$($Q$1)[25$ points in total$]$

Two water tanks A and $B$ are connected through a $40m$ long, $2cm$ diameter cast iron pipe with

sharp$-$edge entrance as shown in Figure $1.$ A gate valve and a check valve are installed along the

pipe. The Water levels in both tanks are the same. The tank $A$ is pressurized, and tank $B$ is open to

the air with atmospheric pressure at $88$kPa. The flow rate remains at a steady state of $1\mathrm{.}2\frac{L}{s}.$ The

water density is $999\mathrm{.}7k\frac{g}{m^3}$ and dynamics viscosity is $1\mathrm{.}307{10}^{-3}k\frac{g}{m}*s.$ The kinematic viscosity is

expressed as the ratio of dynamics viscosity to density. The minor loss coefficient is $0\mathrm{.}5$ for entrance,

$2$ for check value, $0\mathrm{.}2$ for gate valve and $1$ for exit. The roughness of the cast iron pipe is $0\mathrm{.}00026m.$

$($i$)$ Calculate the flow velocity within the pipe. $[5$ points$]$

$($ii$)$ Determine the total head loss using the Colebrook$-$White equation. $[10$ points$]$

$($iii$)$ Estimate the absolute pressure in tank A$.[10$ points$]$

Figure $1.$ Pipe system illustration.