Thin-walled Pressure Vessels

 Key Concepts:  A pressure vessel is generally a "thin˗walled" structure  (the ratio of radius to thickness is large)  subject to internal pressure, p.  The pressure produces normal stresses in the plane of the structure which are determined from equilibrium of an element.

In a Nut Shell:  Thin-walled pressure vessels store and transport gases or liquids under

pressure such as pipelines, water towers, silos, and tanks.  For example, compressors store air pressure in tanks used at gas stations for tire inflation.  Pressure vessels include:

 Spherical Pressure Vessels Cylindrical Pressure Vessels Capped Pressure Vessels – Cylinder capped at each end by a hemisphere

If   r  is the inner radius of the sphere or cylinder and  t  is the wall thickness, then the
sphere or cylinder is considered to be “thin” provided   r/t    10.

First consider the case of a thin-walled spherical pressure vessel with wall thickness, t,
internal radius, r, and internal pressure, p, as shown below.

 σ1  =  σ2  =  pr/2t

where
σ1,  σ2  are the normal stresses on the outer surface in (lb/in2), (lb/ft2), (N/mm2), (N/m2)
p  is the internal pressure  in (lb/in2), (lb/ft2), (N/mm2), (N/m2)
r   is the internal radius of the spherical pressure vessel in (in), (mm), etc
t   is the wall thickness of the spherical pressure vessel in (in), (mm), etc

Note:  The normal stresses, σ1 and σ2 are the same in any direction tangent to the outer
surface and constant throughout the thickness.  They are the principal stresses at every point.