Thick walled cylinders

Thick film technology Thick-walled cylinders Thielavia basicola Thiele-Geddes model Thiele modulus Thiele s hydrocarbon... 

Design of thick-walled cylinders, Design of removable closures, Manufacture of pressure vessels. Manufacture of tubing. 

Partially Plastic Thick-Walled Cylinders. As the internal pressure is increased above the yield pressure, P, plastic deformation penetrates the wad of the cylinder so that the inner layers are stressed plasticady while the outer ones remain elastic. A rigorous analysis of the stresses and strains in a partiady plastic thick-waded cylinder made of a material which work hardens is very compHcated. However, if it is assumed that the material yields at a constant value of the yield shear stress (Fig. 4a), that the elastic—plastic boundary is cylindrical and concentric with the bore of the cylinder (Fig. 4b), and that the axial stress is the mean of the tangential and radial stresses, then it may be shown (10) that the internal pressure, needed to take the boundary to any radius r such that is given by... 

Bursting tests have been carried out on neatly a hundred thick-walled cylinders made of carbon, low alloy, and stainless steels, together with some nonferrous materials. The diameter ratio of the cylinders varied from 1.75 to 5.86, and some tests were carried out at 660°C. An analysis of the results (19) showed that 90% of the cylinders burst within 15% of the value given by equation 17. 

Eig. 7. Pressure expansion curve of a thick-walled cylinder undergoing autofrettage (22). 

Creep of Thick-walled Cylinders. The design of relatively thick-walled pressure vessels for operation at elevated temperatures where creep caimot be ignored is of interest to the oil, chemical, and power industries. In steam power plants, pressures of 35 MPa (5000 psi) and 650°C are used. Quart2 crystals are grown hydrothermaHy, using a batch process, in vessels operating at a temperature of 340—400°C and a pressure of 170 MPa (25,000 psi). In general, in the chemical industry creep is not a problem provided the wall temperature of vessels made of Ni—Cr—Mo steel is below 350°C. 

This formula is not intended for thick-wall cylinders, and for its limitations the appropriate sections of Code B.31 must be consulted. 

The nylon ring may be considered as a thick wall cylinder subjected to this internal pressure (see Appendix D). At the inner surface of the ring there will be a hoop stress, <7, and a radial stress, Cr. Benham et al. shows these to be... 

Treating the bush as a thick wall cylinder subjected to this value of external pressure, then Benham et at. show that at the outer surface of the bush, the stresses are ... 

If the acetal ring is considered as a thick wall cylinder, then at the inner surface there will be hoop stresses and radial stresses if it is constrained in a uniform manner ... 

For a thick-walled cylinder, the rate of conduction of heat through lagging is given by equation 9.21 ... 

Now most of /2E data that are based on cylinder expansion velocities (Table 4) are derived from LRL measurements of velocities that appear to approach an asymptote at about seven-fold cylinder expansion. Hershkowitz Rigdon (Ref 15) used larger cylinders than LRL and obtained velocity measurements of up to 10- to 13-fold expansions. Comparison of these velocities with those obtained for approximately 7-fold expansion is as follows for Comp B, vt 0/v7 = 1.029 for thick-walled cylinders and 1.027 for thin-walled cylinders for 40/40/20 RDX/TNT/AN, v10/v7 = 1.025 for thick-walled cylinders and 1.023 for thin-walled cylinders and for 20/40/40 RDX/TNT/AN, v10/v7 = 1.030 for thick-walled cylinders and 1.022 for thin-walled cylinders... 

Figure 1.4-10. Stresses in an autofrettaged thick-walled cylinder (plastification 50% through the wall)...

The generation of benefitial residual prestresses for larger thick-walled cylinders can be achieved easier by wrapping with welding, shrink-fitting or coiling many thin layers or winding strips onto a core tube, which can be corrosion resistant whereas the other layers stay totally apart from any contact with the fluids involved. 

Fig. 4.3-4. Stresses in shrunk thick-walled cylinders (schematically).

The calculation of multilayer thick-walled cylinders is still a matter of experience and the control of the production method [2][3][5][8][9] applied. 

If the pressure in a thick-walled cylinder is raised beyond the yield pressure pei according to the equation (9), the yield will spread through the wall until it reaches the outer diameter [10]. For a perfectly elastic-plastic material the ultimate pressure for complete plastic deformation of the thick wall pCOmpi-pi, also called collapse pressure, can be calculated by equation (4.3-10). As the ductile materials used for high pressure equipment generally demonstrate strain... 

As a final result of the explanations about strengthening measures the admissible static internal pressure for thick-walled cylinders is compared in Fig. 4.3-7 for different design strategies according to the equations (4.3-9), (4.3-10), (4.3-12) and (4.3-13) and the explained assumptions and optimisations. In the case of the monobloc (A), the two-piece shrink fit and the autofrettaged cylinders the maximum stress at the inner diameter stays within the elastic limit (00.2). Comparatively much larger is the admissible pressure when complete plastic yielding occurs as shown for the collapse pressure (pCOmpi pi. = Pcoii D). 

A number of formulas have been developed for calculating the stress in thick walled cylinders due to internal pressure. From Barlow s formula ... 

Flow of heat through thick-walled cylinder. 

Equation (10.12) can be used to calculate the flow of heat through a thick-walled cylinder. It can be put in a more convenient form by expressing the rate of flow of heat as... 

Derive the equation for steady-state heat transfer through a spherical shell of inner radius and outer radius rj. Arrange the result for easy comparison with the solution for a thick-walled cylinder. 

In 1995 the structure of the LH2 complex from Rps. acidophila was determined by X-ray crystallography (McDermott et al., 1995 Prince et al., 1996) to a resolution of 2.5A. This has now been improved to 2A (Prince, Howard and Papiz, unpublished). The overall structure is an nonamer and is rather like a thick-walled cylinder (Fig. 3). The central transmembrane helices of the a-apoproteins are closely packed, side-by-side, and form the inner wall of the cylinder with a radius of 14A. The nine transmembrane helices of the /3-apoproteins are arranged radially around the a-apoproteins to form the outer wall with a radius of 34A. The a-apoprotein hehces lie nearly perpendicular to the presumed membrane plane whereas the /3-apoprotein helices are more inclined at an angle of -15° to the normal to the membrane plane. The structure is closed off or capped , top and bottom by the N- and C- termini folding over and interacting with each other. All of the pigments are housed within these two rings of apoproteins. 

Much information is available on the deformation and fatigue behavior of simple thick-walled cylinders [10-17], but it must be remembered that most process reactors will not be a simple hollow cylinder. Components such as connectors, threads and sleeves, windows, and removable closures make a complete analytical solution for a high-pressure system design problem quite involved. Useful design criteria for thick-walled vessels can be derived, however, under the assumption that the material of which the vessel is made is isotropic and that the cylinder is long (more than five diameters) and initially free from stress. The radial and tangential stresses in the walls are then only functions of the radius coordinate (r) and the internal pressure. Given the outer-to-inner wall radius ratio as o/i = w, and the yield point (To) of the material, the yield pressure (py) is... 

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