Pressure vessels are containers designed to store fluids under high pressure, commonly used in industries such as petroleum refining, chemical processing, and pharmaceuticals. They can be classified based on construction (cylindrical or spherical, thin-walled or thick-walled) and orientation (horizontal, vertical, or spherical), and face various loads that induce stresses, with potential failure modes including yielding and fatigue. The design of pressure vessels involves determining design pressures and temperatures, analyzing stresses, and utilizing specific equations for both thin and thick-walled vessels.

1. CHAPTER 5
PRESSURE VESSEL

2. Pressure Vessels
• Pressure vessels are containers, used to store
fluids at higher pressure than the ambient.
• They are used in a variety of industries like
• Petroleum refining
• Chemical
• Power
• Food & beverage
• Pharmaceutical
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4. TYPES OF PRESSURE VESSELS
• Pressure vessels can be cylindrical or spherical
by construction.
• Pressure vessels can be thin-walled or thick-
walled.
• If the wall thickness (t) is less than 1/10 of the
internal diameter (di) and/or
the internal pressure (pi) is less than 1/6 of the
allowable stress of the vessel material, it is called
thin-walled otherwise it is called thick-walled.
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There are three main types of pressure vessels based on
their orientation:
 Horizontal Pressure Vessels
 Vertical Pressure Vessels
 Spherical Pressure vessels
• However there are some special types of Vessels like
Regeneration Tower, Reactors, Boilers but these
names are given according to their use only.

6. Horizontal pressure vessel
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7. Vertical pressure vessel
 The max. Shell length to diameter ratio for a small vertical drum is
about 5 : 1
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8. Spherical Pressurized Storage Vessel
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9. Loads Causing Stresses on Pressure Vessel Walls
• Internal or external pressure
• Dead weight of vessel
• Weight of contents under normal or upset conditions
• Weight of attached equipment (piping, decks, ladders, etc)
• Stresses at geometric discontinuities
• Bending moments due to Wind & snow loads
• Thermal expansion, Seismic loads
• Cyclic loads due to pressure or temperature changes
• Residual stresses from manufacture.
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10. Potential Failure Modes `
• Depending upon the application, the pressure
level, the temperature level, the environment, and
the composition of the pressurizing fluid, pressure
vessels are vulnerable to potential failure by many
possible modes.
• PV failure might occur by yielding, ductile
rupture, brittle fracture, fatigue (including low-
cycle, thermal, or corrosion fatigue), stress
corrosion-cracking, creep, or combined creep and
fatigue.
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11. Design pressure
Normal operating pressure:
• The expected pressure at which the process usually
be operated.
Maximum operating pressure:
• The highest pressure expected including upset
conditions such as startup, shutdown, emergency
shutdown.
Design pressure:
• Maximum operating pressure plus a safety margin.
• Margin is typically 10% of maximum operating
pressure.
• Usually specify pressure at top of vessel, where
relief valve is located. 11

12. Design Temperatures
• Maximum:
– Highest mean metal temperature expected in operation,
including transient conditions, plus a margin
– Margin is typically plus 50F/10 degree centigrade.
• Minimum:
– Lowest mean metal temperature expected in operation,
including transient conditions, upsets, auto-
refrigeration, climatic conditions, anything else that
could cause cooling, minus a margin
– Margin is typically -25F
– MDMT: minimum design metal temperature is
important as metals can become brittle at low
temperatures. 12

13. Design of Thin-Walled Pressure Vessel
• In a thin cylinder subjected to an internal pressure, three
principal stresses are induced in circumferential, axial
and radial directions namely: circumferential or
tangential or hoop stress (h), longitudinal or axial stress
(l), radial stress (r)
• The magnitude of radial stress is equal to the internal
pressure at the inner surface and zero at the outer surface
of the cylinder.
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• In thin cylinder, the internal pressure is small, the radial
stress is also small and hence can be neglected.
• Hence, the thin cylinder is considered to be subjected to
h and l.
• It is assumed that theses stresses are constant through out
the thickness of the cylinder.

15. • A thin-walled pressure vessel is mainly subjected to fluid
(gas) force in the longitudinal (axial) ‘x’ direction due to
longitudinal stress (l)
• And in the transverse ‘y’ direction due to hoop stress
(h).
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16. Stresses in Thin Cylindrical Shell due to an Internal
Pressure
The analysis of stresses induced in a thin cylindrical shell
are made on the following assumptions:
1. The effect of curvature of the cylinder wall is neglected.
2. The tensile stresses are uniformly distributed over the
section of the walls.
3. The effect of the restraining action of the heads at the
end of the pressure vessel is neglected.
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17. • When a thin cylindrical shell is subjected to an internal
pressure, it is likely to fail in the following two ways:
1. along the longitudinal section (i.e. circumferentially)
splitting the cylinder into two troughs,
2. across the transverse section (i.e. longitudinally) splitting
the cylinder into two cylindrical shells.
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18. (a) Circumferential or hoop stress,
When a thin cylindrical shell subjected to an internal
pressure, a tensile stress acting in a direction tangential to
the circumference is called circumferential or hoop stress.
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19. • Total force acting on a longitudinal section (i.e. along
the diameter X-X) of the shell,
= Intensity of pressure × Projected area
= P × A = p× d× l ……….....(i)
Where, p = Intensity of internal pressure,
d = Internal diameter of the cylindrical shell,
l = Length of the cylindrical shell,
t = Thickness of the cylindrical shell, and
• Total resisting force acting on the cylinder walls;
= σh × 2t× l (b/c of two sections) ……..(ii)
where, σh = hoop stress for the material of the cylindr shell.
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20. From equations (i) and (ii), we have;
σh × 2t× l = p× d× l
or …….(iii)
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(b) Longitudinal Stress
Consider a closed thin cylindrical shell subjected to an
internal pressure as shown below.
A tensile stress acting in the direction of the axis is called
longitudinal stress.

21. • Let σt2 = Longitudinal stress.
• In this case, the total force acting on the transverse
section (i.e. along Y-Y)
= Intensity of pressure × Cross-sectional area
………………………..(i)
And total resisting force = σt2 × π d.t …….(ii)
From equations (i)and (ii), we have
σl × π d.t ……………………….(iii)
or
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22. Thick Cylindrical Shells Subjected to an Internal
Pressure
• When a cylindrical shell of a pressure vessel,
hydraulic cylinder, gun barrel and a pipe is subjected
to a very high internal fluid pressure, then the walls of
the cylinder must be made extremely thick.
• In thick wall cylinders, the stress over the section of
the walls cannot be assumed to be uniformly
distributed.

23. • We see that the tangential stress is maximum at the
inner surface and minimum at the outer surface of
the shell.
• The radial stress is maximum at the inner surface
and zero at the outer surface of the shell.

24. • In the design of thick cylindrical shells, the
following equations are mostly used:
1. Lame’s equation;
2. Birnie’s equation;
3. Clavarino’s equation; and
4. Barlow’s equation.
• The use of these equations depends upon the type
of material used and the end construction.

25. Lame’s equation.
Assuming that the longitudinal fibers of the
cylindrical shell are equally strained, the tangential
stress at any radius x is:
And radial stress at any radius x:

26. • 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,
And radial stress at any radius x,

27. • We know that the tangential stress is;
• maximum at the inner surface of the shell
(when x= ri ) and
• minimum at the outer surface of the shell
( when x = ro).

28. • 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,
• Since ro = ri + t, therefore substituting this value of
ro in the above expression, we get;

30. Thank you!!!