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The tangent line is the geometric line demarking the cylindrical vessel surface from the double curvature surface of the head. The location of the tangent line (TL) is critical more so from the standpoint of the process design of the vessel than from standpoint of ASME Code rules.
The component on the cylindrical side of the TL must be analyzed as a cylindrical shell by ASME Code rules, and the head must be analyzed by the corresponding rules for its geometry (eg: ellipsoidal, torispherical, hemispherical, etc).
The head may or may not be required to have a "head skirt" or "straight flange"; see UG-32. If a straight flange exists it should be analyzed as a cylindrical shell.
Hemispherical heads are not required to have a straight flange but may have one in some cases. If one exists it is treated as a cylindrical shell.
In some cases the hemispherical head is manufactured such that it does not form a 180° arc. Instead, the weld seam to the adjoining cylindrical shell is located a few inches above the tangent line. In this case the cylindrical shell is extended beyond the tangent line and is tapered to meet the head. The portion of the cylindrical shell extending beyond the tangent line is considered to be part of the head and the required thickness is determined accordingly. See Figure UW-13.1.
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