Knowledge on how to derive formulae for calculating stress & corresponding strains developed inside a thin cylinder due to fluid pressure. And therefore the dimensional changes (length, diameter, & volume) in the cylinder.

NUMERICAL PROBLEM

A cylindrical shell 90cm long 15cm internal diameter, having thickness of metal 8mm is fitted with fluid at atmospheric pressure. If an additional 20cm3 of fluid is pumped into the cylinder, find the pressure exerted by the fluid on the cylinder, and hoop stress induced. Take E = 200 GPa and μ = 0.3

LOGICAL APPROACH

- We are provided with value of Poisson’s ratio, μ that is the ratio of longitudinal strain, Єl to circumferential strain, Єc
- We have, value of change in volume of cylinder, δV due to the additional fluid. And from the given dimensions of the cylinder, we can also calculate its original volume, V. In other words, we have value of volumetric strain, Єv
- Now since, Єv = 2Єc + Єl if we can rewrite Єc and Єl in terms of the fluid pressure; by solving the equation, we can easily find value of pressure, p and hence the value of hoop stress induced.
- To rewrite Єc and Єv in terms of pressure, p we can use the stress-strain relationship equations: Єc = 1/E (σc – μσl) and Єl = 1/E (σl – μσc); where circumferential stress, σc = pd/2t and longitudinal stress, σl = σc/2

ANSWER

Pressure = 14.1138 N/mm2; Hoop stress = 132.316 N/mm2