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Reducing the ratio (9.4) dl dl and on dividing by  , we get the
m t
Laplace’s equation
  P
m  t  . (9.5)
  
m t

The second equation (equations zone), which you need to find the
stress  and  , can be obtained by using equilibrium
m t
conditions of cutoff part of the shell (fig. 9.2).
We consider the cut of the shell filled with liquid or bulk
materials. In the context of "metal" exert tension  in section
m
"for liquids" – pressure p . The radii of the inner and middle
surface membrane are considered to be equally. The condition of
equilibrium of all the forces in the direction of the axis of the
shell has the form
  2 R  cos   P  P   p R 2  0,
m н o
from here

pR P  P
   н o , (9.6)
m
2 cos  2 R  cos
where p - the pressure inside the shell; P - loose weight or body
н
fluids that fill the cut volume; P - weight cut off of the
o
membrane.
When solving practical
problems it is convenient to use
two theorems that we accept
without proof.
Theorem 1. If the uniform
compression acts on an arbitrary
surface, then, regardless of the
surface form, projection of the
resultant pressure forces on a
given axis is equal to the
product of pressure on the
surface area of the projection on
a plane that is perpendicular to a
given axis.
Figure 9.2
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