Thin cylinders

In the Audibert-Amu dilatometer test (91), a thin cylinder of compressed powdered coal contacting a steel piston is heated at a rate not over 5°C/min. The piston movement is used to calculate the percent dilation. 

Hence for good separation, R must be kept small as possible (thin cylinder) in order that high speeds may be used, but this inevitably induces a cost penalty (area volume). 

Some consideration is also given to particles of other shapes (for example, long, thin cylinders), but the mathematics becomes complex and no detailed analysis will be given. 

The pipe wall thickness is selected to resist the internal pressure, with an allowance for corrosion. Processes pipes can normally be considered as thin cylinders only high-pressure pipes, such as high-pressure steam lines, are likely to be classified as thick cylinders and must be given special consideration (see Chapter 13). 

Pipes are often specified by a schedule number (based on the thin cylinder formula). The schedule number is defined by ... 

The minimum wall thickness required to resist the hydrostatic pressure can be calculated from the equations for the membrane stresses in thin cylinders (Section 13.3.4) ... 

The initiation system consists of a nitrogen laser and the necessary optics to lead the beam to the sample cell. The laser emits pulses at 337.1 nm with 800 ps duration, with a typical repetition rate of less than 5 Hz. The optical components, aligned between the laser and the calorimetric cell, consist of an iris (I), a support for neutral density filters (F), and a collimating lens (L). The iris is used to cut out most of the laser output and allow only a thin cylinder of light to pass through its aperture, set to 2 mm. The laser energy that reaches the cell is further... 

Figure 8.7 Stresses in a thin cylinder snbjected to an internal pressure, P (a) cylindrical shell nnder internal flnid pressure (b) longitudinal stress development (c) hoop stress development. Reprinted, by permission, from G. Lewis, Selection of Engineering Materials, p. 139. Copyright 1990 by Prentice-Hill, Inc.

We should point out that Eqs. (6.2) and (6.3) are only valid for a spherically symmetric gel. In the case of gels having different kind of shape, such as a thin cylinder or a thin disk, the equation has to be modified. The fact that the... 

The wear of the pins on the glass disk was observed with an optical microscope. The worn end of the pin was covered with material from the elastomeric domains. As the tests proceeded, the elastomer appeared to be rolled into thin cylinders oriented perpendicular to the sliding direction. 

Below, I will first describe the observation on thin cylinders because the phase coexistence can most clearly be observed in these samples and, moreover, samples of this shape are most frequently used in various experiments. The results of the observation are depicted schematically in Fig. 12. As the temperature was increased from the swollen phase, the sample gradually shrunk following the swelling curve (Fig. 7) and the onset of the transition region was manifested by the appearance of a nucleus of the high-temperature (shrunken) phase at the end of the cylinder. We denote this temperature as Tt. As long as... 

By virtue of simplifications similar to those permitted in formulating point-particle interactions, many results can be derived for the interaction of thin cylinders. It is even possible to include the anisotropy of material within the rod, for example putting ecl and eC for the dielectric response perpendicular and parallel to the rod axis. There are then two kinds of A s [see Table C.4 and Eqs. (L2.224)] ... 

Just as a charged sphere in saltwater surrounds itself with a number of mobile ions different from what would occupy the same region in its absence, so does a charged cylinder. As with spheres, there are low-frequency ionic fluctuations that create attractive forces between like cylinders. In the special case of thin cylinders whose material dielectric response is the same as that of the medium and the distance between cylinders is small compared with the Debye screening length, this ionic-fluctuation force has appealing limiting forms. 

P.lO.c.3. Thin cylinder in a concentric large cylinder, special case R < R2... 

Table C.5.b. Thin cylinders in saltwater, parallel and at an angle, ionic fluctuations...

DIPOLAR FLUCTUATION FORCES BETWEEN THIN CYLINDERS... 

C.5.a. Thin dielectric cylinders in saltwater, parallel and at an angle, low-frequency (n = 0) dipolar and ionic fluctuations C.5.a.l. Parallel, center-to-center separation z C.5.a.2. At an angle 0 with minimum center-to-center separation z C.5.b. Thin cylinders in saltwater, parallel and at an angle, ionic fluctuations, at separations S> Debye length C.5.b.l. Parallel... 

The Stokes diameter of a solid cylinder, diameter d, depends upon its orientation. When the aspect ratio (length/diameter) fl is large the effective Stokes diameter of a long thin cylinder flowing with its major axis parallel to the lines of flow is [7] ... 

---