existing measures cannot be applied to (m, n)-fuzzy data for distinct values of m and n. The results are supported by graphical interpretations, further illustrating the efficacy of the proposed measures.

Analytical analysis of silver-water, silver-blood base nanofluid flow over fluctuating disk with the influence of viscous dissipation over fluctuating disk

This work considers the analytical analysis of silver-water, silver-blood base nanofluid flow over fluctuating disk with the influence of viscous dissipation over fluctuating disk. The primary goal of this study is an effort to improve the heat transfer ratio, which is a core part of the engineering and industrial sectors. Following a continuity check, the problem is modeled using the conservation rules of momentum and energy. Nonlinear PDEs are produced through modeling, which are then transformed into ODEs using a similarity transformation and thermophysical characteristics. The resultant ODEs are resolved using the Optimal Homotopy Asymptotic Method (HAM). The outcomes of this method are compared to authenticate the outcomes of the obtained results. The Mathematica software is used to run HAM methods, and graphical interpretations are given to highlight the influence of dissimilar contributing factors on the velocity profile and temperature distribution. Nusselt’s number, and the skin friction are examined through graphical representation. Convergence of the problem is checked with the help of graphs and tables by using dual solution of the problem.

Analytical analysis of graphene oxide ethylene glycol and graphene oxide blood base nanofluid over a vertical surface

This work considers the analytical analysis of graphene oxide ethylene glycol and graphene oxide blood base nanofluid over a vertical sheet. The principal objective of this study is to make an effort to improve the heat transfer ratio, which is the core part of the engineering and industrial sectors. Following a continuity check, the problem is modeled using the conservation rules of momentum and energy. Nonlinear PDEs are produced through modeling, which are then transformed into ODEs using the similarity transformation and thermophysical characteristics. The resultant ODEs are resolved using the Homotopy Asymptotic Method, and graphical interpretations are given to highlight the influence of different contributing parameters such as unsteady parameter, nanoparticle volume fraction, mixed convection parameter, Grashof number and Prandtl number on the velocity profile and temperature distribution. It is noted that increasing the values of nanoparticle volume fraction and stretching parameter slow down the velocity profile. Also, increasing the values of mixed convection parameter and Grashof number (Gr) enhance the velocity profile, and increasing values of Prandtl number and Graship number reduce the temperature distribution. The Nusselt number and the skin friction are examined through graphical representation. It is noted that increasing the value of mixed convection parameter decreases the skin friction of the fluids, and the Nusselt number decreases with the growing value of Prandtl number.

Fractional mathematical modeling of the Stuxnet virus along with an optimal control problem

In this digital, internet-based world, it is not new to face cyber attacks from time to time. A number of heavy viruses have been made by hackers, and they have successfully given big losses to our systems. In the family of these viruses, the Stuxnet virus is a well-known name. Stuxnet is a very dangerous virus that probably targets the control systems of our industry. The main source of this virus can be an infected USB drive or flash drive. In this research paper, we study a mathematical model to define the dynamical structure or the effects of the Stuxnet virus on our computer systems. To study the given dynamics, we use a modified version of the Caputo-type fractional derivative, which can be used as an old Caputo derivative by fixing some slight changes, which is an advantage of this study. We demonstrate that the given fractional Caputo-type dynamical model has a unique solution using fixed point theory. We derive the solution of the proposed non-linear non-classical model with the application of a recent version of the Predictor–Corrector scheme. We analyze various graphs at different values of the arrival rate of new computers, damage rate, virus transmission rate, and natural removal rate. In the graphical interpretations, we verify the values of fractional orders and simulate 2-D and 3-D graphics to understand the dynamics clearly. The major novelty of this study is that we formulate the optimal control problem and its important consequences both theoretically and mathematically, which can be further extended graphically. The main contribution of this research work is to provide some novel results on the Stuxnet virus dynamics and explore the uses of fractional derivatives in computer science. The given methodology is effective, fully novel, and very easy to understand.

Evaluation of thermal insulation of pipelines in the overhead method of laying in the climatic conditions of the South of Russia

The characteristics of used and new heat-insulating materials for pipelines of heating networks are presented. Functions have been established for determining the outer diameter of a pipeline with thermal insulation for all materials under consideration. A two-factor machine experiment was carried out, as a result of which the quantitative dependence of specific heat losses on the thermal conductivity coefficient and pipeline diameter was determined. Graphical interpretations of the obtained functions are presented. Based on the analysis of the obtained results, it was established which factor has the greatest influence on the value of specific heat losses and which heat-insulating material should be used.

Оценка промышленного потенциала горнодобывающего сектора арктических регионов России

The Arctic regions of Russia are primarily focused on the extraction of raw materials, and the mining sector has witnessed an increase in added value in recent years. On average, 84% of taxes and fees contributed to the budget system of the Russian Federation originate from the Arctic’s mining sector, which highlights the importance of analyzing the activities of this sector. This article aims to assess the industrial potential of the mining sector in the Russian regions located in the Arctic zone. Such an assessment identifies the potential uses of a combination of resources to enhance the economic development of these regions. The study employed various theoretical methods such as generalization, comparison, and systematization, along with empirical analysis including statistical observation and graphical interpretation. The research draws upon scientific publications related to the industrial potential of Russian regions, utilizing data from the Federal State Statistics Service to evaluate the mining sector's potential in the Arctic regions. The article discusses the advantages and limitations of current methodologies for ranking Russian regions based on the industrial potential of the mining sector. Building upon the study, a comprehensive methodology is proposed, which involves assessing the industrial potential of the mining sector through the calculation of indices based on 17 indicators grouped into five domains: materials and technology, innovation and investment, finance, labor, and infrastructure. The proposed methodology was applied to analyze the industrial potential of the mining sector in four Russian regions located within the Arctic zone for the period from 2017 to 2021. The findings indicate that the Murmansk region exhibits the highest industrial potential in Russia’s Arctic mining sector,with the Yamalo-Nenets Autonomous Okrug ranking second. The Nenets Autonomous Okrug and Chukotka Autonomous Okrug display relatively low potential in the mining sector.

BRICS investment policy in contemporary environment

Contemporary instability of the global economy and the consequences of COVID-19 determine the search for new ways to ensure sustainable economic and financial development of any country. This is especially important for developing countries, BRICS in particular. One of the ways of meeting new challenges is to strengthen cooperation between partners, so the paper examines the BRICS countries’ investment policy, seeking to identify new areas of cooperation where harmonious investment could be most beneficial. The research uses comparative, logical, statistical and structural analysis with graphic visualization and interpretation of the obtained results. The authors have been first to identify contemporary investment opportunities for further cooperation within BRICS and to reveal their features in various areas, such as regulation, taxation, labor legislation, infrastructure development. The authors emphasize the necessity of the BRICS member countries’ investment co-operation in reaching the goals of sustainable development and outline the priority areas of investment showing that the BRICS should grant preferential treatment to strategic investments. The paper points out the need to expand the use of national currencies in dealing with green and infrastructure bonds issued to support the national economies and calls for increased participation of BRICS development banks and institutional investors of all forms of ownership in the processes of partnership cooperation.

Agricultural insurance system: review of the experience of developed countries

This review article is aimed at getting acquainted with the experience of developed countries in insuring the risks of agricultural producers. The creation of a reliable mechanism for their insurance protection is currently one of the aspects of ensuring food security of the republic and a special sphere of state interests. The purpose is to show common insurance practices and countries' policies in dealing with this issue. Methods – in the process of analyzing and evaluating the international level of state support for agricultural insurance, the author used the following research methods: content analysis, which allows to identify the main areas related to state financing of agricultural sector; on the basis of a systematic approach, the degree of state participation in insurance operations was determined; graphical interpretation made it possible to visualize this process on the basis of information received. Results – the article presents aspects of state investment of insurance premiums in agricultural sector. The author identifies and graphically displays three main categories of state assistance in agricultural insurance. The results of the review can be used to conduct research in all regions of the republic. Conclusions – world experience shows that subsidizing insurance payments is the most effective way to support small and medium-sized businesses and ensure economic sustainability of the industry, reduce negative consequences, including loss of income in production of products associated with the onset of adverse natural events. A coordinated and strategic approach to managing the insurance market, government support and effective mitigation methods are important, while direct government reimbursements are ineffective in the long run and do not contribute to the prevention of risk situations.

Edaphic properties as pieces of evidence of tailings deposit on soils

Mine tailings are one of the primary contaminant sources of heavy metals and metalloids in the soil. Besides increasing the concentration of potentially toxic elements (PTEs), tailings may modify the edaphic conditions and decrease the buffer capacity of impacted soils. The influence of tailings may reach distances far from the impoundments depending on the transport path and the specific transport mean: air, rain (runoff and infiltration), or acid mine drainage. In this study, soil samples from various horizons were collected in trial pits along a transect, at different distances from sulfide tailings. Soil analysis included texture, organic matter, alkalinity, porous space, carbonates, pH, electrical conductivity, real density, apparent density, total sulfur, main mineralogy, and total concentrations of As, Cd, Pb, Fe, and Zn. Graphical and statistical interpretation of the results showed that real density and porous space are the leading indicators of the tailings dispersion and accumulation and that pH is not a significant parameter (all values were above the neutrality) due to the limestone abundance in the area. However, Zn and Cd concentrations had an inverse relation with pH. Differences in the concentrations of PTEs between the superficial and deep layers that increased toward the tailings were also observed. Gypsum was only present in the closest samples to the tailings and may also be an indicator of tailings’ influence on soils. This study allowed us to identify general edaphic parameters as a first and quick means to determine the tailings contamination of soils.

Analysis of and Decision-Making on the Operational Reliability of Cyber-Physical Systems

Matters concerned with analyzing the operational reliability and recovery process of cyber-physical systems (CPS) are addressed. The proposed approach is based on dividing the CPS life cycle into time intervals with linking them to pre-emergency, emergency, restored and predicted states. The CPS serviceability is restored with respect to extremely critical and mission-critical equipment. In carrying out the analysis, graphs representing the states of cybernetic and physical components are introduced. Differential equations linking the probability of returning into a serviceable state with failure rates and restorations of various types are derived. The solution of the appropriate ordinary differential equations yields a clear graphical interpretation in the time domain and shows the changes in the probability with which the system components transfer from one state to another at different CPS life cycle time slices. By using the developed flow chart of making decisions on restoring or replacing the corresponding component, a reasonable choice can be made among possible options of actions aimed at restoring the serviceability of a multicomponent system. An algorithm for implementing the method has been developed and tested on a numerical example.

Machinability analysis of Ti-6Al-4V under cryogenic condition

Aerospace alloys are termed as hard to cut materials owing to their low thermal conductivity, high temperature strength and elevated chemical reactivity. Cryogenic conditions can be effectively deployed to improve the machinability and productivity while addressing environmental and sustainability concerns connected with high tool wear and the use of conventional cutting fluids. Current work was undertaken to develop a novel tool wear map under cryogenic condition using cutting speed and feed rate as input variables. The developed map was demarcated into regions of low, moderate and high tool wear zones in addition to an unusually high wear zone, termed as avoidance zone existing between cutting speeds of 65–95 m/min and feed rates of 0.18–0.22 mm/rev. Characterization of developed map in terms of tool chip contact length revealed its direct relationship with cutting speed and feed rate accounting for the formation of different wear regions. Elemental analysis of avoidance zone detected high presence of TiN which results in larger tool chip contact length owing to its higher thermal conductivity. Chip morphology characterization highlighted an increase in chip compression ratio and decrease in shear angle due to the reduction of effective tool rake angle, further elevating the cutting zone temperature promoting wear. SEM and EDS spot analysis indicated the presence of adhesive and diffusion-dissolution wear mechanisms as the tool wear progresses. Comparative analysis with dry condition indicated that tool life is enhanced up to 100% using cryogenic media. Analysis of cryogenic tool wear map underscored the importance of careful choice of machining parameters in terms of increase in MRR up to 36% and tool life up to 58%. Overall, cryogenic tool wear map presents graphical interpretation of the machinability of Ti–6Al–4V in terms of tool wear.

RENAL9: REDIEM 2.0: Renal Extremity Device to Measure Impedance, Edema, Movement

Background: Renal failure due to chronic kidney disease (CKD) is a leading cause of global mortality. CKD disrupts fluid balance regulation, inducing comorbidities such as excessive swelling of the extremities (edema) and restless leg syndrome (RLS). Clinical limitations impede the ability to quantitatively track edema and RLS in variable settings. We report on the development of a wearable device capable of continuously measuring and analyzing: 1. leg edema, 2. water content, and 3. RLS-specific leg movements. Methods: An enhanced system (2.0) was designed through integration of flex sensors, accelerometry, electromyography (EMG) and impedance biosensors into a flexible stocking that transmits data to a smartphone application for graphical interpretation. Assessment of components was performed through simulations of RLS and edema. EMG and accelerometry were assessed for identification accuracy by applying sensors to a subject performing movements of set type/frequency to simulate RLS. Subject’s plantar reflex was induced to verify increased EMG response to sudden reflexive motion. Flex sensors were assessed on simulated edema via a measured-fill hydration system with compressed sponges, measuring resistance in relation to circumference during expansion. Results: RLS sensor trials were able to differentiate RLS movement with EMG using peak detection software (Figure A). This was verified using accelerometry, which identified leg movement at >95% recognition accuracy. Edema sensor trials were able to accurately measure linear change in resistance during circumference expansion with an R2 value of 0.949 (Figure B). Further assessment will be performed to confirm water content using impedance sensors. Conclusion: Preliminary data demonstrates measurement and recognition accuracy in all components tested. Correlations identified between circumference expansion and resistance change allow for accurate quantification of swelling via resistance measurements. Motion differentiation/identification allows for tracking of RLS movement incidence and frequency. Ability to perform condition progression analysis on an aggregation of this data over time indicates future utility of the integrated device in CKD treatment. Continued work is intended to demonstrate this viability and conclude with a complete and comprehensive system for use by clinicians and patients.Figure 1. A. Representative EMG demonstrating RLS motion. Peaks identified by detection software are associated with sudden or jerk-like motions. B. Detection of circumference change (edema) via change in resistance using sensor.

РАЗВИТИЕ ЗЕМЕЛЬНЫХ ОТНОШЕНИЙ В РФ С УЧЕТОМ ТРАНСФОРМАЦИИ КАТЕГОРИРОВАНИЯ, ОЦЕНКИ И КАДАСТРА ЗЕМЕЛЬ

In the context of the strategic priorities of the state program on the national spatial data system in the Russian Federation, the issue of comprehensive study of land resources from the point of view of improving their condition and correct management decision-making is being updated. The purpose of the work is to substantiate the study of theoretical and practical aspects of land relations, to identify problems arising in the process of assigning a category to lands, their cadastral valuation and cadastral works. The article uses general scientific methods; graphical interpretation of the data to ensure the reliability of the results of the study. Proposals are given on systematization, collection, processing and consolidation of data; provision of services in the field of state cadastral registration of immovable property and state registration of rights to it; improvement of the process of determining cadastral value in order to increase the efficiency of taxation and development of territories.

Chemically reactive magnetized tangent hyperbolic bidirectional nanofluid flow subject to interaction of gyrotactic moment of microorganisms and nanoparticles

The exploration of nanofluids have many applications in oils, microelectronics, compact heat exchangers, cooling of an infinite metallic plate, in power transportation, mineral water, plastic and rubber sheet manufacturing nuclear reactor design, electronics, solar energy, making it an identical influential scientific field. The inspiration of activation energy occurring within a chemical reaction has been extensively useful in manufacturing of oil reservation, biodiesel, geothermal accomplishment, oil, base liquid procedure, food manufacturing, oil amalgamate, sewage systems, along with a significant renewable energy source. We have studied the effect of MHD on steady 3D tangent hyperbolic nano fluidic flows through an extended surface containing gyrotactic microorganisms by considering new mass flux conditions in this research article. With the help of Rossland's approximation, we determine solar radiation and the activation energy describing the chemical reaction. By using suitable transformation, the mathematical modeling of the determinate flow can provide the set of non-linear differential equations. With the help of different parameters, we obtain a graphical interpretation of the motile density, local Nusselt number and Sherwood number. As an outcome of the stretching parameter and Prandtl number the temperature of the tangent hyperbolic liquid declines. By increasing the thermophoresis and magnetic parameter the nano fluid concentration initiates to ascend directly. The microorganism profile is found to be increasing for improving values of power law index parameter, while an opposite behavior can be observed for bio-convective Lewis number.

Analysis of a Two-Stage Magnetic Precession Gear Dynamics

The aim of this study was to carry out the investigation and analysis of two-stage magnetic precession gear dynamics and the determination of the resonance frequencies, which can be a cause of the powertrain system failures. Graphical interpretation of the two-stage precession gear is presented, and two equations of the dynamics of the movable elements of the presented gearbox were determined. On the basis of these equations, the stiffness coefficients and resonance frequencies of the presented gearbox were mathematically derived. The next step was to develop a numerical model of the magnetic precession gear dynamics in the environment of MATLAB Simulink. The elaborated model allowed us to analyze the influence of varying the input speed and the load torque on the operation of the magnetic precession gear. The performed analyses of the dynamics of the magnetic precession gear showed the occurrence of a resonance phenomenon under the influence of load torque ripples with a frequency close to the natural frequency of the studied system.

Determining a Trustworthy Application for Medical Data Visualizations through a Knowledge-Based Fuzzy Expert System.

Medical data, such as electronic health records, are a repository for a patient's medical records for use in the diagnosis of different diseases. Using medical data for individual patient care raises a number of concerns, including trustworthiness in data management, privacy, and patient data security. The introduction of visual analytics, a computing system that integrates analytics approaches with interactive visualizations, can potentially deal with information overload concerns in medical data. The practice of assessing the trustworthiness of visual analytics tools or applications using factors that affect medical data analysis is known as trustworthiness evaluation for medical data. It has a variety of major issues, such as a lack of important evaluation of medical data, the need to process much of medical data for diagnosis, the need to make trustworthy relationships clear, and the expectation that it will be automated. Decision-making strategies have been utilized in this evaluation process to avoid these concerns and intelligently and automatically analyze the trustworthiness of the visual analytics tool. The literature study found no hybrid decision support system for visual analytics tool trustworthiness in medical data diagnosis. Thus, this research develops a hybrid decision support system to assess and improve the trustworthiness of medical data for visual analytics tools using fuzzy decision systems. This study examined the trustworthiness of decision systems using visual analytics tools for medical data for the diagnosis of diseases. The hybrid multi-criteria decision-making-based decision support model, based on the analytic hierarchy process and sorting preferences by similarity to ideal solutions in a fuzzy environment, was employed in this study. The results were compared to highly correlated accuracy tests. In conclusion, we highlight the benefits of our proposed study, which includes performing a comparison analysis on the recommended models and some existing models in order to demonstrate the applicability of an optimal decision in real-world environments. In addition, we present a graphical interpretation of the proposed endeavor in order to demonstrate the coherence and effectiveness of our methodology. This research will also help medical experts select, evaluate, and rank the best visual analytics tools for medical data.

Simulation of asymmetrical rotational flow in the flow part of a well jet pump

In order to improve the mathematical model of the working process of the above-bit ejection system for the conditions of its asymmetric rotation in the well, a method of modeling the circulating injected flow using a hydrodynamic vortex function, the center of which is shifted relative to the axis of the mixing chamber of the jet pump, has been developed. In the process of modeling the rotating asymmetric movement of the injected flow, the concept of circulation of the vector of the translational velocity of the liquid along a closed circuit is used. With the help of the components of the complex potential of the hydrodynamic circulation function, a graphical interpretation of the equipotential lines and flow lines of the spatial vortex with one-sided and two-sided displacement of the coordinate center was obtained. Using analytical relations for the velocity potential and stream function, the components of the circulation velocity are determined and the analyticity of the function of the complex potential with a shifted vortex center is proven. The fulfillment of the Cauchy-Riemann conditions allowed us to present the resulting velocity of the circulating current with the coordinate center shifted along the vertical axis in the form of a partial derivative of the complex potential. In contrast to the complex potential for a symmetric vortex, the ratio for determining the circulation speed in case of misalignment of the working nozzle and the mixing chamber of the jet pump contains an additional component in the form of the displacement of the vortex center.In the process of analyzing the results of using the proposed mathematical model, it was established that the resulting speed of the circulation current and the relative displacement of the spatial vortex center are directly proportional. The conducted studies proved that the ratio of the velocities of the symmetric and asymmetric circulation flow is a function of the displacement of the center of the vortex flow coordinates and varies from 1 to zero. The magnitude of the relative speed of the circulation flow is inversely proportional to the displacement of the coordinate center and the distance to the mixing chamber of the jet pump. The developed mathematical model can be used to predict the influence of the rotation of the ejection system on its pressure characteristic in the case of radial relative displacement of the working nozzle and the mixing chamber of the jet pump.