Cylinder, correlation

As a first approximation we postulate the existence of an equally sized hard core volume located in the center of each cylinder that defines the excluded volume per segment, according to the degree of interpenetration of neighboring cylinders. This simple construction includes complicated local intersegmental configurations, but it imposes a unique local orientation correlation of segments within the domains of a PE melt The shape of those impenetrable correlation cylinders is assumed also to be cylindrical. 

The essential step to simulate a realistic short range order region with our model is to occupy the local segment exclusion volume with the mean electronic density of the chain segments yielding the correlation cylinders introduced in Sect. 2. 

Fig. 15a. Definition of segmental end-to-end-vector (see text for details), b. Fit into correlation cylinder...

Fig. 16. Cylindrical symmetric electron densities for several numbers of CH2 units within the correlation cylinder...

Fig. 17. Square of the mean segment structure amplitude in the lateral direction for S CH2 units within the correlation cylinder. The structure amplitude drops off very quickly due to the strong electron delocalization...

In the case of the PE melt, the largest part of the configuration entropy is included in the variety of chain conformations. In our model of the PE melt, these chain conformations cause the diameter of the correlation cylinders in which the chain segments are embedded to fluctuate. This leads necessarily to distance fluctuations of next neighbor segments because of steric hindrance of the local segment exclusion volume. Therefore, the inter- and intramolecular distance correlations cannot be discussed independently. 

The distinction between machine conditions and fabricating variables is a necessary one to avoid mistakes in using cause-and-effect relationships to advantage. If the processing variables are properly defined and measured, not necessarily the machine settings, they can be correlated with the parts properties. For example, if one increases cylinder temperature, melt temperatures do not necessarily also increase. Melt temperature is also influenced by screw design, screw rotation rate, back pressure, and dwell times (see Chapter 7). It is much more accurate to measure melt temperature and correlate it with properties than to correlate cylinder settings with properties. 

For the case of flow past cylinders, such as a wet-bulb thermometer, Bedingfield and Drew [Ind. Eng. Chem., 42, 1164 (1950)] obtained a correlation for their data on siiblimation of cylinders into air and for the data of others on wet-bulb thermometers. For wet-bulb thermometers in air they give... 

Even the good heat transfer conditions turned out to be false, however, if the correlation derived for single cylinders by McAdams (1954) were extrapolated to Rep < 100. Nelson and Galloway (1975) pointed out that at low Reynolds numbers the real heat transfer coefficient could be four... 

A widely used correlation for heat transfer from a cylinder in a perpendicular flow is ... 

API Filtration. A filter press is used to determine the wall building characteristics of mud. The press consists of a cylindrical mud chamber made of materials resistant to strongly alkaline solutions. A filler paper is placed on the bottom of the chamber just above a suitable support. The filtration area is 7.1 ( 0.1) in.-. Below the support is a drain tube for discharging the filtrate into a graduate cylinder. The entire assembly is supported by a stand so that a 100-psi pressure can be applied to the mud sample in the chamber. At the end of the 30-min filtration time volume of filtrate is reported as API filtration in milliliters. To obtain correlative results, one thickness of the proper 9-cm filter paper, Whatman No. 50, S S No. 5765, or the equivalent, must be used. 

Cetane number is measured in a single-cylinder laboratory engine, but cetane index (Cl) is more commonly used. Cetane index is a calculated value and correlates adequately with the cetane number. Most refiners use the ASTM equation (Method D-976-80) to calculate the cetane index. The equation uses the 50% boiling point and API gravity (Example 6-1). 

The rotating disc and rotating cylinder have been successfully applied in the laboratory to study the effect of flow on corrosion rates and are much easier to use than actual pipelines and other real geometries. The results of these tests can now be correlated to geometries likely to be found in pipes, pumps, bends, etc. in plant by use of dimensionless group analysis. There-... 

Table 2.2 Correlation between rotating disc, rotating cylinder and smooth tubes...

Correlation of Cylinder Expansion Energy with Heat of Detonation... 

Available expin energy is then correlated with the kinetic energy of the metal cylinder. In Table 3 we see that relative cylinder expansion energies (from Ref 7) correlate fairly well with relative heats of detonation if the latter are taken on a per unit volume basis... 

The differential equation describing the temperature distribution as a function of time and space is subject to several constraints that control the final temperature function. Heat loss from the exterior of the barrel was by natural convection, so a heat transfer coefficient correlation (2) was used for convection from horizontal cylinders. The ends of the cylinder were assumed to be insulated. The equations describing these conditions are ... 

Similar correlations are available with regard to other physical situations such as fluid flow over a flat plate, a sphere or a cylinder. 

However, flow generated by a cylinder rotating at high speed was subsequently used by others, and in particular by King and co-workers (K3, K4a), to demonstrate that dissolution and electrochemical corrosion may both be transport limited. The dependence of the mass-transfer coefficient on the rotation rate and on the diffusivity of the dissolving species was established by correlation of experimental data (see Table VII, System 43). 

Equation (5b), in Table VII, established by Lin et al. (L9) for coaxial flow in annuli with k = 0.5, was originally taken by them to be a striking confirmation of the theoretically derived correlation, Eq. (27), with 0=1. The latter condition, however, corresponds only to the limiting case of Eq. (27), at /c->0, that is, mass transfer to the wall of an outer cylinder, without an inner cylinder present. On these grounds, and because of other experimental conditions, the correlation of Lin et al. (L9) was criticized by Friend and Metzner (F9), who calculated that the constant in Eq. (5b) of... 

Free convection flow around horizontal cylinders and spheres is laminar for moderate values of GrSc (see Table VII, Part C) mass-transfer rates obey correlations of the same type as that for a vertical plate electrode, Eq. (29a) ... 

Rao et al. (R5) and Raju et al. (R2) also investigated mass transfer at vibrating electrodes for low vibration frequencies (higher frequencies would cause cavitation). Mass transfer follows a laminar-type correlation both for a transverse vibration of a vertical cylinder and for a vertical plate vibrating parallel to the face. In the case of the plate, the Reynolds number is based on width, indicating the predominance of form drag. When vibrations take place perpendicular to the thickness, skin friction predominates and the Reynolds number is then preferably based on the equivalent diameter (total surface area divided by transverse perimeter). 

Figure 8.32. PEE 1000/43 at e = 0.88. CDF z(r). The domain peaks are pointing upwards (h) cylinder-height peaks (d) cylinder-diameter peaks (c) inter-domain correlation peaks. Displayed region r 2, D <40 nm... 

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