दाब पात्र

दाब पात्र (pressure vessel) ऐसे पात्रों को कहते हैं जिनमें वायुमण्डलीय दाब से अधिक दाब या उससे कम दाब पर कोई गैस या द्रव रखा जाता हो। किसी भी पात्र में वायुमण्डलीय दाब से अधिक या कम दाब होना खतरनाक हो सकता है और इतिहास में कई भयावह दुर्घटनाएँ हो चुकी हैं। इसलिये दाब-पात्रों की डिजाइन, निर्माण एवं परिचालन (आपरेशन) सम्बन्धित प्रौद्योगिकीविदों द्वारा निर्धारित मानकों के द्वारा नियंत्रित किया जाता है।

For a sphere, the minimum mass of a pressure vessel is

${\displaystyle M={3 \over 2}PV{\rho \over \sigma }}$,

where:

• ${\displaystyle M}$ is mass,
• ${\displaystyle P}$ is the pressure difference from ambient (the gauge pressure),
• ${\displaystyle V}$ is volume,
• ${\displaystyle \rho }$ is the density of the pressure vessel material,
• ${\displaystyle \sigma }$ is the maximum working stress that material can tolerate.^[1]

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.

This is sometimes called a "bullet"^[] for its shape, although in geometric terms it is a capsule.

For a cylinder with hemispherical ends,

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

where

• R is the radius
• W is the middle cylinder width only, and the overall width is W + 2R

In a vessel with an aspect ratio of middle cylinder width to radius of 2:1,

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

Stress in a shallow-walled pressure vessel in the shape of a sphere is

${\displaystyle \sigma _{\theta }=\sigma _{\rm {long}}={\frac {pr}{2t}}}$,

where ${\displaystyle \sigma _{\theta }}$ is hoop stress, or stress in the circumferential direction, ${\displaystyle \sigma _{long}}$ 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 sphere 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.^[2]

Stress in a shallow-walled pressure vessel in the shape of a cylinder is

${\displaystyle \sigma _{\theta }={\frac {pr}{t}}}$,

${\displaystyle \sigma _{\rm {long}}={\frac {pr}{2t}}}$,

where:

• ${\displaystyle \sigma _{\theta }}$ is hoop stress, or stress in the circumferential direction
• ${\displaystyle \sigma _{long}}$ is stress in the longitudinal direction
• p is internal gauge pressure
• r is the inner radius of the cylinder
• 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.

For example, the ASME Boiler and Pressure Vessel Code (BPVC) (UG-27) formulas are:^[3]

Spherical shells:

${\displaystyle \sigma _{\theta }=\sigma _{\rm {long}}={\frac {p(r+0.2t)}{2tE}}}$

Cylindrical shells:

${\displaystyle \sigma _{\theta }={\frac {p(r+0.6t)}{tE}}}$

${\displaystyle \sigma _{\rm {long}}={\frac {p(r-0.4t)}{2tE}}}$

where E is the joint efficient, and all others variables as stated above.

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 thicknes.

• ASME Boiler and Pressure Vessel website
• Journal of Pressure Vessel Technology
• EU Pressure Equipment Directive website
• EU Pressure Equipment Directive 97/23/EC categorization software^{[मृत कड़ियाँ]}
• EU Simple Pressure Vessel Directive
• EU Classification
• [A pressure vessel is a closed container designed to hold gases or liquids at a pressure different from the ambient pressure.

1. ↑ For a sphere the thickness d = rP/2σ, where r is the radius of the tank. The volume of the spherical surface then is 4πr²d = 4πr³P/2σ. The mass is determined by multiplying by the density of the material that makes up the walls of the spherical vessel. Further the volume of the gas is (4πr³)/3. Combining these equations give the above results. The equations for the other geometries are derived in a similar manner
2. ↑ Richard Budynas, J. Nisbett, Shigley's Mechanical Engineering Design, 8th ed., New York:McGraw-Hill, ISBN 978-0-07-312193-2, pg 108
3. ↑ An International Code 2007 ASME Boiler & Pressure Vessel Code. The Americal Society of Mechanical Engineers. 2007. मूल से 2 मई 2013 को पुरालेखित. अभिगमन तिथि 5 जुलाई 2016.