A seamless pipe is to carry a fluid under a pressure of 2 N/mm². The thickness of the cylinder is 10 mm. Calculate the diameter of the pipe if the maximum stress allowed is 100 N/mm².

Explanation:

Consider a thin pressure vessel having closed ends and containing fluid under a gauge pressure P. Then the walls of the cylinder will have longitudinal stress, circumferential stress and radial stress.

As shown in the figure, a point of the shell has stressed from all sides i.e. tri-axial stresses.

σL =  longitudinal stress (tensile), 

σr = radial stress (compressive), σh = circumferential stress (tensile).

As, σr <<<< σL and σh, therefore we neglect σr and assumed the bi-axial stresses.

Circumferential or hoop stress: \({σ _h} = \frac{{Pd}}{{2t}}\) - (1)

Given,

Pressure = 2 N/mm2, Stress = 100 N/mm2 , t = 10 mm

from the equation (1) 

100 = (2 × d)/ (2 × 10 mm)

→ d = 1000 mm = 1 m 

Additional Information

Longitudinal or axial stress:  \({σ _L} = \frac{{Pd}}{{4t}}\)

where d is the internal diameter and t is the wall thickness of the cylinder

In this question, the stress is denoted by ft. Hence replacing σh with ft we get

\({f_t} = \frac{{Pd}}{{2t}}\)

\(T = \frac{Pd}{2f_t}\)