Thick cylinders

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). 

These are the fundamental equations for the design of thick cylinders and are often referred to as Lame s equations, as they were first derived by Lame and Clapeyron (1833). The constants A and B are determined from the boundary conditions for the particular loading condition. 

Figure 13-4. The crystal structure of 1ZB6 colored by B-factor values. The color scale (from blue to white to red) used has a range from 23.0 to 67.0 A2. 1,6-DHN is shown with thick cylinders with an average...

Fig. 1.5 Acetone in water. The QM region is shown as thick cylinders, the MM region as thin sticks.

In the following discussion, cylinders are characterized by the length/diameter ratio E and Re is based on the cylinder diameter. As noted in Section II, drag on a disk in steady free motion is relatively insensitive to its thickness cylinders... 

As established by Knoll et al. [49, 62], exposing thin films to well-controlled vapor pressure with a subsequent fast quench provides reproducible phase behavior under variation of the film thickness and of the polymer volume fraction (Fig. 15). At favored film thicknesses, cylinders orient parallel to the film plane, whereas a perpendicular orientation dominates at intermediate film thicknesses. In films thinner than 1.5 nm domain spacings and at high polymer concentration, the cylindrical... 

Figure 13.43. Thick cylinder multiplying out taking the limit gives ...

ABSTRACT The radiative pyrolysis of wood (thick cylinders and chip beds) has been investigated experimentally for external radiative heat fluxes in the range 28-80kW/m, resulting in maximum sample temperatures of 600-950K. Radial temperature profiles, product yields and composition, and devolatilization rates have been measured. The influences of wood variety (hardwoods and softwoods) on the pyrolysis characteristics are discussed and comparisons are made with biomass (agricultural residues). 

In this study results of an extensive experimental activity are presented on the pyrolysis of wood (chips and thick cylinders) for a wide range of external beating conditions and several varieties, namely, two bard-woods (beech, chestnut) and three soft-woods (Douglas fir, redwood and pine). 

Figure 22. Crystal structures of cyc/o(L-Pro-L-Pro-L-Phe-/3-HGly-/ HGly)215 showing H-bond patterns and another cyclopentapeptide.220 The /3-peptide segments involved in S(13)S(10) and S(12)S(10) transannular H-bonds are rendered as thick cylinders. Newman projections about the Ca—Cp bonds of the (t amino acid residues show a sc conformational preference.

Figure 24. Crystal structure of the linear tripeptide f-Boc-Aib-Aib-/3-HGly-NHMe (where Aib is a-aminoisobutyric acid).224 The S(ll) H bond segment is rendered in thick cylinders. The sc dihedral angle about the Ca—Cp bond of the /3-peptide residue is also indicated.

Figure 25. Crystal structure of the /3-tripeptide t Boc/ 3-HVal-/33 IIAla fp IILeuOMe (3) reported by Seebach223 showing an intrinsic preference for a turned conformation. Two of the /3-peptide residues are rendered as thick cylinders. The Newman protections about the Ca—Cp bonds for these residues are shown, indicating the apparent preference of the /33 substituted residue bearing the bulky substituents to adopt a sc conformation while the residue with the smaller methyl substituents takes on an ap conformation.

Figure 26. Nearest-neighbor H-bonds observed in ( peptides synthesized from l-(aminomethyl)cyclopropanecarboxylic acids.226 This S(8) pattern is an example of residue-induced turn formation, resulting from the dihedral and bond angle constraints introduced into the ft2-2 backbone by the cyclopropyl substituents. The crystal structures show a dipeptide and tripeptide in which the S(8) H-bond segments are rendered in thick cylinders. For the dipeptide, Newman projections are shown looking down the Ca—Cp bond and the C(O)—Ca bond.

Figure 27. Side and top views of ca. one turn of the 14-helix extracted from the crystal structure of Gellman s trans-ACffC hexamer.239 A single S(14) H-bond circuit in the peptide backbone has been rendered as thick cylinders. Additionally, one residue has been rendered as a space filling model to provide a frame of reference between the two views and to more clearly show the spatial relationship between cyclohexyl groups.

Cavitation corrosion of cylinder liners is not caused by high velocity water flow, nor by impingement of coolant streams. Rather, it appears that vibratory effects are primarily responsible. Under the tremendous stresses of fuel compression and combustion in the Diesel cycle, these 3/4 inch thick cylinder liners vibrate or "ring" at frequencies estimated to be in the range of 7,000 to 8,000 cycles per second, and higher. 

The electrical resistance of the composite was measured on an l-mm (eight layers of fiber yarn)-thick cylinder ( 6.5 cm long) mounted on Micarta. The resistance was measured transverse to the winding direction by attaching two copper plates to either end of the cylinder. 

The later form of the Clanny lamp (see p. 64) had a cylinder of gauze of 1296 meshes to the sq. in. at the top and below this a thick cylinder of annealed glass surrounding the flame, so that the lamp gave a better light than Davy s. The air supporting the combustion passed through the meshes down upon the flame. ... 

If sd(S ) is nonorientable, then it is clear from the preceding consideration that instead of a thick cylinder (a full torus) a thick Mobius strip is glued. This completes the proof of the lemma. 

A thick cylinder has an inside diameter of 300 mm and an outside diameter of 450 mm. If the allowable stress is 175 MPa, what is the maximum internal pressure that can be applied ... 

For problem 4, what is the required thickness if thick cylinder equations were used ... 

The formulae given by Timoshenko (Trans. Royal. Society Series A, volume 221, p. 267, 1921) gives the maximum stress (of point B due to an internal pressure in a thick cylinder with an eccentric bore.)... 

The vessel is assumed to consist of a long thick cylinder. 

The penetration velocity of a 1.3 cm diameter steel ball moving at various velocities and impacting a 2.5 cm thick cylinder of PBX-9404 or Composition B was reported by Rice. The data were generated at Ballistic Research Laboratory by R. Frey. Experimental data and Eulerian calculations by Rice indicated that the penetration velocity was markedly decreased, beyond the critical projectile velocity for initiation of detonation, and was signiflcantly less (less than half) than predicted by the ideal model. 

Rice reported Frey s data for the penetration velocity of a steel ball, 1.3 cm in diameter, moving at varying speeds and striking 2.5 cm thick cylinders of either PBX-9404 or Composition B. 

Figure 5.4 Stress distribution in a thick cylinder due to internal pressure.

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