## What is a Pressure Vessel?

The term pressure vessel refers to a closed container that contains gas or liquid at a different pressure than environment pressure. The pressure vessels have a wide scale of applications in our day-to-day lives and other industrial places. Some common examples of pressure vessels are gas cylinders, autoclaves, compressor vessels, etc.

## What are the need of Pressure Vessels?

Whenever there is a requirement to hold gas or liquid at a higher or lower pressure than the environment pressure, the requirement can fulfill with pressure vessels' help. The pressure vessels have different shapes that can be selected according to the required functionality and other conditions. If the pressure of gas or liquid is very large, then thick pressure vessels should be a better choice, whereas if the pressure of gas or liquid is less, thin pressure vessels would be the better option.

## Main components of Pressure Vessels

There are some main components in a pressure vessel that are listed below.

- Head (top or ends part) of pressure vessel
- Shell of pressure vessel
- Nozzle
- Support

## Types of Pressure Vessels

The pressure vessels are generally categorized into two types based on the wall thickness to internal diameter ratio described in the following steps. Further, the pressure vessels can also be categorized based on shape and orientation.

### Thin pressure vessels

Whenever the value of the ratio of wall thickness and internal diameter of a pressure vessel is less than or equal to $\frac{1}{20}$, the pressure vessel is considered a thin pressure vessel. Thin pressure vessels are generally employed where the holding pressure of gas or liquid is not very high. For example- Household LPG cylinder.

### Thick pressure vessels

Whenever the value of the ratio of wall thickness and internal diameter of a pressure vessel is greater than $\frac{1}{20}$, the pressure vessel consider as a thin pressure vessel. Thin pressure vessels are generally employed where the holding pressure of gas or liquid is not very high. For example, the vessel contains gas and liquid in industries.

### Cylindrical pressure vessel

It is a type of pressure vessel that has the shape of a cylinder. It helps to carry gas or liquids up to a certain limit. Some examples of cylindrical pressure vessels are hydraulic cylinders, a barrel of guns, tanks, and boiler containers. The cylindrical pressure vessels are less expensive, but the strength is not very high compared to a spherical pressure vessel.

### Spherical pressure vessel

It is a type of pressure vessel that is spherical in shape and helps to carry fluids to a higher pressure limit than the cylindrical pressure vessel. The spherical pressure vessels are more expensive and have more strength than the cylindrical pressure vessels. Some examples of spherical pressure vessels are high-pressure tanks, pipes, cabins, etc.

### Horizontal pressure vessel

It is a pressure vessel where the longitudinal axis of the pressure vessel lies in the horizontal position. Whenever a requirement due to space or other reasons, to place a pressure vessel in the horizontal position, then their horizontal pressure vessel would be the best choice. The horizontal pressure vessel has less capacity than the vertical pressure vessel.

### Vertical pressure vessel

It is a pressure vessel where the longitudinal axis of the pressure vessel lies in the vertical position. Whenever there is a space issue, then a vertical pressure vessel would be the best choice. The vertical pressure vessel has more capacity than the horizontal pressure vessel.

## Construction Materials

There are various types of materials that can be used in the construction of pressure vessels. Some of the pressure vessels are made up of steel with the help of various manufacturing processes, whereas some of the pressure vessels are made of composite materials, polymer, and ceramics.

## Stresses in thin cylindrical pressure vessel

Generally, three stresses act in a thin cylindrical pressure vessel: hoop stress, longitudinal stress, and radial stress. The hoop stress is referred to as the circumferential stress that works along the circumference, the longitudinal stress works along the longitudinal axis, whereas the radial stress works along the radial direction of the pressure vessel.

The given formula represents the expression of the hoop stress.

${\sigma}_{h}=\frac{Pd}{2t}$

Here, ${\sigma}_{h}$ represents hoop stress, $P$ represents the internal pressure, $d$ represents the internal diameter of the pressure vessel, and $t$ represents the wall thickness.

The given formula represents the expression of the longitudinal stress.

${\sigma}_{l}=\frac{Pd}{4t}$

Here, ${\sigma}_{l}$ represents longitudinal stress.

The value of radial stress in the thin pressure vessel is much less than the hoop and longitudinal stress. It can be neglected.

## Stresses in thin spherical pressure vessel

In a thin spherical pressure vessel, all three stress; hoops, longitudinal and radial stress, have the same values. The representation of stresses in a thin spherical pressure vessel is given below.

The given formula can represent the expression of stress in thin spherical pressure vessel.

$\sigma =\frac{Pd}{4t}$

Here, $\sigma $ represents the stress in the thin spherical pressure vessel.

## Strain in thin cylindrical pressure vessel

In the thin cylindrical pressure vessel, the major two stresses are the hoop and longitudinal stress. Due to these two stresses, three types of strain develop in the pressure vessel: circumferential strain, longitudinal strain, and volumetric strain.

The given formula can represent the expression of circumferential strain.

${\epsilon}_{h}=\frac{Pd}{4tE}\left(2-\mu \right)$

Here, ${\epsilon}_{h}$ represents the circumferential strain, $E$ represents the Young modulus, $\mu $ represents the Poisson's ratio.

The given formula can represent the expression of longitudinal strain.

${\epsilon}_{l}=\frac{Pd}{4tE}\left(1-2\mu \right)$

Here, ${\epsilon}_{l}$ represents the longitudinal strain.

The given formula can represent the expression of volumetric strain.

${\epsilon}_{v}=\frac{Pd}{4tE}\left(5-4\mu \right)$

Here, ${\epsilon}_{v}$ represents the volumetric strain.

## Strain in thin spherical pressure vessel

The strain value in a thin spherical pressure vessel has the same value in the circumferential and longitudinal direction. The expression of the strain in the thin spherical pressure vessel is given below.

${\epsilon}_{h}={\epsilon}_{l}=\frac{Pd}{4tE}\left(1-\mu \right)$

The expression of the volumetric strain in a thin spherical pressure vessel is given as,

${\epsilon}_{v}=\frac{3Pd}{4tE}\left(1-\mu \right)$

Here, ${\epsilon}_{v}$ represents the volumetric strain in thin spherical pressure vessel.

## Shear stress in thin cylindrical pressure vessel

Whenever a fluid is filled in a thin cylindrical pressure vessel then shear stress develops, and that can be represented as,

$\tau =\frac{Pd}{8t}$

Here, $\tau $ represents the shear stress in thin cylindrical pressure vessel.

## Stress in thick pressure vessel

Whenever a fluid (liquid or gas) is placed inside a thick pressure vessel or outside the pressure vessel, then there would be three types of stress develops that are hoop or circumferential stress, longitudinal stress, and radial stress. In the thick pressure vessel, radial stress has a significant value that can not be neglected. Lame's principle helps to obtain the value of stress in thick pressure vessels.

## Method of construction

The construction of a pressure vessel without a leak of fluid can obtain with the help of a welding operation. Seam welding is a continuous welding operation that makes the pressure vessel leak-proof. Various other welding technology helps in the construction of thick pressure vessels that operated under large pressure conditions.

## Application of pressure vessels

The pressure vessels have a very vast application in our daily life as well as in engineering, chemical, petroleum, medical, electrical fields. Some of these are listed below.

- Industrial compressor tank
- Water and oil storage tank
- Diving cylinders
- LPG cylinders
- In Petrochemical industries
- Autoclaves
- Hydraulic reservoir

**Common Mistakes**

- Students sometimes get confused regarding how to identify the difference between thick and thin pressure vessels. However, the ratio of wall thickness and internal diameter indicate the types of pressure vessels.
- Sometimes, students also get confused about the value of radial stress in a thin pressure vessel and a thick pressure vessel. However, the value of radial stress has a significant value in a thick pressure vessel compared to a thin pressure vessel.
- The student also gets confused about the stress profile in thick pressure vessels when the pressure vessel is filled inside and outside with fluid.

**Contexts and Applications**

Pressure vessels are very significant in the several professional exams and courses for undergraduate, Diploma level, graduate, postgraduate. For example:

- Bachelor of Technology in Mechanical Engineering
- Bachelor of Technology in Civil Engineering
- Master of Technology in Mechanical Engineering
- Doctor of Philosophy in Mechanical Engineering
- Diploma in Mechanical and Civil Engineering

**Related Concepts**

- Stress distribution in thick pressure vessel
- Strain
- Components of pressure vessel
- Mechanical and structural applications
- Design specification of pressure vessel
- Safety features
- Construction method
- Corrosion behavior of pressure vessels

**Practice Problems**

Q 1. In the context of thin cylinders, the relation of longitudinal stress with circumferential stress is

a. Half

b. Double

c. One-fourth

d. None of these

**Correct option: (a)**

Q 2. The variation of circumferential stress across thick cylinder filled inside a specific liquid is

a. Uniform throughout thickness

b. Maximum at inner surface and minimum at outer surface

c. Maximum at outer surface and minimum at inner surface

d. None of these

**Correct option: (b)**

Q 3. The thick pressure vessel is governed by the theorem called,

a. Clavarino's theorem

b. Rankine theorem

c. Lame's theorem

d. None of these

**Correct option: (c)**

Q 4. The formula to calculate the hoop/circumferential stress in a thin cylindrical pressure vessel is

a. ${\sigma}_{h}=\frac{Pd}{2t}$

b. ${\sigma}_{h}=\frac{Pd}{4t}$

c. ${\sigma}_{h}=\frac{Pd}{8t}$

d. ${\sigma}_{h}=\frac{Pd}{6t}$

**Correct option: (a)**

Q 5. The formula to calculate the longitudinal stress in a thin cylindrical pressure vessel is

a. ${\sigma}_{h}=\frac{Pd}{4t}$

b. ${\sigma}_{h}=\frac{Pr}{8t}$

c. ${\sigma}_{h}=\frac{Pd}{2t}$

d. None of these

**Correct option: (a)**

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