$($a$)$ Derive the analytical formula for the average potential energy delivered through the pipe per unit length of pipe and calculate the numerical value in units of $[$J$/$kg$]$

$($b$)$ Now the fluid flow is in steady state and gives the loss coefficient $K_L=6\mathrm{.}4$ per unit length of pipe. What is the mean fluid velocity and the frictional loss per unit length? Derive the analytical formula and calculate the numerical values $($velocity $=[\frac{m}{s}],$ frictional loss $=[$J$/$kg$])$