A pressure pipe is in the form of a hollow cylinder of internal radius $400$ mm and

external radius $500$ mm$.$ The pipe is pressurised internally with a pressure p$.$

There is no external pressure and no axial stress.

Derive expressions, involving the pressure p and any radius r$,$ for the radial and

tangential stresses.

Use Hooke$$s Law to write down an expression for the tangential strain $$ at any

radius r$.$

The pipe material has Young$$s modulus $70$ GN$/$m$2$ and Poisson$$s ratio $0\mathrm{.}3.$ If

pressurised to $100$ MPa, what are the radial displacements at the inner and outer

surfaces?

Decide whether the cylinder wall becomes thinner or thicker and comment on the

result.