Hydrostatic equilibrium

About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.

Equilibrium Elastic Stress Field of the Earth's Solid Shell

Abstract: In modern geophysics, hydrostatic dependence of pressure on the depth in the lithosphere is postulated. It is considered evident and requiring no proof. As shown in the present work, the above postulate is erroneous. Proceeding from one of the fundamental laws of physics related to the minimum of potential energy in the equilibrium state, one can derive a nonhydrostatic solution of the elasticity equation with minimum elastic energy referred to as a Gravitational Equilibrium Field with an energy by an order of magnitude less than the hydrostatic field energy. The Earth’s solid shell like a bearing structure carries its own weight, which reduces the pressure on the surface of the liquid nucleus down to zero. The influence of solidity in the subsurface region of the Earth is characteristic. As the calculation shows, although the rock density in the crust is thrice as much as that of the water, the pressure in the ocean at the same depth is higher than the pressure in the solid crust, which is an account for the existence of land. If there was a hydrostatic stress distribution, the pressure under the continents would be thrice as much as that in the ocean and the continents would descend below sea level.

Fluid Inertia Effects on the Characteristics of Spherical Hydrostatic Bearings : Part 2 Stability

Abstract: Based on a first-order perturbation solution in a modified Reynolds number, an analysis is presented to determine the fluid inertia effects on the stability characteristics of a spherical hydrostatic bearing that has continuous spherical surface. This analysis demonstrates that fluid inertia effects increase the stability threshold speed and that the increase in stability threshold depends on the inertia parameter δ=ρω2r02/p★ (ρ=lubricant density, ω=rotational angular velosity, r0=radius of sphere, p★=ambient pressure). It is found that centrifugal effect on load capacity is much greater than the other inertial effects, whereas centrifugal effect on dynamic coefficients is much smaller than the other inertial effects.

Spin, gravity, and moments of inertia of Titan

Abstract: Introduction Analysis of Doppler tracking data and radar images from the Cassini spacecraft have recently provided estimates of the low degree gravity field [1], and spin pole direction [2] of Titan. We examine implications of these measurements for the internal structure and rotational dynamics of that body. We derive separate estimates of the polar moment of inertia of Titan from the degree two gravity field, under the assumption of hydrostatic equilibrium, and from the spin pole direction, under the assumption of a fully damped spin-orbit configuration, or multi-frequency Cassini state. These estimates are quite different. We interpret the gravity-derived value as the actual moment of inertia of Titan, and the larger spin-derived value as an effective moment of inertia of a mechanically decoupled ice shell. This implies a sub-surface ocean, as the decoupling agent. Gravity constraints For a body in hydrostatic equilibrium and synchronous rotation, the imposed tidal and rotational potentials together induce changes in the mass distribution which are mainly manifest as degree two spherical harmonic coefficients in the gravitational potential [3]:  =310

Study on the Sealing Performance of O-ring under High-Pressure Environment

Abstract: The sealing properties of the O-ring of the hydraulic cylinder plunger rod under a high-pressure environment are related to a variety of factors. In this paper, we first establish a simulation model based on an O-ring reciprocating shaft seal under a high pressure-environment through finite element software and study the influence of the compression rate, static pressure, and reciprocating speed of the plunger rod on the sealing performance of O-ring through the simulation model, and then analyze the maximum stress of O-ring during installation, hydrostatic loading and reciprocating motion with the variation of structural parameters. The results indicate that the compression rate of the installation process has a significant effect on the sealing performance of the enhanced O-ring. In the hydrostatic loading process, the equivalent stress of the O-ring is increased with the increase of the compression rate, when the static pressure is low and decreases, and when the static pressure is high, and the equivalent stress shows an increasing trend and the same increase; in the reciprocating motion process, when the static pressure is low, the equivalent stress and contact stress of the O-ring does not change significantly with the compression rate, and when the static pressure is high, there is an obvious phenomenon of abrupt change. The frictional stress of the reciprocating motion is increasing, then decreases, and then increases with the change in static pressure.

On the Hydrostatic Approximation of Compressible Anisotropic Navier–Stokes Equations–Rigorous Justification

Abstract: In this work, we derive the hydrostatic approximation by taking the small aspect ratio limit to the Navier–Stokes equations. The aspect ratio (the ratio of the depth to horizontal width) is a geometrical constraint in the general large scale geophysical motions meaning that the vertical scale is significantly smaller than horizontal. We derive the versatile relative entropy inequality. Applying the versatile relative entropy inequality we gave the rigorous derivation of the limit from the compressible Navier–Stokes equations to the compressible Primitive Equations. This is the first work where the relative entropy inequality was used for proving hydrostatic approximation - the compressible Primitive Equations.