Ellipsoidal heads

The volumes of heads must be calculated separately and added to the volume of the cylindrical portion of the tank. The four types of heads most frequently used are the standard dished head, torispherical or ASME head, ellipsoidal head, and hemispherical head. Dimensions and volumes for all four of these types are given in Luken.s Spun Heads, Lnkens Inc., Coatesville, Pennsylvania. Approximate volumes can also be calculated by the formulas in Table 10-65. Consistent units must be used in these formulas. 

A partially filled horizontal tank requires the determination of the partial volume of the heads. The Lnkens catalog gives approximate volumes for partially filled (axis horizontal) standard ASME and ellipsoidal heads. A formula for partially filled heads, by Doolittle [Ind. 

Figure 12-1 defines the various types of heads. Most production facility vessels use ellipsoidal heads because they are readily available, normally less expensive, and take up less room than hemisphericaj heads. 

Cone-bottom vertical vessels are sometimes used where solids are anticipated to be a problem. Most cones have either a 90 apex (a = 45 ) or a 60 apex ia = 30 ). These are referred to respectively as a 45 or 60 cone because of the angle each makes with the horizontal. Equation 12-4 is for the thickness of a conical head that contains pressure. Some operators use internal cones within vertical vessels with standard ellipsoidal heads as shown in Figure 12-2. The ellipsoidal heads contain the pressure, and thus the internal cone can be made of very thin steel. 

The weight of nozzles and internals can be estimated at 5 to 10% of the sum of the shell and head weights. The weight of a skirt can be estimated as the same weight per foot as the shell with a length given by Equation 12-8 for an ellipsoidal head and Equation 12-9 for a conical head. 

Hemi-ellipsoidal Heads have an ellipsoidal cross section, usually with minor axis equal to one half the major axis—that is, depth = Vi D, or more. 

Dished or Basket Heads consist of a spherical segment normally dished to a radius equal to the inside diameter of the tank cylinder (or within a range of 6 inches plus or minus) and connected to the straight cylindrical flange by a knuckle whose inside radius is usually not less than 6 per cent of the inside diameter of the cylinder nor less than 3 times the thickness of the head plate. Basket heads closely approximate hemi-ellipsoidal heads. 

Note K in above formulas may be determined as follows Hemi-ellipsoidal heads—K is known... 

Volume or contents of partially filled hemi-ellipsoidal heads with major axis vertical ... 

It should be noted that if a/b)2 > 1, or2 will be negative (compressive) and the shell could fail by buckling. This consideration places a limit on the practical proportions of ellipsoidal heads. 

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. 

Most standard ellipsoidal heads are manufactured with a major and minor axis ratio of 2 1. For this ratio, the following equation can be used to calculate the minimum thickness required ... 

So an ellipsoidal head would probably be the most economical. Take as same thickness as wall 15 mm. 

Torispherical and ellipsoidal heads can be designed as equivalent hemispheres. For a torispherical head the radius Rs is taken as equivalent to the crown radius Rc. For an ellipsoidal head the radius can be taken as the maximum radius of curvature that at the top, given by ... 

The ends of the vessel are 2 1 ellipsoidal heads, with an area for the two ends of 2(1.16D2) = 2.32D2. 

Sally takes a deep breath. Instead of having ellipsoidal heads, 4-D sperm might have hyperellipsoidal heads. As the heads intersect our 3-D world, they would first appear as points, then ellipsoids that changed in size. Just before it disappeared, a small blob would remain for some time as the tail passed through. A 4-D man could, in principle, inseminate a 3-D woman without her even seeing him (Fig. 2.11). 

Although they are rarely needed, formulas in terms of outside dimensions, say Dol may be derived from the given ones by substitution of D0 — 2t for D. For the 2 1 ellipsoidal head, for instance,... 

All test accumulators (pressure vessels) were mounted direcdy below the test table. These vessels were mounted vertically with 2 1 ellipsoidal heads on top and bottom. The top head has a well-rounded outlet nozzle sized equal to the SRV inlet to be tested. To test smaller-orifice SRVs, ring-shaped adapter plates having an opening equal to the SRV inlet are used. This arrangement reduces the possibility of starving the flow to the valve. 

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