I was studing some heads for a while, and thougth to summarise the variety in one go…
1. Flanged Head : Normally found in Vessel opertaing at low pressure, genrally water tanks, Boilers etc. They are also used in high pressure application where the diameter is small.
2. Hemispherical Head : Generally, the required thickness of the hemispherical head due to a given Pressure & temperature is half of cylindrical shell with equivalent diameter & Material.
3. Elliptical and Torispherical (ASME Flangged & Dished) heads : they are very popular in pressure vessel, their thickness is ususally same as the cylinder to which they are attached.
This is a quick heads up for variety of heads used in industry. The other type are
1. Conical or Toriconical head: they mostly form bottom end closure for the vessels, and act as hopper, or to give easy drainability. The important thing to consider while designing this heads are, a) they increase the overall height of the vessel. b) ASME need to do discontinuity analysis for half angle >30 deg, or else one need to go ahead with toriconical head to avoid the unbalanced force at the junction.
2. Miscellaneous head: Many chemical process requires unusual vessel configuration, the heads of such vessel can have unlimited configurations. The design of such head is very complicated, and there is no straight forward formula for that.