Оn momentum flow density of the gravitational field

Momentum is considered on the basis of the approach widely used in the calculus of variations and in the optimal control theory, where variation of a cost functional is investigated. In physical theory, it is the action functional. Action variation under Lie dragging can be expressed as a surface integral of some differential form. The momentum density flow is defined using this form. In this work, the momentum balance equation is obtained. This equation shows that the momentum field transforms into a momentum of a mass. Examples showing the momentum flow structure for a mass distribution representing a uniform thin layer are provided.

Jeans-Alfvén instability in quantum dusty magnetoplasmas

The Jeans instability is examined in quantum dusty magnetoplasmas due to low-frequency magnetosonic perturbations. The fluid model consisting of the momentum balance equation for quantum plasmas, Poisson’s equation for the gravitational potential and Maxwell’s equations for electromagnetic magnetosonic perturbations is solved. The numerical analysis elaborates the significant contribution of magnetic field, electron number density and variable dust mass to the Jeans instability.

INTEGRAL METHODS FOR DESCRIBING PULSATILE FLOW

<p>This paper presents an approximate solution of the pulsatile flow of a Newtonian fluid in the laminar flow regime in a rigid tube of constant diameter. The model is represented by two ordinary differential equations. The first equation describes the time evolution of the total flow rate, and the<br />second equation characterizes the reverse flow near the wall. These equations are derived from the momentum balance equation and from the kinetic energy equation, respectively. The accuracy of the derived equations is compared with a solution in which the finite difference method is applied to a partial differential equation.</p>

Influence of quantum energy equation on electronic plasma oscillations

Five-moment approximation in hydrodynamics includes not only a continuity equation and a momentum balance equation, but also an energy equation. A set of hydrodynamic equations in this approximation is presented for a system of nonrelativistic quantum particles with the Coulomb interaction. This set of equations is linearized, and dispersion relation for Langmuir waves in quasi-neutral system of electrons and immobile ions is obtained. The plasma waves suffer damping in this case, and also there is another damping branch.

Velocity Profiles for Flow of Omani Crude Oils and Other Liquids

Velocity profiles of Newtonian immiscible liquids undergoing laminar flow between two horizontal plates under pressure gradient are investigated using a momentum balance equation. The differential equation describing the flow has been solved and equations for the velocity profiles of a two-layer and three-layer liquid systems are presented. As examples, we show flow patterns of two-layer water-crude oil system and three-layer system involving water, tetrachloromethane, xylene, cyclopentane and hexane. A distinctive pattern is noticeable between the velocity profiles of heavy (API 19.19) and light (API 40.89) Omani crude oils.

Electromagnetic momentum balance equation and the force density in material media

We present a momentum balance equation derived directly from Maxwell's equations. This equation contains a force density, which we call Maxwell's force density, which generalizes the Lorentz force density, now including total fields rather than only external fields, and arbitrary charge and current distributions. As a test for this balance equation we derive for gases the electrostatic and magnetostatic Helmholtz force densities. This deduction will be useful for advanced undergraduates and graduate students, as well as for specialists interested in the conceptual aspects of electromagnetism.