Perfect fluid

A perfect fluid is a nonviscous, noucouducting fluid. An example of this type of fluid would be a fluid that has a very small viscosity and conductivity and is at a high Reynolds number. An ideal gas is one that obeys the equation of state ... 

A theoretical ideal fluid situation, a perfect fluid having a constant density and no viscosity, is often used in a theoretical analysis. 

Viscoelasticity A combination of viscous and elastic properties in a plastic with the relative contribution of each being dependent on time, temperature, stress, and strain rate. It relates to the mechanical behavior of plastics in which there is a time and temperature dependent relationship between stress and strain. A material having this property is considered to combine the features of a perfectly elastic solid and a perfect fluid. 

Flows can be classified into two major categories (a) incompressible and (b) compressible flow. Most hqnids fall into the incompressible-flow category, while most gases are compressible in nature. A perfect fluid can be defined as a flnid that is nonviscous and nonconducting. Fluid flow, compressible or incompressible, can be classified by the ratio of the inertial forces to the viscons forces. This ratio is represented by the Reynolds nnmber (Nji,). At a low Reynolds number, the flow is considered to be laminar, and at high Reynolds numbers, the... 

The bp of a perfluoroalkane is only 25-30 °C higher than that of the rare gas with the same molecular weight. This illustrates the perfect fluid character of these compounds, resulting from the low intermolecular interactions. 

Birkhoff et al (Ref 28) gave a fairly complete mathematical theory of cavity-effect phenomenon together with experimental data that aided the formulation and testing of the theory. They based the theory upon the classical thermodynamics of perfect fluids. It is applicable because the strength of metals used for linings can be neglected at the high pressures encountered... 

If a medium is not perfectly elastic or perfectly fluid, but has viscous properties, then the equation for the acoustic displacement u contains an extra term... 

A perfect fluid has no -shear stresses despite shearing deformations in the fluid (Refs 2, 3,... 

FLUID AND FLUID FLOW. The word fluid refers to a state of mailer in which only a uniform isotropic pressure can be supported without indefinite distortion so, a gas or a liquid. The distinction between highly viscous liquids and solids is a difficult one, the same material acting as an ordinary liquid under sonic circumstances and as a solid under others. Fluids may be described in various ways. A perfect fluid is... 

Here ma is the bulk solid-fluid interaction force, T.s the partial Cauchy stress in the solid, p/ the hydrostatic pressure in the perfect fluid, IIS the second-order stress in the solid, ha the density of partial body forces, ta the partial surface tractions, ts the traction corresponding to the second-order stress tensor in the solid and dvs/dn the directional derivative of v.s. along the outward unit normal n to the boundary cXl of C. 

The matter content of the Universe is described as an ensemble of perfect fluids of density pj and pressure Pf. An important quantity is the equation of state parameter Wf defined as... 

The perturbed stress-energy tensor of a perfect fluid can be written... 

The crudest approximation to the density matrix for the system is obtained by assuming that there are no statistical correlations between the elementary excitations (perfect fluid), so that can be written as a simple product of molecular density matrices A. A better approximation is obtained if one does a quantum field theory calculation of the local field effects in the system which in a certain approximation gives the Lorentz-Lorenz correction L(TT) in terms of the refractive index n53). One then writes,... 

In the previous section, it was recognized that for perfect fluid distribution flow direction has only a second order effect on conversion. In this section, the effects of maldistribution are investigated. In order to eliminate the influence of flow direction, a pseudo-homogeneous plug flow model is used with purely radial flow through the catalyst basket. The governing equation is thus Eqn. (14), which in more convenient form is... 

The inviscid perfect fluid is a fluid under only hydrostatic pressure. It has constitutive equations... 

Fluid Dynamics is the study of the relationship between forces resulting motions of a medium that is continuously deformable by shear forces. The fluid medium is called a Newtonian fluid if the shear stress is proportional to the rate of shearing deformation. A perfect fluid has no -shear stresses despite shearing deformations in the fluid (Refs 2, 3, 4, 6 7)... 

This solution will cool to the temperature of the air and remain perfectly fluid, but the moment the cork is withdrawn and atmospheric air gets in, it will begin to crystallise on its upper surface in fine satinlike crystals, which will shoot downwards in a few seconds, like a dense white cloud, and so much heat will be evolved, as to make the bottle very sensibly warm to the hand. 

From the preceding it is clear that the ideas of perfect-fluid flow and of the boundary layer are intimately tied together. Both are generally needed for completely describing physically interesting flows, although sometimes one alone is sufficient. We consider perfect-fluid flows in this chapter and the boundary layer in the next. First we must introduce the idea of streamlines. 

If we use the alternative view of a streamline—a line across which there is no flow—then it is clear that the boundaries of solid objects immersed in the flow must be streamlines. For real fluid flows, the fluid adjacent to the boundary of a solid body does not move relative to the body it clings to the wall. Thus, in real fluids the wall is a streamline of zero velocity. In the theory of perfect-fluid flow, the imaginary perfect fluid has no tendency to cling to walls, because it has no viscosity. Thus, the streamline adjacent to a solid body in perfect-fluid flow is one with finite velocity. This leads to the idea that we may divide a perfect-fluid flow along a streamline and substitute a solid body for the flow on one side of the streamline without changing the mathematical character of the flow on the other side of the streamline. Thus, to compute the flow around some solid body in perfect-fluid theory, we need only find the flow which has a streamline with the same shape as the solid body and then conceptually substitute the solid body for that part of the flow this does not affect the rest of the flow. Several examples of this procedure will be shown. 

What physical meaning should one attach to the velocity potential For the flow of an ideal, frictionless fluid, the velocity potential has no physical meaning whatever. To illustrate this, consider the steady flow of a frictionless, constant-density fluid in a horizontal pipe see Fig. 10.3. (Such a frictionless fluid, once started in motion by some external force, would continue moving forever, because there is no force to stop it.) For such a frictionless fluid, the velocity is uniform over the cross section perpendicular to the flow. From Bernoulli s equation we can see that there is no change with distance of pressure, velocity, or elevation, and by straightforward arguments we can show that there is no change of temperature, refractive index, dielectric constant, or any other measurable property. But from Eq. 10.7 we know that, because is constant, there is a steady decrease of (f> in the x direction. Thus the velocity potential for a perfect fluid (f> is not a function of any measurable physical property of the fluid. 

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