$($b$)$ A $3\mathrm{.}6\frac{m^3}{s}$ of water flows in a steel penstock $2500$ m long when it has a diameter of $1\mathrm{.}5$ m and a thickness of I$2\mathrm{.}5$mm$.$ Determine:

i$)$ Water hammer pressure when the valve at the delivery end is closed in $2\mathrm{.}5$ s and $9$ s respectively

ii$)$ length of pipe from valve subjected to maximum water hammer pressure for the $2\mathrm{.}5$ s closure

iii$)$ the pressure if the pipe was rigid and closed in $2$ s

Take: $K_{\text{w}\text{a}\text{t}\text{e}\text{r}}=2\mathrm{.}06C\frac{N}{m^2}$

$E_{\text{s}\text{t}\text{e}\text{e}\text{l}}=2066\frac{N}{m^2}$

$t=100M\frac{N}{m^2}$