Pressure vessel.html

A pressure vessel is a closed container designed to hold gases or liquids at a pressure different from the ambient pressure.

The pressure differential is potentially 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.

1 Uses
2 Shape of a pressure vessel
3 Design and operation standards
- 3.1 List of standards
4 Alternatives to pressure vessels
5 History of pressure vessels
6 See also
7 External links
8 Further reading
9 References
10 Notes

Uses

A pressure tank connected to a water well and domestic hot water system

A specific water pipe made for use with pressure vessels. The pipe can sustain high pressure water and is relatively small

Pressure vessels are used in a variety of applications in both industry and the private sector. They appear in these sectors as 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.

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 hemispherical end caps called heads. 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 relatively 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

Steel Pressure Vessel

Generally, almost any material with good tensile properties that is chemically stable in the chosen application can be employed.

Many 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 & corrosion resistant material should also be used.

Some pressure vessels are made of 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 trickier to manufacture.

Other very common materials include polymers such as PET in carbonated beverage containers and copper in plumbing.

Scaling

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

Spherical vessel

For a sphere, the mass of a pressure vessel is

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

Where:

M

is mass

P

is the pressure difference from ambient, i.e. 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.

Cylindrical vessel with hemispherical ends

For a cylinder with hemispherical ends:

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

where:

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

2:1 Cylindrical vessel with hemispherical 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 $ρ / σ$ , and very cold helium for best possible $M / p V$ .

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 $σ θ$ is hoop stress, or stress in the circumferential direction, p is internal gauge pressure, r is radius of the sphere, and t is thickness. A vessel can be considered "thin-walled" if the radius is at least 20 times larger than the wall thickness.¹

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 $σ θ$ is hoop stress, or stress in the circumferential direction, $σ l o n g$ is stress in the longitudinal direction, p is internal gauge pressure, r is radius of the cylinder, and t is wall thickness.

Winding angle of carbon fibre vessels

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 and operation standards

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.

Note that where the pressure-volume product is part of a safety standard, any incompressible liquid in the vessel can be excluded as it does not contribute to the potential energy stored in the vessel, so only the volume of the compressible part such as gas is used.

List of standards

BS 4994
EN 13445
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
ASME PVHO (Safety Standard for Pressure Vessels for Human Occupancy)
BS 5500
Stoomwezen
AD Merkblätterasa
CODAP
AS 1210
ISO 11439 ³

Alternatives to pressure vessels

Depending on the application and local circumstances, alternatives have come about which can replace pressure tanks. An example to this is in the private sector (for use in domestic water collection systems). Non-pressure vessel systems are increasingly seen with:

no storage tank or pump at all (gravity controlled systems) ⁴ Gravity-controlled systems are usually created by placing the water harvester on an elevation (e.g. rooftops). This will produce about 0.5 PSI per foot of water head (height difference). However, municipal water or pumped water is typically around 90 PSI.
or with either inline pump controllers or pressure-sensitive pumps ⁵:

History of pressure vessels

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 came about after some large explosions caused loss of life and led to a system of certification.

External links

Wikimedia Commons has media related to: Pressure vessel

References

A.C. Ugural, S.K. Fenster, Advanced Strength and Applied Elasticity, 4th ed.
E.P. Popov, Engineering Mechanics of Solids, 1st ed.
Megyesy, Eugene F. "Pressure Vessel Handbook, 14th Edition." PV Publishing, Inc. Oklahoma City, OK

Notes

^ Richard Budynas, J. Nisbett, Shigley's Mechanical Engineering Design, 8th ed., New York:McGraw-Hill, ISBN 978-0-07-312193-2, pg 108
^ MIT pressure vessel lecture
^ Gas cylinders -- High pressure cylinders for the on-board storage of natural gas as a fuel for automotive vehicles
^ Domestic water collection systems also sometimes able to function on gravity
^ Alternatives to pressure vessels in domestic water systems

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