Compressibility, definition

Since the compressibility of liquids is not entirely negligible, we may derive the velocity profile along the column by integration of the compressibility definition [23]... 

Reservoir fluids (oil, water, gas) and the rock matrix are contained under high temperatures and pressures they are compressed relative to their densities at standard temperature and pressure. Any reduction in pressure on the fluids or rock will result in an increase in the volume, according to the definition of compressibility. As discussed in Section 5.2, isothermal conditions are assumed in the reservoir. Isothermal compressibility is defined as ... 

A still different approach to multilayer adsorption considers that there is a potential field at the surface of a solid into which adsorbate molecules fall. The adsorbed layer thus resembles the atmosphere of a planet—it is most compressed at the surface of the solid and decreases in density outward. The general idea is quite old, but was first formalized by Polanyi in about 1914—see Brunauer [34]. As illustrated in Fig. XVII-12, one can draw surfaces of equipo-tential that appear as lines in a cross-sectional view of the surface region. The space between each set of equipotential surfaces corresponds to a definite volume, and there will thus be a relationship between potential U and volume 0. 

Aerosol technology may be defined as involving the development, preparation, manufacture, and testing of products that depend on the power of a hquefied or compressed gas to expel the contents from a container. This definition can be extended to iaclude the physical, chemical, and toxicological properties of both the finished aerosol system and the propellants. 

CD-XA (CD-extended architecture) is the standard for CD-ROMs for data storage and compressed audio recording (up to four hours music in HiFi-stereo quaUty). The definition of the CD-XA format is also put down in the extended Yellow Book. 

Agriculture. Most forages provide insufficient sodium for animal feeding and may lack adequate chloride. Thus salt supplementation is a critical part of a nutritionally balanced diet for animals. In addition, because animals have a definite appetite for salt, it can be used as a deflvery mechanism to ensure adequate intake of less palatable nutrients and as a feed limiter. Salt is an excellent carrier for trace minerals. Salt, either in loose form or as compressed blocks, can be mixed with feed or fed free-choice to improve animal health and productivity (see Feeds and feed additives). 

The systematic study of piezochromism is a relatively new field. It is clear that, even within the restricted definition used here, many more systems win be found which exhibit piezochromic behavior. It is quite possible to find a variety of potential appUcations of this phenomenon. Many of them center around the estimation of the pressure or stress in some kind of restricted or localized geometry, eg, under a localized impact or shock in a crystal or polymer film, in such a film under tension or compression, or at the interface between bearings. More generally it conveys some basic information about inter- and intramolecular interactions that is useful in understanding processes at atmospheric pressure as well as under compression. 

Critical Compressibility Factor The critical compressibility factor of a compound is calculated from the experimental or predicted values of the critical properties by the definition, Eq. (2-21). 

A key limitation of sizing Eq. (8-109) is the limitation to incompressible flmds. For gases and vapors, density is dependent on pressure. For convenience, compressible fluids are often assumed to follow the ideal-gas-law model. Deviations from ideal behavior are corrected for, to first order, with nommity values of compressibihty factor Z. (See Sec. 2, Thvsical and Chemical Data, for definitions and data for common fluids.) For compressible fluids... 

This expression shows the relationship between filtration time and filtrate volume. The equation is applicable to both incompressible or compressible calces, because at constant AP the values and x are constant. For constant AP, an increase in the filtrate volume results in a reduction in the filtration rate. If we assume a definite filtering apparatus and set up a constant temperature and filtration pressure, then the values of Rf, r , fi and AP will be constant. We now take note of the well-known filtration constants K and C, which are derived from the above expressions ... 

The exact relationship can be derived from experiments in a device called a compression-permeability cell. Once this relationship is defined, the integral of the right side of Equation 34 may be evaluated analytically (or if the relationship is in the form of a curve, the evaluation may be made graphically). The interrelation between W and Pj is established by the pump characteristics, which define q = f(W) in Equation 34. Filtration time may then be determined from the following definition ... 

The sign associated with the pressure is opposite to that associated with the normal viscous stress. The usual sign convention assumes that a tensile stress is the positive normal stress so that the pressure, which by definition has compressive normal stress, has a negative sign. 

The study clearly shows that the observed electrical signals are electrochemical in origin, and the first-order description of the process is consistent with that expected from atmospheric pressure behaviors. Nevertheless, the complications introduced by the shock compression do not permit definitive conclusions on values of electrochemical potentials without considerable additional work. 

Use of the term mean-bulk temperature is to define the model from which temperatures are computed. In shock-compression modeling, especially in porous solids, temperatures computed are model dependent and are without definition unless specification of assumptions used in the calculations is given. The term mean-bulk temperature describes a model calculation in which the compressional energy is uniformly distributed throughout the sample without an attempt to specify local effects. In the energy localization case, it is well known that the computed temperatures can vary by an order of magnitude depending on the assumptions used in the calculation. 

How big is an atom or a molecule It should be fairly obvious that atoms and molecules do take up a definite amount of space. A gas can be compressed into a smaller volume but only so far. Liquids and solids cannot be easily compressed. While the individual molecules in a gas are widely separated and can be pushed into a much smaller volume, the molecules in a liquid or a solid are already close together and cannot be squeezed much further. The bottom line is that atoms and molecules require a certain amount of space. But how much ... 

It is again clear that the two benefits of increased sensitivity and better resolution are both achieved, where these arise from zone compression and phase selectivity, respectively. However, since this mode of analysis is relatively new, it has yet to be tested for a wide range of applications such studies will be required to fully demonstrate its general utility. It is unclear whether this operational mode of selective MDGC constitutes a mode which is consistent with the definition of comprehensive... 

The flow of compressible and non-compressible liquids, gases, vapors, suspensions, slurries and many other fluid systems has received sufficient study to allow definite evaluation of conditions for a variety of process situations for Newtonian fluids. For the non-Newtonian fluids, considerable data is available. However, its correlation is not as broad in application, due to the significant influence of physical and rheological properties. This presentation is limited to Newtonian systems, except where noted. 

Soil specific weight is the measure of the concentration of packing of particles in a soil mass. It is also an index of compressibility. Less dense, or loosely packed, soils are much more compressible under loads. Soil specific weight may be expressed numerically as soil ratio and ptorosity (porosity for soils being basically the same definition as that for rocks discussed earlier in this section). Soil porosity e is... 

The compressive data are of limited design value. They can be used for comparative material evaluation and design purposes if the conditions of the test approximate those of the application. The data are of definite value for materials that fail in the compressive test by a shattering fracture. On the other hand, for those that do not fail in this manner, the compressive information is arbitrary and is determined by selecting a point of compressive deformation at which it is considered that a complete failure of the material has taken place. About 10% of deformation are viewed in most cases as maximum. 

Thus, from an investigation of the compressibility of a gas we can deduce the values of its critical constants. We observe that, according to van der Waals theory, liquid and gas are really two distant states on the same isotherm, and having therefore the same characteristic equation. Another theory supposes that each state has its own characteristic equation, with definite constants, which however vary with the temperature, so that both equations continuously coalesce at the critical point. The correlation of the liquid and gaseous states effected by van der Waals theory is, however, rightly regarded as one of the greatest achievements of molecular theory. 

Again, if we consider the initial substances in the state of liquids or solids, these will have a definite vapour pressure, and the free energy changes, i.e., the maximum work of an isothermal reaction between the condensed forms, may be calculated by supposing the requisite amounts drawn off in the form of saturated vapours, these expanded or compressed to the concentrations in the equilibrium box, passed into the latter, and the products then abstracted from the box, expanded to the concentrations of the saturated vapours, and finally condensed on the solids or liquids. Since the changes of volume of the condensed phases are negligibly small, the maximum work is again ... 

A system is the region in space that is the subject of the thermodynamic study. It can be as large or small, or as simple or complex, as we want it to be, but it must be carefully and consistently defined. Sometimes the system has definite and precise physical boundaries, such as a gas enclosed in a cylinder so that it can be compressed or expanded by a piston. However, it may be also something as diffuse as the gaseous atmosphere surrounding the earth. 

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