Similarity principle

The hemispherical analyser shown in Figure 8.5(d) works on a similar principle buf has fhe advanfage of collecting more phofoelecfrons. An analyser consisting of two concentric plates which are parts of hemispheres, so-called spherical sector plates, is often used in a spectiomefer which operafes for bofh UPS and XPS. 

Another advantage of PC technology is the plaimed and partially realized use of multiftmction drives for operation of either CD-ROM, WORM, or PC-R disks alternatively in the same disk drive. This is technically feasible, since for reading (in CD-ROM, WORM, PC-R) as well as for writing (WORM, PC-R) similar principles and hardware are used (108). However, the reflectivity change of PC disks (40/70%) is in general lower than the CD-ROM standard (30/70%) requires. 

These reactors all work on very similar principles and will be discussed based on the example of the Berty reactor, of which more than 500 are in operation around the world. The Berty reactor shown in Figure 2.4.3 a has much empty volume and is laborious to open and close. Another version of the Berty reactor (made by Basic Technology, Inc.) is shown in Figure 2.4.3 b. This 2-inch model was developed for quick exploratory studies on small samples of catalysts. The maximum catalyst sample volume is 15... 

Physical modeling involves searching for the same or nearly the same similarity criteria for the model and the real process. The full-scale process is modeled on an increasing scale with the principal linear dimensions scaled-up in proportion, based on the similarity principle. For relatively simple systems, the similarity criteria and physical modeling are acceptable because the number of criteria involved is limited. For complex systems and processes involving a complex system of equations, a large set of similarity criteria is required, which are not simultaneously compatible and, as a consequence, cannot be realized. 

Using Similarity Principles in Planning Experiments 1193 References 1195... 

Similarity principles for a physical process can either be derived from an assumption of the number of physical parameters involved (Buckingham s... 

The next step toward the similarity principles is to develop the governing equations in a nondimensional form. The equations are normalized by first defining the dimensionless, independent variables as... 

It is difficult to obtain the correct temperature boundary conditions in a model. Radiation between surfaces in a room and conduction throu the surfaces are important for the level of the surface temperature T, x,y,z). It is difficult to establish the similarity principles based on radiation and conduction. A practical method is to estimate the influence of radiation and conduction and include this level in the boundary values of the model. In this way it... 

It is useful to take similarity principles and dimensionless numbers into consideration when planning experiments. Experiments may involve different levels of velocities and temperature differences. It is important to select values that give a large variation of Archimedes number (12,56) to obtain a high possibility of large physical effects in the measurements. 

Figure 12.42 shows another example of the use of similarity principles in experiments. The temperature effectiveness ej is measured in a room ventilated by displacement ventilation. The measurements are made at different flow rates to the room, at different loads (from 100 W to 500 W) and by... 

This section describes how this set of equations can be solved analytically by the introduction of various simplifications. First, gas dynamics is linearized, thus permitting an acoustic approach. Next, a class of solutions based on the similarity principle is presented. The simplest and most tractable results are obtained from the most extensive simplifications. 

Similar principles apply to ortho- and para-deuterium except that, as the nuclear spin quantum number of the deuteron is 1 rather than as for the proton, the system is described by Bose-Einstein statistics rather than the more familiar Eermi-Dirac statistics. Eor this reason, the stable low-temperature form is orriio-deuterium and at high temperatures the statistical weights are 6 ortho 3 para leading to an upper equilibrium concentration of 33.3% para-deuterium above about 190K as shown in Eig. 3.1. Tritium (spin 5) resembles H2 rather than D2. 

The most common of the organizations operating in today s industrial scene is the joint stock company with limited liability. In different countries there exist variants of this format, but there is a wide spread of organizations based upon broadly similar principles. 

Thus, effectiveness of basic (alkaline) additives has been greatly improved by increasing their solubility in base stocks, by exploiting synergistic action between two similar additive types and by the use of a third additive to enhance (catalyse) the performance of the other two. Similar principles have been used to augment the performance of oxidation inhibitors. 

A variety of chromatographic techniques are now in common use, all of which work on a similar principle. The mixture to be separated is dissolved in a solvent, called the mobile phase, and passed over an adsorbent material, called the stationary phase. Because different compounds adsorb to the stationary phase to different extents, they migrate along the phase at different rates and are separated as they emerge (elute) from the end of the chromatography column. 

A less accurate but more colorful way to measure pH uses a universal indicator, which is a mixture of acid-base indicators that shows changes in color at different pH values (Figure 13.5, p. 359). A similar principle is used with pH paper. Strips of this paper are coated with a mixture of pH-sensitive dyes these strips are widely used to test the pH of biological fluids,... 

Exchange of organic ions. Although similar principles apply to the exchange of organic ions, the following features must also be taken into consideratioa... 

Figure 3. Alfred Mayer s experiments with magnets floating in water (illustrated in one of his publications with this sketch) were the template J. J. Thomson used to develop hi9 first electron configurations (see Figure 4. Mayer found that the magnets adopted different patterns depending on the number introduced, leading Thomson to suspect that similar principles would pertain to electron configurations.

Fixed Water Level, Submerged Electrode Boilers These boilers operate on a similar principle to the HW boilers, except that the vessel is not flooded but held to a fixed water level. Steam is produced in the space between the electrodes and neutral and escapes at the waterline. 

With ft2 and ft3 known, k could thus be determined. In a related example, a number of reactions of alkyl radicals (CH, C2H, etc.) have been studied by the application of similar principles. An intensely colored probe that reacts with R was added with (or without) the substrate of interest. The probe is a species like the methyl viologen radical ion, MV,+. If S represents the substrate, the scheme is... 

Rings with more than two differently substituted carbons can be dealt with on similar principles. In some cases, it is not easy to tell the number of isomers by inspection. The best method for the student is to count the number n of differently substituted carbons (these will usually be asymmetric, but not always, e.g., in 68) and then to draw 2" structures, crossing out those that can be superimposed on others (usually the easiest method is to look for a plane of symmetry). By this means, it can be determined that for 1,2,3-cyclohexanetriol there are two meso compounds and a dl pair and for 1,2,3,4,5,6-hexachlorocyclohexane there are seven meso compounds and a dl pair. The drawing of these structures is left as an exercise for the student. 

Similar principles apply to heterocyelie rings as long as there are carbons (or other ring atoms) containing two different groups. 

Similar principles apply to the actinides. The -i-2 oxidation state is present in dipositive aqueous ions and alkaline earth-like dihalides. In the first half of the... 

Tape >System of Analysis. A tape system which is used widely for analysis in the Pediatric Laboratory is a system whose principle was developed by the author. A reagent is placed on a paper tape. The paper is covered with a membrane, such as cellophane, cellulose nitrate or cellulose acetate, porous to low molecular weight substances. Finally, the serum is placed above the porous membrane, so that diffusion of the components of serum take place and a stain is produced on the paper (60). This principle has been incorporated for example, with glucose oxidase, in the conmercially available Dextro-Sticks. In addition, a similar principle is being applied by some for the analysis of components in urine (Ames Co., South Bend, Indiana). 

Thin films of ternary cadmium sulfoselenide CdS Sei-x have been electrodeposited from a non-aqueous organic bath by Baranski et al. [67], as well as by Loutfy and Ng [121], who employed similar principles (deposition from ethylene glycol solution... 

S.3.2.3. Scale-up based on similarity principles scale-up correlations... 

Melamine resins [1617] and phenol-formaldehyde resins [1620] can be gelled in situ to reduce the permeability. Various classes of polymers can be gelled by similar principles [882]. 

Controlled contact between two immiscible liquids has also been achieved by flowing one liquid along a solid support submerged in the second phase [28,29]. Several different arrangements have been used, although all are based on similar principles. For example, a wetted wall column which offered liquid-liquid contact times of 0.5-10 s was used to measure solute transfer rates [29]. 

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