Hydrostatic equilibrium

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

General Solution of the Problem of Hydrostatic Equilibrium of the Earth

Abstract: Summary If de Sitter’s hydrostatic equations are developed independent of the external potential theory, the hydrostatic geopotential coefficient Jh occurs explicitly on the right-hand side of these equations. Since this Jh has to be treated as an unknown in the solution of the problem, it becomes rather difficult to solve these hydrostatic equations independently, regardless of which of the dynamical parameters associated with the Earth is taken as the initial datum. The solution of these equations is possible, however, with the help of a boundary condition derived from the external potential theory which neither assumes nor discounts the presence of equilibrium conditions in the Earth’s interior. If a general solution is constructed on these lines, the three particular solutions, usually quoted in literature, stem from it in the wake of the appropriate assumptions. Of course, out of these the only meaningful solution is that corresponding to the polar moment of inertia as the initial datum. It is essential that the solution be constructed in this way in order to demonstrate clearly the correct structure of the problem of hydrostatic equilibrium. The anomalous gravity field of the Earth referred to the hydrostatic figure is compared with that referred to the international reference ellipsoid.

Control of an oil film thickness in a hydrostatic journal bearing under different dynamic conditions

Abstract: In order to meet the requirements of supporting heavy loads, high stiffness, and precise movement, the hydrostatic journal bearings are getting popularity from day to day. The efficiency of hydrostatic bearing for supporting the external load, depends upon the external source of pressure, which is responsible for supplying fluid at a certain pressure. Normally pump is used to supply fluid at a certain pressure, which has poor performance and low efficiency. This paper presents servo valve with a feedback control algorithm to achieve uniform oil thickness for positioning of a shaft in a hydrostatic journal bearing. To check the effectiveness of a proposed strategy, a number of experiments have been done in Matlab/Simulink using different conditions of external load and viscosity. It is found that proposed strategy not only has good results under the different value of viscosity but also has a linear relationship between external load and change in oil film thickness under a wide range of external load.

Gravity currents in rotating channels. Part 1. Steady-state theory

Abstract: A theory is developed for the speed and structure of steady-state non-dissipative gravity currents in rotating channels. The theory is an extension of that of Benjamin (1968) for non-rotating gravity currents, and in a similar way makes use of the steady-state and perfect-fluid (incompressible, inviscid and immiscible) approximations, and supposes the existence of a hydrostatic ‘control point’ in the current some distance away from the nose. The model allows for fully non-hydrostatic and ageostrophic motion in a control volume V ahead of the control point, with the solution being determined by the requirements, consistent with the perfect-fluid approximation, of energy and momentum conservation in V, as expressed by Bernoulli's theorem and a generalized flow-force balance. The governing parameter in the problem, which expresses the strength of the background rotation, is the ratio W = B/R, where B is the channel width and R = (g′H)1/2/f is the internal Rossby radius of deformation based on the total depth of the ambient fluid H. Analytic solutions are determined for the particular case of zero front-relative flow within the gravity current. For each value of W there is a unique non-dissipative two-layer solution, and a non-dissipative one-layer solution which is specified by the value of the wall-depth h0. In the two-layer case, the non-dimensional propagation speed c = cf(g′H)−1/2 increases smoothly from the non-rotating value of 0.5 as W increases, asymptoting to unity for W → ∞. The gravity current separates from the left-hand wall of the channel at W = 0.67 and thereafter has decreasing width. The depth of the current at the right-hand wall, h0, increases, reaching the full depth at W = 1.90, after which point the interface outcrops on both the upper and lower boundaries, with the distance over which the interface slopes being 0.881R. In the one-layer case, the wall-depth based propagation speed Froude number c0 = cf(g′h0)−1/2 = 21/2, as in the non-rotating one-layer case. The current separates from the left-hand wall of the channel at W0 ≡ B/R0 = 2−1/2, and thereafter has width 2−1/2R0, where R0 = (g′h0)1/2/f is the wall-depth based deformation radius.

Hydrostatic equilibrium configurations of neutron stars in a non-minimal geometry-matter coupling theory of gravity

Abstract: In this work we analyze hydrostatic equilibrium configurations of neutron stars in a non-minimal geometry-matter coupling (GMC) theory of gravity. We begin with the derivation of the hydrostatic equilibrium equations for the f(R, L) gravity theory, where R and L are the Ricci scalar and Lagrangian of matter, respectively. We assume $$f(R,L)=R/2+[1+\sigma R]L$$ , with $$\sigma $$ constant. To describe matter inside neutron stars we assume a relativistic polytropic equation of state $$p=K \rho ^{\gamma }$$ , with $$\rho $$ being the energy density, K and $$\gamma = 5/3 $$ being constants. We also consider the more realistic equation of state (EoS) known as SLy4, which is a Skyrme type one based on effective nuclear interaction. We show that in this theory it is possible to reach the mass of massive pulsars, such as PSR J2215 + 5135, for both equations of state. Also, results for mass-radius relation in GMC gravity are strongly dependent on the stiffness of the EoS.