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Hydrostatic equilibrium
About: Hydrostatic equilibrium is a research topic. Over the lifetime, 2451 publications have been published within this topic receiving 62172 citations.
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5 citations
02 Apr 2010
TL;DR: In this article, it was shown that the non-isothermal hydrodynamic model becomes convectively unstable above r −2/7 with heliocentric distance r, where the temperature lapse rate becomes superadiabatic, and an additional mechanism is then required to transport energy flux away from the Sun into interplanetary space.
Abstract: Chapman’s conductive model of the solar corona is characterized by a temperature varying as r−2/7 with heliocentric distance r. The density distribution in this non‐isothermal hydrostatic model has a minimum value at 123 RS, and increases with r above that altitude. It is shown that this hydrostatic model becomes convectively unstable above r = 35 RS, where the temperature lapse rate becomes superadiabatic. Beyond this radial distance heat conduction fails to be efficient enough to keep the temperature gradient smaller than the adiabatic lapse rate. We report the results obtained by Lemaire who showed that an additional mechanism is then required to transport the energy flux away from the Sun into interplanetary space. He pointed out that this additional mechanism is advection: i.e. the stationary hydrodynamic expansion of the corona. In other words the corona is unable to stay in hydrostatic equilibrium. The hydrodynamic solar wind expansion is thus a physical consequence of the too steep (superadiabatic...
4 citations
Patent•
09 Jun 19884 citations
TL;DR: In this paper, a model for treating unknown density and elevation variations along a hydrostatic line was developed, where it was assumed that gravity was constant along the line and that the hydrostatic fluid was incompressible.
Abstract: A previous paper has developed a model for treating the unknown density and elevation variations along a hydrostatic line. For convenience, it was assumed that gravity was constant along the line and that the hydrostatic fluid was incompressible. This paper extends the model to cover gravity variations and fluid compressibility, and comments on the significance of the results.
4 citations
TL;DR: For a static single-zone planet assuming that the pressure and density are connected by the equationP =KQ1+1/n−s, a complete spherical symmetry is preserved and the system is in hydrostatic equilibrium, the expressions for the field equations have been obtained in suitable dimensionless forms as mentioned in this paper.
Abstract: For a static single-zone planet assuming that 1) the pressure and density are connected by the equationP =K
Q
1+1/n–s, 2) a complete spherical symmetry is preserved and the system is in hydrostatic equilibrium; in section II, the expressions for the field equations have been obtained in suitable dimensionless forms. In section III the solution of the field equations forn=0 (which represents a homogeneous liquid) has been given in explicit form; for other prescribed value ofn=2/5 it has been pointed out that solutions must be performed by numerical integrations. Expressions for the mass-radius relation, the ratio of central to average density, the total energy, the proper energy and gravitational potential energy, which give some informations about the internal structure of the planet, have also been given in this section. Section IV discusses the velocity of sound at the centre of the planet. A few concluding remarks regarding the structure of the planet have been given in section V.
4 citations