Showing papers on "Hydrostatic equilibrium published in 1979"

Divergences Among the Born and Classical Stability Criteria for Cubic Crystals under Hydrostatic Loading

Abstract: The classical criterion for the stability of cubic crystals under constant hydrostatic pressure is distinguished from the notional criterion of stability introduced by Born. Although the latter has been widely used in the literature, theoretical computations demonstrate appreciable quantitative and qualitative divergences between the criteria. The computations are made within the framework of a crystal model that is both mathematically tractable and sufficiently realistic for the intended purpose.

On the two-dimensional, hydrostatic flow of a stream of moist air over a mountain ridge

Abstract: The small perturbation of a steady, two-dimensional horizontal stream of a moist inviscid, Boussinesq fluid is treated analytically by use of an asymptotic method when a certain parameter ∊ is small and numerically by use of an iterative method for general values of ∊. This parameter is a measure of the difference between dry and wet adiabats in the model atmosphere, which is absolutely stable and which contains a moist layer near the ground. Vapour condenses (evaporates) where the vertical displacement of a fluid particle exceeds the ascent condensation level and the vertical motion is upward (downward). The condensation of vapour and release of latent heat are nonlinear phenomena which are treated, but otherwise the equations of motion and boundary conditions are linearized. We limit our attention to an airflow of uniform properties over a mountain ridge. The hydrostatic approximation is made. As a result, the horizontal wavelengths must be long compared to the vertical ones and lee waves are a...

Hydrostatic figure and related properties of the earth.

Abstract: Summary. The second‐order internal theory of hydrostatic equilibrium initially developed by Kopal is extended to form equations equivalent to those of de Sitter. This new development is used together with the density distribution of Dziewonski, Hales & Lapwood to compute flattening, precessional constant and moments of inertia of the hydrostatic earth. These values are compared with those of the real Earth. Copyright

A Non-Archimedean Approach to the Equations of Convection Dynamics

Abstract: A new formulation of the momentum equations in convection dynamics is presented, dividing the pressure into separate hydrostatic and dynamic components. In this formulation, termed non-Archimedean, convection is envisaged as developing through the horizontal gradient of a time-dependent hydrostatic pressure, rather than the customary buoyancy. It is shown that in the vertical momentum equation there is only one forcing term, viz., the vertical gradient of the dynamic pressure rather than the customary combination of perturbation-pressure gradient and buoyancy force. In the multi-dimensional case, the new formulation leaves the vorticity form of the momentum equation unchanged from that obtained in the customary approach. A diagnostic equation is presented for computing the dynamic pressure component.

Hydrostatic transmission lubrication

Abstract: A hydrostatic transmission having a pump and a motor of the radial piston type with each cylinder slipper bearing rotatably supported by a hybrid or combination hydrostatic and hydrodynamic bearing on an internal bearing. The hydrostatic bearing component has a restricted port connecting hydrostatic pressure fluid from the cylinder to supply a distribution recess in the slipper bearing surface for hydrostatic pressure feed of the fluid film providing hydrostatic balancing pressure gradient between the slipper and internal bearing to balance a high percentage of the hydrostatic pressure load and to meet flow requirements for low speed operation. The hydrodynamic bearing component has a low pressure source to spray fluid on the internal bearing, annular dams on each side retaining fluid on the internal bearing, and a taper at the leading edge of the slipper bearing to force fluid into the bearing clearance and provide a hydrodynamic balancing pressure component and fluid flow increasing with speed to balance the centrifugal load and effect balancing of the remaining hydrostatic load and to meet flow requirements which increase with speed. The total hydrostatic and hydrodynamic balancing pressure balances the total load.

On the hydrostatic equilibrium of the interstellar gas.

Abstract: The hydrostatic equilibrium of the interstellar gas-field system perpendicular to the galactic plane in the neighborhood of the Sun has been reexamined. It is demonstrated that the hydrostatic equilibrium condition of the interstellar gas may be formulated independently from the dynamics of halo gas and halo magnetic fields. The distribution of interstellar gas and magnetic fields satisfying hydrostatic and Poisson's equations with distance above the galactic plane is evaluated and compared with the observed distribution as inferred from 21 cm and synchrotron radiation measurements. It appears from the present study that a single-phase description of the interstellar gas is not adequate to account for the observations, whereas a two-component gas model, assuming that the interstellar gas clouds are not directly coupled to the interstellar magnetic field, seems to provide a natural explanation of the distribution of interstellar gas and magnetic fields perpendicular to the galactic plane up to distances of about 500 pc above and below the midplane.

Thermal relaxation oscillations in a two-zone model.

Abstract: We simulate the behavior of stars in those advanced evolutionary phases in which thermal cycles have been reported. To this end we consider a two-zone stellar model in hydrostatic equilibrium, consisting of a thin energy-generating shell and a buffer zone on top of it with the rest of the star acting as boundary conditions. Under the conditions apposite to thin-shell helium burning we show that this model can exhibit rigorous thermal limit cycle oscillations. By the same token our result implies that the two-time asymptotic method may be used to bridge such otherwise inaccessible evolutionary phases.

A luminosity-temperature relation for cluster X-ray sources

Abstract: Luminosity-temperature (L-T) relations are derived for a self-gravitating isothermal gas sphere and for an isothermal gas sphere in hydrostatic equilibrium with the total mass of a cluster of galaxies. The relationships are compared with X-ray data for 13 clusters of galaxies. The L-T relation for the self-gravitating isothermal gas sphere is found to predict X-ray luminosities that are considerably larger than those observed, and the corresponding model is ruled out. It is shown, however, that the L-T relation for the isothermal gas sphere in hydrostatic equilibrium with total cluster mass is consistent with X-ray observations for reasonable choices of the ratio between central density and confining-mass density. Core radii or gas temperatures are predicted for five of the 13 clusters considered.

Hydrostatic transmission and controls

Abstract: A hydrostatic transmission, especially for a steer drive of a propulsion and steer drive transmission, having a variable displacement pump, a fixed displacement motor, and a pump displacement control, and including a low pressure fluid source supplying the charging and lubrication systems of the hydrostatic transmission and a high pressure source. The high pressure source, in a normal range of low hydrostatic power pressure values, provides control pressure regulated in proportion to high hydrostatic power pressure to meet the pressure requirements of the pump displacement control which increase with high hydrostatic power pressure. In an abnormal and lower range of low hydrostatic pressure values, the control pressure is regulated to decrease to zero as the low hydrostatic power pressure decreases to a minimum operating pressure value. In the abnormal range, the reduction of control pressure reduces load capacity and thus steer capacity, with decreasing low pressure supplied to the charging and lubrication systems to advise the operator of the abnormal pressures and to discontinue hydrostatic transmission operation to prevent operation with insufficient charging and lubrication pressures.

Soft X-ray structure of the Coma cluster of galaxies

Abstract: An X-ray image of the Coma cluster of galaxies was obtained in the 0.15--2.0 keV band with an imaging telescope. In contrast to the Virgo and Perseus clusters, which were observed previously with the same instrument, there is no indication of a strong contribution from an individual galaxy. However, there is granularity within the central region of the X-ray source that is suggestive of the galaxy distribution. For the 0.15--0.28 keV band only, the flux is much larger in the region north of the cluster center as compared to the south. We interpret this as a Galactic feature accidentally superposed upon the cluster.There is a marginal indication of ellipticity in the region between 10' and 25' from the center. The major axis is approximately along the E-W direction and is 1.2 +- 0.1 times larger than the minor axis. This is consistent with the distribution of galaxies.Assuming radial symmetry, three models containing a free parameter were fitted to the radial distribution of surface brightness: isothermal hydrostatic, adiabatic hydrostatic, and the isothermal sphere. All three fit the data with an acceptable value for the chi/sup 2/. Of the three, the isothermal hydrostatic model is unique in its prediction of an extendedmore » halo beyond the range of measurements. For this model ..beta..=0.49, meaning that gas density falls off with radius approximately as the square root of the galaxy density. This value of of ..beta.. is in agreement with the number computed from optical data and the X-ray temperature. Comparison of our 0.5--2.0 keV intensity with an extrapolation of a higher energy measurement obtained with a broader field of view detector aboard OSO 8 provides tentative evidence that the isothermal hydrostatic model is the most appropriate of the three models considered.« less

A statistical theory of the non-local convection.

Abstract: The existing problems in the theory of local convection are analysed. It is shown that the effect of turbulent pressure on the structure and the vibrational stability of stars with extensive convective envelopes is not negligible. The physical significance of Henvey’s numerical instability in calculations of convective envelopes is elucidated. When the effect of turbulet pressure on hydrostatic equilibrium of stars is considered, we have to abandon the local treatment of convection. From dynamic equations of correlation functions, we propose a theory of non-local convection.

The temperature equivalence assumption for binary system hydrostatic levelling

Abstract: The assumption of sensible temperature equivalence between the fluids of a binary hydrostatic line is examined. Errors in determining the difference in dynamic heights of the ends of the line, due to reasonable temperature differences between the fluids, are likely to be no greater than those resulting from errors in pressure measurement.

Hall measurements to 40 kilobars under hydrostatic pressure in a piston-cylinder device.

Abstract: A technique for Hall measurements under truly hydrostatic pressures to 40 kilobars is described. The method employs the piston‐cylinder apparatus with a Teflon cell to contain a suitable fluid. The necessary magnetic field is generated by a coil placed inside the cell. Hall data can be obtained over the full pressure range, at temperatures from 150 to 300 K. Results for an AlxGa1−xAs sample are presented as an example.

The wider application of hydrostatic levelling

Abstract: The determination of heights for vertical control purposes has been performed successfully by the hydrostatic technique many times in the past under conditions where the line was laid in a body of water with its ends at approximately the same level. The possibility of a more general application such as to the measurement of height differences under conditions in which the line is subject to variable and extreme environmental conditions is discussed. It is concluded that a hydrostatic heighting system might be developed capable of measuring, for example, height differences of up to 10m in hydrostatic lines up to 1000 m in length, with an accuracy of 1 nun or better.

Temperature distribution in the transition region and inner corona

Abstract: The energy balance equation for a general solar atmosphere without assuming the plane-parallel approximation is solved analytically. This leads to models for both the transition region and inner corona as well as for the outer corona. The form of the latter is very similar to that of the hydrostatic conduction model of Chapman (1957). However, in this paper we confine ourselves only to the former.

Non-hydrostatic Kelvin waves in the ocean

Abstract: A theory of the coastal Kelvin wave is presented in which the pressure is assumed not to be hydrostatic. The results show that the non-hydrostatic Kelvin wave is dispersive and that the e−1 decay distance of the wave amplitude from the coast decreases as the wave length becomes shorter. Similar conclusions can be drawn on the equatorial Kelvin wave.

On the use of an analytic solution in estimating eddy viscosity distribution and water vapour flux in a mature hurricane

Abstract: An analytic solution, in p coordinates, of the dynamical equations of a mature hurricane system is used to determine the p dependence of eddy viscosity coefficients for an assumed quasi-stationary and axisymmetric phase. The solution is based on: (i) eddy viscosity coefficients K1 and K2, describing respectively horizontal and vertical transfers of momentum, expressed as general functions of p; and (ii) the premise that the radial variation of the magnitudes of the tangential and radial components of velocity are of similar form. This leads to an integral equation for the tangential velocity. Explicit expressions for K1 and K2 are finally obtained by choosing power law forms, in the p variable, which lead to good agreement of the tangential velocity solution with observed distributions. By using this (inverse) method of calculating K1 and K2, the whole eddy system, ranging from eddies created by the very strong velocity shear close to the sea surface to those connected with violent cloud convection, is described by continuous mathematical functions. The associated temperature and condensation heating distributions are then calculated from the hydrostatic relation and the thermodynamic equation. To complete the model an integral water vapour flux condition relates the sea surface temperature to prescribed humidity conditions at the outer boundary of the model.

Gradient elution under hydrostatic equilibrium in liquid chromatography. Part 1

Abstract: The theory of gradient elution under hydrostatic equilibrium is developed for the case where only one reservoir and one mixing chamber are used and where both solvents have equal densities. Given the shapes of the two vessels, effluent concentration curve equations are deduced for different mixing chamber-reservoir combinations. On the other hand, given the equation for the effluent concentration curve, the reservoir cross-sectional area, as a function of height, can be deduced when the mixing chamber has a constant cross-section. The varying cross-section of the reservoir is accomplished by inserting thin discs of different areas on top of one another inside a regular vessel of constant cross-section. Except for complicated gradients, a given gradient can be accomplished using a reservoir with a cross-sectional area which varies linearly with height. In the case of complex gradients, a reservoir having two or more linear segments becomes necessary. A numerical method is given for the calculation of the continuously varying reservoir cross-section for the exact duplication of a given gradient.

Analytical evaluation of lower critical hydrostatic pressure for imperfect long cylindrical shells

Abstract: The paper deals with the analytical evaluation of the lower hydrostatic critical pressure for imperfect long cylindrical shells. Nevertheless the proposed method has a general character. The lower hydrostatic critical pressure has been effectively determined using the method of generalized power series. The basic equations have been assumed in the form given by W.A. Nash. The number of circumferential half-wavelengths has been assumed m = 2, which is characteristic for shells of considerable length. It has been shown that the dependence of the lower critical pressure on the imperfection parameter V is linear, i.e. less than in the case of the upper critical pressure, which decreases proportionally to V 2 3 .