Hydrostatic equilibrium

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

Analysis of Effect of Internal Pressure on Natural Frequencies of Bending Vibrations of a Straight Pipe with Fluid

Abstract: Three computational methods were compared to evaluate the correctness of determining the natural frequencies of bending vibrations of a straight pipe with a fluid. Natural frequencies of bending vibrations of a pipe were computed by the finite element method using ANSYS Mechanical, module Modal Acoustic, and ACT Acoustic. Using ANSYS Mechanical, the estimation of changes in the internal volume of a straight pipe is received depending on the internal pressure. To solve this problem, Shell and Solid elements for the pipe and Solid, Fluid, and Hydrostatic Fluid for fluid are used. Using ANSYS Mechanical, the natural frequencies are obtained for the pipe with the fluid depending on the density and internal pressure. In this case, the density of the fluid is taken into account in the equivalent density of the tube material. In accordance with the results of calculations, the paper proposes an analytical dependence of the first natural frequency of the tube bending vibrations and fluid density, taking into account the internal pressure and the change in the internal volume. The obtained dependences makes it possible to determine with high accuracy, the density of the fluid by the magnitude of its natural frequency and internal pressure, including taking into account the change in the internal volume of the tube. As it is discussed in the paper, the computational method can be extended to a curved tube Coriolis meter in calculating the fluid density based on the experimental natural frequency.

Invasion of a porous medium under gravity: A quantitative analysis

Abstract: The structure of a Wood's metal [1] slow invasion front into homogeneous crushed glass is analyzed in the framework of a “gradient percolation” model allowing to account for the influence of gravity. We show that this model accounts quantitatively well for experimental observations and permits a detailed analysis of the experimental front structures. Invasion of a porous medium by a non-wetting fluid at low velocity and under zero gravity is correctly described by the “invasion percolation” model [2]. However, in most 3D systems, it is not possible to neglect the influence of gravity. The hydrostatic component adds up with the applied injection pressure: this creates a vertical gradient of the effective injection pressure. This missing gradient term has been recently introduced to analyse 2D and 3D diffusion processes [3]. In the “gradient percolation” model a linear variation of the percolation parameter is introduced along a lattice axis. As a consequence there appears a “front” connected to the high occupation region by a continuous chain of occupied sites. This “front” is equivalent to the front surface limiting the invaded volume in the invasion experiment [4]. Experiments can be shortly described as follows [1]: Wood's metal is injected at the bottom of a vertical evacuated crushed glass column. The flow velocity is kept low (a few mm/h) so that viscous pressure losses can be neglected. When the front has reached a given height, the injection is stopped and the liquid is solidified; then horizontal sections of the front corresponding to various heights z are analyzed. The pictures are digitized into a square lattice of pixels and “invaded” or “empty” pixels are discriminated by a threshold procedure. The correlation function C ( r ) of the metal distribution in horizontal planes is determined and compared to the corresponding quantity obtained from the numerical simulation for sites located on the gradient front: it is the key tool for comparing experimental and theoretical data. In both cases, close to p c in a range of r values between the individual grain size d and an upper limit γ (crossover length), C ( r ) varies roughly as: C ( r ) ∝ r D fr −2 indicating that the cut structure is fractal with a dimension D fr at short distances. When r is larger than γ, C ( r ) is constant and equal to a value S proportional to the mean metal saturation. We show that the experimental 2D correlation function C ( r ) follows the universal behaviour predicted by the gradient percolation model. A good fit is obtained for realistic values of the geometric adjustable parameters; however the value D fr = 2.4 obtained for the fractal dimension of the front is smaller than the value 2.54 expected for classical 3D percolation. The variations of the mean fluid saturation and crossover length γ with the cut height are in agreement with the numerical simulation results.

Structure of Magnetic Tower Jets in Stratified Atmospheres

Abstract: Based on a new approach on modeling the magnetically dominated outflows from AGNs (Li et al. 2006), we study the propagation of magnetic tower jets in gravitationally stratified atmospheres (such as a galaxy cluster environment) in large scales ($>$ tens of kpc) by performing three-dimensional magnetohydrodynamic (MHD) simulations. We present the detailed analysis of the MHD waves, the cylindrical radial force balance, and the collimation of magnetic tower jets. As magnetic energy is injected into a small central volume over a finite amount of time, the magnetic fields expand down the background density gradient, forming a collimated jet and an expanded ``lobe'' due to the gradually decreasing background density and pressure. Both the jet and lobes are magnetically dominated. In addition, the injection and expansion produce a hydrodynamic shock wave that is moving ahead of and enclosing the magnetic tower jet. This shock can eventually break the hydrostatic equilibrium in the ambient medium and cause a global gravitational contraction. This contraction produces a strong compression at the head of the magnetic tower front and helps to collimate radially to produce a slender-shaped jet. At the outer edge of the jet, the magnetic pressure is balanced by the background (modified) gas pressure, without any significant contribution from the hoop stress. On the other hand, along the central axis of the jet, hoop stress is the dominant force in shaping the central collimation of the poloidal current. The system, which possesses a highly wound helical magnetic configuration, never quite reaches a force-free equilibrium state though the evolution becomes much slower at late stages. The simulations were performed without any initial perturbations so the overall structures of the jet remain mostly axisymmetric.

Dynamical behavior of nuclear reaction systems disturbed by fluid motion in the solar core

Abstract: Using Euler's equation of motion, the equation for disturbed fluid motion against a hydrostatic equilibrium has been derived, and the nonequilibrium dynamical equation of a P-PI nuclear reaction system driven by He3 has been analysed using developed nonequilibrium theory. We find that the system in the solar core is unstable in the layer extending from about 0.2R ⊙ to 0.4R ⊙ if the core is disturbed by fluid motion; this instability may be related to thermal diffusion.

Hydrostatic analysis of naval hull forms using pressure integration

Abstract: A pressure integrated technique for hydrostatic stability analysis of marine structures has been developed at University College London. The technique integrates hydrostatic pressures acting over the submerged surface of a floating body to yield its hydrostatic characteristics and large angle stability curves. the method is implemented by discretising the body surface into a set of panels or patches. Initially, the pressure integration method utilised triangular and rectangular patches of zero curvature and single constant curvature patches. The work presented in this paper extends the method to include bi-cubic Coons patch descriptions of hull forms, similar to those used in the Ministry of Defence's ship design system GODDESS. The theory associated with this implementation and verification studies comparing results from the pressure integration technique with those from the GODDESS suite are presented. The pressure integration technique is also capable of yielding accurate results for free surface corrections in internal fluid tanks of complex geometry. The corrections are calculated from righting moment losses due to the vectoral shift in the centre of gravity of the fluid volume following rotation. Results from the two methods for righting lever corrections are presented. These results provide further validation of the techniques used when integrating hydrostatic pressures over areas rather than deriving hydrostatic properties via volume integrals. The increasing use of pressure integration techniques in hydrostatic design calculations is discussed.