Showing papers on "Hydrostatic equilibrium published in 1971"

Hydrostatic equilibrium and gravitational collapse of relativistic charged fluid balls.

Abstract: We obtain the metric corresponding to an arbitrary spherically symmetric distribution of charged perfect fluid without restricting consideration to the static case, and we show that it joins onto the standard Reissner-Nordstr\"om exterior solution of Einstein's equations. We also generalize the Oppenheimer-Volkoff equations of hydrostatic equilibrium to the charged case, and we discuss their applicability. Using our formalism, we then rederive a formula of Christodoulou which splits the mass of a charged black hole into an irreducible part and a reducible electrical part. Finally, we derive the equations for the gravitational collapse of a charged fluid ball, and we draw some general conclusions from them.

Interpretation of the solar continuum from 1680 to 600 Å. Model of the transition region photosphere-chromosphere and of the chromosphere

Abstract: An interpretation is given of the observations of the continuous solar radiation in the spectral range 600–1700 A. The model allows for deviations from LTE of H, C, Si and S, and is in hydrostatic equilibrium. The predicted intensity from 1680 to 1520 A has virtually no dependence on the electron temperature variation in the optical depth range 10−3–4 × 10−5, at 5000 A; the brightness temperature is compatible with a low electronic temperature minimum near the optical depth 10−4. The model of the low chromosphere is characterized by a steep temperature gradient. The model satisfies observations at millimeter wavelengths.

Optimization of conical hydrostatic bearing for minimum friction

Abstract: Equations for flow rate, load capacity, and friction torque for conical hydrostatic bearings under laminar and turbulent flow conditions

Automatically controlled hydrostatic bearing

Abstract: This invention is concerned with an automatically controlled hydrostatic bearing. The automatically controlled hydrostatic bearing comprises a hydrostatic bearing which has two opposite bearing recesses each communicating with a fixed linear external restrictor and a pressure-balance type control valve which has its restrictors formed with gaps of parallel plates and which functions so as to keep constant the ratio between the supply pressures to the fixed linear external restrictors and the pressures in the corresponding bearing recesses.

On baroclinic instability of ultra-long waves'

Abstract: Baroclinic instability of ultra-long waves (wave numbers 1, 2, and 3) is studied with a 40-layer, geostrophic, hydrostatic, adiabatic model which is later modified to include Newtonian heating. The assumption of a meridionally-varying zonal current linear in pressure upon which are superimposed localized wavelike perturbations traveling in the west-east direction and static stability dependent only upon the inverse of pressure allows the reduction of the basic equations to a single second-order homogeneous ordinary differential equation in vertical pressure velocity having latitude as an implicit parameter. The “shooting method”, a numerical search procedure to determine the eigenvalue, perturbation phase velocity, is employed under the simplifying boundary conditions that vertical pressure velocity is zero at the top and bottom of the atmosphere. This method requires one exact solution, and a procedure is given to determine it. The adiabatic and Newtonian models are each solved for a zonal wind profile based upon the annual average, 1963 500 mb zonal wind from 25° N to 80° N. It is found that perturbation instability, which is decreased by Newtonian heating, is maximum at 35° N which, in the adiabatic model, corresponds to an e-folding time for the third harmonic of six days. Here, the phase speed, equivalent for adiabatic and Newtonian flow and independent of wave number, is 6 m sec?1. Near equivalence between the models is observed in the vertical structure, the waves tilting westward with decreasing pressure. Instantaneous energetics of the adiabatic and Newtonian models is studied by calculation of the vertical variation and total in a latitudinal strip 10° wide centered on the latitude of maximum instability of the normalized conversion from zonal to eddy available potential energy, C ( A z , A E ), and normalized conversion from eddy available potential energy to eddy kinetic energy, C ( A E , K E ). Here it is found, after summing over all pressures, that C ( A z , A E > 0 and C ( A E , K E ) > 0 for both models which agrees with the time-averaged energetics as observed in the atmosphere. DOI: 10.1111/j.2153-3490.1971.tb00573.x

An Experimental Study on the Deformation of Materials under High Hydrostatic Pressures : 2nd Report, On Torsional Deformation

Abstract: Many papers on the behaviour of materials under hydrostatic pressure have been published; but it is still not sufficiently clear whether hydrostatic pressure has any effect on the elasto-plastic properties of metals. This may possibly be due to the difficulties in the measurement of the stress and strain under hydrostatic pressure, where various measuring errors are likely to be involved. In the present investigation on torsion, in order to eliminate the largest conceivable of these measuring errors, namely those due to friction and distortion of torsion grips, a new apparatus is introduced. In this apparatus, the specimen, with a torque bar connected in series, is twisted in a high pressure vessel and both the strains of the specimen and torque bar are measured by electric-resistance strain gages. The effects of hydrostatic pressures up to 4000 kg/cm2 on the deformation of aluminum and a zinc alloy and on the lower yield point of low carbon steel were investigated, and the results are as follows: (1) With aluminum, in both annealed and extruded states, there is no effect on the shape of stress-strain curve. (2) With low carbon steel, there is no effect on the lower yield point. (3) With a zinc alloy, there is evidence of a little rise in the stress-strain curve.

The Origins of Abnormal Fluid Pressures

Abstract: This paper has been prepared to serve petroleum geologists who may be responsible for planning and executing drilling programs. Several modes of origin of abnormal fluid pressures are discussed: each contains a brief qualitative sketch of the nature of the related abnormal pressure, and where practical, some estimate of the value of pre-drilling detection techniques. Abnormal fluid pressures are considered both within a reference framework of hydrostatic and hydrodynamic environments and in relation to potential energies within subsurface fluids. Various normal hydrostatic gradients are discussed, and a practical normal gradient for the Gulf Coast is justified. The normal compactional process produces a stress system in sediments. The stress system is in equilibrium when the overburden pressure on a given rock equals the sum of the fluid pressure and the grain pressure within the rock. Processes which impose changes in the stress system may generate abnormal pressures, and several different modes of origin are analyzed in relation to the stress system. Abnormal pressures may be generated if changes in overburden pressure result from vertical compression (static load), horizontal compression (dynamic load), or uplift. Abnormal pressures may also result if changes in fluid pressure result from fluid density contrast or recharge, or if the expulsion of fluid from compacting rocks is inhibited by some mechanical or physical processes such as faulting, adsorption, and osmosis.

A Review of Models of the Solar Photosphere and Low Chromosphere: The Temperature-Height Profile

Abstract: The solar photosphere and low chromosphere may be defined as the regions of the solar atmosphere in which the temperature is less than 9000 K. The deeper photospheric layers with T > 9000 K are inaccessible to direct observation. The temperature rise through the chromosphere is probably severe above the height corresponding to T 9000 K and, therefore, this transition region between the chromosphere and corona is not discussed in this paper. Athay (I969) shows that the coronal pressure provides a strict boundary condition for a model chromosphere; the temperature T = 10000 K must be reached within 2000 km above the limb. The deepest observable layers are about 300 km below the surface. This paper is devoted to a discussion of models to represent these 2300 km of the solar atmosphere. A complete model would specify the magnitude and height variation of all significant variables; e.g. temperature, gas density, electron pressure, magnetic field and the velocity fields. The model would also include a representation of the spatial and temporal properties of the observable inhomogeneities, e.g. granulation, supergranulation and the chromospheric fine structures. The emphasis throughout this review is on empirical derivations of the temperature-height relation. Pure theoretical models are discussed briefly in ? 5. The Bilderberg continuum atmosphere (Gingerich & de Jager I968) is an empirical model which may be adopted as a convenient reference model against which the more recent observational and theoretical results may be set. The abbreviation B.c.a. is adopted. The majority of published measurements of the solar continuous spectrum have been obtained under conditions in which direct information on the fine scale structures is lost. Thus, the numerous empirical models in the literature were constructed as a representation of average conditions in the solar atmosphere. Direct observational studies of the fine scale features (e.g. granulation) are discussed in ? 6. An empirical model is based upon a set of near standard assumptions. The atmosphere is considered to be composed of homogeneous plane-parallel layers which are in hydrostatic equilibrium. It is widely supposed that a condition of local thermodynamic equilibrium (l.t.e.) exists throughout the atmosphere. These assumptions provide the fundamental integral equation relating the emergent continuous intensity IA(0, 0) to the temperature distribution TQrA) in the atmosphere

Distribution of the Magnetic Force in the Surface Layers of Sunspots

Abstract: At the beginning the problem of constructing the three-dimensional magnetohydrostatic models of the photospheric layers in sunspots is discussed in some detail. It is pointed out that the construction of such models by solving the set of equations of magnetohydrostatics cannot be effectively carried out.

The equilibrium and stability of the gaseous component of the galaxy, 1

Abstract: The distribution of gas satisfying hydrostatic and Poisson conditions with distance above the galactic plane is derived and compared with Schmidt's observations of the gas density, rho sub g (z). Equipartition magnetic and cosmic ray (Pc-r) components are assumed. The gas density is calculated for two limiting cases: (1) the total mass density at the galactic plane is equal to the sum of the observed gas and star densities in the solar neighborhood, and (2) Oort's data on the z component of the galactic gravitational acceleration are used. The rms z turbulent gas velocity dispersion is found. An expression is derived for the half-thickness of the equilibrium disk of galactic gas. Using the Innanen galactic mass model, the half-thickness is computed as a function of distance from the galactic center over the range 4kpc or = R or = 14kpc and compared to the observations of McGee and Milton. The observed increase in half-thickness at distances beyond the solar distance is reproduced theoretically. A galactic mass model is derived, using the observed layer half-width and constant value for Q.