Question
Download Solution PDFA 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.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
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:
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:
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
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