In practice, an inviscid flow is an idealization , one that facilitates mathematical treatment. In fact, purely inviscid flows are only known to be realized in the case of superfluidity. Otherwise, fluids are generally viscous , a property that is often most important within a boundary layer near a solid surface, [2] where the flow must match onto the no-slip condition at the solid. In some cases, the mathematics of a fluid mechanical system can be treated by assuming that the fluid outside of boundary layers is inviscid, and then matching its solution onto that for a thin laminar boundary layer.
For fluid flow over a porous boundary, the fluid velocity can be discontinuous between the free fluid and the fluid in the porous media this is related to the Beavers and Joseph condition. Further, it is useful at low subsonic speeds to assume that a gas is incompressible —that is, the density of the gas does not change even though the speed and static pressure change. A Newtonian fluid named after Isaac Newton is defined to be a fluid whose shear stress is linearly proportional to the velocity gradient in the direction perpendicular to the plane of shear.
This definition means regardless of the forces acting on a fluid, it continues to flow.
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For example, water is a Newtonian fluid, because it continues to display fluid properties no matter how much it is stirred or mixed. A slightly less rigorous definition is that the drag of a small object being moved slowly through the fluid is proportional to the force applied to the object. Important fluids, like water as well as most gases, behave—to good approximation—as a Newtonian fluid under normal conditions on Earth. By contrast, stirring a non-Newtonian fluid can leave a "hole" behind.
This will gradually fill up over time—this behaviour is seen in materials such as pudding, oobleck , or sand although sand isn't strictly a fluid. Alternatively, stirring a non-Newtonian fluid can cause the viscosity to decrease, so the fluid appears "thinner" this is seen in non-drip paints. There are many types of non-Newtonian fluids, as they are defined to be something that fails to obey a particular property—for example, most fluids with long molecular chains can react in a non-Newtonian manner.
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The constant of proportionality between the viscous stress tensor and the velocity gradient is known as the viscosity. A simple equation to describe incompressible Newtonian fluid behaviour is. For a Newtonian fluid, the viscosity, by definition, depends only on temperature and pressure , not on the forces acting upon it. If the fluid is incompressible the equation governing the viscous stress in Cartesian coordinates is.
If the fluid is not incompressible the general form for the viscous stress in a Newtonian fluid is. If a fluid does not obey this relation, it is termed a non-Newtonian fluid , of which there are several types. Non-Newtonian fluids can be either plastic, Bingham plastic, pseudoplastic, dilatant, thixotropic, rheopectic, viscoelastic. In some applications another rough broad division among fluids is made: An Ideal fluid is non-viscous and offers no resistance whatsoever to a shearing force.
An ideal fluid really does not exist, but in some calculations, the assumption is justifiable. One example of this is the flow far from solid surfaces. In many cases the viscous effects are concentrated near the solid boundaries such as in boundary layers while in regions of the flow field far away from the boundaries the viscous effects can be neglected and the fluid there is treated as it were inviscid ideal flow.
The equation reduced in this form is called the Euler equation. From Wikipedia, the free encyclopedia. This article needs additional citations for verification. Please help improve this article by adding citations to reliable sources. Unsourced material may be challenged and removed. Enables you to easily advance from fluid flow principles to applications Fluid Flow for the Practicing Chemical Engineer helps readers move comfortably from fluid flow principles to fluid flow applications.
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Fluid mechanics - Wikipedia
Fluid Flow for the Practicing Chemical Engineer. Added to Your Shopping Cart. Description This book teaches the fundamentals of fluid flow by including both theory and the applications of fluid flow in chemical engineering. It puts fluid flow in the context of other transport phenomena such as mass transfer and heat transfer, while covering the basics, from elementary flow mechanics to the law of conservation.
Fluid Flow for the Practicing Chemical Engineer
The book then examines the applications of fluid flow, from laminar flow to filtration and ventilization. It closes with a discussion of special topics related to fluid flow, including environmental concerns and the economic reality of fluid flow applications. About the Author James P.