Pressure Vessel

pressure vessel is a closed container designed to hold gases or liquids at a pressure substantially different from the ambient pressure. The pressure differential is dangerous and many fatal accidents have occurred in the history of their development and operation. Consequently, their design, manufacture, and operation are regulated by engineering authorities backed up by laws. 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.


Pressure vessels are used in a variety of applications in both industry and the private sector. They appear in these sectors as industrial compressed airreceivers and domestic hot water storage tanks. Other examples of pressure vessels are: diving cylinder, recompression chamber, distillation towers,autoclaves and many other vessels in mining or oil refineries and petrochemical plants, nuclear reactor vessel, habitat of a space ship, habitat of asubmarine, pneumatic reservoir, hydraulic reservoir under pressure, rail vehicle airbrake reservoir, road vehicle airbrake reservoir and storage vessels for liquified gases such as ammonia, chlorine, propane, butane and LPG.

Shape of a pressure vessel

Pressure vessels may theoretically be almost any shape, but shapes made of sections of spheres, cylinders, and cones are usually employed. A common design is a cylinder with end caps called heads. Head shapes are frequently either hemispherical or dished (torispherical). More complicated shapes have historically been much harder to analyze for safe operation and are usually far more difficult to construct. Theoretically, a sphere would be the optimal shape of a pressure vessel. Unfortunately, a spherical shape is difficult to manufacture, 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. A disadvantage of these vessels is that larger diameters make them 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 diameter of 914.4 millimetres (36 in) and a length of 1,701.8 millimetres (67 in) including the 2:1 semi-elliptical domed end caps.

Construction materials

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. Many pressure vessels are made of steel. To manufacture a cyllindrical or spherical pressure vessel, rolled and possibly forged parts would have to be welded together. Some mechanical properties of steel, achieved by rolling or forging, could be adversely affected by welding, unless special precautions are taken. In addition to adequate mechanical strength, current standards dictate the use of steel with a high impact resistance, especially for vessels used in low temperatures. In applications where carbon steel would suffer corrosion, special corrosion resistant material should also be used. Some pressure vessels are made of composite materials, such as wound carbon fibre held in place with a polymer. Due to the very high tensile strength of carbon fibre these vessels can be very light, but are much more difficult to manufacture. The composite material may be wound around a metal liner, forming a composite overwrapped pressure vessel. Other very common materials include polymers such as PET in carbonated beverage containers and copper in plumbing. Pressure vessels may be lined with a various metals, ceramics, or polymers to prevent leaking and protect the structure of the vessel from the contained fluid. This liner may also carry a significant portion of the pressure load.


No matter what shape it takes, the minimum mass of a pressure vessel scales with the pressure and volume it contains and is inversely proportional to thestrength to weight ratio of the construction material (minimum mass decreases as strength increases).

Spherical vessel

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, i.e. the gauge pressure
V is volume
? is the density of the pressure vessel material
? is the maximum working stress that material can tolerate.

Other shapes besides a sphere have constants larger than 3/2 (infinite cylinders take 2), although some tanks, such as non-spherical wound composite tanks can approach this.

Cylindrical vessel with hemispherical ends

This is sometimes called a “bullet” on account of its shape. For a cylinder with hemispherical ends:

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


  • R is the radius
  • L is the middle cylinder length only, and the overall length is L + 2R

2:1 Cylindrical vessel with semi-elliptical ends

In a vessel with a 2:1 aspect ratio:

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

Gas storage

In looking at the first equation, the factor PV, in SI units, is in units of (pressurization) energy. For a stored gas, PV is proportional to the mass of gas at a given temperature, thus:

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

The other factors are constant for a given vessel shape and material. So we can see that there is no theoretical “efficiency of scale”, in terms of the ratio of pressure vessel mass to pressurization energy, or of pressure vessel mass to stored gas mass. For storing gases, “tankage efficiency” is independent of pressure, at least for the same temperature. 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 ? / ?, and very cold helium for best possible M / pV.

Stress in thin-walled pressure vessels

Stress in a thin-walled pressure vessel in the shape of a sphere is: \sigma_\theta = \frac{pr}{2t} Where ?? is hoop stress, or stress in the circumferential direction, p is internal gauge pressure, r is the inner radius of the sphere, and t is thickness. A vessel can be considered “thin-walled” if the diameter is at least 10 times (sometimes cited as 20 times) larger than the wall thickness. Stress in a thin-walled pressure vessel in the shape of a cylinder is: \sigma_\theta = \frac{pr}{t} \sigma_{\rm long} = \frac{pr}{2t} Where ?? is hoop stress, or stress in the circumferential direction, ?long is stress in the longitudinal direction, p is internal gauge pressure, r is the inner radius of the cylinder, and t is wall thickness.

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Comments : 1
  1. saintdo Reply

    Good job!

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