Introduction to Pressure Vessel Classification Tangential Stress and Radial Stress Lame’s Equation Clavarino’s Equation Birnie’s Equation Barlow’s equation

1. Subject :Design of Machine Element (2151907)
Topic :Thick Wall Pressure Vessel
GANDHINAGAR INSTITUTE
OF TECHNOLOGY(012)

2. Content
• Introduction to Pressure Vessel
• Classification
• Tangential Stress and Radial Stress
• Lame’s Equation
• Clavarino’s Equation
• Birnie’s Equation
• Barlow’s equation

3. Introduction to Pressure Vessel
• Pressure vessels are the containers for fluids under
high pressure.
• They are used in a variety of industries like
• Petroleum refining
• Chemical
• Power
• Food & beverage
• Pharmaceutical

4. Classification
• They are classified into two main categories:-
* Thin wall cylinder :A cylinder is considered thin
when the ratio of its inner diameter to the wall
thickness is more than 15. Boiler shells, pipes, tubes,
and storage tanks are treated as thin cylinders
-Cylindrical
-Spherical
* Thick wall cylinder

5. Thick wall cylinder
• When the ratio of the inner diameter of the cylinder to
the wall thickness is less than 15, the cylinder is
called a ‘thick-walled’ cylinder or simply ‘thick’
cylinder. Hydraulic cylinders, high-pressure pipes
and gun barrels are examples of thick cylinders

6. • The difference between the analysis of stresses in thin
and thick cylinders is as follows:
(i) In thin cylinders, it is assumed that the tangential
stress is uniformly distributed over the cylinder wall
thickness. In thick cylinders, the tangential stress has
highest magnitude at the inner surface of the cylinder
and gradually decreases towards the outer surface.
• (ii) The radial stress is neglected in thin cylinders,
while it is of significant magnitude in case of thick
cylinders.

7. Tangential stress and Radial Stress

8. • Tangential Stress:-
• Radial Stress:-

9. Lame’s Equation
• When the material of the cylinder is brittle, such as
cast iron or cast steel, Lame’s equation is used to
determine the wall thickness.
• It is based on the maximum principal stress theory of
failure, where maximum principal stress is equated to
permissible stress for the material.

10. Clavarino’s Equation
• Clavarino’s equation is applicable to cylinders with
closed ends and made of ductile materials. When the
cylinder ends are open

11. Birnie’s Equation
• Birnie’s equation is applicable to open cylinders
made of ductile material.

12. Barlow’s equation
• It is used for high-pressure oil and gas pipes. Where
(Do) is the outer diameter of the cylinder. Barlow's
equation is analogous to thin cylinder equation except
that the outer diameter (Do) is used instead of inner
the diameter (Di).