Calculating the total resistance for a tube with a variable cross section

A study has been made on the decisive effect from the exit cone on the total resistance of a variable cross section tube composed of alternating divergent and convergent parts, whose radii vary on a cosine law. Numerical calculations have been performed for steady-state stabilized laminar flow of a viscous incompressible liquid. The frictional and pressure resistance coefficients have been calculated. The contribution from those resistances to the total resistance has been examined.Donetsk. Translated from Teoreticheskaya i Prikladnaya Mekhanika, No. 21, pp. 120–124, 1990.     

Hydrodynamics of artificial heart valves

The use of a pulsating-type hydrodynamic bench apparatus for studying the functioning of heart-valve prostheses at various values of the volume flow rate is described. A complex of hydrodynamic characteristics is developed and the dependence of these characteristics on the minute volume, flow regime, and the ratio of the linear dimensions of the prosthesis is examined for various types of artificial heart valves. The operation of the heart-value prostheses under different hydrodynamic conditions is analyzed, and the design defects of certain types of prostheses are noted.     

Liquid flow in a tube with deforming walls in the presence of valves

A numerical solution is presented for the flow of a viscous liquid in a tube of finite length with valves at the ends and elastic properties of the tube walls periodically changing with time. Such conditions may be encountered in the flow of blood through veins equipped with valves to prevent reverse flow.Scientific-Research Institute of Mechanics. M. V. Lomonosov State University, Moscow. Translated from Mekhanika Polimerov, No. 5, pp. 903–908, September–October, 1972.     

Buoyant Poiseuille–Couette flow with viscous dissipation in a vertical channel

Steady combined forced and free convection is investigated in a vertical channel having a wall at rest and a moving wall subjected to a prescribed shear stress. The moving wall is thermally insulated, while the wall at rest is kept at a uniform temperature. The analysis deals with the fully–developed parallel flow regime. The governing equations yield a boundary value problem, that is solved analytically by employing a power series expansion of the velocity field with respect to the transverse coordinate. It is shown that the nonlinear interplay between buoyancy and viscous dissipation may determine the existence of dual solutions of the boundary value problem corresponding to fixed values of the applied shear stress on the moving wall and of the hydrodynamic pressure gradient. It is shown that a nontrivial fully separated flow may occur such that the hydrodynamic pressure gradient is zero and the shear stress vanishes on both walls. E. Magyari: On leave from Institute of Building Technology, ETH – Zürich     

A numerical computation of a non-dimensional form of stream water quality model with hydrodynamic advection–dispersion–reaction equations

Mathematical models of water quality assessment problems often arise in environmental science. The modelling often involves numerical methods to solve the equations. In this research, two mathematical models are used to simulate pollution due to sewage effluent in the nonuniform flow of water in a stream with varied current velocity. The first is a hydrodynamic model that provides the velocity field and elevation of the water flow. The second is a dispersion model, where the commonly used governing factor is the one-dimensional advection–dispersion–reaction equation that gives the pollutant concentration fields. In the simulation processes, we used the Crank–Nicolson method system of a hydrodynamic model and the backward time central space scheme for the dispersion model. Finally, we present a numerical simulation that confirms the results of the techniques.     

Nonlinear Pressure Control of a Switched Hydraulic System

Hydraulic power transmission is often used in a variety of technical applications. Due to the nonlinear and often non smooth behaviour of some hydraulic components concerning their volume flow characteristics, the development of control strategies for hydraulic systems is challenging. Most developed control strategies base on linearized models, allowing only local operation in the environment of certain operating points. In this contribution, a nonlinear control strategy, based on the feedback linearization technique, allowing a global compensation of the nonlinearities [2], is developed for a minimal hydraulic circuit consisting of a pressure regulation valve, a vane pump and an ideal consumer. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Calculation of the resistance to the flow of polymeric systems through short channels

A method is proposed for calculating the pressure drop associated with the flow of polymeric systems (solutions, melts, and rubber blends) through short capillaries in which the steady-state flow regime is not established. The method is based on the assumption that the duration of deformation in the prestationary stage plays a decisive role. The results of the calculations are in good agreement with the experimental data.All-Union Scientific-Research and Design-Engineering Institute of the Rubber Industry, Volzhskii. Topchiev Institute of Petrochemical Synthesis, Academy of Sciences of the USSR, Moscow. Volgograd Polytechnic Institute. Translated from Mekhanika Polimerov, No. 1, pp. 171–174, January–February, 1973.     

Expanding ball in the scalar field model and in the relativistic theory of gravity

The first-order approximations for the internal and external fields of an expanding ball are evaluated in the scalar field model and in the relativistic theory of gravity. The similarity of the corresponding solutions is pointed out. It is suggested how the nonstatic properties possessed by solutions in the original inertial coordinates can be observed experimentally.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 104, No. 2, pp. 348–355, August, 1995.     

On transcritical states in viscous flow passing the edge of a horizontal plate

This contribution puts forward some recent advances in the rigorous (asymptotic) theory of gravity- (and capillarity-)driven shallow flow of a viscous liquid past a horizontal plate, originating in jet impingement oblique to it. Hence, our concern is twofold: with steady developed flow over the distance from the jet centre to the trailing edge of the plate, referred to as a pronounced hydraulic jump blurred by viscous diffusion; with the predominantly inviscid transcritical limit arising near the edge due to scale reduction given an intrinsic expansive singularity taking place there. In the latter situation envisaged briefly, condensing nonlinear inertial effects, weak time dependence, and (very) weak streamline curvature as the essential ingredients into a distinguished limit demonstrates the generation of a weak (transcritical) hydraulic jump by a plate-mounted obstacle. (© 2017 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Saturated and unsaturated flow of ground water to a regular horizontal drain system in nonhomogeneous layered soils

The paper presents a mathematical formulation of the problem of drainage of nonhomogeneous soil by a regular system of horizontal drains in the framework of hydrodynamic and hydraulic theories. Algorithms for approximate solution of the problem are described. Comparison of numerical and analytical solutions substantiates the theoretical dependences.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 65–73, 1988.     

Numerical Simulation of the Two-Hydrodynamic Film Thickness

We investigate, from a numerical point of view, the coefficients identification problem, for the Elrod–Adams model of cavitation, in the frame of the hydrodynamic lubrication. We relax the control problem, and propose a relaxed augmented Lagrangian algorithm, with a given loop length. Some numerical results are given.     

Extrusion of a viscocompressible material through a circular opening in an infinite wall

On the assumption that the motion of the visco-compressible material is slow and that the viscosity coefficients are constant, the author examines the simple problem of extrusion through a circular opening in an infinite wall. A formula is obtained for the flow rate as a function of the pressure drop, viscosity coefficients, radius of the opening, bulk modulus, and time.Mekhanika Polimerov, Vol. 2, No. 4, pp. 611–616, 1966     

Flow of a viscous fluid in a deformable valved tube in the presence of gravity

The problem of the flow of a viscous incompressible fluid in a tube of finite length with valves at the ends is solved numerically with allowance for gravity and elastic wall properties that vary periodically with time.Paper presented at the First All-Union Conference on Engineering and Medical Biomechanics, Riga, October, 1975.M. V. Lomonosov Moscow State University. Translated from Mekhanika Polimerov, No. 4, pp. 756–760, July–August, 1975.     

On the uniqueness of solutions to some boundary-value problems for differential equations in a domain with algebraic boundary

Classes of differential equations with constant coefficients admitting unique solutions of Dirichlet and Cauchy boundary-value problems are considered in a bounded domain with algebraic boundary. For the Dirichlet problem in a ball, the necessary and sufficient conditions for the uniqueness of the solution are obtained in the form of a countable sequence of inequalities polynomial in the coefficients of the equation.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 45, No. 7, pp. 898–906, July, 1993.     

Influence of heat transfer on a peristaltic transport of Herschel–Bulkley fluid in a non-uniform inclined tube

Peristaltic transport in a two-dimensional non-uniform tube filled with Herschel–Bulkley fluid is studied under the assumptions of long wavelength and low Reynold number. The fluid flow is investigated in the wave frame of reference moving with the velocity of the peristaltic wave. Exact solution for the velocity field, the temperature profile, the stream functions and the pressure gradient are obtained. The physical behavior of τ, n, α and on the pressure rise versus flow rate are discussed through graphs. At the end of the article trapping phenomena for Herschel–Bulkley and also for Newtonian, Bingham and power law (which are the special cases of Herschel–Bulkley fluid) fluid are discussed.     

Technological anisotropy of chaotically reinforced glass-fiber-resin materials

The authors investigate the strength properties of chaotically reinforced glass-fiber-resin materials in compression-molded and injection-molded artifacts of complex shape and also the density, water absorption, and binder content in various zones in the artifacts. They find anisotropy to be present in the strength indices, owing to orientation of the reinforcing elements during flow of material in the mold. They determine the coefficients of anisotropy of the strength (these are defined as the ratios of the strength in the flow direction to the strength in a perpendicular direction). They suggest a method of estimating the degree of orientation of the reinforcing elements in artifacts made of nonoriented glass-fiber-resin materials.All-Union Scientific-Research Institute of Glass-Fiber-Reinforced Plastics and Glass Fiber, Moscow Region. Translated from Mekhanika Polimerov, Vol. 9, No. 3, pp. 507–515, May–June, 1973.     

Nonlinear Volume Flow Control of a Variable Displacement Vane Pump

Variable displacement vane pumps are used for mid-pressure applications in a variety of systems. Due to their potential for power loss reduction they are most prominently featured in automotive applications. They provide a hydraulic consumer with varying levels of volume flow, depending on the eccentricity of the cam ring of the pump. Eccentricity control is typically achieved by means of hydraulic actuation. In this contribution, a model of a hydraulic aggregate featuring a VDVP with a nonlinear control technique based on input-output-linearization for volume flow tracking requirements is presented. (© 2015 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim)     

On the theory of non-Newtonian polymer flow

Shear flow of polymers is examined on the assumption that the main contribution to polymer viscosity is made by the dissipation of energy in the destruction of the fluctuation network. A simple physicomechanical model of the flow process is proposed and used to obtain an expression for the polymer viscosity in terms of certain functions reflecting the influence of the molecular structure.Mekhanika Polimerov, Vol. 2, No. 3, pp. 429–434, 1966     

Viscous incompressible flow past a finite plate

We consider the problem of viscous incompressible flow past a finite plate. The apparatus of hydrodynamic potential reduces the problem to Volterra— Fredholm boundary-value equations. Numerical results are reported.Translated from Vychislitel'naya i Prikladnaya Matematika, No. 64, pp. 103–107, 1988.     

Molecular hydrodynamics of a weakly degenerate nonideal bose-gas II. Green functions and kinetic coefficients

The nonideal degenerate Bose-system at a temperature close to zero is investigated by N. N. Bogolyubov and D. N. Zubarev's method of collective variables. Applicable to a wide range of frequencies and wave vectors, interpolated expressions for the Green functions of the densities of conserved quantities and for the superfluid velocity potential are derived from exact relations. The criteria defining the validity domain of the hydrodynamic approximation are obtained. The kinetic coefficients of two-liquid hydrodynamics at temperatures close to zero are calculated for a weakly nonideal Bose-gas. A comparison with the method employing the kinetic equation for quasi-particles is made.Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 105, No. 1, pp. 77–129, October, 1995.