A cast iron pipe with $20-cm$ diameter and $15-mm$ wall thickness is carrying water when the outlet is suddenly closed. Use $E_{\text{w}\text{a}\text{t}\text{e}\text{r}}=2\mathrm{.}17{10}^9\frac{N}{m^2}$ and $E_P=161011\frac{N}{m}.$ If the design discharge is $40\frac{l}{s},$ calculate the water hammer pressure rise for:

$($a$)$ rigid pipe walls;

$($b$)$ consider stretching of pipe walls, neglecting the longitudinal stress;

$($c$)$ pipeline that is anchored at upstream end only.