# Pressure vessel: Wikis

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# Encyclopedia

A 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.

## Uses

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

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 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 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. [1][2]

### Scaling

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 the strength to weight ratio of the construction material (minimum mass decreases as strength increases[3]).

#### 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

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

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

where:

• 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 ρ / σ, 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 σθ 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 radius is at least 20 times larger than the wall thickness.[4]

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 σθ is hoop stress, or stress in the circumferential direction, σlong is stress in the longitudinal direction, p is internal gauge pressure, r is the inner 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.[5]

## 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, Société Générale de Surveillance (SGS S.A.), 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: The current European standard, harmonized with the Pressure Equipment Directive.
• ASME Code Section VIII Division 1: US standard, widely used.
• 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: Former British Standard, replaced in the UK by EN 13445 but retained under the name PD 5500 for the design and construction of export equipment.
• Stoomwezen
• AD Merkblätter: German standard, harmonized with the Pressure Equipment Directive.
• CODAP
• AS 1210
• API 510 [6]
• ISO 11439 [7]
• IS 2825-1969 (RE1977)_code_unfired_Pressure_vessels
• FRP Tanks and Vessels
• EN 286 (Parts 1 to 4): European standard for simple pressure vessels, harmonized with Council Directive 87/404/EEC.
• AIAA S-080-1998: AIAA Standard for Space Systems - Metallic Pressure Vessels, Pressurized Structures, and Pressure Components
• AIAA S-081A-2006: AIAA Standard for Space Systems - Composite Overwrapped Pressure Vessels (COPVs)

### Leak Before Burst

Leak before burst describes a pressure vessel designed such that a crack in the vessel will grow through the wall, allowing the contained fluid to escape and reducing the pressure, prior to growing so large as to cause fracture at the operating pressure.

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. [8]

## 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) [9] Gravity-controlled systems are usually created by placing the water harvester on an elevation (e.g. rooftops). This will produce about .5 pounds per square inch (3.4 kPa) per foot of water head (height difference). However, municipal water or pumped water is typically around 90 pounds per square inch (620 kPa).
• or with either inline pump controllers or pressure-sensitive pumps:[10]

## History of pressure vessels

A 10,000 psi (69 MPa) pressure vessel from 1919, wrapped with high tensile steel banding and steel rods to secure the end caps.

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.

In an early effort to design a tank capable of withstanding pressures up to 10,000 psi (69 MPa), a 6-inch (150 mm) diameter tank was developed in 1919 that was spirally-wound with two layers of high tensile strength steel wire to prevent sidewall rupture, and the end caps longitudinally reinforced with lengthwise high-tensile rods.[11]

• 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.
• Megyesy, Eugene F. "Pressure Vessel Handbook, 14th Edition." PV Publishing, Inc. Oklahoma City, OK

## Notes

1. ^ NASA Tech Briefs, "Making a Metal-Lined Composite Overwrapped Pressure Vessel", 1 Mar 2005.
2. ^ Frietas, O., "Maintenance and Repair of Glass-Lined Equipment", Chemical Engineering, 1 Jul 2007.
3. ^ Puskarich, Paul (2009-05-01) (PDF). Strengthened Glass for Pipleine Systems. MIT. Retrieved 2009-04-17.
4. ^ Richard Budynas, J. Nisbett, Shigley's Mechanical Engineering Design, 8th ed., New York:McGraw-Hill, ISBN 978-0-07-312193-2, pg 108
5. ^ MIT pressure vessel lecture
6. ^
7. ^
8. ^ ANSI/AIAA S-080-1998, Space Systems - Metallic Pressure Vessels, Pressurized Structures, and Pressure Components, §5.1
9. ^ Pushard, Doug (2005). "Domestic water collection systems also sometimes able to function on gravity". Harvesth2o.com. Retrieved 2009-04-17.
10. ^ Pushard, Doug. "Alternatives to pressure vessels in domestic water systems". Harvesth2o.com. Retrieved 2009-04-17.
11. ^ Ingenious Coal-Gas Motor Tank, Popular Science monthly, January 1919, page 27, Scanned by Google Books: http://books.google.com/books?id=HykDAAAAMBAJ&pg=PA13