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Hydrostatic equilibrium
About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.
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TL;DR: In this article, the authors used finite volume method on numerical simulation of pressure field of heavy hydrostatic bearing in constant and variable viscosity respectively and in different rotational velocity, whereafter, viscoity influence on load capacity of heavy bearing was discussed.
Abstract: Lubricant viscosity is one of the key parameters in hydrostatic bearing research. In order to solve the load capacity of hydrostatic bearing in the heavy equipment, viscosity-temperature equation of lubricant film is established, and the viscosity-temperature curve is fitted by B-Spline curve. Finite volume method is used on numerical simulation of pressure field of heavy hydrostatic bearing in constant and variable viscosity respectively and in different rotational velocity, whereafter, viscosity influence on load capacity of heavy hydrostatic bearing is discussed. The results show that, viscosity impose a minor influence on cavity pressure of hydrostatic bearing when rational velocity is low; whereas, when rational velocity is high, especially to the heavy hydrostatic bearing which with high liner velocity influence of viscosity changing must be taken into account in calculation. Numerical simulation results reflect the pressure distributing state of bearing veritably; furthermore, these provide theoretical basis for hydrostatic bearing design and lectotype in practical application.
10 citations
TL;DR: In this paper, a simple model for the structure of dense regions in turbulence is presented, in which the density distribution behind isothermal shocks originates from rough hydrostatic balance between the pressure gradient behind the shock and its deceleration from ram pressure applied by the background fluid.
Abstract: The properties of supersonic isothermal turbulence influence a variety of astrophysical phenomena, including the structure and evolution of star forming clouds. This work presents a simple model for the structure of dense regions in turbulence in which the density distribution behind isothermal shocks originates from rough hydrostatic balance between the pressure gradient behind the shock and its deceleration from ram pressure applied by the background fluid. Using simulations of supersonic isothermal turbulence and idealized waves moving through a background medium, we show that the structural properties of dense, shocked regions broadly agree with our analytical model. Our work provides a new conceptual picture for describing the dense regions, which complements theoretical efforts to understand the bulk statistical properties of turbulence and attempts to model the more complex features of star forming clouds like magnetic fields, self-gravity, or radiative properties.
10 citations
TL;DR: In this article, the wave velocity equations are deduced from Biot's theory of stress by assuming that the effects of gravity are equivalent to a type of initial stress of a hydrostatic nature.
Abstract: In this paper formulae are derived for surface waves in a viscoelastic medium of Voigt type under the influence of gravity. The wave velocity equations are deduced from Biot's theory of stress by assuming that the effects of gravity are equivalent to a type of initial stress of a hydrostatic nature. The resulting equations are used to briefly investigate the particular surface waves of Rayleigh, Love and Stoneley type. In all cases the final results are in agreement with the corresponding classical results when the effects of gravity and viscosity are neglected.
10 citations
TL;DR: In this paper, a simple and quasi-symmetrical system of differential equations is obtained for the infinitesimal adiabatic perturbations of the most general continuous zonal air flow.
Abstract: By a proper choice of coordinates and variables, a simple and quasi-symmetrical system of differential equations is obtained for the infinitesimal adiabatic perturbations of the most general continuous zonal air-flow. The coordinate surfaces are those of the orthogonal system built up with the isentropic surfaces and the meridians, and the variables are the displacements of the fluid in the directions of the coordinate lines, and the local disturbance of the pressure. From these perturbation equations a differential equation for the pressure disturbance alone is derived in the case of a wave, and it is then shown that this wave equation can be always greatly simplified if account is taken of the order of magnitude of the various parameters. Simplified expressions are also given for the components of the vibration (fluid displacement). More particular equations and formulae are then derived for short-period, middle-period and long-period waves successively, this classification being made according to the value of the orbital frequency compared to the coefficient of hydrostatic stability and Coriolis parameter, and special cases are also considered where the wave equation reduces to one with constant coefficients (elastic, gravitational, Rossby's waves). Finally some incorrect recently published results are discussed. DOI: 10.1111/j.2153-3490.1950.tb00309.x
9 citations
01 Dec 1993
TL;DR: In this article, solar flare model atmospheres are computed under the assumption of energetic equilibrium in the chromosphere by the corona by using a static, one-dimensional plane parallel geometry and are designed within a physically self-consistent coronal loop.
Abstract: Solar flare model atmospheres computed under the assumption of energetic equilibrium in the chromosphere are presented. The models use a static, one-dimensional plane parallel geometry and are designed within a physically self-consistent coronal loop. Assumed flare heating mechanisms include collisions from a flux of non-thermal electrons and x-ray heating of the chromosphere by the corona. The heating by energetic electrons accounts explicitly for variations of the ionized fraction with depth in the atmosphere. X-ray heating of the chromosphere by the corona incorporates a flare loop geometry by approximating distant portions of the loop with a series of point sources, while treating the loop leg closest to the chromospheric footpoint in the plane-parallel approximation. Coronal flare heating leads to increased heat conduction, chromospheric evaporation and subsequent changes in coronal pressure; these effects are included self-consistently in the models. Cooling in the chromosphere is computed in detail for the important optically thick HI, CaII and MgII transitions using the non-LTE prescription in the program MULTI. Hydrogen ionization rates from x-ray photo-ionization and collisional ionization by non-thermal electrons are included explicitly in the rate equations. The models are computed in the 'impulsive' and 'equilibrium' limits, and in a set of intermediate 'evolving' states. The impulsive atmospheres have the density distribution frozen in pre-flare configuration, while the equilibrium models assume the entire atmosphere is in hydrostatic and energetic equilibrium. The evolving atmospheres represent intermediate stages where hydrostatic equilibrium has been established in the chromosphere and corona, but the corona is not yet in energetic equilibrium with the flare heating source. Thus, for example, chromospheric evaporation is still in the process of occurring.
9 citations