CHAPTER FIVE
PRESSURE VESSELS
5.1 Introduction

The pressure vessels (i.e. cylinders or
tanks) are used to store fluids under
pressure.

The pressure vessels are designed with
great care
because rupture of a pressure
which may cause loss of life and property.

The material of pressure vessels may be
brittle such as cast iron, or ductile such as
mild steel
Vertical PV
5.2. Classification and application
Classification of pressure vessel
1. According to ratio of internal diameter (d) to thickness (t)
of the shell
i. When, t < d/10; thin shell
ii. When, t > d/10; thick shell
2. According to the end connection
i) Open end ; e.g. cylinder with piston ( usually engine cylinder)
ii) Closed end; e.g. boiler, container and air compressor receiver tank
3. According to the end heads/end covers
i) Flat headed ii) convex headed or iii) dished headed
4. According to geometric shape
i)
Cylindrical ii) spherical
iii) conical
spherical
conical
iv) Elliptical
5. According to the direction of fluid pressure acting on the
wall of cylinder
i) Internal pressure
ii) External pressure
6. Based on manufacturing material
i) Steel
ii) Non ferrous
7. Based on design pressure
iii) Non metallic
8. Based on operating
temperature
i) Low (0.1 – 1.6MPa)
i) Low (≤ −𝟐𝟎℃)
ii) Medium (1.6 – 10MPa)
ii) Normal (-20 ℃ -150℃)
iii) High (10MPa – 100MPa)
iii) Medium (150℃ − 𝟒𝟓𝟎℃)
iv) Ultra- high (≤ 100MPa)
iv) High (≥ 𝟒𝟓𝟎℃)
9. Based on usage mode
i) Fixed ii) movable
10. Based on type of joint used for the fabrication of joint
i) Riveted ii) welded iii) forged
11. Based on installation
Horizontal Pressure Vessels
Vertical Pressure Vessels
Spherical Pressure vessels
I. HORIZONTAL PRESSURE VESSEL
II. VERTICAL & SPHERICAL PRESSURE VESSEL
VERTICAL
SPHERICAL
5.4.MAIN COMPONENTS OF PRESSURE VESSEL
The main pressure vessel components are as follow:
 Shell: the primary component that contains the
pressure. Most pressure vessel shells are cylindrical,
spherical and conical in shape.
 Head: All pressure vessel shells must be closed at the
ends by heads. Ellipsoidal, Hemispherical, Tori spherical,
Conical, Tori conical and flat are the common types of
heads.
 Nozzle: a cylindrical component that penetrates the
shell or heads of a pressure vessel. Attach piping for flow
into or out of the vessel. Attach instrument connections,
(e.g., level gauges or pressure gauges).
 Support: The type of support that is used depends
primarily on the size and orientation of the pressure
vessel. Saddle, skirt and lug
Cont’d
Saddle; For horizontal pressure
vessel
Lug support
Lug support; Lugs that are welded to the pressure vessel
shell and used to support vertical pressure vessels
Skirt support: Tall, vertical, cylindrical pressure vessels (e.g.,
the tower and reactor) are typically supported by skirts.
A support skirt is a cylindrical shell section that is welded
either to the lower portion of the vessel shell
5.5. Failure of a cylindrical shell
5.5.1 THIN CYLINDERS
When the thickness is less than or equal to 1/20 of
internal diameter , the cylindrical vessel is thin.
5.5.2.Circumferential or Hoop Stress
 A tensile stress acting in a direction tangential to the
circumference is called circumferential or hoop stress. In other
words, it is a tensile stress on longitudinal section (or on the
cylindrical walls).
5.5.3.Longitudinal Stress
A tensile stress acting in the direction of the axis is called
longitudinal stress. In other words, it is a tensile stress
acting on the transverse or circumferential section Y-Y (or
on the ends of the vessel).
 It is seen that the circumferential stress (σt ) is twice the
longitudinal stress (σl ). Therefore, we have the following
criteria: In case of thin cylinders subjected to internal
pressure, the circumferential stress should be the criterion
for determining the cylinder wall thickness.
A seamless cylinder with a storage capacity of 0.025 m3 is
subjected to an internal pressure of 20 MPa. The length of the cylinder is twice
its internal diameter. The cylinder is made of plain carbon steel 20C8 (Sut = 390
N/mm2) and the factor of safety is 2.5. Determine the dimensions of the
cylinder.
Example 5.1.
5.6. THIN SPHERICAL VESSELS
A spherical pressure vessel with a thin wall, cut into two halves, is
shown in Fig. 5.2. Considering equilibrium of forces for each half
Stresses in Spherical Shell
5.7. Thick Cylindrical Shell under Internal
Pressure
 In case of thick cylinders, the metal thickness ‘t’ is
more than ‘d/20’, where ‘d’ is the internal diameter of
the cylinder
Hydraulic cylinders, high-pressure pipes and gun barrels
are examples of thick cylinders
 The difference between the analysis of stresses in thin and
thick cylinders is as follows:
 In thin cylinders, it is assumed that the tangential stress (σt
) is uniformly distributed over the cylinder wall thickness.
 In thick cylinders, the tangential stress (σt ) has highest
magnitude at the inner surface of the cylinder and gradually
decreases towards the outer surface
The radial stress (σr ) is neglected in thin cylinders,
while it is of significant magnitude in case of thick
cylinders.
5.7.1 Stress distribution in thick cylindrical
shells subjected to internal pressure
Lame’s equation.
 Assuming that the longitudinal fibers of the cylindrical
shell are equally strained, Lame has shown that the
tangential stress at any radius x is:
and radial stress at any radius x
 Since we are concerned with the internal pressure
( 𝑃𝑖 = 𝑃) only, therefore substituting the value of
external pressure, 𝑃𝑜 = 0.
Tangential stress at any radius x
Radial stress at any radius x
Substituting the value of x = ri and x = ro in equation (i), we find that
the maximum tangential stress at the inner and minimum at outer
surface of the shell can be given by.
The radial stress is maximum at the inner surface of the
shell and zero at the outer surface of the shell.
Substituting the value of x = ri and x = ro in equation (ii).
Maximum radial stress at the inner surface of the shell
Minimum radial stress at the outer surface of the shell
In designing a thick cylindrical shell of brittle material
(e.g. cast iron, hard steel and cast aluminum) with closed
or open ends and in accordance with the maximum normal
stress theory failure, the tangential stress induced in
the cylinder wall.
The value of σt for brittle materials may be taken as
0.125 times the ultimate tensile strength (σu) &
For ductile material use σt = 0.8 times yield stress (σy)
Example 5.3. hydraulic press has a maximum capacity of
10kN. The pressure in the cylinder is 10MPa. The cylinder is
made of cast iron FG 200 ( Sut= 200GPa) and the factor of
safety is 5. Determine the diameter and the thickness of the
cylinder
5.8. CLAVARINO’S EQUATIONS
(µ) is Poisson’s ratio
5.9. BIRNIE’S EQUATION
In case of open-end cylinders (such as pump cylinders,
rams, gun barrels etc.) made of ductile material (i.e. low
carbon steel, brass, bronze, and aluminium alloys),
Birnie’s equation for the wall thickness of a cylinder is
[Ans = t= 8mm]