PRESSURE VESSEL

A pressure vessel is a closed, rigid container designed to hold gases or liquids at a pressure different from the ambient pressure. The end caps fitted to the cylindrical body are called heads.

In addition to industrial compressed air receivers 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 a submarine, 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.

In the industrial sector, pressure vessels are designed to operate safely at a specific pressure and temperature, technically referred to as the "Design Pressure" and "Design Temperature". A vessel that is inadequately designed to handle a high pressure constitutes a very significant safety hazard. Because of that, the design and certification of pressure vessels is governed by design codes such as the ASME Boiler and Pressure Vessel Code in North America, the Pressure Equipment Directive of the EU (PED), Japanese Industrial Standard (JIS), CSA B51 in Canada, AS1210 in Australia and other international standards like Lloyd's, Germanischer Lloyd, Det Norske Veritas, Stoomwezen etc.

Shape of a pressure vessel

Theoretically a sphere would be the optimal shape of a pressure vessel. Most pressure vessels are made of steel. To manufacture a spherical pressure vessel, forged parts would have to be welded together. Some mechanical properties of steel are increased by forging, but welding can sometimes reduce these desirable properties. In case of welding, in order to make the pressure vessel meet international safety standards, carefully selected steel with a high impact resistance should be used. Most pressure vessels are arranged from a pipe and two covers. Disadvantage of these vessels is the fact that larger diameters make them relatively more expensive, so that for example the most economic shape of a 1000 litres, 250 bar (25,000 kPa) pressure vessel might be a diameter of 450 mm and a length of 6500 mm.

Scaling

No matter what shape it takes, the minimum mass of a pressure vessel scales with the pressure and volume it contains.

For a sphere, the mass of a pressure vessel is

Where:

M is mass

p is the pressure difference from ambient- the gauge pressure

V is volume

ρ is the density of the pressure vessel material

σ 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.

As can be seen from the equation, there is no theoretical efficiency of scale to be had in a pressure vessel; and further, for storing gases at high pressure relative to ambient, tankage efficiency can be shown to be independent of pressure.

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 ρ / σ, and very cold helium for best possible M / pV.

Stress in thin-walled pressure vessels

The stress in a thin-walled pressure vessel in the shape of a sphere is:

Where σ_θ is the hoop stress, or stress in the circumferential direction, p is the internal gage pressure, r is the radius of the sphere, and t is the thickness. A vessel can be considered "thin-walled" if the radius is at least 20 times larger than the wall thickness.^[1]

The stress in a thin-walled pressure vessel in the shape of a cylinder is:


Where σ_θ is the hoop stress, or stress in the circumferential direction, σ_long is the stress in the longitudinal direction, p is the internal gage pressure, r is the radius of the cylinder, and t is the wall thickness.

Wound infinite cylindrical shapes optimally take a winding angle of 54.7 degrees, as this gives the necessary twice the strength in the circumferential direction to the longitudinal.^[2]

Design Standards

• BS 4994
• ASME Code Section VIII Division 1
• ASME Code Section VIII Division 2 Alternative Rule
• ASME Code Section VIII Division 3 Alternative Rule for Construction of High Pressure Vessel
• BS 5500
• Stoomwezen
• AD Merkblätter
• CODAP
• AS 1210

Further reading

• Megyesy, Eugene F. (2004, 13th ed.) Pressure Vessel Handbook. Pressure Vessel Publishing, Inc.: Tulsa, Oklahoma, USA. Design handbook for pressure vessels based on the ASME code.

References

• A.C. Ugural, S.K. Fenster, Advanced Strength and Applied Elasticity, 4th ed.
• E.P. Popov, Engineering Mechanics of Solids, 1st ed.

Notes

1. ^ Richard Budynas, J. Nisbett, Shigley's Mechanical Engineering Design, 8th ed., New York:McGraw-Hill, ISBN 978-0-07-312193-2, pg 108
2. ^ MIT pressure vessel lecture