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Hydrostatic Equilibrium
In fluid mechanics, hydrostatic equilibrium, also called hydrostatic balance and hydrostasy, is the condition of a fluid or plastic solid at rest, which occurs when external forces, such as gravity, are balanced by a pressure-gradient force. In the planetary physics of Earth, the pressure-gradient force prevents gravity from collapsing the atmosphere of Earth into a thin, dense shell, whereas gravity prevents the pressure-gradient force from diffusing the atmosphere into outer space. In general, it is what causes objects in space to be spherical. Hydrostatic equilibrium is the distinguishing criterion between dwarf planets and small solar system bodies, and features in astrophysics and planetary geology. Said qualification of equilibrium indicates that the shape of the object is symmetrically rounded, mostly due to rotation, into an ellipsoid, where any irregular surface features are consequent to a relatively thin solid crust. In addition to the Sun, there are a dozen or s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Newton's Laws Of Motion
Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body remains at rest, or in motion at a constant speed in a straight line, unless it is acted upon by a force. # At any instant of time, the net force on a body is equal to the body's acceleration multiplied by its mass or, equivalently, the rate at which the body's momentum is changing with time. # If two bodies exert forces on each other, these forces have the same magnitude but opposite directions. The three laws of motion were first stated by Isaac Newton in his ''Philosophiæ Naturalis Principia Mathematica'' (''Mathematical Principles of Natural Philosophy''), originally published in 1687. Newton used them to investigate and explain the motion of many physical objects and systems. In the time since Newton, new insights, especially around t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrostatics
Hydrostatics is the branch of fluid mechanics that studies fluids at hydrostatic equilibrium and "the pressure in a fluid or exerted by a fluid on an immersed body". The word "hydrostatics" is sometimes used to refer specifically to water and other liquids, but more often it includes both gases and liquids, whether compressible or incompressible. It encompasses the study of the conditions under which fluids are at rest in stable equilibrium. It is opposed to ''fluid dynamics'', the study of fluids in motion. Hydrostatics is fundamental to ''hydraulics'', the engineering of equipment for storing, transporting and using fluids. It is also relevant to geophysics and astrophysics (for example, in understanding plate tectonics and the anomalies of the Earth's gravitational field), to meteorology, to medicine (in the context of blood pressure), and many other fields. Hydrostatics offers physical explanations for many phenomena of everyday life, such as why atmospheric pressur ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Tolman–Oppenheimer–Volkoff Equation
In astrophysics, the Tolman–Oppenheimer–Volkoff (TOV) equation constrains the structure of a spherically symmetric body of isotropic material which is in static gravitational equilibrium, as modeled by general relativity. The equation is :\frac=-\frac\rho\left(1+\frac\right)\left(1+\frac\right)\left(1-\frac\right)^ Here, r is a radial coordinate, and \rho(r) and P(r) are the density and pressure, respectively, of the material at radius r. The quantity m(r), the total mass within r, is discussed below. The equation is derived by solving the Einstein equations for a general time-invariant, spherically symmetric metric. For a solution to the Tolman–Oppenheimer–Volkoff equation, this metric will take the form :ds^2=e^ c^2 \,dt^2 - \left(1-\frac\right)^ \,dr^2 - r^2\left(d\theta^2 + \sin^2 \theta \,d\phi^2\right) where \nu (r) is determined by the constraint :\frac=- \left(\frac \right) \frac When supplemented with an equation of state, F(\rho,P)=0, which relates de ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Einstein Field Equations
In the General relativity, general theory of relativity, the Einstein field equations (EFE; also known as Einstein's equations) relate the geometry of spacetime to the distribution of Matter#In general relativity and cosmology, matter within it. The equations were published by Albert Einstein in 1915 in the form of a Tensor, tensor equation which related the local ' (expressed by the Einstein tensor) with the local energy, momentum and stress within that spacetime (expressed by the stress–energy tensor). Analogously to the way that electromagnetic fields are related to the distribution of Charge (physics), charges and Electric current, currents via Maxwell's equations, the EFE relate the spacetime geometry to the distribution of mass–energy, momentum and stress, that is, they determine the Metric tensor (general relativity), metric tensor of spacetime for a given arrangement of stress–energy–momentum in the spacetime. The relationship between the metric tensor and the Ei ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Perfect Fluid
In physics, a perfect fluid or ideal fluid is a fluid that can be completely characterized by its rest frame mass density \rho_m and ''isotropic'' pressure . Real fluids are viscous ("sticky") and contain (and conduct) heat. Perfect fluids are idealized models in which these possibilities are ignored. Specifically, perfect fluids have no shear stresses, viscosity, or heat conduction. A quark–gluon plasma and graphene are examples of nearly perfect fluids that could be studied in a laboratory. Non-relativistic fluid mechanics In classical mechanics, ideal fluids are described by Euler equations. Ideal fluids produce no drag according to d'Alembert's paradox. If a fluid produced drag, then work would be needed to move an object through the fluid and that work would produce heat or fluid motion. However, a perfect fluid can not dissipate energy and it can't transmit energy infinitely far from the object. A flock of birds in the medium of air is an example of a perfect fluid; ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Navier–Stokes Equations
The Navier–Stokes equations ( ) are partial differential equations which describe the motion of viscous fluid substances. They were named after French engineer and physicist Claude-Louis Navier and the Irish physicist and mathematician George Gabriel Stokes. They were developed over several decades of progressively building the theories, from 1822 (Navier) to 1842–1850 (Stokes). The Navier–Stokes equations mathematically express momentum balance for Newtonian fluids and make use of conservation of mass. They are sometimes accompanied by an equation of state relating pressure, temperature and density. They arise from applying Isaac Newton's second law to fluid motion, together with the assumption that the stress in the fluid is the sum of a diffusing viscous term (proportional to the gradient of velocity) and a pressure term—hence describing ''viscous flow''. The difference between them and the closely related Euler equations is that Navier–Stokes equat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Infinitesimal
In mathematics, an infinitesimal number is a non-zero quantity that is closer to 0 than any non-zero real number is. The word ''infinitesimal'' comes from a 17th-century Modern Latin coinage ''infinitesimus'', which originally referred to the "infinity- th" item in a sequence. Infinitesimals do not exist in the standard real number system, but they do exist in other number systems, such as the surreal number system and the hyperreal number system, which can be thought of as the real numbers augmented with both infinitesimal and infinite quantities; the augmentations are the reciprocals of one another. Infinitesimal numbers were introduced in the development of calculus, in which the derivative was first conceived as a ratio of two infinitesimal quantities. This definition was not rigorously formalized. As calculus developed further, infinitesimals were replaced by limits, which can be calculated using the standard real numbers. In the 3rd century BC Archimedes used what ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Standard Gravity
The standard acceleration of gravity or standard acceleration of free fall, often called simply standard gravity and denoted by or , is the nominal gravitational acceleration of an object in a vacuum near the surface of the Earth. It is a constant defined by standard as . This value was established by the third General Conference on Weights and Measures (1901, CR 70) and used to define the standard weight of an object as the product of its mass and this nominal acceleration. The acceleration of a body near the surface of the Earth is due to the combined effects of gravity and centrifugal acceleration from the rotation of the Earth (but the latter is small enough to be negligible for most purposes); the total (the apparent gravity) is about 0.5% greater at the poles than at the Equator. Although the symbol is sometimes used for standard gravity, (without a suffix) can also mean the local acceleration due to local gravity and centrifugal acceleration, which varies depending on on ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Density
Density (volumetric mass density or specific mass) is the ratio of a substance's mass to its volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter rho), although the Latin letter ''D'' (or ''d'') can also be used: \rho = \frac, where ''ρ'' is the density, ''m'' is the mass, and ''V'' is the volume. In some cases (for instance, in the United States oil and gas industry), density is loosely defined as its weight per unit volume, although this is scientifically inaccurate this quantity is more specifically called specific weight. For a pure substance, the density is equal to its mass concentration. Different materials usually have different densities, and density may be relevant to buoyancy, purity and packaging. Osmium is the densest known element at standard conditions for temperature and pressure. To simplify comparisons of density across different systems of units, it is sometimes replaced by the dimensionless quantity "relative den ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
