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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] |
Fluid Dynamics
In physics, physical chemistry and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids – liquids and gases. It has several subdisciplines, including (the study of air and other gases in motion) and (the study of water and other liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moment (physics), moments on aircraft, determining the mass flow rate of petroleum through pipeline transport, pipelines, weather forecasting, predicting weather patterns, understanding nebulae in interstellar space, understanding large scale Geophysical fluid dynamics, geophysical flows involving oceans/atmosphere and Nuclear weapon design, modelling fission weapon detonation. Fluid dynamics offers a systematic structure—which underlies these practical disciplines—that embraces empirical and semi-empirical laws derived from flow measurement and used to solve practical problems. The solution to a fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Reynolds Number
In fluid dynamics, the Reynolds number () is a dimensionless quantity that helps predict fluid flow patterns in different situations by measuring the ratio between Inertia, inertial and viscous forces. At low Reynolds numbers, flows tend to be dominated by laminar flow, laminar (sheet-like) flow, while at high Reynolds numbers, flows tend to be turbulence, turbulent. The turbulence results from differences in the fluid's speed and direction, which may sometimes intersect or even move counter to the overall direction of the flow (Eddy (fluid dynamics), eddy currents). These eddy currents begin to churn the flow, using up energy in the process, which for liquids increases the chances of cavitation. The Reynolds number has wide applications, ranging from liquid flow in a pipe to the passage of air over an aircraft wing. It is used to predict the transition from laminar–turbulent transition, laminar to turbulent flow and is used in the scaling of similar but different-sized fl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hilding Faxén
Olov Hilding Faxén (29 March 1892 – 1 June 1970) was a Swedish physicist who was primarily active within mechanics. Faxén received his doctorate in 1921 at Uppsala University with the thesis ''Einwirkung der Gefässwände auf den Widerstand gegen die Bewegung einer kleinen Kugel in einer zähen Flüssigkeit'' ("Influence of the container walls on the resistance against movement by a small ball in a viscous fluid"). One of his contributions was to formulate Faxén's law, which is a correction to Stokes' law for the friction on spherical objects in a viscous fluid, valid in the case when the object moves close to a wall of the container. This was a problem previously treated by Carl Wilhelm Oseen (1910) and Horace Lamb (1911), but incompletely solved. After the death of Ivar Fredholm, Faxén temporarily upheld the chair in mathematical physics at Stockholm University College, before Oskar Klein was made the new professor. Faxén then served as professor at Chalmers Institu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Uppsala University
Uppsala University (UU) () is a public university, public research university in Uppsala, Sweden. Founded in 1477, it is the List of universities in Sweden, oldest university in Sweden and the Nordic countries still in operation. Initially founded in the 15th century, the university rose to significance during the rise of Swedish Empire, Sweden as a great power at the end of the 16th century and was then given relative financial stability with a large donation from Monarchy of Sweden, King Gustavus Adolphus of Sweden, Gustavus Adolphus in the early 17th century. Uppsala also has an important historical place in Swedish national culture, and national identity, identity for the Swedish establishment: in historiography, religion, literature, politics, and music. Many aspects of Swedish academic culture in general, such as the white student cap, originated in Uppsala. It shares some peculiarities, such as the student nation system, with Lund University and the University of Helsink ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stokes' Law
In fluid dynamics, Stokes' law gives the frictional force – also called drag force – exerted on spherical objects moving at very small Reynolds numbers in a viscous fluid. It was derived by George Gabriel Stokes in 1851 by solving the Stokes flow limit for small Reynolds numbers of the Navier–Stokes equations.Batchelor (1967), p. 233. Statement of the law The force of viscosity on a small sphere moving through a viscous fluid is given by: :_ = - 6 \pi \mu R where (in SI units): * _ is the frictional force – known as Stokes' drag – acting on the interface between the fluid and the particle (newtons, kg m s−2); * (some authors use the symbol ) is the dynamic viscosity ( Pascal-seconds, kg m−1 s−1); * is the radius of the spherical object (meters); * is the flow velocity relative to the object (meters per second). Note the minus sign in the equation, the drag force points in the opposite direction to the relative velocity: drag opposes the motion. Stokes' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viscosity
Viscosity is a measure of a fluid's rate-dependent drag (physics), resistance to a change in shape or to movement of its neighboring portions relative to one another. For liquids, it corresponds to the informal concept of ''thickness''; for example, syrup has a higher viscosity than water. Viscosity is defined scientifically as a force multiplied by a time divided by an area. Thus its SI units are newton-seconds per metre squared, or pascal-seconds. Viscosity quantifies the internal friction, frictional force between adjacent layers of fluid that are in relative motion. For instance, when a viscous fluid is forced through a tube, it flows more quickly near the tube's center line than near its walls. Experiments show that some stress (physics), stress (such as a pressure difference between the two ends of the tube) is needed to sustain the flow. This is because a force is required to overcome the friction between the layers of the fluid which are in relative motion. For a tube ... [...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] |
Immersed Boundary Method
In computational fluid dynamics, the immersed boundary method originally referred to an approach developed by Charles Peskin in 1972 to simulate fluid-structure (fiber) interactions. Treating the coupling of the structure deformations and the fluid flow poses a number of challenging problems for numerical simulations (the elastic boundary changes the flow of the fluid and the fluid moves the elastic boundary simultaneously). In the immersed boundary method the fluid is represented in an Eulerian coordinate system and the structure is represented in Lagrangian coordinates. For Newtonian fluids governed by the 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 Georg ..., the fluid equations are : \rho \left(\frac + \cdot\nabla\right) = -\nabla p + \mu\, \Delta u(x, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
