Question one

a$)$ A steel pipe $(($:$E=2100{10}^8(Pa),(K)=2100{10}^6(Pa),(L)=1000(m),D=200(mm),e=12(mm)\}$ conveys water. The initial velocity is $V=1\mathrm{.}2\frac{m}{s}.$ A valve at the downstream end is closed so rapidly that the motion is considered to be instantaneous, reducing the velocity to zero. Determine

i$.$ The pressure pulse wave speed in the pipe. $(8$ marks$)$

ii$.$ The speed of sound in an unbounded water medium. $(4$ marks$)$

b$)$ Determine the rise in pressure at the valve in $($a$)$ if it is closed in $4$ seconds and the flow is assumed incompressible. $(8$ marks$)$