Pressure vessels ellipsoidal dished

Although spherical vessels have a limited process application, the majority of pressure vessels are made with cylindrical shells. The heads may be flat if they are suitably buttressed, but preferably they are some curved shape. The more common types of heads are illustrated on Figure 18.16. Formulas for wall thicknesses are in Table 18.3. Other data relating to heads and shells are collected in Table 18.5. Included are the full volume V0 and surface S as well as the volume fraction V/V0 corresponding to a fractional depth H/D in a horizontal vessel. Figure 18.17 graphs this last relationship. For ellipsoidal and dished heads the formulas for V/V0 are not exact but are within 2% over the whole range. 

Figure 18.17. Types of heads for cylindrical pressure vessels, (a) Flat flanged KR = knuckle radius, SF= straight flange, (b) Torispherical (dished), (c) Ellipsoidal, (d) Spherical, (c) Conical, without knuckle, (f) Conical, with knuckle, (g) Nonstandard, one of many possible types in use.

The ellipsoidal dished head with a major to minor axis ratio of 2 1 is popular for economic reasons, even though the theory for thin-walled vessels predicts that the head of this shape should have twice the thickness of a hemispherical head where the major and minor axes are equal. Such an ellipsoidal head used for vessels under internal pressure has the same thickness as the cylindrical shell if the same allowable stresses and joint efficiencies are applied to both parts. The 1962 ASME Code Section VIII, Division 1 gives the following equation for the thin-walled ellipsoidal dished heads with a 2 1 major to minor axis ratio ... 

Standard torispherical heads (dished ends) are the most commonly used end closure for vessels up to operating pressures of 15 bar. They can be used for higher pressures, but above 10 bar their cost should be compared with that of an equivalent ellipsoidal head. Above 15 bar an ellipsoidal head will usually prove to be the most economical closure to use. 

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