Pressure vessels calculations

The cylindrical shell is frequently used in pressure vessel design. For initial designs, it is useful to calculate the stresses in a thin-walled cylindrical shell that is uniformly loaded with internal pressure. For thin-walled pressure vessel calculations to be valid, the radial stresses in the shell need to be negligible. This is usually taken to be a valid assumption when the ratio of the vessel inner radius to the wall thickness (R/t) is greater than 10. "... 

Rg. 3.1-85 High-temperature tensile strength and fracture strain of titanium, and values used for titanium pressure vessel calculations (105 h)... 

Hechmer and Hollinger have proposed ten guidelines on the evaluation of stresses in pressure vessels calculated by finite-element method in the spirit of the ASME Boiler and Pressure Vessel Code. ... 

The calculation was carried out using the ANSYS F.E.M. code. The pressure vessel was meshed with a 4 nodes shell element. Fig. 18 shows a view of the results of calculation of the sum of principal stresses on the vessel surface represented on the undeformed shape. For the calculation it was assumed an internal pressure equal to 5 bar and the same mechanical characteristics for the test material. 

Pressure-vessel weights are obtained by calculating the cylindrical... 

Blast Characteristics Accurate calculation of the magnitude of the blast wave from an exploding pressure vessel is not possible, but it may be estimated from several approximate methods that are available. 

The coefficient of discharge method (Kj = 0.62) was specified to calculate the capacity of the rupture disc device. However, the validity of this method is limited to a disc mounted close to the pressure vessel and the discharging to atmosphere. The ASME Code provides guidance for the limited use of this method ... 

A filament wound composite cylindrical pressure vessel has a diameter of 1200 mm and a wall thickness of 3 mm. It is made up of 10 plies of continuous glass fibres in a polyester resin. The anangement of the plies is [O3/6O/ — 60],. Calculate the axial and hoop strain in the cylinder when an internal pressure of 3 MN/m is applied. The properties of the individual plies are... 

The previous chapter described the consequences of a nuclear reactor accident. Chemical process accidents are more varied and do not usually have the energy to melt thick pressure vessels and concrete basemats. The consequences of a chemical process accident that releases a toxic plume, like Bhopal did, are calculated similarly to calculating the dose from inhalation from a radioactive plume but usually calculating chemical process accidents differ from nuclear accidents for which explosions do not occur. 

Often, a slightly higher MAWP than that calculated from Tabl possible at almost no additional cost. Once a preliminary MAWP is cted from Table 12-1, it is necessary to calculate a wall thicl r shell and heads of the pressure vessel. The procedure for doii s... 

Fire. The relief valve must be sized to handle the gases evolving from liquids il the equipment is exposed to an external fire. A procedure for calculating this is presented in API RP 520. This condition may be critical for large, low-pressure vessels and tanks but does not normally govern for other pressure vessels. 

This section addresses the effects of BLEVE blasts and pressure vessel bursts. Actually, the blast effect of a BLEVE results not only from rapid evaporation (flashing) of liquid, but also from the expansion of vapor in the vessel s vapor (head) space. In many accidents, head-space vapor expansion probably produces most of the blast effects. Rapid expansion of vapor produces a blast identical to that of other pressure vessel ruptures, and so does flashing liquid. Therefore, it is necessary to calculate blast from pressure vessel mpture in order to calculate a BLEVE blast effect. 

This section first presents literature review on pressure vessel bursts and BLEVEs. Evaluation of energy from BLEVE explosions and pressure vessel bursts is emphasized because this value is the most important parameter in determining blast strength. Next, practical methods for estimating blast strength and duration are presented, followed by a discussion of the accuracy of each method. Example calculations are given in Chapter 9. 

The pressure vessel under consideration in this subsection is spherical and is located far from surfaces that might reflect the shock wave. Furthermore, it is assumed that the vessel will fracture into many massless fragments, that the energy required to mpture the vessel is negligible, and that the gas inside the vessel behaves as an ideal gas. The first consequence of these assumptions is that the blast wave is perfectly spherical, thus permitting the use of one-dimensional calculations. Second, all energy stored in the compressed gas is available to drive the blast wave. Certain equations can then be derived in combination with the assumption of ideal gas behavior. 

At the instant a pressure vessel ruptures, pressure at the contact surface is given by Eq. (6.3.22). The further development of pressure at the contact surface can only be evaluated numerically. However, the actual p-V process can be adequately approximated by the dashed curve in Figure 6.12. In this process, the constant-pressure segment represents irreversible expansion against an equilibrium counterpressure P3 until the gas reaches a volume V3. This is followed by an isentropic expansion to the end-state pressure Pq. For this process, the point (p, V3) is not on the isentrope which emanates from point (p, V,), since the first phase of the expansion process is irreversible. Adamczyk calculates point (p, V3) from the conservation of energy law and finds... 

When a pressure vessel is not a sphere, or if the vessel does not fracture evenly, the resulting blast wave will be nonspherical. This, of course, is the case in almost every actual pressure vessel burst. Loss of symmetry means that detailed calculations... 

In the method which will be presented in Section 6.3.3., the blast parameters of pressure vessel bursts are read from curves of pentolite, a high explosive, for nondimensional distance R above two. For these ranges, using TNT equivalence makes sense. Pentolite has a specific heat of detonation of 5.11 MJ/kg, versus 4.52 MJ/kg for TNT (Baker et al. 1983). The equivalent mass of TNT can be calculated as follows for a ground burst of a pressure vessel ... 

In this section, three methods for calculating the blast parameters of pressure vessel bursts and BLEVEs will be presented. All methods are related that is, one basic method and two variations are presented. The choice of method depends upon phase of the vessel s contents and distance to the blast wave s target, as illustrated in Figure 6.19. 

Baker et al. (1975) developed a method, presented below, for predicting blast effects fiom the rupture of gas-filled pressure vessels. They include a method for calculating the overpressure and impulse of blast waves from the rupture of spherical or cylindri-... 

The general procedure of the basic method is shown in Figure 6.20. This method is suitable for calculations of bursts of spherical and cylindrical pressure vessels which are filled with an ideal gas, placed on a flat surface, and distant from other obstacles which might interfere with the blast wave. 

Rgure 6.29. Calculation of energy of flashing liquids and pressure vessel bursts filled with vapor or nonideal gas. 

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