Problem $2$: Tube under internal pressure

Let us consider a circular tube inner radius $r,$ thickness $e$ and assumed to be infinite and free to

expand in the $z$ direction $($see Figure $2).$ The tube is subjected to internal pressure $p.$ Gravity

and atmospheric pressure are neglected.

Figure $2$: Circular tube subjected to internal pressure

Q$1$: Write all the static admissibility equation.

Q$2$ : Let's assume that ${}_{{?}_{?}}{?}_{?}$ depends only on $r.$ How can you justify that.

Q$3$: What can you say about $g_{{?}_{?}}$ using the assumption $g_{{?}_{?}}(r)$ and the equilibrium equation.