A cylinder whose thickness is 20 times less than the diameter is known as thin cylinder. When a liquid or gas flows through a pipe it cause stress to the pipe. There are three types of stresses induced.
Circumferential stress which will cause stress along the length of the cylinder. This will split the cylinder along the length. This is known as Hoop stress. Longitudinal stress which will cause stress along the diameter of the cylinder. This will split the cylinder into two pieces along the diameter. Radial stress is negligible so it is ignored. Both the circumferential and longitudinal stresses are tensile. This is an important point to be remembered to find the change in volume.
Resisting force by cylinder along length of pipe = force due to fluid pressure along length of pipe.
Resisting force by cylinder along diameter of pipe = force due to fluid pressure along diameter of pipe.
p – Pressure due to liquid or gas
D – Diameter of cylinder
t– Thickness of cylinder
L – Length of cylinder
η– Efficiency of joint it may vary due to stress.
From Hooke‟s law strain
This is the general equation for strain from which change in dimension can be found.
Strain due to circumferential stress cause increase in diameter
Strain due to longitudinal stress cause increase in length