Standard radii

It is convenient to give Eg a value (n g = 0.262) such as to make F(p) equal to unity for p = 0.75 this causes Rq to be equal to the sum of the standard radii of cation and anion for crystals with this radius ratio, which was selected as standard in Section 13-2 because it is ap-... 

The standard radii and r for the ions have the same values as the corresponding crystal radii (to within 0.008 A) except for F and Cs+, which show somewhat larger deviations, —0.019 and —0.034 A, re-... 

It is possible to extend the treatment of this section, based on Equation 13-9, to crystals other than the alkali halogenides, with suitable choice of standard radii. It is found that the standard radii differ somewhat in general from the univalent radii of Table 13-3, because of the different choice of values of n. An approximate value for the standard radius of a multivalent ion can be obtained by multiplying its crystal radius by z f z being the magnitude of the valence of the ion this is the correction factor from crystal radius to univalent radius qorresponding to n = 9. 

Example 8 Compressible Flow with Friction Losses Calculate the discharge rate of air to the atmosphere from a reservoir at 10 Pa gauge and 20 G through 10 m of straight 2-in Schedule 40 steel pipe (inside diameter = 0.0525 m), and 3 standard radius, flanged 90 elhows. Assume 0.5 velocity heads lost for the elhows. 

It is necessary to modify the edge of the hole in various ways to reduce these stress concentrations. Some methods of modification are priming, plunging, and standard radiusing and polishing methods. In the Dry Low NOx Combustors, especially in the lean pre-mix chambers, pressure fluctuations can set up very high vibrations, which lead to major failures. 

The commonly used values for ionic radii are based on an arbitrarily assigned standard radius for a certain ion. In this way, a consistent set of radii for other ions can be... 

Take as equivalent pipe diameters. All bends will be taken as 90° standard radius elbow. Line to pump suction ... 

The distillation column operates at a pressure of 500 mmHg (500 mm of mercury, absolute). The feed point to the column is 12 m above the base of the tank. The tank and column are connected by a 50 mm internal diameter commercial steel pipe, 200 m long. The pipe run from the tank to the column contains the following valves and fittings 20 standard radius 90° elbows two gate valves to isolate the pump (operated fully open) an orifice plate and a flow-control valve. 

Equation 14.11 introduces the notion of radius of influence, which is one of the important design parameters of S VE systems. Theoretically, the maximum radius of influence of a well is the distance at which the pressure becomes equal to the ambient atmospheric pressure, i.e., P = Patm. In practice, Pj is determined as the distance at which a sufficient level of vacuum still exists to induce airflow, e.g., 1% of the vacuum in the extraction well.912 The extraction wells are usually constructed using pipes with a standard radius, e.g., Pw = 5.1 cm (2 in.) or 10.2 cm (4 in.), and the vacuum applied in the wells typically ranges from 0.05 to 0.15 atm, i.e., Pw = 0.95-0.85 atm.9 12 If the vacuum required in the radius of influence is 1% of the vacuum in the extraction well, the... 

The pressure loss through the bends and check valves can be included in the line pressure-loss calculations as an equivalent length of pipe . The equivalent-length recommendations are taken from Ref. P1 (p.164). All the bends are assumed to be 90 elbows of standard radius, and the isolation valves as plug-type valves. 

Tlie losses from Table 6-4 in terms of velocity heads K are K = 0.5 for the sudden contraction andX= 0.52 for the butterfly valve. For the 90° standard radius (r/D = 1), the table gives K = 0.75. Tire method of Eq. (6-94), using Fig. 6-14, gives... 

Already in a relatively early study, Evans [121] had concerned himself with the theoretical treatment of the diffusion process, according to which an injected dye is uniformly mixed in a turbulent pipe flow. He calculated the courses of the standardized concentration c/cg (cg is the average concentration after molecular mixing) over the standardized radius r/R for a uniform and for a parabolic distribution of diffusion coefficients and compared them with the measured concentration profiles at various distances along the mixing length... 

As mentioned above, X-ray structures only give a precise knowledge of the distances between the atoms. While this is not so important for pure metals, as the interatomic distance is simply divided by two to obtain the metallic radius, this simple method will not work for ionic compounds. To begin, it is assumed that the individual ions are spherical and in contact. The strategy then used to derive ionic radii is to take the radius of one commonly occurring ion, such as the oxide ion, O2-, as a standard. Other consistent radii can then be derived by subtracting the standard radius from measured inter-ionic distances. 

Example 5-3 Consider the conditions of Example 4-3 for the transport of coal. The pressure drop per unit length is given as 113.7 N/m /m. Assume that a system has 15.24 m of vertical length and ten 90° elbows of standard radius and gate valve in the open position. Estimate the total pressure drop for the system using the design suggestion procedures. 

Thus, as pointed out by Cohan who first suggested this model, condensation and evaporation occur at difi erent relative pressures and there is hysteresis. The value of r calculated by the standard Kelvin equation (3.20) for a given uptake, will be equal to the core radius r,. if the desorption branch of the hysteresis loop is used, but equal to twice the core radius if the adsorption branch is used. The two values of should, of course, be the same in practice this is rarely found to be so. 

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