The Shape of Pressure Vessel Heads

A pressure vessel is a container designed to hold gases or liquids at a pressure that is substantially different from ambient pressure. Pressure vessels can be dangerous and pressure vessel design, manufacture, and operation are regulated by engineering authorities backed by legislation. 

Why are most pressure vessels cylindrical? 

Pressure is defined as force per unit area. The geometry of a shape providing minimum surface area is the sphere. Therefore, the area available for deformation is less on a curved surface for a given pressure than with an equal volume based on flat surfaces. While pressure vessels can theoretically be almost any shape, spheres and cylinders are usually employed.  

Theoretically, a spherical pressure vessel has approximately twice the strength of a cylindrical pressure vessel with the same wall thickness and is the ideal shape to hold internal pressure. However, a spherical shape is difficult and expensive to manufacture, and a common design is a cylinder, called a ‘shell’, with end caps called ‘heads’.  

Cylinders are not as strong as spheres due to the weak point at each end, but weakness is reduced by fitting hemispherical or rounded heads. The most frequently used head shapes are: 

  • Ellipsoidal – The head has an elliptical form, and is more economical, because the height of the head is just a fraction of the diameter. 
  • Torispherical (or flanged and dished heads) – These heads have a dish with a fixed radius and a transition between the cylinder and the dish, called the ‘knuckle’ with a toroidal shape. 
  • Hemispherical – These heads have a simple radial geometry, and the radius of the head equals the radius of the cylindrical part of the vessel. This is commonly used in large diameter or high-pressure applications as two opposing hemispherical heads make a storage sphere, the most efficient shape for pressurised storage. 
  • Conical – With the shape of concentric cone and a toroidal knuckle, the conical head is typically applied as the bottom head of a pressure vessel to facilitate the collection and removal of internal materials and for the connection of two-stage vessels of varying diameters.

The head design depends entirely on the application, and sometimes involves a combination of different head types. For example, pressure vessels for brewery applications often require a torispherical top head and a steep-coned bottom head.  

For a cylindrical vessel, the main components are the cylindrical shell and two heads and just 3 welds to join all these components. Minimising the number of welds reduces the risk of pressure vessel failure and reduces the number of steps required for manufacture. 

Why do cylindrical pressure vessels have dished ends rather than flat ones? 
Any angularity in a cylindrical vessel that is pressurised within or externally, detracts from the strength. With a flat head at the junction of the shell, there is a sudden 90-degree change in cross section that results in stress concentration. In addition, a flat end is an unsupported diaphragm with almost no resistance to pressure that results in a bowing force that weakens the integrity of the metal. The bending stresses are very high compared to normal tensile and compressive stresses, so the thickness of the flat end would be much higher, leading to high material cost and weight. For example, a 10mm hemispherical head for pressure vessel would require 30-50mm for a flat end. 

Concave or convex dish ends?   
While it may appear practical that ends should be convex rather than concave because internal pressure would convert tensile to compression loads, the welding of a convex end to a cylinder would undermine the strength of the container as it would create an in-built angularity. 


A&G Engineering have been manufacturing stainless steel storage tanks and pressure vessels for 60 years. The unmatched combination of experience, flexibility, expertise, and technology for every A&G project serve to minimise production risk and ensure on-time, on-budget, and as-specified delivery.   

If you have a technical query or want to find out how A&G can help with your next project, talk to our expert team by calling us on (02) 6964 3422 or email with your inquiry. We look forward to hearing from you.