Thin-walled vessels

Figure 9.4 A thick-walled pressure vessel might be economical when compared with a thin-walled vessel and its relief and venting system.

For the purposes of design and analysis, pressure vessels are sub-divided into two classes depending on the ratio of the wall thickness to vessel diameter thin-walled vessels, with a thickness ratio of less than 1 10 and thick-walled above this ratio. 

The principal stresses (see Section 13.3.1) acting at a point in the wall of a vessel, due to a pressure load, are shown in Figure 13.1. If the wall is thin, the radial stress comparison with the other stresses, and the longitudinal and circumferential stresses o and <72 can be taken as constant over the wall thickness. In a thick wall, the magnitude of the radial stress will be significant, and the circumferential stress will vary across the wall. The majority of the vessels used in the chemical and allied industries are classified as thin-walled vessels. Thick-walled vessels are used for high pressures, and are discussed in Section 13.15. 

Elastic buckling is the decisive criterion in the design of thin-walled vessels under external pressure. 

THE DESIGN OF THIN-WALLED VESSELS UNDER INTERNAL PRESSURE... 

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. 

The third principal stress, that in the radial direction or3, will usually be negligible for thin-walled vessels (see Section 13.1.1). As an approximation it can be taken as equal to one-half the pressure loading... 

Thick walls are required to contain high pressures, and the assumptions made in the earlier sections of this chapter to develop the design equations for thin-walled vessels will not be valid. The radial stress will not be negligible and the tangential (hoop) stress will vary across the wall. 

Figure 20. Cell walls of a vessel (V) and adjacent fiber (F) in cross-sectional view. Note the very large S2 layer in the thick-walled fiber and the small S2 layer in the thin-walled vessel.

Most vessels in the process industries are thin-walled vessels, which have a wall thickness of less than about 5% of the inside diameter of a vessel. Internal pressure acting on the walls of a cylindrical vessel produces a longitudinal and radial stress, also called hoop stress. For thin-wall vessels, it may be assumed that the radial stress is approximately uniform across the wall. Rase and Borrow [1], for example, showed that the radial stress, produced by an internal pressure, P, is given by Equation 6.1. 

Even in a thin-walled vessel the radial stress is not exactly imiform over the vessel thickness. To correct for this, the internal pressiue in the denominator of Equation 6.4 is multiplied by 1.2 to obtain a more accurate formula. Thus,... 

Local invasion through the basement membrane and into the surrounding stroma is enabled by increased production of proteases by tumor cells themselves (Duffy, 1996), or by their ability to induce such a response in host stromal cells (Basset et al., 1990 Ahmad et al., 1997). Thin-walled vessels, such as newly forming capillaries or lymphatic channels, offer very little resistance to penetration by tumor cells and provide the most common pathways for tumor cell entry into the circulation. 

The relationships for steady heat flow can also be applied to the solution of a transient heat transfer problem, namely to the calculation of the temperature change with time during the heating and cooling of a thin walled vessel filled with a liquid. Two simplifications have to be made ... 

The first assumption is true for most cases, as free or forced convection due to an agitator in the vessel, lead to almost the same temperature throughout the liquid. The second is only correct when the heat capacity of the contents is much larger than the heat capacity of the vessel wall. This happens in the heating and cooling of liquids in thin walled vessels, but may not be applied to vessels containing gases, which have either thick or well insulated walls. 

Fig. 1.17 Temperature profile for the cooling of a thin walled vessel...

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