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Force Density
In fluid mechanics, the force density is the negative gradient of pressure. It has the physical dimensions of force per unit volume. Force density is a vector field representing the flux density of the hydrostatic force within the bulk of a fluid. Force density is represented by the symbol f, and given by the following equation, where ''p'' is the pressure: :\mathbf = - \nabla p . The net force on a differential volume element ''dV'' of the fluid is: :d\mathbf = \mathbfdV Force density acts in different ways which is caused by the boundary conditions. There are stick-slip boundary conditions and stick boundary conditions which affect force density. In a sphere placed in an arbitrary non-stationary flow field of viscous incompressible fluid for stick boundary conditions where the force density's calculations leads to show the generalisation of Faxen's theorem to force multipole moments of arbitrary order. In a sphere moving in an incompressible fluid in a non-stationary f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kilogram
The kilogram (also spelled kilogramme) is the base unit of mass in the International System of Units (SI), equal to one thousand grams. It has the unit symbol kg. The word "kilogram" is formed from the combination of the metric prefix kilo- (meaning one thousand) and gram; it is colloquially shortened to "kilo" (plural "kilos"). The kilogram is an SI base unit, defined ultimately in terms of three defining constants of the SI, namely a specific transition frequency of the caesium-133 atom, the speed of light, and the Planck constant. A properly equipped metrology laboratory can calibrate a mass measurement instrument such as a Kibble balance as a primary standard for the kilogram mass. The kilogram was originally defined in 1795 during the French Revolution as the mass of one litre of water (originally at 0 °C, later changed to the temperature of its maximum density, approximately 4 °C). The current definition of a kilogram agrees with this original defini ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid
In physics, a fluid is a liquid, gas, or other material that may continuously motion, move and Deformation (physics), deform (''flow'') under an applied shear stress, or external force. They have zero shear modulus, or, in simpler terms, are Matter, substances which cannot resist any shear force applied to them. Although the term ''fluid'' generally includes both the liquid and gas phases, its definition varies among branches of science. Definitions of ''solid'' vary as well, and depending on field, some substances can have both fluid and solid properties. Non-Newtonian fluids like Silly Putty appear to behave similar to a solid when a sudden force is applied. Substances with a very high viscosity such as Pitch (resin), pitch appear to behave like a solid (see pitch drop experiment) as well. In particle physics, the concept is extended to include fluidic matters other than liquids or gases. A fluid in medicine or biology refers to any liquid constituent of the body (body fluid ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pressure Gradient
In hydrodynamics and hydrostatics, the pressure gradient (typically of air but more generally of any fluid) is a physical quantity that describes in which direction and at what rate the pressure increases the most rapidly around a particular location. The pressure gradient is a dimensional quantity expressed in units of pascals per metre (Pa/m). Mathematically, it is the gradient of pressure as a function of position. The gradient of pressure in hydrostatics is equal to the ''body force density'' (generalised Stevin's Law). In petroleum geology and the petrochemical sciences pertaining to oil wells, and more specifically within hydrostatics, pressure gradients refer to the gradient of vertical pressure in a column of fluid within a wellbore and are generally expressed in pounds per square inch per foot (psi/ft). This column of fluid is subject to the compound pressure gradient of the overlying fluids. The path and geometry of the column is totally irrelevant; only the vertical ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Body Force
In physics, a body force is a force that acts throughout the volume of a body.Springer site - Book 'Solid mechanics'preview paragraph 'Body forces'./ref> Forces due to gravity, electric fields and magnetic fields are examples of body forces. Body forces contrast with ''contact forces'' or '' surface forces'' which are exerted to the surface of an object. Fictitious forces such as the centrifugal force, Euler force, and the Coriolis effect are other examples of body forces. Definition Qualitative A body force is simply a type of force, and so it has the same dimensions as force, L] sup>−2. However, it is often convenient to talk about a body force in terms of either the force per unit volume or the force per unit mass. If the force per unit volume is of interest, it is referred to as the force density throughout the system. A body force is distinct from a contact force in that the force does not require contact for transmission. Thus, common forces associated with press ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Acceleration
In mechanics, acceleration is the Rate (mathematics), rate of change of the velocity of an object with respect to time. Acceleration is one of several components of kinematics, the study of motion. Accelerations are Euclidean vector, vector quantities (in that they have Magnitude (mathematics), magnitude and Direction (geometry), direction). The orientation of an object's acceleration is given by the orientation of the ''net'' force acting on that object. The magnitude of an object's acceleration, as described by Newton's second law, is the combined effect of two causes: * the net balance of all external forces acting onto that object — magnitude is Direct proportionality, directly proportional to this net resulting force; * that object's mass, depending on the materials out of which it is made — magnitude is Inverse proportionality, inversely proportional to the object's mass. The International System of Units, SI unit for acceleration is metre per second squared (, \ma ... [...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] |
Faxén's Law
In fluid dynamics, Faxén's laws relate a sphere's velocity \mathbf and angular velocity \mathbf to the forces, torque, stresslet and flow it experiences under low Reynolds number (creeping flow) conditions. First law Faxen's first law was introduced in 1922 by Swedish physicist Hilding Faxén, who at the time was active at Uppsala University, and is given byDurlofsky, Louis, John F. Brady, and Georges Bossis. "Dynamic simulation of hydrodynamically interacting particles." Journal of fluid mechanics 180.1 (1987): 21–49 , equations (2.15a, b, c). Note sign change. : \mathbf = 6 \pi \mu a \left \left( 1 + \frac \nabla^2\right) \mathbf' - (\mathbf - \mathbf^\infty) \right where * \mathbf is the force exerted by the fluid on the sphere * \mu is the Newtonian viscosity of the solvent in which the sphere is placed * a is the sphere's radius * \mathbf is the (translational) velocity of the sphere * \mathbf' is the disturbance velocity caused by the other spheres in suspension (not by th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Volume Element
In mathematics, a volume element provides a means for integrating a function with respect to volume in various coordinate systems such as spherical coordinates and cylindrical coordinates. Thus a volume element is an expression of the form \mathrmV = \rho(u_1,u_2,u_3)\,\mathrmu_1\,\mathrmu_2\,\mathrmu_3 where the u_i are the coordinates, so that the volume of any set B can be computed by \operatorname(B) = \int_B \rho(u_1,u_2,u_3)\,\mathrmu_1\,\mathrmu_2\,\mathrmu_3. For example, in spherical coordinates \mathrmV = u_1^2\sin u_2\,\mathrmu_1\,\mathrmu_2\,\mathrmu_3, and so \rho = u_1^2\sin u_2. The notion of a volume element is not limited to three dimensions: in two dimensions it is often known as the area element, and in this setting it is useful for doing surface integrals. Under changes of coordinates, the volume element changes by the absolute value of the Jacobian determinant of the coordinate transformation (by the change of variables formula). This fact allows volume ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pressure
Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and even by industry. Further, both spellings are often used ''within'' a particular industry or country. Industries in British English-speaking countries typically use the "gauge" spelling. is the pressure relative to the ambient pressure. Various #Units, units are used to express pressure. Some of these derive from a unit of force divided by a unit of area; the International System of Units, SI unit of pressure, the Pascal (unit), pascal (Pa), for example, is one newton (unit), newton per square metre (N/m2); similarly, the Pound (force), pound-force per square inch (Pound per square inch, psi, symbol lbf/in2) is the traditional unit of pressure in the imperial units, imperial and United States customary units, US customary systems. Pressure ma ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hydrostatic Force
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 pressure ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Metre
The metre (or meter in US spelling; symbol: m) is the base unit of length in the International System of Units (SI). Since 2019, the metre has been defined as the length of the path travelled by light in vacuum during a time interval of of a second, where the second is defined by a hyperfine transition frequency of caesium. The metre was originally defined in 1791 by the French National Assembly as one ten-millionth of the distance from the equator to the North Pole along a great circle, so the Earth's polar circumference is approximately . In 1799, the metre was redefined in terms of a prototype metre bar. The bar used was changed in 1889, and in 1960 the metre was redefined in terms of a certain number of wavelengths of a certain emission line of krypton-86. The current definition was adopted in 1983 and modified slightly in 2002 to clarify that the metre is a measure of proper length. From 1983 until 2019, the metre was formally defined as the length of the pat ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flux
Flux describes any effect that appears to pass or travel (whether it actually moves or not) through a surface or substance. Flux is a concept in applied mathematics and vector calculus which has many applications in physics. For transport phenomena, flux is a vector quantity, describing the magnitude and direction of the flow of a substance or property. In vector calculus flux is a scalar quantity, defined as the surface integral of the perpendicular component of a vector field over a surface. Terminology The word ''flux'' comes from Latin: ''fluxus'' means "flow", and ''fluere'' is "to flow". As '' fluxion'', this term was introduced into differential calculus by Isaac Newton. The concept of heat flux was a key contribution of Joseph Fourier, in the analysis of heat transfer phenomena. His seminal treatise ''Théorie analytique de la chaleur'' (''The Analytical Theory of Heat''), defines ''fluxion'' as a central quantity and proceeds to derive the now well-known expre ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
