Pressure vessel

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Vertical pressure vessels installed in a structure


The pressure differential is dangerous and fatal accidents have occurred in the history of pressure vessel development and operation. Consequently, pressure vessel design, manufacture, and operation are regulated by engineering authorities backed by legislation. For these reasons, the definition of a pressure vessel varies from country to country, but involves parameters such as maximum safe operating pressure and temperature.


A pressure tank connected to a water well and domestic hot water system
A few pressure tanks, here used to hold propane


A unique application of a pressure vessel is the passenger cabin of an airliner; The outer skin carries both the aircraft maneuvering loads and the cabin pressurization loads.

Pressure vessel features[edit]

Shape of a pressure vessel[edit]


Theoretically, a spherical pressure vessel has approximately twice the strength of a cylindrical pressure vessel with the same wall thickness.[1] However, a spherical shape is difficult to manufacture, and therefore more expensive, so most pressure vessels are cylindrical with 2:1 semi-elliptical heads or end caps on each end. Smaller pressure vessels are assembled from a pipe and two covers. For cylindrical vessels with a diameter up to 600 mm, it is possible to use seamless pipe for the shell, thus avoiding many inspection and testing issues. A disadvantage of these vessels is that greater breadths are more expensive, so that for example the most economic shape of a 1,000 litres (35 cu ft), 250 bars (3,600 psi) pressure vessel might be a breadth of 914.4 millimetres (36 in) and a width of 1,701.8 millimetres (67 in) including the 2:1 semi-elliptical domed end caps.

Construction materials[edit]

Steel pressure vessel

Theoretically almost any material with good tensile properties that is chemically stable in the chosen application could be employed. However, pressure vessel design codes and application standards (ASME BPVC Section II, EN 13445-2 etc.) contain long lists of approved materials with associated limitations in temperature range.








Scaling of stress in walls of vessel[edit]



Spherical vessel[edit]

For a sphere, the mass of a pressure vessel is

M = {3 \over 2} P V {\rho \over \sigma},


M is mass,
P is the pressure difference from ambient (the gauge pressure),
V is volume,
\rho is the density of the pressure vessel material,
\sigma is the maximum working stress that material can tolerate.[7]


Cylindrical vessel with hemispherical ends[edit]


For a cylinder with hemispherical ends,

M = 2 \pi R^2 (R + W) P {\rho \over \sigma},


  • R is the radius

2:1 Cylindrical vessel with semi-elliptical ends[edit]


M = 6 \pi R^3 P {\rho \over \sigma}.

Gas storage[edit]


M = {3 \over 2} nRT {\rho \over \sigma}. (see gas law)


So, for example, a typical design for a minimum mass tank to hold helium (as a pressurant gas) on a rocket would use a spherical chamber for a minimum shape constant, carbon fiber for best possible \rho / \sigma, and very cold helium for best possible M / {pV}.

Stress in thin-walled pressure vessels[edit]


\sigma_\theta = \sigma_{\rm long} = \frac{pr}{2t},

where \sigma_\theta is hoop stress, or stress in the circumferential direction, \sigma_{long} is stress in the longitudinal direction, p is internal gauge pressure, r is the inner radius of the sphere, and t is thickness of the cylinder wall. A vessel can be considered "shallow-walled" if the diameter is at least 10 times (sometimes cited as 20 times) greater than the wall depth.[8]


\sigma_\theta = \frac{pr}{t},

where \sigma_\theta is hoop stress, or stress in the circumferential direction, \sigma_{long} is stress in the longitudinal direction, p is internal gauge pressure, r is the inner radius of the cylinder, and t is thickness of the cylinder wall.

Almost all pressure vessel design standards contain variations of these two formulas with additional empirical terms to account for wall thickness tolerances, quality control of welds and in-service corrosion allowances.


Spherical shells:

\sigma_\theta = \sigma_{\rm long} = \frac{p(r + 0.2t)}{2tE}

Cylindrical shells:

\sigma_\theta = \frac{p(r + 0.6t)}{tE}
\sigma_{\rm long} = \frac{p(r - 0.4t)}{2tE}


The Factor of safety is often included in these formulas as well, in the case of the ASME BPVC this term is included in the material stress value when solving for Pressure or Thickness.

Winding angle of carbon fibre vessels[edit]


Design and operation standards[edit]



List of standards[edit]

  • CODAP: French Code for Construction of Unfired Pressure Vessel.
  • AS/NZS 1200: Pressure equipment.[11]
  • AS 3788 Pressure equipment - In-service inspection
  • API 510.[12]
  • ISO 11439: Compressed natural gas (CNG) cylinders[13]
  • IS 2825-1969 (RE1977)_code_unfired_Pressure_vessels.
  • FRP tanks and vessels.
  • HSE guidelines for pressure systems.

Design Features[edit]

Leak before burst[edit]


Many pressure vessel standards, including the ASME Boiler and Pressure Vessel Code and the AIAA metallic pressure vessel standard, either require pressure vessel designs to be leak before burst, or require pressure vessels to meet more stringent requirements for fatigue and fracture if they are not shown to be leak before burst.[14]

Safety valves[edit]


Pressure vessel closures[edit]

Pressure vessel closures are pressure retaining structures designed to provide quick access to pipelines, pressure vessels, pig traps, filters and filtration systems. Typically pressure vessel closures allow maintenance personnel to load a sphere or pig into a pig trap for pipeline cleaning purposes.[15]

Alternatives to pressure vessels[edit]


  • Inline pump controllers or pressure-sensitive pumps.[17]

History of pressure vessels[edit]


Large pressure vessels were invented during the industrial revolution, particularly in Great Britain, to be used as boilers for making steam to drive steam engines.

Design and testing standards and a system of certification came about as the result of fatal boiler explosions.


See also[edit]


  1. ^ Hearn, E.J. (1997). Mechanics of Materials 1, An Introduction to the Mechanics of Elastic and Plastic Deformation of Solids and Structural Materials - Third Edition. Chapter 9: Butterworth-Heinemann. pp. 199–203. ISBN 0-7506-3265-8. 
  5. ^ Puskarich, Paul (2009-05-01). Strengthened Glass for Pipleine Systems (PDF). MIT. Retrieved 2009-04-17. 
  6. ^ Ferdinand P. Beer, E. Russel Johnston, Jr., and John T. DeWolf. "7.9". Mechanics of Materials (fourth ed.). McGraw-Hill. p. 463. ISBN [[Special:BookSources/780073659350|780073659350 [[Category:Articles with invalid ISBNs]]]] Check |isbn= value (help). 
  10. ^ MIT pressure vessel lecture
  11. ^ "AS 1200 Pressure Vessels". SAI Global. Retrieved 14 November 2011. 
  15. ^ Pressure Vessel Closure



Further reading[edit]


External links[edit]