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No-slip Condition
In fluid dynamics, the no-slip condition for viscous fluids assumes that at a solid boundary, the fluid will have zero velocity relative to the boundary. The fluid velocity at all fluid–solid boundaries is equal to that of the solid boundary. Conceptually, one can think of the outermost molecules of fluid as stuck to the surfaces past which it flows. Because the solution is prescribed at given locations, this is an example of a Dirichlet boundary condition. Physical justification Particles close to a surface do not move along with a flow when adhesion is stronger than cohesion. At the fluid-solid interface, the force of attraction between the fluid particles and solid particles (Adhesive forces) is greater than that between the fluid particles (Cohesive forces). This force imbalance brings down the fluid velocity to zero. The no slip condition is only defined for viscous flows and where continuum concept is valid. Exceptions As with most of the engineering approximations, the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Fluid Dynamics
In physics and engineering, fluid dynamics is a subdiscipline of fluid mechanics that describes the flow of fluids— liquids and gases. It has several subdisciplines, including ''aerodynamics'' (the study of air and other gases in motion) and hydrodynamics (the study of liquids in motion). Fluid dynamics has a wide range of applications, including calculating forces and moments on aircraft, determining the mass flow rate of petroleum through pipelines, predicting weather patterns, understanding nebulae in interstellar space and 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 fluid dynamics problem typically involves the calculation of various properties of the fluid, such as flow velocity, pressure, density, and temperature, as functions of space and ti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Inviscid Flow
In fluid dynamics, inviscid flow is the flow of an inviscid (zero-viscosity) fluid, also known as a superfluid. The Reynolds number of inviscid flow approaches infinity as the viscosity approaches zero. When viscous forces are neglected, such as the case of inviscid flow, the Navier–Stokes equation can be simplified to a form known as the Euler equation. This simplified equation is applicable to inviscid flow as well as flow with low viscosity and a Reynolds number much greater than one. Using the Euler equation, many fluid dynamics problems involving low viscosity are easily solved, however, the assumed negligible viscosity is no longer valid in the region of fluid near a solid boundary (the boundary layer) or, more generally in regions with large velocity gradients which are evidently accompanied by viscous forces. Inviscid flows are broadly classified into potential flows (or, irrotational flows) and rotational inviscid flows. Prandtl hypothesis Ludwig Prandtl d ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
ScienceWorld
Wolfram Research, Inc. ( ) is an American multinational company that creates computational technology. Wolfram's flagship product is the technical computing program Wolfram Mathematica, first released on June 23, 1988. Other products include WolframAlpha, Wolfram SystemModeler, Wolfram Workbench, gridMathematica, Wolfram Finance Platform, webMathematica, the Wolfram Cloud, and the Wolfram Programming Lab. Wolfram Research founder Stephen Wolfram is the CEO. The company is headquartered in Champaign, Illinois, United States. History The company launched Wolfram Alpha, an answer engine on May 16, 2009. It brings a new approach to knowledge generation and acquisition that involves large amounts of curated computable data in addition to semantic indexing of text. Wolfram Research acquired MathCore Engineering AB on March 30, 2011. On July 21, 2011, Wolfram Research launched the Computable Document Format (CDF). CDF is an electronic document format designed to allow easy ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shell Balance
In fluid mechanics, a shell balance can be used to determine how fluid velocity changes across a flow. A shell is a differential element of the flow. By looking at the momentum and forces on one small portion, it is possible to integrate over the flow to see the larger picture of the flow as a whole. The balance is determining what goes into and out of the shell. Momentum is created within the shell through fluid entering and leaving the shell and by shear stress. In addition, there are pressure and gravitational forces on the shell. The goal of a shell balance is to determine the velocity profile of the flow. The velocity profile is an equation to calculate the velocity based on a specific location in the flow. From this, it is possible to find a velocity for any point across the flow. Applications Shell Balances can be used in many situations. For example, flow in a pipe, the flow of multiple fluids around each other, or flow due to pressure difference. Although terms in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Shear Stress
Shear stress, often denoted by (Greek: tau), is the component of stress coplanar with a material cross section. It arises from the shear force, the component of force vector parallel to the material cross section. ''Normal stress'', on the other hand, arises from the force vector component perpendicular to the material cross section on which it acts. General shear stress The formula to calculate average shear stress is force per unit area.: : \tau = , where: : = the shear stress; : = the force applied; : = the cross-sectional area of material with area parallel to the applied force vector. Other forms Wall shear stress Wall shear stress expresses the retarding force (per unit area) from a wall in the layers of a fluid flowing next to the wall. It is defined as: \tau_w:=\mu\left(\frac\right)_ Where \mu is the dynamic viscosity, u the flow velocity and y the distance from the wall. It is used, for example, in the description of arterial blood flow in which case which t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Wind Gradient
In common usage, wind gradient, more specifically wind speed gradient or wind velocity gradient, or alternatively shear wind, is the vertical component of the gradient of the mean horizontal wind speed in the lower atmosphere. It is the rate of increase of wind strength with unit increase in height above ground level. In metric units, it is often measured in units of meters per second of speed, per kilometer of height (m/s/km), which reduces to the standard unit of shear rate, inverse seconds (s−1). Simple explanation Surface friction forces the surface wind to slow and turn near the surface of the Earth, blowing directly towards the low pressure, when compared to the winds in the nearly frictionless flow well above the Earth's surface. This layer, where surface friction slows the wind and changes the wind direction, is known as the planetary boundary layer. Daytime solar heating due to insolation thickens the boundary layer as winds warmed by contact with the ear ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer. The air next to a human is heated resulting in gravity-induced convective airflow, airflow which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Contact Angle
The contact angle is the angle, conventionally measured through the liquid, where a liquid–vapor interface meets a solid surface. It quantifies the wettability of a solid surface by a liquid via the Young equation. A given system of solid, liquid, and vapor at a given temperature and pressure has a unique equilibrium contact angle. However, in practice a dynamic phenomenon of contact angle hysteresis is often observed, ranging from the advancing (maximal) contact angle to the receding (minimal) contact angle. The equilibrium contact is within those values, and can be calculated from them. The equilibrium contact angle reflects the relative strength of the liquid, solid, and vapour molecular interaction. The contact angle depends upon the medium above the free surface of the liquid, and the nature of the liquid and solid in contact. It is independent of the inclination of solid to the liquid surface. It changes with surface tension and hence with the temperature and purity of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Capillary Surface
In fluid mechanics and mathematics, a capillary surface is a surface that represents the interface between two different fluids. As a consequence of being a surface, a capillary surface has no thickness in slight contrast with most real fluid interfaces. Capillary surfaces are of interest in mathematics because the problems involved are very nonlinear and have interesting properties, such as discontinuous dependence on boundary data at isolated points. In particular, static capillary surfaces with gravity absent have constant mean curvature, so that a minimal surface is a special case of static capillary surface. They are also of practical interest for fluid management in space (or other environments free of body forces), where both flow and static configuration are often dominated by capillary effects. The stress balance equation The defining equation for a capillary surface is called the stress balance equation, which can be derived by considering the forces and stresses acti ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Boundary Layer
In physics and fluid mechanics, a boundary layer is the thin layer of fluid in the immediate vicinity of a bounding surface formed by the fluid flowing along the surface. The fluid's interaction with the wall induces a no-slip boundary condition (zero velocity at the wall). The flow velocity then monotonically increases above the surface until it returns to the bulk flow velocity. The thin layer consisting of fluid whose velocity has not yet returned to the bulk flow velocity is called the velocity boundary layer. The air next to a human is heated resulting in gravity-induced convective airflow, airflow which results in both a velocity and thermal boundary layer. A breeze disrupts the boundary layer, and hair and clothing protect it, making the human feel cooler or warmer. On an aircraft wing, the velocity boundary layer is the part of the flow close to the wing, where viscous forces distort the surrounding non-viscous flow. In the Earth's atmosphere, the atmospheric bo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viscosity
The viscosity of a fluid is a measure of its resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity quantifies the internal 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 axis than near its walls. Experiments show that some 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 with a constant rate of flow, the strength of the compensating force is proportional to the fluid's viscosity. In general, viscosity depends on a fluid's state, such as its temperature, pressure, and rate of deformation. However, the dependence on some of these properties is ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Viscous Fluid
In condensed matter physics and physical chemistry, the terms viscous liquid, supercooled liquid, and glassforming liquid are often used interchangeably to designate liquids that are at the same time highly viscous (see Viscosity of amorphous materials), can be or are supercooled, and able to form a glass. Working points in glass processing The mechanical properties of glass-forming liquids depend primarily on the viscosity. Therefore, the following working points are defined in terms of viscosity. The temperature is indicated for industrial soda lime glass: Fragile-strong classification In a widespread classification, due to chemist Austen Angell, a glass-forming liquid is called strong if its viscosity approximately obeys an Arrhenius law (log η is linear in 1/''T'' ). In the opposite case of clearly non-Arrhenius behaviour the liquid is called fragile. This classification has no direct relation with the common usage of the word "fragility" to mean br ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
