Showing papers on "Hydrostatic equilibrium published in 1974"

Calculations of the Early Evolution of Jupiter

Abstract: The evolution of the protoplanet Jupiter is followed, using a hydrodynamic computer code with radiative energy transport. Jupiter is assumed to have formed as a subcondensation in the primitive solar nebula at a density just high enough for gravitational collapse to occur. The initial state has a density of 0.0015 nanograms per cu cm and a temperature of 43 K; the calculations are carried to an equilibrium state where the central density reaches 0.5 g per cu cm and the central temperature reaches 25,000 K. During the early part of the evolution the object contracts in quasi-hydrostatic equilibrium; later on hydrodynamic collapse occurs, induced by the dissociation of hydrogen molecules. After dissociation is complete, the planet regains hydrostatic equilibrium with a radius of a few times the present value. Further evolution beyond this point is not treated here; however the results are consistent with the existence of a high-luminosity phase shortly after the planet settles into its final quasi-static contraction.-

Martian tidal pressure and wind fields obtained from the Mariner 9 infrared spectroscopy experiment

Abstract: Using temperature fields derived from the Mariner 9 infrared spectroscopy experiment, the Martian atmospheric tidal pressure and wind fields are calculated. Temperature as a function of local time, latitude, and atmospheric pressure level is obtained by secular and longitudinal averaging of the data. The resulting temperature field is approximated by a spherical harmonic expansion, retaining one symmetric and one asymmetric term for wavenumber zero and wavenumber one. Vertical averaging of the linearized momentum and continuity equations results in an inhomogeneous tidal equation for surface pressure fluctuations with the driving function related to the temperature field through the geopotential function and the hydrostatic equation. Solutions of the tidal equation show a diurnal fractional pressure amplitude approximately equal to one half of the vertically averaged diurnal fractional temperature amplitude.

Thickness of lithosphere deduced from gravity edge effects across the Mendocino Fault

Abstract: THE evolution of a lithospheric plate, as it migrates away from the accreting boundary (mid-ocean ridge crest), is mostly a result of vertical cooling by conduction. As density is a function of temperature and pressure, the density structure should be a function of the age of the plate and, in order to preserve isostatic equilibrium, the seafloor should subside as the plate cools1. Thus, the variation of heat flow, seafloor depth and the gravity field are different expressions of the same process, progressive cooling, occurring over the whole thickness of the plate. Sclater and Francheteau2 have verified these properties through an analysis of the variation of heat flow and depth with the age of the plate. Their model assumed that the plate remains a constant thickness and is floating in hydrostatic equilibrium over the asthenosphere. This led to an estimate of 75 km for the thickness of the plate.

Finite Element Method in the Analysis of the Hydrostatic Bulging of a Sheet Metal (Part 2)

Abstract: An incremental finite element method of the large elastic-plasic deformation of non-axisymmetric metal diaphragms which are edge-clamped and bulged by hydrostatic pressure has been formulated. The diaphragm is divided into a number of flat triangular elements and the behavior of a typical element is described in terms of the displacements of its nodes. The authors derive stiffness matrices, taking account of effects of shape change on the equilibrium equations, from a total differential of the equivalent nodal forces. In order to check the theory, numerical calculations were carried out for the bulging of a circular diaphragm under hydrostatic pressure. Theoretical results were in reasonable agreement with experiments for aluminium sheet and also with numerical solutions by means of a finite difference method.

Void Behavior as Influenced by Pressure and Plastic Deformation

Abstract: Void behavior has a pronounced effect on the properties and soundness of most materials, and is strongly influenced by the magnitude of hydrostatic pressure during plastic deformation. Using the upper bound theorem approach with a model of idealized geometry to simulate a void-material composite, an analytical criterion for the minimum effective pressure necessary to initiate a permanent void volume change is developed. This pressure is called critical pressure, and its absolute value is the same whether for compression and void closure or tension and void opening. A deviation parameter is also defined, and it indicates that voids of a given geometry will start to open faster under tension than they will start to close under compression of the same magnitude. To compare the aforementioned analytical predictions with real material behavior, copper split billets with artificially introduced voids of predetermined geometries were deformed under different magnitudes of hydrostatic pressure: the process of wire drawing for low pressure deformation, and the fluid environment of hydrostatic extrusion for higher pressure deformation. Those characteristics found to lead to significant void volume change are: (a) high void volume fraction, (b) large relative void size, and (c) voids of unity or greater aspect ratio. Experimental data compared well with the analytical curves; thus, the analytical expressions should be useful in explaining and predicting the behavior of voids in some real materials.

Hydrostatic profile of ferrofluid around a vertical current‐carrying wire

Abstract: The classical Langevin theory for noninteracting magnetic particles together with an interfacial force balance of hydrostatic pressures and Maxwell stresses is found to describe the experimental results of Neuringer and Rosensweig for the hydrostatic profile of ferrofluid around a vertical current‐carrying wire. If r is the distance from the center of the wire, the fluid height varies as r−2 for small magnetic fields, where the ferrofluid is magnetically linear, and as r−1 for large magnetic fields, where the ferrofluid is in saturation. The experimentally obtained r−4/3 dependence is an intermediate behavior between the linear and saturation magnetization regimes of the ferrofluid. No fundamental significance is attributable to the 43 power law. To obtain the r−4/3 dependence over as large a range of r values as found experimentally, it is necessary to use a realistic distribution of particle sizes.

The equilibrium of a rotating body of arbitrary density

Abstract: This paper extends Clairaut's theory of rotational equilibrium to third order terms in a small parameter and is meant to be a sequel to a 1962 publication by the author bearing on the same topic. It has been feasible to obtain the Clairaut equation, which governs the deformation of the equipotential surfaces within a rapidly rotating mass in hydrostatic equilibrium, as an ordinary differential equation. This has been achieved by eliminating the two integral terms which appeared in the original formulation. It is expected that the numerical integration of this newly obtained equation will contribute toward a more precise solution of certain geophysical problems — e.g., the determination of the geoid to an accuracy of ±1 m, and the correction to the travel-time of seismic waves; it should also assist in some planetary questions like the determination of the exterior shape for the rapidly rotating planets Jupiter and Saturn.

Hydrostatics and steady dynamics of spatially varying electromechanical flow structures

Abstract: The hydrostatic and steady laminar hydrodynamic equilibria of spatially varying electromechanical flow structures are investigated. Under certain conditions the relationship between the dielectric height of rise and the applied voltage is found to be double valued. It is found that one of the two equilibrium values is always unstable. This gives rise to the experimentally observed spontaneous rise of the fluid to the top of the structure, once a certain critical voltage is reached. Starting above this critical voltage with the structure completely filled and decreasing the applied voltage toward the critical value results in pinch-in failure at an intermediate point along the structure and trapping of dielectric fluid at the top. The simple mathematical model developed predicts all these phenomena, without recourse to tedious point-by-point surface force equilibrium determination. Experiments are reported which verify the results for the hydrostatic case.

Temperature effects in hydrostatic levelling

Abstract: The effect of temperature variations along hydrostatic levelling lines is to introduce errors which may be of unacceptable magnitude. This paper shows that the variety of circumstances likely to be met in practice can be reduced to a simple, but general, theoretical model. Further, the solution of the physical equations for this model demonstrates that a high degree of accuracy may be possible with the hydrostatic method, in applications other than those for which it has been traditionally used.

Effect of Moisture on the Hydrostatic Pressure

Abstract: This Note describes a method of deriving a modified form of the hydrostatic equation by making allowance for the presence of moisture in an atmospheric column.

Estimates for the Derivatives of the Velocity and Pressure in Shallow Water Flow and Approximate Shallow Water Equations

Abstract: Estimates are derived on the time and space derivatives of the velocity and pressure of a shallow fluid flow. These estimates depend upon the velocity and pressure being bounded and the free surface having a long wavelength compared to the depth of the fluid. The technique used is to derive $L_2 $-estimates on the derivatives of the velocity and pressure and then convert these to pointwise estimates. As a consequence of these results, the horizontal velocity is shown to be independent of the depth and the pressure hydrostatic to the first approximation. Higher order estimates lead to second order approximate equations which, under additional physically motivated assumptions, correspond to the Boussinesq and Korteweg–deVries equations.