Hydrostatic equilibrium

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

Investigation of the nature of structural damage in metal-forming processes.

Abstract: : An experimental investigation of the structural damage in sheet drawing of tough-pitch copper, aluminum alloy 6061-T6, and 60-40 brass was undertaken with regard to the role of the stress state, particularly the hydrostatic component of stress, during deformation. Sheet drawing was carried out at ambient atmosphere and at high external fluid pressure. For the latter case, a novel high-pressure facility was employed that permits manipulation inside a 5-inch ID vessel at pressures up to 100,000 psi. Stresses within the deforming zone were determined from the Hill-Tupper slip-line field solution, the conditions of the experiments being made to match as closely as possible the assumptions of the theory regarding plane strain, constancy of yield stress, die geometry, and the absence of die friction. Although friction was indeed present, use of a Teflon spray lubricant satisfactorily lowered the coefficient of friction such that, with little error, the drawing operation could be considered frictionless. This was verified from an analysis made of the slip-line field and resulting stress state in which die friction was included. An important result from the analysis is that, depending on the die angle and reduction per pass, severe hydrostatic tension can develop at the center line of the strip, while hydrostatic compression occurs at the surfaces for the case where the external pressure is ambient.

A new depth-integrated non-hydrostatic model for free surface flows

Abstract: A new depth-integrated model deploying a non-hydrostatic pressure distribution is presented. With the pressure divided into hydrostatic and dynamic components, the horizontal momentum equations were obtained by integrating the Navier-Stokes equations from the bottom to the free surface. The vertical momentum equation, in which the convective and viscosity terms were omitted, was approximated by the Keller-box scheme. The model has two steps. First, the dynamic pressure gradient terms were discretized semi-implicitly and the other terms were in explicit scheme. Second, the velocities expressed as the unknown dynamic pressure were substituted into the continuity equation, resulting in a five-diagonal symmetric matrix linear system that was solved by the conjugate gradient method. The model was validated with the propagation of a solitary wave and sinusoidal wave, indicating that it can predict free surface flows well.

Power transmission having a hydrostatic drive combined with a hydrodynamic drive

Abstract: A power transmission having a hydrostatic portion and a hydrodynamic portion. The hydrostatic portion, operable through an infinitely variable range, is combined with a planetary gear reduction unit to provide a low speed range. The hydrostatic and hydrodynamic portions are combined to provide an infinitely variable high speed range.

Photoelastic study of dense granular free-surface flows

Abstract: In this study, we perform experiments that reveal the distribution of dynamic forces in the bulk of granular free-surface flows. We release photoelastic disks from an incline to create steady two-dimensional avalanches. These gravity-driven dry granular flows are in the slow to intermediate regime ($I\ensuremath{\le}1$), dense ($\ensuremath{\varphi}\ensuremath{\approx}0.8$), and thin ($h\ensuremath{\approx}10d$). The transition between solidlike (quasisteady) and fluidlike (inertial) regimes is observable for certain experimental settings. We measure constant density and quasilinear velocity profiles through particle tracking at several points down the chute, for two different basal topographies. The photoelastic technique allows the visualization and quantification of instantaneous forces transmitted between particles during individual collisions. From the measured forces we obtain coarse-grained profiles of all stress tensor components at various positions along the chute. The discreteness of the system leads to highly fluctuating individual force chains which form preferentially in the directions of the bulk external forces: in this case, gravity and shear. The behavior of the coarse-grained stress tensor within a dynamic granular flow is analogous to that of a continuous fluid flow, in that we observe a hydrostatic increase of the mean pressure with depth. Furthermore, we identify a preferential direction for the principal stress orientation, which depends on the local magnitudes of the frictional and gravitational forces. These results allow us to draw an analogy between discrete and continuous flow models.