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Ostroumov Flow
In fluid dynamics, the Ostroumov flow, also known as the Ostroumov–Birikh–Hansen–Rattray flow describes fluid motion driven by horizontal density gradients within horizontal channels, pipes, or open water bodies such as rivers and estuaries. The flow is named after Georgy Andreyevich Ostroumov (1952), R. V. Birikh (1966), Donald V. Hansen and Maurice Rattray Jr (1965). Unlike the Poiseuille flow or the Couette flow, the velocity profile in the Ostroumov flow is a cubic function of the coordinate normal to gravity. Planar channel Consider a two-dimensional planar channel of width 2h and their walls located at z=-h and z=+h. The gravity vector is given by \mathbf=-g\mathbf_z, where g is the gravitational acceleration. Suppose that there exists a horizontal density gradient in the fluid, i.e., \rho=\rho(x,y) with a characteristic length scale l. Such gradients can be induced by some scalar field such as temperature or solute concentration, present within the fluid. Whenever hor ... [...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] |
Couette Flow
In fluid dynamics, Couette flow is the flow of a viscosity, viscous fluid in the space between two surfaces, one of which is moving tangentially relative to the other. The relative motion of the surfaces imposes a shear stress on the fluid and induces flow. Depending on the definition of the term, there may also be an applied pressure gradient in the flow direction. The Couette configuration models certain practical problems, like the Earth's mantle and Atmosphere of Earth, atmosphere, and flow in lightly loaded Fluid bearing, journal bearings. It is also employed in Viscometer, viscometry and to demonstrate approximations of Time reversibility, reversibility. It is named after Maurice Couette, a Professor of Physics at the French University of Angers in the late 19th century. Isaac Newton first defined the problem of Couette flow in Proposition 51 of his Philosophiæ Naturalis Principia Mathematica, ''Philosophiæ Naturalis Principia Mathematica'', and expanded upon the ideas i ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Gravitational Acceleration
In physics, gravitational acceleration is the acceleration of an object in free fall within a vacuum (and thus without experiencing drag (physics), drag). This is the steady gain in speed caused exclusively by gravitational attraction. All bodies accelerate in vacuum at the same rate, regardless of the masses or compositions of the bodies; the measurement and analysis of these rates is known as gravimetry. At a fixed point on the surface, the magnitude of gravity of Earth, Earth's gravity results from combined effect of gravitation and the centrifugal force from Earth's rotation. At different points on Earth's surface, the free fall acceleration ranges from , depending on altitude, latitude, and longitude. A conventional standard gravity, standard value is defined exactly as 9.80665 m/s² (about 32.1740 ft/s²). Locations of significant variation from this value are known as gravity anomaly, gravity anomalies. This does not take into account other effects, such as buoyancy or d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lubrication Theory
In fluid dynamics, lubrication theory describes the flow of fluids (liquids or gases) in a geometry in which one dimension is significantly smaller than the others. An example is the flow above air hockey tables, where the thickness of the air layer beneath the puck is much smaller than the dimensions of the puck itself. Internal flows are those where the fluid is fully bounded. Internal flow lubrication theory has many industrial applications because of its role in the design of fluid bearings. Here a key goal of lubrication theory is to determine the pressure distribution in the fluid volume, and hence the forces on the bearing components. The working fluid in this case is often termed a lubricant. Free film lubrication theory is concerned with the case in which one of the surfaces containing the fluid is a free surface. In that case, the position of the free surface is itself unknown, and one goal of lubrication theory is then to determine this. Examples include the flow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hele-Shaw Flow
Hele-Shaw flow is defined as flow taking place between two parallel flat plates separated by a narrow gap satisfying certain conditions, named after Henry Selby Hele-Shaw, who studied the problem in 1898. Various problems in fluid mechanics can be approximated to Hele-Shaw flows and thus the research of these flows is of importance. Approximation to Hele-Shaw flow is specifically important to micro-flows. This is due to manufacturing techniques, which creates shallow planar configurations, and the typically low Reynolds numbers of micro-flows. The conditions that needs to be satisfied are :\frac \ll 1, \qquad \frac \frac \ll 1 where h is the gap width between the plates, U is the characteristic velocity scale, l is the characteristic length scale in directions parallel to the plate and \nu is the kinematic viscosity. Specifically, the Reynolds number \mathrm=Uh/\nu need not always be small, but can be order unity or greater as long as it satisfies the condition \mathrm(h/l) \ll 1. ... [...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] |
Rayleigh Number
In fluid mechanics, the Rayleigh number (, after Lord Rayleigh) for a fluid is a dimensionless number associated with buoyancy-driven flow, also known as free (or natural) convection. It characterises the fluid's flow regime: a value in a certain lower range denotes laminar flow; a value in a higher range, turbulent flow. Below a certain critical value, there is no fluid motion and heat transfer is by conduction rather than convection. For most engineering purposes, the Rayleigh number is large, somewhere around 106 to 108. The Rayleigh number is defined as the product of the Grashof number (), which describes the relationship between buoyancy and viscosity within a fluid, and the Prandtl number (), which describes the relationship between momentum diffusivity and thermal diffusivity: . Hence it may also be viewed as the ratio of buoyancy and viscosity forces multiplied by the ratio of momentum and thermal diffusivities: . It is closely related to the Nusselt number (). D ... [...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] |
Erdogan–Chatwin Equation
In fluid dynamics, Erdogan–Chatwin equation refers to a nonlinear diffusion equation for the scalar field, that accounts for shear-induced dispersion due to horizontal buoyancy forces. The equation was named after M. Emin Erdogan and Phillip C. Chatwin, who derived the equation in 1967. The equation for the scalar field \varphi(x,t) readsSmith, R. (1982). Similarity solutions of a non-linear diffusion equation. IMA Journal of Applied Mathematics (Institute of Mathematics and Its Applications), 28(2), 149-149. :\varphi_t = (\varphi_x+a\varphi_x^3)_x, where a is a positive constant. For a\ll 1, the equation reduces to the linear heat equation, \varphi_t = \varphi_ and for a\gg 1, the equation reduces to \varphi_t = 3a\varphi_x^2\varphi_. See also *Ostroumov flow In fluid dynamics, the Ostroumov flow, also known as the Ostroumov–Birikh–Hansen–Rattray flow describes fluid motion driven by horizontal density gradients within horizontal channels, pipes, or open water bodies s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Flow Regimes
Flow may refer to: Science and technology * Flow (fluid), Fluid flow, the motion of a gas or liquid * Flow (geomorphology), a type of mass wasting or slope movement in geomorphology * Flow (mathematics), a group action of the real numbers on a set * Flow (psychology), a mental state of being fully immersed and focused * Flow, a spacecraft of NASA's GRAIL program Computing * Flow network, graph-theoretic version of a mathematical flow * Dataflow, a broad concept in computer systems with many different meanings * Microsoft Flow (renamed to Power Automate in 2019), a workflow toolkit in Microsoft Dynamics * Neos Flow, a free and open source web application framework written in PHP * webMethods Flow, a graphical programming language * FLOW (programming language), an educational programming language from the 1970s * Flow (web browser), a web browser with a proprietary rendering engine * Flow (Google), a generative AI video creation tool Arts, entertainment and media * Flow (journal), ' ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
