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The paper considers a stationary flow of an incompressible fluid in a flat layer caused by an inhomogeneous source that induces heating or cooling of the lower boundary (there are four types of heating). Regularities in the distribution of hydrodynamic velocity fields between the types of heating are revealed, estimates of the parameters of dimensionless similarity numbers for each type of heating corresponding to counterflows and stagnant zones are obtained.

One-dimensional movement of tensioned viscous material stream is considered. With the help of the laws of mass and momentum conservation it is shown that the stationary flow is characterized by exponential decrease of stream width and corresponding increase of stream velocity. Equations for perturbations of station variables are derived, which depend on the defining parameter. This parameter characterizes the combined influence of viscosity, density, initial velocity and length of the considered interval. For small parameter values dynamic stability of one-dimensional material motion is established.

The present study provides a designing the floating buoy system. The floating buoy is designed to determine the mid-frequency hydroacoustic set location, located in the underwater position, using sonar communication signals. The approach considers the stability at large angles of inclination analysis. For this reason, the main stability criteria is recovery moment. As a result, the following diagrams are plotted – statical stability curve and dynamical stability curve to estimate the research. Moreover, the study includes defining spatial configuration at steady flow. It is also important to mention the basic requirements for the construction of the buoy are ensuring positive buoyancy according to the terms of reference, lack of sea water absorption, sustainability to hydrostatic pressure and corrosion resistance. The study reveals designing the construction, which is able to prevent capsizing. Consequently, the buoy has positive stability, sufficient recovery moment enable to return the structure to its original position and meet the claimed buoyancy requirements.

In this note, we consider the stability of geodesics on volume-preserving diffeomorphism groups with one-side invariant metric. We showed that for non-Beltrami fields on a three-dimensional compact manifold, there does not exist Eulerian stable flow which is Lagrangian exponential unstable. We noticed that a stationary flow corresponding to the KdV equation can be Eulerian stable while the corresponding motion of the fluid is at most exponentially unstable.

Conical diffusers of various configurations are used in many kinds of technical equipment and manufacturing processes. Therefore, it is a relevant objective to obtain reliable experimental and mathematical data on the aerodynamic characteristics of diffusers. This article presents experimental data on the aerodynamics of stationary flows in a vertical conical diffuser when air is supplied through tubes with various cross sections (circle, square, and triangle). Instantaneous values of air flow velocity are measured with a constant-temperature hot-wire anemometer. Data are obtained on the velocity fields and turbulence intensity along the height and the diameter of the diffuser’s cylindrical part when air is supplied through tubes of various configurations. It is established that air supply through profiled tubes has a significant effect on the shape of the velocity field and turbulence intensity in a vertical conical diffuser. For example, higher values of turbulence intensity are typical of air supplied through profiled tubes (the differences reach 50%). A mathematical formulation (linear and exponential equations) of the change in the average speed and intensity of air flow turbulence along the height of the diffuser’s cylindrical part for various initial conditions and supply tube configurations is presented. The obtained findings will make it possible to refine mathematical models and update algorithms for engineering the design of diffusers for various engineering processes and pieces of technical equipment.

The model of a multicomponent medium containing large particles was proposed by Academician Kh. A. Rakhmatulin, where a generalized theory of filtration is considered taking into account the motion of solid particles. In this article, a two-dimensional stationary motion in a layer of a mixture consisting of an incompressible liquid and weighty solid particles is studied.

The study of the spectra of flow is carried out by experimental methods. The paper summarizes the authors’ experience in the design, construction and use of hydrodynamic installations for the visualization of liquid or gas flow using hydrogen bubbles obtained by electrolysis of water. The design of a vertical hydrodynamic pipe, the technology of making experimental models, the design and purpose of the main equipment are considered. Research methods and procedures are described. The article presents the results of the studies that make it possible to evaluate the capabilities of the experimental equipment and picture physical processes around the bodies that change the kinematic parameters of motion in the incident flow according to a given law. The proposed research methods and experimental equipment are distinguished by originality. They can be used to study the features of macrostructures around bodies of complex geometric shapes and laws of motion.

In this paper, we study the classical problem of the wind in the steady atmospheric Ekman layer with constant eddy viscosity. Three dimensional Ekman flows with constant vorticity is considered in the $$\beta $$ -plane approximation. It is remarkable that we explore a totally new approach, which is much different from procedure in (Martin J Fluid Mech 865:762–774, 2019; Chu and Yang J Differ Equ 269:9336–9347, 2020), to show that any Ekman flow with a flat surface and constant vorticity vector is the stationary flow with vanishing velocity field.

International audience; This works deals with the Traffic State Estimation (TSE) problem for urban networks, using heterogeneous sources of data such as stationary flow sensors, Floating Car Data (FCD), and Automatic Vehicle Identifiers (AVI). A data-based flow and density estimation method is presented and tested using real traffic data. This work presents a study case applied to the downtown of the city of Grenoble in France, using the Grenoble Traffic Lab for urban networks (GTL-Ville) which is an experimental platform for real-time collection and analysis of traffic data.

This paper investigates the steady coherent solutions, bifurcated from the linear stability of a stationary flow, in two-dimensional (2-D) penetrative convection. The results show that the thickness of the upper stably stratified layer, which is measured by .

A flow reactor setup for noninvasive monitoring of reactions using a compact benchtop nuclear magnetic resonance (NMR) spectrometer is presented, in which a tubular flow reactor is inserted into the bore of the NMR spectrometer and operated at stationary conditions. To monitor the composition change of the reaction mixture in the flow reactor, the entire reactor is moved to different longitudinal positions in the bore. As the flow is stationary, the composition of the reaction mixture does not change with time at a fixed reactor position. Thus, also time-consuming 2D NMR techniques can be applied to elucidate unknown products. As quantitative information is obtained directly from the NMR spectrum without calibration, the method is also appropriate for quantifying substances that are unstable as pure components. As test cases, two esterification reactions, the formation of methyl formate and the formation of methyl acetate from the pure alcohols and acids, were investigated using this technique. In addition, three 2D NMR pulse sequences (H–H–COSY, HETCOR, and HMBC) were applied in flow. The comparison of the results of the present work to literature data shows that the new method gives reliable results.

A tensorial approach to the theory of classical Hamiltonian integrable systems is proposed, based on the geometry of Haantjes tensors. We introduce the class of symplectic-Haantjes manifolds (or $\omega \mathscr{H}$ manifolds), as a natural setting where the notion of integrability can be formulated. We prove that the existence of suitable Haantjes algebras of (1,1) tensor fields with vanishing Haantjes torsion is a necessary and sufficient condition for a Hamiltonian system to be integrable in the Liouville-Arnold sense. We also show that new integrable models arise from the Haantjes geometry. Finally, we present an application of our approach to the study of the Post-Winternitz system and of a stationary flow of the KdV hierarchy., Comment: 32 pages

Abstract Our quest is for the thumb and finger positions that maximize drag in front crawl swimming and thus maximize propulsion efficiency. We focus on drag in a stationary flow. Swimming is in water, but using Reynolds similarity the drag experiments are done in a wind tunnel. We measure the forces on real-life models of a forearm with hands, flexing the thumb and fingers in various positions. We study the influence on drag of cupping the hand and flexing the thumb. We find that cupping the hand is detrimental for drag. Swimming is most efficient with a flat hand. Flexing the thumb has a small effect on the drag, such that the drag is largest for the opened (abducted) thumb. Flow structures around the hand are visualized using robotic volumetric particle image velocimetry. From the time-averaged velocity fields we reconstruct the pressure distribution on the hand. These pressures are compared to the result of a direct measurement. The reached accuracy of $$\approx$$ ≈ 10% does not yet suffice to reproduce the small drag differences between the hand postures. Graphical Abstract

Pressure surges seen as wastewater reflux and geyser, overflowing and pipes burst are likely to be related to the solid deposit layer development in closed collectors. However, this danger still needs to be not fully understood. In this work, we evaluated the effect of pipes bottom modification due to the solid deposit on the pressure changes. Exner Saint Venant equations under the hypothesis of uniform and stationary flow were used for the solid deposit layer development effect on pressure changes modeling. Both analytical and numerical solutions in gravity as well as in a pressurized pipe were calculated. Since the solid flow is an important parameter in this calculus, we used the Wang and the Graf formulas as well as several different others proposed in the literature to ensure its estimation. Then, we compared the obtained results in order to select the suitable one that neither underestimates nor overestimates the pressure change. The results showed that the pressurizing of free surface flow pipes are significantly affected and that pressurized conduits are more exposed to this danger due to the solid deposit layer. Thus, to avoid this phenomenon, the pipes bottom and the pressure modification have to be evaluated using the most appropriate solid flow formula.

This chapter differs from the previous chapter by using sources in the unbounded fluid as Green functions. Thus, also the free surface (including ship waves) around the hull must be covered by source panels. The described method includes the interaction of oscillatory and stationary potentials; the latter is assumed stationary not in inertial, but in ship-fixed coordinates for higher accuracy. Also, the method to satisfy the radiation conditions (no disturbance from outside, no wave reflections) is important for accuracy: For the stationary flow, a back-shift of sources by 1 panel length is used, whereas for the oscillatory flow damping is applied everywhere on the free surface.

It is known that the initial level of gas flow turbulence has a noticeable effect on the development and structure of the boundary layer and on the intensity of heat transfer, respectively. Many scientists have evaluated the influence of the flow turbulence number on the level of heat transfer for various applications, among them Dyban E.P., Kestin J., Simonich JC, Isomoto K., Dreitser G.A., Terekhov V.I., MacMullin R. and etc. In all cases, the turbulence of the flow led to the intensification of heat transfer. However, insufficient attention is paid to studies of the effect of turbulence on the heat transfer of flows in pipes. The studies were carried out on the basis of numerical modeling of gas dynamics and heat transfer of stationary flows based on the CFD method. The results of numerical modeling to assess the influence of the turbulence scale of gas flows on heat transfer in a long smooth pipe are presented in the article. It has been established that a growth in the heat transfer coefficient by about 3% occurs with an increase in the turbulence scale from 10 to 30% with a Reynolds number equal to 250,000. © Published under licence by IOP Publishing Ltd. The work has been supported by the Russian Science Foundation (grant No. 18-79-10003).

Many processes such as motion of substances in technological systems or motion of migrants can be modelled by a flow of a substance in a channel of network. It can happen however that two substances flow in the same channel of network. In addition the substances may react and then the question arises about the distribution of the amounts of the substances in the nodes of the channel. We study the case of stationary flow of the substances and present analytical relationships for the distributions of the substances in the nodes of the channel.

We consider here three-dimensional water flows in the $\unicode[STIX]{x1D6FD}$-plane approximation. In a quite general setting we show that the only flow exhibiting a constant vorticity vector is the stationary flow with vanishing velocity field and flat free surface.

In this paper, we propose an imaging technique for the detection of porous inclusions in a stationary flow governed by Stokes–Brinkmann equations. We introduce the velocity method to perform the shape deformation, and derive the structure of shape gradient for the cost functional based on the continuous adjoint method and the function space parametrization technique. Moreover, we present a gradient-type algorithm to the shape inverse problem. The numerical results demonstrate the proposed algorithm is feasible and effective for the quite high Reynolds numbers problems.

The plane stationary flow of viscous gas is considered, which is induced by the jet impacting the unbounded space and the domain between two diverging flat walls. Existence criteria of the Landau self-similar solutions are established for the source of gas flowing from the apex of a wedge with the thermally insulated walls and of wedge with the prescribed walls temperature. The analytical solutions are constructed in the case when the gas temperature is constant along the lines of flow and when the transfer coefficients are power functions of temperature.

The present analytical work studies the modeling of a catalytic microcombustor with the stationary flame. In this model, the nonasymptotic solution of energy and mole fraction equations with self-s...

An asymptotic formula for the spectrum of a linearized problem of the stability of stationary flows of a polymer fluid with a space charge is obtained.

The aim of this paper is to study the stationary flow of an Oldroyd fluid with particular diffusive stress, flowing through a thin 3D pipe. An asymptotic expansion with respect to a small parameter describing the ratio between the diameter of the cross section and the length is calculated and rigorously justified. The result obtained is compared against a numerical solution in the particular case of axisymmetric geometries.

We study the classical problem of a supersonic stationary flow of a nonviscous nonheat-conducting gas in local thermodynamic equilibrium past an infinite plane wedge. Under the Lopatinskiĭ condition on the shock wave (neutral stability), we prove the well-posedness of the linearized mixed problem (the main solution is a weak shock wave), obtain a representation of the classical solution, where, in this case (in contrast to the case of the uniform Lopatinskiĭ condition—an absolutely stable shock wave), plane waves additionally appear in the representation. If the initial data have compact support, the solution reaches the given regime in infinite time.

We study the stationary flow of an incompressible non-Newtonian fluid of Bingham type, mathematically described by means of a nonlinear boundary value problem governed by PDEs. The variational formulation which we propose is a mixed variational problem with Lagrange multipliers. First, we obtain existence, uniqueness, and stability results into an abstract framework. Then, we discuss the well-posedness of the mechanical model based on the auxiliary abstract results.

The article considers the problem of stationary blood flow in vessels with permeable walls. To determine the hydraulic resistance in an arterial vessel, the blood is considered Newtonian viscous fluid, and the flow is stationary. When solving problems, formulas were obtained for determining the corresponding hydrodynamic parameters, such as speed, fluid flow rate and pressure gradient. The impedance method is determined by the hydraulic resistance. In a stationary flow, the hydraulic resistance in the permeable vessel substantially depends on the permeability coefficient: with an increase in this coefficient, it decreases.

The problem of fluid dynamics can be greatly simplified if, for every point in space, the strain-rate tensor is diagonalized. This tensor is introduced into the Navier-Stokes equations via material law and divergence of the stress tensor. This article shows that local SO(3)xU(1) gauge fields can be used to locally diagonalize the diffusion components of the strain-rate tensor. The gauge fields resulting from the connection can be interpreted as convection components of the flow, they show properties of quasiparticles and can be interpreted as elementary vortices. Thus, the proposed approach not only offers new insights for the solution and situative simplification of the Navier-Stokes equations, it also uncovers hidden symmetries within the flow convection, allowing - depending on boundary conditions - further interpretation.

U ovom radu definiran nam je uzdužni presjek kanala, načelni poprečni presjek kanala, te tlocrt dna kanala. Na temelju karakteristika kanala i odabranih protoka u rasponu od 5 do 50 (m3/s) definirana je i nacrtana krivulja protoka na uzvodnom kraju kanala. Zbog promjenjive protjecajne površine kanala (neprizmatično korito) ostvareno je nejednoliko stacionarno strujanje u kanalu te je određivanje kritične dubine provedeno iterativnom Newtonovom metodom. Proračun vodnog lica određen je integracijom diferencijalne jednadžbe vodnog lica te primjenom Bernoullijeve jednadžbe. Na kraju samog rada njihovi rezultati su uspoređeni., In this paper, we have defined the longitudinal section of the channel, the principal cross-section of the channel, and the floor plan of the channel bottom. Based on channel characteristics and selected flows in range of 5 to 50 (m3/s) we have defined and drawn the flow curve at the upper side of the channel. Due to the variable flow area of the channel, non-uniform stationary flow in the channel was obtained, and the critical depth was determined by iterative Newton method. At the end of the paper, their results were compared.

U ovom radu definiran nam je uzdužni presjek kanala, načelni poprečni presjek kanala, te tlocrt dna kanala. Na temelju karakteristika kanala i odabranih protoka u rasponu od 5 do 50 (m3/s) definirana je i nacrtana krivulja protoka na uzvodnom kraju kanala. Zbog promjenjive protjecajne površine kanala (neprizmatično korito) ostvareno je nejednoliko stacionarno strujanje u kanalu te je određivanje kritične dubine provedeno iterativnom Newtonovom metodom. Proračun vodnog lica određen je integracijom diferencijalne jednadžbe vodnog lica te primjenom Bernoullijeve jednadžbe. Na kraju samog rada njihovi rezultati su uspoređeni. In this paper, we have defined the longitudinal section of the channel, the principal cross-section of the channel, and the floor plan of the channel bottom. Based on channel characteristics and selected flows in range of 5 to 50 (m3/s) we have defined and drawn the flow curve at the upper side of the channel. Due to the variable flow area of the channel, non-uniform stationary flow in the channel was obtained, and the critical depth was determined by iterative Newton method. At the end of the paper, their results were compared.

Izvršen je proračun vodnog lica u kanalu jojolikog poprečnog presjeka za stacionarno tečenje. Proračun vodnog lica proveden je numeričkom integracijom diferencijalne jednadžbe vodnog lica s mješovitim postupkom. Proračuni vodnog lica provedeni su u mirnom i u silovitom režimu strujanja. Normalna i kritična dubina određene su Newton-ovom metodom., Calculation of water table in ovoid cross section channel for stationary flow was performed.The water table calcultion was performed by numerical integration of differential water equation with mixed metod. Calculations of water table were performed in sub-critical and in super-critical flow. Normal and critical depth were determined by Newton's method.

Izvršen je proračun vodnog lica u kanalu jojolikog poprečnog presjeka za stacionarno tečenje. Proračun vodnog lica proveden je numeričkom integracijom diferencijalne jednadžbe vodnog lica s mješovitim postupkom. Proračuni vodnog lica provedeni su u mirnom i u silovitom režimu strujanja. Normalna i kritična dubina određene su Newton-ovom metodom. Calculation of water table in ovoid cross section channel for stationary flow was performed.The water table calcultion was performed by numerical integration of differential water equation with mixed metod. Calculations of water table were performed in sub-critical and in super-critical flow. Normal and critical depth were determined by Newton's method.

The effect of acoustic wave propagating in longitudinal direction on stationary convective flow in a horizontal channel of rectangular cross-section in the presence of horizontal temperature gradient and its stability is studied. It is shown that in the presence of sufficiently intensive acoustic wave stationary flow is of coaxial character, the fluid moves in the direction of temperature gradient near sidewalls and in the opposite direction in the interior of the channel. At Pr

Stationary flow bench testing is a standard experimental methodology used by the automotive industry to characterize a cylinder head. In order to reduce the development time, the use of a CFD-based virtual test bench is nowadays a standard practice too. The use of a conventional \RANS\ methodology for the simulation of the flow through the ducts of an engine head allows to get only the mean flow variables distributions because the time average of the generic flow variable fluctuation is zero by definition, but the fluid-dynamics of a stationary flow bench is not really stationary due to the flow instability induced by the duct design and the interaction between valve jets in a multi-duct head. In order to obtain an in-depth knowledge of the fluid-dynamics of a stationary flow bench test rig a \LES\ simulation of a heavy duty \DI\ diesel engine head with two intake ducts, for which experimental data was available, has been carried out using OpenFOAM®. The comparison between LES, experimental and conventional \RANS\ results widened the understanding of the test-bench fluid-dynamics and of the swirl generation process. Due to the high computational cost of the \LES\ approach, the outcomes of this latter have been also used to evaluate potential accuracy improvements of the \RANS\ simulation, namely using a model sensible to flow anisotropies and curvatures such as a \RSTM\ model. The simulation with the new turbulence model has been carried out and compared with the previous results demonstrating predictive improvements with an affordable computational cost for industrial routine usage.

The purpose of the work is to study the effect of a pulsed surface discharge (plasma sheet) on the transverse flow upon its initiation in an unsteady gas-dynamic flow in a channel with an obstacle on the wall. Also a comparison with the effect of a pulsed volume discharge under similar conditions was studied. The dynamics of the blast waves propagating from the separation zone behind the obstacle after self-localization of the discharge plasma there is investigated.

Context. The problem of mass transfer of a cylindrical body with a uniform translational flow of a viscous incompressible fluid is examined in the paper. Objective. The purpose of this work is to develop a new method for numerical analysis of the problem of mass transfer of a cylindrical body with a uniform translational flow, which based on the joint application of the R-functions structural method and the Galerkin projection method. Method. In general case, the problem of stationary mass transfer of a cylindrical body with a viscous incompressible fluid flow is reduced to the solution of the equation of hydrodynamic flow passing a surface and an equation for concentration with corresponding boundary conditions on the surface of the body and far away from it. The geometry of the area, and also the boundary conditions (including the condition at infinity) may be taken into account precisely by using the constructive apparatus of the R-functions theory by V. L. Rvachev, the Academician of Ukrainian National Academy of Sciences. In this study, a complete structure of the solution of a linear boundary value problem for the concentration that exactly satisfies the boundary conditions on the boundary and condition at infinity is constructed on the basis of the R-functions theory methods, and this made it possible to lead the tasks in the infinite domain to tasks in the finite domain. To solve the linear problem for concentration the numerical algorithm on the basis of Galerkin method is developed. Results. The computational experiment for the problem of the flow past circular and elliptical cylinders at various Reynolds and Peclet numbers was carried out. Conclusions. The conducted experiments have confirmed the efficiency of the proposed method of numerical analysis of the problem of mass transfer of a cylindrical body with a uniform translational flow, based on the joint application of the R-functions structural method and Galerkin projection method. The prospects for the further research may be to use the developed method for the implementation of iterative methods for solving the task of nonlinear mass transfer, semi-discrete and projection methods for solving the non-stationary tasks, as well as in solving the tasks of optimal management of relevant technological processes.

We consider the situation of a large-scale stationary flow subjected to small-scale fluctuations. Assuming that the stable and unstable manifolds of the large-scale flow are known, we quantify the mean behavior and stochastic fluctuations of particles close to the unperturbed stable and unstable manifolds and their evolution in time. The mean defines a smooth curve in physical space, while the variance provides a time- and space-dependent quantitative estimate where particles are likely to be found. This allows us to quantify transport properties such as the expected volume of mixing as the result of the stochastic fluctuations of the transport barriers. We corroborate our analytical findings with numerical simulations in both compressible and incompressible flow situations. We moreover demonstrate the intimate connection of our results with finite-time Lyapunov exponent fields, and with spatial mixing regions.

Context. The nonlinear stationary problem of flow past a body of revolution by a viscous incompressible fluid is examined in this article. Objective. The purpose of this work is to develop a new method of numerical analysis of stationary problems of flow around bodies of revolution by viscous incompressible fluid. Method. The mathematical model of the process under consideration is a nonlinear boundary value problem for the stream function obtained by the transition from the system of Navier-Stokes equations to one nonlinear equation of the fourth order. A special feature of the formulation the task of the flow past body is that the boundary value problem is considered in an infinite region and both boundary conditions on the boundary of the streamlined body and the condition at infinity are imposed for the stream function. Using the structural method (the R-functions method), the task solution structure, that exactly satisfies all the boundary conditions of the task, and also guarantees the necessary behavior of the stream function at infinity, is constructed. Two approaches are proposed to approximate the uncertain components of the structure. The first approach is based on the use of the successive approximations method, which makes it possible to reduce the solution of the initial nonlinear task to the solution of a sequence of linear boundary value problems. These linear tasks are solved by the Bubnov-Galerkin method at each step of the iteration process. The second approach for approximating the uncertain components of the structure is based on the usage of the nonlinear Galerkin method and it is proposed to use it in the case of divergence of successive approximations. In this case, the solution of the initial nonlinear task reduces to solving a system of nonlinear algebraic equations. Results. A computational experiment was carried out for the task of flow past a sphere, an ellipsoid of rotation and two articulated ellipsoids for various Reynolds numbers. Conclusions. The conducted experiments have confirmed the efficiency of the proposed method of numerical analysis of stationary problems of flow around bodies of revolution by viscous incompressible fluid. The prospects for further research may consist in using the method developed for the implementation of semi-discrete and projection methods for solving non-stationary problems.

U ovome radu prikazane su hidrauličke analize protočnosti pod utjecajem različitih oblika poprečnih presjeka i vrste obloženosti kanala. Prilikom analize različitih oblika poprečnih presjeka izrađen je hidraulički proračun za jednoliko stacionarno tečenje za trokutni, pravokutni, trapezni i polukružni oblik poprečnog presjeka kanala. Prvom provedenom hidrauličkom analizom uspostavilo se da je, u pogledu protočnosti kanala, najpovoljniji polukružni oblik poprečnog presjeka kanala. U drugoj hidrauličkoj analizi promatrane su različite vrste obloženosti stijenki kanala te se u tu svrhu također proveo hidraulički proračun za jednoliko stacionarno tečenje u kojem su promatrane različite obloge kanala, odnosno koeficijenta hrapavosti na protočnost. Provedena analiza pokazala je kako veći koeficijenti hrapavosti daju manju protočnost u kanalu i obrnuto. Samim time, prilikom dimenzioniranja kanala, odnosno hidrauličkog proračuna, potrebno je uzeti u obzir odgovarajući poprečni presjek kanala te vrstu obloženosti kanala kako bi dimenzionirani kanal bio najpovoljniji u pogledu što manjih hidrauličkih gubitaka i što veće propusne moći., This paper presents hydraulic analysis of flow in channels under the influence of various cross-sections and type of covering of the channel. During the analysis of different cross sections, a hydraulic design was made for uniform stationary flow for the triangular, rectangular, trapezoidal and semicircular cross-sectional shape of the channel. First performed hydraulic analysis established that the semicircular cross-section of the channel is the most favorable in terms of flow. In the second hydraulic analysis, various types of covering of the channel were observed and a hydraulic design for uniform stationary flow was carried out in order to observe different channel coverings, i.e. the coefficient of roughness. The analysis showed that higher coefficients of roughness give a smaller flow in the channel and smaller coefficients of roughness give a higher flow in the channel. In this case, when dimensioning the channel or the hydraulic design, the appropriate cross section of the channel and the type of covering of the channel should be taken into consideration so that the dimensioned channel is most favorable in terms of smaller hydraulic losses and greater flow in the channel.

Under study is a boundary-value problem for a quasilinear elliptic equation. The solution to this problem defines the velocity profile for a stationary flow of an incompressible viscoelastic polymeric fluid in a channel with elliptical cross section. The problem is solved numerically with a nonlocal algorithm without saturation.

The stationary flow field in a quasi-two-dimensional hopper is investigated experimentally. The behavior of materials consisting of beads and elongated particles with different aspect ratio is compared. We show, that while the vertical velocity in the flowing region can be fitted with a Gaussian function for beads, in the case of elongated grains the flowing channel is narrower and is bordered with sharper velocity gradient. For this case, we quantify deviations from the Gaussian velocity profile. Relative velocity fluctuations are considerably larger and slower for elongated grains.

An extensive data set of water level measurements of the September 2015 Chilean tsunami in rivers in Japan and a new methodology for data processing are used to verify that tsunami dissipation in a river at each instant and locality depends on the tidally-modified wave-locked slope of the river surface. As deduced from the observations, a relatively small tsunami or ocean noise traveling at mild wave-locked slopes can propagate virtually without losses to the upstream locations where observed tidal ranges are a fraction of that downstream; though at the higher slopes, tidal and riverine currents combined efficiently damp the shorter waves. The observed correlations between the tsunami admittance upriver and the traveled wave-locked slopes are explained analytically under the fully-nonlinear shallow-water approximation. It is found that the wave-locked slope in a purely incident wave relates to the bottom drag in the same manner as a steady surface slope does for a stationary flow. For a small-amplitude tsunami in the study rivers, the wave-locked slope in a co-propagating tidal wave defines the background current and thereby friction experienced by the tsunami., 25 pages, 12 figures