A pipeline has a $1500-m$ long elastic pipe with a diameter of $250mm,$ a wall thickness of $30mm,$ and a bulk modulus of elastic of $2\mathrm{.}6{10}^8$kPa. Water flowing in the pipe has a velocity of $1\mathrm{.}2\frac{m}{s}$ when the valve is closed. The water has a density of $999\mathrm{.}7k\frac{g}{m}3$ and a bulk modulus of elastic of $2\mathrm{.}10{10}^6$kPa.

Determine:

a$)$ The pressure wave speed $c($in $\frac{m}{s}).$

b$)$ The water hammer pressure $p($in kPa $).$

c$)$ If the valve closure takes $2\mathrm{.}5s,$ is the maximum pressure increase greater than, less than, or equal to $p?$ Justify your answer.