Parallel cylinders

Usually this would be handled in two parallel cylinders. 

A single cylinder will do this capacity however, usually it can be handled in two parallel cylinders for... 

By examining the curve for the initial compression with no unloaders, it shows that the horsepower requirement crosses the +3% overload line about one-third of the way through the suction pressure range. Figure 12-32 shows the effect of adding first one unloader and then a second one. The simplest way to handle this is a head-end unloader on each of the two parallel cylinders. 

Example 13-1. Surge Drums and Piping for Double-Acting, Parallel Cylinder, Compressor Installation... 

Shapes of pores have a great effect on diffusion through them. They are greatly varied and usually cannot be observed directly for commercial materials. For theoretical comparisons they may be assumed parallel cylinders of some mean diameter. Diffusion experments also have been performed with parallel small capillaries. 

The first phenomenon, to be discussed in 2.2, concerns the saturation of the force of repulsion between two symmetrically charged bodies (particles) in an electrolyte solution as their charge increases. This effect is a direct consequence of the saturation of the electric field at a finite distance from the surfaces of the bodies and of the field properties at infinity. In the one-dimensional case (for parallel plates) the relevant features follow from a direct computation (see, e.g., [9]). In 2.2 the corresponding effect will be discussed for parallel cylinders and spheres [10]. 

This result, which in the one-dimensional case (for parallel plates) follows from a direct computation (e.g., [9]), is shown below (Proposition 2.1), for parallel cylinders and for spheres. 

Saturation of the force of repulsion between two symmetrically charged parallel cylinders in an electrolyte solution. In... 

In an attempt to clarify matters further by studying a specific example, let us evaluate the total force, acting per unit length of two parallel cylinders of radius R, symmetrically charged to a positive surface potential and... 

For many applications the wetting behavior of a network of fibres is important. An example is the water repellent ability of clothing. As a simple model we consider a bundle of parallel cylinders which are separated by a certain spacing. This spacing is assumed to be small compared to the capillary constant, so that the shape of the liquid surface is assumed to be determined only by the Laplace equation. Practically, this leads to cylindrical liquid surfaces. 

Dimensionally intermediate between spheres and planes, the interactions of cylinders reveal properties possessed by neither. In particular, there is always torque as well as force the energy of interaction depends not only on separation zbut also on mutual angle 0. For parallel cylinders of length indefinite compared with thickness and separation, the interaction is expressed as force or energy per unit length. As with spheres, there are few exact expressions for cylinder-cylinder van der Waals forces. The many approximate expressions must be used circumspectly (see Fig. LI.50). 

In the limit in which the dielectric responses of cylinder and medium do not greatly differ, with the neglect of retardation, at separations large compared with thickness, the interaction of parallel cylinders goes as the inverse-fifth power of the interaxial separation z Ri, R2 (see Table C.3.b.2) ... 

Table C.l. Parallel cylinders at separations small compared with radius, Derjaguin transform from full Lifshitz result, including retardation...

C.3.a. Two parallel cylinders, retardation screening neglected, solved by multiple reflection... 

Source Taken from D. Langbein, Phys. Kondens. Mat., 15, 61-86(1972) [Eqs. (41), p. 71, and Table 2, p. 79] for the energy of interaction between two parallel cylinders of length L much greater than their radii and separation. The expression given on p. 79 apparently lacked a factor tt in the denominator and should have read... 

In this summation then K1q is replaced with 4jrkT52n=o (ArmA2m), and the energy E12 is seen as a work or free energy of interaction between parallel cylinders GC C ... 

C.3.b. Two parallel cylinders, pairwise-summation approximation, Hamaker-Lifshitz hybrid, retardation screening neglected C.3.b.l. All separations... 

This is identical to the result [G(z a)]/a for a 00 just above and similar in form to the Lifshitz result for two like parallel cylinders of radius R, Table C.4.a. The 1/r6 integrations are taken from A. G. DeRocco and W. G. Hoover, "On the interaction of colloidal particles," Proc. Natl. Acad. Sci. USA, 46, 1057-1065 (1960). 

The integrahon over oppositely curved cylindrical surfaces is the energy of interaction GpP(h) per unit area between planes, weighted here by Ri d0, where 02 can be written as though going over an infinite range from —00 to +00. The energy of interaction between parallel cylinders becomes... 

Problem Pr.4 Try something harder than spheres. Consider parallel cylinders of radius R, fixed length L, and surface separation Z. Use the tabulated energy per unit length... 

C.2.b. Free energy per interaction C.2.c. Nonretarded (infinite light velocity) limit C.2.d. Light velocities taken everywhere equal to that in the medium, small Aji, Aji, q = 1 C.2.e. Hamaker-Lifshitz hybrid form C.3. Two parallel cylinders... 

Figure 2 shows a topological plot of the electrostatic potential, if/, outside and adjacent to three neighboring parallel cylinders as obtained by the BEM. These calculations were performed on a PC. 

The model consisted of a regular arrangement of three sets of parallel cylinders, each set being orthogonal to the other two (10). 

Figure 10 (a) Equipotential and current lines for two parallel cylinders in the primary... 

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