Cylindrical Shell

Two types of process vessel are likely to be subjected to external pressure those operated under vacuum, where the maximum pressure will be 1 bar (atm) and jacketed vessels, where the inner vessel will be under the jacket pressure. For jacketed vessels, the maximum pressure difference should be taken as the full jacket pressure, as a situation may arise in which the pressure in the inner vessel is lost. Thin-walled vessels subject to external pressure are liable to failure through elastic instability (buckling) and it is this mode of failure that determines the wall thickness required. 

For an open-ended cylinder, the critical pressure to cause buckling Pc is given by the following expression see Windenburg and Trilling (1934)  

For long tubes and cylindrical vessels this expression can be simplified by neglecting terms with the group (2L/nDo)2 in the denominator the equation then becomes  

The minimum value of the critical pressure will occur when the number of lobes is 2, and substituting this value into equation 13.49 gives  

For most pressure-vessel materials Poisson s ratio can be taken as 0.3 substituting this in equation 13.50 gives  

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A fluid of viscosity 17 is confined within the gap between two concentric cylinders as shown in Fig. 2.3b. Consider a cylindrical shell of radius r, length 1, and thickness dr located within that gap. 

Figure 9.5a shows a portion of a cylindrical capillary of radius R and length 1. We measure the general distance from the center axis of the liquid in the capillary in terms of the variable r and consider specifically the cylindrical shell of thickness dr designated by the broken line in Fig. 9.5a. In general, gravitational, pressure, and viscous forces act on such a volume element, with the viscous forces depending on the velocity gradient in the liquid. Our first task, then, is to examine how the velocity of flow in a cylindrical shell such as this varies with the radius of the shell.

Equation (9.28) describes the velocity with which a cylindrical shell of liquid moves through a capillary under stationary-state conditions. This velocity times the cross-sectional area of the shell gives the incremental volume of liquid dV which is delivered from the capillary in an interval of time At. The total volume delivered in this interval AV is obtained by integrating this product over all values of r ... 

The Sweedand filter, a significant departure from the standard end-opening design, has the cylindrical shell spHt in a horizontal plane into two parts, where the bottom half can be swung open for cake discharge. The upper half is rigidly supported and both the feed and the filtrate piping are fixed to it. 

Equations 1 to 3 enable the stresses which exist at any point across the wall thickness of a cylindrical shell to be calculated when the material is stressed elastically by applying an internal pressure. The principal stresses cannot be used to determine how thick a shell must be to withstand a particular pressure until a criterion of elastic failure is defined in terms of some limiting combination of the principal stresses. 

Cone-Roof Tanks. Cone-roof tanks are cylindrical shells having a vertical axis of symmetry. The bottom is usually flat and the top made ia the form of a shallow cone. These are the most widely used tanks for storage of relatively large quantities of fluid because they are economic to build and the market supports a number of contractors capable of building them. They can be shop-fabricated ia small sizes but are most often field-erected. Cone-roof tanks typically have roof rafters and support columns except ia very small-diameter tanks when they are self-supporting (see Fig. 4b and c Table 3). 

Frequently cost savings for cylindrical shells can result from reducing the effective length-to-diameter ratio and thereby reducing shell thickness. This can be accomplished by adding circumferential stiffeners to the shell. Rules are included for designing and locating the stiffeners. 

When a cylindrical shell is drilled for the insertion of multiple tubes, the shell is significantly weakened and the code provides rules for tube-hole patterns and the reduction in strength that must be accommodated. 

Figure 8.16. Comparison of calculation and experiment for explosive implosion fragmentation data on uranium cylindrical shells.

Figure 16.1 shows part of a steel tank which came from a road tank vehicle. The tank consisted of a cylindrical shell about 6 m long. A hemispherical cap was welded to each end of the shell with a circumferential weld. The tank was used to transport liquid ammonia. In order to contain the liquid ammonia the pressure had to be equal to the saturation pressure (the pressure at which a mixture of liquid and vapour is in equilibrium). The saturation pressure increases rapidly with temperature at 20°C the absolute pressure is 8.57 bar at 50°C it is 20.33 bar. The gauge pressure at 50°C is 19.33 bar, or 1.9MN m . Because of this the tank had to function as a pressure vessel. The maximum operating pressure was 2.07 MN m" gauge. This allowed the tank to be used safely to 50°C, above the maximum temperature expected in even a hot climate. 

Fig. 14. High resolution TEM observations of three multi-wall carbon nanotubes with N concentric carbon nanotubes with various outer diameters do (a) N = 5, do = 6.7 nm, (b) N = 2, do = 5.5 nm, and (c) N = 7, do = 6.5 nm. The inner diameter of (c) is d = 2.3 nm. Each cylindrical shell is described by its own diameter and chiral angle [151].

Major discontinuities, such as the transitions from the cylindrical shell to the top head and the basemat. 

A laminate is a bonded stack of laminae with various orientations of principal material directions in the laminae as in Figure 1-9. Note that the fiber orientation of the layers in Figure 1-9 is not symmetric about the middle surface of the laminate. The layers of a laminate are usually bonded together by the same matrix material that is used in the individual laminae. That is, some of the matrix material in a lamina coats the surfaces of a lamina and is used to bond the lamina to its adjacent laminae without the addition of more matrix material. Laminates can be composed of plates of different materials or, in the present context, layers of fiber-reinforced laminae. A laminated circular cylindrical shell can be constructed by winding resin-coated fibers on a removable core structure called a mandrel first with one orientation to the shell axis, then another, and so on until the desired thickness is achieved. 

Figure 2-9 Helically Wound Fiber-Reinforced Circular Cylindrical Shell...

S. A. Ambartsumyan, The Axisymmetric Problem of a Circular Cylindrical Shell Made of Material with Different Stiffness in Tension etnd Compression, Izvesttya Akademii Nauk SSSR Mekhanika, No. 4, 1965, pp. 77-85 English translation N69-11070, STAR. 

Robert M. Jones, Buckling of Stiffened Multilayered Circular Cylindrical Shells with Different Orthotropic Moduli in Tension and Compression, AtAA Journal, May 1971, pp. 917-923. 

B. O. Almroth, Influence of Edge Conditions on the Stability of Axially Compressed Cylindrical Shells, AIAA Journal, January 1966, pp. 134-140. 

Robert M. Jones and Jose C. F. Hennemann, Effect of Prebuckling Deformations on Buckling of Laminated Composite Circular Cylindrical Shells, AIM Journal, January 1980, pp. 110-115. 

Robert M. Jones, Plastic Buckling of Eccentrically Stiffened Circular Cylindrical Shells, Aerospace Corporation Report No. TR-0158(S3816-72)-1, San Bernardino, California, December 1967. See also AIM Journal, June 1967, pp. 1147-1152. 

S. Cheng and B. P. C. Ho, Stability of Heterogeneous Aeolotropic Cylindrical Shells under Combined Loading, AIAA Journal, April 1963, pp. 892-898. 

Robert M. Jones, Buckling of Circular Cylindrical Shells with Multiple Orthotropic Layers and Eccentric Stiffeners, AIAA Journal, December 1968, pp. 2301-2305. Errata, October 1969, p. 2048. 

Robert M. Jones and Harold S. Morgem, Buckling and Vibration of Cross-Ry Laminated Circular Cylindrical Shells, AIAA Journal, May 1975, pp. 664-671. 

Essentially, a shell and lube exchanger consists of a bundle of lubes enclosed in a cylindrical shell. The ends of the lubes are fitted into tube sheets which separate Ihe shell-side and lube-side fluids. Baffles are provided in the shell to direct the fluid flow and increase heal transfer. ... 

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